10-Q

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 10-Q

☒    QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

For the period ended September 30, 2022

OR

☐         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

For the transition period from          to         

Commission file number 1-8993

WHITE MOUNTAINS INSURANCE GROUP, LTD.

(Exact name of Registrant as specified in its charter)

Bermuda
(State or other jurisdiction of incorporation or organization)	94-2708455
23 South Main Street, Suite 3B	(I.R.S. Employer Identification No.)
Hanover,	03755-2053
New Hampshire	(Zip Code)
(Address of principal executive offices)

Registrant’s telephone number, including area code: (603) 640-2200

 Securities registered pursuant to Section 12(b) of the Act:

Title of each class	Trading Symbol(s)	Name of each exchange on which registered
Common Shares, par value $1.00	WTM	New York Stock Exchange
per share		Bermuda Stock Exchange

Indicate by check mark whether the Registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the Registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes   ý   No   ☐

Indicate by check mark whether the Registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the Registrant was required to submit such files). Yes   ý    No   ☐

Indicate by check mark whether the Registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company.  See the definitions of “large accelerated filer,” “accelerated filer”, “smaller reporting company” and “emerging growth company” in Rule 12b-2 of the Exchange Act.

Large accelerated filer	ý	Accelerated filer		☐	Non-accelerated filer		☐
Smaller reporting company			☐	Emerging growth company		☐

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.  o

Indicate by check mark whether the Registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes  ☐   No  ý

As of November 3, 2022, 2,576,232 common shares with a par value of $1.00 per share were outstanding (which includes 38,350 restricted common shares that were not vested at such date).

WHITE MOUNTAINS INSURANCE GROUP, LTD.

Table of Contents

		Page No.
PART I.	FINANCIAL INFORMATION
Item 1.	Financial Statements (Unaudited)
	Consolidated Balance Sheets, September 30, 2022 and December 31, 2021	1
	Consolidated Statements of Operations and Comprehensive Income,
	Three and Nine Months Ended September 30, 2022 and 2021	3
	Consolidated Statements of Changes in Equity,	6
	Three and Nine Months Ended September 30, 2022 and 2021
	Consolidated Statements of Cash Flows, Nine Months Ended September 30, 2022 and 2021	8
	Notes to Consolidated Financial Statements	9
Item 2.	Management’s Discussion and Analysis of Financial Condition and Results of Operations	48
	Results of Operations for the Three and Nine Months Ended September 30, 2022 and 2021	48
	Liquidity and Capital Resources	70
	Non-GAAP Financial Measures	74
	Critical Accounting Estimates	75
	Forward-Looking Statements	76
Item 3.	Quantitative and Qualitative Disclosures About Market Risk	77
Item 4.	Controls and Procedures	77
PART II.	OTHER INFORMATION	77
Items 1 through 6.		77
SIGNATURES		78

Part I.FINANCIAL INFORMATION.

Item 1.Financial Statements

WHITE MOUNTAINS INSURANCE GROUP, LTD.

CONSOLIDATED BALANCE SHEETS

(Unaudited)

	September 30, 2022		December 31, 2021
Millions, except share and per share amounts
Assets
Financial Guarantee (HG Global/BAM)
Fixed maturity investments, at fair value	$	874.4	$	934.1
Short-term investments, at fair value	62.3		32.4
Total investments	936.7		966.5
Cash	17.3		19.8
Insurance premiums receivable	6.6		6.9
Deferred acquisition costs	34.9		33.1
Other assets	22.3		18.5
Total Financial Guarantee assets	1,017.8		1,044.8
P&C Insurance and Reinsurance (Ark)
Fixed maturity investments, at fair value	741.8		688.6
Common equity securities, at fair value	286.4		251.1
Short-term investments, at fair value	309.4		296.2
Other long-term investments	329.7		326.2
Total investments	1,667.3		1,562.1
Cash	123.4		67.8
Reinsurance recoverables	550.9		448.4
Insurance premiums receivable	698.6		416.0
Ceded unearned premiums	59.7		67.1
Deferred acquisition costs and value of in-force business acquired	151.4		108.2
Goodwill and other intangible assets	292.5		292.5
Other assets	62.9		64.9
Total P&C Insurance and Reinsurance assets	3,606.7		3,027.0
Asset Management (Kudu)
Other long-term investments	813.2		669.5
Cash (restricted $8.9 and $4.5)	76.6		21.4
Accrued investment income	12.5		16.9
Goodwill and other intangible assets	8.7		8.9
Other assets	9.7		10.4
Total Asset Management assets	920.7		727.1
Other Operations
Fixed maturity investments, at fair value	238.1		286.2
Short-term investments, at fair value	824.7		129.5
Common equity securities, at fair value	46.4		—
Investment in MediaAlpha, at fair value	148.2		261.6
Other long-term investments	479.8		382.1
Total investments	1,737.2		1,059.4
Cash	28.4		38.7
Goodwill and other intangible assets	92.0		39.1
Other assets	142.2		59.5
Assets held for sale - NSM Group	—		989.0
Assets held for sale - Other	—		16.1
Total Other Operations assets	1,999.8		2,201.8
Total assets	$	7,545.0	$	7,000.7

See Notes to Consolidated Financial Statements

1

CONSOLIDATED BALANCE SHEETS (CONTINUED)

(Unaudited)

	September 30, 2022		December 31, 2021
Millions, except share and per share amounts
Liabilities
Financial Guarantee (HG Global/BAM)
Unearned insurance premiums	$	286.7	$	266.3
Debt	146.4		—
Accrued incentive compensation	21.6		24.7
Other liabilities	29.5		30.9
Total Financial Guarantee liabilities	484.2		321.9
P&C Insurance and Reinsurance (Ark)
Loss and loss adjustment expense reserves	1,329.4		894.7
Unearned insurance premiums	781.3		495.9
Debt	180.0		185.9
Reinsurance payable	312.7		424.1
Contingent consideration	32.9		28.0
Other liabilities	107.6		93.8
Total P&C Insurance and Reinsurance liabilities	2,743.9		2,122.4
Asset Management (Kudu)
Debt	253.5		218.2
Other liabilities	59.7		42.8
Total Asset Management liabilities	313.2		261.0
Other Operations
Debt	35.6		16.8
Accrued incentive compensation	67.2		48.5
Other liabilities	34.6		30.1
Liabilities held for sale - NSM Group	—		495.3
Total Other Operations liabilities	137.4		590.7
Total liabilities	3,678.7		3,296.0
Equity
White Mountains’s common shareholders’ equity
White Mountains’s common shares at $1 par value per share—authorized 50,000,000    shares; issued and outstanding 2,576,232 and 3,017,772 shares	2.6		3.0
Paid-in surplus	532.7		585.9
Retained earnings	3,175.9		2,957.5
Accumulated other comprehensive income (loss), after-tax:
Net unrealized gains (losses) from foreign currency translation and     interest rate swap	(3.2)		1.7
Total White Mountains’s common shareholders’ equity	3,708.0		3,548.1
Non-controlling interests	158.3		156.6
Total equity	3,866.3		3,704.7
Total liabilities and equity	$	7,545.0	$	7,000.7

See Notes to Consolidated Financial Statements

2

WHITE MOUNTAINS INSURANCE GROUP, LTD.

CONSOLIDATED STATEMENTS OF OPERATIONS

(Unaudited)

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Revenues:
Financial Guarantee (HG Global/BAM)
Earned insurance premiums	$	7.1	$	6.7	$	26.0	$	19.6
Net investment income	5.7		4.4		15.1		13.2
Net realized and unrealized investment gains (losses)	(38.8)		(4.0)		(114.0)		(15.6)
Other revenues	1.3		.3		3.7		.9
Total Financial Guarantee revenues	(24.7)		7.4		(69.2)		18.1
P&C Insurance and Reinsurance (Ark)
Earned insurance premiums	346.1		213.4		757.8		435.8
Net investment income	4.9		.6		9.7		1.8
Net realized and unrealized investment gains (losses)	(14.4)		.3		(76.5)		10.3
Other revenues	6.6		3.4		10.1		9.4
Total P&C Insurance and Reinsurance revenues	343.2		217.7		701.1		457.3
Asset Management (Kudu)
Net investment income	14.8		9.5		41.2		26.1
Net realized and unrealized investment gains (losses)	41.1		18.9		45.8		62.5
Other revenues	—		.1		—		.2
Total Asset Management revenues	55.9		28.5		87.0		88.8
Other Operations
Net investment income	8.5		5.0		13.6		16.1
Net realized and unrealized investment gains (losses)	(17.3)		15.3		2.8		34.0
Net realized and unrealized investment gains (losses) from       investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(325.5)
Commission revenues	3.2		2.4		8.7		7.0
Other revenues	33.0		28.1		89.6		57.6
Total Other Operations revenues	8.8		(346.0)		1.4		(210.8)
Total revenues	$	383.2	$	(92.4)	$	720.3	$	353.4

See Notes to Consolidated Financial Statements

3

CONSOLIDATED STATEMENTS OF OPERATIONS (CONTINUED)

(Unaudited)

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Expenses:
Financial Guarantee (HG Global/BAM)
Insurance acquisition expenses	$	1.7	$	3.0	$	9.5	$	6.5
General and administrative expenses	15.8		12.4		49.5		42.7
Interest expense	2.0		—		5.4		—
Total Financial Guarantee expenses	19.5		15.4		64.4		49.2
P&C Insurance and Reinsurance (Ark)
Loss and loss adjustment expenses	213.7		129.2		456.2		247.8
Insurance and reinsurance acquisition expenses	74.8		53.7		174.9		124.4
General and administrative expenses	26.9		21.8		79.8		84.4
Interest expense	3.7		2.1		10.6		4.5
Total P&C Insurance and Reinsurance expenses	319.1		206.8		721.5		461.1
Asset Management (Kudu)
General and administrative expenses	4.5		3.3		10.2		9.0
Amortization of other intangible assets	—		—		.2		.2
Interest expense	4.2		1.9		10.3		9.2
Total Asset Management expenses	8.7		5.2		20.7		18.4
Other Operations
Cost of sales	25.0		24.0		68.8		45.9
General and administrative expenses	39.9		14.4		118.9		79.4
Amortization of other intangible assets	1.4		2.0		3.2		2.9
Interest expense	.6		.4		1.2		1.1
Total Other Operations expenses	66.9		40.8		192.1		129.3
Total expenses	414.2		268.2		998.7		658.0
Pre-tax income (loss) from continuing operations	(31.0)		(360.6)		(278.4)		(304.6)
Income tax (expense) benefit	7.4		(28.6)		26.1		(52.2)
Net income (loss) from continuing operations	(23.6)		(389.2)		(252.3)		(356.8)
Net income (loss) from discontinued operations, net of tax -    NSM Group	6.3		5.3		16.4		(23.8)
Net gain (loss) from sale of discontinued operations, net of tax -    NSM Group	886.8		—		886.8		—
Net gain (loss) from sale of discontinued operations, net of tax -    Sirius Group	—		—		—		18.7
Net income (loss)	869.5		(383.9)		650.9		(361.9)
Net (income) loss attributable to non-controlling interests	18.7		12.5		101.5		53.7
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)

See Notes to Consolidated Financial Statements

4

WHITE MOUNTAINS INSURANCE GROUP, LTD.

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(Unaudited)

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Other comprehensive income (loss), net of tax	(1.4)		—		(3.0)		(.3)
Other comprehensive income (loss) from discontinued operations,    net of tax - NSM Group	.7		(2.2)		(5.2)		.9
Net gain (loss) from foreign currency translation from sale of    discontinued operations, net of tax - NSM Group	2.9		—		2.9		—
Comprehensive income (loss)	890.4		(373.6)		747.1		(307.6)
Other comprehensive (income) loss attributable to    non-controlling interests	(.3)		.2		.4		—
Comprehensive income (loss) attributable to    White Mountains’s common shareholders	$	890.1	$	(373.4)	$	747.5	$	(307.6)

Earnings (loss) per share attributable to White Mountains’s common shareholders:
Basic earnings (loss) per share
Continuing operations	$	(1.66)	$	(121.90)	$	(50.73)	$	(98.16)
Discontinued operations	308.59		1.72		304.97		(1.29)
Total consolidated operations	$	306.93	$	(120.18)	$	254.24	$	(99.45)
Diluted earnings (loss) per share
Continuing operations	$	(1.66)	$	(121.90)	$	(50.73)	$	(98.16)
Discontinued operations	308.59		1.72		304.97		(1.29)
Total consolidated operations	$	306.93	$	(120.18)	$	254.24	$	(99.45)
Dividends declared and paid per White Mountains’s    common share	$	—	$	—	$	1.00	$	1.00

See Notes to Consolidated Financial Statements.

5

WHITE MOUNTAINS INSURANCE GROUP, LTD.

CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY

(Unaudited)

	White Mountains’s Common Shareholders’ Equity
Millions	Common shares and paid-in surplus		Retained earnings		AOCI, after tax		Total		Non-controlling interest		Total Equity
Balance at June 30, 2022	$	603.2	$	2,725.1	$	(5.0)	$	3,323.3	$	168.7	$	3,492.0
Net loss	—		888.2		—		888.2		(18.7)		869.5
Net change in foreign currency translation and other	—		—		(1.1)		(1.1)		.3		(.8)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	—		—		2.9		2.9		—		2.9
Total comprehensive loss	—		888.2		1.8		890.0		(18.4)		871.6
Dividends to non-controlling interests	—		—		—		—		(.5)		(.5)
Repurchases and retirements of common shares	(71.5)		(437.4)		—		(508.9)		—		(508.9)
BAM member surplus contribution, net of tax	—		—		—		—		26.0		26.0
Amortization of restricted share awards	3.8		—		—		3.8		—		3.8
Recognition of equity-based compensation expense    of subsidiaries	.4		—		—		.4		.2		.6
Net contributions and dilution from other    non-controlling interests	(.6)		—		—		(.6)		(.2)		(.8)
Disposition of non-controlling interests	—		—		—		—		(17.5)		(17.5)
Balance at September 30, 2022	$	535.3	$	3,175.9	$	(3.2)	$	3,708.0	$	158.3	$	3,866.3

	White Mountains’s Common Shareholders’ Equity
Millions	Common shares and paid-in surplus		Retained earnings		AOCI, after tax		Total		Non-controlling interest		Total Equity
Balance at June 30, 2021	$	597.2	$	3,378.6	$	2.4	$	3,978.2	$	129.8	$	4,108.0
Net income (loss)	—		(371.4)		—		(371.4)		(12.5)		(383.9)
Net change in foreign currency translation and other	—		—		(2.2)		(2.2)		(.2)		(2.4)
Total comprehensive income (loss)	—		(371.4)		(2.2)		(373.6)		(12.7)		(386.3)
Dividends to non-controlling interests	—		—		—		—		(.6)		(.6)
Repurchases and retirements of common shares	(15.2)		(71.9)		—		(87.1)		—		(87.1)
BAM member surplus contributions, net of tax	—		—		—		—		14.7		14.7
Amortization of restricted share awards	3.6		—		—		3.6		—		3.6
Recognition of equity-based compensation expense    of subsidiary	.2		—		—		.2		—		.2
Net contributions and dilution from other    non-controlling interests	.4		—		—		.4		1.4		1.8
Balance at September 30, 2021	$	586.2	$	2,935.3	$	.2	$	3,521.7	$	132.6	$	3,654.3

See Notes to Consolidated Financial Statements.

6

CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY (CONTINUED)

(Unaudited)

	White Mountains’s Common Shareholders’ Equity
Millions	Common shares and paid-in surplus		Retained earnings		AOCI, after tax		Total		Non-controlling interest		Total Equity
Balance at January 1, 2022	$	588.9	$	2,957.5	$	1.7	$	3,548.1	$	156.6	$	3,704.7
Net income (loss)	—		752.4		—		752.4		(101.5)		650.9
Other comprehensive income (loss), net of tax	—		—		(7.8)		(7.8)		(.4)		(8.2)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	—		—		2.9		2.9		—		2.9
Total comprehensive income (loss)	—		752.4		(4.9)		747.5		(101.9)		645.6
Dividends declared on common shares	—		(3.0)		—		(3.0)		—		(3.0)
Dividends to non-controlling interests	—		—		—		—		(7.5)		(7.5)
Issuances of common shares	3.0		—		—		3.0		—		3.0
Issuance of shares of non-controlling interests	—		—		—		—		74.6		74.6
Repurchases and retirements of common shares	(89.2)		(521.3)		—		(610.5)		—		(610.5)
BAM member surplus contributions, net of tax	—		—		—		—		62.3		62.3
Amortization of restricted share awards	10.3		—		—		10.3		—		10.3
Recognition of equity-based compensation expense    of subsidiaries	8.1		—		—		8.1		.8		8.9
Net contributions and dilution from other    non-controlling interests	14.2		(9.7)		—		4.5		(9.1)		(4.6)
Disposition of non-controlling interests	—		—		—		—		(17.5)		(17.5)
Balance at September 30, 2022	$	535.3	$	3,175.9	$	(3.2)	$	3,708.0	$	158.3	$	3,866.3

	White Mountains’s Common Shareholders’ Equity
Millions	Common shares and paid-in surplus		Retained earnings		AOCI, after tax		Total		Non-controlling interest		Total Equity
Balance at January 1, 2021	$	595.2	$	3,311.2	$	(.4)	$	3,906.0	$	(88.1)	$	3,817.9
Net income (loss)	—		(308.2)		—		(308.2)		(53.7)		(361.9)
Other comprehensive income (loss), net of tax	—		—		.4		.4		—		.4
Total comprehensive income (loss)	—		(308.2)		.4		(307.8)		(53.7)		(361.5)
Dividends declared on common shares	—		(3.1)		—		(3.1)		—		(3.1)
Dividends to non-controlling interests	—		—		—		—		(1.8)		(1.8)
Issuances of common shares	1.7		—		—		1.7		—		1.7
Issuance of shares of non-controlling interests	—		—		—		—		6.1		6.1
Repurchases and retirements of common shares	(16.6)		(78.0)		—		(94.6)		—		(94.6)
BAM member surplus contributions, net of tax	—		—		—		—		44.8		44.8
Amortization of restricted share awards	11.1		—		—		11.1		—		11.1
Recognition of equity-based compensation expense    of subsidiary	2.0		—		—		2.0		.3		2.3
Net contributions and dilution from other    non-controlling interests	(7.2)		13.4		.2		6.4		(5.3)		1.1
Acquisition of non-controlling interests	—		—		—		—		230.3		230.3
Balance at September 30, 2021	$	586.2	$	2,935.3	$	.2	$	3,521.7	$	132.6	$	3,654.3

See Notes to Consolidated Financial Statements.

7

WHITE MOUNTAINS INSURANCE GROUP, LTD.

CONSOLIDATED STATEMENTS OF CASH FLOWS

(Unaudited)	Nine Months Ended September 30,
Millions	2022		2021
Cash flows from operations:
Net income (loss)	$	650.9	$	(361.9)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses	141.9		(91.2)
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	113.3		325.5
Deferred income tax expense	22.1		36.7
Amortization of restricted share awards	10.3		11.1
Amortization and depreciation	7.0		13.6
Net (income) loss from discontinued operation, net of tax - NSM Group	(16.4)		23.8
Net (gain) loss from sale of discontinued operations, net of tax - NSM Group and Sirius Group	(886.8)		(18.7)
Other operating items:
Net change in reinsurance recoverables	(102.5)		(32.3)
Net change in insurance premiums receivable	(282.3)		(245.7)
Net change in ceded unearned premiums	7.4		78.1
Net change in loss and loss adjustment expense reserves	434.7		194.9
Net change in unearned insurance premiums	305.8		290.0
Net change in deferred acquisition costs	(45.0)		(60.0)
Net change in reinsurance payable	(111.4)		(46.8)
Net change in restricted cash	4.4		4.5
Investments in Kudu Participation Contracts	(97.9)		(141.6)
Net change in other assets and liabilities, net	(37.3)		25.7
Net cash provided from (used for) operations - continuing operations	118.2		5.7
Net cash provided from (used for) operations - NSM Group discontinued operations (Note 19)	38.7		40.3
Net cash provided from (used for) operations	156.9		46.0
Cash flows from investing activities:
Net change in short-term investments	(735.4)		(83.7)
Sales of fixed maturity investments	212.4		215.9
Maturities, calls and paydowns of fixed maturity investments	107.3		144.6
Sales of common equity securities and investment in MediaAlpha	—		176.8
Distributions and redemptions of other long-term investments	55.0		98.2
Proceeds from the sale of NSM Group, net of cash sold of $143.9 and $0.0	1,364.8		—
Proceeds from the sale of Other Operations, net of cash sold of $0.5 and $0.0	19.5		—
Release of cash pre-funded/placed in escrow for Ark Transaction	—		646.3
Purchases of consolidated subsidiaries, net of cash acquired of $0.3 and $52.2	(67.9)		10.6
Purchases of other long-term investments	(136.9)		(206.5)
Purchases of common equity securities	(88.0)		(119.7)
Purchases of fixed maturity investments	(474.1)		(996.0)
Other investing activities, net	3.7		(1.3)
Net cash provided from (used for) investing activities - continuing operations	260.4		(114.8)
Net cash provided from (used for) investing activities - NSM Group discontinued operations (Note 19)	7.1		(54.6)
Net cash provided from (used for) investing activities	267.5		(169.4)
Cash flows from financing activities:
Draw down of debt and revolving line of credit	211.8		368.9
Repayment of debt and revolving line of credit	(10.5)		(94.8)
Cash dividends paid to the Company’s common shareholders	(3.0)		(3.1)
Common shares repurchased	(610.5)		(94.6)
Net distributions from non-controlling interest shareholders	(9.2)		1.1
Contributions from discontinued operations	11.6		—
Capital contributions from BAM members	62.3		44.8
Acquisition of subsidiary shares by non-controlling interest shareholders	74.6		6.1
Fidus Re premium payment	(5.6)		(6.9)
Other financing activities, net	(2.1)		(13.0)
Net cash provided from (used for) financing activities - continuing operations	(280.6)		208.5
Net cash provided from (used for) financing activities - NSM Group discontinued operations (Note 19)	(17.5)		13.8
Net cash provided from (used for) financing activities	(298.1)		222.3
Net change in cash during the period - continuing operations	98.0		99.4
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes    discontinued operations cash balances of $111.6 and $126.6)	147.7		84.6
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued    operations cash balances of $0.0 and 126.7)	$	245.7	$	184.0
Supplemental cash flows information:
Interest paid	$	(10.9)	$	(5.3)
Net income tax payments	$	(3.2)	$	(2.1)

See Notes to Consolidated Financial Statements

8

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (Unaudited)

Note 1. Basis of Presentation and Significant Accounting Policies

Basis of Presentation

White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”) is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report.

The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of the Company, its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.

These interim financial statements include all adjustments considered necessary by management to fairly state the financial position, results of operations and cash flows of White Mountains. These interim financial statements may not be indicative of financial results for the full year and should be read in conjunction with the Company’s 2021 Annual Report on Form 10-K.

Reportable Segments

White Mountains has determined its reportable segments based on the nature of the underlying businesses, the manner in which the Company’s subsidiaries and affiliates are organized and managed and the organization of the financial information provided to the chief operating decision maker to assess performance and make decisions regarding allocation of resources. As of September 30, 2022, White Mountains’s reportable segments were HG Global/BAM, Ark and Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations.

The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM (the “BAM Surplus Notes”). As of September 30, 2022 and December 31, 2021, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a variable interest entity for which White Mountains is the primary beneficiary. BAM’s results are all attributed to non-controlling interests.

The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. Ark underwrites select coverages through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”) and its wholly-owned subsidiary Group Ark Insurance Limited (“GAIL”). White Mountains acquired a controlling ownership interest in Ark on January 1, 2021 (the “Ark Transaction”). See Note 2 — “Significant Transactions.” As of September 30, 2022 and December 31, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within results of operations and other comprehensive income are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.

9

The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions typically are structured as minority preferred equity stakes with distribution rights, generally tied to gross revenues and designed to generate strong, stable cash yields. As of September 30, 2022 and December 31, 2021, White Mountains owned 89.3% and 99.3% of the basic units outstanding (76.1% and 84.7% on a fully diluted, fully converted basis).

White Mountains’s Other Operations consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC (“WM Capital”), its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/DavidShield”), Elementum Holdings LP (“Elementum”), and certain other consolidated and unconsolidated entities (“Other Operating Businesses”) and certain other assets.

Discontinued Operations

On August 1, 2022, White Mountains Holdings (Luxembourg) S.à r.l. (“WTM Holdings Seller”), an indirect wholly owned subsidiary of White Mountains, completed the previously announced sale of White Mountains Catskill Holdings, Inc. and NSM Insurance HoldCo, LLC (“NSM” and, collectively with White Mountains Catskill Holdings, Inc., the “NSM Group”) to Riser Merger Sub, Inc., an affiliate of The Carlyle Group Inc. (the “NSM Transaction”), pursuant to the terms of the securities purchase agreement, dated as of May 9, 2022. See Note 2 — “Significant Transactions.” NSM is a full-service managing general agent (“MGA”) and program administrator with delegated binding authorities for specialty property and casualty insurance. As of December 31, 2021, White Mountains owned 96.5% of the basic units outstanding of NSM (87.3% on a fully diluted, fully converted basis).

As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

Significant Accounting Policies

Refer to the Company’s 2021 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies.

Note 2. Significant Transactions

NSM

On August 1, 2022, the NSM Transaction closed. White Mountains received $1.4 billion in net cash proceeds at closing and recognized a net transaction gain of $875.7 million, which was comprised of $886.8 million of net gain from sale of discontinued operations and $2.9 million of comprehensive income related to the recognition of foreign currency translation gains (losses) from the sale, partially offset by $14.0 million of compensation and other costs related to the transaction recorded in Other Operations.

Kudu

On May 26, 2022, Kudu raised $114.5 million of equity capital (the “Kudu Transaction”) from Massachusetts Mutual Life Insurance Company (“Mass Mutual”), White Mountains and Kudu management. Mass Mutual, White Mountains and Kudu management contributed $64.1 million, $50.0 million and $0.4 million and in each case, at a pre-money valuation of 1.3x, or $114.0 million above the December 31, 2021 equity value of Kudu’s go-forward portfolio of participation contracts. As of September 30, 2022, Kudu’s go-forward portfolio of participation contracts excludes $41.1 million of enterprise value relating to two portfolio companies that had announced sale transactions prior to the capital raise. As a result of the Kudu Transaction, White Mountains’s basic ownership of Kudu decreased from 99.1% to 89.3%.

10

Ark

On October 1, 2020, White Mountains entered into a subscription and purchase agreement (the “Ark SPA”) with Ark and certain selling shareholders (collectively with Ark, the “Ark Sellers”). Under the terms of the Ark SPA, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and to purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020, White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the Ark Transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a credit facility agreement and $366.3 million placed in escrow.

On January 1, 2021, White Mountains completed the Ark Transaction in accordance with the terms of the Ark SPA. As of September 30, 2022, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0%) after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing.

White Mountains recognized total assets acquired related to the Ark Transaction of $2.5 billion, including goodwill and other intangible assets of $292.5 million, and total liabilities of $1.7 billion, including contingent consideration of $22.5 million and non-controlling interest of $220.2 million. Ark incurred transaction costs of $25.3 million in the first quarter of 2021.     

In the third quarter of 2021, Ark issued $163.3 million of floating rate unsecured subordinated notes (the “Ark 2021 Subordinated Notes”) in three separate transactions. See Note 7 — “Debt.” In connection with the issuance of the Ark 2021 Subordinated Notes, White Mountains and Ark terminated White Mountains’s commitment to provide up to $200.0 million of additional equity capital to Ark in 2021.

The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date:

Millions	As of January 1, 2021
Investments	$	594.3
Cash	52.0		(1)
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696.0)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	$	283.6

(1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction.

The values of net tangible assets acquired and the resulting goodwill, other intangible assets and contingent consideration were recorded at fair value using Level 3 inputs. The majority of the tangible assets acquired and liabilities assumed were recorded at their carrying values, as their carrying values approximated their fair values due to their short-term nature. The fair values of goodwill, other intangible assets and the contingent consideration liability were internally estimated primarily based on the income approach. The income approach estimates fair value based on the present value of the cash flows that the assets are expected to generate in the future. White Mountains developed internal estimates for the expected future cash flows and discount rates used in the present value calculations.

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The value of in-force business acquired represents the estimated profits relating to the unexpired contracts, net of related prepaid reinsurance, at the acquisition date through the expiration date of the contracts. For the three and nine months ended September 30, 2022, Ark recognized $0.7 million and $6.8 million of amortization expense on the value of in-force business acquired. For the three and nine months ended September 30, 2021, Ark recognized $11.0 million and $54.9 million of amortization expense on the value of in-force business acquired. The value of the syndicate underwriting capacity intangible asset was estimated using net cash flows attributable to Ark’s rights to write business in the Lloyd’s market. The value of the in-force business acquired and the syndicate underwriting capacity were estimated using a discounted cash flow method. Significant inputs to the valuation models include estimates of growth in premium revenues, investment returns, claim costs, expenses and discount rates based on a weighted average cost of capital.

In evaluating the fair value of Ark’s loss and loss adjustment expense reserves (“LAE”), White Mountains determined that the risk-free rate of interest was approximately equal to the risk factor reflecting the uncertainty within the reserves and that no adjustment was necessary.

As of September 30, 2022 and December 31, 2021, Ark recognized total contingent consideration liabilities of $32.9 million and $28.0 million. Any future adjustments to contingent consideration liabilities will be recognized through pre-tax income (loss). For the three and nine months ended September 30, 2022, Ark recognized pre-tax expense of $2.7 million and $4.9 million for the change in the fair value of its contingent consideration liabilities. For both the three and nine months ended September 30, 2021, Ark recognized pre-tax expense of $1.5 million for the change in the fair value of its contingent consideration liabilities.

MediaAlpha

On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3.6 million shares at $19.00 per share ($17.67 per share net of underwriting fees) and received total proceeds of $63.8 million. White Mountains also received $55.0 million of net proceeds related to a dividend recapitalization at MediaAlpha.

Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock, and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet.

On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160.3 million.

As of September 30, 2022, White Mountains owned 16.9 million shares, representing a 27.4% basic ownership interest (25.0% fully-diluted/fully-converted basis). At this current level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $6.60 per share increase or decrease in White Mountains’s book value per share. At the September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 16 — “Equity-Method Eligible Investments.”

PassportCard/DavidShield

On January 24, 2018, White Mountains acquired a 50.0% ownership interest in DavidShield, its joint venture partner in PassportCard. DavidShield is an MGA that is the leading provider of expatriate medical insurance in Israel and uses the same card-based delivery system as PassportCard. As part of the transaction, White Mountains reorganized its equity stake in PassportCard so that White Mountains and its partner in DavidShield would each own 50.0% of both businesses. To facilitate the transaction, White Mountains provided financing to its partner in the form of a non-interest-bearing loan that is secured by the partner’s equity in PassportCard and DavidShield. The gross purchase price for the 50.0% interest in DavidShield was $41.8 million, or $28.3 million net of the financing provided for the restructuring.

On May 7, 2020, White Mountains made an additional $15.0 million investment in PassportCard/DavidShield to support operations through the ongoing COVID-19 pandemic. The transaction increased White Mountains’s ownership interest from 50.0% to 53.8%, but had no impact on the governance structure of the companies, including White Mountains’s board representation or other investor rights. The governance structures for both PassportCard and DavidShield were designed to give White Mountains and its co-investor equal power to make the decisions that most significantly impact the operations of PassportCard and DavidShield. Because White Mountains does not have the unilateral power to direct the operations of PassportCard or DavidShield, White Mountains does not hold a controlling financial interest in either PassportCard or DavidShield and does not consolidate either entity. White Mountains’s ownership interest gives White Mountains the opportunity to exert significant influence over the significant financial and operating activities of PassportCard and DavidShield. Accordingly, PassportCard and DavidShield meet the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard and DavidShield. Changes in the fair value of PassportCard and DavidShield are recorded in realized and unrealized investment gains. White Mountains’s maximum exposure to loss on its equity investment in PassportCard/DavidShield and the non-interest-bearing loan to its partner is limited to the total carrying value of $143.0 million.

12

Note 3.  Investment Securities

White Mountains’s portfolio of investment securities held for general investment purposes consists of fixed maturity investments, short-term investments, common equity securities, its investment in MediaAlpha and other long-term investments, which are classified as trading securities. Trading securities are reported at fair value as of the balance sheet date.  Net realized and unrealized investment gains (losses) on trading securities are reported in pre-tax revenues.

White Mountains’s fixed maturity investments are generally valued using industry standard pricing methodologies. Key inputs include benchmark yields, benchmark securities, reported trades, issuer spreads, bids, offers, credit ratings and prepayment speeds. Income on mortgage and asset-backed securities is recognized using an effective yield based on anticipated prepayments and the estimated economic life of the securities. When actual prepayments differ significantly from anticipated prepayments, the estimated economic life is recalculated and the remaining unamortized premium or discount is amortized prospectively over the remaining economic life.

Realized investment gains (losses) resulting from sales of investment securities are accounted for using the specific identification method. Premiums and discounts on all fixed maturity investments are amortized or accreted to income over the anticipated life of the investment. Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year.  Short-term investments are carried at fair value, which approximated amortized cost, as of September 30, 2022 and December 31, 2021.

Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits, insurance-linked securities (“ILS”) funds and private debt investments.

Net Investment Income

White Mountains’s net investment income is comprised primarily of interest income associated with White Mountains’s fixed maturity investments and short-term investments, dividend income from common equity securities, distributions from its investment in MediaAlpha and distributions from other long-term investments.

The following table presents pre-tax net investment income for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Fixed maturity investments	$	11.1	$	8.2	$	28.6	$	21.9
Short-term investments	6.7		—		7.2		.5
Common equity securities	.1		.1		.2		.1
Other long-term investments	17.1		12.0		45.9		37.1
Amount attributable to TPC Providers	(.3)		(.2)		(.8)		(.8)
Total investment income	34.7		20.1		81.1		58.8
Third-party investment expenses	(.8)		(.6)		(1.5)		(1.6)
Net investment income, pre-tax	$	33.9	$	19.5	$	79.6	$	57.2

13

Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Realized investment gains (losses)
Fixed maturity investments	$	(4.9)	$	1.0	$	(10.8)	$	3.8
Short-term investments	(.1)		(.3)		(.4)		—
Common equity securities	—		—		—		.4
Investment in MediaAlpha	—		—		—		160.3
Other long-term investments	3.4		9.2		24.1		0.9
Net realized investment gains (losses)	(1.6)		9.9		12.9		165.4
Unrealized investment gains (losses)
Fixed maturity investments	(58.8)		(7.9)		(192.9)		(27.0)
Short-term investments	(2.1)		—		(2.6)		—
Common equity securities	4.3		1.6		(6.3)		7.3
Investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(485.8)
Other long-term investments	27.5		28.4		40.8		112.3
Net unrealized investment gains (losses)	(47.7)		(374.7)		(274.3)		(393.2)
Net realized and unrealized investment gains (losses), before    amount attributable to TPC providers(1)	(49.3)		(364.8)		(261.4)		(227.8)
Amount attributable to TPC Providers	1.3		(1.7)		6.2		(6.5)
Net realized and unrealized investment gains (losses)	$	(48.0)	$	(366.5)	$	(255.2)	$	(234.3)
Fixed maturity and short-term investments
Net realized and unrealized investment gains (losses)	$	(65.9)	$	(7.2)	$	(206.7)	$	(23.2)
Less: net realized and unrealized gains (losses) on investment           securities sold during the period	.1		(5.7)		(3.0)		(6.9)
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(66.0)	$	(1.5)	$	(203.7)	$	(16.3)
Common equity securities and investment in MediaAlpha
Net realized and unrealized investment gains (losses) on common    equity securities	$	4.3	$	1.6	$	(6.3)	$	7.7
Net realized and unrealized investment gains (losses) from    investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(325.5)
Total net realized and unrealized investment gains (losses)	(14.3)		(395.2)		(119.6)		(317.8)
Less: net realized and unrealized gains (losses) on investment          securities sold during the period	—		.4		—		20.3
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(14.3)	$	(395.6)	$	(119.6)	$	(338.1)

(1) For the three months ended September 30, 2022 and 2021, includes $(22.6) and $(7.0) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2022 and 2021, includes $(44.4) and $(7.4) of realized and unrealized investment gains (losses) related to foreign currency exchange.

The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and nine months ended September 30, 2022 and 2021 for investments still held at the end of the period:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Other long-term investments	$	40.8	$	26.5	$	57.7	$	75.5
Total net unrealized investment gains, pre-tax - Level 3 investments	$	40.8	$	26.5	$	57.7	$	75.5

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Investment Holdings

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses) and carrying values of White Mountains’s fixed maturity investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	227.9	$	—	$	(11.0)	$	—	$	216.9
Debt securities issued by corporations	1,068.8		—		(91.2)		(3.1)		974.5
Municipal obligations	289.3		—		(24.4)		—		264.9
Mortgage and asset-backed securities	278.3		—		(37.6)		—		240.7
Collateralized loan obligations	169.7		—		(7.6)		(4.8)		157.3
Total fixed maturity investments	$	2,034.0	$	—	$	(171.8)	$	(7.9)	$	1,854.3

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	212.1	$	.5	$	(1.1)	$	—	$	211.5
Debt securities issued by corporations	993.3		8.7		(8.7)		(.4)		992.9
Municipal obligations	276.4		16.8		(1.3)		—		291.9
Mortgage and asset-backed securities	277.2		2.9		(2.5)		—		277.6
Collateralized loan obligations	136.5		—		(.4)		(1.1)		135.0
Total fixed maturity investments	$	1,895.5	$	28.9	$	(14.0)	$	(1.5)	$	1,908.9

The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2022. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.

	September 30, 2022
Millions	Cost or Amortized Cost		Carrying Value
Due in one year or less	$	207.5	$	203.8
Due after one year through five years	917.9		849.4
Due after five years through ten years	354.8		309.3
Due after ten years	105.8		93.8
Mortgage and asset-backed securities and collateralized loan obligations	448.0		398.0
Total fixed maturity investments	$	2,034.0	$	1,854.3

15

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of common equity securities, White Mountains’s investment in MediaAlpha and other long-term investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	324.2	$	32.7	$	(8.7)	$	(15.4)	$	332.8
Investment in MediaAlpha	$	—	$	148.2	$	—	$	—	$	148.2
Other long-term investments	$	1,390.7	$	345.0	$	(90.0)	$	(23.0)	$	1,622.7

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	236.3	$	16.1	$	—	$	(1.3)	$	251.1
Investment in MediaAlpha	$	—	$	261.6	$	—	$	—	$	261.6
Other long-term investments	$	1,186.7	$	239.0	$	(44.1)	$	(3.8)	$	1,377.8

Fair Value Measurements

Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (observable inputs) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (unobservable inputs). Quoted prices in active markets for identical assets or liabilities have the highest priority (Level 1), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (Level 2) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (Level 3). See Note 17 — “Fair Value of Financial Instruments.”

As of September 30, 2022 and December 31, 2021, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 69% and 68% of the investment portfolio.

Fair Value Measurements by Level

The following tables present White Mountains’s fair value measurements for investments as of September 30, 2022 and December 31, 2021 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate.

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	September 30, 2022
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	216.9	$	216.9	$	—	$	—
Debt securities issued by corporations:
Financials	269.0		—		269.0		—
Consumer	181.4		—		181.4		—
Industrial	115.8		—		115.8		—
Healthcare	114.3		—		114.3		—
Technology	110.8		—		110.8		—
Utilities	75.9		—		75.9		—
Communications	49.1		—		49.1		—
Energy	36.1		—		36.1		—
Materials	22.1		—		22.1		—
Total debt securities issued by corporations	974.5		—		974.5		—
Municipal obligations	264.9		—		264.9		—
Mortgage and asset-backed securities	240.7		—		240.7		—
Collateralized loan obligations	157.3		—		157.3		—
Total fixed maturity investments	1,854.3		216.9		1,637.4		—
Short-term investments	1,196.4		1,196.4		—		—
Common equity securities (1)	332.8		46.4		286.4		—
Investment in MediaAlpha	148.2		148.2		—		—
Other long-term investments	1,058.0		—		13.9		1,044.1
Other long-term investments — NAV (2)	564.7		—		—		—
Total other long-term investments	1,622.7		—		13.9		1,044.1
Total investments	$	5,154.4	$	1,607.9	$	1,937.7	$	1,044.1

(1) Consist of investments in exchange traded funds (“ETFs”) and listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at net asset value (“NAV”) using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

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	December 31, 2021
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	211.5	$	211.5	$	—	$	—
Debt securities issued by corporations:
Financials	264.2		—		264.2		—
Consumer	178.1		—		178.1		—
Technology	117.9		—		117.9		—
Industrial	112.9		—		112.9		—
Healthcare	112.8		—		112.8		—
Utilities	70.9		—		70.9		—
Communications	56.0		—		56.0		—
Energy	48.0		—		48.0		—
Materials	32.1		—		32.1		—
Total debt securities issued by corporations	992.9		—		992.9		—
Municipal obligations	291.9		—		291.9		—
Mortgage and asset-backed securities	277.6		—		277.6		—
Collateralized loan obligations	135.0		—		135.0		—
Total fixed maturity investments	1,908.9		211.5		1,697.4		—
Short-term investments	465.9		465.9		—		—
Common equity securities (1)	251.1		—		251.1		—
Investment in MediaAlpha	261.6		261.6		—		—
Other long-term investments	895.3		—		4.7		890.6
Other long-term investments — NAV (2)	482.5		—		—		—
Total other long-term investments	1,377.8		—		4.7		890.6
Total investments	$	4,265.3	$	939.0	$	1,953.2	$	890.6

(1) Consist of investments in listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

Investments Held on Deposit or as Collateral

As of September 30, 2022 and December 31, 2021, investments of $455.1 million and $479.5 million were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM.

BAM is required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $4.6 million and $4.8 million as of September 30, 2022 and December 31, 2021.

Lloyd’s trust deposits are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. As of September 30, 2022 and December 31, 2021, Ark held Lloyd’s trust deposits with a fair value of $117.8 million and $113.8 million

The underwriting capacity of a member of Lloyd’s must be supported by providing a deposit (“Funds at Lloyd’s”) in the form of cash, securities or letters of credit in an amount determined by Lloyd’s. The amount of such deposit is calculated for each member through the completion of an annual capital adequacy exercise. These requirements allow Lloyd’s to evaluate that each member has sufficient assets to meet its underwriting liabilities plus a required solvency margin. As of September 30, 2022 and December 31, 2021, the fair value of Ark’s Funds at Lloyd’s investment deposits totaled $311.4 million and $342.8 million.

As of September 30, 2022 and December 31, 2021, Ark had $49.8 million and $50.0 million of short-term investments pledged as collateral under an uncommitted standby letter of credit. See Note 7 — “Debt.”

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Debt Securities Issued by Corporations

The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
AAA	$	11.2	$	12.0
AA	90.5		85.0
A	524.0		490.4
BBB	343.0		396.8
Other	5.8		8.7
Debt securities issued by corporations (1)	$	974.5	$	992.9

(1)    Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.

Mortgage and Asset-backed Securities and Collateralized Loan Obligations

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022						December 31, 2021
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	114.1	$	114.1	$	—	$	125.4	$	125.4	$	—
FHLMC	74.5		74.5		—		90.5		90.5		—
GNMA	28.9		28.9		—		40.1		40.1		—
Total agency (1)	217.5		217.5		—		256.0		256.0		—
Non-agency: Residential	.4		.4		—		.5		.5		—
Total non-agency	.4		.4		—		.5		.5		—
Total mortgage-backed securities	217.9		217.9		—		256.5		256.5		—
Other asset-backed securities:
Credit card receivables	11.9		11.9		—		12.3		12.3		—
Vehicle receivables	10.9		10.9		—		8.8		8.8		—
Total other asset-backed securities	22.8		22.8		—		21.1		21.1		—
Total mortgage and asset-backed securities	240.7		240.7		—		277.6		277.6		—
Collateralized loan obligations	157.3		157.3		—		135.0		135.0		—
Total mortgage and asset-backed securities and collateralized loan obligations	$	398.0	$	398.0	$	—	$	412.6	$	412.6	$	—

(1)    Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed

by a government sponsored entity (i.e., FNMA, FHLMC).

As of September 30, 2022, White Mountains’s investment portfolio included $157.3 million of collateralized loan obligations that are within the senior tranches of their respective fund securitization structures. All of White Mountains’s collateral loan obligations were rated AAA or AA as of September 30, 2022.

Investment in MediaAlpha

Following the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and is presented as a separate line item on the balance sheet.

At the September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 2 — “Significant Transactions.”

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Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
Kudu’s Participation Contracts	$	813.2	$	669.5
PassportCard/DavidShield	132.0		120.0
Elementum Holdings, L.P.	45.0		45.0
Other unconsolidated entities (1)	37.0		34.4
Total unconsolidated entities	1,027.2		868.9
Private equity funds and hedge funds	239.8		153.8
Bank loan fund	155.7		163.0
Lloyd’s trust deposits	117.8		113.8
ILS funds	49.4		51.9
Private debt investments	13.0		14.1
Other	19.8		12.3
Total other long-term investments	$	1,622.7	$	1,377.8

(1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, convertible preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments.

Private Equity Funds and Hedge Funds

White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held investments in 16 private equity funds and two hedge funds. The largest investment in a single private equity fund or hedge fund was $49.3 million and $31.3 million as of September 30, 2022 and December 31, 2021.

The following table presents the fair value of investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments
Private equity funds
Aerospace/Defense/Government	$	102.9	$	45.1	$	69.8	$	11.8
Financial services	77.9		54.9		67.7		29.3
Real estate	4.3		2.5		4.3		2.9
Total private equity funds	185.1		102.5		141.8		44.0
Hedge funds
Long/short equity financials and business services	49.3		—		—		—
European small/mid cap	5.4		—		12.0		—
Total hedge funds	54.7		—		12.0		—
Total private equity funds and hedge funds    included in other long-term investments	$	239.8	$	102.5	$	153.8	$	44.0

 

Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period.

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The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2022:

Millions	1 – 3 years	3 – 5 years	5 – 10 years	>10 years	Total
Private equity funds — expected lock-up period remaining	$27.5	$19.0	$135.4	$3.2	$185.1

Investors in private equity funds are generally subject to indemnification obligations outside of the capital commitment period and prior to the winding up of the fund. As of September 30, 2022 and December 31, 2021, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds. 

Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. Advance notice requirements for redemptions from White Mountains’s hedge funds investments range from 45 to 90 days. One of White Mountains’s hedge fund investments also limits redemptions to every second anniversary following the date of the initial investment.

Bank Loan Fund

White Mountains’s other long-term investments include a bank loan fund with a fair value of $155.7 million as of September 30, 2022. The fair value of this investment is estimated using the NAV of the fund. The bank loan fund’s investment objective is to provide, on an unleveraged basis, high current income consistent with preservation of capital and low duration. The bank loan fund primarily invests in a broad portfolio of U.S. dollar-denominated, non-investment grade, floating-rate senior secured loans and may invest in other financial instruments, such as secured and unsecured corporate debt, credit default swaps, reverse repurchase agreements, synthetic indices and cash and cash equivalents.

The investment in the bank loan fund is subject to restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. White Mountains may redeem all or a portion of its bank loan fund investment as of any calendar month-end upon 15 calendar days advanced written notice.

Lloyd’s Trust Deposits

White Mountains’s other long-term investments include Lloyd’s trust deposits, which consist of non-U.K. deposits and Canadian comingled pooled funds. The Lloyd’s trust deposits invest primarily in short-term government securities, agency securities and corporate bonds held in trusts that are managed by Lloyd's of London. These investments are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. The fair value of the Lloyd’s trust deposits is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held Lloyd’s trust deposits with a fair value of $117.8 million.

Insurance-Linked Securities Funds

White Mountains’s other long-term investments include ILS fund investments. The fair value of these investments is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held investments in ILS funds with a fair value of $49.4 million.

Investments in ILS funds are generally subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, non-renewal clauses, restrictions on redemption frequency and advance notice periods for redemptions. From time to time, natural catastrophe, liquidity, market or other events will occur that make the determination of fair value for underlying investments in ILS funds less certain due to the potential for loss development. In such circumstances, the impacted investments may be subject to additional lock-up provisions.

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ILS funds are typically subject to monthly and annual restrictions on redemptions and advance redemption notice period requirements that range between 30 and 90 days. Amounts requested for redemption remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period.

One of the ILS funds in White Mountains’s portfolio requires shareholders to provide advance redemption notice on or before September 15 of each calendar year. Amounts requested for redemption in this fund remain subject to market fluctuation until the underlying investment has fully matured or been commuted, which may be up to a period of three years from the start of each calendar year.

Rollforward of Level 3 Investments

Level 3 measurements as of September 30, 2022 and 2021 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities. The following table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the nine months ended September 30, 2022 and 2021:

Level 3 Investments
Millions	Other Long-term Investments			Other Long-term Investments
Balance at December 31, 2021	$	890.6	Balance at December 31, 2020	$	614.2
Net realized and unrealized gains	57.3		Net realized and unrealized gains	79.0
Amortization/accretion	—		Amortization/accretion	—
Purchases	127.9		Purchases	143.6
Sales	(31.7)		Sales	(31.9)
Effect of Ark Transaction	—		Effect of Ark Transaction	9.6
Transfers in	—		Transfers in	—
Transfers out	—		Transfers out	—
Balance at September 30, 2022	$	1,044.1	Balance at September 30, 2021	$	814.5

Fair Value Measurements — Transfers Between Levels - Nine months ended September 30, 2022 and 2021

Transfers between levels are recorded using the fair value measurement as of the end of the quarterly period in which the event or change in circumstance giving rise to the transfer occurred.

During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements.

During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 measurements.

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Significant Unobservable Inputs

The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s other long-term investments, classified within Level 3 as of September 30, 2022 and December 31, 2021. The tables below exclude $42.9 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds.

$ in Millions	September 30, 2022
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$813.2	17% - 24%	7x - 16x
PassportCard/DavidShield	Discounted cash flow	$132.0	24%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	18%	4%
Private debt investments	Discounted cash flow	$11.0	10%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 9.7x.

(4) As of September 30, 2022, three of Kudu’s Participation Contracts with a total fair value of $312.4 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(5) In 2022, Kudu deployed a total of $97.9 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

$ in Millions	December 31, 2021
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$669.5	18% - 23%	7x - 13x
PassportCard/DavidShield	Discounted cash flow	$120.0	23%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	17%	4%
Private debt investments	Discounted cash flow	$9.4	8%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 10x.

(4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management.

(5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

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Note 4. Goodwill and Other Intangible Assets

    White Mountains accounts for purchases of businesses using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. The estimated acquisition date fair values, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date.

The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by reportable segment as of September 30, 2022 and December 31, 2021:

$ in Millions	Weighted Average Economic  Life (in years)	September 30, 2022						December 31, 2021
		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value
Goodwill:
Ark	N/A	$	116.8	$	—	$	116.8	$	116.8	$	—	$	116.8
Kudu	N/A	7.6		—		7.6		7.6				7.6
Other Operations	N/A	51.1		—		51.1		17.9		—		17.9
Total goodwill		175.5		—		175.5		142.3		—		142.3
Other intangible assets:
Ark
Underwriting capacity	N/A	175.7		—		175.7		175.7		—		175.7
Kudu
Trade names	7	2.2		1.1		1.1		2.2		.9		1.3
Other Operations
Trade names	15.9	17.9		2.4		15.5		8.2		1.5		6.7
Customer relationships	12.4	29.5		6.6		22.9		18.8		4.5		14.3
Other	12.1	2.8		.3		2.5		.3		.1		.2
Subtotal		50.2		9.3		40.9		27.3		6.1		21.2
Total other intangible assets		228.1		10.4		217.7		205.2		7.0		198.2
Total goodwill and other intangible assets		$	403.6	$	10.4	393.2		$	347.5	$	7.0	340.5
Goodwill and other intangible assets attributed to    non-controlling interests						(103.1)						(91.8)
Goodwill and other intangible assets included in White Mountains’s    common shareholders’ equity						$	290.1					$	248.7

Intangible Assets Valuation Methods

The goodwill recognized for the entities shown above is attributed to expected future cash flows. The acquisition date fair values of other intangible assets with finite lives are estimated using income approach techniques, which use future expected cash flows to develop a discounted present value amount.

The multi-period-excess-earnings method estimates fair value using the present value of the incremental after-tax cash flows attributable solely to the other intangible asset over its remaining life. This approach was used to estimate the fair value of other intangible assets associated with the underwriting capacity, trade names, customer relationships and contracts and information technology.

The relief-from-royalty method was used to estimate fair value for other intangible assets that relate to rights that could be obtained via a license from a third-party owner. Under this method, the fair value is estimated using the present value of license fees avoided by owning rather than leasing the asset. This technique was used to estimate the fair value of domain names, certain trademarks and brand names.

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The with-or-without method estimates the fair value of other intangible assets that provide an incremental benefit. Under this method, the fair value of the other intangible asset is calculated by comparing the value of the entity with and without the other intangible asset. This approach was used to estimate the fair value of favorable lease terms.

On at least an annual basis beginning no later than the interim period included in the one-year anniversary of an acquisition, White Mountains evaluates goodwill and other intangible assets for potential impairment. Between annual evaluations, White Mountains considers changes in circumstances or events subsequent to the most recent evaluation that may indicate that an impairment may exist and, if necessary will perform an interim review for potential impairment.

The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022:

$ in Millions	Goodwill and Other intangible asset (1)		Acquisition Date
Acquisition of subsidiary/ asset
Ark	$	292.5	January 1, 2021
Other Operations	$	86.6	Various

(1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	201.8	$	196.2	$	398.0	$	151.5	$	201.1	$	352.6
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)		—		(3.4)		(.4)		—		(.4)
Amortization	—		(1.4)		(1.4)		—		(2.0)		(2.0)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

	Nine Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	142.3	$	198.2	$	340.5	$	19.2	$	26.4	$	45.6
Ark Transaction	—		—		—		116.8		175.7		292.5
Acquisition of businesses (1)	59.5		—		59.5		15.8		—		15.8
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)				(3.4)		(.7)		.1		(.6)
Amortization	—		(3.4)		(3.4)		—		(3.1)		(3.1)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the nine

months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

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Note 5.  Loss and Loss Adjustment Expense Reserves

The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Gross beginning balance	$	1,022.1	$	760.0	$	894.7	$	696.0
Less: beginning reinsurance recoverable on unpaid losses (1)	(375.5)		(425.3)		(428.9)		(433.4)
Net loss and LAE reserves	646.6		334.7		465.8		262.6
Loss and LAE incurred relating to:
Current year losses	222.9		141.9		491.8		269.0
Prior year losses	(9.2)		(12.7)		(35.6)		(21.2)
Net incurred losses and LAE	213.7		129.2		456.2		247.8
Loss and LAE paid relating to:
Current year losses	(6.1)		(9.0)		(20.8)		(11.5)
Prior year losses	(37.0)		(20.3)		(130.8)		(62.1)
Net paid loss and LAE	(43.1)		(29.3)		(151.6)		(73.6)
Change in TPC Providers’ participation (2)	—		—		57.5		(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)		(1.2)		(19.9)		(1.2)
Net ending balance	808.0		433.4		808.0		433.4
Plus: ending reinsurance recoverable on unpaid losses (3)	521.4		457.5		521.4		457.5
Gross ending balance	$	1,329.4	$	890.9	$	1,329.4	$	890.9

(1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $182.4 and $314.6 for the three months ended September 30, 2022 and 2021 and $276.8 and $319.2 for the nine months ended September 30, 2022 and 2021.

(2) Amount represents the impact to net loss and LAE reserves due to a change in the TPC Providers’ participation related to the annual reinsurance to close (“RITC”) process.

(3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $168.0 and $299.9 as of September 30, 2022 and 2021.

For the three and nine months ended September 30, 2022, Ark recognized $9.2 million and $35.6 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2022 was driven primarily by good claims experience across most classes including the property and accident & health and specialty reserving lines of business, predominantly from business underwritten in London. For the three and nine months ended September 30, 2021, Ark recognized $12.7 million and $21.2 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2021 was driven primarily by the property and accident & health reserving line of business.

TPC Providers’ Participation

For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by TPC Providers using whole account reinsurance contracts with Ark’s corporate member. The TPC Providers’ participation in the Syndicates for the 2020 open year of account is 42.8% of the total net result of the Syndicates. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates.

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An RITC agreement is generally put in place after the third year of operations for a year of account such that the outstanding loss and LAE reserves, including future development thereon, are reinsured into the next year of account. As a result, and in combination with the changing participation provided by TPC Providers, Ark’s participation on outstanding loss and LAE reserves reinsured into the next year of account may change, perhaps significantly. During the first quarter of 2022, an RITC was executed such that the outstanding loss and LAE reserves for claims arising out of the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%, were reinsured into the 2020 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates is 42.8%. During the first quarter of 2021, an RITC was executed such that the outstanding loss and LAE reserves for claims arising out of the 2018 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 57.6%, were reinsured into the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%.

Municipal Bond Guarantee Insurance

HG Re and BAM do not have any outstanding loss and LAE reserves related to BAM’s municipal bond guarantee insurance business.

Note 6.  Third-Party Reinsurance

In the normal course of business, Ark may seek to limit losses that may arise from catastrophes or other events by reinsuring certain risks with third-party reinsurers. Ark remains liable for risks reinsured in the event that the reinsurer does not honor its obligations under reinsurance contracts.

The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for Ark for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Gross	$	215.5	$	162.4	$	1,252.5	$	895.0
Ceded	(22.9)		(41.5)		(246.0)		(169.5)
Net written premiums	$	192.6	$	120.9	$	1,006.5	$	725.5
Earned premiums:
Gross	$	454.9	$	284.5	$	966.6	$	622.0
Ceded	(108.8)		(71.1)		(208.8)		(186.2)
Net earned premiums	$	346.1	$	213.4	$	757.8	$	435.8
Losses and loss adjustment expenses:
Gross	$	391.4	$	193.5	$	712.9	$	372.7
Ceded	(177.7)		(64.3)		(256.7)		(124.9)
Net losses and loss adjustment expenses	$	213.7	$	129.2	$	456.2	$	247.8

As of September 30, 2022, Ark had $521.4 million and $29.5 million of reinsurance recoverables on unpaid and paid losses. As of September 30, 2021, Ark had $457.5 million and $8.1 million of reinsurance recoverables on unpaid and paid losses. As reinsurance contracts do not relieve Ark of its obligation to its policyholders, Ark seeks to reduce the credit risk associated with reinsurance balances by avoiding over-reliance on specific reinsurers through the application of concentration limits and thresholds. Ark is selective with its reinsurers, placing reinsurance with only those reinsurers having a strong financial condition. Ark monitors the financial strength of its reinsurers on an ongoing basis.

As of September 30, 2022, Ark’s reinsurance recoverables of $550.9 million included $168.0 million attributable to TPC Providers, which are collateralized. As of September 30, 2021, Ark’s reinsurance recoverables of $465.6 million included $299.9 million related to TPC Providers, which are collateralized.

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The following table provides a listing of Ark’s remaining gross and net reinsurance recoverables, excluding amounts attributable to TPC Providers, by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) rating and the percentage of total recoverables as of September 30, 2022:

$ in Millions	As of September 30, 2022
A.M. Best Rating(1)	Gross		Collateral		Net		% of Total
A+ or better	$	178.3	$	—	$	178.3	67.7	%
A- to A	78.9		—		78.9		29.9
B++ or lower and not rated	125.7		119.4		6.3		2.4
Total	$	382.9	$	119.4	$	263.5	100.0	%

(1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good).

See Note 10 — “Municipal Bond Guarantee Insurance” for third-party reinsurance balances related to White Mountains’s financial guarantee business.

Reinsurance Contracts Accounted for as Deposits

Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), which is accounted for using the deposit method and recorded within other assets. Ark earns an annual crediting rate of 3.0%, which is recorded within other revenue. During the fourth quarter of 2021, Ark negotiated a reduction of $31.7 million, including accrued interest, to the aggregate excess of loss contract with SiriusPoint. As of September 30, 2022, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.3 million.

See Note 10 — “Municipal Bond Guarantee Insurance” for reinsurance contracts accounted for as deposits related to White Mountains’s financial guarantee business.

Note 7.  Debt

The following table presents White Mountains’s debt outstanding as of September 30, 2022 and December 31, 2021:

$ in Millions	September 30, 2022		Effective   Rate	(1)	December 31, 2021		Effective   Rate	(1)
HG Global Senior Notes	$	150.0	8.6%		$	—	N/A
Unamortized discount and issuance cost	(3.6)				—
HG Global Senior Notes, carrying value	146.4				—
Ark 2007 Subordinated Notes, carrying value	30.0				30.0
Ark 2021 Notes Tranche 1	37.6				44.2
Ark 2021 Notes Tranche 2	47.0				47.0
Ark 2021 Notes Tranche 3	70.0				70.0
Unamortized issuance cost	(4.6)				(5.3)
Ark 2021 Subordinated Notes, carrying value	150.0				155.9
Total Ark Subordinated Notes, carrying value	180.0		7.3%		185.9		6.9%
Kudu Credit Facility	260.4		5.6%		225.4		4.3%
Unamortized issuance cost	(6.9)				(7.2)
Kudu Credit Facility, carrying value	253.5				218.2
Other Operations debt	36.4		7.1%		17.1		7.5%
Unamortized issuance cost	(.8)				(.3)
Other Operations debt, carrying value	35.6				16.8
Total debt	$	615.5			$	420.9

 (1) Effective rate includes the effect of the amortization of debt issuance costs.

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HG Global Senior Notes

On April 29, 2022, HG Global received the proceeds of its $150.0 million face value floating rate secured senior notes (the “HG Global Senior Notes”). The HG Global Senior Notes, which mature in April 2032, accrue interest at a floating rate equal to the three-month Secured Overnight Financing Rate (“SOFR”) plus 6.3% per annum. Subsequent to the five-year anniversary of the funding date, absent the occurrence of an early amortization trigger event, HG Global will make payments of principal on a quarterly basis totaling $15.0 million annually. Upon the occurrence of an early amortization trigger event, HG Global is required to use all available cash flow to repay the notes. Early amortization trigger events include scenarios in which HG Re is effectively in run off. HG Global has the option to redeem, in whole or in part, the HG Global Senior Notes after the five-year anniversary of the funding date at the outstanding principal amounts plus accrued interest.

The HG Global Senior Notes require HG Global to maintain an interest reserve account of eight times the interest accrued for the most recent quarterly interest period, which is included in short-term investments. As of September 30, 2022, the interest reserve account is $26.4 million.

The HG Global Senior Notes are secured by the capital stock and other equity interests of HG Global’s subsidiaries, the interest reserve account, and all cash and non-cash proceeds from the foregoing collateral. The HG Global Senior Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

If the payments of principal and interest under the HG Global Senior Notes become subject to tax withholding on behalf of a relevant governmental authority for certain indemnified taxes, the HG Global Senior Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The HG Global Senior Notes require the payment of additional interest of 1.0% per annum if the HG Global Senior Notes receive a non-investment grade rating or are no longer rated.

As of September 30, 2022, the HG Global Senior Notes had an outstanding principal balance of $150.0 million.

Ark Subordinated Notes

In March 2007, GAIL issued $30.0 million face value of floating rate unsecured junior subordinated deferrable interest notes to Alesco Preferred Funding XII Ltd., Alesco Preferred Funding XIII Ltd. and Alesco Preferred Funding XIV Ltd (the “Ark 2007 Subordinated Notes”). The Ark 2007 Subordinated Notes, which mature in June 2037, accrue interest at a floating rate equal to the three-month U.S. London Inter-Bank Offered Rate (“LIBOR”) plus 4.6% per annum. As of September 30, 2022, the Ark 2007 Subordinated Notes had an outstanding principal balance of $30.0 million.

In the third quarter of 2021, GAIL issued $163.3 million face value floating rate subordinated notes at par in three separate transactions for proceeds of $157.8 million, net of debt issuance costs. The unsecured subordinated notes (the “Ark 2021 Subordinated Notes”) were issued in private placement offerings that were exempt from the registration requirements of the Securities Act of 1933. On July 13, 2021, Ark issued €39.1 million ($46.3 million based upon the foreign exchange spot rate as of the date of the transaction) face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 1”). The Ark 2021 Notes Tranche 1, which mature in July 2041, accrue interest at a floating rate equal to the three-month EURIBOR plus 5.75% per annum. On August 11, 2021, Ark issued $47.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 2”). The Ark 2021 Notes Tranche 2, which mature in August 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 5.75% per annum. On September 8, 2021, Ark issued $70.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 3”). The Ark 2021 Notes Tranche 3, which mature in September 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 6.1% per annum. On the ten-year anniversary of the issue dates, the interest rate for the Ark 2021 Subordinated Notes will increase by 1.0% per annum. Ark has the option to redeem, in whole or in part, the Ark 2021 Subordinated Notes ahead of contractual maturity at the outstanding principal amounts plus accrued interest at the ten-year anniversary or any subsequent interest payment date.

All payments of principal and interest under the Ark 2021 Subordinated Notes are conditional upon GAIL’s solvency and compliance with the enhanced capital requirements of the Bermuda Monetary Authority (“BMA”). The deferral of payments of principal and interest under these conditions does not constitute a default by Ark and does not give the noteholders any rights to accelerate repayment of the Ark 2021 Subordinated Notes or take any enforcement action under the Ark 2021 Subordinated Notes.

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If the payments of principal and interest under the Ark 2021 Subordinated Notes become subject to tax withholding on behalf of Bermuda or any political subdivision there, the Ark 2021 Subordinated Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The Ark 2021 Notes Tranche 3 require the payment of additional interest of 1.0% per annum upon the occurrence of a premium load event until such event is remedied. Premium load events include the failure to meet payment obligations of the Ark 2021 Notes Tranche 3 when due, failure of GAIL to maintain an investment grade credit rating, failure to maintain 120% of GAIL’s Bermuda solvency capital requirement, failure of GAIL to maintain a debt to capital ratio below 40%, late filing of GAIL’s or Ark’s financial information, and making a restricted payment or distribution on GAIL’s common stock or other securities that rank junior or pari passu with the Ark 2021 Notes Tranche 3 when a different premium load event exists or will be caused by the restricted payment.

As of September 30, 2022, the Ark 2021 Notes Tranche 1 had an outstanding principal balance of €39.1 million ($37.6 million based upon the foreign exchange spot rate as of September 30, 2022), the Ark 2021 Notes Tranche 2 had an outstanding principal balance of $47.0 million, and the Ark 2021 Notes Tranche 3 had an outstanding principal balance of $70.0 million.

The Ark Subordinated Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

Ark Standby Letter of Credit Facilities

In December 2021, Ark entered into two uncommitted standby letter of credit facility agreements to support the continued growth and expansion of its GAIL insurance and reinsurance operations. The standby letter of credit facility agreements were executed with ING Bank N.V., London Branch (the “ING LOC Facility”) with capacity of $50.0 million on an uncollateralized basis and with Citibank Europe Plc (the “Citibank LOC Facility”) with capacity of $100.0 million on a collateralized basis. In September 2022, Ark entered another uncommitted standby letter of credit facility agreement with Lloyds Bank Corporate Markets PLC (the “Lloyds LOC Facility”) with capacity of $50.0 million on a collateralized basis.

As of September 30, 2022, the ING LOC Facility and Lloyds LOC Facility were undrawn. As of September 30, 2022, the Citibank LOC Facility had an outstanding principal balance of $36.2 million. As of September 30, 2022, $49.8 million of short-term investments were pledged as collateral under the Citibank LOC Facility. Ark’s uncommitted standby letter of credit facility agreements contain various representations, warranties and covenants that White Mountains considers to be customary for such borrowings.

Kudu Credit Facility and Kudu Bank Facility

On December 23, 2019, Kudu entered into a secured credit facility with Monroe Capital Management Advisors, LLC (the “Kudu Bank Facility”). On March 23, 2021, Kudu replaced the Kudu Bank Facility and entered into a secured revolving credit facility (the “Kudu Credit Facility”) with Mass Mutual to repay the Kudu Bank Facility, and to fund new investments and related transaction expenses. The maximum borrowing capacity of the Kudu Credit Facility is $300.0 million. The Kudu Credit Facility matures on March 23, 2036. In connection with the replacement of the Kudu Bank Facility, Kudu recognized a total loss of $4.1 million, representing debt issuance costs and prepayment fees, which are included within interest expense for the year to date period ended September 30, 2021.

The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of September 30, 2022, the interest reserve account is $8.9 million. The Kudu Credit Facility requires Kudu to maintain a ratio of the outstanding balance to the sum of the fair market value of the participation contracts and cash held in certain accounts (the “LTV Percentage”) of less than 50% in years 0-3, 40% in years 4-6, 25% in years 7-8, 15% in years 9-10, and 0% thereafter. As of September 30, 2022, Kudu has a 35% LTV Percentage.

Kudu may borrow undrawn balances within the initial three-year availability period, subject to customary terms and conditions, to the extent the amount borrowed under the Kudu Credit Facility does not exceed the borrowing base, which is equal to 35% of the fair value of qualifying Kudu Participation Contracts. As of September 30, 2022, the available undrawn balance was $39.6 million.

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The following table presents the change in debt under the Kudu Bank Facility and Kudu Credit Facility for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Kudu Bank Facility
Beginning balance	$	—	$	—	$	—	$	89.2
Term loans
Borrowings	—		—		—		3.0
Repayments	—		—		—		(92.2)
Ending balance	$	—	$	—	$	—	$	—
Kudu Credit Facility
Beginning balance	$	260.4	$	203.0	$	225.4	$	—
Term loans
Borrowings	—		—		35.0		203.0
Repayments	—		—		—		—
Ending balance	$	260.4	$	203.0	$	260.4	$	203.0

The Kudu Credit Facility is secured by all property of the loan parties and contains various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

Other Operations Debt

As of September 30, 2022, White Mountains’s Other Operations had debt with an outstanding principal balance of $36.4 million, which consisted of five secured credit facilities (collectively, “Other Operations debt”).

Compliance

At September 30, 2022, White Mountains was in compliance in all material respects with the covenants under all of its debt instruments.

Note 8.  Income Taxes

The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law such that taxes are imposed, the Bermuda Exempted Undertakings Tax Protection Act of 1966 states that the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035. The Company has subsidiaries and branches that operate in various other jurisdictions around the world and are subject to tax in the jurisdictions in which they operate.  As of September 30, 2022, the primary jurisdictions in which the Company’s subsidiaries and branches were subject to tax were Ireland, Israel, Luxembourg, the United Kingdom and the United States.

White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2022 represented an effective tax rate of 23.9% and 9.4%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by full year forecasted income in jurisdictions with lower tax rates than the United States, partially offset by a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes.

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White Mountains’s income tax expense related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2021 represented an effective tax rate of (7.9)% and (17.1)%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by losses in jurisdictions with lower tax rates than the United States, a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes. For the nine months ended September 30, 2021, the effective rate was also different from the U.S. statutory rate of 21.0% due to additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities.

On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19.0% to 25.0% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective.

On August 16, 2022, the U.S. enacted the Inflation Reduction Act (the “IRA”). White Mountains has evaluated the tax provisions of the IRA, the most significant of which relate to the corporate alternative minimum tax and the tax on share repurchases, and does not expect the legislation to have a material impact on its results of operations.

In arriving at the effective tax rate for the three and nine months ended September 30, 2022 and 2021, White Mountains forecasted all income and expense items including the change in unrealized investment gains (losses) and realized investment gains (losses) for the years ending December 31, 2022 and 2021.

White Mountains records a valuation allowance against deferred tax assets if it becomes more likely than not that all or a portion of a deferred tax asset will not be realized. Changes in valuation allowances from period to period are included in income tax expense in the period of change. In determining whether or not a valuation allowance, or change therein, is warranted, White Mountains considers factors such as prior earnings history, expected future earnings, carryback and carryforward periods and strategies that if executed would result in the realization of a deferred tax asset.

With few exceptions, White Mountains is no longer subject to U.S. federal, state, or non-U.S. income tax examinations by tax authorities for years before 2016.

Note 9. Derivatives

HG Global Interest Rate Cap

On June 16, 2022, HG entered into an interest rate cap agreement, effective on July 25, 2022, to limit its exposure to the risk of interest rate increases on the HG Global Senior Notes. The notional amount of the interest rate cap is $150.0 million and the termination date is July 25, 2025.

HG paid initial premiums of $3.3 million for the interest rate cap. Under the terms of the interest rate cap agreement, if the current three-month SOFR rate at the measurement date exceeds 3.5%, HG will receive payments from the counterparty equal to the difference between the three-month SOFR rate on the determination date and 3.5%, multiplied by the notional amount of the cap based on the number of days in the quarter and a year equal to 360 days. As of September 30, 2022, the three-month SOFR rate was 3.6%.

HG accounts for the interest rate cap as a derivative at fair value, with changes in fair value recognized in current period earnings within interest expense. For the three and nine months ended September 30, 2022, White Mountains recognized a gain of $2.1 million and $0.6 million related to the change in fair value on the interest rate cap within interest expense. As of September 30, 2022, the estimated fair value of the interest rate cap recorded in other assets was $3.9 million. White Mountains classifies the interest rate cap as a Level 2 measurement.

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Note 10. Municipal Bond Guarantee Insurance

HG Global was established to fund the startup of BAM, a mutual municipal bond insurer. HG Global, together with its subsidiaries, provided the initial capitalization of BAM through the purchase of $503.0 million of the BAM Surplus Notes.

Reinsurance Treaties

FLRT

BAM is a party to a first loss reinsurance treaty (“FLRT”) with HG Re under which HG Re provides first loss protection up to 15%-of-par outstanding on each municipal bond insured by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. In return, BAM cedes up to 60% of the risk premium charged for insuring the municipal bond, which is net of a ceding commission. The FLRT is a perpetual agreement with terms that can be renegotiated after a specified period of time. During 2021, BAM and HG Re agreed that the terms may be renegotiated at the end of 2024, and each subsequent five-year period thereafter.

Fidus Re

BAM is party to a collateralized financial guarantee excess of loss reinsurance agreement that serves to increase BAM’s claims paying resources and is provided by Fidus Re Ltd. (“Fidus Re”).

In 2018, Fidus Re was initially capitalized by the issuance of $100.0 million of insurance-linked securities (the “Fidus Re 2018 Agreement”). The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. The insurance-linked securities were issued by Fidus Re with an initial term of 12 years and are callable five years after the date of issuance. Under the Fidus Re 2018 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $165.0 million on a portion of BAM’s financial guarantee portfolio (the “2018 Covered Portfolio”) up to a total reimbursement of $100.0 million. The Fidus Re 2018 Agreement does not provide coverage for losses in excess of $276.1 million. The 2018 Covered Portfolio consists of approximately 28% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022.

In the first quarter of 2021, Fidus Re issued an additional $150.0 million of insurance-linked securities (the “Fidus Re 2021 Agreement”) with an initial term of 12 years and are callable five years after the date of issuance. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. Under the Fidus Re 2021 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $135.0 million on a portion of BAM’s financial guarantee portfolio (the “2021 Covered Portfolio”) up to a total reimbursement of $150.0 million. The Fidus Re 2021 Agreement does not provide coverage for losses in excess of $301.7 million. The 2021 Covered Portfolio consists of approximately 33% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022.

The Fidus Re agreements are accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as they do not meet the risk transfer requirements necessary to be accounted for as reinsurance.

XOLT

In January 2020, BAM entered into an excess of loss reinsurance agreement (the “XOLT”) with HG Re. Under the XOLT, HG Re provides last dollar protection for exposures on municipal bonds insured by BAM in excess of New York State Department of Financial Services (“NYDFS”) single issuer limits. As of September 30, 2022, the XOLT is subject to an aggregate limit equal to the lesser of $125.0 million or the assets held in the supplemental collateral trust (the “Supplemental Trust”) at any point in time. The agreement is accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as the agreement does not meet the risk transfer requirements necessary to be accounted for as reinsurance.

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Collateral Trusts

HG Re’s obligations under the FLRT are limited to the assets in two collateral trusts: the Supplemental Trust and a Regulation 114 Trust (together, the “Collateral Trusts”). Losses required to be reimbursed under the FLRT are subject to an aggregate limit equal to the assets held in the Collateral Trusts at any point in time.

On a monthly basis, BAM deposits cash equal to ceded premiums, net of ceding commissions, due to HG Re under the FLRT directly into the Regulation 114 Trust. The Regulation 114 Trust target balance is equal to gross ceded unearned premiums and unpaid ceded loss and LAE, if any. If, at the end of any quarter, the Regulation 114 Trust balance is below the target balance, funds will be withdrawn from the Supplemental Trust and deposited into the Regulation 114 Trust in an amount equal to the shortfall. If, at the end of any quarter, the Regulation 114 Trust balance is above 102% of the target balance, funds will be withdrawn from the Regulation 114 Trust and deposited into the Supplemental Trust. The Regulation 114 Trust balance as of September 30, 2022 and December 31, 2021 was $259.4 million and $250.2 million.

The Supplemental Trust target balance is $603.0 million, less the amount of cash and securities in the Regulation 114 Trust in excess of its target balance (the “Supplemental Trust Target Balance”). If, at the end of any quarter, the Supplemental Trust balance exceeds the Supplemental Trust Target Balance, such excess may be distributed to HG Re. The distribution will be made first as an assignment of accrued interest on the BAM Surplus Notes and second in cash and/or fixed income securities.

As the BAM Surplus Notes are repaid over time, the BAM Surplus Notes will be replaced in the Supplemental Trust by cash and fixed income securities. The Supplemental Trust balance as of September 30, 2022 and December 31, 2021 was $574.5 million and $601.8 million.

As of September 30, 2022 and December 31, 2021, the Collateral Trusts held assets of $833.9 million and $852.0 million, which included $457.7 million and $481.7 million of cash and investments, $364.6 million and $364.6 million of BAM Surplus Notes and $11.6 million and $5.7 million of interest receivable on the BAM Surplus Notes.

BAM Surplus Notes

Through 2024, the interest rate on the BAM Surplus Notes is a variable rate equal to the one-year U.S. Treasury rate plus 300 basis points, set annually. During 2022, the interest rate on the BAM Surplus Notes is 3.2%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. Under its agreements with HG Global, BAM is required to seek regulatory approval to pay interest and principal on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS.

In December 2021, BAM made a $33.8 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $23.6 million was a repayment of principal held in the Supplemental Trust, $0.4 million was a payment of accrued interest held inside the Supplemental Trust and $9.8 million was a payment of accrued interest held outside the Supplemental Trust.

During the three and nine months ended September 30, 2022 and 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest.

As of September 30, 2022 and December 31, 2021, the principal balance on the BAM Surplus Notes was $364.6 million and $364.6 million and total interest receivable on the BAM Surplus Notes was $166.4 million and $157.6 million.

Insured Obligations and Premiums

The following table presents a schedule of BAM’s insured obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022		December 31, 2021
Contracts outstanding	13,094		12,350
Remaining weighted average contract period outstanding (in years)	10.8		10.8
Contractual debt service outstanding (in millions):
Principal	$	98,619.0	$	89,196.5
Interest	47,595.0		41,486.5
Total debt service outstanding	$	146,214.0	$	130,683.0
Gross unearned insurance premiums (in millions)	$	286.7	$	266.3

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The following table presents a schedule of BAM’s future premium revenues as of September 30, 2022:

Millions	September 30, 2022
October 1, 2022 - December 31, 2022	$	6.9
January 1, 2023 - March 31, 2023	6.8
April 1, 2023 - June 30, 2023	6.7
July 1, 2023 - September 30, 2023	6.6
October 1, 2023 - December 31, 2023	6.4
Total 2023	26.5
2024	24.9
2025	23.2
2026	21.6
2027	20.1
2028 and thereafter	163.5
Total gross unearned insurance premiums	$	286.7

The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Direct	$	18.4	$	12.8	$	44.9	$	34.5
Assumed	1.3		—		1.3		4.5
Gross written premiums (1)	$	19.7	$	12.8	$	46.2	$	39.0
Earned premiums:
Direct	$	6.5	$	5.9	$	22.0	$	16.8
Assumed	.6		.8		4.0		2.8
Gross earned premiums (1)	$	7.1	$	6.7	$	26.0	$	19.6

(1) There are no ceded premium amounts in the periods presented and gross earned premiums are equivalent to net written premiums and net earned premiums.

In January 2021, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $805.5 million.

In September 2022, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $42.5 million.

None of the contracts assumed under these reinsurance agreements were non-performing, and no loss reserves have been established for any of the contracts, either as of the transaction date or as of September 30, 2022. The agreements, which cover future claims exposure only, meet the risk transfer criteria under ASC 944-20, Insurance Activities and accordingly have been accounted for as reinsurance.

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Note 11. Earnings Per Share

White Mountains calculates earnings per share using the two-class method, which allocates earnings between common shares and unvested restricted common shares. Both classes of shares participate equally in dividends and earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares.

The following table presents the Company’s computation of earnings per share from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: total income (loss) from discontinued operations, net of tax (1)	893.1		5.3		903.2		(5.1)
Less: net (income) loss from discontinued operations attributable    to non-controlling interests	$	(.1)	$	—	$	(.7)	$	1.1
Net income (loss) from continuing operations attributable to    White Mountains’s common shareholders	$	(4.8)	$	(376.7)	$	(150.1)	$	(304.2)
Allocation of (earnings) losses to participating restricted    common shares (2)	.1		4.6		1.8		3.5
Basic and diluted earnings (losses) per share numerators	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings per share (in dollars) - continuing    operations:
Distributed earnings - dividends declared and paid	$	—	$	—	$	1.00	$	1.00
Undistributed earnings (losses)	(1.66)		(121.90)		(51.73)		(99.16)
Basic and diluted earnings (losses) per share	$	(1.66)	$	(121.90)	$	(50.73)	$	(98.16)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group and net gain (loss) from sale of discontinued operations, net of tax - Sirius Group. See Note 19 — “Held for Sale and Discontinued Operations.”

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

The following table presents the undistributed net earnings (losses) from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Undistributed net earnings (losses) - continuing operations:
Net income (losses) attributable to White Mountains’s common    shareholders, net of restricted common share amounts	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Dividends declared, net of restricted common share amounts (1)	—		—		(3.0)		(3.1)
Total undistributed net earnings (losses), net of restricted    common share amounts	$	(4.7)	$	(372.1)	$	(151.3)	$	(303.8)

(1) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

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Note 12. Employee Share-Based Incentive Compensation Plans

White Mountains’s Long-Term Incentive Plan (the “WTM Incentive Plan”) provides for grants of various types of share-based and non-share-based incentive awards to key employees of White Mountains. As of September 30, 2022 and 2021, White Mountains’s share-based compensation incentive awards consist of performance shares and restricted shares.

Performance Shares

Performance shares are designed to reward employees for meeting company-wide performance targets. Performance shares are conditional grants of a specified maximum number of common shares or an equivalent amount of cash. Awards generally vest at the end of a three-year service period, are subject to the attainment of pre-specified performance goals, and are valued based on the market value of common shares at the time awards are paid. Performance shares earned under the WTM Incentive Plan are typically paid in cash but may be paid in common shares. Compensation expense is recognized for the vested portion of the awards over the related service periods. The level of payout ranges from zero to two times the number of shares initially granted, depending on White Mountains’s financial performance. Performance shares become payable at the conclusion of a performance cycle (typically 3 years) if pre-defined financial targets are met. The performance measures used for determining performance share payouts are growth in White Mountains’s adjusted book value per share and intrinsic value per share. Intrinsic value per share is generally calculated by adjusting adjusted book value per share for differences between the adjusted book value of certain assets and liabilities and White Mountains’s estimate of their underlying intrinsic values.

The following table presents the performance share activity for the three and nine months ended September 30, 2022 and 2021 for performance shares granted under the WTM Incentive Plan:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense
Beginning of period	39,449	$	41.2	41,252	$	45.7	40,828	$	42.2	42,458	$	56.3
Shares paid (1)	—	—		(219)	(.6)		(14,625)	(26.4)		(14,336)	(35.2)
New grants	—	—		—	—		13,225	—		13,475	—
Forfeitures and   cancellations (2)	—	(.1)		(205)	.2		21	(.2)		(769)	.4
Expense recognized	—	11.9		—	(6.5)		—	37.4		—	17.3
End of period	39,449	$	53.0	40,828	$	38.8	39,449	$	53.0	40,828	$	38.8

(1) Includes WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target and WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in March 2021 at 200% of target. 

(2) Amounts include changes in assumed forfeitures, as required under GAAP.

During the nine months ended September 30, 2022, White Mountains granted 13,225 performance shares for the 2022-2024 performance cycle. During the nine months ended September 30, 2021, White Mountains granted 13,475 performance shares for the 2021-2023 performance cycle.

For the 2019-2021 performance cycle, the Company issued common shares for 750 performance shares earned and all other performance shares earned were settled in cash. For the 2018-2020 performance cycle, all performance shares earned were settled in cash. If all the outstanding WTM performance shares had vested on September 30, 2022, the total additional compensation cost to be recognized would have been $41.2 million, based on accrual factors (common share price and payout assumptions) as of September 30, 2022.

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The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of September 30, 2022 for each performance cycle:

	Nine Months Ended September 30, 2022
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense
Performance cycle:
2020 – 2022	13,350	$	31.9
2021 – 2023	13,475	14.7
2022 – 2024	13,225	7.2
Sub-total	40,050	53.8
Assumed forfeitures	(601)	(.8)
September 30, 2022	39,449	$	53.0

Restricted Shares

Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions,  except share amounts	Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value
Non-vested,
Beginning of period	38,350	$	23.0	38,280	$	23.2	37,850	$	15.9	43,105	$	15.2
Issued	—	—		—	—		13,225	13.8		13,475	16.1
Vested	—	—		(219)	—		(12,725)	—		(17,936)	—
Forfeited	—	—		(211)	(.2)		—	—		(794)	(.8)
Expense recognized	—	(3.8)		—	(3.6)		—	(10.5)		—	(11.1)
End of period	38,350	$	19.2	37,850	$	19.4	38,350	$	19.2	37,850	$	19.4

During the nine months ended September 30, 2022, White Mountains issued 13,225 restricted shares that vest on January 1, 2025. During the nine months ended September 30, 2021, White Mountains issued 13,475 restricted shares that vest on January 1, 2024. The unamortized issue date fair value as of September 30, 2022 is expected to be recognized ratably over the remaining vesting periods. 

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Note 13. Leases

White Mountains has entered into lease agreements, primarily for office space. These leases are classified as operating leases, with lease expense recognized on a straight-line basis over the term of the lease. Lease incentives, such as free rent or landlord reimbursements for leasehold improvements, are recognized at lease inception and amortized on a straight-line basis over the term of the lease. Lease expense and the amortization of leasehold improvements are recognized within general and administrative expenses. Lease payments related to options to extend or renew the lease term are excluded from the calculation of lease liabilities unless White Mountains is reasonably certain of exercising those options.

As of September 30, 2022 and December 31, 2021, the right of use (“ROU”) lease assets were $24.5 million and $28.1 million and lease liabilities were $26.5 million and $30.0 million.

The following table summarizes net lease expense recognized in White Mountains’s consolidated statements of operations for the three and nine months ended September 30, 2022 and 2021:

Millions	Three Months Ended September 30,				Nine Months Ended September 30,
Lease Cost	2022		2021		2022		2021
Lease cost	$	1.9	$	1.9	$	5.9	$	4.8
Less: sublease income	.2		.1		.5		.3
Net lease cost	$	1.7	$	1.8	$	5.4	$	4.5

The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2022:

Millions	As of September 30, 2022
Remainder of 2022	$	1.7
2023	8.1
2024	7.1
2025	4.9
2026	2.6
Thereafter	5.0
Total undiscounted lease payments	29.4
Less: present value adjustment	2.9
Operating lease liabilities	$	26.5

The following tables present lease related assets and liabilities by reportable segment as of September 30, 2022 and December 31, 2021:

	As of September 30, 2022
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	6.2	$	6.6	$	5.9	$	5.8	$	24.5	4.1%
Lease liabilities	$	6.7	$	6.6	$	6.8	$	6.4	$	26.5

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

	As of December 31, 2021
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	7.6	$	7.0	$	6.4	$	7.1	$	28.1	4.0%
Lease liabilities	$	8.1	$	7.0	$	7.1	$	7.8	$	30.0

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

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Note 14. Non-controlling Interests

Non-controlling interests consist of the ownership interests of non-controlling shareholders in consolidated entities and are presented separately on the balance sheet.

The following table presents the balance of non-controlling interests included in White Mountains’s total equity and the ownership interests held by non-controlling shareholders as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
$ in Millions	Non-controlling Percentage (1)		Non-controlling Equity		Non-controlling Percentage (1)		Non-controlling Equity
Non-controlling interests, excluding BAM
HG Global	3.1	%	$	(.3)	3.1	%	$	8.9
Ark	28.0	%	217.1		28.0	%	230.7
Kudu	10.7	%	80.8		.7	%	12.4
NSM (2)	—	%	—		3.5	%	16.7
Other	various		20.8		various		11.9
Total, excluding BAM			318.4				280.6
BAM	100.0	%	(160.1)		100.0	%	(124.0)
Total non-controlling interests			$	158.3			$	156.6

(1) The non-controlling percentage represents the basic ownership interests held by non-controlling shareholders with the exception of HG Global, for which the non-controlling percentage represents the preferred share ownership held by non-controlling shareholders.

(2) As a result of the NSM Transaction, NSM has been classified as discontinued operations through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations.”

Note 15. Segment Information

As of September 30, 2022, White Mountains conducted its operations through four segments: (1) HG Global/BAM, (2) Ark, (3) Kudu, and (4) Other Operations. As a result of the NSM Transaction, the results of operations for NSM, previously reported as a segment, have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the chief operating decision makers and the Board of Directors. Significant intercompany transactions among White Mountains’s segments have been eliminated herein.

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The following tables present the financial information for White Mountains’s segments:

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2022
Earned insurance premiums	$	7.1	$	346.1	$	—	$	—	$	353.2
Net investment income	5.7		4.9		14.8		8.5		33.9
Net realized and unrealized investment    gains (losses)	(38.8)		(14.4)		41.1		(17.3)		(29.4)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(18.6)		(18.6)
Commission revenues	—		—		—		3.2		3.2
Other revenues	1.3		6.6		—		33.0		40.9
Total revenues	(24.7)		343.2		55.9		8.8		383.2
Loss and loss adjustment expenses	—		213.7		—		—		213.7
Insurance and reinsurance acquisition expenses	1.7		74.8		—		—		76.5
Cost of sales	—		—		—		25.0		25.0
General and administrative expenses	15.8		26.9		4.5		39.9		87.1
Amortization of other intangible assets	—		—		—		1.4		1.4
Interest expense	2.0		3.7		4.2		.6		10.5
Total expenses	19.5		319.1		8.7		66.9		414.2
Pre-tax income (loss) from continuing operations	$	(44.2)	$	24.1	$	47.2	$	(58.1)	$	(31.0)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2021
Earned insurance premiums	$	6.7	$	213.4	$	—	$	—	$	220.1
Net investment income	4.4		.6		9.5		5.0		19.5
Net realized and unrealized investment    gains (losses)	(4.0)		.3		18.9		15.3		30.5
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(396.8)		(396.8)
Commission revenues	—		—		—		2.4		2.4
Other revenues	.3		3.4		.1		28.1		31.9
Total revenues	7.4		217.7		28.5		(346.0)		(92.4)
Losses and loss adjustment expenses	—		129.2		—		—		129.2
Insurance and reinsurance acquisition expenses	3.0		53.7		—		—		56.7
Cost of sales	—		—		—		24.0		24.0
General and administrative expenses	12.4		21.8		3.3		14.4		51.9
Amortization of other intangible assets	—		—		—		2.0		2.0
Interest expense	—		2.1		1.9		.4		4.4
Total expenses	15.4		206.8		5.2		40.8		268.2
Pre-tax income (loss) from continuing operations	$	(8.0)	$	10.9	$	23.3	$	(386.8)	$	(360.6)

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Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2022
Earned insurance premiums	$	26.0	$	757.8	$	—	$	—	$	783.8
Net investment income	15.1		9.7		41.2		13.6		79.6
Net realized and unrealized investment    gains (losses)	(114.0)		(76.5)		45.8		2.8		(141.9)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(113.3)		(113.3)
Commission revenues	—		—		—		8.7		8.7
Other revenues	3.7		10.1		—		89.6		103.4
Total revenues	(69.2)		701.1		87.0		1.4		720.3
Loss and loss adjustment expenses	—		456.2		—		—		456.2
Insurance and reinsurance acquisition expenses	9.5		174.9		—		—		184.4
Cost of sales	—		—		—		68.8		68.8
General and administrative expenses	49.5		79.8		10.2		118.9		258.4
Amortization of other intangible assets	—		—		.2		3.2		3.4
Interest expense	5.4		10.6		10.3		1.2		27.5
Total expenses	64.4		721.5		20.7		192.1		998.7
Pre-tax income (loss) from continuing operations	$	(133.6)	$	(20.4)	$	66.3	$	(190.7)	$	(278.4)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2021
Earned insurance premiums	$	19.6	$	435.8	$	—	$	—	$	455.4
Net investment income	13.2		1.8		26.1		16.1		57.2
Net realized and unrealized investment    gains (losses)	(15.6)		10.3		62.5		34.0		91.2
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(325.5)		(325.5)
Commission revenues	—		—		—		7.0		7.0
Other revenues	.9		9.4		.2		57.6		68.1
Total revenues	18.1		457.3		88.8		(210.8)		353.4
Losses and loss adjustment expenses	—		247.8		—		—		247.8
Insurance and reinsurance acquisition expenses	6.5		124.4		—		—		130.9
Cost of sales	—		—		—		45.9		45.9
General and administrative expenses	42.7		84.4		9.0		79.4		215.5
Amortization of other intangible assets	—		—		.2		2.9		3.1
Interest expense	—		4.5		9.2		1.1		14.8
Total expenses	49.2		461.1		18.4		129.3		658.0
Pre-tax income (loss) from continuing operations	$	(31.1)	$	(3.8)	$	70.4	$	(340.1)	$	(304.6)

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Note 16. Equity-Method Eligible Investments

White Mountains’s equity method eligible investments include White Mountains’s investment in MediaAlpha, certain other unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds in which White Mountains has the ability to exert significant influence over the investee’s operating and financial policies.

The following table presents the ownership interests and carrying values of White Mountains’s equity method eligible investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Ownership Interest		Carrying Value		Ownership Interest		Carrying Value
Kudu Participation Contracts (1)	4.1 - 33.0%		$	813.2	3.2 - 32.0%		$	669.5
Investment in MediaAlpha	27.4	%	148.2		28.0	%	261.6
PassportCard/DavidShield	53.8	%	132.0		53.8	%	120.0
Elementum Holdings, L.P.	29.7	%	45.0		29.7	%	45.0
Other equity method eligible investments, at fair value	Under 50.0%		102.7		Under 50.0%		109.3
Other equity method eligible investments, at fair value	50.0% and over		27.7		50.0% and over		17.8

(1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are non-controlling equity interests in the form of revenue and earnings participation contracts.

For the three and nine months ended September 30, 2022, White Mountains received dividend and income distributions from equity method eligible investments of $16.1 million and $42.9 million, which were recorded within net investment income in the consolidated statements of operations. For the three and nine months ended September 30, 2021, White Mountains received dividend and income distributions from equity method eligible investments of $13.0 million, and $37.7 million, which were recorded within net investment income in the consolidated statements of operations.

Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock, and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet. See Note 2 — “Significant Transactions.” For the nine months ended September 30, 2021, MediaAlpha was considered a significant subsidiary.

The following tables present summarized financial information for MediaAlpha as of September 30, 2022 and December 31, 2021 and for the three and nine months ended September 30, 2022 and 2021:

Millions	September 30, 2022		December 31, 2021
Balance sheet data:
Total assets	$	265.2	$	289.8
Total liabilities	$	333.6	$	351.4

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Income statement data:
Total revenues	$	89.0	$	152.7	$	335.1	$	483.7
Total expenses	$	110.2	$	157.0	$	379.2	$	488.2
Net income (loss)	$	(21.2)	$	(4.3)	$	(44.1)	$	(4.5)

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Note 17. Fair Value of Financial Instruments

    White Mountains records its financial instruments at fair value with the exception of debt obligations, which are recorded as debt at face value less unamortized original issue discount. See Note 7 — “Debt.”

    The following tables presents the fair value and carrying value of these financial instruments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Carrying Value		Fair Value		Carrying Value
HG Global Senior Notes	$	146.1	$	146.4	$	—	$	—
Ark 2007 Subordinated Notes	$	26.2	$	30.0	$	27.6	$	30.0
Ark 2021 Subordinated Notes	$	149.4	$	150.0	$	162.8	$	155.9
Kudu Credit Facility	$	265.5	$	253.5	$	246.8	$	218.2
Other Operations debt	$	36.8	$	35.6	$	17.7	$	16.8

The fair value estimates for the HG Global Senior Notes, Ark 2007 Subordinated Notes, Ark 2021 Subordinated Notes, Kudu Credit Facility and Other Operations debt have been determined based on a discounted cash flow approach and are considered to be Level 3 measurements.

For the fair value level measurements associated with White Mountains’s investment securities. See Note 3 — “Investment Securities.” For the fair value level measurements associated with White Mountains’s derivative instruments. See Note 9 — “Derivatives.”

Note 18. Commitments and Contingencies

Legal Contingencies

White Mountains, and the insurance industry in general, is routinely subject to claims related litigation and arbitration in the normal course of business, as well as litigation and arbitration that do not arise from, nor are directly related to, claims activity. White Mountains’s estimates of the costs of settling matters routinely encountered in claims activity are reflected in the reserves for unpaid loss and LAE. See Note 5 — “Losses and Loss Adjustment Expense Reserves.”

White Mountains considers the requirements of ASC 450 when evaluating its exposure to non-claims related litigation and arbitration. ASC 450 requires that accruals be established for litigation and arbitration if it is probable that a loss has been incurred and it can be reasonably estimated. ASC 450 also requires that litigation and arbitration be disclosed if it is probable that a loss has been incurred or if there is a reasonable possibility that a loss may have been incurred. White Mountains does not have any current non-claims related litigation that may have a material adverse effect on White Mountains’s financial condition, results of operations or cash flows.

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Note 19. Held for Sale and Discontinued Operations

NSM

On August 1, 2022, White Mountains closed the NSM Transaction. See Note 2 — “Significant Transactions.” As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation.

Sirius Group

On April 18, 2016, White Mountains completed the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) to CM International Pte. Ltd. and CM Bermuda Limited (collectively “CMI”). In connection with the sale, White Mountains indemnified Sirius Group against the loss of certain interest deductions claimed by Sirius Group related to periods prior to the sale of Sirius Group to CMI that had been disputed by the Swedish Tax Agency. In late October 2018, the Swedish Administrative Court ruled against Sirius Group on its appeal of the Swedish Tax Agency’s denial of these interest deductions. As a result, in 2018 White Mountains recorded a loss of $17.3 million within net gain (loss) on sale of discontinued operations reflecting the value of these interest deductions.

As of December 31, 2020, White Mountains’s liability related to the tax indemnification provided in connection with the sale of Sirius Group in 2016 was $18.7 million. In April 2021, the Swedish Tax Agency informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal and that the interest deductions should not be disallowed. In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor. For the nine months ended September 30, 2021, White Mountains recorded a gain of $17.6 million in discontinued operations to reverse the liability accrued as of December 31, 2020 and $1.1 million gain related to foreign currency translation.

Summary of Reclassified Balances and Related Items

Net Assets Held for Sale

The following summarizes the assets and liabilities associated with NSM Group classified as held for sale. As of December 31, 2021, the amounts presented exclude $16.1 million of insurance licenses, investments and cash classified as assets held for sale related to one of the Other Operating Businesses.

Millions	December 31, 2021
Assets held for sale
Short-term investments, at fair value	$	7.8
Cash (restricted $89.2)	111.6
Premiums and commissions receivable	85.0
Goodwill and other intangible assets	725.4
Other assets	59.2
Total assets held for sale	$	989.0
Liabilities held for sale
Debt	$	272.1
Premiums payable	135.9
Contingent consideration	6.8
Other liabilities	80.5
Total liabilities held for sale	495.3
Net assets held for sale	$	493.7

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Net Income (Loss) from Discontinued Operations 

The following summarizes the results of operations, including related income taxes associated with the businesses classified as discontinued operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022 (1)		2021		2022 (1)		2021
Revenues
Commission revenues	$	26.6	$	67.0	$	176.9	$	194.6
Other revenues	7.0		15.3		48.1		46.8
Total revenues - NSM Group	33.6		82.3		225.0		241.4
Expenses
General and administrative expenses	15.7		48.9		126.8		142.4
Broker commission expenses	8.2		20.4		52.9		60.9
Change in fair value of contingent consideration	—		.6		.1		.8
Amortization of other intangible assets	—		8.2		9.1		25.0
Loss on assets held for sale	—		—		—		28.7
Interest expense	1.6		5.9		12.1		17.7
Total expenses - NSM Group	25.5		84.0		201.0		275.5
Pre-tax income (loss) from discontinued operations -    NSM Group	8.1		(1.7)		24.0		(34.1)
Income tax (expense) benefit	(1.8)		7.0		(7.6)		10.3
Net income (loss) from discontinued operations, net of    tax - NSM Group	6.3		5.3		16.4		(23.8)
Net gain (loss) from sale of discontinued operations, net of    tax - NSM Group	886.8		—		886.8		—
Net gain (loss) from sale of discontinued operations, net of    tax - Sirius Group	—		—		—		18.7
Total income (loss) from discontinued operations,    net of tax	893.1		5.3		903.2		(5.1)
Net (income) loss from discontinued operations    attributable to non-controlling interests	(.2)		—		(.8)		1.1
Total income (loss) from discontinued operations    attributable to White Mountains’s common    shareholders	892.9		5.3		902.4		(4.0)
Other comprehensive income (loss) from discontinued    operations, net of tax - NSM Group	.7		(1.7)		(5.2)		.9
Net gain (loss) from foreign currency translation from sale    of discontinued operations, net of tax - NSM Group	2.9		—		2.9		—
Comprehensive income (loss) from discontinued    operations	896.5		3.6		900.1		(3.1)
Other comprehensive income (loss) from discontinued    operations attributable to non-controlling interests	(.1)		—		.2		(.1)
Comprehensive income (loss) from discontinued    operations attributable to White Mountains’s common    shareholders	$	896.4	$	3.6	$	900.3	$	(3.2)

(1) As a result of the NSM Transaction, the results of operations for NSM Group are presented for the periods from July 1, 2022 to August 1, 2022 and January 1, 2022 to August 1, 2022.

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Net Change in Cash from Discontinued Operations

The following summarizes the net change in cash associated with the businesses classified as discontinued operations for the nine months ended September 30, 2022 and 2021:

	Nine Months Ended September 30,
Millions	2022		2021
Net cash provided from (used for) operations	$	38.7	$	40.3
Net cash provided from (used for) investing activities	7.1		(54.6)
Net cash used from (used for) financing activities	(17.5)		13.8
Effect of exchange rate changes on cash	4.0		.6
Net change in cash during the period	32.3		.1
Cash balances at beginning of period (includes restricted cash of $89.2 and $78.4)	111.6		126.6
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)	(143.9)		—
Cash balances at end of period (includes restricted cash of $0.0 and $92.2)	—		126.7
Supplemental cash flows information:
Interest paid	$	(12.0)	$	(16.6)
Net income tax payments	$	—	$	—

Earnings Per Share from Discontinued Operations

White Mountains calculates earnings per share using the two-class method, which allocates earnings between common and unvested restricted common shares. Both classes of shares participate equally in earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares. Diluted earnings per share amounts are also impacted by the net effect of potentially dilutive common shares outstanding. The following table presents the Company’s computation of earnings per share for discontinued operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: net income (loss) from continuing operations	$	(23.6)	$	(389.2)	$	(252.3)	$	(356.8)
Less: net (income) loss from continuing operations attributable to    non-controlling interests	$	18.8	$	12.5	$	102.2	$	52.6
Total gain (loss) from discontinued operations attributable to White    Mountains’s common shareholders (1)	$	893.0	$	5.3	$	902.5	$	(4.0)
Allocation of earnings to participating restricted common shares (2)	(11.8)		(.1)		(10.8)		—
Basic and diluted earnings per share numerators (3)	$	881.2	$	5.2	$	891.7	$	(4.0)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings (losses) per share (in dollars) -    discontinued operations:	$	308.59	$	1.72	$	304.97	$	(1.29)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - Sirius Group and net (income) loss from discontinued operations attributable to non-controlling interests.

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three and nine months ended September 30, 2022 and 2021.

(4) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

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Item 2. Management’s Discussion and Analysis of Financial Condition and Results of Operations.

The following discussion contains “forward-looking statements.” White Mountains intends statements that are not historical in nature, which are hereby identified as forward-looking statements, to be covered by the safe harbor provisions of the Private Securities Litigation Reform Act of 1995. White Mountains cannot promise that its expectations in such forward-looking statements will turn out to be correct. White Mountains’s actual results could be materially different from and worse than its expectations. See “FORWARD-LOOKING STATEMENTS” on page 76 for specific important factors that could cause actual results to differ materially from those contained in forward-looking statements.

The following discussion also includes nine non-GAAP financial measures: (i) adjusted book value per share, (ii) Ark’s adjusted loss and LAE ratio, (iii) Ark’s adjusted insurance acquisition expense ratio, (iv) Ark’s adjusted other underwriting expense ratio, (v) Ark’s adjusted combined ratio (vi) Kudu’s earnings before interest, taxes, depreciation and amortization (“EBITDA”), (vii) Kudu’s adjusted EBITDA, (viii) total consolidated portfolio returns excluding MediaAlpha, and (ix) adjusted capital, that have been reconciled from their most comparable GAAP financial measures on page 74. White Mountains believes these measures to be useful in evaluating White Mountains’s financial performance and condition.

RESULTS OF OPERATIONS FOR THE THREE AND NINE MONTHS ENDED SEPTEMBER 30, 2022 AND 2021

Overview

White Mountains reported book value per share of $1,439 and adjusted book value per share of $1,471 as of September 30, 2022. Book value per share and adjusted book value per share both increased 28% in the third quarter of 2022. For the first nine months of 2022, book value increased 23% and adjusted book value increased 24%, including dividends. The increases in book value per share and adjusted book value per share were driven primarily by the net gain from the sale of NSM of approximately $300 per share (based on 2.9 million shares outstanding at August 1, 2022). In addition, the growth in White Mountains’s book value per share and adjusted book value per share reflect good operating results at its businesses, partially offset by net realized and unrealized losses in its fixed income portfolio and investment in MediaAlpha. White Mountains reported book value per share of $1,162 and adjusted book value per share of $1,176 as of September 30, 2021. Book value per share and adjusted book value per share both decreased 9% in the third quarter of 2021. Book value per share decreased 8% and adjusted book value per share decreased 7% in the first nine months of 2021, including dividends. Results in the third quarter and first nine months of 2021 were driven primarily by $397 million and $326 million of net realized and unrealized investment losses from White Mountains’s investment in MediaAlpha, resulting from decreases in the MediaAlpha share price.

On August 1, 2022, White Mountains closed the NSM Transaction. White Mountains received $1.4 billion in net cash proceeds at closing and recognized a net gain of $876 million, which was comprised of $887 million of net gain from sale of discontinued operations and $3 million of comprehensive income related to the recognition of foreign currency translation gains (losses) from the sale, partially offset by $14 million of compensation and other costs related to the transaction recorded in Other Operations.

During the third quarter of 2022, White Mountains repurchased and retired 366,645 of its common shares for $509 million at an average share price of $1,388.24, or 96% of White Mountains’s September 30, 2022 book value per share and 94% of White Mountains’s September 30, 2022 adjusted book value per share. As of September 30, 2022, White Mountains’s undeployed capital was approximately $1.1 billion.

In the HG Global/BAM segment, gross written premiums and MSC collected totaled $46 million and $109 million in the third quarter and first nine months of 2022 compared to $28 million and $84 million in the third quarter and first nine months of 2021. Total pricing was 110 and 81 basis points in the third quarter and first nine months of 2022 compared to 69 and 66 basis points in the third quarter and first nine months of 2021. BAM insured municipal bonds with par value of $4.1 billion and $13.5 billion in the third quarter and first nine months of 2022 compared to $4.0 billion and $12.6 billion in the third quarter and first nine months of 2021. BAM’s total claims paying resources were $1,260 million as of September 30, 2022 compared to $1,192 million as of December 31, 2021 and $1,181 million as of September 30, 2021.

48

Ark reported a GAAP combined ratio of 87% and 90% in the third quarter and first nine months of 2022 compared to 92% and 95% in the third quarter and first nine months of 2021. Ark’s adjusted combined ratio, which adds back amounts attributable to TPC providers, was 86% and 90% in the third quarter and first nine months of 2022 compared to 89% and 93% in the third quarter and first nine months of 2021. The adjusted combined ratio for the third quarter and first nine months of 2022 included 21 points and 17 points of catastrophe losses compared to 21 points and 16 points in the third quarter and first nine months of 2021. Catastrophe losses for the third quarter and first nine months of 2022 included $51 million related to Hurricane Ian on a net basis after reinstatement premiums. The adjusted combined ratio in the third quarter and first nine months of 2022 also included four points and five points of favorable prior year development compared to six points and five points in the third quarter and first nine months of 2021, principally in property lines. Ark reported gross written premiums of $216 million and $1,253 million, net written premiums of $193 million and $1,007 million and net earned premiums of $346 million and $758 million in the third quarter and first nine months of 2022 compared to gross written premiums of $162 million and $895 million, net written premiums of $121 million and $726 million and net earned premiums of $213 million and $436 million and in the third quarter and first nine months of 2021. Ark reported pre-tax income (loss) of $24 million and $(20) million in the third quarter and first nine months of 2022 compared to $11 million and $(4) million in third quarter and first nine months of 2021. Ark’s results included net realized and unrealized investment gains (losses) of $(14) million and $(77) million in the third quarter and first nine months of 2022 compared to $0.3 million and $10 million in the third quarter and first nine months of 2021. Ark’s pre-tax loss for the first nine months of 2021 also included $25 million of transaction expenses related to White Mountains’s transaction with Ark

Kudu reported total revenue of $56 million, pre-tax income of $47 million and adjusted EBITDA of $12 million in the third quarter of 2022 compared to total revenue of $29 million, pre-tax income of $23 million and adjusted EBITDA of $7 million in the third quarter of 2021. Total revenues and pre-tax income in the third quarter of 2022 included $41 million of net realized and unrealized investment gains on Kudu’s participation contracts compared to $19 million of net realized and unrealized investment gains on Kudu’s participation contracts in the third quarter of 2021. Kudu reported total revenue of $87 million, pre-tax income of $66 million and adjusted EBITDA of $33 million in the first nine months of 2022 compared to total revenue of $89 million, pre-tax income of $70 million and adjusted EBITDA of $19 million in the first nine months of 2021. Total revenues and pre-tax income in the first nine months of 2022 included $46 million of net realized and unrealized investment gains on Kudu’s participation contracts compared to $63 million of net realized and unrealized investment gains on Kudu’s participation contracts in the first nine months of 2021.

As of September 30, 2022, the market value of White Mountains’s investment in MediaAlpha was $148 million, which was down from $167 million as of June 30, 2022. As of September 30, 2022, the closing price was $8.75 per share, which decreased from $9.85 as of June 30, 2022. Based on White Mountains’s ownership of 16.9 million shares of MediaAlpha as of September 30, 2022, each $1.00 per share increase or decrease in the stock price of MediaAlpha will result in an approximate $6.60 per share increase or decrease in White Mountains’s book value per share and adjusted book value per share.

White Mountains’s pre-tax total consolidated portfolio return on invested assets was 0.4% in the third quarter of 2022. This return included $19 million of unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 0.5% in the third quarter of 2022. Excluding MediaAlpha, investment returns in the third quarter of 2022 were driven primarily by favorable other long-term investment results, which more than offset net realized and unrealized investment losses in the fixed income portfolio due to rising interest rates. White Mountains’s pre-tax total consolidated portfolio return on invested assets was -8.0% in the third quarter of 2021. This return included $397 million of unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 1.4% in the third quarter of 2021. Excluding MediaAlpha, investment returns in the third quarter of 2021 were driven primarily by favorable other long-term investments results.

White Mountains’s pre-tax total consolidated portfolio return on invested assets was -3.6% in the first nine months of 2022. This return included $113 million of net unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was -1.4% in the first nine months of 2022. Excluding MediaAlpha, investment returns in the first nine months of 2022 were driven primarily by net unrealized investment losses in the fixed income portfolio due to rising interest rates, partially offset by favorable other long-term investment results. White Mountains’s pre-tax total consolidated portfolio return on invested assets was -3.7% in the first nine months of 2021. This return included $326 million of net realized and unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 4.6% in the first nine months of 2021. Excluding MediaAlpha, investment returns in the first nine months of 2021 were driven primarily by favorable other long-term investment results.

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Adjusted Book Value Per Share

The following table presents White Mountains’s book value per share and reconciles it to adjusted book value per share, a non-GAAP measure as of September 30, 2022, June 30, 2022, December 31, 2021, and September 30, 2021. See NON-GAAP FINANCIAL MEASURES on page 74.

	September 30, 2022		June 30, 2022		December 31, 2021		September 30, 2021
Book value per share numerators (in millions):
White Mountains’s common shareholders’ equity -   GAAP book value per share numerator	$	3,708.0	$	3,323.3	$	3,548.1	$	3,521.7
Time value of money discount on expected future    payments on the BAM Surplus Notes (1)	(110.8)		(115.9)		(125.9)		(128.0)
HG Global’s unearned premium reserve (1)	232.2		221.6		214.6		206.8
HG Global’s net deferred acquisition costs (1)	(65.9)		(62.6)		(60.8)		(58.1)
Adjusted book value per share numerator	$	3,763.5	$	3,366.4	$	3,576.0	$	3,542.4
Book value per share denominators (in thousands of shares):
Common shares outstanding - GAAP book value    per share denominator	2,576.2		2,942.9		3,017.8		3,029.6
Unearned restricted common shares	(17.5)		(20.9)		(13.7)		(17.0)
Adjusted book value per share denominator	2,558.7		2,922.0		3,004.1		3,012.6
GAAP book value per share	$	1,439.31	$	1,129.27	$	1,175.73	$	1,162.44
Adjusted book value per share	$	1,470.84	$	1,152.12	$	1,190.39	$	1,175.86
Year-to-date dividends paid per share	$	1.00	$	1.00	$	1.00	$	1.00

(1) Amount reflects White Mountains’s preferred share ownership in HG Global of 96.9%.

Goodwill and Other Intangible Assets

The following table presents a summary of goodwill and other intangible assets that are included in White Mountains’s book value as of September 30, 2022, June 30, 2022, December 31, 2021, and September 30, 2021:

Millions	September 30, 2022			June 30, 2022			December 31, 2021		September 30, 2021
Goodwill:
Ark	$	116.8		$	116.8		$	116.8	$	116.8
Kudu	7.6			7.6			7.6		7.6
Other Operations	51.1		(1)	77.4		(1)	17.9		17.4
Total goodwill	175.5			201.8			142.3		141.8
Other intangible assets:
Ark	175.7			175.7			175.7		175.7
Kudu	1.1			1.1			1.3		1.4
Other Operations	40.9			19.4			21.2		31.3
Total other intangible assets	217.7			196.2			198.2		208.4
Total goodwill and other intangible assets (2)	393.2			398			340.5		350.2
Goodwill and other intangible assets attributed to      non-controlling interests	(103.1)			(103.4)			(91.8)		(92.0)
Goodwill and other intangible assets included in    White Mountains’s common shareholders’    equity	$	290.1		$	294.6		$	248.7	$	258.2

(1) The relative fair values of goodwill and other intangible assets recognized in connection with recent acquisitions had not yet been finalized as of September 30, 2022 and June 30, 2022.

(2) See Note 4 — “Goodwill and Other Intangible Assets” for details of goodwill and other intangible assets.

50

Summary of Consolidated Results

The following table presents White Mountains’s consolidated financial results for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Revenues
Financial Guarantee revenues	$	(24.7)	$	7.4	$	(69.2)	$	18.1
P&C Insurance and Reinsurance revenues	343.2		217.7		701.1		457.3
Asset Management revenues	55.9		28.5		87.0		88.8
Other Operations revenues	8.8		(346.0)		1.4		(210.8)
Total revenues	383.2		(92.4)		720.3		353.4
Expenses
Financial Guarantee expenses	19.5		15.4		64.4		49.2
P&C Insurance and Reinsurance expenses	319.1		206.8		721.5		461.1
Asset Management expenses	8.7		5.2		20.7		18.4
Other Operations expenses	66.9		40.8		192.1		129.3
Total expenses	414.2		268.2		998.7		658.0
Pre-tax income (loss)
Financial Guarantee pre-tax income (loss)	(44.2)		(8.0)		(133.6)		(31.1)
P&C Insurance and Reinsurance pre-tax income (loss)	24.1		10.9		(20.4)		(3.8)
Asset Management pre-tax income (loss)	47.2		23.3		66.3		70.4
Other Operations pre-tax income (loss)	(58.1)		(386.8)		(190.7)		(340.1)
Total pre-tax income (loss) from continuing operations	(31.0)		(360.6)		(278.4)		(304.6)
Income tax (expense) benefit	7.4		(28.6)		26.1		(52.2)
Net income (loss) from continuing operations	(23.6)		(389.2)		(252.3)		(356.8)
Net income (loss) from discontinued operations, net of tax -    NSM Group	6.3		5.3		16.4		(23.8)
Net gain (loss) from sale of discontinued operations, net of    tax - NSM Group	886.8		—		886.8		—
Net gain (loss) from sale of discontinued operations, net of    tax - Sirius Group	—		—		—		18.7
Net income (loss)	869.5		(383.9)		650.9		(361.9)
Net (income) loss attributable to non-controlling interests	18.7		12.5		101.5		53.7
Net income (loss) attributable to White Mountains’s    common shareholders	888.2		(371.4)		752.4		(308.2)
Other comprehensive income (loss), net of tax	(1.4)		—		(3.0)		(.3)
Other comprehensive income (loss) from discontinued    operations, net of tax - NSM Group	.7		(2.2)		(5.2)		.9
Recognition of foreign currency translation from sale of    NSM Group, net of tax	2.9		—		2.9		—
Comprehensive income (loss)	890.4		(373.6)		747.1		(307.6)
Other comprehensive (income) loss attributable to    non-controlling interests	(.3)		.2		.4		—
Comprehensive income (loss) attributable to White    Mountains’s common shareholders	$	890.1	$	(373.4)	$	747.5	$	(307.6)

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I. Summary of Operations By Segment

As of September 30, 2022, White Mountains conducted its operations through four segments: (1) HG Global/BAM, (2) Ark, (3) Kudu and (4) Other Operations. A discussion of White Mountains’s consolidated investment operations is included after the discussion of operations by segment. White Mountains’s segment information is presented in Note 15 — “Segment Information” to the Consolidated Financial Statements.

As a result of the NSM Transaction, the results of operations for NSM Group have been classified as discontinued operations and are presented separately, net of related income taxes, in the statement of comprehensive income through the closing of the transaction. Prior year amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

HG Global/BAM

HG Global/BAM consists of the consolidated results of HG Global, HG Re and BAM. BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through HG Re, to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM.

The following tables present the components of pre-tax income (loss) included in White Mountains’s HG Global/BAM segment related to the consolidation of HG Global, which includes HG Re and its other wholly-owned subsidiaries, and BAM for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30, 2022
Millions	HG Global		BAM		Eliminations		Total
Direct written premiums	$	—	$	18.4	$	—	$	18.4
Assumed written premiums	16.8		1.3		(16.8)		1.3
Gross written premiums	16.8		19.7		(16.8)		19.7
Ceded written premiums	—		(16.8)		16.8		—
Net written premiums	$	16.8	$	2.9	$	—	$	19.7
Earned insurance premiums	$	5.9	$	1.2	$	—	$	7.1
Net investment income	2.8		2.9		—		5.7
Net investment income - BAM Surplus Notes	2.9		—		(2.9)		—
Net realized and unrealized investment gains (losses)	(19.6)		(19.2)		—		(38.8)
Other revenues	.1		1.2		—		1.3
Total revenues	(7.9)		(13.9)		(2.9)		(24.7)
Insurance acquisition expenses	1.6		.1		—		1.7
General and administrative expenses	.6		15.2		—		15.8
Interest expense - HG Global Senior Notes	2.0		—		—		2.0
Interest expense - BAM Surplus Notes	—		2.9		(2.9)		—
Total expenses	4.2		18.2		(2.9)		19.5
Pre-tax income (loss)	$	(12.1)	$	(32.1)	$	—	$	(44.2)
Supplemental information:
MSC collected (1)	$	—	$	26.0	$	—	$	26.0

(1) MSC collected are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.

52

	Three Months Ended September 30, 2021
Millions	HG Global		BAM		Eliminations		Total
Direct written premiums	$	—	$	12.8	$	—	$	12.8
Assumed written premiums	10.9		—		(10.9)		—
Gross written premiums	10.9		12.8		(10.9)		12.8
Ceded written premiums	—		(10.9)		10.9		—
Net written premiums	$	10.9	$	1.9	$	—	$	12.8
Earned insurance premiums	$	5.5	$	1.2	$	—	$	6.7
Net investment income	1.9		2.5		—		4.4
Net investment income - BAM Surplus Notes	3.1		—		(3.1)		—
Net realized and unrealized investment gains	(2.0)		(2.0)		—		(4.0)
Other revenues	.1		.2		—		.3
Total revenues	8.6		1.9		(3.1)		7.4
Insurance acquisition expenses	1.5		1.5		—		3.0
General and administrative expenses	.2		12.2		—		12.4
Interest expense - BAM Surplus Notes	—		3.1		(3.1)		—
Total expenses	1.7		16.8		(3.1)		15.4
Pre-tax income (loss)	$	6.9	$	(14.9)	$	—	$	(8.0)
Supplemental information:
MSC collected (1)	$	—	$	14.7	$	—	$	14.7

(1) MSC collected are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.

	Nine Months Ended September 30, 2022
Millions	HG Global		BAM		Eliminations		Total
Direct written premiums	$	—	$	44.9	$	—	$	44.9
Assumed written premiums	39.6		1.3		(39.6)		1.3
Gross written premiums	39.6		46.2		(39.6)		46.2
Ceded written premiums	—		(39.6)		39.6		—
Net written premiums	$	39.6	$	6.6	$	—	$	46.2
Earned insurance premiums	$	21.5	$	4.5	$	—	$	26.0
Net investment income	7.1		8.0		—		15.1
Net investment income - BAM Surplus Notes	8.8		—		(8.8)		—
Net realized and unrealized investment gains (losses)	(57.8)		(56.2)		—		(114.0)
Other revenues	.3		3.4		—		3.7
Total revenues	(20.1)		(40.3)		(8.8)		(69.2)
Insurance acquisition expenses	7.6		1.9		—		9.5
General and administrative expenses	2.1		47.4		—		49.5
Interest expense - HG Global Senior Notes	5.4		—		—		5.4
Interest expense - BAM Surplus Notes	—		8.8		(8.8)		—
Total expenses	15.1		58.1		(8.8)		64.4
Pre-tax income (loss)	$	(35.2)	$	(98.4)	$	—	$	(133.6)
Supplemental information:
MSC collected (1)	$	—	$	62.3	$	—	$	62.3

(1) MSC collected are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.

53

	Nine Months Ended September 30, 2021
Millions	HG Global		BAM		Eliminations		Total
Direct written premiums	$	—	$	34.5	$	—	$	34.5
Assumed written premiums	33.4		4.5		(33.4)		4.5
Gross written premiums	33.4		39.0		(33.4)		39.0
Ceded written premiums	—		(33.4)		33.4		—
Net written premiums	$	33.4	$	5.6	$	—	$	39.0
Earned insurance premiums	$	16.1	$	3.5	$	—	$	19.6
Net investment income	5.4		7.8		—		13.2
Net investment income - BAM Surplus Notes	9.1		—		(9.1)		—
Net realized and unrealized investment losses	(9.5)		(6.1)		—		(15.6)
Other revenues	.3		.6		—		.9
Total revenues	21.4		5.8		(9.1)		18.1
Insurance acquisition expenses	4.3		2.2		—		6.5
General and administrative expenses	1.3		41.4		—		42.7
Interest expense - BAM Surplus Notes	—		9.1		(9.1)		—
Total expenses	5.6		52.7		(9.1)		49.2
Pre-tax income (loss)	$	15.8	$	(46.9)	$	—	$	(31.1)
Supplemental information:
MSC collected (1)	$	—	44.8		$	—	$	44.8

(1) MSC are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.

HG Global/BAM Results—Three Months Ended September 30, 2022 versus Three Months Ended September 30, 2021

BAM is required to prepare its financial statements on a statutory accounting basis for the NYDFS and does not report stand-alone GAAP financial results. BAM charges an insurance premium on each municipal bond insurance policy it writes. A portion of the premium is MSC and the remainder is a risk premium. In the event of a municipal bond refunding, a portion of the MSC from original issuance can be reutilized, in effect serving as a credit against the total insurance premium on the refunding of the municipal bond.

Gross written premiums and MSC collected in the HG Global/BAM segment totaled $46 million in the third quarter of 2022 compared to $28 million in the third quarter of 2021. BAM insured $4.1 billion of municipal bonds, $3.3 billion of which were in the primary market, in the third quarter of 2022 compared to $4.0 billion of municipal bonds, $3.8 billion of which were in the primary market, in the third quarter of 2021. In the third quarter of 2022, BAM completed an assumed reinsurance transaction to reinsure municipal bonds with a par value of $43 million.

Insured penetration in the primary market decreased to 6.2% in the third quarter of 2022 compared to 8.6% in the third quarter of 2021, primarily as a result of a decrease in large transactions insured in the third quarter of 2022 compared to the third quarter of 2021.

Total pricing, which reflects both gross written premiums and MSC, increased to 110 basis points in the third quarter of 2022 compared to 69 basis points in the third quarter of 2021. The increase in total pricing was driven primarily by increased secondary market activity, higher pricing in the primary market and an assumed reinsurance transaction in the third quarter of 2022. Pricing in the primary market increased to 79 basis points in the third quarter of 2022 compared to 59 basis points in the third quarter of 2021. Pricing in the combined secondary and assumed reinsurance markets, which is more transaction specific than pricing in the primary market, decreased to 229 basis points in the third quarter of 2022 compared to 309 basis points in the third quarter of 2021.

54

The following table presents the gross par value of primary and secondary market policies issued, the gross par value of assumed reinsurance, the gross written premiums and MSC collected and total pricing for the three months ended September 30, 2022 and 2021:

	Three Months Ended September 30,
$ in Millions	2022		2021
Gross par value of primary market policies issued	$	3,269.0	$	3,813.7
Gross par value of secondary market policies issued	826.5		157.4
Gross par value of assumed reinsurance	42.5		—
Total gross par value of market policies issued	$	4,138.0	$	3,971.1
Gross written premiums	$	19.7	$	12.8
MSC collected	26.0		14.7
Total gross written premiums and MSC collected	$	45.7	$	27.5
Total pricing	110 bps		69 bps

HG Global reported pre-tax income (loss) of $(12) million in the third quarter of 2022 compared to $7 million in the third quarter of 2021. The change in pre-tax income (loss) was driven primarily by $20 million of net unrealized investment losses on the HG Global fixed income portfolio, as interest rates increased in the third quarter of 2022. Results in the third quarter of 2022 and 2021 both included $3 million of interest income on the BAM Surplus Notes.

BAM is a mutual insurance company that is owned by its members. BAM’s results are consolidated into White Mountains’s GAAP financial statements and attributed to non-controlling interests. White Mountains reported $32 million of GAAP pre-tax loss from BAM in the third quarter of 2022 compared to $15 million in the third quarter of 2021. The change in pre-tax loss was driven primarily by $19 million of net unrealized investment losses on the BAM fixed income portfolio, as interest rates increased in the third quarter of 2022. Results in the third quarter of 2022 included $3 million of interest expense on the BAM Surplus Notes and $15 million of general and administrative expenses, compared to $3 million of interest expense and $12 million of general and administrative expenses in the third quarter of 2021.

HG Global/BAM Results—Nine Months Ended September 30, 2022 versus Nine Months Ended September 30, 2021

Gross written premiums and MSC collected in the HG Global/BAM segment totaled $109 million in the first nine months of 2022 compared to $84 million in the first nine months of 2021. BAM insured $13.5 billion of municipal bonds, $10.1 billion of which were in the primary market, in the first nine months of 2022 compared to $12.6 billion of municipal bonds, $11.2 billion of which were in the primary market, in the first nine months of 2021. In the first nine months of 2022 and 2021, BAM completed assumed reinsurance transactions to reinsure municipal bonds with par values of $43 million and $806 million.

Total pricing, which reflects both gross written premiums and MSC, increased to 81 basis points in the first nine months of 2022 compared to 66 basis points in the first nine months of 2021. The increase in total pricing was driven primarily by increased secondary market activity in the first nine months of 2022 compared to the first nine months of 2021. Pricing in the primary market increased to 57 basis points in the first nine months of 2022, compared to 56 basis points in the first nine months of 2021. Pricing in the secondary and assumed reinsurance markets, which is more transaction specific than pricing in the primary market, increased to 152 basis points in the first nine months of 2022, compared to 150 basis points in the first nine months of 2021.

55

The following table presents the gross par value of primary and secondary market policies issued, the gross par value of assumed reinsurance, the gross written premiums and MSC collected and total pricing for the nine months ended September 30, 2022 and 2021:

	Nine Months Ended September 30,
$ in Millions	2022		2021
Gross par value of primary market policies issued	$	10,147.8	$	11,171.2
Gross par value of secondary market policies issued	3,269.4		646.6
Gross par value of assumed reinsurance	42.5		805.5
Total gross par value of market policies issued	$	13,459.7	$	12,623.3
Gross written premiums	46.2		39.0
MSC collected	62.3		44.8
Total gross written premiums and MSC collected	$	108.5	$	83.8
Total pricing	81 bps		66 bps

HG Global reported pre-tax income (loss) of $(35) million in the first nine months of 2022 compared to $16 million in the first nine months of 2021. The change in pre-tax income (loss) was driven primarily by $58 million of net unrealized investment losses on the HG Global fixed income portfolio, as interest rates increased in the first nine months of 2022. Results in the first nine months of 2022 and 2021 both included $9 million of interest income on the BAM Surplus Notes.

On April 29, 2022, HG Global received the proceeds of its new $150 million, 10-year term loan credit facility. In turn, on May 2, 2022, HG Global paid a $120 million cash dividend to shareholders, of which $116 million was paid to White Mountains.

White Mountains reported $98 million of GAAP pre-tax loss from BAM in the first nine months of 2022 compared to $47 million in the first nine months of 2021. The increase in pre-tax loss was driven primarily by $56 million of net unrealized investment losses on the BAM fixed income portfolio, as interest rates increased in the first nine months of 2022. Results in the first nine months of 2022 included $9 million of interest expense on the BAM Surplus Notes and $47 million of general and administrative expenses, compared to $9 million of interest expense and $41 million of general and administrative expenses in the first nine months of 2021.

Claims Paying Resources

BAM’s claims paying resources represent the capital and other financial resources BAM has available to pay claims and, as such, is a key indication of BAM’s financial strength.

BAM’s claims paying resources were $1,260 million as of September 30, 2022 compared to $1,192 million as of December 31, 2021 and $1,181 million as of September 30, 2021. The increase in claims paying resources as of September 30, 2022 compared to December 31, 2021 was driven primarily by increases in the statutory value of the collateral trusts resulting from deposits of ceded premiums and an increase in BAM’s qualified statutory capital resulting from business operations for the nine months ended September 30, 2022.

The following table presents BAM’s total claims paying resources as of September 30, 2022, December 31, 2021 and September 30, 2021:

Millions	September 30, 2022		December 31, 2021		September 30, 2021
Policyholders’ surplus	$	316.9	$	298.1	$	322.8
Contingency reserve	113.9		101.8		102.7
Qualified statutory capital	430.8		399.9		425.5
Net unearned premiums	53.3		49.5		48.3
Present value of future installment premiums and MSC	13.3		13.8		13.9
HG Re Collateral trusts at statutory value	512.7		478.9		442.8
Fidus Re Collateral trust at statutory value	250.0		250.0		250.0
Claims paying resources	$	1,260.1	$	1,192.1	$	1,180.5

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HG Global/BAM Balance Sheets

The following tables present amounts from HG Global, which includes HG Re and its other wholly-owned subsidiaries, and BAM that are contained within White Mountains’s consolidated balance sheet as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	HG Global		BAM		Eliminations and Segment Adjustment		Total
Assets
Fixed maturity investments, at fair value	$	443.6	$	430.8	$	—	$	874.4
Short-term investments, at fair value	38.0		24.3		—		62.3
Total investments	481.6		455.1		—		936.7
Cash	5.2		12.1		—		17.3
BAM Surplus Notes	364.6		—		(364.6)		—
Accrued interest receivable on BAM Surplus Notes	166.4		—		(166.4)		—
Insurance premiums receivable	4.7		6.6		(4.7)		6.6
Deferred acquisition costs	68.0		34.9		(68.0)		34.9
Other assets	6.5		16.1		(.3)		22.3
Total assets	$	1,097.0	$	524.8	$	(604.0)	$	1,017.8
Liabilities
BAM Surplus Notes(1)	$	—	$	364.6	$	(364.6)	$	—
Accrued interest payable on BAM Surplus Notes(2)	—		166.4		(166.4)		—
Preferred dividends payable to White Mountains(3)	327.2		—		—		327.2
Preferred dividends payable to non-controlling interests	12.1		—		—		12.1
Unearned insurance premiums	239.7		47.0		—		286.7
Debt - HG Global Senior Notes	146.4		—		—		146.4
Accrued incentive compensation	1.0		20.6		—		21.6
Other liabilities	4.1		86.3		(73.0)		17.4
Total liabilities	730.5		684.9		(604.0)		811.4
Equity
White Mountains’s common shareholders’ equity	366.8		—		—		366.8
Non-controlling interests	(0.3)		(160.1)		—		(160.4)
Total equity	366.5		(160.1)		—		206.4
Total liabilities and equity	$	1,097.0	$	524.8	$	(604.0)	$	1,017.8

(1)    Under GAAP, the BAM Surplus Notes are classified as debt by the issuer. Under U.S. Statutory accounting, they are classified as policyholders’ surplus.

(2)    Under GAAP, interest accrues daily on the BAM Surplus Notes. Under U.S. Statutory accounting, interest is not accrued on the BAM Surplus Notes until it has been approved for payment by insurance regulators.

(3)    HG Global preferred dividends payable to White Mountains are eliminated in White Mountains’s consolidated financial statements. For segment reporting, the HG Global preferred dividends payable to White Mountains included within the HG Global/BAM segment are eliminated against the offsetting receivable included within Other Operations, and therefore are added back to White Mountains’s common shareholders’ equity within the HG Global/BAM segment.

57

	December 31, 2021
Millions	HG Global		BAM		Eliminations and Segment Adjustment		Total Segment
Assets
Fixed maturity investments, at fair value	$	461.7	$	472.4	$	—	$	934.1
Short-term investments, at fair value	17.8		14.6		—		32.4
Total investments	479.5		487.0		—		966.5
Cash	13.4		6.4		—		19.8
BAM Surplus Notes	364.6		—		(364.6)		—
Accrued interest receivable on BAM Surplus Notes	157.6		—		(157.6)		—
Insurance premiums receivable	4.3		6.9		(4.3)		6.9
Deferred acquisition costs	62.7		33.1		(62.7)		33.1
Other assets	2.1		16.6		(.2)		18.5
Total assets	$	1,084.2	$	550.0	$	(589.4)	$	1,044.8
Liabilities
BAM Surplus Notes(1)	$	—	$	364.6	$	(364.6)	$	—
Accrued interest payable on BAM Surplus Notes(2)	—		157.6		(157.6)		—
Preferred dividends payable to White Mountains(3)	400.5		—		—		400.5
Preferred dividends payable to non-controlling interests	14.2		—		—		14.2
Unearned insurance premiums	221.5		44.8		—		266.3
Accrued incentive compensation	1.1		23.6		—		24.7
Other liabilities	.5		83.4		(67.2)		16.7
Total liabilities	637.8		674.0		(589.4)		722.4
Equity
White Mountains’s common shareholders’ equity	437.5		—		—		437.5
Non-controlling interests	8.9		(124.0)		—		(115.1)
Total equity	446.4		(124.0)		—		322.4
Total liabilities and equity	$	1,084.2	$	550.0	$	(589.4)	$	1,044.8

(1)    Under GAAP, the BAM Surplus Notes are classified as debt by the issuer. Under U.S. Statutory accounting, they are classified as policyholders’ surplus.

(2)    Under GAAP, interest accrues daily on the BAM Surplus Notes. Under U.S. Statutory accounting, interest is not accrued on the BAM Surplus Notes until it has been approved for payment by insurance regulators.

(3)    HG Global preferred dividends payable to White Mountains are eliminated in White Mountains’s consolidated financial statements. For segment reporting, the HG Global preferred dividends payable to White Mountains included within the HG Global/BAM segment are eliminated against the offsetting receivable included within Other Operations, and therefore are added back to White Mountains’s common shareholders’ equity within the HG Global/BAM segment.

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Ark

Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. Ark underwrites select coverages through its two major subsidiaries in the United Kingdom and Bermuda.

The following table presents the components of pre-tax income (loss) included in White Mountains’s Ark segment for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Earned insurance premiums	$	346.1	$	213.4	$	757.8	$	435.8
Net investment income	4.9		.6		9.7		1.8
Net realized and unrealized investment gains (losses)	(14.4)		.3		(76.5)		10.3
Other revenues	6.6		3.4		10.1		9.4
Total revenues	343.2		217.7		701.1		457.3
Losses and LAE	213.7		129.2		456.2		247.8
Insurance and reinsurance acquisition expenses	74.8		53.7		174.9		124.4
General and administrative expenses - other underwriting	13.2		13.3		53.9		43.6
General and administrative expenses - all other	13.7		8.5		25.9		40.8
Interest expense	3.7		2.1		10.6		4.5
Total expenses	319.1		206.8		721.5		461.1
Pre-tax income (loss)	$	24.1	$	10.9	$	(20.4)	$	(3.8)

For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by TPC Providers using whole account reinsurance contracts with Ark’s corporate member. The TPC Providers’ participation in the Syndicates for the 2020 open year of account is 43% of the total net result of the Syndicates. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within Ark’s results of operations are shown net of amounts relating to the TPC Providers’ share of the Syndicates’ results, including investment results.

Ark Results—Three Months Ended September 30, 2022 versus Three Months Ended September 30, 2021

Ark reported gross written premiums of $216 million, net written premiums of $193 million and net earned premiums of $346 million in the third quarter of 2022 compared to gross written premiums of $162 million, net written premiums of $121 million and net earned premiums of $213 million in the third quarter of 2021. Premium growth at Ark has been supported by favorable market conditions across most classes with general inflationary concerns, capacity withdrawal in catastrophe lines, and the ongoing conflict in Ukraine driving positive rate momentum.

Ark reported pre-tax income of $24 million in the third quarter of 2022 compared to $11 million in the third quarter of 2021. Ark’s pre-tax income for the third quarter of 2022 included $14 million of net realized and unrealized investment losses, driven primarily by unrealized losses on fixed income securities and the impact of foreign currency on its investment portfolio, compared to $0.3 million of net realized and unrealized investment gains in the third quarter of 2021.

Ark’s GAAP combined ratio was 87% in the third quarter of 2022 compared to 92% in the third quarter of 2021. The GAAP combined ratio for the third quarter of 2022 included 21 points of natural catastrophe losses, driven primarily by Hurricane Ian, compared to 23 points of natural catastrophe losses in the third quarter of 2021, driven primarily by Hurricane Ida and European floods. Catastrophe losses for the third quarter of 2022 included $51 million related to Hurricane Ian on a net basis after reinstatement premiums. The GAAP combined ratio for the third quarter of 2022 included three points of favorable prior year development, driven primarily by the property and accident & health and specialty reserving lines of business, predominantly from business underwritten in London. This compared to six points of favorable prior year development in the third quarter of 2021, driven primarily by the property and accident & health reserving line of business.

Ark’s adjusted combined ratio, which adds back amounts attributable to TPC Providers, was 86% in the third quarter of 2022 compared to 89% in the third quarter of 2021. The adjusted combined ratio for the third quarter of 2022 and 2021 both included 21 points of natural catastrophe losses. The adjusted combined ratio for the third quarter of 2022 included four points of favorable prior year development compared to six points of favorable prior year development in the third quarter of 2021. The underlying drivers of year-over-year changes were the same as those impacting the GAAP combined ratio.

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The following table presents Ark’s loss and LAE, insurance acquisition expense, other underwriting expense and combined ratios on both a GAAP-basis and an adjusted basis, which adds back amounts attributable to TPC Providers, for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30, 2022
$ in Millions	GAAP			TPC Providers’ Share		Adjusted (1)
Insurance premiums:
Gross written premiums	$	215.5		$	—	$	215.5
Net written premiums	$	192.6		$	2.1	$	194.7
Net earned premiums	$	346.1		$	3.3	$	349.4
Insurance expenses:
Loss and loss adjustment expenses	$	213.7		$	(1.5)	$	212.2
Insurance and reinsurance acquisition expenses	74.8			—		74.8
Other underwriting expenses	13.2			.9		14.1
Total insurance expenses	$	301.7		$	(.6)	$	301.1
Ratios:
Loss and loss adjustment expense	61.7		%			60.7		%
Insurance and reinsurance acquisition expense	21.6					21.4
Other underwriting expense	3.8					4.0
Combined Ratio	87.1		%			86.1		%

(1) See “NON-GAAP FINANCIAL MEASURES” on page 74.

	Three Months Ended September 30, 2021
$ in Millions	GAAP			TPC Providers’ Share		Adjusted (1)
Insurance premiums:
Gross written premiums	$	162.4		$	—	$	162.4
Net written premiums	$	120.9		$	2.0	$	122.9
Net earned premiums	$	213.4		$	18.2	$	231.6
Insurance expenses:
Loss and loss adjustment expenses	$	129.2		$	9.0	$	138.2
Insurance and reinsurance acquisition expenses	53.7			—		53.7
Other underwriting expenses	13.3			.4		13.7
Total insurance expenses	$	196.2		$	9.4	$	205.6
Ratios:
Loss and loss adjustment expense	60.5		%			59.7		%
Insurance and reinsurance acquisition expense	25.2					23.2
Other underwriting expense	6.2					5.9
Combined Ratio	91.9		%			88.8		%

(1) See “NON-GAAP FINANCIAL MEASURES” on page 74.

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Gross Written Premiums

Gross written premiums increased 33% to $216 million in the third quarter of 2022 compared to the third quarter of 2021, with risk adjusted rate change up approximately 6% year over year. The increase in gross written premiums was driven primarily by the property line of business for both insurance and reinsurance across London and Bermuda resulting from favorable market conditions, as well as increased writings in specialty lines, predominantly in cyber. The following table presents Ark’s gross written premiums by line of business for the three months ended September 30, 2022 and 2021:

	Three Months Ended September 30,
Millions	2022		2021
Property	$	102.6	$	74.7
Specialty	43.5		32.0
Marine & Energy	36.0		29.5
Casualty	21.4		17.3
Accident & Health	12.0		8.9
Total Gross Written Premium	$	215.5	$	162.4

Ark Results— Nine Months Ended September 30, 2022 versus Nine Months Ended September 30, 2021

Ark reported gross written premiums of $1,253 million, net written premiums of $1,007 million and net earned premiums of $758 million in the first nine months of 2022 compared to gross written premiums of $895 million, net written premiums of $726 million and net earned premiums of $436 million in the first nine months of 2021. Premium growth at Ark has been supported by favorable market conditions across most classes with inflationary concerns, capacity withdrawal in catastrophe lines, and the ongoing conflict in Ukraine driving positive rate momentum.

Ark reported pre-tax loss of $20 million in the first nine months of 2022 compared to $4 million in the first nine months of 2021. Ark’s pre-tax loss for the first nine months of 2022 included $77 million of net realized and unrealized investment losses, driven primarily by unrealized losses on fixed income securities and the impact of foreign currency on its investment portfolio, compared to $10 million of net realized and unrealized investment gains in the third quarter of 2021. Ark’s pre-tax loss for the first nine months of 2021 also reflected $25 million of transaction expenses related to the Ark Transaction.

Ark’s GAAP combined ratio was 90% in the first nine months of 2022 compared to 95% in the first nine months of 2021. The GAAP combined ratio for the first nine months of 2022 included 13 points of natural catastrophe losses, driven primarily by Hurricane Ian. This compared to 16 points of natural catastrophe losses in the first nine months of 2021, driven primarily by Hurricane Ida, Winter Storm Uri and European floods. Catastrophe losses for the first nine months of 2022 included $51 million related to Hurricane Ian on a net basis after reinstatement premiums. The GAAP combined ratio for the first nine months of 2022 also included four points related to the ongoing conflict in Ukraine within the specialty and marine & energy lines of business. The GAAP combined ratio for the first nine months of 2022 included five points of favorable prior year development, driven primarily by the property and accident & health and specialty reserving lines of business, predominantly from business underwritten in London. This compared to five points of prior year favorable development in the first nine months to 2021, driven primarily by the property and accident & health reserving line of business.

Ark’s adjusted combined ratio, which adds back amounts attributable to TPC Providers, was 90% in the first nine months of 2022 compared to 93% in the first nine months of 2021. The adjusted combined ratio for the first nine months of 2022 included 13 points of natural catastrophe losses compared to 16 points of natural catastrophe losses in the first nine months of 2021. The adjusted combined ratio for the first nine months of 2022 also included four points related to the ongoing conflict in Ukraine. The adjusted combined ratio for the first nine months of 2022 and 2021 both included five points of favorable prior year development. The underlying drivers of year-over-year changes were the same as those impacting the GAAP combined ratio.

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The following table presents Ark’s loss and loss adjustment expense, insurance acquisition expense, other underwriting expense and combined ratios on both a GAAP-basis and an adjusted basis, which adds back amounts ceded to TPC Providers, for the nine months ended September 30, 2022 and 2021:

	Nine Months Ended September 30, 2022
$ in Millions	GAAP			TPC Providers’ Share		Adjusted (1)
Insurance premiums:
Gross written premiums	$	1,252.5		$	—	$	1,252.5
Net written premiums	$	1,006.5		$	3.4	$	1,009.9
Net earned premiums	$	757.8		$	9.2	$	767.0
Insurance expenses:
Loss and loss adjustment expenses	$	456.2		$	1.9	$	458.1
Insurance and reinsurance acquisition expenses	174.9			—		174.9
Other underwriting expenses	53.9			2.7		56.6
Total insurance expenses	$	685.0		$	4.6	$	689.6
Ratios:
Loss and loss adjustment expense	60.2		%			59.7		%
Insurance and reinsurance acquisition expense	23.1					22.8
Other underwriting expense	7.1					7.4
Combined Ratio	90.4		%			89.9		%

(1) See “NON-GAAP FINANCIAL MEASURES” on page 74.

	Nine Months Ended September 30, 2021
$ in Millions	GAAP			TPC Providers’ Share		Adjusted (1)
Insurance premiums:
Gross written premiums	$	895.0		$	—	$	895.0
Net written premiums	$	725.5		$	(5.9)	$	719.6
Net earned premiums	$	435.8		$	65.0	$	500.8
Insurance expenses:
Loss and loss adjustment expenses	$	247.8		$	47.2	$	295.0
Insurance and reinsurance acquisition expenses	124.4			—		124.4
Other underwriting expenses	43.6			1.6		45.2
Total insurance expenses	$	415.8		$	48.8	$	464.6
Ratios:
Loss and loss adjustment expense	56.9		%			58.9		%
Insurance and reinsurance acquisition expense	28.5					24.8
Other underwriting expense	10.0					9.0
Combined Ratio	95.4		%			92.7		%

(1) See “NON-GAAP FINANCIAL MEASURES” on page 74.

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Gross Written Premiums

Gross written premiums increased 40% to $1,253 million in the first nine months of 2022, compared to the first nine months of 2021, with risk adjusted rate change up approximately 9%. Ark’s premium growth has impacted almost all lines of business supported by the build out of the Bermuda platform launched in 2021 and favorable market conditions, notably within the property and specialty lines of business. The following table presents Ark’s gross written premiums by line of business for the first nine months ended September 30, 2022 and 2021:

	For the Nine Months Ended
Millions	September 30, 2022		September 30, 2021
Property	$	521.7	$	355.0
Specialty	327.2		210.5
Marine & Energy	271.2		219.7
Casualty	72.2		48.1
Accident & Health	60.2		61.7
Total Gross Written Premium	$	1,252.5	$	895.0

Catastrophe Risk Management

Ark has exposure to losses caused by unpredictable catastrophic events including natural and other disasters such as hurricanes, windstorms, earthquakes, floods, wildfires, tornadoes, tsunamis, and severe winter weather all over the world. Catastrophes can also include large losses driven by public health crises, terrorist attacks, explosions, infrastructure failures, cyber-attacks and armed conflicts. The extent of a catastrophe loss is a function of both the severity of the event and total amount of insured exposure to the event, as well as the coverage provided to customers.

Ark seeks to manage its exposure to catastrophic losses by limiting and monitoring the aggregate insured value of policies in geographic areas with exposure to catastrophic events and by buying reinsurance. To manage, monitor and analyze insured values and potential losses, Ark utilizes proprietary and third-party catastrophe management software to estimate potential losses for many different catastrophe scenarios.

With peak U.S. windstorm season substantially over, Ark’s near-term largest probable maximum loss natural catastrophe scenario on a per occurrence basis at a 1-in-250-year return period is U.S. earthquake. The October 2022 net after-tax estimated impact of a 1-in-250-year return period U.S. earthquake loss represents roughly 25% of Ark’s total tangible capital (shareholders equity and subordinated debt). This net impact is after income taxes, reinstatement premiums, amounts ceded to third-party reinsurers and amounts attributable to TPC Providers.

In addition, Ark also has loss exposures to other global events including, but not limited to, Japanese earthquakes, Japanese windstorms, European windstorms, Southeast U.S. windstorms and U.S. wildfires. Outside of natural catastrophe losses, Ark has exposure to non-natural or man-made large losses. The current largest exposures are cyber, offshore energy production platforms, terrorism events and political risk.

Kudu

Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance, and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time.

As of September 30, 2022, Kudu had deployed a total of $711 million in 20 asset and wealth management firms globally, including one that was exited. As of September 30, 2022, the asset and wealth management firms had combined assets under management of approximately $67 billion, spanning a range of asset classes, including real estate, wealth management, hedge funds, private equity and alternative credit strategies.

As a result of the Kudu Transaction, White Mountains’s basic ownership of Kudu decreased from 99.1% to 89.3%. See Note 2 — “Significant Transactions.”

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The following table presents the components of GAAP net income, EBITDA and adjusted EBITDA included in White Mountains’s Kudu segment for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Net investment income	$	14.8	$	9.5	$	41.2	$	26.1
Net realized and unrealized investment gains (losses)	41.1		18.9		45.8		62.5
Other revenues	—		.1		—		.2
Total revenues	55.9		28.5		87.0		88.8
General and administrative expenses	4.5		3.3		10.2		9.0
Amortization of other intangible assets	—		—		.2		.2
Interest expense	4.2		1.9		10.3		9.2
Total expenses	8.7		5.2		20.7		18.4
GAAP pre-tax income (loss)	47.2		23.3		66.3		70.4
Income tax (expense) benefit	(16.6)		(7.9)		(21.1)		(25.4)
GAAP net income (loss)	30.6		15.4		45.2		45.0
Add back:
Interest expense	4.2		1.9		10.3		9.2
Income tax expense (benefit)	16.6		7.9		21.1		25.4
General and administrative expenses - depreciation	—		—		—		—
Amortization of other intangible assets	—		—		.2		.2
EBITDA (1)	51.4		25.2		76.8		79.8
Exclude:
Net realized and unrealized investment (gains) losses	(41.1)		(18.9)		(45.8)		(62.5)
Non-cash equity-based compensation expense	—		.2		.1		.4
Transaction expenses	1.2		.9		1.4		.9
Adjusted EBITDA (1)	$	11.5	$	7.4	$	32.5	$	18.6

(1) See “NON-GAAP FINANCIAL MEASURES” on page 74.

Kudu Results—Three Months Ended September 30, 2022 versus Three Months Ended September 30, 2021

Kudu reported total revenues of $56 million, pre-tax income of $47 million and adjusted EBITDA of $12 million in the third quarter of 2022 compared to total revenues of $29 million, pre-tax income of $23 million and adjusted EBITDA of $7 million in the third quarter of 2021. Total revenues and pre-tax income in the third quarter of 2022 included $41 million of net realized and unrealized gains on Kudu’s Participation Contracts compared to $19 million in the third quarter of 2021. Net realized and unrealized gains on Kudu’s Participation Contracts in the third quarter of 2022 were driven primarily by $59 million of increases in the fair value of two Participation Contracts resulting from pending sale transactions, partially offset by declines in assets under management at several managers with public equity exposure and unrealized foreign currency losses. However, Kudu’s Participation Contracts performed well relative to market benchmarks in a volatile quarter. Total revenues, pre-tax income and adjusted EBITDA in the third quarter of 2022 also included $15 million of net investment income compared to $10 million in the third quarter of 2021. The increase in net investment income was driven primarily by amounts earned from the $182 million in new deployments, including $2 million of transaction costs, that Kudu made subsequent to September 30, 2021.

Kudu Results—Nine Months Ended September 30, 2022 versus Nine Months Ended September 30, 2021

Kudu reported total revenues of $87 million, pre-tax income of $66 million and adjusted EBITDA of $33 million in the first nine months of 2022 compared to total revenues of $89 million, pre-tax income of $70 million and adjusted EBITDA of $19 million in the first nine months of 2021. Total revenues and pre-tax income in the first nine months of 2022 included $46 million of net realized and unrealized gains on Kudu’s Participation Contracts compared to $63 million in the first nine months of 2021. Net realized and unrealized gains on Kudu’s Participation Contracts in the first nine months of 2022 were driven primarily by $92 million of increases in the fair value of two Participation Contracts resulting from pending sale transactions, partially offset by declines in assets under management at several managers with public equity exposure and unrealized foreign currency losses. Total revenues, pre-tax income and adjusted EBITDA in the first nine months of 2022 also included $41 million of net investment income compared to $26 million in the first nine months of 2021. The increase in net investment income was driven primarily by amounts earned from $324 million in new deployments, including $3 million of transaction costs, that Kudu made in 2022 and 2021.

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Other Operations

The following table presents the components of pre-tax income (loss) included in White Mountains’s Other Operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Net investment income	$	8.5	$	5.0	$	13.6	$	16.1
Net realized and unrealized investment gains (losses)	(17.3)		15.3		2.8		34.0
Net realized and unrealized investment gains (losses) from    investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(325.5)
Commission revenues	3.2		2.4		8.7		7.0
Other revenues	33.0		28.1		89.6		57.6
Total revenues	8.8		(346.0)		1.4		(210.8)
Cost of sales	25.0		24.0		68.8		45.9
General and administrative expenses	39.9		14.4		118.9		79.4
Amortization of other intangible assets	1.4		2.0		3.2		2.9
Interest expense	.6		.4		1.2		1.1
Total expenses	66.9		40.8		192.1		129.3
Pre-tax income (loss)	$	(58.1)	$	(386.8)	$	(190.7)	$	(340.1)

Other Operations Results—Three Months Ended September 30, 2022 versus Three Months Ended September 30, 2021

White Mountains’s Other Operations reported pre-tax loss of $58 million in the third quarter of 2022 compared to $387 million in the third quarter of 2021. White Mountains’s Other Operations reported net unrealized investment losses from its investment in MediaAlpha of $19 million in the third quarter of 2022 compared to $397 million in the third quarter of 2021. Excluding MediaAlpha, White Mountains’s Other Operations reported net realized and unrealized investment gains (losses) of $(17) million in the third quarter of 2022 compared to $15 million in the third quarter of 2021, driven primarily by losses in the fixed income portfolio due to rising interest rates in the third quarter of 2022 and gains on other long-term investments in the third quarter of 2021. White Mountains’s Other Operations reported net investment income of $9 million in the third quarter of 2022 compared to $5 million in the third quarter of 2021, driven primarily by higher yields and an increase in the asset base of short-term investments and fixed maturity investments within Other Operations in the third quarter of 2022 compared to the third quarter of 2021. See Summary of Investment Results on page 66.

White Mountains’s Other Operations reported $33 million of other revenues in the third quarter of 2022 compared to $28 million in the third quarter of 2021. White Mountains’s Other Operations reported $25 million of cost of sales in the third quarter of 2022 compared to $24 million in the third quarter of 2021. The increase in other revenues was driven primarily by recent acquisitions within Other Operations.

White Mountains’s Other Operations reported general and administrative expenses of $40 million in the third quarter of 2022 compared to $14 million in the third quarter of 2021. The increase in general and administrative expenses in the third quarter of 2022 compared to the third quarter of 2021 was driven by higher incentive compensation costs, primarily in connection with the NSM Transaction and a higher share price.

Other Operations Results—Nine Months Ended September 30, 2022 versus Nine Months Ended September 30, 2021

White Mountains’s Other Operations reported pre-tax loss of $191 million in the first nine months of 2022 compared to $340 million in the first nine months of 2021. White Mountains’s Other Operations reported net realized and unrealized investment losses from its investment in MediaAlpha of $113 million in the first nine months of 2022 compared to $326 million in the first nine months of 2021. Excluding MediaAlpha, White Mountains’s Other Operations reported net realized and unrealized investment gains of $3 million in the first nine months of 2022 compared to $34 million in the first nine months of 2021. White Mountains’s Other Operations reported net investment income of $14 million in the first nine months of 2022 compared to $16 million in the first nine months of 2021, driven primarily by lower distributions from private equity funds in the first nine months of 2022 compared to the first nine months of 2021. See Summary of Investment Results on page 66.

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White Mountains’s Other Operations reported $90 million of other revenues in the first nine months of 2022 compared to $58 million in the first nine months of 2021. White Mountains’s Other Operations reported $69 million of cost of sales in the first nine months of 2022 compared to $46 million in the first nine months of 2021. The increases in other revenues and cost of sales were driven primarily by recent acquisitions within Other Operations.

White Mountains’s Other Operations reported general and administrative expenses of $119 million in the first nine months of 2022 compared to $79 million in the first nine months of 2021. The increase in general and administrative expenses in the first nine months of 2022 compared to the first nine months of 2021 was driven by higher incentive compensation costs, primarily in connection with the NSM Transaction and a higher share price.

II. Summary of Investment Results

White Mountains’s total investment results include results from all segments. For purposes of discussing rates of return, all percentages are presented gross of management fees and trading expenses and are calculated before any adjustments for TPC Providers in order to produce a better comparison to benchmark returns.

Gross Investment Returns and Benchmark Returns

The following table presents the pre-tax investment returns for White Mountains’s consolidated portfolio for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Fixed income investments	(0.8)	%	—	%	(6.3)	%	(0.1)	%
Bloomberg Barclays U.S. Intermediate Aggregate Index	(3.8)	%	—	%	(11.0)	%	(0.8)	%
Common equity securities	1.8	%	1.2	%	(2.0)	%	7.0	%
Investment in MediaAlpha	(11.2)	%	(55.6)	%	(43.3)	%	(51.8)	%
Other long-term investments	3.0	%	4.0	%	7.7	%	14.5	%
Total common equity securities, investment in MediaAlpha and other long-term investments	1.6	%	(17.2)	%	(0.7)	%	(8.2)	%
Total common equity securities and other long-term investments	2.8	%	3.7	%	6.0	%	13.5	%
S&P 500 Index (total return)	(4.9)	%	0.6	%	(23.9)	%	15.9	%
Total consolidated portfolio	0.4	%	(8.0)	%	(3.6)	%	(3.7)	%
Total consolidated portfolio - excluding MediaAlpha	0.5	%	1.4	%	(1.4)	%	4.6	%

Investment Returns—Three and Nine Months Ended September 30, 2022 versus Three and Nine Months Ended September 30, 2021

White Mountains’s pre-tax total consolidated portfolio return on invested assets was 0.4% in the third quarter of 2022. This return included $19 million of unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 0.5% in the third quarter of 2022. Excluding MediaAlpha, investment returns in the third quarter of 2022 were driven primarily by favorable other long-term investment results, which more than offset net unrealized investment losses in the fixed income portfolio due to rising interest rates. White Mountains’s pre-tax total consolidated portfolio return on invested assets was -8.0% in the third quarter of 2021. This return included $397 million of unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 1.4% in the third quarter of 2021. Excluding MediaAlpha, investment returns in the third quarter of 2021 were driven primarily by favorable other long-term investments results.

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White Mountains’s pre-tax total consolidated portfolio return on invested assets was -3.6% in the first nine months of 2022. This return included $113 million of net unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was -1.4% in first nine months of 2022. Excluding MediaAlpha, investment returns in the first nine months of 2022 were driven primarily by net unrealized investment losses in the fixed income portfolio due to rising interest rates, partially offset by favorable other long-term investment results. White Mountains’s pre-tax total consolidated portfolio return on invested assets was -3.7% in the first nine months of 2021. This return included $326 million of net realized and unrealized investment losses from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total consolidated portfolio return on invested assets was 4.6% in the first nine months of 2021. Excluding MediaAlpha, investment returns in the first nine months of 2021 were driven primarily by favorable other long-term investment results.

Fixed Income Results

White Mountains’s fixed income portfolio, including short-term investments, was $3.1 billion and $2.4 billion as of September 30, 2022 and December 31, 2021, which represented 59% and 56% of total invested assets. The increase was driven primarily by the receipt of cash proceeds from the NSM Transaction, partially offset by cash outflows relating to White Mountains’s self-tender offer in the third quarter of 2022. The duration of White Mountains’s fixed income portfolio, including short-term investments, was 2.2 years and 2.6 years as of September 30, 2022 and December 31, 2021. White Mountains’s fixed income portfolio includes fixed maturity investments and short-term investments in the HG Re Collateral Trusts of $455 million and $480 million as of September 30, 2022 and December 31, 2021.

White Mountains’s fixed income portfolio return was -0.8% in the third quarter of 2022 compared to a flat return in the third quarter of 2021, outperforming and in line with the Bloomberg Barclays U.S. Intermediate Aggregate Index returns of -3.8% and 0.0% for the comparable periods. White Mountains’s fixed income portfolio returned -6.3% in the first nine months of 2022, compared to -0.1% in the first nine months of 2021, outperforming the Bloomberg Barclays U.S. Intermediate Aggregate Index returns of -11.0% and -0.8% for the comparable periods.

The results in the third quarter and first nine months of 2022 were driven primarily by the impact of White Mountains’s short duration positioning as interest rates increased in both periods. The results in the third quarter and first nine months of 2021 were driven primarily by the short duration positioning of White Mountains’s fixed income portfolio as interest rates increased in both periods.

Common Equity Securities, Investment in MediaAlpha and Other Long-Term Investments Results

White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments was $2.1 billion and $1.9 billion as of September 30, 2022 and December 31, 2021, which represented 41% and 44% of total invested assets. See Note 3 — “Investment Securities.”

White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned 1.6% in the third quarter of 2022, which included $19 million of unrealized investment losses from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 2.8% in the third quarter of 2022. White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned -17.2% in the third quarter of 2021, which included $397 million of unrealized investment losses from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 3.7% in the third quarter of 2021.

White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned -0.7% in the first nine months of 2022, which included $113 million of net unrealized investment losses from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 6.0% in the first nine months of 2022. White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned -8.2% in the first nine months of 2021, which included $326 million of net realized and unrealized investment losses from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 13.5% in the first nine months of 2021.

White Mountains’s portfolio of common equity securities consists of passive ETFs that seek to provide investment results that generally correspond to the performance of the S&P 500 Index and international listed equity funds. White Mountains’s portfolio of common equity securities was $333 million and $251 million as of September 30, 2022 and December 31, 2021.

White Mountains’s portfolio of common equity securities returned 1.8% in the third quarter of 2022 compared to 1.2% in the third quarter of 2021, outperforming the S&P 500 Index, returns of -4.9% and 0.6% for the comparable periods. White Mountains’s portfolio of common equity securities returned -2.0% in the first nine months of 2022 compared to 7.0% in the first nine months of 2021, outperforming and underperforming the S&P 500 Index returns of -23.9% and 15.9% for the comparable periods. The results in the third quarter and first nine months of 2022 and 2021 were driven primarily by relative outperformance and underperformance in White Mountains’s international listed equity funds as compared to the S&P 500 Index.

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White Mountains maintains a portfolio of other long-term investments that consists primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits, ILS funds and private debt investments. White Mountains’s portfolio of other long-term investments was $1.6 billion and $1.4 billion as of September 30, 2022 and December 31, 2021.

White Mountains’s other long-term investments portfolio returned 3.0% in the third quarter of 2022 compared to 4.0% in the third quarter of 2021. Investment returns for the third quarter of 2022 were driven primarily by net investment income, net unrealized investment gains and unrealized foreign currency losses from Kudu’s Participation Contracts, partially offset by net unrealized and realized investment losses from private equity funds and hedge funds and unrealized losses from foreign currency on Lloyd’s trust deposits. Investment returns for the third quarter of 2021 were driven primarily by net investment income and unrealized investment gains from Kudu’s Participation Contracts, an increase in the fair value of White Mountains’s investment in PassportCard/DavidShield and net investment income and realized and unrealized investment gains from private equity funds.

White Mountains’s other long-term investments portfolio returned 7.7% in the first nine months of 2022 compared to 14.5% in the first nine months of 2021. Investment returns for the first nine months of 2022 were driven primarily by net investment income, net realized and unrealized investment gains and unrealized foreign currency losses from Kudu’s Participation Contracts, net investment income and net realized and unrealized investment gains from private equity funds and hedge funds and unrealized losses from foreign currency on Lloyd’s trust deposits. Investment returns in the first nine months of 2021 were driven primarily by net investment income and unrealized investment gains from Kudu’s Participation Contracts, an increase in the fair value of White Mountain’s investment in PassportCard/DavidShield and realized and unrealized investment gains from private equity funds.

Foreign Currency Exposure

As of September 30, 2022, White Mountains had foreign currency exposure on $168 million of net assets from continuing operations primarily related to Ark’s non-U.S. business, Kudu’s non-U.S. Participation Contracts, and certain other foreign consolidated and unconsolidated entities within Other Operations.

The following table presents the fair value of White Mountains’s foreign denominated net assets (net liabilities) by segment as of September 30, 2022:

Currency $ in Millions	Ark		Kudu		Other Operations		Total Fair Value		% of Total Shareholders’ Equity
CAD	$	57.4	$	72.7	$	—	$	130.1	3.4	%
AUD	18.1		35.7		—		53.8		1.4
GBP	16.3		—		—		16.3		.4
EUR	(46.4)		—		11.2		(35.2)		(.9)
All other	—		—		3.0		3.0		.1
Total	$	45.4	$	108.4	$	14.2	$	168.0	4.4	%

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III. Income Taxes

The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law such that taxes are imposed, the Bermuda Exempted Undertakings Tax Protection Act of 1966 states that the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035. The Company has subsidiaries and branches that operate in various other jurisdictions around the world and are subject to tax in the jurisdictions in which they operate.  As of September 30, 2022, the primary jurisdictions in which the Company’s subsidiaries and branches were subject to tax were Ireland, Israel, Luxembourg, the United Kingdom and the United States.

White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2022 represented an effective tax rate of 24% and 9%. The effective tax rate was different from the U.S. statutory rate of 21%, driven primarily by full year forecasted income in jurisdictions with lower tax rates than the United States, partially offset by a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes.

White Mountains’s income tax expense related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2021 represented an effective tax rate of (8)% and (17)%. The effective tax rate was different from the U.S. statutory rate of 21%, driven primarily by losses in jurisdictions with lower tax rates than the United States, a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes. For the nine months ended September 30, 2021, the effective rate was also different from the U.S. statutory rate of 21.0% due to additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities. On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19% to 25% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective.

IV. Discontinued Operations

NSM

On August 1, 2022, White Mountains closed the NSM Transaction. White Mountains received $1.4 billion in net cash proceeds at closing and recognized a net gain of $876 million, which was comprised of $887 million of net gain from sale of discontinued operations and $3 million of comprehensive income related to the recognition of foreign currency translation gains (losses) from the sale, partially offset by $14 million of compensation and other costs related to the transaction recorded in Other Operations. See Note 2 — “Significant Transactions.”

White Mountains reported net income from discontinued operations, net of tax, for NSM Group of $6 million for the period from July 1, 2022 to August 1, 2022 and $16 million for the period from January 1, 2022 to August 1, 2022. White Mountains reported net income (losses) from discontinued operations, net of tax, for NSM Group of $5 million and $(24) million for the third quarter and first nine months of 2021. The net income (losses) from discontinued operations, net of tax, for NSM Group in the first nine months of 2021 included a loss of $29 million related to the sale of a subsidiary. See Note 19 — “Held for Sale and Discontinued Operations.”

Sirius Group

In the first quarter of 2021, White Mountains recorded an $18 million gain within discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius Group in 2016 and a $1 million gain related to foreign currency translation. The liability related to certain interest deductions claimed by Sirius Group that had been disputed by the Swedish Tax Agency. In April 2021, the Swedish Tax Agency informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal (and that the interest deductions should not be disallowed). In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor. See Note 19 — “Held for Sale and Discontinued Operations.”

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LIQUIDITY AND CAPITAL RESOURCES

Operating Cash and Short-term Investments

Holding Company Level 

The primary sources of cash for the Company and certain of its intermediate holding companies are expected to be distributions from its insurance, reinsurance and other operating subsidiaries, net investment income, proceeds from sales, repayments and maturities of investments, capital raising activities and, from time to time, proceeds from sales of operating subsidiaries. The primary uses of cash are expected to be general and administrative expenses, purchases of investments, payments to tax authorities, payments on and repurchases/retirements of debt obligations, dividend payments to holders of the Company’s common shares, distributions to non-controlling interest holders of consolidated subsidiaries, contributions to operating subsidiaries and, from time to time, purchases of operating subsidiaries and repurchases of the Company’s common shares.

Operating Subsidiary Level 

The primary sources of cash for White Mountains’s insurance, reinsurance and other operating subsidiaries are expected to be premiums, fee revenues, commissions, net investment income, proceeds from sales, repayments and maturities of investments, contributions from holding companies and capital raising activities. The primary uses of cash are expected to be claim payments, policy acquisition costs, general and administrative expenses, broker commission expenses, cost of sales, purchases of investments, payments to tax authorities, payments on and repurchases/retirements of debt obligations, distributions made to holding companies, distributions to non-controlling interest holders and, from time to time, purchases of operating subsidiaries.

Both internal and external forces influence White Mountains’s financial condition, results of operations and cash flows. Premiums, fee revenues, investment returns, claims payments and cost of sales may be impacted by changing rates of inflation and other economic conditions. Some time may lapse between the occurrence of an insured loss, the reporting of the loss to White Mountains’s insurance and reinsurance operating subsidiaries and the settlement of the liability for that loss. The exact timing of the payment of losses cannot be predicted with certainty. White Mountains’s insurance and reinsurance operating subsidiaries maintain portfolios of invested assets with varying maturities and a substantial amount of cash and short-term investments to provide adequate liquidity for the payment of claims.

Management believes that White Mountains’s cash balances, cash flows from operations and routine sales and maturities of investments are adequate to meet expected cash requirements for the foreseeable future on both a holding company and insurance, reinsurance and other operating subsidiary level.

Dividend Capacity

Following is a description of the dividend capacity of White Mountains’s insurance and reinsurance and other operating subsidiaries:

HG Global/BAM

As of September 30, 2022, HG Global had $619 million face value of preferred shares outstanding, of which White Mountains owned 96.9%. Holders of the HG Global preferred shares receive cumulative dividends at a fixed annual rate of 6.0% on a quarterly basis, when and if declared by HG Global. As of September 30, 2022, HG Global has accrued $339 million of dividends payable to holders of its preferred shares, $327 million of which is payable to White Mountains and is eliminated in consolidation.

On April 29, 2022, HG Global received the proceeds of its new $150 million, 10-year term loan credit facility. In turn, on May 2, 2022, HG Global paid a $120 million cash dividend to shareholders, of which $116 million was paid to White Mountains.

As of September 30, 2022, HG Global and its subsidiaries had $3 million of net unrestricted cash outside of HG Re.

HG Re is a Special Purpose Insurer subject to regulation and supervision by the BMA, but it does not require regulatory approval to pay dividends. However, HG Re’s dividend capacity is limited to amounts held outside of the Collateral Trusts pursuant to the FLRT with BAM. As of September 30, 2022, HG Re had $1 million of net unrestricted cash and investments and $120 million of accrued interest on the BAM Surplus Notes held outside the Collateral Trusts. As of September 30, 2022, HG Re had $718 million of statutory capital and surplus and $834 million of assets held in the Collateral Trusts pursuant to the FLRT with BAM.

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On a monthly basis, BAM deposits cash equal to ceded premiums, net of ceding commissions, due to HG Re under the FLRT directly into the Regulation 114 Trust.  The Regulation 114 Trust target balance is equal to gross ceded unearned premiums and unpaid ceded loss and LAE expenses, if any.  If, at the end of any quarter, the Regulation 114 Trust balance is below the target balance, funds will be withdrawn from the Supplemental Trust and deposited into the Regulation 114 Trust in an amount equal to the shortfall.  If, at the end of any quarter, the Regulation 114 Trust balance is above 102% of the target balance, funds will be withdrawn from the Regulation 114 Trust and deposited into the Supplemental Trust. 

The Supplemental Trust Target Balance is $603 million, less the amount of cash and securities in the Regulation 114 Trust in excess of its target balance.  If, at the end of any quarter, the Supplemental Trust balance exceeds the Supplemental Trust Target Balance, such excess may be distributed to HG Re.  The distribution will be made first as an assignment of accrued interest on the BAM Surplus Notes and second in cash and/or fixed income securities.  As the BAM Surplus Notes are repaid over time, the BAM Surplus Notes will be replaced in the Supplemental Trust by cash and fixed income securities.

As of September 30, 2022, the Collateral Trusts held assets of $834 million, which included $458 million of cash and investments, $365 million of BAM Surplus Notes and $11 million of interest receivable on the BAM Surplus Notes.

Through 2024, the interest rate on the BAM Surplus Notes is a variable rate equal to the one-year U.S. Treasury rate plus 300 basis points, set annually. During 2022, the interest rate on the BAM Surplus Notes is 3.2%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. Under its agreements with HG Global, BAM is required to seek regulatory approval to pay interest and principal on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS.

During the three and nine months ended September 30, 2022, BAM made no repayments of the BAM Surplus Notes or accrued interest. See Note 10 — “Municipal Bond Guarantee Insurance.”

Ark

During any 12-month period, GAIL, a class 4 licensed Bermuda insurer, has the ability to (i) make capital distributions based on 15% of its total statutory capital per the previous year’s statutory financial statements, or (ii) make dividend payments based on 25% of its total statutory capital and surplus per the previous year’s statutory financial statements, without prior approval of Bermuda regulatory authorities. Accordingly, White Mountains expects GAIL will have the ability to make capital distributions of $114 million during 2022, which is equal to 15% of its December 31, 2021 statutory capital of $758 million, subject to meeting all appropriate liquidity and solvency requirements. During the nine months ended September 30, 2022, GAIL did not pay a dividend to its immediate parent.

During the nine months ended September 30, 2022, Ark paid $11 million of dividend to shareholders, $8 million of which was paid to White Mountains. As of September 30, 2022, Ark and its intermediate holding companies had $21 million of net unrestricted cash, short-term investments and fixed maturity investments outside of its regulated and unregulated insurance and reinsurance operating subsidiaries.

Kudu

During the nine months ended September 30, 2022, Kudu distributed $19 million to unitholders, substantially all of which was paid to White Mountains. As of September 30, 2022, Kudu had $68 million of net unrestricted cash.

Other Operations

During the nine months ended September 30, 2022, White Mountains paid a $3 million common share dividend. As of September 30, 2022, the Company and its intermediate holding companies had $1,076 million of net unrestricted cash, short-term investments and fixed maturity investments, $148 million of MediaAlpha common stock, $46 million of common equity securities and $292 million of private equity and hedge funds, ILS funds and unconsolidated entities.

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Financing

The following table presents White Mountains’s capital structure as of September 30, 2022 and December 31, 2021:

$ in Millions	September 30, 2022			December 31, 2021
HG Global Senior Notes (1)	$	146.4		$	—
Ark 2007 Subordinated Notes (1)	30.0			30.0
Ark 2021 Subordinated Notes (1)(2)	150.0			155.9
Kudu Credit Facility (1)(2)	253.5			218.2
Other Operations debt (1)(2)	35.6			16.8
Total debt from continuing operations	615.5			420.9
Debt from discontinued operations (2)(3)	—			272.1
Total debt	615.5			693.0
Non-controlling interests—excluding BAM	318.4			280.6
Total White Mountains’s common shareholders’ equity	3,708.0			3,548.1
Total capital	4,641.9			4,521.7
Time-value discount on expected future payments on the BAM Surplus Notes (4)	(110.8)			(125.9)
HG Global’s unearned premium reserve (4)	232.2			214.6
HG Global’s net deferred acquisition costs (4)	(65.9)			(60.8)
Total adjusted capital	$	4,697.4		$	4,549.6
Total debt to total adjusted capital	13.1		%	15.2		%

(1) See Note 7 — “Debt” for details of debt arrangements from continuing operations.

(2) Net of unamortized issuance costs.

(3) The NSM bank facility with Ares Capital Corporation and the other NSM debt was settled in conjunction with the closing of the NSM Transaction and has been classified as held for sale as of December 31, 2021.

(4) Amount reflects White Mountains’s preferred share ownership in HG Global of 96.9%.

Management believes that White Mountains has the flexibility and capacity to obtain funds externally through debt or equity financing on both a short-term and long-term basis. However, White Mountains can provide no assurance that, if needed, it would be able to obtain additional debt or equity financing on satisfactory terms, if at all.

It is possible that, in the future, one or more of the rating agencies may lower White Mountains’s existing ratings. If one or more of its ratings were lowered, White Mountains could incur higher borrowing costs on future borrowings and its ability to access the capital markets could be impacted.

Covenant Compliance

As of September 30, 2022, White Mountains was in compliance in all material respects with all of the covenants under its debt instruments.

Share Repurchases

White Mountains’s board of directors has authorized the Company to repurchase its common shares from time to time, subject to market conditions. The repurchase authorizations do not have a stated expiration date. As of September 30, 2022, White Mountains may repurchase an additional 324,626 shares under these board authorizations. In addition, from time to time White Mountains has also repurchased its common shares through self-tender offers that were separately approved by its board of directors.

During the nine months ended September 30, 2022, White Mountains repurchased and retired 457,180 of its common shares for $611 million at an average share price of $1,335, which was approximately 91% of White Mountains’s adjusted book value per share as of September 30, 2022. The majority of these shares were repurchased through a “modified Dutch auction” self-tender offer that White Mountains completed on September 26, 2022, through which it repurchased 327,795 of its common shares at a purchase price of $1,400 per share for a total cost of approximately $461 million, including expenses. Of the shares White Mountains repurchased in the first nine months of 2022, 4,011 were to satisfy employee income tax withholding pursuant to employee benefit plans, which do not reduce the board authorizations.

During the nine months ended September 30, 2021, White Mountains repurchased and retired 86,512 of its common shares for $95 million, at an average share price of $1,094, which was approximately 93% of White Mountains’s September 30, 2021 adjusted book value per share. Of the shares White Mountains repurchased in the first nine months of 2021, 7,218 were to satisfy employee income tax withholding pursuant to employee benefit plans, which do not reduce the board authorizations.

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Cash Flows

Detailed information concerning White Mountains’s cash flows during the nine months ended September 30, 2022 and 2021 follows:

Cash flows from operations for the nine months ended September 30, 2022 and September 30, 2021

Net cash provided from (used for) operations was $118 million for the nine months ended September 30, 2022 compared to $6 million for the nine months ended September 30, 2021. The increase in cash provided from operations was driven primarily by cash provided from Ark’s operations in 2022 compared to cash used for Ark’s operations in 2021, which included expenses from the Ark Transaction. This increase in cash provided from operations was partially offset by the increase in investments in Kudu Participation Contracts in 2022. As of September 30, 2022, the Company and its intermediate holding companies had $1,076 million of net unrestricted cash, short-term investments and fixed maturity investments, $148 million of MediaAlpha common stock, $46 million of common equity securities and $292 million of private equity funds, hedge funds, ILS funds and unconsolidated entities.

Cash flows from investing and financing activities for the nine months ended September 30, 2022

Financing and Other Capital Activities

During the nine months ended September 30, 2022, the Company declared and paid a $3 million cash dividend to its common shareholders.

During the nine months ended September 30, 2022, White Mountains repurchased and retired 457,180 of its common shares for $611 million. The majority of these shares were repurchased through a “modified Dutch auction” self-tender offer that White Mountains completed on September 26, 2022, through which it repurchased 327,795 of its common shares at a purchase price of $1,400 per share for a total cost of approximately $461 million, including expenses. Of the shares White Mountains repurchased in the first nine months of 2022, 4,011 were to satisfy employee income tax withholding pursuant to employee benefit plans.

During the nine months ended September 30, 2022, HG Global received net proceeds of $147 million from the issuance of the HG Global Senior Notes.

During the nine months ended September 30, 2022, BAM received $62 million in MSC.

During the nine months ended September 30, 2022, Kudu borrowed $35 million in term loans under the Kudu Credit Facility.

Acquisitions and Dispositions

On May 26, 2022, Kudu raised $115 million of equity capital from the Kudu Transaction. Mass Mutual, White Mountains and Kudu management contributed $64 million, $50 million and $1 million in the Kudu Transaction, respectively.

On August 1, 2022, White Mountains closed the previously announced NSM Transaction. White Mountains received $1.4 billion in net cash proceeds at closing.

Cash flows from investing and financing activities for the nine months ended September 30, 2021

Financing and Other Capital Activities

During the nine months ended September 30, 2021, the Company declared and paid a $3 million cash dividend to its common shareholders.

During the nine months ended September 30, 2021, White Mountains repurchased and retired 86,512 of its common shares for $95 million, 7,218 of which were repurchased under employee benefit plans for statutory withholding tax payments.

During the nine months ended September 30, 2021, BAM received $45 million in MSC.

During the nine months ended September 30, 2021, HG Global declared and paid $22 million of preferred dividends, of which $21 million was paid to White Mountains.

During the third quarter of 2021, Ark issued $163 million face value floating rate unsecured subordinated notes at par in three transactions for proceeds of $158 million, net of debt issuance costs.

During the nine months ended September 30, 2021, Kudu borrowed $3 million in term loans under the Kudu Bank Facility.

On March 23, 2021, Kudu entered into the Kudu Credit Facility with an initial draw of $102 million, of which $92 million was used to repay the outstanding principal balance on its term loans under the Kudu Bank Facility.

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Acquisitions and Dispositions

On January 1, 2021 White Mountains completed the Ark Transaction, which included contributing $605 million of equity capital to Ark, at a pre-money valuation of $300 million, and purchasing $41 million of shares from certain selling shareholders. In the fourth quarter of 2020, White Mountains prefunded/placed in escrow a total of $646 million in preparation for closing the Ark Transaction.

On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160 million.

NON-GAAP FINANCIAL MEASURES

This report includes nine non-GAAP financial measures that have been reconciled from their most comparable GAAP financial measures.

Adjusted book value per share

Adjusted book value per share is a non-GAAP financial measure, which is derived by adjusting (i) the GAAP book value per share numerator and (ii) the common shares outstanding denominator, as described below.

The GAAP book value per share numerator is adjusted (i) to include a discount for the time value of money arising from the modeled timing of cash payments of principal and interest on the BAM Surplus Notes and (ii) to add back the unearned premium reserve, net of deferred acquisition costs, at HG Global.

Under GAAP, White Mountains is required to carry the BAM Surplus Notes, including accrued interest, at nominal value with no consideration for time value of money. Based on a debt service model that forecasts operating results for BAM through maturity of the BAM Surplus Notes, the present value of the BAM Surplus Notes, including accrued interest and using an 8% discount rate, was estimated to be $114 million, $120 million, $130 million and $132 million less than the nominal GAAP carrying values as of September 30, 2022, June 30, 2022, December 31, 2021 and September 30, 2021, respectively.

The value of HG Global’s unearned premium reserve, net of deferred acquisition costs, was $172 million, $164 million, $159 million and $154 million as of September 30, 2022, June 30, 2022, December 31, 2021 and September 30, 2021, respectively.

White Mountains believes these adjustments are useful to management and investors in analyzing the intrinsic value of HG Global, including the value of the BAM Surplus Notes and the value of the in-force business at HG Re, HG Global’s reinsurance subsidiary.

The denominator used in the calculation of adjusted book value per share equals the number of common shares outstanding, adjusted to exclude unearned restricted common shares, the compensation cost of which, at the date of calculation, has yet to be amortized. Restricted common shares are earned on a straight-line basis over their vesting periods. The reconciliation of GAAP book value per share to adjusted book value per share is included on page 50.

Ark’s adjusted loss and LAE, adjusted insurance acquisition expense, adjusted other underwriting expense and adjusted combined ratios

Ark’s adjusted loss and LAE ratio, adjusted insurance acquisition expense ratio, adjusted other underwriting expense ratio and adjusted combined ratio are non-GAAP financial measures, which are derived by adjusting the GAAP ratios to add back the impact of whole-account quota-share reinsurance arrangements attributable to TPC Providers for the Syndicates. The impact of these reinsurance arrangements relates to years of account prior to the Ark Transaction. White Mountains believes these adjustments are useful to management and investors in evaluating Ark’s results on a fully aligned basis (i.e., 100% of the Syndicates’ results). The reconciliation from the GAAP ratios to the adjusted ratios is included on page 60.

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Kudu’s EBITDA and Kudu’s adjusted EBITDA

Kudu's EBITDA and adjusted EBITDA are non-GAAP financial measures. EBITDA is a non-GAAP financial measure that excludes interest expense on debt, income tax (expense) benefit, depreciation and amortization of other intangible assets from GAAP net income (loss). Adjusted EBITDA is a non-GAAP financial measure that excludes certain other items in GAAP net income (loss) in addition to those excluded from EBITDA. The adjustments relate to (i) net realized and unrealized investment gains (losses) on Kudu's Participation Contracts, (ii) non-cash equity-based compensation expense and (iii) transaction expenses. A description of each adjustment follows:

•Net realized and unrealized investment gains (losses) - Represents net unrealized investment gains and losses on Kudu’s Participation Contracts, which are recorded at fair value under GAAP, and realized investment gains and losses on Kudu’s Participation Contracts sold during the period.

•Non-cash equity-based compensation expense - Represents non-cash expenses related to Kudu’s management compensation that are settled with equity units in Kudu.

•Transaction expenses - Represents costs directly related to Kudu’s mergers and acquisitions activity, such as external lawyer, banker, consulting and placement agent fees, which are not capitalized and are expensed under GAAP.

White Mountains believes that these non-GAAP financial measures are useful to management and investors in evaluating Kudu’s performance. The reconciliation of Kudu’s GAAP net income (loss) to EBITDA and adjusted EBITDA is included on page 64.

Total consolidated portfolio return excluding MediaAlpha

Total consolidated portfolio return excluding MediaAlpha is a non-GAAP financial measure that removes the net investment income and net realized and unrealized investment gains (losses) from White Mountains’s investment in MediaAlpha. White Mountains believes this measure to be useful to management and investors by showing the underlying performance of White Mountains’s investment portfolio without regard to MediaAlpha. The following tables present reconciliations from GAAP to the reported percentages for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30, 2022						Three Months Ended September 30, 2021
	GAAP Return		Remove MediaAlpha		Return - Excluding MediaAlpha		GAAP Return		Remove MediaAlpha		Return - Excluding MediaAlpha
Total consolidated portfolio    return	0.4	%	0.1	%	0.5	%	(8.0)	%	9.4	%	1.4	%

	Nine Months Ended September 30, 2022						Nine Months Ended September 30, 2021
	GAAP Return		Remove MediaAlpha		Return - Excluding MediaAlpha		GAAP Return		Remove MediaAlpha		Return - Excluding MediaAlpha
Total consolidated portfolio    return	(3.6)	%	2.2	%	(1.4)	%	(3.7)	%	8.3	%	4.6	%

Adjusted capital

Total capital at White Mountains is comprised of White Mountains’s common shareholders’ equity, debt and non-controlling interests other than non-controlling interests attributable to BAM. Total adjusted capital is a non-GAAP financial measure, which is derived by adjusting total capital (i) to include a discount for the time value of money arising from the expected timing of cash payments of principal and interest on the BAM Surplus Notes and (ii) to add back the unearned premium reserve, net of deferred acquisition costs, at HG Global. The reconciliation of total capital to total adjusted capital is included on page 72.

CRITICAL ACCOUNTING ESTIMATES

Refer to the Company’s 2021 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s critical accounting estimates.

75

FORWARD-LOOKING STATEMENTS

This report may contain “forward-looking statements” within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934. All statements, other than statements of historical facts, included or referenced in this report which address activities, events or developments which White Mountains expects or anticipates will or may occur in the future are forward-looking statements. The words “could”, “will”, “believe”, “intend”, “expect”, “anticipate”, “project”, “estimate”, “predict” and similar expressions are also intended to identify forward-looking statements. These forward-looking statements include, among others, statements with respect to White Mountains’s:

•change in book value per share, adjusted book value per share or return on equity;

•business strategy;

•financial and operating targets or plans;

•incurred loss and LAE and the adequacy of its loss and LAE reserves and related reinsurance;

•projections of revenues, income (or loss), earnings (or loss) per share, EBITDA, adjusted EBITDA, dividends, market share or other financial forecasts of White Mountains or its businesses;

•expansion and growth of its business and operations; and

•future capital expenditures.

These statements are based on certain assumptions and analyses made by White Mountains in light of its experience and perception of historical trends, current conditions and expected future developments, as well as other factors believed to be appropriate in the circumstances. However, whether actual results and developments will conform to its expectations and predictions is subject to risks and uncertainties that could cause actual results to differ materially from expectations, including:

•the risks that are described from time to time in White Mountains’s filings with the Securities and Exchange Commission, including but not limited to White Mountains’s Annual Report on Form 10-K for the fiscal year ended December 31, 2021;

•claims arising from catastrophic events, such as hurricanes, earthquakes, floods, fires, severe winter weather, public health crises, terrorist attacks, explosions, infrastructure failures, cyber-attacks or armed conflicts;

•recorded loss reserves subsequently proving to have been inadequate;

•the market value of White Mountains’s investment in MediaAlpha;

•the trends and uncertainties from the COVID-19 pandemic, including judicial interpretations on the extent of insurance coverage provided by insurers for COVID-19 pandemic related claims;

•business opportunities (or lack thereof) that may be presented to it and pursued;

•actions taken by rating agencies, such as financial strength or credit ratings downgrades or placing ratings on negative watch;

•the continued availability of capital and financing;

•deterioration of general economic, market or business conditions, including due to outbreaks of contagious disease (including the COVID-19 pandemic) and corresponding mitigation efforts;

•competitive forces, including the conduct of other insurers;

•changes in domestic or foreign laws or regulations, or their interpretation, applicable to White Mountains, its competitors or its customers; and

•other factors, most of which are beyond White Mountains’s control.

Consequently, all of the forward-looking statements made in this report are qualified by these cautionary statements, and there can be no assurance that the actual results or developments anticipated by White Mountains will be realized or, even if substantially realized, that they will have the expected consequences to, or effects on, White Mountains or its business or operations. White Mountains assumes no obligation to publicly update any such forward-looking statements, whether as a result of new information, future events or otherwise.

76

Item 3.Quantitative and Qualitative Disclosures About Market Risk.

Refer to White Mountains’s 2021 Annual Report on Form 10-K and in particular Item 7A. - “Quantitative and Qualitative Disclosures About Market Risk.” 

Item 4.Controls and Procedures.

The Principal Executive Officer (“PEO”) and the Principal Financial Officer (“PFO”) of White Mountains have evaluated the effectiveness of its disclosure controls and procedures (as defined in Rule 13a-15(e) and 15d-15(e) of the Exchange Act) as of the end of the period covered by this report. Based on that evaluation, the PEO and PFO have concluded that White Mountains’s disclosure controls and procedures are effective.

There were no significant changes with respect to the Company’s internal control over financial reporting or in other factors that materially affected, or are reasonably likely to materially affect, internal control over financial reporting during the quarter ended September 30, 2022.

Part II.OTHER INFORMATION

Item 1.Legal Proceedings.

None.

Item 1A. Risk Factors.

There have been no material changes to any of the risk factors previously disclosed in the Registrant’s 2021 Annual Report

on Form 10-K.

Item 2.Issuer Purchases of Equity Securities.

Months	Total Number of Shares Purchased	Average Price Paid per Share		Total Number of Shares  Purchased as Part of  Publicly Announced Plans (1)	Maximum Number of Shares that May Yet Be Purchased Under the Plans (1)
July 1 - July 30, 2022	33,926	$	1,238.15	33,926	329,550
August 1 - August 31, 2022	4,924	$	1,247.63	4,924	324,626
September 1 - September 30, 2022(2)	327,795	$	1,405.89	—	324,626
Total	366,645	$	1,388.24	38,850	324,626

(1) White Mountains’s board of directors has authorized the Company to repurchase its common shares, from time to time, subject to market conditions. The repurchase authorizations do not have a stated expiration date.

(2) On September 26, 2022, White Mountains completed a “modified Dutch auction” self-tender offer, through which it repurchased 327,795 of its common shares at a purchase price of $1,400 per share ($1,406 including expenses).

Item 3. Defaults Upon Senior Securities.

None.

Item 4.Mine Safety Disclosures.

None.

Item 5.Other Information.

None.

77

Item 6.Exhibits.

(a)	Exhibit number		Name
	2.1	—	Plan of Reorganization (incorporated by reference herein to the Company’s Registration Statement on S-4 (No. 333-87649) dated September 23, 1999)
	3.1	—	Memorandum of Continuance of the Company (incorporated by reference herein to Exhibit (3)(i) of the Company’s Current Report on Form 8-K dated November 1, 1999)
	3.2	—	Amended and Restated Bye-Laws of the Company (incorporated by reference herein to Exhibit 3 of the Company’s Report on Form 10-Q dated May 2, 2017)
	31.1	—	Principal Executive Officer Certification Pursuant to Rule 13a-14 (a) of the Securities Exchange Act of 1934, as Amended. (*)
	31.2	—	Principal Financial Officer Certification Pursuant to Rule 13a-14 (a) of the Securities Exchange Act of 1934, as Amended. (*)
	32.1	—	Principal Executive Officer Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002. (*)
	32.2	—	Principal Financial Officer Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002. (*)
	101	—	XBRL Instance Document - the instance document does not appear in the Interactive Data File because its XBRL tags are embedded within the Inline XBRL document.

(*) Included herein

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the Registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.

		WHITE MOUNTAINS INSURANCE GROUP, LTD.
		(Registrant)
Date:	November 7, 2022		By: /s/ Michaela J. Hildreth
			Michaela J. Hildreth
			Managing Director and Chief Accounting Officer

78

EX-31.1

Exhibit 31.1

PRINCIPAL EXECUTIVE OFFICER CERTIFICATION PURSUANT TO RULE 13a-14(a)

OF THE SECURITIES EXCHANGE ACT OF 1934

I, G. Manning Rountree, certify that:

1. I have reviewed this quarterly report on Form 10-Q of White Mountains Insurance Group, Ltd.;

2. Based on my knowledge, this quarterly report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and we have:

(a)Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this quarterly report is being prepared;

(b)Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

(c)Evaluated the effectiveness of the registrant's disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

(d)Disclosed in this report any change in the registrant's internal control over financial reporting that occurred during the registrant's most recent fiscal quarter (the registrant's fourth fiscal quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant's auditors and the audit committee of the registrant's board of directors (or persons performing the equivalent functions):

(a)All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant's ability to record, process, summarize and report financial information; and

(b)Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant's internal control over financial reporting.

November 7, 2022

By:

/s/ G. Manning Rountree

Chief Executive Officer

(Principal Executive Officer)

C-1

EX-31.2

Exhibit 31.2

PRINCIPAL FINANCIAL OFFICER CERTIFICATION PURSUANT TO RULE 13a-14(a)

OF THE SECURITIES EXCHANGE ACT OF 1934

I, Liam P. Caffrey, certify that:

1. I have reviewed this quarterly report on Form 10-Q of White Mountains Insurance Group, Ltd.;

2. Based on my knowledge, this quarterly report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial information included in this report, fairly present in all material respects the financial condition, results of operations and cash flows of the registrant as of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for establishing and maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the registrant and we have:

(a)Designed such disclosure controls and procedures, or caused such disclosure controls and procedures to be designed under our supervision, to ensure that material information relating to the registrant, including its consolidated subsidiaries, is made known to us by others within those entities, particularly during the period in which this quarterly report is being prepared;

(b)Designed such internal control over financial reporting, or caused such internal control over financial reporting to be designed under our supervision, to provide reasonable assurance regarding the reliability of financial reporting and the preparation of financial statements for external purposes in accordance with generally accepted accounting principles;

(c)Evaluated the effectiveness of the registrant's disclosure controls and procedures and presented in this report our conclusions about the effectiveness of the disclosure controls and procedures, as of the end of the period covered by this report based on such evaluation; and

(d)Disclosed in this report any change in the registrant's internal control over financial reporting that occurred during the registrant's most recent fiscal quarter (the registrant's fourth fiscal quarter in the case of an annual report) that has materially affected, or is reasonably likely to materially affect, the registrant's internal control over financial reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our most recent evaluation of internal control over financial reporting, to the registrant's auditors and the audit committee of the registrant's board of directors (or persons performing the equivalent functions):

(a)All significant deficiencies and material weaknesses in the design or operation of internal control over financial reporting which are reasonably likely to adversely affect the registrant's ability to record, process, summarize and report financial information; and

(b)Any fraud, whether or not material, that involves management or other employees who have a significant role in the registrant's internal control over financial reporting.

November 7, 2022

By:

/s/ Liam P. Caffrey

Executive Vice President and Chief Financial Officer

(Principal Financial Officer)

C- 2

EX-32.1

Exhibit 32.1

PRINCIPAL EXECUTIVE OFFICER

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the quarterly report on Form 10-Q of White Mountains Insurance Group, Ltd. (the “Company”), for the period ending September 30, 2022 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, G. Manning Rountree, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

•The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and,

•The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the periods presented in the Report.

/s/ G. Manning Rountree

Chief Executive Officer
(Principal Executive Officer)

November 7, 2022

C-3

EX-32.2

Exhibit 32.2

PRINCIPAL FINANCIAL OFFICER

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the quarterly report on Form 10-Q of White Mountains Insurance Group, Ltd. (the “Company”), for the period ending September 30, 2022 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Liam P. Caffrey, Executive Vice President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

•The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and,

•The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of and for the periods presented in the Report.

/s/ Liam P. Caffrey

Executive Vice President and Chief Financial Officer
(Principal Financial Officer)

November 7, 2022

C-4

XML

Cover Page - shares	9 Months Ended
	Sep. 30, 2022	Nov. 03, 2022
Cover [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Sep. 30, 2022
Document Transition Report	false
Entity File Number	1-8993
Entity Registrant Name	WHITE MOUNTAINS INSURANCE GROUP, LTD
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	94-2708455
Entity Address, Address Line One	23 South Main Street, Suite 3B
Entity Address, City or Town	Hanover,
Entity Address, State or Province	NH
Entity Address, Postal Zip Code	03755-2053
City Area Code	603
Local Phone Number	640-2200
Title of 12(b) Security	Common Shares, par value $1.00
Trading Symbol	WTM
Security Exchange Name	NYSE
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Common Stock, Shares Outstanding (in shares)		2,576,232
Entity Central Index Key	0000776867
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2022
Document Fiscal Period Focus	Q3
Amendment Flag	false

XML

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Investments
Other long-term investments	$ 1,622.7	$ 1,377.8
Total assets	7,545.0	7,000.7
Liabilities
Loss and loss adjustment expense reserves	1,329.4	894.7
Debt	615.5	420.9
Total liabilities	3,678.7	3,296.0
White Mountains’s common shareholders’ equity
White Mountains’s common shares at $1 par value per share—authorized 50,000,000 shares; issued and outstanding 2,576,232 and 3,017,772 shares	2.6	3.0
Paid-in surplus	532.7	585.9
Retained earnings	3,175.9	2,957.5
Accumulated other comprehensive income (loss), after-tax:
Net unrealized gains (losses) from foreign currency translation and interest rate swap	(3.2)	1.7
Total White Mountains’s common shareholders’ equity	3,708.0	3,548.1
Non-controlling interests	158.3	156.6
Total equity	3,866.3	3,704.7
Total liabilities and equity	7,545.0	7,000.7
Financial Guarantee (HG Global/BAM)
Investments
Fixed maturity investments, at fair value	874.4	934.1
Short-term investments, at fair value	62.3	32.4
Total investments	936.7	966.5
Cash	17.3	19.8
Insurance premiums receivable	6.6	6.9
Deferred acquisition costs	34.9	33.1
Other assets	22.3	18.5
Total assets	1,017.8	1,044.8
Liabilities
Unearned insurance premiums	286.7	266.3
Debt	146.4	0.0
Accrued incentive compensation	21.6	24.7
Other liabilities	29.5	30.9
Total liabilities	484.2	321.9
P&C Insurance and Reinsurance (Ark)
Investments
Fixed maturity investments, at fair value	741.8	688.6
Common equity securities, at fair value	286.4	251.1
Short-term investments, at fair value	309.4	296.2
Other long-term investments	329.7	326.2
Total investments	1,667.3	1,562.1
Cash	123.4	67.8
Reinsurance recoverables	550.9	448.4
Insurance premiums receivable	698.6	416.0
Ceded unearned premiums	59.7	67.1
Deferred acquisition costs	151.4	108.2
Goodwill and other intangible assets	292.5	292.5
Other assets	62.9	64.9
Total assets	3,606.7	3,027.0
Liabilities
Loss and loss adjustment expense reserves	1,329.4	894.7
Unearned insurance premiums	781.3	495.9
Debt	180.0	185.9
Reinsurance payable	312.7	424.1
Contingent consideration	32.9	28.0
Other liabilities	107.6	93.8
Total liabilities	2,743.9	2,122.4
Asset Management (Kudu)
Investments
Other long-term investments	813.2	669.5
Cash	76.6	21.4
Accrued investment income	12.5	16.9
Goodwill and other intangible assets	8.7	8.9
Other assets	9.7	10.4
Total assets	920.7	727.1
Liabilities
Debt	253.5	218.2
Other liabilities	59.7	42.8
Total liabilities	313.2	261.0
Other Operations
Investments
Fixed maturity investments, at fair value	238.1	286.2
Common equity securities, at fair value	46.4	0.0
Short-term investments, at fair value	824.7	129.5
Investment in MediaAlpha, at fair value	148.2	261.6
Other long-term investments	479.8	382.1
Total investments	1,737.2	1,059.4
Cash	28.4	38.7
Goodwill and other intangible assets	92.0	39.1
Other assets	142.2	59.5
Assets held for sale - NSM	0.0	989.0
Assets held for sale - Other	0.0	16.1
Total assets	1,999.8	2,201.8
Liabilities
Debt	35.6	16.8
Accrued incentive compensation	67.2	48.5
Other liabilities	34.6	30.1
Liabilities held for sale - NSM Group	0.0	495.3
Total liabilities	$ 137.4	$ 590.7

XML

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Common shares, par value per share (in dollars per share)	$ 1	$ 1
Common shares, authorized shares (in shares)	50,000,000	50,000,000
Common shares, issued shares (in shares)	2,576,232	3,017,772
Common shares, outstanding shares (in shares)	2,576,232	3,017,772
Asset Management (Kudu)
Restricted cash	$ 8.9	$ 4.5

XML

CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Revenues:
Earned insurance premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Net investment income	33.9	19.5	79.6	57.2
Net realized and unrealized investment gains (losses)	(29.4)	30.5	(141.9)	91.2
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7.0
Other revenues	40.9	31.9	103.4	68.1
Total revenues	383.2	(92.4)	720.3	353.4
Expenses:
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	76.5	56.7	184.4	130.9
Cost of sales	25.0	24.0	68.8	45.9
General and administrative expenses	87.1	51.9	258.4	215.5
Amortization of other intangible assets	1.4	2.0	3.4	3.1
Interest expense	10.5	4.4	27.5	14.8
Total expenses	414.2	268.2	998.7	658.0
Pre-tax income (loss) from continuing operations	(31.0)	(360.6)	(278.4)	(304.6)
Income tax (expense) benefit	7.4	(28.6)	26.1	(52.2)
Net income (loss) from continuing operations	(23.6)	(389.2)	(252.3)	(356.8)
Net income (loss) from discontinued operations, net of tax - NSM Group	6.3	5.3	16.4	(23.8)
Net gain (loss) from sale of discontinued operations, net of tax			886.8	18.7
Net income (loss)	869.5	(383.9)	650.9	(361.9)
Net (income) loss attributable to non-controlling interests	18.7	12.5	101.5	53.7
Net income (loss) attributable to White Mountains’s common shareholders	888.2	(371.4)	752.4	(308.2)
Sirius Group
Expenses:
Net gain (loss) from sale of discontinued operations, net of tax	0.0	0.0	0.0	18.7
NSM Insurance Group
Expenses:
Net gain (loss) from sale of discontinued operations, net of tax	886.8	0.0	886.8	0.0
Financial Guarantee (HG Global/BAM)
Revenues:
Earned insurance premiums	7.1	6.7	26.0	19.6
Net investment income	5.7	4.4	15.1	13.2
Net realized and unrealized investment gains (losses)	(38.8)	(4.0)	(114.0)	(15.6)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	1.3	0.3	3.7	0.9
Total revenues	(24.7)	7.4	(69.2)	18.1
Expenses:
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	1.7	3.0	9.5	6.5
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	15.8	12.4	49.5	42.7
Amortization of other intangible assets	0.0	0.0	0.0	0.0
Interest expense	2.0	0.0	5.4	0.0
Total expenses	19.5	15.4	64.4	49.2
Pre-tax income (loss) from continuing operations	(44.2)	(8.0)	(133.6)	(31.1)
P&C Insurance and Reinsurance (Ark)
Revenues:
Earned insurance premiums	346.1	213.4	757.8	435.8
Net investment income	4.9	0.6	9.7	1.8
Net realized and unrealized investment gains (losses)	(14.4)	0.3	(76.5)	10.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	6.6	3.4	10.1	9.4
Total revenues	343.2	217.7	701.1	457.3
Expenses:
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	74.8	53.7	174.9	124.4
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	26.9	21.8	79.8	84.4
Amortization of other intangible assets	0.0	0.0	0.0	0.0
Interest expense	3.7	2.1	10.6	4.5
Total expenses	319.1	206.8	721.5	461.1
Pre-tax income (loss) from continuing operations	24.1	10.9	(20.4)	(3.8)
Asset Management (Kudu)
Revenues:
Earned insurance premiums	0.0	0.0	0.0	0.0
Net investment income	14.8	9.5	41.2	26.1
Net realized and unrealized investment gains (losses)	41.1	18.9	45.8	62.5
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	0.0	0.1	0.0	0.2
Total revenues	55.9	28.5	87.0	88.8
Expenses:
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	0.0	0.0	0.0	0.0
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	4.5	3.3	10.2	9.0
Amortization of other intangible assets	0.0	0.0	0.2	0.2
Interest expense	4.2	1.9	10.3	9.2
Total expenses	8.7	5.2	20.7	18.4
Pre-tax income (loss) from continuing operations	47.2	23.3	66.3	70.4
Other Operations
Revenues:
Earned insurance premiums	0.0	0.0	0.0	0.0
Net investment income	8.5	5.0	13.6	16.1
Net realized and unrealized investment gains (losses)	(17.3)	15.3	2.8	34.0
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7.0
Other revenues	33.0	28.1	89.6	57.6
Total revenues	8.8	(346.0)	1.4	(210.8)
Expenses:
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	0.0	0.0	0.0	0.0
Cost of sales	25.0	24.0	68.8	45.9
General and administrative expenses	39.9	14.4	118.9	79.4
Amortization of other intangible assets	1.4	2.0	3.2	2.9
Interest expense	0.6	0.4	1.2	1.1
Total expenses	66.9	40.8	192.1	129.3
Pre-tax income (loss) from continuing operations	$ (58.1)	$ (386.8)	$ (190.7)	$ (340.1)

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CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Statement of Comprehensive Income [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Other comprehensive income (loss), net of tax	(1.4)	0.0	(3.0)	(0.3)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group	0.7	(2.2)	(5.2)	0.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	0.0	2.9	0.0
Comprehensive income (loss)	890.4	(373.6)	747.1	(307.6)
Other comprehensive (income) loss attributable to non-controlling interests	(0.3)	0.2	0.4	0.0
Comprehensive income (loss) attributable to White Mountains’s common shareholders	$ 890.1	$ (373.4)	$ 747.5	$ (307.6)
Basic earnings (loss) per share
Continuing operations (in usd per share)	$ (1.66)	$ (121.90)	$ (50.73)	$ (98.16)
Discontinued operations (in usd per share)	308.59	1.72	304.97	(1.29)
Total consolidated operations (in usd per share)	306.93	(120.18)	254.24	(99.45)
Diluted earnings (loss) per share
Continuing operations (in usd per share)	(1.66)	(121.90)	(50.73)	(98.16)
Discontinued operations (in usd per share)	308.59	1.72	304.97	(1.29)
Total consolidated operations (in usd per share)	306.93	(120.18)	254.24	(99.45)
Dividends declared and paid per White Mountains’s common share (in usd per share)	$ 0	$ 0	$ 1.00	$ 1.00

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CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY (Unaudited) - USD ($) $ in Millions	Total	Total	Common shares and paid-in surplus	Retained earnings	AOCI, after tax	Non-controlling interest	Total Equity	BAM Non-controlling interest	BAM Total Equity
Beginning Balances at Dec. 31, 2020		$ 3,906.0	$ 595.2	$ 3,311.2	$ (0.4)	$ (88.1)	$ 3,817.9
Increase (Decrease) in Shareholders' Equity
Net income (loss)	$ (361.9)	(308.2)		(308.2)		(53.7)	(361.9)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	0.0
Other comprehensive income (loss), net of tax	(0.3)	0.4			0.4		0.4
Comprehensive income (loss)	(307.6)	(307.8)		(308.2)	0.4	(53.7)	(361.5)
Dividends declared on common shares		(3.1)		(3.1)			(3.1)
Dividends to non-controlling interests						(1.8)	(1.8)
Issuances of common shares		1.7	1.7				1.7
Issuances of shares of non-controlling interests						6.1	6.1
Repurchases and retirements of common shares		(94.6)	(16.6)	(78.0)			(94.6)
BAM member surplus contribution, net of tax								$ 44.8	$ 44.8
Amortization of restricted share awards		11.1	11.1				11.1
Recognition of equity-based compensation expense of subsidiaries		2.0	2.0			0.3	2.3
Net contributions and dilution from other non-controlling interests		6.4	(7.2)	13.4	0.2	(5.3)	1.1
Acquisition of non-controlling interests						230.3	230.3
Ending Balances at Sep. 30, 2021		3,521.7	586.2	2,935.3	0.2	132.6	3,654.3
Beginning Balances at Jun. 30, 2021		3,978.2	597.2	3,378.6	2.4	129.8	4,108.0
Increase (Decrease) in Shareholders' Equity
Net income (loss)	(383.9)	(371.4)		(371.4)		(12.5)	(383.9)
Net change in foreign currency translation and other		(2.2)			(2.2)	(0.2)	(2.4)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	0.0
Other comprehensive income (loss), net of tax	0.0
Comprehensive income (loss)	(373.6)	(373.6)		(371.4)	(2.2)	(12.7)	(386.3)
Dividends to non-controlling interests						(0.6)	(0.6)
Repurchases and retirements of common shares		(87.1)	(15.2)	(71.9)			(87.1)
BAM member surplus contribution, net of tax								14.7	14.7
Amortization of restricted share awards		3.6	3.6				3.6
Recognition of equity-based compensation expense of subsidiaries		0.2	0.2				0.2
Net contributions and dilution from other non-controlling interests		0.4	0.4			1.4	1.8
Ending Balances at Sep. 30, 2021		3,521.7	586.2	2,935.3	0.2	132.6	3,654.3
Beginning Balances at Dec. 31, 2021	3,704.7	3,548.1	588.9	2,957.5	1.7	156.6	3,704.7
Increase (Decrease) in Shareholders' Equity
Net income (loss)	650.9	752.4		752.4		(101.5)	650.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	2.9			2.9		2.9
Other comprehensive income (loss), net of tax	(3.0)	(7.8)			(7.8)	(0.4)	(8.2)
Comprehensive income (loss)	747.1	747.5		752.4	(4.9)	(101.9)	645.6
Dividends declared on common shares		(3.0)		(3.0)			(3.0)
Dividends to non-controlling interests						(7.5)	(7.5)
Issuances of common shares		3.0	3.0				3.0
Issuances of shares of non-controlling interests						74.6	74.6
Repurchases and retirements of common shares		(610.5)	(89.2)	(521.3)			(610.5)
BAM member surplus contribution, net of tax								62.3	62.3
Amortization of restricted share awards		10.3	10.3				10.3
Recognition of equity-based compensation expense of subsidiaries		8.1	8.1			0.8	8.9
Net contributions and dilution from other non-controlling interests		4.5	14.2	(9.7)		(9.1)	(4.6)
Disposition of non-controlling interests						(17.5)	(17.5)
Ending Balances at Sep. 30, 2022	3,866.3	3,708.0	535.3	3,175.9	(3.2)	158.3	3,866.3
Beginning Balances at Jun. 30, 2022		3,323.3	603.2	2,725.1	(5.0)	168.7	3,492.0
Increase (Decrease) in Shareholders' Equity
Net income (loss)	869.5	888.2		888.2		(18.7)	869.5
Net change in foreign currency translation and other		(1.1)			(1.1)	0.3	(0.8)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	2.9			2.9		2.9
Other comprehensive income (loss), net of tax	(1.4)
Comprehensive income (loss)	890.4	890.0		888.2	1.8	(18.4)	871.6
Dividends to non-controlling interests						(0.5)	(0.5)
Repurchases and retirements of common shares		(508.9)	(71.5)	(437.4)			(508.9)
BAM member surplus contribution, net of tax								$ 26.0	$ 26.0
Amortization of restricted share awards		3.8	3.8				3.8
Recognition of equity-based compensation expense of subsidiaries		0.4	0.4			0.2	0.6
Net contributions and dilution from other non-controlling interests		(0.6)	(0.6)			(0.2)	(0.8)
Disposition of non-controlling interests	(17.5)					(17.5)
Ending Balances at Sep. 30, 2022	$ 3,866.3	$ 3,708.0	$ 535.3	$ 3,175.9	$ (3.2)	$ 158.3	$ 3,866.3

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CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Cash flows from operations:
Net income (loss)	$ 650.9	$ (361.9)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses	141.9	(91.2)
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	113.3	325.5
Deferred income tax expense	22.1	36.7
Amortization of restricted share awards	10.3	11.1
Amortization and depreciation	7.0	13.6
Net (income) loss from discontinued operation, net of tax - NSM Group	(16.4)	23.8
Net gain (loss) from sale of discontinued operations, net of tax	(886.8)	(18.7)
Other operating items:
Net change in reinsurance recoverables	(102.5)	(32.3)
Net change in insurance premiums receivable	(282.3)	(245.7)
Net change in ceded unearned premiums	7.4	78.1
Net change in loss and loss adjustment expense reserves	434.7	194.9
Net change in unearned insurance premiums	305.8	290.0
Net change in deferred acquisition costs	(45.0)	(60.0)
Net change in reinsurance payable	(111.4)	(46.8)
Net change in restricted cash	4.4	4.5
Investments in Kudu Participation Contracts	(97.9)	(141.6)
Net change in other assets and liabilities, net	(37.3)	25.7
Net cash provided from (used for) operations - continuing operations	118.2	5.7
Net cash provided from (used for) operations - NSM Group discontinued operations (Note 19)	38.7	40.3
Net cash provided from (used for) operations	156.9	46.0
Cash flows from investing activities:
Net change in short-term investments	(735.4)	(83.7)
Sales of fixed maturity investments	212.4	215.9
Maturities, calls and paydowns of fixed maturity investments	107.3	144.6
Sales of common equity securities and investment in MediaAlpha	0.0	176.8
Distributions and redemptions of other long-term investments	55.0	98.2
Release of cash pre-funded/placed in escrow for Ark Transaction	0.0	646.3
Purchases of consolidated subsidiaries, net of cash acquired of $0.3 and $52.2	(67.9)	10.6
Purchases of other long-term investments	(136.9)	(206.5)
Purchases of common equity securities	(88.0)	(119.7)
Purchases of fixed maturity investments	(474.1)	(996.0)
Other investing activities, net	3.7	(1.3)
Net cash provided from (used for) investing activities - continuing operations	260.4	(114.8)
Net cash provided from (used for) investing activities - NSM Group discontinued operations (Note 19)	7.1	(54.6)
Net cash provided from (used for) investing activities	267.5	(169.4)
Cash flows from financing activities:
Draw down of debt and revolving line of credit	211.8	368.9
Repayment of debt and revolving line of credit	(10.5)	(94.8)
Cash dividends paid to the Company’s common shareholders	(3.0)	(3.1)
Common shares repurchased	(610.5)	(94.6)
Net distributions from non-controlling interest shareholders	(9.2)	1.1
Contributions from discontinued operations	11.6	0.0
Capital contributions from BAM members	62.3	44.8
Acquisition of subsidiary shares by non-controlling interest shareholders	74.6	6.1
Fidus Re premium payment	(5.6)	(6.9)
Other financing activities, net	(2.1)	(13.0)
Net cash provided from (used for) financing activities - continuing operations	(280.6)	208.5
Net cash provided from (used for) financing activities - NSM Group discontinued operations (Note 19)	(17.5)	13.8
Net cash provided from (used for) financing activities	(298.1)	222.3
Net change in cash during the period	98.0	99.4
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)	147.7	84.6
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)	245.7	184.0
Supplemental cash flows information:
Interest paid	(10.9)	(5.3)
Net income tax payments	(3.2)	(2.1)
NSM Insurance Group
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net gain (loss) from sale of discontinued operations, net of tax	(886.8)	0.0
Cash flows from investing activities:
Proceeds from the sale of consolidated subsidiaries, net of cash sold	1,364.8	0.0
Other Operations
Cash flows from investing activities:
Proceeds from the sale of consolidated subsidiaries, net of cash sold	19.5	0.0
Marketing Technology (MediaAlpha)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	$ 113.3	$ 325.5

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CONSOLIDATED STATEMENTS OF CASH FLOWS (Parenthetical) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Cash acquired from acquisition	$ 0.3	$ 52.2
Restricted cash balance	8.9	4.0
Discontinued operations cash balance	245.7	184.0
NSM Insurance Group
Cash sold in subsidiary transaction	143.9	0.0
Other Operations
Cash sold in subsidiary transaction	0.5	0.0
Discontinued Operations, Held-for-sale | NSM Insurance Group
Cash sold in subsidiary transaction	(143.9)	0.0
Restricted cash balance	0.0	92.2
Discontinued operations cash balance	$ 0.0	$ 126.7

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Basis of Presentation and Significant Accounting Policies

9 Months Ended

Sep. 30, 2022

Accounting Policies [Abstract]

Basis of Presentation and Significant Accounting Policies

Basis of Presentation and Significant Accounting Policies

Basis of Presentation

White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”) is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report.

The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of the Company, its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.

These interim financial statements include all adjustments considered necessary by management to fairly state the financial position, results of operations and cash flows of White Mountains. These interim financial statements may not be indicative of financial results for the full year and should be read in conjunction with the Company’s 2021 Annual Report on Form 10-K.

Reportable Segments

White Mountains has determined its reportable segments based on the nature of the underlying businesses, the manner in which the Company’s subsidiaries and affiliates are organized and managed and the organization of the financial information provided to the chief operating decision maker to assess performance and make decisions regarding allocation of resources. As of September 30, 2022, White Mountains’s reportable segments were HG Global/BAM, Ark and Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations.

The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM (the “BAM Surplus Notes”). As of September 30, 2022 and December 31, 2021, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a variable interest entity for which White Mountains is the primary beneficiary. BAM’s results are all attributed to non-controlling interests.

The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. Ark underwrites select coverages through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”) and its wholly-owned subsidiary Group Ark Insurance Limited (“GAIL”). White Mountains acquired a controlling ownership interest in Ark on January 1, 2021 (the “Ark Transaction”). See Note 2 — “Significant Transactions.” As of September 30, 2022 and December 31, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within results of operations and other comprehensive income are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.

The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions typically are structured as minority preferred equity stakes with distribution rights, generally tied to gross revenues and designed to generate strong, stable cash yields. As of September 30, 2022 and December 31, 2021, White Mountains owned 89.3% and 99.3% of the basic units outstanding (76.1% and 84.7% on a fully diluted, fully converted basis).

White Mountains’s Other Operations consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC (“WM Capital”), its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/DavidShield”), Elementum Holdings LP (“Elementum”), and certain other consolidated and unconsolidated entities (“Other Operating Businesses”) and certain other assets.

Discontinued Operations

On August 1, 2022, White Mountains Holdings (Luxembourg) S.à r.l. (“WTM Holdings Seller”), an indirect wholly owned subsidiary of White Mountains, completed the previously announced sale of White Mountains Catskill Holdings, Inc. and NSM Insurance HoldCo, LLC (“NSM” and, collectively with White Mountains Catskill Holdings, Inc., the “NSM Group”) to Riser Merger Sub, Inc., an affiliate of The Carlyle Group Inc. (the “NSM Transaction”), pursuant to the terms of the securities purchase agreement, dated as of May 9, 2022. See Note 2 — “Significant Transactions.” NSM is a full-service managing general agent (“MGA”) and program administrator with delegated binding authorities for specialty property and casualty insurance. As of December 31, 2021, White Mountains owned 96.5% of the basic units outstanding of NSM (87.3% on a fully diluted, fully converted basis).

As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

Significant Accounting Policies

Refer to the Company’s 2021 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies.

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Significant Transactions

9 Months Ended

Sep. 30, 2022

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Significant Transactions

Significant Transactions

NSM

On August 1, 2022, the NSM Transaction closed. White Mountains received $1.4 billion in net cash proceeds at closing and recognized a net transaction gain of $875.7 million, which was comprised of $886.8 million of net gain from sale of discontinued operations and $2.9 million of comprehensive income related to the recognition of foreign currency translation gains (losses) from the sale, partially offset by $14.0 million of compensation and other costs related to the transaction recorded in Other Operations.

Kudu

On May 26, 2022, Kudu raised $114.5 million of equity capital (the “Kudu Transaction”) from Massachusetts Mutual Life Insurance Company (“Mass Mutual”), White Mountains and Kudu management. Mass Mutual, White Mountains and Kudu management contributed $64.1 million, $50.0 million and $0.4 million and in each case, at a pre-money valuation of 1.3x, or $114.0 million above the December 31, 2021 equity value of Kudu’s go-forward portfolio of participation contracts. As of September 30, 2022, Kudu’s go-forward portfolio of participation contracts excludes $41.1 million of enterprise value relating to two portfolio companies that had announced sale transactions prior to the capital raise. As a result of the Kudu Transaction, White Mountains’s basic ownership of Kudu decreased from 99.1% to 89.3%.

Ark

On October 1, 2020, White Mountains entered into a subscription and purchase agreement (the “Ark SPA”) with Ark and certain selling shareholders (collectively with Ark, the “Ark Sellers”). Under the terms of the Ark SPA, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and to purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020, White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the Ark Transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a credit facility agreement and $366.3 million placed in escrow.

On January 1, 2021, White Mountains completed the Ark Transaction in accordance with the terms of the Ark SPA. As of September 30, 2022, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0%) after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing.

White Mountains recognized total assets acquired related to the Ark Transaction of $2.5 billion, including goodwill and other intangible assets of $292.5 million, and total liabilities of $1.7 billion, including contingent consideration of $22.5 million and non-controlling interest of $220.2 million. Ark incurred transaction costs of $25.3 million in the first quarter of 2021.     

In the third quarter of 2021, Ark issued $163.3 million of floating rate unsecured subordinated notes (the “Ark 2021 Subordinated Notes”) in three separate transactions. See Note 7 — “Debt.” In connection with the issuance of the Ark 2021 Subordinated Notes, White Mountains and Ark terminated White Mountains’s commitment to provide up to $200.0 million of additional equity capital to Ark in 2021.

The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date:

Millions	As of January 1, 2021
Investments	$	594.3
Cash	52.0		(1)
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696.0)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	$	283.6

(1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction.

The values of net tangible assets acquired and the resulting goodwill, other intangible assets and contingent consideration were recorded at fair value using Level 3 inputs. The majority of the tangible assets acquired and liabilities assumed were recorded at their carrying values, as their carrying values approximated their fair values due to their short-term nature. The fair values of goodwill, other intangible assets and the contingent consideration liability were internally estimated primarily based on the income approach. The income approach estimates fair value based on the present value of the cash flows that the assets are expected to generate in the future. White Mountains developed internal estimates for the expected future cash flows and discount rates used in the present value calculations.

The value of in-force business acquired represents the estimated profits relating to the unexpired contracts, net of related prepaid reinsurance, at the acquisition date through the expiration date of the contracts. For the three and nine months ended September 30, 2022, Ark recognized $0.7 million and $6.8 million of amortization expense on the value of in-force business acquired. For the three and nine months ended September 30, 2021, Ark recognized $11.0 million and $54.9 million of amortization expense on the value of in-force business acquired. The value of the syndicate underwriting capacity intangible asset was estimated using net cash flows attributable to Ark’s rights to write business in the Lloyd’s market. The value of the in-force business acquired and the syndicate underwriting capacity were estimated using a discounted cash flow method. Significant inputs to the valuation models include estimates of growth in premium revenues, investment returns, claim costs, expenses and discount rates based on a weighted average cost of capital.

In evaluating the fair value of Ark’s loss and loss adjustment expense reserves (“LAE”), White Mountains determined that the risk-free rate of interest was approximately equal to the risk factor reflecting the uncertainty within the reserves and that no adjustment was necessary.

As of September 30, 2022 and December 31, 2021, Ark recognized total contingent consideration liabilities of $32.9 million and $28.0 million. Any future adjustments to contingent consideration liabilities will be recognized through pre-tax income (loss). For the three and nine months ended September 30, 2022, Ark recognized pre-tax expense of $2.7 million and $4.9 million for the change in the fair value of its contingent consideration liabilities. For both the three and nine months ended September 30, 2021, Ark recognized pre-tax expense of $1.5 million for the change in the fair value of its contingent consideration liabilities.

MediaAlpha

On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3.6 million shares at $19.00 per share ($17.67 per share net of underwriting fees) and received total proceeds of $63.8 million. White Mountains also received $55.0 million of net proceeds related to a dividend recapitalization at MediaAlpha.

Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock, and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet.

On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160.3 million.

As of September 30, 2022, White Mountains owned 16.9 million shares, representing a 27.4% basic ownership interest (25.0% fully-diluted/fully-converted basis). At this current level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $6.60 per share increase or decrease in White Mountains’s book value per share. At the September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 16 — “Equity-Method Eligible Investments.”

PassportCard/DavidShield

On January 24, 2018, White Mountains acquired a 50.0% ownership interest in DavidShield, its joint venture partner in PassportCard. DavidShield is an MGA that is the leading provider of expatriate medical insurance in Israel and uses the same card-based delivery system as PassportCard. As part of the transaction, White Mountains reorganized its equity stake in PassportCard so that White Mountains and its partner in DavidShield would each own 50.0% of both businesses. To facilitate the transaction, White Mountains provided financing to its partner in the form of a non-interest-bearing loan that is secured by the partner’s equity in PassportCard and DavidShield. The gross purchase price for the 50.0% interest in DavidShield was $41.8 million, or $28.3 million net of the financing provided for the restructuring.

On May 7, 2020, White Mountains made an additional $15.0 million investment in PassportCard/DavidShield to support operations through the ongoing COVID-19 pandemic. The transaction increased White Mountains’s ownership interest from 50.0% to 53.8%, but had no impact on the governance structure of the companies, including White Mountains’s board representation or other investor rights. The governance structures for both PassportCard and DavidShield were designed to give White Mountains and its co-investor equal power to make the decisions that most significantly impact the operations of PassportCard and DavidShield. Because White Mountains does not have the unilateral power to direct the operations of PassportCard or DavidShield, White Mountains does not hold a controlling financial interest in either PassportCard or DavidShield and does not consolidate either entity. White Mountains’s ownership interest gives White Mountains the opportunity to exert significant influence over the significant financial and operating activities of PassportCard and DavidShield. Accordingly, PassportCard and DavidShield meet the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard and DavidShield. Changes in the fair value of PassportCard and DavidShield are recorded in realized and unrealized investment gains. White Mountains’s maximum exposure to loss on its equity investment in PassportCard/DavidShield and the non-interest-bearing loan to its partner is limited to the total carrying value of $143.0 million.

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Investment Securities

9 Months Ended

Sep. 30, 2022

Investments, Debt and Equity Securities [Abstract]

Investment Securities

Investment Securities

White Mountains’s portfolio of investment securities held for general investment purposes consists of fixed maturity investments, short-term investments, common equity securities, its investment in MediaAlpha and other long-term investments, which are classified as trading securities. Trading securities are reported at fair value as of the balance sheet date.  Net realized and unrealized investment gains (losses) on trading securities are reported in pre-tax revenues.

White Mountains’s fixed maturity investments are generally valued using industry standard pricing methodologies. Key inputs include benchmark yields, benchmark securities, reported trades, issuer spreads, bids, offers, credit ratings and prepayment speeds. Income on mortgage and asset-backed securities is recognized using an effective yield based on anticipated prepayments and the estimated economic life of the securities. When actual prepayments differ significantly from anticipated prepayments, the estimated economic life is recalculated and the remaining unamortized premium or discount is amortized prospectively over the remaining economic life.

Realized investment gains (losses) resulting from sales of investment securities are accounted for using the specific identification method. Premiums and discounts on all fixed maturity investments are amortized or accreted to income over the anticipated life of the investment. Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year.  Short-term investments are carried at fair value, which approximated amortized cost, as of September 30, 2022 and December 31, 2021.

Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits, insurance-linked securities (“ILS”) funds and private debt investments.

Net Investment Income

White Mountains’s net investment income is comprised primarily of interest income associated with White Mountains’s fixed maturity investments and short-term investments, dividend income from common equity securities, distributions from its investment in MediaAlpha and distributions from other long-term investments.

The following table presents pre-tax net investment income for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Fixed maturity investments	$	11.1	$	8.2	$	28.6	$	21.9
Short-term investments	6.7		—		7.2		.5
Common equity securities	.1		.1		.2		.1
Other long-term investments	17.1		12.0		45.9		37.1
Amount attributable to TPC Providers	(.3)		(.2)		(.8)		(.8)
Total investment income	34.7		20.1		81.1		58.8
Third-party investment expenses	(.8)		(.6)		(1.5)		(1.6)
Net investment income, pre-tax	$	33.9	$	19.5	$	79.6	$	57.2

Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Realized investment gains (losses)
Fixed maturity investments	$	(4.9)	$	1.0	$	(10.8)	$	3.8
Short-term investments	(.1)		(.3)		(.4)		—
Common equity securities	—		—		—		.4
Investment in MediaAlpha	—		—		—		160.3
Other long-term investments	3.4		9.2		24.1		0.9
Net realized investment gains (losses)	(1.6)		9.9		12.9		165.4
Unrealized investment gains (losses)
Fixed maturity investments	(58.8)		(7.9)		(192.9)		(27.0)
Short-term investments	(2.1)		—		(2.6)		—
Common equity securities	4.3		1.6		(6.3)		7.3
Investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(485.8)
Other long-term investments	27.5		28.4		40.8		112.3
Net unrealized investment gains (losses)	(47.7)		(374.7)		(274.3)		(393.2)
Net realized and unrealized investment gains (losses), before    amount attributable to TPC providers(1)	(49.3)		(364.8)		(261.4)		(227.8)
Amount attributable to TPC Providers	1.3		(1.7)		6.2		(6.5)
Net realized and unrealized investment gains (losses)	$	(48.0)	$	(366.5)	$	(255.2)	$	(234.3)
Fixed maturity and short-term investments
Net realized and unrealized investment gains (losses)	$	(65.9)	$	(7.2)	$	(206.7)	$	(23.2)
Less: net realized and unrealized gains (losses) on investment           securities sold during the period	.1		(5.7)		(3.0)		(6.9)
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(66.0)	$	(1.5)	$	(203.7)	$	(16.3)
Common equity securities and investment in MediaAlpha
Net realized and unrealized investment gains (losses) on common    equity securities	$	4.3	$	1.6	$	(6.3)	$	7.7
Net realized and unrealized investment gains (losses) from    investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(325.5)
Total net realized and unrealized investment gains (losses)	(14.3)		(395.2)		(119.6)		(317.8)
Less: net realized and unrealized gains (losses) on investment          securities sold during the period	—		.4		—		20.3
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(14.3)	$	(395.6)	$	(119.6)	$	(338.1)

(1) For the three months ended September 30, 2022 and 2021, includes $(22.6) and $(7.0) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2022 and 2021, includes $(44.4) and $(7.4) of realized and unrealized investment gains (losses) related to foreign currency exchange.

The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and nine months ended September 30, 2022 and 2021 for investments still held at the end of the period:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Other long-term investments	$	40.8	$	26.5	$	57.7	$	75.5
Total net unrealized investment gains, pre-tax - Level 3 investments	$	40.8	$	26.5	$	57.7	$	75.5

Investment Holdings

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses) and carrying values of White Mountains’s fixed maturity investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	227.9	$	—	$	(11.0)	$	—	$	216.9
Debt securities issued by corporations	1,068.8		—		(91.2)		(3.1)		974.5
Municipal obligations	289.3		—		(24.4)		—		264.9
Mortgage and asset-backed securities	278.3		—		(37.6)		—		240.7
Collateralized loan obligations	169.7		—		(7.6)		(4.8)		157.3
Total fixed maturity investments	$	2,034.0	$	—	$	(171.8)	$	(7.9)	$	1,854.3

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	212.1	$	.5	$	(1.1)	$	—	$	211.5
Debt securities issued by corporations	993.3		8.7		(8.7)		(.4)		992.9
Municipal obligations	276.4		16.8		(1.3)		—		291.9
Mortgage and asset-backed securities	277.2		2.9		(2.5)		—		277.6
Collateralized loan obligations	136.5		—		(.4)		(1.1)		135.0
Total fixed maturity investments	$	1,895.5	$	28.9	$	(14.0)	$	(1.5)	$	1,908.9

The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2022. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.

	September 30, 2022
Millions	Cost or Amortized Cost		Carrying Value
Due in one year or less	$	207.5	$	203.8
Due after one year through five years	917.9		849.4
Due after five years through ten years	354.8		309.3
Due after ten years	105.8		93.8
Mortgage and asset-backed securities and collateralized loan obligations	448.0		398.0
Total fixed maturity investments	$	2,034.0	$	1,854.3

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of common equity securities, White Mountains’s investment in MediaAlpha and other long-term investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	324.2	$	32.7	$	(8.7)	$	(15.4)	$	332.8
Investment in MediaAlpha	$	—	$	148.2	$	—	$	—	$	148.2
Other long-term investments	$	1,390.7	$	345.0	$	(90.0)	$	(23.0)	$	1,622.7

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	236.3	$	16.1	$	—	$	(1.3)	$	251.1
Investment in MediaAlpha	$	—	$	261.6	$	—	$	—	$	261.6
Other long-term investments	$	1,186.7	$	239.0	$	(44.1)	$	(3.8)	$	1,377.8

Fair Value Measurements

Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (observable inputs) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (unobservable inputs). Quoted prices in active markets for identical assets or liabilities have the highest priority (Level 1), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (Level 2) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (Level 3). See Note 17 — “Fair Value of Financial Instruments.”

As of September 30, 2022 and December 31, 2021, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 69% and 68% of the investment portfolio.

Fair Value Measurements by Level

The following tables present White Mountains’s fair value measurements for investments as of September 30, 2022 and December 31, 2021 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate.

	September 30, 2022
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	216.9	$	216.9	$	—	$	—
Debt securities issued by corporations:
Financials	269.0		—		269.0		—
Consumer	181.4		—		181.4		—
Industrial	115.8		—		115.8		—
Healthcare	114.3		—		114.3		—
Technology	110.8		—		110.8		—
Utilities	75.9		—		75.9		—
Communications	49.1		—		49.1		—
Energy	36.1		—		36.1		—
Materials	22.1		—		22.1		—
Total debt securities issued by corporations	974.5		—		974.5		—
Municipal obligations	264.9		—		264.9		—
Mortgage and asset-backed securities	240.7		—		240.7		—
Collateralized loan obligations	157.3		—		157.3		—
Total fixed maturity investments	1,854.3		216.9		1,637.4		—
Short-term investments	1,196.4		1,196.4		—		—
Common equity securities (1)	332.8		46.4		286.4		—
Investment in MediaAlpha	148.2		148.2		—		—
Other long-term investments	1,058.0		—		13.9		1,044.1
Other long-term investments — NAV (2)	564.7		—		—		—
Total other long-term investments	1,622.7		—		13.9		1,044.1
Total investments	$	5,154.4	$	1,607.9	$	1,937.7	$	1,044.1

(1) Consist of investments in exchange traded funds (“ETFs”) and listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at net asset value (“NAV”) using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

	December 31, 2021
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	211.5	$	211.5	$	—	$	—
Debt securities issued by corporations:
Financials	264.2		—		264.2		—
Consumer	178.1		—		178.1		—
Technology	117.9		—		117.9		—
Industrial	112.9		—		112.9		—
Healthcare	112.8		—		112.8		—
Utilities	70.9		—		70.9		—
Communications	56.0		—		56.0		—
Energy	48.0		—		48.0		—
Materials	32.1		—		32.1		—
Total debt securities issued by corporations	992.9		—		992.9		—
Municipal obligations	291.9		—		291.9		—
Mortgage and asset-backed securities	277.6		—		277.6		—
Collateralized loan obligations	135.0		—		135.0		—
Total fixed maturity investments	1,908.9		211.5		1,697.4		—
Short-term investments	465.9		465.9		—		—
Common equity securities (1)	251.1		—		251.1		—
Investment in MediaAlpha	261.6		261.6		—		—
Other long-term investments	895.3		—		4.7		890.6
Other long-term investments — NAV (2)	482.5		—		—		—
Total other long-term investments	1,377.8		—		4.7		890.6
Total investments	$	4,265.3	$	939.0	$	1,953.2	$	890.6

(1) Consist of investments in listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

Investments Held on Deposit or as Collateral

As of September 30, 2022 and December 31, 2021, investments of $455.1 million and $479.5 million were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM.

BAM is required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $4.6 million and $4.8 million as of September 30, 2022 and December 31, 2021.

Lloyd’s trust deposits are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. As of September 30, 2022 and December 31, 2021, Ark held Lloyd’s trust deposits with a fair value of $117.8 million and $113.8 million

The underwriting capacity of a member of Lloyd’s must be supported by providing a deposit (“Funds at Lloyd’s”) in the form of cash, securities or letters of credit in an amount determined by Lloyd’s. The amount of such deposit is calculated for each member through the completion of an annual capital adequacy exercise. These requirements allow Lloyd’s to evaluate that each member has sufficient assets to meet its underwriting liabilities plus a required solvency margin. As of September 30, 2022 and December 31, 2021, the fair value of Ark’s Funds at Lloyd’s investment deposits totaled $311.4 million and $342.8 million.

As of September 30, 2022 and December 31, 2021, Ark had $49.8 million and $50.0 million of short-term investments pledged as collateral under an uncommitted standby letter of credit. See Note 7 — “Debt.”

Debt Securities Issued by Corporations

The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
AAA	$	11.2	$	12.0
AA	90.5		85.0
A	524.0		490.4
BBB	343.0		396.8
Other	5.8		8.7
Debt securities issued by corporations (1)	$	974.5	$	992.9

(1)    Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.

Mortgage and Asset-backed Securities and Collateralized Loan Obligations

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022						December 31, 2021
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	114.1	$	114.1	$	—	$	125.4	$	125.4	$	—
FHLMC	74.5		74.5		—		90.5		90.5		—
GNMA	28.9		28.9		—		40.1		40.1		—
Total agency (1)	217.5		217.5		—		256.0		256.0		—
Non-agency: Residential	.4		.4		—		.5		.5		—
Total non-agency	.4		.4		—		.5		.5		—
Total mortgage-backed securities	217.9		217.9		—		256.5		256.5		—
Other asset-backed securities:
Credit card receivables	11.9		11.9		—		12.3		12.3		—
Vehicle receivables	10.9		10.9		—		8.8		8.8		—
Total other asset-backed securities	22.8		22.8		—		21.1		21.1		—
Total mortgage and asset-backed securities	240.7		240.7		—		277.6		277.6		—
Collateralized loan obligations	157.3		157.3		—		135.0		135.0		—
Total mortgage and asset-backed securities and collateralized loan obligations	$	398.0	$	398.0	$	—	$	412.6	$	412.6	$	—

(1)    Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed

by a government sponsored entity (i.e., FNMA, FHLMC).

As of September 30, 2022, White Mountains’s investment portfolio included $157.3 million of collateralized loan obligations that are within the senior tranches of their respective fund securitization structures. All of White Mountains’s collateral loan obligations were rated AAA or AA as of September 30, 2022.

Investment in MediaAlpha

Following the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and is presented as a separate line item on the balance sheet.

At the September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 2 — “Significant Transactions.”

Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
Kudu’s Participation Contracts	$	813.2	$	669.5
PassportCard/DavidShield	132.0		120.0
Elementum Holdings, L.P.	45.0		45.0
Other unconsolidated entities (1)	37.0		34.4
Total unconsolidated entities	1,027.2		868.9
Private equity funds and hedge funds	239.8		153.8
Bank loan fund	155.7		163.0
Lloyd’s trust deposits	117.8		113.8
ILS funds	49.4		51.9
Private debt investments	13.0		14.1
Other	19.8		12.3
Total other long-term investments	$	1,622.7	$	1,377.8

(1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, convertible preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments.

Private Equity Funds and Hedge Funds

White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held investments in 16 private equity funds and two hedge funds. The largest investment in a single private equity fund or hedge fund was $49.3 million and $31.3 million as of September 30, 2022 and December 31, 2021.

The following table presents the fair value of investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments
Private equity funds
Aerospace/Defense/Government	$	102.9	$	45.1	$	69.8	$	11.8
Financial services	77.9		54.9		67.7		29.3
Real estate	4.3		2.5		4.3		2.9
Total private equity funds	185.1		102.5		141.8		44.0
Hedge funds
Long/short equity financials and business services	49.3		—		—		—
European small/mid cap	5.4		—		12.0		—
Total hedge funds	54.7		—		12.0		—
Total private equity funds and hedge funds    included in other long-term investments	$	239.8	$	102.5	$	153.8	$	44.0

 

Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period.

The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2022:

Millions	1 – 3 years	3 – 5 years	5 – 10 years	>10 years	Total
Private equity funds — expected lock-up period remaining	$27.5	$19.0	$135.4	$3.2	$185.1

Investors in private equity funds are generally subject to indemnification obligations outside of the capital commitment period and prior to the winding up of the fund. As of September 30, 2022 and December 31, 2021, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds. 

Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. Advance notice requirements for redemptions from White Mountains’s hedge funds investments range from 45 to 90 days. One of White Mountains’s hedge fund investments also limits redemptions to every second anniversary following the date of the initial investment.

Bank Loan Fund

White Mountains’s other long-term investments include a bank loan fund with a fair value of $155.7 million as of September 30, 2022. The fair value of this investment is estimated using the NAV of the fund. The bank loan fund’s investment objective is to provide, on an unleveraged basis, high current income consistent with preservation of capital and low duration. The bank loan fund primarily invests in a broad portfolio of U.S. dollar-denominated, non-investment grade, floating-rate senior secured loans and may invest in other financial instruments, such as secured and unsecured corporate debt, credit default swaps, reverse repurchase agreements, synthetic indices and cash and cash equivalents.

The investment in the bank loan fund is subject to restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. White Mountains may redeem all or a portion of its bank loan fund investment as of any calendar month-end upon 15 calendar days advanced written notice.

Lloyd’s Trust Deposits

White Mountains’s other long-term investments include Lloyd’s trust deposits, which consist of non-U.K. deposits and Canadian comingled pooled funds. The Lloyd’s trust deposits invest primarily in short-term government securities, agency securities and corporate bonds held in trusts that are managed by Lloyd's of London. These investments are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. The fair value of the Lloyd’s trust deposits is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held Lloyd’s trust deposits with a fair value of $117.8 million.

Insurance-Linked Securities Funds

White Mountains’s other long-term investments include ILS fund investments. The fair value of these investments is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held investments in ILS funds with a fair value of $49.4 million.

Investments in ILS funds are generally subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, non-renewal clauses, restrictions on redemption frequency and advance notice periods for redemptions. From time to time, natural catastrophe, liquidity, market or other events will occur that make the determination of fair value for underlying investments in ILS funds less certain due to the potential for loss development. In such circumstances, the impacted investments may be subject to additional lock-up provisions.

ILS funds are typically subject to monthly and annual restrictions on redemptions and advance redemption notice period requirements that range between 30 and 90 days. Amounts requested for redemption remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period.

One of the ILS funds in White Mountains’s portfolio requires shareholders to provide advance redemption notice on or before September 15 of each calendar year. Amounts requested for redemption in this fund remain subject to market fluctuation until the underlying investment has fully matured or been commuted, which may be up to a period of three years from the start of each calendar year.

Rollforward of Level 3 Investments

Level 3 measurements as of September 30, 2022 and 2021 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities. The following table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the nine months ended September 30, 2022 and 2021:

Level 3 Investments
Millions	Other Long-term Investments			Other Long-term Investments
Balance at December 31, 2021	$	890.6	Balance at December 31, 2020	$	614.2
Net realized and unrealized gains	57.3		Net realized and unrealized gains	79.0
Amortization/accretion	—		Amortization/accretion	—
Purchases	127.9		Purchases	143.6
Sales	(31.7)		Sales	(31.9)
Effect of Ark Transaction	—		Effect of Ark Transaction	9.6
Transfers in	—		Transfers in	—
Transfers out	—		Transfers out	—
Balance at September 30, 2022	$	1,044.1	Balance at September 30, 2021	$	814.5

Fair Value Measurements — Transfers Between Levels - Nine months ended September 30, 2022 and 2021

Transfers between levels are recorded using the fair value measurement as of the end of the quarterly period in which the event or change in circumstance giving rise to the transfer occurred.

During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements.

During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 measurements.

Significant Unobservable Inputs

The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s other long-term investments, classified within Level 3 as of September 30, 2022 and December 31, 2021. The tables below exclude $42.9 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds.

$ in Millions	September 30, 2022
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$813.2	17% - 24%	7x - 16x
PassportCard/DavidShield	Discounted cash flow	$132.0	24%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	18%	4%
Private debt investments	Discounted cash flow	$11.0	10%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 9.7x.

(4) As of September 30, 2022, three of Kudu’s Participation Contracts with a total fair value of $312.4 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(5) In 2022, Kudu deployed a total of $97.9 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

$ in Millions	December 31, 2021
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$669.5	18% - 23%	7x - 13x
PassportCard/DavidShield	Discounted cash flow	$120.0	23%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	17%	4%
Private debt investments	Discounted cash flow	$9.4	8%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 10x.

(4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management.

(5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

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Goodwill and Other Intangible Assets

9 Months Ended

Sep. 30, 2022

Goodwill and Intangible Assets Disclosure [Abstract]

Goodwill and Other Intangible Assets

Goodwill and Other Intangible Assets

    White Mountains accounts for purchases of businesses using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. The estimated acquisition date fair values, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date.

The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by reportable segment as of September 30, 2022 and December 31, 2021:

$ in Millions	Weighted Average Economic  Life (in years)	September 30, 2022						December 31, 2021
		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value
Goodwill:
Ark	N/A	$	116.8	$	—	$	116.8	$	116.8	$	—	$	116.8
Kudu	N/A	7.6		—		7.6		7.6				7.6
Other Operations	N/A	51.1		—		51.1		17.9		—		17.9
Total goodwill		175.5		—		175.5		142.3		—		142.3
Other intangible assets:
Ark
Underwriting capacity	N/A	175.7		—		175.7		175.7		—		175.7
Kudu
Trade names	7	2.2		1.1		1.1		2.2		.9		1.3
Other Operations
Trade names	15.9	17.9		2.4		15.5		8.2		1.5		6.7
Customer relationships	12.4	29.5		6.6		22.9		18.8		4.5		14.3
Other	12.1	2.8		.3		2.5		.3		.1		.2
Subtotal		50.2		9.3		40.9		27.3		6.1		21.2
Total other intangible assets		228.1		10.4		217.7		205.2		7.0		198.2
Total goodwill and other intangible assets		$	403.6	$	10.4	393.2		$	347.5	$	7.0	340.5
Goodwill and other intangible assets attributed to    non-controlling interests						(103.1)						(91.8)
Goodwill and other intangible assets included in White Mountains’s    common shareholders’ equity						$	290.1					$	248.7

Intangible Assets Valuation Methods

The goodwill recognized for the entities shown above is attributed to expected future cash flows. The acquisition date fair values of other intangible assets with finite lives are estimated using income approach techniques, which use future expected cash flows to develop a discounted present value amount.

The multi-period-excess-earnings method estimates fair value using the present value of the incremental after-tax cash flows attributable solely to the other intangible asset over its remaining life. This approach was used to estimate the fair value of other intangible assets associated with the underwriting capacity, trade names, customer relationships and contracts and information technology.

The relief-from-royalty method was used to estimate fair value for other intangible assets that relate to rights that could be obtained via a license from a third-party owner. Under this method, the fair value is estimated using the present value of license fees avoided by owning rather than leasing the asset. This technique was used to estimate the fair value of domain names, certain trademarks and brand names.

The with-or-without method estimates the fair value of other intangible assets that provide an incremental benefit. Under this method, the fair value of the other intangible asset is calculated by comparing the value of the entity with and without the other intangible asset. This approach was used to estimate the fair value of favorable lease terms.

On at least an annual basis beginning no later than the interim period included in the one-year anniversary of an acquisition, White Mountains evaluates goodwill and other intangible assets for potential impairment. Between annual evaluations, White Mountains considers changes in circumstances or events subsequent to the most recent evaluation that may indicate that an impairment may exist and, if necessary will perform an interim review for potential impairment.

The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022:

$ in Millions	Goodwill and Other intangible asset (1)		Acquisition Date
Acquisition of subsidiary/ asset
Ark	$	292.5	January 1, 2021
Other Operations	$	86.6	Various

(1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	201.8	$	196.2	$	398.0	$	151.5	$	201.1	$	352.6
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)		—		(3.4)		(.4)		—		(.4)
Amortization	—		(1.4)		(1.4)		—		(2.0)		(2.0)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

	Nine Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	142.3	$	198.2	$	340.5	$	19.2	$	26.4	$	45.6
Ark Transaction	—		—		—		116.8		175.7		292.5
Acquisition of businesses (1)	59.5		—		59.5		15.8		—		15.8
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)				(3.4)		(.7)		.1		(.6)
Amortization	—		(3.4)		(3.4)		—		(3.1)		(3.1)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the nine

months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

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Loss and Loss Adjustment Expense Reserves

9 Months Ended

Sep. 30, 2022

Insurance Loss Reserves [Abstract]

Loss and Loss Adjustment Expense Reserves

Loss and Loss Adjustment Expense Reserves

The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Gross beginning balance	$	1,022.1	$	760.0	$	894.7	$	696.0
Less: beginning reinsurance recoverable on unpaid losses (1)	(375.5)		(425.3)		(428.9)		(433.4)
Net loss and LAE reserves	646.6		334.7		465.8		262.6
Loss and LAE incurred relating to:
Current year losses	222.9		141.9		491.8		269.0
Prior year losses	(9.2)		(12.7)		(35.6)		(21.2)
Net incurred losses and LAE	213.7		129.2		456.2		247.8
Loss and LAE paid relating to:
Current year losses	(6.1)		(9.0)		(20.8)		(11.5)
Prior year losses	(37.0)		(20.3)		(130.8)		(62.1)
Net paid loss and LAE	(43.1)		(29.3)		(151.6)		(73.6)
Change in TPC Providers’ participation (2)	—		—		57.5		(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)		(1.2)		(19.9)		(1.2)
Net ending balance	808.0		433.4		808.0		433.4
Plus: ending reinsurance recoverable on unpaid losses (3)	521.4		457.5		521.4		457.5
Gross ending balance	$	1,329.4	$	890.9	$	1,329.4	$	890.9

(1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $182.4 and $314.6 for the three months ended September 30, 2022 and 2021 and $276.8 and $319.2 for the nine months ended September 30, 2022 and 2021.

(2) Amount represents the impact to net loss and LAE reserves due to a change in the TPC Providers’ participation related to the annual reinsurance to close (“RITC”) process.

(3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $168.0 and $299.9 as of September 30, 2022 and 2021.

For the three and nine months ended September 30, 2022, Ark recognized $9.2 million and $35.6 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2022 was driven primarily by good claims experience across most classes including the property and accident & health and specialty reserving lines of business, predominantly from business underwritten in London. For the three and nine months ended September 30, 2021, Ark recognized $12.7 million and $21.2 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2021 was driven primarily by the property and accident & health reserving line of business.

TPC Providers’ Participation

For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by TPC Providers using whole account reinsurance contracts with Ark’s corporate member. The TPC Providers’ participation in the Syndicates for the 2020 open year of account is 42.8% of the total net result of the Syndicates. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates.

An RITC agreement is generally put in place after the third year of operations for a year of account such that the outstanding loss and LAE reserves, including future development thereon, are reinsured into the next year of account. As a result, and in combination with the changing participation provided by TPC Providers, Ark’s participation on outstanding loss and LAE reserves reinsured into the next year of account may change, perhaps significantly. During the first quarter of 2022, an RITC was executed such that the outstanding loss and LAE reserves for claims arising out of the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%, were reinsured into the 2020 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates is 42.8%. During the first quarter of 2021, an RITC was executed such that the outstanding loss and LAE reserves for claims arising out of the 2018 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 57.6%, were reinsured into the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%.

Municipal Bond Guarantee Insurance

HG Re and BAM do not have any outstanding loss and LAE reserves related to BAM’s municipal bond guarantee insurance business.

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Third-Party Reinsurance

9 Months Ended

Sep. 30, 2022

Reinsurance Disclosures [Abstract]

Third-Party Reinsurance

Third-Party Reinsurance

In the normal course of business, Ark may seek to limit losses that may arise from catastrophes or other events by reinsuring certain risks with third-party reinsurers. Ark remains liable for risks reinsured in the event that the reinsurer does not honor its obligations under reinsurance contracts.

The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for Ark for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Gross	$	215.5	$	162.4	$	1,252.5	$	895.0
Ceded	(22.9)		(41.5)		(246.0)		(169.5)
Net written premiums	$	192.6	$	120.9	$	1,006.5	$	725.5
Earned premiums:
Gross	$	454.9	$	284.5	$	966.6	$	622.0
Ceded	(108.8)		(71.1)		(208.8)		(186.2)
Net earned premiums	$	346.1	$	213.4	$	757.8	$	435.8
Losses and loss adjustment expenses:
Gross	$	391.4	$	193.5	$	712.9	$	372.7
Ceded	(177.7)		(64.3)		(256.7)		(124.9)
Net losses and loss adjustment expenses	$	213.7	$	129.2	$	456.2	$	247.8

As of September 30, 2022, Ark had $521.4 million and $29.5 million of reinsurance recoverables on unpaid and paid losses. As of September 30, 2021, Ark had $457.5 million and $8.1 million of reinsurance recoverables on unpaid and paid losses. As reinsurance contracts do not relieve Ark of its obligation to its policyholders, Ark seeks to reduce the credit risk associated with reinsurance balances by avoiding over-reliance on specific reinsurers through the application of concentration limits and thresholds. Ark is selective with its reinsurers, placing reinsurance with only those reinsurers having a strong financial condition. Ark monitors the financial strength of its reinsurers on an ongoing basis.

As of September 30, 2022, Ark’s reinsurance recoverables of $550.9 million included $168.0 million attributable to TPC Providers, which are collateralized. As of September 30, 2021, Ark’s reinsurance recoverables of $465.6 million included $299.9 million related to TPC Providers, which are collateralized.

The following table provides a listing of Ark’s remaining gross and net reinsurance recoverables, excluding amounts attributable to TPC Providers, by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) rating and the percentage of total recoverables as of September 30, 2022:

$ in Millions	As of September 30, 2022
A.M. Best Rating(1)	Gross		Collateral		Net		% of Total
A+ or better	$	178.3	$	—	$	178.3	67.7	%
A- to A	78.9		—		78.9		29.9
B++ or lower and not rated	125.7		119.4		6.3		2.4
Total	$	382.9	$	119.4	$	263.5	100.0	%

(1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good).

See Note 10 — “Municipal Bond Guarantee Insurance” for third-party reinsurance balances related to White Mountains’s financial guarantee business.

Reinsurance Contracts Accounted for as Deposits

Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), which is accounted for using the deposit method and recorded within other assets. Ark earns an annual crediting rate of 3.0%, which is recorded within other revenue. During the fourth quarter of 2021, Ark negotiated a reduction of $31.7 million, including accrued interest, to the aggregate excess of loss contract with SiriusPoint. As of September 30, 2022, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.3 million.

See Note 10 — “Municipal Bond Guarantee Insurance” for reinsurance contracts accounted for as deposits related to White Mountains’s financial guarantee business.

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Debt

9 Months Ended

Sep. 30, 2022

Debt Disclosure [Abstract]

Debt

Debt

The following table presents White Mountains’s debt outstanding as of September 30, 2022 and December 31, 2021:

$ in Millions	September 30, 2022		Effective   Rate	(1)	December 31, 2021		Effective   Rate	(1)
HG Global Senior Notes	$	150.0	8.6%		$	—	N/A
Unamortized discount and issuance cost	(3.6)				—
HG Global Senior Notes, carrying value	146.4				—
Ark 2007 Subordinated Notes, carrying value	30.0				30.0
Ark 2021 Notes Tranche 1	37.6				44.2
Ark 2021 Notes Tranche 2	47.0				47.0
Ark 2021 Notes Tranche 3	70.0				70.0
Unamortized issuance cost	(4.6)				(5.3)
Ark 2021 Subordinated Notes, carrying value	150.0				155.9
Total Ark Subordinated Notes, carrying value	180.0		7.3%		185.9		6.9%
Kudu Credit Facility	260.4		5.6%		225.4		4.3%
Unamortized issuance cost	(6.9)				(7.2)
Kudu Credit Facility, carrying value	253.5				218.2
Other Operations debt	36.4		7.1%		17.1		7.5%
Unamortized issuance cost	(.8)				(.3)
Other Operations debt, carrying value	35.6				16.8
Total debt	$	615.5			$	420.9

 (1) Effective rate includes the effect of the amortization of debt issuance costs.

HG Global Senior Notes

On April 29, 2022, HG Global received the proceeds of its $150.0 million face value floating rate secured senior notes (the “HG Global Senior Notes”). The HG Global Senior Notes, which mature in April 2032, accrue interest at a floating rate equal to the three-month Secured Overnight Financing Rate (“SOFR”) plus 6.3% per annum. Subsequent to the five-year anniversary of the funding date, absent the occurrence of an early amortization trigger event, HG Global will make payments of principal on a quarterly basis totaling $15.0 million annually. Upon the occurrence of an early amortization trigger event, HG Global is required to use all available cash flow to repay the notes. Early amortization trigger events include scenarios in which HG Re is effectively in run off. HG Global has the option to redeem, in whole or in part, the HG Global Senior Notes after the five-year anniversary of the funding date at the outstanding principal amounts plus accrued interest.

The HG Global Senior Notes require HG Global to maintain an interest reserve account of eight times the interest accrued for the most recent quarterly interest period, which is included in short-term investments. As of September 30, 2022, the interest reserve account is $26.4 million.

The HG Global Senior Notes are secured by the capital stock and other equity interests of HG Global’s subsidiaries, the interest reserve account, and all cash and non-cash proceeds from the foregoing collateral. The HG Global Senior Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

If the payments of principal and interest under the HG Global Senior Notes become subject to tax withholding on behalf of a relevant governmental authority for certain indemnified taxes, the HG Global Senior Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The HG Global Senior Notes require the payment of additional interest of 1.0% per annum if the HG Global Senior Notes receive a non-investment grade rating or are no longer rated.

As of September 30, 2022, the HG Global Senior Notes had an outstanding principal balance of $150.0 million.

Ark Subordinated Notes

In March 2007, GAIL issued $30.0 million face value of floating rate unsecured junior subordinated deferrable interest notes to Alesco Preferred Funding XII Ltd., Alesco Preferred Funding XIII Ltd. and Alesco Preferred Funding XIV Ltd (the “Ark 2007 Subordinated Notes”). The Ark 2007 Subordinated Notes, which mature in June 2037, accrue interest at a floating rate equal to the three-month U.S. London Inter-Bank Offered Rate (“LIBOR”) plus 4.6% per annum. As of September 30, 2022, the Ark 2007 Subordinated Notes had an outstanding principal balance of $30.0 million.

In the third quarter of 2021, GAIL issued $163.3 million face value floating rate subordinated notes at par in three separate transactions for proceeds of $157.8 million, net of debt issuance costs. The unsecured subordinated notes (the “Ark 2021 Subordinated Notes”) were issued in private placement offerings that were exempt from the registration requirements of the Securities Act of 1933. On July 13, 2021, Ark issued €39.1 million ($46.3 million based upon the foreign exchange spot rate as of the date of the transaction) face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 1”). The Ark 2021 Notes Tranche 1, which mature in July 2041, accrue interest at a floating rate equal to the three-month EURIBOR plus 5.75% per annum. On August 11, 2021, Ark issued $47.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 2”). The Ark 2021 Notes Tranche 2, which mature in August 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 5.75% per annum. On September 8, 2021, Ark issued $70.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 3”). The Ark 2021 Notes Tranche 3, which mature in September 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 6.1% per annum. On the ten-year anniversary of the issue dates, the interest rate for the Ark 2021 Subordinated Notes will increase by 1.0% per annum. Ark has the option to redeem, in whole or in part, the Ark 2021 Subordinated Notes ahead of contractual maturity at the outstanding principal amounts plus accrued interest at the ten-year anniversary or any subsequent interest payment date.

All payments of principal and interest under the Ark 2021 Subordinated Notes are conditional upon GAIL’s solvency and compliance with the enhanced capital requirements of the Bermuda Monetary Authority (“BMA”). The deferral of payments of principal and interest under these conditions does not constitute a default by Ark and does not give the noteholders any rights to accelerate repayment of the Ark 2021 Subordinated Notes or take any enforcement action under the Ark 2021 Subordinated Notes.

If the payments of principal and interest under the Ark 2021 Subordinated Notes become subject to tax withholding on behalf of Bermuda or any political subdivision there, the Ark 2021 Subordinated Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The Ark 2021 Notes Tranche 3 require the payment of additional interest of 1.0% per annum upon the occurrence of a premium load event until such event is remedied. Premium load events include the failure to meet payment obligations of the Ark 2021 Notes Tranche 3 when due, failure of GAIL to maintain an investment grade credit rating, failure to maintain 120% of GAIL’s Bermuda solvency capital requirement, failure of GAIL to maintain a debt to capital ratio below 40%, late filing of GAIL’s or Ark’s financial information, and making a restricted payment or distribution on GAIL’s common stock or other securities that rank junior or pari passu with the Ark 2021 Notes Tranche 3 when a different premium load event exists or will be caused by the restricted payment.

As of September 30, 2022, the Ark 2021 Notes Tranche 1 had an outstanding principal balance of €39.1 million ($37.6 million based upon the foreign exchange spot rate as of September 30, 2022), the Ark 2021 Notes Tranche 2 had an outstanding principal balance of $47.0 million, and the Ark 2021 Notes Tranche 3 had an outstanding principal balance of $70.0 million.

The Ark Subordinated Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

Ark Standby Letter of Credit Facilities

In December 2021, Ark entered into two uncommitted standby letter of credit facility agreements to support the continued growth and expansion of its GAIL insurance and reinsurance operations. The standby letter of credit facility agreements were executed with ING Bank N.V., London Branch (the “ING LOC Facility”) with capacity of $50.0 million on an uncollateralized basis and with Citibank Europe Plc (the “Citibank LOC Facility”) with capacity of $100.0 million on a collateralized basis. In September 2022, Ark entered another uncommitted standby letter of credit facility agreement with Lloyds Bank Corporate Markets PLC (the “Lloyds LOC Facility”) with capacity of $50.0 million on a collateralized basis.

As of September 30, 2022, the ING LOC Facility and Lloyds LOC Facility were undrawn. As of September 30, 2022, the Citibank LOC Facility had an outstanding principal balance of $36.2 million. As of September 30, 2022, $49.8 million of short-term investments were pledged as collateral under the Citibank LOC Facility. Ark’s uncommitted standby letter of credit facility agreements contain various representations, warranties and covenants that White Mountains considers to be customary for such borrowings.

Kudu Credit Facility and Kudu Bank Facility

On December 23, 2019, Kudu entered into a secured credit facility with Monroe Capital Management Advisors, LLC (the “Kudu Bank Facility”). On March 23, 2021, Kudu replaced the Kudu Bank Facility and entered into a secured revolving credit facility (the “Kudu Credit Facility”) with Mass Mutual to repay the Kudu Bank Facility, and to fund new investments and related transaction expenses. The maximum borrowing capacity of the Kudu Credit Facility is $300.0 million. The Kudu Credit Facility matures on March 23, 2036. In connection with the replacement of the Kudu Bank Facility, Kudu recognized a total loss of $4.1 million, representing debt issuance costs and prepayment fees, which are included within interest expense for the year to date period ended September 30, 2021.

The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of September 30, 2022, the interest reserve account is $8.9 million. The Kudu Credit Facility requires Kudu to maintain a ratio of the outstanding balance to the sum of the fair market value of the participation contracts and cash held in certain accounts (the “LTV Percentage”) of less than 50% in years 0-3, 40% in years 4-6, 25% in years 7-8, 15% in years 9-10, and 0% thereafter. As of September 30, 2022, Kudu has a 35% LTV Percentage.

Kudu may borrow undrawn balances within the initial three-year availability period, subject to customary terms and conditions, to the extent the amount borrowed under the Kudu Credit Facility does not exceed the borrowing base, which is equal to 35% of the fair value of qualifying Kudu Participation Contracts. As of September 30, 2022, the available undrawn balance was $39.6 million.

The following table presents the change in debt under the Kudu Bank Facility and Kudu Credit Facility for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Kudu Bank Facility
Beginning balance	$	—	$	—	$	—	$	89.2
Term loans
Borrowings	—		—		—		3.0
Repayments	—		—		—		(92.2)
Ending balance	$	—	$	—	$	—	$	—
Kudu Credit Facility
Beginning balance	$	260.4	$	203.0	$	225.4	$	—
Term loans
Borrowings	—		—		35.0		203.0
Repayments	—		—		—		—
Ending balance	$	260.4	$	203.0	$	260.4	$	203.0

The Kudu Credit Facility is secured by all property of the loan parties and contains various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.

Other Operations Debt

As of September 30, 2022, White Mountains’s Other Operations had debt with an outstanding principal balance of $36.4 million, which consisted of five secured credit facilities (collectively, “Other Operations debt”).

Compliance

At September 30, 2022, White Mountains was in compliance in all material respects with the covenants under all of its debt instruments.

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Income Taxes

9 Months Ended

Sep. 30, 2022

Income Tax Disclosure [Abstract]

Income Taxes

Income Taxes

The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law such that taxes are imposed, the Bermuda Exempted Undertakings Tax Protection Act of 1966 states that the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035. The Company has subsidiaries and branches that operate in various other jurisdictions around the world and are subject to tax in the jurisdictions in which they operate.  As of September 30, 2022, the primary jurisdictions in which the Company’s subsidiaries and branches were subject to tax were Ireland, Israel, Luxembourg, the United Kingdom and the United States.

White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2022 represented an effective tax rate of 23.9% and 9.4%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by full year forecasted income in jurisdictions with lower tax rates than the United States, partially offset by a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes.

White Mountains’s income tax expense related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2021 represented an effective tax rate of (7.9)% and (17.1)%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by losses in jurisdictions with lower tax rates than the United States, a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes. For the nine months ended September 30, 2021, the effective rate was also different from the U.S. statutory rate of 21.0% due to additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities.

On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19.0% to 25.0% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective.

On August 16, 2022, the U.S. enacted the Inflation Reduction Act (the “IRA”). White Mountains has evaluated the tax provisions of the IRA, the most significant of which relate to the corporate alternative minimum tax and the tax on share repurchases, and does not expect the legislation to have a material impact on its results of operations.

In arriving at the effective tax rate for the three and nine months ended September 30, 2022 and 2021, White Mountains forecasted all income and expense items including the change in unrealized investment gains (losses) and realized investment gains (losses) for the years ending December 31, 2022 and 2021.

White Mountains records a valuation allowance against deferred tax assets if it becomes more likely than not that all or a portion of a deferred tax asset will not be realized. Changes in valuation allowances from period to period are included in income tax expense in the period of change. In determining whether or not a valuation allowance, or change therein, is warranted, White Mountains considers factors such as prior earnings history, expected future earnings, carryback and carryforward periods and strategies that if executed would result in the realization of a deferred tax asset.

With few exceptions, White Mountains is no longer subject to U.S. federal, state, or non-U.S. income tax examinations by tax authorities for years before 2016.

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Derivatives

9 Months Ended

Sep. 30, 2022

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Derivatives

Derivatives

HG Global Interest Rate Cap

On June 16, 2022, HG entered into an interest rate cap agreement, effective on July 25, 2022, to limit its exposure to the risk of interest rate increases on the HG Global Senior Notes. The notional amount of the interest rate cap is $150.0 million and the termination date is July 25, 2025.

HG paid initial premiums of $3.3 million for the interest rate cap. Under the terms of the interest rate cap agreement, if the current three-month SOFR rate at the measurement date exceeds 3.5%, HG will receive payments from the counterparty equal to the difference between the three-month SOFR rate on the determination date and 3.5%, multiplied by the notional amount of the cap based on the number of days in the quarter and a year equal to 360 days. As of September 30, 2022, the three-month SOFR rate was 3.6%.

HG accounts for the interest rate cap as a derivative at fair value, with changes in fair value recognized in current period earnings within interest expense. For the three and nine months ended September 30, 2022, White Mountains recognized a gain of $2.1 million and $0.6 million related to the change in fair value on the interest rate cap within interest expense. As of September 30, 2022, the estimated fair value of the interest rate cap recorded in other assets was $3.9 million. White Mountains classifies the interest rate cap as a Level 2 measurement.

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Municipal Bond Guarantee Insurance

9 Months Ended

Sep. 30, 2022

Guarantees [Abstract]

Municipal Bond Guarantee Insurance

Municipal Bond Guarantee Insurance

HG Global was established to fund the startup of BAM, a mutual municipal bond insurer. HG Global, together with its subsidiaries, provided the initial capitalization of BAM through the purchase of $503.0 million of the BAM Surplus Notes.

Reinsurance Treaties

FLRT

BAM is a party to a first loss reinsurance treaty (“FLRT”) with HG Re under which HG Re provides first loss protection up to 15%-of-par outstanding on each municipal bond insured by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. In return, BAM cedes up to 60% of the risk premium charged for insuring the municipal bond, which is net of a ceding commission. The FLRT is a perpetual agreement with terms that can be renegotiated after a specified period of time. During 2021, BAM and HG Re agreed that the terms may be renegotiated at the end of 2024, and each subsequent five-year period thereafter.

Fidus Re

BAM is party to a collateralized financial guarantee excess of loss reinsurance agreement that serves to increase BAM’s claims paying resources and is provided by Fidus Re Ltd. (“Fidus Re”).

In 2018, Fidus Re was initially capitalized by the issuance of $100.0 million of insurance-linked securities (the “Fidus Re 2018 Agreement”). The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. The insurance-linked securities were issued by Fidus Re with an initial term of 12 years and are callable five years after the date of issuance. Under the Fidus Re 2018 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $165.0 million on a portion of BAM’s financial guarantee portfolio (the “2018 Covered Portfolio”) up to a total reimbursement of $100.0 million. The Fidus Re 2018 Agreement does not provide coverage for losses in excess of $276.1 million. The 2018 Covered Portfolio consists of approximately 28% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022.

In the first quarter of 2021, Fidus Re issued an additional $150.0 million of insurance-linked securities (the “Fidus Re 2021 Agreement”) with an initial term of 12 years and are callable five years after the date of issuance. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. Under the Fidus Re 2021 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $135.0 million on a portion of BAM’s financial guarantee portfolio (the “2021 Covered Portfolio”) up to a total reimbursement of $150.0 million. The Fidus Re 2021 Agreement does not provide coverage for losses in excess of $301.7 million. The 2021 Covered Portfolio consists of approximately 33% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022.

The Fidus Re agreements are accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as they do not meet the risk transfer requirements necessary to be accounted for as reinsurance.

XOLT

In January 2020, BAM entered into an excess of loss reinsurance agreement (the “XOLT”) with HG Re. Under the XOLT, HG Re provides last dollar protection for exposures on municipal bonds insured by BAM in excess of New York State Department of Financial Services (“NYDFS”) single issuer limits. As of September 30, 2022, the XOLT is subject to an aggregate limit equal to the lesser of $125.0 million or the assets held in the supplemental collateral trust (the “Supplemental Trust”) at any point in time. The agreement is accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as the agreement does not meet the risk transfer requirements necessary to be accounted for as reinsurance.

Collateral Trusts

HG Re’s obligations under the FLRT are limited to the assets in two collateral trusts: the Supplemental Trust and a Regulation 114 Trust (together, the “Collateral Trusts”). Losses required to be reimbursed under the FLRT are subject to an aggregate limit equal to the assets held in the Collateral Trusts at any point in time.

On a monthly basis, BAM deposits cash equal to ceded premiums, net of ceding commissions, due to HG Re under the FLRT directly into the Regulation 114 Trust. The Regulation 114 Trust target balance is equal to gross ceded unearned premiums and unpaid ceded loss and LAE, if any. If, at the end of any quarter, the Regulation 114 Trust balance is below the target balance, funds will be withdrawn from the Supplemental Trust and deposited into the Regulation 114 Trust in an amount equal to the shortfall. If, at the end of any quarter, the Regulation 114 Trust balance is above 102% of the target balance, funds will be withdrawn from the Regulation 114 Trust and deposited into the Supplemental Trust. The Regulation 114 Trust balance as of September 30, 2022 and December 31, 2021 was $259.4 million and $250.2 million.

The Supplemental Trust target balance is $603.0 million, less the amount of cash and securities in the Regulation 114 Trust in excess of its target balance (the “Supplemental Trust Target Balance”). If, at the end of any quarter, the Supplemental Trust balance exceeds the Supplemental Trust Target Balance, such excess may be distributed to HG Re. The distribution will be made first as an assignment of accrued interest on the BAM Surplus Notes and second in cash and/or fixed income securities.

As the BAM Surplus Notes are repaid over time, the BAM Surplus Notes will be replaced in the Supplemental Trust by cash and fixed income securities. The Supplemental Trust balance as of September 30, 2022 and December 31, 2021 was $574.5 million and $601.8 million.

As of September 30, 2022 and December 31, 2021, the Collateral Trusts held assets of $833.9 million and $852.0 million, which included $457.7 million and $481.7 million of cash and investments, $364.6 million and $364.6 million of BAM Surplus Notes and $11.6 million and $5.7 million of interest receivable on the BAM Surplus Notes.

BAM Surplus Notes

Through 2024, the interest rate on the BAM Surplus Notes is a variable rate equal to the one-year U.S. Treasury rate plus 300 basis points, set annually. During 2022, the interest rate on the BAM Surplus Notes is 3.2%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. Under its agreements with HG Global, BAM is required to seek regulatory approval to pay interest and principal on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS.

In December 2021, BAM made a $33.8 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $23.6 million was a repayment of principal held in the Supplemental Trust, $0.4 million was a payment of accrued interest held inside the Supplemental Trust and $9.8 million was a payment of accrued interest held outside the Supplemental Trust.

During the three and nine months ended September 30, 2022 and 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest.

As of September 30, 2022 and December 31, 2021, the principal balance on the BAM Surplus Notes was $364.6 million and $364.6 million and total interest receivable on the BAM Surplus Notes was $166.4 million and $157.6 million.

Insured Obligations and Premiums

The following table presents a schedule of BAM’s insured obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022		December 31, 2021
Contracts outstanding	13,094		12,350
Remaining weighted average contract period outstanding (in years)	10.8		10.8
Contractual debt service outstanding (in millions):
Principal	$	98,619.0	$	89,196.5
Interest	47,595.0		41,486.5
Total debt service outstanding	$	146,214.0	$	130,683.0
Gross unearned insurance premiums (in millions)	$	286.7	$	266.3

The following table presents a schedule of BAM’s future premium revenues as of September 30, 2022:

Millions	September 30, 2022
October 1, 2022 - December 31, 2022	$	6.9
January 1, 2023 - March 31, 2023	6.8
April 1, 2023 - June 30, 2023	6.7
July 1, 2023 - September 30, 2023	6.6
October 1, 2023 - December 31, 2023	6.4
Total 2023	26.5
2024	24.9
2025	23.2
2026	21.6
2027	20.1
2028 and thereafter	163.5
Total gross unearned insurance premiums	$	286.7

The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Direct	$	18.4	$	12.8	$	44.9	$	34.5
Assumed	1.3		—		1.3		4.5
Gross written premiums (1)	$	19.7	$	12.8	$	46.2	$	39.0
Earned premiums:
Direct	$	6.5	$	5.9	$	22.0	$	16.8
Assumed	.6		.8		4.0		2.8
Gross earned premiums (1)	$	7.1	$	6.7	$	26.0	$	19.6

(1) There are no ceded premium amounts in the periods presented and gross earned premiums are equivalent to net written premiums and net earned premiums.

In January 2021, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $805.5 million.

In September 2022, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $42.5 million.

None of the contracts assumed under these reinsurance agreements were non-performing, and no loss reserves have been established for any of the contracts, either as of the transaction date or as of September 30, 2022. The agreements, which cover future claims exposure only, meet the risk transfer criteria under ASC 944-20, Insurance Activities and accordingly have been accounted for as reinsurance.

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Earnings Per Share

9 Months Ended

Sep. 30, 2022

Earnings Per Share [Abstract]

Earnings Per Share

Earnings Per Share

White Mountains calculates earnings per share using the two-class method, which allocates earnings between common shares and unvested restricted common shares. Both classes of shares participate equally in dividends and earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares.

The following table presents the Company’s computation of earnings per share from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: total income (loss) from discontinued operations, net of tax (1)	893.1		5.3		903.2		(5.1)
Less: net (income) loss from discontinued operations attributable    to non-controlling interests	$	(.1)	$	—	$	(.7)	$	1.1
Net income (loss) from continuing operations attributable to    White Mountains’s common shareholders	$	(4.8)	$	(376.7)	$	(150.1)	$	(304.2)
Allocation of (earnings) losses to participating restricted    common shares (2)	.1		4.6		1.8		3.5
Basic and diluted earnings (losses) per share numerators	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings per share (in dollars) - continuing    operations:
Distributed earnings - dividends declared and paid	$	—	$	—	$	1.00	$	1.00
Undistributed earnings (losses)	(1.66)		(121.90)		(51.73)		(99.16)
Basic and diluted earnings (losses) per share	$	(1.66)	$	(121.90)	$	(50.73)	$	(98.16)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group and net gain (loss) from sale of discontinued operations, net of tax - Sirius Group. See Note 19 — “Held for Sale and Discontinued Operations.”

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

The following table presents the undistributed net earnings (losses) from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Undistributed net earnings (losses) - continuing operations:
Net income (losses) attributable to White Mountains’s common    shareholders, net of restricted common share amounts	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Dividends declared, net of restricted common share amounts (1)	—		—		(3.0)		(3.1)
Total undistributed net earnings (losses), net of restricted    common share amounts	$	(4.7)	$	(372.1)	$	(151.3)	$	(303.8)

(1) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

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Employee Share-Based Incentive Compensation Plans

9 Months Ended

Sep. 30, 2022

Share-Based Payment Arrangement [Abstract]

Employee Share-Based Incentive Compensation Plans

Employee Share-Based Incentive Compensation Plans

White Mountains’s Long-Term Incentive Plan (the “WTM Incentive Plan”) provides for grants of various types of share-based and non-share-based incentive awards to key employees of White Mountains. As of September 30, 2022 and 2021, White Mountains’s share-based compensation incentive awards consist of performance shares and restricted shares.

Performance Shares

Performance shares are designed to reward employees for meeting company-wide performance targets. Performance shares are conditional grants of a specified maximum number of common shares or an equivalent amount of cash. Awards generally vest at the end of a three-year service period, are subject to the attainment of pre-specified performance goals, and are valued based on the market value of common shares at the time awards are paid. Performance shares earned under the WTM Incentive Plan are typically paid in cash but may be paid in common shares. Compensation expense is recognized for the vested portion of the awards over the related service periods. The level of payout ranges from zero to two times the number of shares initially granted, depending on White Mountains’s financial performance. Performance shares become payable at the conclusion of a performance cycle (typically 3 years) if pre-defined financial targets are met. The performance measures used for determining performance share payouts are growth in White Mountains’s adjusted book value per share and intrinsic value per share. Intrinsic value per share is generally calculated by adjusting adjusted book value per share for differences between the adjusted book value of certain assets and liabilities and White Mountains’s estimate of their underlying intrinsic values.

The following table presents the performance share activity for the three and nine months ended September 30, 2022 and 2021 for performance shares granted under the WTM Incentive Plan:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense
Beginning of period	39,449	$	41.2	41,252	$	45.7	40,828	$	42.2	42,458	$	56.3
Shares paid (1)	—	—		(219)	(.6)		(14,625)	(26.4)		(14,336)	(35.2)
New grants	—	—		—	—		13,225	—		13,475	—
Forfeitures and   cancellations (2)	—	(.1)		(205)	.2		21	(.2)		(769)	.4
Expense recognized	—	11.9		—	(6.5)		—	37.4		—	17.3
End of period	39,449	$	53.0	40,828	$	38.8	39,449	$	53.0	40,828	$	38.8

(1) Includes WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target and WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in March 2021 at 200% of target. 

(2) Amounts include changes in assumed forfeitures, as required under GAAP.

During the nine months ended September 30, 2022, White Mountains granted 13,225 performance shares for the 2022-2024 performance cycle. During the nine months ended September 30, 2021, White Mountains granted 13,475 performance shares for the 2021-2023 performance cycle.

For the 2019-2021 performance cycle, the Company issued common shares for 750 performance shares earned and all other performance shares earned were settled in cash. For the 2018-2020 performance cycle, all performance shares earned were settled in cash. If all the outstanding WTM performance shares had vested on September 30, 2022, the total additional compensation cost to be recognized would have been $41.2 million, based on accrual factors (common share price and payout assumptions) as of September 30, 2022.

The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of September 30, 2022 for each performance cycle:

	Nine Months Ended September 30, 2022
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense
Performance cycle:
2020 – 2022	13,350	$	31.9
2021 – 2023	13,475	14.7
2022 – 2024	13,225	7.2
Sub-total	40,050	53.8
Assumed forfeitures	(601)	(.8)
September 30, 2022	39,449	$	53.0

Restricted Shares

Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions,  except share amounts	Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value
Non-vested,
Beginning of period	38,350	$	23.0	38,280	$	23.2	37,850	$	15.9	43,105	$	15.2
Issued	—	—		—	—		13,225	13.8		13,475	16.1
Vested	—	—		(219)	—		(12,725)	—		(17,936)	—
Forfeited	—	—		(211)	(.2)		—	—		(794)	(.8)
Expense recognized	—	(3.8)		—	(3.6)		—	(10.5)		—	(11.1)
End of period	38,350	$	19.2	37,850	$	19.4	38,350	$	19.2	37,850	$	19.4

During the nine months ended September 30, 2022, White Mountains issued 13,225 restricted shares that vest on January 1, 2025. During the nine months ended September 30, 2021, White Mountains issued 13,475 restricted shares that vest on January 1, 2024. The unamortized issue date fair value as of September 30, 2022 is expected to be recognized ratably over the remaining vesting periods.

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Leases

9 Months Ended

Sep. 30, 2022

Leases [Abstract]

Leases

Leases

White Mountains has entered into lease agreements, primarily for office space. These leases are classified as operating leases, with lease expense recognized on a straight-line basis over the term of the lease. Lease incentives, such as free rent or landlord reimbursements for leasehold improvements, are recognized at lease inception and amortized on a straight-line basis over the term of the lease. Lease expense and the amortization of leasehold improvements are recognized within general and administrative expenses. Lease payments related to options to extend or renew the lease term are excluded from the calculation of lease liabilities unless White Mountains is reasonably certain of exercising those options.

As of September 30, 2022 and December 31, 2021, the right of use (“ROU”) lease assets were $24.5 million and $28.1 million and lease liabilities were $26.5 million and $30.0 million.

The following table summarizes net lease expense recognized in White Mountains’s consolidated statements of operations for the three and nine months ended September 30, 2022 and 2021:

Millions	Three Months Ended September 30,				Nine Months Ended September 30,
Lease Cost	2022		2021		2022		2021
Lease cost	$	1.9	$	1.9	$	5.9	$	4.8
Less: sublease income	.2		.1		.5		.3
Net lease cost	$	1.7	$	1.8	$	5.4	$	4.5

The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2022:

Millions	As of September 30, 2022
Remainder of 2022	$	1.7
2023	8.1
2024	7.1
2025	4.9
2026	2.6
Thereafter	5.0
Total undiscounted lease payments	29.4
Less: present value adjustment	2.9
Operating lease liabilities	$	26.5

The following tables present lease related assets and liabilities by reportable segment as of September 30, 2022 and December 31, 2021:

	As of September 30, 2022
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	6.2	$	6.6	$	5.9	$	5.8	$	24.5	4.1%
Lease liabilities	$	6.7	$	6.6	$	6.8	$	6.4	$	26.5

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

	As of December 31, 2021
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	7.6	$	7.0	$	6.4	$	7.1	$	28.1	4.0%
Lease liabilities	$	8.1	$	7.0	$	7.1	$	7.8	$	30.0

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

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Non-controlling Interests

9 Months Ended

Sep. 30, 2022

Noncontrolling Interest [Abstract]

Non-controlling Interests

Non-controlling Interests

Non-controlling interests consist of the ownership interests of non-controlling shareholders in consolidated entities and are presented separately on the balance sheet.

The following table presents the balance of non-controlling interests included in White Mountains’s total equity and the ownership interests held by non-controlling shareholders as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
$ in Millions	Non-controlling Percentage (1)		Non-controlling Equity		Non-controlling Percentage (1)		Non-controlling Equity
Non-controlling interests, excluding BAM
HG Global	3.1	%	$	(.3)	3.1	%	$	8.9
Ark	28.0	%	217.1		28.0	%	230.7
Kudu	10.7	%	80.8		.7	%	12.4
NSM (2)	—	%	—		3.5	%	16.7
Other	various		20.8		various		11.9
Total, excluding BAM			318.4				280.6
BAM	100.0	%	(160.1)		100.0	%	(124.0)
Total non-controlling interests			$	158.3			$	156.6

(1) The non-controlling percentage represents the basic ownership interests held by non-controlling shareholders with the exception of HG Global, for which the non-controlling percentage represents the preferred share ownership held by non-controlling shareholders.

(2) As a result of the NSM Transaction, NSM has been classified as discontinued operations through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations.”

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Segment Information

9 Months Ended

Sep. 30, 2022

Segment Reporting [Abstract]

Segment Information

Segment Information

As of September 30, 2022, White Mountains conducted its operations through four segments: (1) HG Global/BAM, (2) Ark, (3) Kudu, and (4) Other Operations. As a result of the NSM Transaction, the results of operations for NSM, previously reported as a segment, have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the chief operating decision makers and the Board of Directors. Significant intercompany transactions among White Mountains’s segments have been eliminated herein.

The following tables present the financial information for White Mountains’s segments:

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2022
Earned insurance premiums	$	7.1	$	346.1	$	—	$	—	$	353.2
Net investment income	5.7		4.9		14.8		8.5		33.9
Net realized and unrealized investment    gains (losses)	(38.8)		(14.4)		41.1		(17.3)		(29.4)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(18.6)		(18.6)
Commission revenues	—		—		—		3.2		3.2
Other revenues	1.3		6.6		—		33.0		40.9
Total revenues	(24.7)		343.2		55.9		8.8		383.2
Loss and loss adjustment expenses	—		213.7		—		—		213.7
Insurance and reinsurance acquisition expenses	1.7		74.8		—		—		76.5
Cost of sales	—		—		—		25.0		25.0
General and administrative expenses	15.8		26.9		4.5		39.9		87.1
Amortization of other intangible assets	—		—		—		1.4		1.4
Interest expense	2.0		3.7		4.2		.6		10.5
Total expenses	19.5		319.1		8.7		66.9		414.2
Pre-tax income (loss) from continuing operations	$	(44.2)	$	24.1	$	47.2	$	(58.1)	$	(31.0)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2021
Earned insurance premiums	$	6.7	$	213.4	$	—	$	—	$	220.1
Net investment income	4.4		.6		9.5		5.0		19.5
Net realized and unrealized investment    gains (losses)	(4.0)		.3		18.9		15.3		30.5
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(396.8)		(396.8)
Commission revenues	—		—		—		2.4		2.4
Other revenues	.3		3.4		.1		28.1		31.9
Total revenues	7.4		217.7		28.5		(346.0)		(92.4)
Losses and loss adjustment expenses	—		129.2		—		—		129.2
Insurance and reinsurance acquisition expenses	3.0		53.7		—		—		56.7
Cost of sales	—		—		—		24.0		24.0
General and administrative expenses	12.4		21.8		3.3		14.4		51.9
Amortization of other intangible assets	—		—		—		2.0		2.0
Interest expense	—		2.1		1.9		.4		4.4
Total expenses	15.4		206.8		5.2		40.8		268.2
Pre-tax income (loss) from continuing operations	$	(8.0)	$	10.9	$	23.3	$	(386.8)	$	(360.6)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2022
Earned insurance premiums	$	26.0	$	757.8	$	—	$	—	$	783.8
Net investment income	15.1		9.7		41.2		13.6		79.6
Net realized and unrealized investment    gains (losses)	(114.0)		(76.5)		45.8		2.8		(141.9)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(113.3)		(113.3)
Commission revenues	—		—		—		8.7		8.7
Other revenues	3.7		10.1		—		89.6		103.4
Total revenues	(69.2)		701.1		87.0		1.4		720.3
Loss and loss adjustment expenses	—		456.2		—		—		456.2
Insurance and reinsurance acquisition expenses	9.5		174.9		—		—		184.4
Cost of sales	—		—		—		68.8		68.8
General and administrative expenses	49.5		79.8		10.2		118.9		258.4
Amortization of other intangible assets	—		—		.2		3.2		3.4
Interest expense	5.4		10.6		10.3		1.2		27.5
Total expenses	64.4		721.5		20.7		192.1		998.7
Pre-tax income (loss) from continuing operations	$	(133.6)	$	(20.4)	$	66.3	$	(190.7)	$	(278.4)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2021
Earned insurance premiums	$	19.6	$	435.8	$	—	$	—	$	455.4
Net investment income	13.2		1.8		26.1		16.1		57.2
Net realized and unrealized investment    gains (losses)	(15.6)		10.3		62.5		34.0		91.2
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(325.5)		(325.5)
Commission revenues	—		—		—		7.0		7.0
Other revenues	.9		9.4		.2		57.6		68.1
Total revenues	18.1		457.3		88.8		(210.8)		353.4
Losses and loss adjustment expenses	—		247.8		—		—		247.8
Insurance and reinsurance acquisition expenses	6.5		124.4		—		—		130.9
Cost of sales	—		—		—		45.9		45.9
General and administrative expenses	42.7		84.4		9.0		79.4		215.5
Amortization of other intangible assets	—		—		.2		2.9		3.1
Interest expense	—		4.5		9.2		1.1		14.8
Total expenses	49.2		461.1		18.4		129.3		658.0
Pre-tax income (loss) from continuing operations	$	(31.1)	$	(3.8)	$	70.4	$	(340.1)	$	(304.6)

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Equity-Method Eligible Investments

9 Months Ended

Sep. 30, 2022

Equity Method Investments and Joint Ventures [Abstract]

Equity-Method Eligible Investments

Equity-Method Eligible Investments

White Mountains’s equity method eligible investments include White Mountains’s investment in MediaAlpha, certain other unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds in which White Mountains has the ability to exert significant influence over the investee’s operating and financial policies.

The following table presents the ownership interests and carrying values of White Mountains’s equity method eligible investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Ownership Interest		Carrying Value		Ownership Interest		Carrying Value
Kudu Participation Contracts (1)	4.1 - 33.0%		$	813.2	3.2 - 32.0%		$	669.5
Investment in MediaAlpha	27.4	%	148.2		28.0	%	261.6
PassportCard/DavidShield	53.8	%	132.0		53.8	%	120.0
Elementum Holdings, L.P.	29.7	%	45.0		29.7	%	45.0
Other equity method eligible investments, at fair value	Under 50.0%		102.7		Under 50.0%		109.3
Other equity method eligible investments, at fair value	50.0% and over		27.7		50.0% and over		17.8

(1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are non-controlling equity interests in the form of revenue and earnings participation contracts.

For the three and nine months ended September 30, 2022, White Mountains received dividend and income distributions from equity method eligible investments of $16.1 million and $42.9 million, which were recorded within net investment income in the consolidated statements of operations. For the three and nine months ended September 30, 2021, White Mountains received dividend and income distributions from equity method eligible investments of $13.0 million, and $37.7 million, which were recorded within net investment income in the consolidated statements of operations.

Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock, and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet. See Note 2 — “Significant Transactions.” For the nine months ended September 30, 2021, MediaAlpha was considered a significant subsidiary.

The following tables present summarized financial information for MediaAlpha as of September 30, 2022 and December 31, 2021 and for the three and nine months ended September 30, 2022 and 2021:

Millions	September 30, 2022		December 31, 2021
Balance sheet data:
Total assets	$	265.2	$	289.8
Total liabilities	$	333.6	$	351.4

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Income statement data:
Total revenues	$	89.0	$	152.7	$	335.1	$	483.7
Total expenses	$	110.2	$	157.0	$	379.2	$	488.2
Net income (loss)	$	(21.2)	$	(4.3)	$	(44.1)	$	(4.5)

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Fair Value of Financial Instruments

9 Months Ended

Sep. 30, 2022

Fair Value Disclosures [Abstract]

Fair Value of Financial Instruments

Fair Value of Financial Instruments

    White Mountains records its financial instruments at fair value with the exception of debt obligations, which are recorded as debt at face value less unamortized original issue discount. See Note 7 — “Debt.”

    The following tables presents the fair value and carrying value of these financial instruments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Carrying Value		Fair Value		Carrying Value
HG Global Senior Notes	$	146.1	$	146.4	$	—	$	—
Ark 2007 Subordinated Notes	$	26.2	$	30.0	$	27.6	$	30.0
Ark 2021 Subordinated Notes	$	149.4	$	150.0	$	162.8	$	155.9
Kudu Credit Facility	$	265.5	$	253.5	$	246.8	$	218.2
Other Operations debt	$	36.8	$	35.6	$	17.7	$	16.8

The fair value estimates for the HG Global Senior Notes, Ark 2007 Subordinated Notes, Ark 2021 Subordinated Notes, Kudu Credit Facility and Other Operations debt have been determined based on a discounted cash flow approach and are considered to be Level 3 measurements.

For the fair value level measurements associated with White Mountains’s investment securities. See Note 3 — “Investment Securities.” For the fair value level measurements associated with White Mountains’s derivative instruments. See Note 9 — “Derivatives.”

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Commitments and Contingencies

9 Months Ended

Sep. 30, 2022

Commitments and Contingencies Disclosure [Abstract]

Commitments and Contingencies

Commitments and Contingencies

Legal Contingencies

White Mountains, and the insurance industry in general, is routinely subject to claims related litigation and arbitration in the normal course of business, as well as litigation and arbitration that do not arise from, nor are directly related to, claims activity. White Mountains’s estimates of the costs of settling matters routinely encountered in claims activity are reflected in the reserves for unpaid loss and LAE. See Note 5 — “Losses and Loss Adjustment Expense Reserves.”

White Mountains considers the requirements of ASC 450 when evaluating its exposure to non-claims related litigation and arbitration. ASC 450 requires that accruals be established for litigation and arbitration if it is probable that a loss has been incurred and it can be reasonably estimated. ASC 450 also requires that litigation and arbitration be disclosed if it is probable that a loss has been incurred or if there is a reasonable possibility that a loss may have been incurred. White Mountains does not have any current non-claims related litigation that may have a material adverse effect on White Mountains’s financial condition, results of operations or cash flows.

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Held for Sale and Discontinued Operations

9 Months Ended

Sep. 30, 2022

Discontinued Operations and Disposal Groups [Abstract]

Held for Sale and Discontinued Operations

Held for Sale and Discontinued Operations

NSM

On August 1, 2022, White Mountains closed the NSM Transaction. See Note 2 — “Significant Transactions.” As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation.

Sirius Group

On April 18, 2016, White Mountains completed the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) to CM International Pte. Ltd. and CM Bermuda Limited (collectively “CMI”). In connection with the sale, White Mountains indemnified Sirius Group against the loss of certain interest deductions claimed by Sirius Group related to periods prior to the sale of Sirius Group to CMI that had been disputed by the Swedish Tax Agency. In late October 2018, the Swedish Administrative Court ruled against Sirius Group on its appeal of the Swedish Tax Agency’s denial of these interest deductions. As a result, in 2018 White Mountains recorded a loss of $17.3 million within net gain (loss) on sale of discontinued operations reflecting the value of these interest deductions.

As of December 31, 2020, White Mountains’s liability related to the tax indemnification provided in connection with the sale of Sirius Group in 2016 was $18.7 million. In April 2021, the Swedish Tax Agency informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal and that the interest deductions should not be disallowed. In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor. For the nine months ended September 30, 2021, White Mountains recorded a gain of $17.6 million in discontinued operations to reverse the liability accrued as of December 31, 2020 and $1.1 million gain related to foreign currency translation.

Summary of Reclassified Balances and Related Items

Net Assets Held for Sale

The following summarizes the assets and liabilities associated with NSM Group classified as held for sale. As of December 31, 2021, the amounts presented exclude $16.1 million of insurance licenses, investments and cash classified as assets held for sale related to one of the Other Operating Businesses.

Millions	December 31, 2021
Assets held for sale
Short-term investments, at fair value	$	7.8
Cash (restricted $89.2)	111.6
Premiums and commissions receivable	85.0
Goodwill and other intangible assets	725.4
Other assets	59.2
Total assets held for sale	$	989.0
Liabilities held for sale
Debt	$	272.1
Premiums payable	135.9
Contingent consideration	6.8
Other liabilities	80.5
Total liabilities held for sale	495.3
Net assets held for sale	$	493.7

Earnings Per Share from Discontinued Operations

White Mountains calculates earnings per share using the two-class method, which allocates earnings between common and unvested restricted common shares. Both classes of shares participate equally in earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares. Diluted earnings per share amounts are also impacted by the net effect of potentially dilutive common shares outstanding. The following table presents the Company’s computation of earnings per share for discontinued operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: net income (loss) from continuing operations	$	(23.6)	$	(389.2)	$	(252.3)	$	(356.8)
Less: net (income) loss from continuing operations attributable to    non-controlling interests	$	18.8	$	12.5	$	102.2	$	52.6
Total gain (loss) from discontinued operations attributable to White    Mountains’s common shareholders (1)	$	893.0	$	5.3	$	902.5	$	(4.0)
Allocation of earnings to participating restricted common shares (2)	(11.8)		(.1)		(10.8)		—
Basic and diluted earnings per share numerators (3)	$	881.2	$	5.2	$	891.7	$	(4.0)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings (losses) per share (in dollars) -    discontinued operations:	$	308.59	$	1.72	$	304.97	$	(1.29)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - Sirius Group and net (income) loss from discontinued operations attributable to non-controlling interests.

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three and nine months ended September 30, 2022 and 2021.

(4) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

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Basis of Presentation and Significant Accounting Policies (Policies)

9 Months Ended

Sep. 30, 2022

Accounting Policies [Abstract]

Basis of Presentation

Basis of Presentation

White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”) is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report.

The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of the Company, its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation.

The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.

These interim financial statements include all adjustments considered necessary by management to fairly state the financial position, results of operations and cash flows of White Mountains. These interim financial statements may not be indicative of financial results for the full year and should be read in conjunction with the Company’s 2021 Annual Report on Form 10-K.

Reportable Segments

Reportable Segments

White Mountains has determined its reportable segments based on the nature of the underlying businesses, the manner in which the Company’s subsidiaries and affiliates are organized and managed and the organization of the financial information provided to the chief operating decision maker to assess performance and make decisions regarding allocation of resources. As of September 30, 2022, White Mountains’s reportable segments were HG Global/BAM, Ark and Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations.

The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM (the “BAM Surplus Notes”). As of September 30, 2022 and December 31, 2021, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a variable interest entity for which White Mountains is the primary beneficiary. BAM’s results are all attributed to non-controlling interests.

The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. Ark underwrites select coverages through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”) and its wholly-owned subsidiary Group Ark Insurance Limited (“GAIL”). White Mountains acquired a controlling ownership interest in Ark on January 1, 2021 (the “Ark Transaction”). See Note 2 — “Significant Transactions.” As of September 30, 2022 and December 31, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within results of operations and other comprehensive income are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.

The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions typically are structured as minority preferred equity stakes with distribution rights, generally tied to gross revenues and designed to generate strong, stable cash yields. As of September 30, 2022 and December 31, 2021, White Mountains owned 89.3% and 99.3% of the basic units outstanding (76.1% and 84.7% on a fully diluted, fully converted basis). White Mountains’s Other Operations consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC (“WM Capital”), its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/DavidShield”), Elementum Holdings LP (“Elementum”), and certain other consolidated and unconsolidated entities (“Other Operating Businesses”) and certain other assets.

Discontinued Operations

Discontinued Operations

On August 1, 2022, White Mountains Holdings (Luxembourg) S.à r.l. (“WTM Holdings Seller”), an indirect wholly owned subsidiary of White Mountains, completed the previously announced sale of White Mountains Catskill Holdings, Inc. and NSM Insurance HoldCo, LLC (“NSM” and, collectively with White Mountains Catskill Holdings, Inc., the “NSM Group”) to Riser Merger Sub, Inc., an affiliate of The Carlyle Group Inc. (the “NSM Transaction”), pursuant to the terms of the securities purchase agreement, dated as of May 9, 2022. See Note 2 — “Significant Transactions.” NSM is a full-service managing general agent (“MGA”) and program administrator with delegated binding authorities for specialty property and casualty insurance. As of December 31, 2021, White Mountains owned 96.5% of the basic units outstanding of NSM (87.3% on a fully diluted, fully converted basis).

As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

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Significant Transactions (Tables)

9 Months Ended

Sep. 30, 2022

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Schedule of Recognized Identified Assets Acquired and Liabilities Assumed

The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date:

Millions	As of January 1, 2021
Investments	$	594.3
Cash	52.0		(1)
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696.0)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	$	283.6

(1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction.

The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022:

$ in Millions	Goodwill and Other intangible asset (1)		Acquisition Date
Acquisition of subsidiary/ asset
Ark	$	292.5	January 1, 2021
Other Operations	$	86.6	Various

(1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

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Investment Securities (Tables)

9 Months Ended

Sep. 30, 2022

Investments, Debt and Equity Securities [Abstract]

Pre-tax net investment income

The following table presents pre-tax net investment income for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Fixed maturity investments	$	11.1	$	8.2	$	28.6	$	21.9
Short-term investments	6.7		—		7.2		.5
Common equity securities	.1		.1		.2		.1
Other long-term investments	17.1		12.0		45.9		37.1
Amount attributable to TPC Providers	(.3)		(.2)		(.8)		(.8)
Total investment income	34.7		20.1		81.1		58.8
Third-party investment expenses	(.8)		(.6)		(1.5)		(1.6)
Net investment income, pre-tax	$	33.9	$	19.5	$	79.6	$	57.2

Schedule of net realized and unrealized investment gains and losses

The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Realized investment gains (losses)
Fixed maturity investments	$	(4.9)	$	1.0	$	(10.8)	$	3.8
Short-term investments	(.1)		(.3)		(.4)		—
Common equity securities	—		—		—		.4
Investment in MediaAlpha	—		—		—		160.3
Other long-term investments	3.4		9.2		24.1		0.9
Net realized investment gains (losses)	(1.6)		9.9		12.9		165.4
Unrealized investment gains (losses)
Fixed maturity investments	(58.8)		(7.9)		(192.9)		(27.0)
Short-term investments	(2.1)		—		(2.6)		—
Common equity securities	4.3		1.6		(6.3)		7.3
Investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(485.8)
Other long-term investments	27.5		28.4		40.8		112.3
Net unrealized investment gains (losses)	(47.7)		(374.7)		(274.3)		(393.2)
Net realized and unrealized investment gains (losses), before    amount attributable to TPC providers(1)	(49.3)		(364.8)		(261.4)		(227.8)
Amount attributable to TPC Providers	1.3		(1.7)		6.2		(6.5)
Net realized and unrealized investment gains (losses)	$	(48.0)	$	(366.5)	$	(255.2)	$	(234.3)
Fixed maturity and short-term investments
Net realized and unrealized investment gains (losses)	$	(65.9)	$	(7.2)	$	(206.7)	$	(23.2)
Less: net realized and unrealized gains (losses) on investment           securities sold during the period	.1		(5.7)		(3.0)		(6.9)
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(66.0)	$	(1.5)	$	(203.7)	$	(16.3)
Common equity securities and investment in MediaAlpha
Net realized and unrealized investment gains (losses) on common    equity securities	$	4.3	$	1.6	$	(6.3)	$	7.7
Net realized and unrealized investment gains (losses) from    investment in MediaAlpha	(18.6)		(396.8)		(113.3)		(325.5)
Total net realized and unrealized investment gains (losses)	(14.3)		(395.2)		(119.6)		(317.8)
Less: net realized and unrealized gains (losses) on investment          securities sold during the period	—		.4		—		20.3
Net unrealized investment gains (losses) on investment    securities held at the end of the period	$	(14.3)	$	(395.6)	$	(119.6)	$	(338.1)

(1) For the three months ended September 30, 2022 and 2021, includes $(22.6) and $(7.0) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2022 and 2021, includes $(44.4) and $(7.4) of realized and unrealized investment gains (losses) related to foreign currency exchange.

Net unrealized investment gains (losses) for Level 3 investments

The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and nine months ended September 30, 2022 and 2021 for investments still held at the end of the period:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Other long-term investments	$	40.8	$	26.5	$	57.7	$	75.5
Total net unrealized investment gains, pre-tax - Level 3 investments	$	40.8	$	26.5	$	57.7	$	75.5

Investment holdings, equity securities, convertible fixed maturities and other long-term investments

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses) and carrying values of White Mountains’s fixed maturity investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	227.9	$	—	$	(11.0)	$	—	$	216.9
Debt securities issued by corporations	1,068.8		—		(91.2)		(3.1)		974.5
Municipal obligations	289.3		—		(24.4)		—		264.9
Mortgage and asset-backed securities	278.3		—		(37.6)		—		240.7
Collateralized loan obligations	169.7		—		(7.6)		(4.8)		157.3
Total fixed maturity investments	$	2,034.0	$	—	$	(171.8)	$	(7.9)	$	1,854.3

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	212.1	$	.5	$	(1.1)	$	—	$	211.5
Debt securities issued by corporations	993.3		8.7		(8.7)		(.4)		992.9
Municipal obligations	276.4		16.8		(1.3)		—		291.9
Mortgage and asset-backed securities	277.2		2.9		(2.5)		—		277.6
Collateralized loan obligations	136.5		—		(.4)		(1.1)		135.0
Total fixed maturity investments	$	1,895.5	$	28.9	$	(14.0)	$	(1.5)	$	1,908.9

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of common equity securities, White Mountains’s investment in MediaAlpha and other long-term investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	324.2	$	32.7	$	(8.7)	$	(15.4)	$	332.8
Investment in MediaAlpha	$	—	$	148.2	$	—	$	—	$	148.2
Other long-term investments	$	1,390.7	$	345.0	$	(90.0)	$	(23.0)	$	1,622.7

	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	236.3	$	16.1	$	—	$	(1.3)	$	251.1
Investment in MediaAlpha	$	—	$	261.6	$	—	$	—	$	261.6
Other long-term investments	$	1,186.7	$	239.0	$	(44.1)	$	(3.8)	$	1,377.8

Schedule of fixed maturity investment holdings

The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2022. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.

	September 30, 2022
Millions	Cost or Amortized Cost		Carrying Value
Due in one year or less	$	207.5	$	203.8
Due after one year through five years	917.9		849.4
Due after five years through ten years	354.8		309.3
Due after ten years	105.8		93.8
Mortgage and asset-backed securities and collateralized loan obligations	448.0		398.0
Total fixed maturity investments	$	2,034.0	$	1,854.3

Fair value measurements by level, investment securities

The following tables present White Mountains’s fair value measurements for investments as of September 30, 2022 and December 31, 2021 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate.

	September 30, 2022
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	216.9	$	216.9	$	—	$	—
Debt securities issued by corporations:
Financials	269.0		—		269.0		—
Consumer	181.4		—		181.4		—
Industrial	115.8		—		115.8		—
Healthcare	114.3		—		114.3		—
Technology	110.8		—		110.8		—
Utilities	75.9		—		75.9		—
Communications	49.1		—		49.1		—
Energy	36.1		—		36.1		—
Materials	22.1		—		22.1		—
Total debt securities issued by corporations	974.5		—		974.5		—
Municipal obligations	264.9		—		264.9		—
Mortgage and asset-backed securities	240.7		—		240.7		—
Collateralized loan obligations	157.3		—		157.3		—
Total fixed maturity investments	1,854.3		216.9		1,637.4		—
Short-term investments	1,196.4		1,196.4		—		—
Common equity securities (1)	332.8		46.4		286.4		—
Investment in MediaAlpha	148.2		148.2		—		—
Other long-term investments	1,058.0		—		13.9		1,044.1
Other long-term investments — NAV (2)	564.7		—		—		—
Total other long-term investments	1,622.7		—		13.9		1,044.1
Total investments	$	5,154.4	$	1,607.9	$	1,937.7	$	1,044.1

(1) Consist of investments in exchange traded funds (“ETFs”) and listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at net asset value (“NAV”) using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

	December 31, 2021
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	211.5	$	211.5	$	—	$	—
Debt securities issued by corporations:
Financials	264.2		—		264.2		—
Consumer	178.1		—		178.1		—
Technology	117.9		—		117.9		—
Industrial	112.9		—		112.9		—
Healthcare	112.8		—		112.8		—
Utilities	70.9		—		70.9		—
Communications	56.0		—		56.0		—
Energy	48.0		—		48.0		—
Materials	32.1		—		32.1		—
Total debt securities issued by corporations	992.9		—		992.9		—
Municipal obligations	291.9		—		291.9		—
Mortgage and asset-backed securities	277.6		—		277.6		—
Collateralized loan obligations	135.0		—		135.0		—
Total fixed maturity investments	1,908.9		211.5		1,697.4		—
Short-term investments	465.9		465.9		—		—
Common equity securities (1)	251.1		—		251.1		—
Investment in MediaAlpha	261.6		261.6		—		—
Other long-term investments	895.3		—		4.7		890.6
Other long-term investments — NAV (2)	482.5		—		—		—
Total other long-term investments	1,377.8		—		4.7		890.6
Total investments	$	4,265.3	$	939.0	$	1,953.2	$	890.6

(1) Consist of investments in listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

Debt securities issued by corporations, credit ratings

The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
AAA	$	11.2	$	12.0
AA	90.5		85.0
A	524.0		490.4
BBB	343.0		396.8
Other	5.8		8.7
Debt securities issued by corporations (1)	$	974.5	$	992.9

(1)    Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.

Mortgage-backed, asset-backed securities

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022						December 31, 2021
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	114.1	$	114.1	$	—	$	125.4	$	125.4	$	—
FHLMC	74.5		74.5		—		90.5		90.5		—
GNMA	28.9		28.9		—		40.1		40.1		—
Total agency (1)	217.5		217.5		—		256.0		256.0		—
Non-agency: Residential	.4		.4		—		.5		.5		—
Total non-agency	.4		.4		—		.5		.5		—
Total mortgage-backed securities	217.9		217.9		—		256.5		256.5		—
Other asset-backed securities:
Credit card receivables	11.9		11.9		—		12.3		12.3		—
Vehicle receivables	10.9		10.9		—		8.8		8.8		—
Total other asset-backed securities	22.8		22.8		—		21.1		21.1		—
Total mortgage and asset-backed securities	240.7		240.7		—		277.6		277.6		—
Collateralized loan obligations	157.3		157.3		—		135.0		135.0		—
Total mortgage and asset-backed securities and collateralized loan obligations	$	398.0	$	398.0	$	—	$	412.6	$	412.6	$	—

(1)    Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed

by a government sponsored entity (i.e., FNMA, FHLMC).

Schedule of carrying values for other long-term investments

The following table presents the carrying values of White Mountains’s other long-term investments as of September 30, 2022 and December 31, 2021:

	Fair Value at
Millions	September 30, 2022		December 31, 2021
Kudu’s Participation Contracts	$	813.2	$	669.5
PassportCard/DavidShield	132.0		120.0
Elementum Holdings, L.P.	45.0		45.0
Other unconsolidated entities (1)	37.0		34.4
Total unconsolidated entities	1,027.2		868.9
Private equity funds and hedge funds	239.8		153.8
Bank loan fund	155.7		163.0
Lloyd’s trust deposits	117.8		113.8
ILS funds	49.4		51.9
Private debt investments	13.0		14.1
Other	19.8		12.3
Total other long-term investments	$	1,622.7	$	1,377.8

(1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, convertible preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments.

Other long-term investments

The following table presents the fair value of investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments
Private equity funds
Aerospace/Defense/Government	$	102.9	$	45.1	$	69.8	$	11.8
Financial services	77.9		54.9		67.7		29.3
Real estate	4.3		2.5		4.3		2.9
Total private equity funds	185.1		102.5		141.8		44.0
Hedge funds
Long/short equity financials and business services	49.3		—		—		—
European small/mid cap	5.4		—		12.0		—
Total hedge funds	54.7		—		12.0		—
Total private equity funds and hedge funds    included in other long-term investments	$	239.8	$	102.5	$	153.8	$	44.0

Fair value of private equity funds subject to lock-up periods

The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2022:

Millions	1 – 3 years	3 – 5 years	5 – 10 years	>10 years	Total
Private equity funds — expected lock-up period remaining	$27.5	$19.0	$135.4	$3.2	$185.1

Rollforward of fair value investments by level

The following table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the nine months ended September 30, 2022 and 2021:

Level 3 Investments
Millions	Other Long-term Investments			Other Long-term Investments
Balance at December 31, 2021	$	890.6	Balance at December 31, 2020	$	614.2
Net realized and unrealized gains	57.3		Net realized and unrealized gains	79.0
Amortization/accretion	—		Amortization/accretion	—
Purchases	127.9		Purchases	143.6
Sales	(31.7)		Sales	(31.9)
Effect of Ark Transaction	—		Effect of Ark Transaction	9.6
Transfers in	—		Transfers in	—
Transfers out	—		Transfers out	—
Balance at September 30, 2022	$	1,044.1	Balance at September 30, 2021	$	814.5

Schedule of significant unobservable inputs used in estimating the fair value of investment securities

The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s other long-term investments, classified within Level 3 as of September 30, 2022 and December 31, 2021. The tables below exclude $42.9 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds.

$ in Millions	September 30, 2022
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$813.2	17% - 24%	7x - 16x
PassportCard/DavidShield	Discounted cash flow	$132.0	24%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	18%	4%
Private debt investments	Discounted cash flow	$11.0	10%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 9.7x.

(4) As of September 30, 2022, three of Kudu’s Participation Contracts with a total fair value of $312.4 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(5) In 2022, Kudu deployed a total of $97.9 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

$ in Millions	December 31, 2021
Description	Valuation Technique(s) (1)	Fair Value (2)	Unobservable Inputs
			Discount Rate (6)	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)
Kudu’s Participation Contracts (3)(4)(5)	Discounted cash flow	$669.5	18% - 23%	7x - 13x
PassportCard/DavidShield	Discounted cash flow	$120.0	23%	4%
Elementum Holdings, L.P.	Discounted cash flow	$45.0	17%	4%
Private debt investments	Discounted cash flow	$9.4	8%	N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 20% and 10x.

(4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management.

(5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction.

(6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.

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Goodwill and Other Intangible Assets (Tables)

9 Months Ended

Sep. 30, 2022

Goodwill and Intangible Assets Disclosure [Abstract]

Schedule of Intangible Assets and Goodwill

The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by reportable segment as of September 30, 2022 and December 31, 2021:

$ in Millions	Weighted Average Economic  Life (in years)	September 30, 2022						December 31, 2021
		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value		Acquisition Date Fair Value		Accumulated Amortization		Net Carrying Value
Goodwill:
Ark	N/A	$	116.8	$	—	$	116.8	$	116.8	$	—	$	116.8
Kudu	N/A	7.6		—		7.6		7.6				7.6
Other Operations	N/A	51.1		—		51.1		17.9		—		17.9
Total goodwill		175.5		—		175.5		142.3		—		142.3
Other intangible assets:
Ark
Underwriting capacity	N/A	175.7		—		175.7		175.7		—		175.7
Kudu
Trade names	7	2.2		1.1		1.1		2.2		.9		1.3
Other Operations
Trade names	15.9	17.9		2.4		15.5		8.2		1.5		6.7
Customer relationships	12.4	29.5		6.6		22.9		18.8		4.5		14.3
Other	12.1	2.8		.3		2.5		.3		.1		.2
Subtotal		50.2		9.3		40.9		27.3		6.1		21.2
Total other intangible assets		228.1		10.4		217.7		205.2		7.0		198.2
Total goodwill and other intangible assets		$	403.6	$	10.4	393.2		$	347.5	$	7.0	340.5
Goodwill and other intangible assets attributed to    non-controlling interests						(103.1)						(91.8)
Goodwill and other intangible assets included in White Mountains’s    common shareholders’ equity						$	290.1					$	248.7

The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	201.8	$	196.2	$	398.0	$	151.5	$	201.1	$	352.6
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)		—		(3.4)		(.4)		—		(.4)
Amortization	—		(1.4)		(1.4)		—		(2.0)		(2.0)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

	Nine Months Ended September 30,
	2022						2021
Millions	Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets		Goodwill		Other Intangible Assets		Total Goodwill and Other Intangible Assets
Beginning balance	$	142.3	$	198.2	$	340.5	$	19.2	$	26.4	$	45.6
Ark Transaction	—		—		—		116.8		175.7		292.5
Acquisition of businesses (1)	59.5		—		59.5		15.8		—		15.8
Attribution of acquisition date fair value estimates    between goodwill and other intangible assets (1)	(22.9)		22.9		—		(9.3)		9.3		—
Measurement period adjustments (2)	(3.4)				(3.4)		(.7)		.1		(.6)
Amortization	—		(3.4)		(3.4)		—		(3.1)		(3.1)
Ending balance	$	175.5	$	217.7	$	393.2	$	141.8	$	208.4	$	350.2

(1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period.

(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the nine

months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

Schedule of Recognized Identified Assets Acquired and Liabilities Assumed

The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date:

Millions	As of January 1, 2021
Investments	$	594.3
Cash	52.0		(1)
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696.0)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	$	283.6

(1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction.

The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022:

$ in Millions	Goodwill and Other intangible asset (1)		Acquisition Date
Acquisition of subsidiary/ asset
Ark	$	292.5	January 1, 2021
Other Operations	$	86.6	Various

(1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

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Loss and Loss Adjustment Expense Reserves (Tables)

9 Months Ended

Sep. 30, 2022

Insurance Loss Reserves [Abstract]

Schedule of Liability for Unpaid Claims and Claims Adjustment Expense

The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Gross beginning balance	$	1,022.1	$	760.0	$	894.7	$	696.0
Less: beginning reinsurance recoverable on unpaid losses (1)	(375.5)		(425.3)		(428.9)		(433.4)
Net loss and LAE reserves	646.6		334.7		465.8		262.6
Loss and LAE incurred relating to:
Current year losses	222.9		141.9		491.8		269.0
Prior year losses	(9.2)		(12.7)		(35.6)		(21.2)
Net incurred losses and LAE	213.7		129.2		456.2		247.8
Loss and LAE paid relating to:
Current year losses	(6.1)		(9.0)		(20.8)		(11.5)
Prior year losses	(37.0)		(20.3)		(130.8)		(62.1)
Net paid loss and LAE	(43.1)		(29.3)		(151.6)		(73.6)
Change in TPC Providers’ participation (2)	—		—		57.5		(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)		(1.2)		(19.9)		(1.2)
Net ending balance	808.0		433.4		808.0		433.4
Plus: ending reinsurance recoverable on unpaid losses (3)	521.4		457.5		521.4		457.5
Gross ending balance	$	1,329.4	$	890.9	$	1,329.4	$	890.9

(1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $182.4 and $314.6 for the three months ended September 30, 2022 and 2021 and $276.8 and $319.2 for the nine months ended September 30, 2022 and 2021.

(2) Amount represents the impact to net loss and LAE reserves due to a change in the TPC Providers’ participation related to the annual reinsurance to close (“RITC”) process.

(3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $168.0 and $299.9 as of September 30, 2022 and 2021.

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Third-Party Reinsurance (Tables)

9 Months Ended

Sep. 30, 2022

Reinsurance Disclosures [Abstract]

Effects of Reinsurance

The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for Ark for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Gross	$	215.5	$	162.4	$	1,252.5	$	895.0
Ceded	(22.9)		(41.5)		(246.0)		(169.5)
Net written premiums	$	192.6	$	120.9	$	1,006.5	$	725.5
Earned premiums:
Gross	$	454.9	$	284.5	$	966.6	$	622.0
Ceded	(108.8)		(71.1)		(208.8)		(186.2)
Net earned premiums	$	346.1	$	213.4	$	757.8	$	435.8
Losses and loss adjustment expenses:
Gross	$	391.4	$	193.5	$	712.9	$	372.7
Ceded	(177.7)		(64.3)		(256.7)		(124.9)
Net losses and loss adjustment expenses	$	213.7	$	129.2	$	456.2	$	247.8

The following table provides a listing of Ark’s remaining gross and net reinsurance recoverables, excluding amounts attributable to TPC Providers, by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) rating and the percentage of total recoverables as of September 30, 2022:

$ in Millions	As of September 30, 2022
A.M. Best Rating(1)	Gross		Collateral		Net		% of Total
A+ or better	$	178.3	$	—	$	178.3	67.7	%
A- to A	78.9		—		78.9		29.9
B++ or lower and not rated	125.7		119.4		6.3		2.4
Total	$	382.9	$	119.4	$	263.5	100.0	%

(1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good).

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Debt (Tables)

9 Months Ended

Sep. 30, 2022

Debt Disclosure [Abstract]

Schedule of debt outstanding

The following table presents White Mountains’s debt outstanding as of September 30, 2022 and December 31, 2021:

$ in Millions	September 30, 2022		Effective   Rate	(1)	December 31, 2021		Effective   Rate	(1)
HG Global Senior Notes	$	150.0	8.6%		$	—	N/A
Unamortized discount and issuance cost	(3.6)				—
HG Global Senior Notes, carrying value	146.4				—
Ark 2007 Subordinated Notes, carrying value	30.0				30.0
Ark 2021 Notes Tranche 1	37.6				44.2
Ark 2021 Notes Tranche 2	47.0				47.0
Ark 2021 Notes Tranche 3	70.0				70.0
Unamortized issuance cost	(4.6)				(5.3)
Ark 2021 Subordinated Notes, carrying value	150.0				155.9
Total Ark Subordinated Notes, carrying value	180.0		7.3%		185.9		6.9%
Kudu Credit Facility	260.4		5.6%		225.4		4.3%
Unamortized issuance cost	(6.9)				(7.2)
Kudu Credit Facility, carrying value	253.5				218.2
Other Operations debt	36.4		7.1%		17.1		7.5%
Unamortized issuance cost	(.8)				(.3)
Other Operations debt, carrying value	35.6				16.8
Total debt	$	615.5			$	420.9

 (1) Effective rate includes the effect of the amortization of debt issuance costs.

The following table presents the change in debt under the Kudu Bank Facility and Kudu Credit Facility for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Kudu Bank Facility
Beginning balance	$	—	$	—	$	—	$	89.2
Term loans
Borrowings	—		—		—		3.0
Repayments	—		—		—		(92.2)
Ending balance	$	—	$	—	$	—	$	—
Kudu Credit Facility
Beginning balance	$	260.4	$	203.0	$	225.4	$	—
Term loans
Borrowings	—		—		35.0		203.0
Repayments	—		—		—		—
Ending balance	$	260.4	$	203.0	$	260.4	$	203.0

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Municipal Bond Guarantee Insurance (Tables)

9 Months Ended

Sep. 30, 2022

Guarantees [Abstract]

Schedule of Municipal Bond Guarantee Insured Obligations

The following table presents a schedule of BAM’s insured obligations as of September 30, 2022 and December 31, 2021:

	September 30, 2022		December 31, 2021
Contracts outstanding	13,094		12,350
Remaining weighted average contract period outstanding (in years)	10.8		10.8
Contractual debt service outstanding (in millions):
Principal	$	98,619.0	$	89,196.5
Interest	47,595.0		41,486.5
Total debt service outstanding	$	146,214.0	$	130,683.0
Gross unearned insurance premiums (in millions)	$	286.7	$	266.3

Financial Guarantee Insurance Contracts, Premium Received over Contract Period

The following table presents a schedule of BAM’s future premium revenues as of September 30, 2022:

Millions	September 30, 2022
October 1, 2022 - December 31, 2022	$	6.9
January 1, 2023 - March 31, 2023	6.8
April 1, 2023 - June 30, 2023	6.7
July 1, 2023 - September 30, 2023	6.6
October 1, 2023 - December 31, 2023	6.4
Total 2023	26.5
2024	24.9
2025	23.2
2026	21.6
2027	20.1
2028 and thereafter	163.5
Total gross unearned insurance premiums	$	286.7

Schedule of Net Written Premiums

The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Written premiums:
Direct	$	18.4	$	12.8	$	44.9	$	34.5
Assumed	1.3		—		1.3		4.5
Gross written premiums (1)	$	19.7	$	12.8	$	46.2	$	39.0
Earned premiums:
Direct	$	6.5	$	5.9	$	22.0	$	16.8
Assumed	.6		.8		4.0		2.8
Gross earned premiums (1)	$	7.1	$	6.7	$	26.0	$	19.6

(1) There are no ceded premium amounts in the periods presented and gross earned premiums are equivalent to net written premiums and net earned premiums.

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Earnings Per Share (Tables)

9 Months Ended

Sep. 30, 2022

Earnings Per Share [Abstract]

Computation of earnings per share

The following table presents the Company’s computation of earnings per share from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: total income (loss) from discontinued operations, net of tax (1)	893.1		5.3		903.2		(5.1)
Less: net (income) loss from discontinued operations attributable    to non-controlling interests	$	(.1)	$	—	$	(.7)	$	1.1
Net income (loss) from continuing operations attributable to    White Mountains’s common shareholders	$	(4.8)	$	(376.7)	$	(150.1)	$	(304.2)
Allocation of (earnings) losses to participating restricted    common shares (2)	.1		4.6		1.8		3.5
Basic and diluted earnings (losses) per share numerators	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (3)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings (losses) per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings per share (in dollars) - continuing    operations:
Distributed earnings - dividends declared and paid	$	—	$	—	$	1.00	$	1.00
Undistributed earnings (losses)	(1.66)		(121.90)		(51.73)		(99.16)
Basic and diluted earnings (losses) per share	$	(1.66)	$	(121.90)	$	(50.73)	$	(98.16)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group and net gain (loss) from sale of discontinued operations, net of tax - Sirius Group. See Note 19 — “Held for Sale and Discontinued Operations.”

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

Schedule of Undistributed Net Earnings (Losses) from Continuing Operations

The following table presents the undistributed net earnings (losses) from continuing operations for the three and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.”

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
Millions	2022		2021		2022		2021
Undistributed net earnings (losses) - continuing operations:
Net income (losses) attributable to White Mountains’s common    shareholders, net of restricted common share amounts	$	(4.7)	$	(372.1)	$	(148.3)	$	(300.7)
Dividends declared, net of restricted common share amounts (1)	—		—		(3.0)		(3.1)
Total undistributed net earnings (losses), net of restricted    common share amounts	$	(4.7)	$	(372.1)	$	(151.3)	$	(303.8)

(1) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

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Employee Share-Based Incentive Compensation Plans (Tables)

9 Months Ended

Sep. 30, 2022

Share-Based Payment Arrangement [Abstract]

Summary of performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan

The following table presents the performance share activity for the three and nine months ended September 30, 2022 and 2021 for performance shares granted under the WTM Incentive Plan:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense		Target Performance Shares Outstanding	Accrued Expense
Beginning of period	39,449	$	41.2	41,252	$	45.7	40,828	$	42.2	42,458	$	56.3
Shares paid (1)	—	—		(219)	(.6)		(14,625)	(26.4)		(14,336)	(35.2)
New grants	—	—		—	—		13,225	—		13,475	—
Forfeitures and   cancellations (2)	—	(.1)		(205)	.2		21	(.2)		(769)	.4
Expense recognized	—	11.9		—	(6.5)		—	37.4		—	17.3
End of period	39,449	$	53.0	40,828	$	38.8	39,449	$	53.0	40,828	$	38.8

(1) Includes WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target and WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in March 2021 at 200% of target. 

(2) Amounts include changes in assumed forfeitures, as required under GAAP.

Share-based Compensation, Performance Shares Award Outstanding Activity

The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of September 30, 2022 for each performance cycle:

	Nine Months Ended September 30, 2022
Millions, except share amounts	Target Performance Shares Outstanding	Accrued Expense
Performance cycle:
2020 – 2022	13,350	$	31.9
2021 – 2023	13,475	14.7
2022 – 2024	13,225	7.2
Sub-total	40,050	53.8
Assumed forfeitures	(601)	(.8)
September 30, 2022	39,449	$	53.0

Summary of restricted shares activity

Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,						Nine Months Ended September 30,
	2022			2021			2022			2021
Millions,  except share amounts	Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value		Restricted Shares	Unamortized Issue Date Fair Value
Non-vested,
Beginning of period	38,350	$	23.0	38,280	$	23.2	37,850	$	15.9	43,105	$	15.2
Issued	—	—		—	—		13,225	13.8		13,475	16.1
Vested	—	—		(219)	—		(12,725)	—		(17,936)	—
Forfeited	—	—		(211)	(.2)		—	—		(794)	(.8)
Expense recognized	—	(3.8)		—	(3.6)		—	(10.5)		—	(11.1)
End of period	38,350	$	19.2	37,850	$	19.4	38,350	$	19.2	37,850	$	19.4

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Leases (Tables)

9 Months Ended

Sep. 30, 2022

Leases [Abstract]

Summary of Lease Expense

The following table summarizes net lease expense recognized in White Mountains’s consolidated statements of operations for the three and nine months ended September 30, 2022 and 2021:

Millions	Three Months Ended September 30,				Nine Months Ended September 30,
Lease Cost	2022		2021		2022		2021
Lease cost	$	1.9	$	1.9	$	5.9	$	4.8
Less: sublease income	.2		.1		.5		.3
Net lease cost	$	1.7	$	1.8	$	5.4	$	4.5

Schedule of Future Maturities of Operating Lease Liabilities, Lessee

The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2022:

Millions	As of September 30, 2022
Remainder of 2022	$	1.7
2023	8.1
2024	7.1
2025	4.9
2026	2.6
Thereafter	5.0
Total undiscounted lease payments	29.4
Less: present value adjustment	2.9
Operating lease liabilities	$	26.5

Schedule of Right-of-Use Assets and Lease Liabilities

The following tables present lease related assets and liabilities by reportable segment as of September 30, 2022 and December 31, 2021:

	As of September 30, 2022
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	6.2	$	6.6	$	5.9	$	5.8	$	24.5	4.1%
Lease liabilities	$	6.7	$	6.6	$	6.8	$	6.4	$	26.5

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

	As of December 31, 2021
Millions	HG/BAM		Ark		Kudu		Other Operations		Total		Weighted Average Incremental Borrowing Rate (1)
ROU lease assets	$	7.6	$	7.0	$	6.4	$	7.1	$	28.1	4.0%
Lease liabilities	$	8.1	$	7.0	$	7.1	$	7.8	$	30.0

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

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Non-controlling Interests (Tables)

9 Months Ended

Sep. 30, 2022

Noncontrolling Interest [Abstract]

Non-controlling Interests

The following table presents the balance of non-controlling interests included in White Mountains’s total equity and the ownership interests held by non-controlling shareholders as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
$ in Millions	Non-controlling Percentage (1)		Non-controlling Equity		Non-controlling Percentage (1)		Non-controlling Equity
Non-controlling interests, excluding BAM
HG Global	3.1	%	$	(.3)	3.1	%	$	8.9
Ark	28.0	%	217.1		28.0	%	230.7
Kudu	10.7	%	80.8		.7	%	12.4
NSM (2)	—	%	—		3.5	%	16.7
Other	various		20.8		various		11.9
Total, excluding BAM			318.4				280.6
BAM	100.0	%	(160.1)		100.0	%	(124.0)
Total non-controlling interests			$	158.3			$	156.6

(1) The non-controlling percentage represents the basic ownership interests held by non-controlling shareholders with the exception of HG Global, for which the non-controlling percentage represents the preferred share ownership held by non-controlling shareholders.

(2) As a result of the NSM Transaction, NSM has been classified as discontinued operations through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations.”

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Segment Information (Tables)

9 Months Ended

Sep. 30, 2022

Segment Reporting [Abstract]

Schedule of Financial Information for White Mountains' Segments

The following tables present the financial information for White Mountains’s segments:

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2022
Earned insurance premiums	$	7.1	$	346.1	$	—	$	—	$	353.2
Net investment income	5.7		4.9		14.8		8.5		33.9
Net realized and unrealized investment    gains (losses)	(38.8)		(14.4)		41.1		(17.3)		(29.4)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(18.6)		(18.6)
Commission revenues	—		—		—		3.2		3.2
Other revenues	1.3		6.6		—		33.0		40.9
Total revenues	(24.7)		343.2		55.9		8.8		383.2
Loss and loss adjustment expenses	—		213.7		—		—		213.7
Insurance and reinsurance acquisition expenses	1.7		74.8		—		—		76.5
Cost of sales	—		—		—		25.0		25.0
General and administrative expenses	15.8		26.9		4.5		39.9		87.1
Amortization of other intangible assets	—		—		—		1.4		1.4
Interest expense	2.0		3.7		4.2		.6		10.5
Total expenses	19.5		319.1		8.7		66.9		414.2
Pre-tax income (loss) from continuing operations	$	(44.2)	$	24.1	$	47.2	$	(58.1)	$	(31.0)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Three Months Ended September 30, 2021
Earned insurance premiums	$	6.7	$	213.4	$	—	$	—	$	220.1
Net investment income	4.4		.6		9.5		5.0		19.5
Net realized and unrealized investment    gains (losses)	(4.0)		.3		18.9		15.3		30.5
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(396.8)		(396.8)
Commission revenues	—		—		—		2.4		2.4
Other revenues	.3		3.4		.1		28.1		31.9
Total revenues	7.4		217.7		28.5		(346.0)		(92.4)
Losses and loss adjustment expenses	—		129.2		—		—		129.2
Insurance and reinsurance acquisition expenses	3.0		53.7		—		—		56.7
Cost of sales	—		—		—		24.0		24.0
General and administrative expenses	12.4		21.8		3.3		14.4		51.9
Amortization of other intangible assets	—		—		—		2.0		2.0
Interest expense	—		2.1		1.9		.4		4.4
Total expenses	15.4		206.8		5.2		40.8		268.2
Pre-tax income (loss) from continuing operations	$	(8.0)	$	10.9	$	23.3	$	(386.8)	$	(360.6)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2022
Earned insurance premiums	$	26.0	$	757.8	$	—	$	—	$	783.8
Net investment income	15.1		9.7		41.2		13.6		79.6
Net realized and unrealized investment    gains (losses)	(114.0)		(76.5)		45.8		2.8		(141.9)
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(113.3)		(113.3)
Commission revenues	—		—		—		8.7		8.7
Other revenues	3.7		10.1		—		89.6		103.4
Total revenues	(69.2)		701.1		87.0		1.4		720.3
Loss and loss adjustment expenses	—		456.2		—		—		456.2
Insurance and reinsurance acquisition expenses	9.5		174.9		—		—		184.4
Cost of sales	—		—		—		68.8		68.8
General and administrative expenses	49.5		79.8		10.2		118.9		258.4
Amortization of other intangible assets	—		—		.2		3.2		3.4
Interest expense	5.4		10.6		10.3		1.2		27.5
Total expenses	64.4		721.5		20.7		192.1		998.7
Pre-tax income (loss) from continuing operations	$	(133.6)	$	(20.4)	$	66.3	$	(190.7)	$	(278.4)

Millions	HG Global/ BAM		Ark		Kudu		Other Operations		Total
Nine Months Ended September 30, 2021
Earned insurance premiums	$	19.6	$	435.8	$	—	$	—	$	455.4
Net investment income	13.2		1.8		26.1		16.1		57.2
Net realized and unrealized investment    gains (losses)	(15.6)		10.3		62.5		34.0		91.2
Net realized and unrealized investment gains    (losses) from investment in MediaAlpha	—		—		—		(325.5)		(325.5)
Commission revenues	—		—		—		7.0		7.0
Other revenues	.9		9.4		.2		57.6		68.1
Total revenues	18.1		457.3		88.8		(210.8)		353.4
Losses and loss adjustment expenses	—		247.8		—		—		247.8
Insurance and reinsurance acquisition expenses	6.5		124.4		—		—		130.9
Cost of sales	—		—		—		45.9		45.9
General and administrative expenses	42.7		84.4		9.0		79.4		215.5
Amortization of other intangible assets	—		—		.2		2.9		3.1
Interest expense	—		4.5		9.2		1.1		14.8
Total expenses	49.2		461.1		18.4		129.3		658.0
Pre-tax income (loss) from continuing operations	$	(31.1)	$	(3.8)	$	70.4	$	(340.1)	$	(304.6)

Schedule of Reconciliation of Revenue from Segments to Consolidated

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Equity-Method Eligible Investments (Tables)

9 Months Ended

Sep. 30, 2022

Equity Method Investments and Joint Ventures [Abstract]

Equity Method Investments

The following table presents the ownership interests and carrying values of White Mountains’s equity method eligible investments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Ownership Interest		Carrying Value		Ownership Interest		Carrying Value
Kudu Participation Contracts (1)	4.1 - 33.0%		$	813.2	3.2 - 32.0%		$	669.5
Investment in MediaAlpha	27.4	%	148.2		28.0	%	261.6
PassportCard/DavidShield	53.8	%	132.0		53.8	%	120.0
Elementum Holdings, L.P.	29.7	%	45.0		29.7	%	45.0
Other equity method eligible investments, at fair value	Under 50.0%		102.7		Under 50.0%		109.3
Other equity method eligible investments, at fair value	50.0% and over		27.7		50.0% and over		17.8

(1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are non-controlling equity interests in the form of revenue and earnings participation contracts.

The following tables present summarized financial information for MediaAlpha as of September 30, 2022 and December 31, 2021 and for the three and nine months ended September 30, 2022 and 2021:

Millions	September 30, 2022		December 31, 2021
Balance sheet data:
Total assets	$	265.2	$	289.8
Total liabilities	$	333.6	$	351.4

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022		2021		2022		2021
Income statement data:
Total revenues	$	89.0	$	152.7	$	335.1	$	483.7
Total expenses	$	110.2	$	157.0	$	379.2	$	488.2
Net income (loss)	$	(21.2)	$	(4.3)	$	(44.1)	$	(4.5)

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Fair Value of Financial Instruments (Tables)

9 Months Ended

Sep. 30, 2022

Fair Value Disclosures [Abstract]

Summary of the fair value and carrying value of financial instruments

The following tables presents the fair value and carrying value of these financial instruments as of September 30, 2022 and December 31, 2021:

	September 30, 2022				December 31, 2021
Millions	Fair Value		Carrying Value		Fair Value		Carrying Value
HG Global Senior Notes	$	146.1	$	146.4	$	—	$	—
Ark 2007 Subordinated Notes	$	26.2	$	30.0	$	27.6	$	30.0
Ark 2021 Subordinated Notes	$	149.4	$	150.0	$	162.8	$	155.9
Kudu Credit Facility	$	265.5	$	253.5	$	246.8	$	218.2
Other Operations debt	$	36.8	$	35.6	$	17.7	$	16.8

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Held for Sale and Discontinued Operations (Tables)

9 Months Ended

Sep. 30, 2022

Discontinued Operations and Disposal Groups [Abstract]

Schedule of Discontinued Operations

The following summarizes the assets and liabilities associated with NSM Group classified as held for sale. As of December 31, 2021, the amounts presented exclude $16.1 million of insurance licenses, investments and cash classified as assets held for sale related to one of the Other Operating Businesses.

Millions	December 31, 2021
Assets held for sale
Short-term investments, at fair value	$	7.8
Cash (restricted $89.2)	111.6
Premiums and commissions receivable	85.0
Goodwill and other intangible assets	725.4
Other assets	59.2
Total assets held for sale	$	989.0
Liabilities held for sale
Debt	$	272.1
Premiums payable	135.9
Contingent consideration	6.8
Other liabilities	80.5
Total liabilities held for sale	495.3
Net assets held for sale	$	493.7

The following summarizes the results of operations, including related income taxes associated with the businesses classified as discontinued operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended September 30,				Nine Months Ended September 30,
Millions	2022 (1)		2021		2022 (1)		2021
Revenues
Commission revenues	$	26.6	$	67.0	$	176.9	$	194.6
Other revenues	7.0		15.3		48.1		46.8
Total revenues - NSM Group	33.6		82.3		225.0		241.4
Expenses
General and administrative expenses	15.7		48.9		126.8		142.4
Broker commission expenses	8.2		20.4		52.9		60.9
Change in fair value of contingent consideration	—		.6		.1		.8
Amortization of other intangible assets	—		8.2		9.1		25.0
Loss on assets held for sale	—		—		—		28.7
Interest expense	1.6		5.9		12.1		17.7
Total expenses - NSM Group	25.5		84.0		201.0		275.5
Pre-tax income (loss) from discontinued operations -    NSM Group	8.1		(1.7)		24.0		(34.1)
Income tax (expense) benefit	(1.8)		7.0		(7.6)		10.3
Net income (loss) from discontinued operations, net of    tax - NSM Group	6.3		5.3		16.4		(23.8)
Net gain (loss) from sale of discontinued operations, net of    tax - NSM Group	886.8		—		886.8		—
Net gain (loss) from sale of discontinued operations, net of    tax - Sirius Group	—		—		—		18.7
Total income (loss) from discontinued operations,    net of tax	893.1		5.3		903.2		(5.1)
Net (income) loss from discontinued operations    attributable to non-controlling interests	(.2)		—		(.8)		1.1
Total income (loss) from discontinued operations    attributable to White Mountains’s common    shareholders	892.9		5.3		902.4		(4.0)
Other comprehensive income (loss) from discontinued    operations, net of tax - NSM Group	.7		(1.7)		(5.2)		.9
Net gain (loss) from foreign currency translation from sale    of discontinued operations, net of tax - NSM Group	2.9		—		2.9		—
Comprehensive income (loss) from discontinued    operations	896.5		3.6		900.1		(3.1)
Other comprehensive income (loss) from discontinued    operations attributable to non-controlling interests	(.1)		—		.2		(.1)
Comprehensive income (loss) from discontinued    operations attributable to White Mountains’s common    shareholders	$	896.4	$	3.6	$	900.3	$	(3.2)

(1) As a result of the NSM Transaction, the results of operations for NSM Group are presented for the periods from July 1, 2022 to August 1, 2022 and January 1, 2022 to August 1, 2022.

Net Change in Cash from Discontinued Operations

The following summarizes the net change in cash associated with the businesses classified as discontinued operations for the nine months ended September 30, 2022 and 2021:

	Nine Months Ended September 30,
Millions	2022		2021
Net cash provided from (used for) operations	$	38.7	$	40.3
Net cash provided from (used for) investing activities	7.1		(54.6)
Net cash used from (used for) financing activities	(17.5)		13.8
Effect of exchange rate changes on cash	4.0		.6
Net change in cash during the period	32.3		.1
Cash balances at beginning of period (includes restricted cash of $89.2 and $78.4)	111.6		126.6
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)	(143.9)		—
Cash balances at end of period (includes restricted cash of $0.0 and $92.2)	—		126.7
Supplemental cash flows information:
Interest paid	$	(12.0)	$	(16.6)
Net income tax payments	$	—	$	—

The following table presents the Company’s computation of earnings per share for discontinued operations for the three and nine months ended September 30, 2022 and 2021:

	Three Months Ended				Nine Months Ended
	September 30,				September 30,
	2022		2021		2022		2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s    common shareholders	$	888.2	$	(371.4)	$	752.4	$	(308.2)
Less: net income (loss) from continuing operations	$	(23.6)	$	(389.2)	$	(252.3)	$	(356.8)
Less: net (income) loss from continuing operations attributable to    non-controlling interests	$	18.8	$	12.5	$	102.2	$	52.6
Total gain (loss) from discontinued operations attributable to White    Mountains’s common shareholders (1)	$	893.0	$	5.3	$	902.5	$	(4.0)
Allocation of earnings to participating restricted common shares (2)	(11.8)		(.1)		(10.8)		—
Basic and diluted earnings per share numerators (3)	$	881.2	$	5.2	$	891.7	$	(4.0)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Basic earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,893.8		3,090.3		2,959.3		3,099.4
Average unvested restricted common shares (4)	(38.3)		(37.8)		(35.5)		(36.0)
Diluted earnings per share denominator	2,855.5		3,052.5		2,923.8		3,063.4
Basic and diluted earnings (losses) per share (in dollars) -    discontinued operations:	$	308.59	$	1.72	$	304.97	$	(1.29)

(1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - Sirius Group and net (income) loss from discontinued operations attributable to non-controlling interests.

(2) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

(3) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three and nine months ended September 30, 2022 and 2021.

(4) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

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Basis of Presentation and Significant Accounting Policies (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021	Jul. 31, 2012
Ark
Basis of Presentation
Percent of shares outstanding	12.50%
Ark | Ark
Basis of Presentation
Ownership interest (as a percent)	72.00%	72.00%
Asset Management (Kudu)
Basis of Presentation
Ownership interest (as a percent)	89.30%	99.30%
Fully diluted ownership interest (as a percent)	76.10%	84.70%
NSM Insurance Group
Basis of Presentation
Ownership interest (as a percent)		96.50%
Fully diluted ownership interest (as a percent)		87.30%
Preferred Stock | HG Global
Basis of Presentation
Ownership interest (as a percent)	96.90%	96.90%
Common equity securities | HG Global
Basis of Presentation
Ownership interest (as a percent)	88.40%	88.40%
HG Global
Basis of Presentation
Percentage of par value of policy reinsured	15.00%
Surplus notes	$ 503.0		$ 503.0
Ark | Ark
Basis of Presentation
Fully diluted ownership interest (as a percent)	63.00%	63.00%
Ark | Ark
Basis of Presentation
Ownership interest (as a percent)	72.00%
Fully diluted ownership interest (as a percent)	63.00%

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Significant Transactions - NSM (Details) - USD ($) $ in Millions		3 Months Ended		9 Months Ended
	Aug. 01, 2022	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Other Significant Noncash Transactions [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group				$ 886.8	$ 18.7
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group		$ 2.9	$ 0.0	2.9	0.0
NSM Insurance Group
Other Significant Noncash Transactions [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group		$ 886.8	$ 0.0	$ 886.8	$ 0.0
Discontinued Operations, Disposed of by Sale | NSM Insurance Group
Other Significant Noncash Transactions [Line Items]
Transaction value	$ 1,400.0
Gain on transaction	875.7
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group	886.8
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9
Compensation and other costs	$ 14.0

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Significant Transactions - Kudu (Details) $ in Millions		9 Months Ended
	May 26, 2022 USD ($)	Sep. 30, 2022 USD ($)	May 25, 2022
Kudu
Other Significant Noncash Transactions [Line Items]
Basic ownership	89.30%		99.10%
Mass Mutual
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 64.1
Kudu Investment Management, LLC
Other Significant Noncash Transactions [Line Items]
Equity capital raised	0.4
White Mountains
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 50.0
Kudu
Other Significant Noncash Transactions [Line Items]
Pre-money valuation	1.3
Pre-money valuation, amount	$ 114.0
Enterprise value excluded		$ 41.1
Kudu
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 114.5

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Significant Transactions - Ark (Details) - USD ($) $ in Millions			3 Months Ended			9 Months Ended
	Jan. 01, 2021	Oct. 01, 2020	Sep. 30, 2022	Sep. 30, 2021	Mar. 31, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021	Dec. 31, 2020
Ark
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									$ 366.3
Other Operations
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									646.3
Goodwill and other intangible assets			$ 92.0			$ 92.0		$ 39.1
Ark
Other Significant Noncash Transactions [Line Items]
Goodwill and other intangible assets			292.5			292.5		292.5
Contingent consideration			32.9			32.9		28.0
Change in fair value of contingent consideration liabilities			2.7	$ 1.5		4.9	$ 1.5
Ark | In-force Business Acquired
Other Significant Noncash Transactions [Line Items]
Amortization			$ 0.7	11.0		$ 6.8	54.9
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			72.00%			72.00%
Fully diluted ownership interest (as a percent)			63.00%			63.00%
Ark | Lloyd
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									$ 280.0
Ark
Other Significant Noncash Transactions [Line Items]
Merger agreement, equity capital contributed	$ 605.4
Equity capital, pre money valuation amount		$ 300.0
Additional equity purchase from shareholders		40.9
Investment, potential additional contribution of equity capital		$ 200.0
Assets acquired	2,500.0
Goodwill and other intangible assets	292.5
Liabilities acquired	1,700.0
Contingent consideration	22.5
Noncontrolling interest acquired	$ 220.2
Transaction costs					$ 25.3
Investment, potential additional contribution of equity capital terminated								$ 200.0
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			72.00%			72.00%		72.00%
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Fully diluted ownership interest (as a percent)			63.00%			63.00%		63.00%
Percent of outstanding shares after performance obligations are satisfied			12.50%			12.50%
Ark | Group Ark Insurance Limited | Unsecured Subordinated Debt
Other Significant Noncash Transactions [Line Items]
Notes issued				$ 163.3			$ 163.3

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Significant Transactions - Schedule of Assets Acquired and Liabilities Assumed, Ark (Details) - USD ($) $ in Millions	Jan. 01, 2021	Sep. 30, 2022	Dec. 31, 2021
Other Significant Transactions [Line Items]
Goodwill		$ 175.5	$ 142.3
Ark
Other Significant Transactions [Line Items]
Investments	$ 594.3
Cash	52.0
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696.0)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	283.6
Merger agreement, equity capital contributed	$ 605.4

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Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions			9 Months Ended
	Mar. 23, 2021	Oct. 30, 2020	Sep. 30, 2022	Dec. 31, 2021
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Share price (in usd per share)			$ 8.75
Investment owned, balance			$ 148.2
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			27.40%	28.00%
IPO | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)		3,600,000
Sale of stock, price per share (in usd per share)		$ 19.00
Sale of stock, price per share, net of underwriting fees (in USD per share)		$ 17.67
Sale of stock, consideration received in transaction		$ 63.8
Proceeds from dividends received		$ 55.0
Investment owned (in shares)			16,900,000
Fully diluted ownership interest (as a percent)			25.00%
Increase in investment owned (in dollars per share)			$ 1.00
Increase in book value per share (in dollars per share)			6.60
Share price (in usd per share)			$ 8.75
Investment owned, balance			$ 148.2
IPO | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			27.40%
Secondary Offering | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	3,600,000
Secondary Offering | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	8,050,000.00
Sale of stock, price per share (in usd per share)	$ 46.00
Sale of stock, price per share, net of underwriting fees (in USD per share)	$ 44.62
Sale of stock, consideration received in transaction	$ 160.3

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Significant Transactions - PassportCard/DavidShield (Details) - USD ($) $ in Millions	May 07, 2020	Jan. 24, 2018	Sep. 30, 2022	Dec. 31, 2021	May 06, 2020
DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50.00%
PassportCard
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50.00%
PassportCard/DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	53.80%		53.80%	53.80%	50.00%
Payments to acquire businesses, gross		$ 41.8
Payments to acquire business, net		$ 28.3
Stock issued during period, value, acquisitions	$ 15.0
Maximum loss exposure			$ 143.0

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Investment Securities - Schedule of Interest Income on Fixed Maturity Investments (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Schedule of Investments [Line Items]
Total investment income	$ 34.7	$ 20.1	$ 81.1	$ 58.8
Third-party investment expenses	(0.8)	(0.6)	(1.5)	(1.6)
Net investment income	33.9	19.5	79.6	57.2
Fixed maturity investments
Schedule of Investments [Line Items]
Total investment income	11.1	8.2	28.6	21.9
Short-term investments
Schedule of Investments [Line Items]
Total investment income	6.7	0.0	7.2	0.5
Common equity securities
Schedule of Investments [Line Items]
Total investment income	0.1	0.1	0.2	0.1
Other long-term investments
Schedule of Investments [Line Items]
Total investment income	17.1	12.0	45.9	37.1
TPC Providers
Schedule of Investments [Line Items]
Total investment income	$ 0.3	$ 0.2	$ 0.8	$ 0.8

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Investment Securities - Net Realized and Unrealized Investment Gains (Losses) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	$ (1.6)	$ 9.9	$ 12.9	$ 165.4
Net unrealized investment gains (losses)	(47.7)	(374.7)	(274.3)	(393.2)
Net unrealized investment gains (losses) on investment securities held at the end of the period	(18.6)	(396.8)	(113.3)	(325.5)
Gain (loss) on investments, exchange rate effect	(22.6)	(7.0)	(44.4)	(7.4)
Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment gains (losses)	(48.0)	(366.5)	(255.2)	(234.3)
Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(4.9)	1.0	(10.8)	3.8
Net unrealized investment gains (losses)	(58.8)	(7.9)	(192.9)	(27.0)
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(0.1)	(0.3)	(0.4)	0.0
Net unrealized investment gains (losses)	(2.1)	0.0	(2.6)	0.0
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	0.0	0.0	0.0	0.4
Net unrealized investment gains (losses)	4.3	1.6	(6.3)	7.3
Net unrealized investment gains (losses) on investment securities held at the end of the period	4.3	1.6	(6.3)	7.7
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	0.0	0.0	0.0	160.3
Net unrealized investment gains (losses)	(18.6)	(396.8)	(113.3)	(485.8)
Net unrealized investment gains (losses) on investment securities held at the end of the period	(18.6)	(396.8)	(113.3)	(325.5)
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	3.4	9.2	24.1	0.9
Net unrealized investment gains (losses)	27.5	28.4	40.8	112.3
Net realized and unrealized investment (losses) gains
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(49.3)	(364.8)	(261.4)	(227.8)
TPC Providers
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	1.3	(1.7)	6.2	(6.5)
Fixed maturity and short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(65.9)	(7.2)	(206.7)	(23.2)
Net realized and unrealized investment gains (losses)	0.1	(5.7)	(3.0)	(6.9)
Fixed maturity and short-term investments | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(66.0)	(1.5)	(203.7)	(16.3)
Common equity securities and investment in MediaAlpha
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(14.3)	(395.2)	(119.6)	(317.8)
Net realized and unrealized investment gains (losses)	0.0	(0.4)	0.0	(20.3)
Common equity securities and investment in MediaAlpha | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	$ (14.3)	$ (395.6)	$ (119.6)	$ (338.1)

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Investment Securities - Investment gains (losses) for Level 3 (Details) - Level 3 - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 40.8	$ 26.5	$ 57.7	$ 75.5
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 40.8	$ 26.5	$ 57.7	$ 75.5

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Investment Securities - Investment Holdings Fixed Maturity Table (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 227.9	$ 212.1
Gross Unrealized Gains	0.0	0.5
Gross Unrealized Losses	(11.0)	(1.1)
Net Foreign Currency Gains (Losses)	0.0	0.0
Carrying Value	216.9	211.5
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,068.8	993.3
Gross Unrealized Gains	0.0	8.7
Gross Unrealized Losses	(91.2)	(8.7)
Net Foreign Currency Gains (Losses)	(3.1)	(0.4)
Carrying Value	974.5	992.9
Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	289.3	276.4
Gross Unrealized Gains	0.0	16.8
Gross Unrealized Losses	(24.4)	(1.3)
Net Foreign Currency Gains (Losses)	0.0	0.0
Carrying Value	264.9	291.9
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	278.3	277.2
Gross Unrealized Gains	0.0	2.9
Gross Unrealized Losses	(37.6)	(2.5)
Net Foreign Currency Gains (Losses)	0.0	0.0
Carrying Value	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	169.7	136.5
Gross Unrealized Gains	0.0	0.0
Gross Unrealized Losses	(7.6)	(0.4)
Net Foreign Currency Gains (Losses)	(4.8)	(1.1)
Carrying Value	157.3	135.0
Total fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	2,034.0	1,895.5
Gross Unrealized Gains	0.0	28.9
Gross Unrealized Losses	(171.8)	(14.0)
Net Foreign Currency Gains (Losses)	(7.9)	(1.5)
Carrying Value	$ 1,854.3	$ 1,908.9

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Investment Securities - Cost and Amortized Cost Maturity Schedule (Details) $ in Millions	Sep. 30, 2022 USD ($)
Cost or Amortized Cost
Total fixed maturity investments	$ 2,034.0
Carrying Value
Total fixed maturity investments	1,854.3
Fixed Maturities and Convertible Fixed Maturities Excluding Mortgage Backed Securities
Cost or Amortized Cost
Due in one year or less	207.5
Due after one year through five years	917.9
Due after five years through ten years	354.8
Due after ten years	105.8
Carrying Value
Due in one year or less	203.8
Due after one year through five years	849.4
Due after five years through ten years	309.3
Due after ten years	93.8
Mortgage and asset-backed securities
Cost or Amortized Cost
Mortgage and asset-backed securities and collateralized loan obligations	448.0
Carrying Value
Mortgage and asset-backed securities and collateralized loan obligations	$ 398.0

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Investment Securities - Investment Holding Common Equities/ Other Investments/ MediaAlpha (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 324.2	$ 236.3
Gross Unrealized Gains	32.7	16.1
Gross Unrealized Losses	(8.7)	0.0
Net Foreign Currency Gains (Losses)	(15.4)	(1.3)
Common equity securities, at fair value	332.8	251.1
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	0.0	0.0
Gross Unrealized Gains	148.2	261.6
Gross Unrealized Losses	0.0	0.0
Net Foreign Currency Gains (Losses)	0.0	0.0
Common equity securities, at fair value	148.2	261.6
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,390.7	1,186.7
Gross Unrealized Gains	345.0	239.0
Gross Unrealized Losses	(90.0)	(44.1)
Net Foreign Currency Gains (Losses)	(23.0)	(3.8)
Common equity securities, at fair value	$ 1,622.7	$ 1,377.8

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Investment Securities - Fair Value Measurements (Details)	9 Months Ended	12 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Investments, Debt and Equity Securities [Abstract]
Percentage of investments recorded at fair value	69.00%	68.00%

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Investment Securities - Fair Value Measurement by Level (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Dec. 31, 2020
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 1,622.7	$ 1,377.8
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	974.5	992.9
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Level 3 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,044.1	890.6	$ 814.5	$ 614.2
Fair value measured on a recurring basis
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	5,154.4	4,265.3
Other long-term investments	1,622.7	1,377.8
Fair value measured on a recurring basis | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	148.2	261.6
Fair value measured on a recurring basis | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	216.9	211.5
Fair value measured on a recurring basis | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	974.5	992.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	269.0	264.2
Fair value measured on a recurring basis | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	181.4	178.1
Fair value measured on a recurring basis | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	115.8	112.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.3	112.8
Fair value measured on a recurring basis | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	110.8	117.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	75.9	70.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	49.1	56.0
Fair value measured on a recurring basis | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	36.1	48.0
Fair value measured on a recurring basis | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.1	32.1
Fair value measured on a recurring basis | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	264.9	291.9
Fair value measured on a recurring basis | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Fair value measured on a recurring basis | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Fair value measured on a recurring basis | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,854.3	1,908.9
Fair value measured on a recurring basis | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	1,196.4	465.9
Fair value measured on a recurring basis | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	332.8	251.1
Fair value measured on a recurring basis | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	1,058.0	895.3
Fair value measured on a recurring basis | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	564.7	482.5
Fair value measured on a recurring basis | Level 1
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,607.9	939.0
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	148.2	261.6
Fair value measured on a recurring basis | Level 1 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	216.9	211.5
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	216.9	211.5
Fair value measured on a recurring basis | Level 1 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	1,196.4	465.9
Fair value measured on a recurring basis | Level 1 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	46.4	0.0
Fair value measured on a recurring basis | Level 1 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 1 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 2
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,937.7	1,953.2
Other long-term investments	13.9	4.7
Fair value measured on a recurring basis | Level 2 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 2 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	974.5	992.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	269.0	264.2
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	181.4	178.1
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	115.8	112.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.3	112.8
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	110.8	117.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	75.9	70.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	49.1	56.0
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	36.1	48.0
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.1	32.1
Fair value measured on a recurring basis | Level 2 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	264.9	291.9
Fair value measured on a recurring basis | Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Fair value measured on a recurring basis | Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Fair value measured on a recurring basis | Level 2 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,637.4	1,697.4
Fair value measured on a recurring basis | Level 2 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	0.0	0.0
Fair value measured on a recurring basis | Level 2 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	286.4	251.1
Fair value measured on a recurring basis | Level 2 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	13.9	4.7
Fair value measured on a recurring basis | Level 2 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 3
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,044.1	890.6
Other long-term investments	1,044.1	890.6
Fair value measured on a recurring basis | Level 3 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Fair value measured on a recurring basis | Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	1,044.1	890.6
Fair value measured on a recurring basis | Level 3 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 0.0	$ 0.0

XML

Investment Securities - Investments Held on Deposit or as Collateral (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	$ 455.1	$ 479.5
Assets held by insurance regulators	4.6	4.8
Other long-term investments	1,622.7	1,377.8
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	117.8	113.8
Short-term investments | Asset Pledged as Collateral | Citibank LOC Facility
Debt and Equity Securities, FV-NI [Line Items]
Investments pledged as collateral	49.8	50.0
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	117.8
Fair value investments	$ 311.4	$ 342.8

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Investment Securities - Debt securities issued by corporation (Details) - Debt securities issued by corporations - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 974.5	$ 992.9
AAA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.2	12.0
AA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	90.5	85.0
A
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	524.0	490.4
BBB
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	343.0	396.8
Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 5.8	$ 8.7

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Investment Securities - Mortgage-backed Asset Securities Table (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 217.9	$ 256.5
Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.8	21.1
Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	398.0	412.6
Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.9	256.5
Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.8	21.1
Level 2 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135.0
Level 2 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	398.0	412.6
Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Level 3 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
FNMA | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.1	125.4
FNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.1	125.4
FNMA | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
FHLMC | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	74.5	90.5
FHLMC | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	74.5	90.5
FHLMC | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
GNMA | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	28.9	40.1
GNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	28.9	40.1
GNMA | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Total agency | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.5	256.0
Total agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.5	256.0
Total agency | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Non-agency: Residential | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
Non-agency: Residential | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
Non-agency: Residential | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Total non-agency | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
Total non-agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
Total non-agency | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Credit card receivables | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.9	12.3
Credit card receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.9	12.3
Credit card receivables | Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	0.0
Vehicle receivables | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	10.9	8.8
Vehicle receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	10.9	8.8
Vehicle receivables | Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.0	$ 0.0
Collateralized mortgage obligations | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 157.3

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Investment Securities - Investment in MediaAlpha textual (Details) - Marketing Technology (MediaAlpha) $ / shares in Units, $ in Millions	Sep. 30, 2022 USD ($) $ / shares
Subsidiary, Sale of Stock [Line Items]
Share price (in usd per share) | $ / shares	$ 8.75
Investment owned, balance | $	$ 148.2

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Investment Securities - Other long-term investments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 1,622.7	$ 1,377.8
Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	813.2	669.5
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	132.0	120.0
Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	45.0	45.0
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	37.0	34.4
Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	1,027.2	868.9
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	239.8	153.8
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	155.7	163.0
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	117.8	113.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	49.4	51.9
Private debt investments
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	13.0	14.1
Other
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 19.8	$ 12.3

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Investment Securities - Hedge Funds and Private Equity Funds (Details) $ in Millions	9 Months Ended		12 Months Ended
	Sep. 30, 2022 USD ($) fund	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Investments in trading securities	$ 97.9	$ 141.6
TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management | Kudu
Debt and Equity Securities, FV-NI [Line Items]
Investments in trading securities			$ 223.4
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments | fund	16
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments | fund	2
Total private equity funds and hedge funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Largest single fund investment	$ 49.3		$ 31.3

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Investment Securities - Fair Value of Hedge Funds and Private Equity Funds (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Total private equity funds and hedge funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 239.8	$ 153.8
Unfunded Commitments	102.5	44.0
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	185.1	141.8
Unfunded Commitments	102.5	44.0
Private equity funds | Aerospace/Defense/Government
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	102.9	69.8
Unfunded Commitments	45.1	11.8
Private equity funds | Financial services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	77.9	67.7
Unfunded Commitments	54.9	29.3
Private equity funds | Real estate
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	4.3	4.3
Unfunded Commitments	2.5	2.9
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	54.7	12.0
Unfunded Commitments	0.0	0.0
Hedge funds | Long/short equity financials and business services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	49.3	0.0
Unfunded Commitments	0.0	0.0
Hedge funds | European small/mid cap
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	5.4	12.0
Unfunded Commitments	$ 0.0	$ 0.0

XML

Investment Securities - Investments In Private Equity Funds Subject to Lock-Up Periods (Details) - Private equity funds $ in Millions	Sep. 30, 2022 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 185.1
1 – 3 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	27.5
3 – 5 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	19.0
5 – 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	135.4
Greater than 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 3.2

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Investment Securities - Lloyd's Trust Deposits, Bank Loan Fund, and Insurance-Linked Securities Funds (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	$ 455.1	$ 479.5
Hedge funds | Minimum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	45 days
Hedge funds | Maximum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 155.7
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	311.4	$ 342.8
Investments held in trusts	117.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 49.4
ILS funds | Minimum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	30 days
ILS funds | Maximum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days

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Investment Securities - Rollforward of Fair Value Measurements by Level (Details) - Other long-term investments - Level 3 Investments - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	$ 890.6	$ 614.2
Net realized and unrealized gains	57.3	79.0
Amortization/accretion	0.0	0.0
Purchases	127.9	143.6
Sales	(31.7)	(31.9)
Transfers in	0.0	0.0
Transfers out	0.0	0.0
Ending balance	1,044.1	814.5
Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	$ 0.0	$ 9.6

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Investment Securities - Significant Unobservable Inputs (Details) $ in Millions	9 Months Ended		12 Months Ended
	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities	$ 97.9	$ 141.6
Kudu investments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, pretax discount rate	0.20		0.20
Cash flow exit multiple, pretax	9.7		10
TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management | Kudu
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities			$ 223.4
Level 3 | Other long-term investments | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 42.9		46.7
Level 3 | Kudu investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	813.2		669.5
Level 3 | Kudu investments | Standard Poors NR Rating | Probability weighted expected return method
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 312.4		$ 78.8
Level 3 | Kudu investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	17.00%		18.00%
Level 3 | Kudu investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	24.00%		23.00%
Level 3 | Kudu investments | Terminal Multiple | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal cash flow exit multiple	7		7
Level 3 | Kudu investments | Terminal Multiple | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal cash flow exit multiple	16		13
Level 3 | PassportCard/DavidShield | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 132.0		$ 120.0
Level 3 | PassportCard/DavidShield | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	24.00%		23.00%
Level 3 | PassportCard/DavidShield | Measurement Input, Long-term Revenue Growth Rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate	4.00%		4.00%
Level 3 | Elementum Holdings, L.P. | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 45.0		$ 45.0
Level 3 | Elementum Holdings, L.P. | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	18.00%		17.00%
Level 3 | Elementum Holdings, L.P. | Measurement Input, Long-term Revenue Growth Rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate	4.00%		4.00%
Level 3 | Private debt investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 11.0		$ 9.4
Level 3 | Private debt investments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	10.00%		8.00%
Level 3 | Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities	$ 97.9

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Goodwill and Other Intangible Assets - Schedule of Acquisition Date Fair Values, Accumulated Amortization and Net Carrying Values for Other Intangibles Assets and Goodwill, By Company (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	$ 175.5	$ 142.3
Goodwill, net carrying value	175.5	142.3
Total Equity Including Noncontrolling Interest
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	403.6	347.5
Other intangible assets, accumulated amortization	10.4	7.0
Total goodwill and other intangible assets	393.2	340.5
Non-controlling interest
Acquired Finite-Lived Intangible Assets [Line Items]
Total goodwill and other intangible assets	103.1	91.8
Total
Acquired Finite-Lived Intangible Assets [Line Items]
Total goodwill and other intangible assets	290.1	248.7
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	228.1	205.2
Other intangible assets, accumulated amortization	10.4	7.0
Other intangible assets, net carrying value	217.7	198.2
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	116.8	116.8
Goodwill, net carrying value	116.8	116.8
Ark | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Indefinite-Lived Intangible Assets (Excluding Goodwill)	175.7	175.7
Asset Management (Kudu)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	7.6	7.6
Goodwill, net carrying value	$ 7.6	7.6
Asset Management (Kudu) | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	7 years
Other intangible assets, acquisition date fair value	$ 2.2	2.2
Other intangible assets, accumulated amortization	1.1	0.9
Other intangible assets, net carrying value	1.1	1.3
Other Operations
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	51.1	17.9
Goodwill, net carrying value	51.1	17.9
Other intangible assets, acquisition date fair value	50.2	27.3
Other intangible assets, accumulated amortization	9.3	6.1
Other intangible assets, net carrying value	$ 40.9	21.2
Other Operations | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	15 years 10 months 24 days
Other intangible assets, acquisition date fair value	$ 17.9	8.2
Other intangible assets, accumulated amortization	2.4	1.5
Other intangible assets, net carrying value	$ 15.5	6.7
Other Operations | Customer relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	12 years 4 months 24 days
Other intangible assets, acquisition date fair value	$ 29.5	18.8
Other intangible assets, accumulated amortization	6.6	4.5
Other intangible assets, net carrying value	$ 22.9	14.3
Other Operations | Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	12 years 1 month 6 days
Other intangible assets, acquisition date fair value	$ 2.8	0.3
Other intangible assets, accumulated amortization	0.3	0.1
Other intangible assets, net carrying value	$ 2.5	$ 0.2

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Goodwill and Other Intangible Assets - Summary of the Acquisition Date Fair Values of Goodwill and Other Intangible Assets (Details) $ in Millions	Sep. 30, 2022 USD ($)
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 292.5
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 86.6

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Goodwill and Other Intangible Assets - Schedule of Goodwill and Other Intangible Assets Rollforward (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance			$ 142.3
Amortization of other intangible assets	$ (1.4)	$ (2.0)	(3.4)	$ (3.1)
Goodwill, ending balance	175.5		175.5
Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance	201.8	151.5	142.3	19.2
Acquisition of businesses			59.5	15.8
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	(22.9)	(9.3)	(22.9)	(9.3)
Measurement period adjustments	(3.4)	(0.4)	(3.4)	(0.7)
Amortization of other intangible assets	0.0	0.0	0.0	0.0
Goodwill, ending balance	175.5	141.8	175.5	141.8
Goodwill | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill acquired			0.0	116.8
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets (excluding goodwill), beginning balance	196.2	201.1	198.2	26.4
Acquisition of businesses			0.0	0.0
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	22.9	9.3	22.9	9.3
Measurement period adjustments	0.0	0.0		0.1
Amortization of other intangible assets	(1.4)	(2.0)	(3.4)	(3.1)
Other intangible assets (excluding goodwill), ending balance	217.7	208.4	217.7	208.4
Other | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Intangible assets acquired			0.0	175.7
Total Goodwill and Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, gross (including goodwill), beginning balance	398.0	352.6	340.5	45.6
Acquisition of businesses			59.5	15.8
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	0.0	0.0	0.0	0.0
Measurement period adjustments	(3.4)	(0.4)	(3.4)	(0.6)
Amortization of other intangible assets	(1.4)	(2.0)	(3.4)	(3.1)
Other intangible assets, gross (including goodwill), ending balance	$ 393.2	$ 350.2	393.2	350.2
Total Goodwill and Other Intangible Assets | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets acquired			$ 0.0	$ 292.5

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Loss and Loss Adjustment Expense Reserves (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance	$ 1,022.1	$ 760.0	$ 894.7	$ 696.0
Less: beginning reinsurance recoverable on unpaid losses	(375.5)	(425.3)	(428.9)	(433.4)
Net loss and LAE reserves	646.6	334.7	465.8	262.6
Loss and LAE incurred relating to:
Current year losses	222.9	141.9	491.8	269.0
Prior year losses	(9.2)	(12.7)	(35.6)	(21.2)
Net incurred losses and LAE	213.7	129.2	456.2	247.8
Loss and LAE paid relating to:
Current year losses	(6.1)	(9.0)	(20.8)	(11.5)
Prior year losses	(37.0)	(20.3)	(130.8)	(62.1)
Net paid loss and LAE	(43.1)	(29.3)	(151.6)	(73.6)
Change in TPC providers’ participation	0.0	0.0	57.5	(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)	(1.2)	(19.9)	(1.2)
Net ending balance	808.0	433.4	808.0	433.4
Plus: ending reinsurance recoverable on unpaid losses	521.4	457.5	521.4	457.5
Gross ending balance	1,329.4	890.9	1,329.4	890.9
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	521.4	457.5	521.4	457.5	$ 428.9	$ 433.4
Ark
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance			894.7
Loss and LAE paid relating to:
Gross ending balance	1,329.4		1,329.4
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	550.9	465.6	550.9	465.6	$ 448.4
TPC Providers | Ark
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	168.0	299.9	168.0	299.9
TPC Providers
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Less: beginning reinsurance recoverable on unpaid losses	(182.4)	(314.6)
Loss and LAE paid relating to:
Plus: ending reinsurance recoverable on unpaid losses	276.8	319.2	276.8	319.2
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	$ 276.8	319.2	$ 276.8	319.2
Reinsurance recoverables		$ 299.9		$ 299.9
Ark | TPC Providers
Liability for Claims and Claims Adjustment Expense [Line Items]
Percent of underwriting capital provided by third parties						42.80%	58.30%	57.60%

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Third-Party Reinsurance - Effects of Reinsurance (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earned premiums:
Net earned premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Ark
Written premiums:
Gross	215.5	162.4	1,252.5	895.0
Ceded	(22.9)	(41.5)	(246.0)	(169.5)
Net written premiums	192.6	120.9	1,006.5	725.5
Earned premiums:
Gross	454.9	284.5	966.6	622.0
Ceded	(108.8)	(71.1)	(208.8)	(186.2)
Net earned premiums	346.1	213.4	757.8	435.8
Losses and loss adjustment expenses:
Gross	391.4	193.5	712.9	372.7
Ceded	(177.7)	(64.3)	(256.7)	(124.9)
Net losses and loss adjustment expenses	$ 213.7	$ 129.2	$ 456.2	$ 247.8

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Third-Party Reinsurance - Narrative (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2021	Sep. 30, 2022	Sep. 30, 2021
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses		$ 521.4	$ 457.5
Reinsurance recoverables on paid losses		29.5	8.1
TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables			299.9
Ark
Reinsurance [Line Items]
Reinsurance recoverables	$ 448.4	550.9	465.6
Ark | TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables		168.0	$ 299.9
Ark | Third Point Re
Reinsurance [Line Items]
Annual crediting rate	3.00%
Decrease in investment	$ 31.7
Carrying value of investment		$ 20.3

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Third-Party Reinsurance - Remaining Gross and Net Reinsurance Recoverables (Details) - All Entities Except TCP Providers $ in Millions	Sep. 30, 2022 USD ($)
Reinsurance [Line Items]
Reinsurance recoverables	$ 382.9
Reinsurance Recoverables, Collateral	119.4
Net Reinsurance Recoverables	$ 263.5
Percent of reinsurance recoverables from insurers that are collateralized	100.00%
A+ or better
Reinsurance [Line Items]
Reinsurance recoverables	$ 178.3
Reinsurance Recoverables, Collateral	0.0
Net Reinsurance Recoverables	$ 178.3
Percent of reinsurance recoverables from insurers that are collateralized	67.70%
A- to A
Reinsurance [Line Items]
Reinsurance recoverables	$ 78.9
Reinsurance Recoverables, Collateral	0.0
Net Reinsurance Recoverables	$ 78.9
Percent of reinsurance recoverables from insurers that are collateralized	29.90%
B++ or lower and not rated
Reinsurance [Line Items]
Reinsurance recoverables	$ 125.7
Reinsurance Recoverables, Collateral	119.4
Net Reinsurance Recoverables	$ 6.3
Percent of reinsurance recoverables from insurers that are collateralized	2.40%

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Debt - Summary of Debt Outstanding (Details) € in Millions, $ in Millions	Sep. 30, 2022 USD ($)	Sep. 30, 2022 EUR (€)	Dec. 31, 2021 USD ($)
Debt Instrument
Total debt	$ 615.5		$ 420.9
Ark Subordinated Debt
Debt Instrument
Unamortized issuance cost	(4.6)		(5.3)
Ark 2007 Subordinated Notes, carrying value | Ark Subordinated Debt
Debt Instrument
Amount borrowed	30.0		30.0
Ark 2021 Notes Tranche 1
Debt Instrument
Amount borrowed | €		€ 39.1
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	37.6		44.2
Ark 2021 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	47.0		47.0
Ark 2021 Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	70.0		70.0
Ark 2021 Notes | Ark Subordinated Debt
Debt Instrument
Total debt	$ 150.0		$ 155.9
Ark
Debt Instrument
Effective percentage	7.30%	7.30%	6.90%
Ark | Ark Subordinated Debt
Debt Instrument
Total debt	$ 180.0		$ 185.9
Kudu Credit Facility
Debt Instrument
Total debt	253.5		218.2
Other
Debt Instrument
Total debt	$ 35.6
HG Global
Debt Instrument
Effective percentage	8.60%	8.60%
Secured Debt | HG Global Senior Notes
Debt Instrument
Amount borrowed	$ 150.0
Unamortized issuance cost	(3.6)
Total debt	146.4
Term Loan | Kudu Credit Facility
Debt Instrument
Amount borrowed	260.4		225.4
Unamortized issuance cost	$ (6.9)		$ (7.2)
Effective percentage	5.60%	5.60%	4.30%
Term Loan | Other Operations
Debt Instrument
Amount borrowed	$ 36.4		$ 17.1
Unamortized issuance cost	$ (0.8)		$ (0.3)
Effective percentage	7.10%	7.10%	7.50%
Term Loan | Other
Debt Instrument
Total debt			$ 16.8

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Debt - Narrative (Details) € in Millions			1 Months Ended				3 Months Ended		9 Months Ended
	Apr. 29, 2022 USD ($)	Sep. 08, 2021 USD ($)	Sep. 30, 2021 USD ($)	Aug. 31, 2021	Jul. 31, 2021	Mar. 31, 2007 USD ($)	Sep. 30, 2022 USD ($) credit_facility	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($) credit_facility	Sep. 30, 2021 USD ($)	Sep. 30, 2022 EUR (€) credit_facility	Jun. 30, 2022 USD ($)	Dec. 31, 2021 USD ($)	Aug. 11, 2021 USD ($)	Jul. 13, 2021 USD ($)	Jul. 13, 2021 EUR (€)	Jun. 30, 2021 USD ($)	Dec. 31, 2020 USD ($)
Debt Instrument
Debt							$ 615,500,000		$ 615,500,000				$ 420,900,000
Debt covenant, maximum loan to value percent, period one							50.00%		50.00%		50.00%
Debt covenant, maximum loan to value percent, period two							40.00%		40.00%		40.00%
Debt covenant, maximum loan to value percent, period three							25.00%		25.00%		25.00%
Debt covenant, maximum loan to value percent, period four							15.00%		15.00%		15.00%
Debt covenant, maximum loan to value percent, period five							0.00%		0.00%		0.00%
Debt covenant, maximum loan to value percent							35.00%		35.00%		35.00%
Other
Debt Instrument
Secured credit facilities | credit_facility							5		5		5
Ark
Debt Instrument
Debt							$ 180,000,000.0		$ 180,000,000.0				185,900,000
Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Borrowings								$ 157,800,000
Unsecured Subordinated Debt | Group Ark Insurance Limited | Ark
Debt Instrument
Notes issued			$ 163,300,000					163,300,000		$ 163,300,000
HG Global Senior Notes | Secured Debt
Debt Instrument
Borrowings	$ 150,000,000
Annual payments							15,000,000		15,000,000
Interest reserve account							26,400,000		$ 26,400,000
Additional interest rate									1.00%
Outstanding balance							150,000,000.0		$ 150,000,000.0
Debt							146,400,000		146,400,000
HG Global Senior Notes | Secured Debt | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Debt Instrument
Basis spread on variable rate	6.30%
Ark 2007 Subordinated Notes, carrying value | Ark Subordinated Debt
Debt Instrument
Outstanding balance							30,000,000.0		30,000,000.0				30,000,000.0
Ark 2007 Subordinated Notes, carrying value | Junior Notes | Ark
Debt Instrument
Face value						$ 30,000,000
Debt							30,000,000		30,000,000
Ark 2007 Subordinated Notes, carrying value | Junior Notes | USD-LIBOR | Ark
Debt Instrument
Basis spread on variable rate						4.60%
Ark 2021 Notes Tranche 1
Debt Instrument
Outstanding balance | €											€ 39.1
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							37,600,000		37,600,000				44,200,000
Ark 2021 Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Notes issued															$ 46,300,000	€ 39.1
Ark 2021 Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited | EURIBOR
Debt Instrument
Basis spread on variable rate					5.75%
Ark 2021 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							47,000,000.0		47,000,000.0				47,000,000.0
Ark 2021 Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Notes issued														$ 47,000,000
Ark 2021 Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR
Debt Instrument
Basis spread on variable rate				5.75%
Ark 2021 Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							70,000,000.0		70,000,000.0				70,000,000.0
Ark 2021 Notes Tranche 3 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Additional interest rate		1.00%
Notes issued		$ 70,000,000
Solvency capital requirement			120.00%
Debt to capital requirement			40.00%
Ark 2021 Notes Tranche 3 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR
Debt Instrument
Basis spread on variable rate		6.10%
ING LOC Facility | Secured Debt | Ark | Letter of Credit | Uncollateralized
Debt Instrument
Total commitment under revolving credit facility													50,000,000
Citibank LOC Facility | Short-term investments | Asset Pledged as Collateral
Debt Instrument
Investments pledged as collateral							49,800,000		49,800,000				50,000,000
Citibank LOC Facility | Secured Debt
Debt Instrument
Line of credit							36,200,000		36,200,000
Citibank LOC Facility | Secured Debt | Ark | Letter of Credit | Collateral Pledged
Debt Instrument
Total commitment under revolving credit facility													100,000,000
Lloyds LOC Facility | Secured Debt | Ark | Letter of Credit | Collateral Pledged
Debt Instrument
Total commitment under revolving credit facility							50,000,000		50,000,000
Kudu Bank Facility | Kudu
Debt Instrument
Total commitment under revolving credit facility							300,000,000		300,000,000
Kudu Bank Facility | Revolving Credit Facility | Kudu
Debt Instrument
Loss on debt extinguishment									4,100,000
Kudu Bank Facility | Line of Credit | Kudu
Debt Instrument
Interest reserve							8,900,000		8,900,000
Kudu Bank Facility | Term Loan | Kudu
Debt Instrument
Borrowings							0	0	0	3,000,000.0
Debt			$ 0				$ 0	$ 0	$ 0	$ 0		$ 0	0				$ 0	$ 89,200,000
Percentage of borrowing base							35.00%		35.00%		35.00%
Remaining borrowing capacity under revolving credit facility							$ 39,600,000		$ 39,600,000
Other Operations | Term Loan
Debt Instrument
Outstanding balance							$ 36,400,000		$ 36,400,000				$ 17,100,000

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Debt - Schedule of the Change in Debt (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt Instrument
Beginning balance			$ 420.9
Repayments			(10.5)	$ (94.8)
Ending balance	$ 615.5		615.5
Kudu Credit Facility
Debt Instrument
Beginning balance			218.2
Ending balance	253.5		253.5
Kudu | Term Loan | Kudu Bank Facility
Debt Instrument
Beginning balance	0.0	$ 0.0	0.0	89.2
Borrowings	0.0	0.0	0.0	3.0
Repayments	0.0	0.0	0.0	(92.2)
Ending balance	0.0	0.0	0.0	0.0
Kudu | Term Loan | Kudu Credit Facility
Debt Instrument
Beginning balance	260.4	203.0	225.4	0.0
Borrowings	0.0	0.0	35.0	203.0
Repayments	0.0	0.0	0.0	0.0
Ending balance	$ 260.4	$ 203.0	$ 260.4	$ 203.0

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Income Taxes (Details)	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation, percent	23.90%	(7.90%)	9.40%	(17.10%)

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Derivatives (Details) - HG Global - Interest Rate Cap - USD ($)		3 Months Ended	9 Months Ended
	Jun. 16, 2022	Sep. 30, 2022	Sep. 30, 2022
Derivative [Line Items]
Notional amount	$ 150,000,000
Premiums paid	$ 3,300,000
Derivative, fair value, net		$ 3,900,000	$ 3,900,000
Interest Expense
Derivative [Line Items]
Change in fair value of derivative instruments		$ 2,100,000	$ 600,000
Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Derivative [Line Items]
Derivative, cap interest rate	3.50%
3-month variable rate		3.60%	3.60%

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Municipal Bond Guarantee Insurance - Narrative (Details) - USD ($) $ in Millions	1 Months Ended			3 Months Ended		9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021	Jan. 31, 2021	Mar. 31, 2021	Jun. 30, 2018	Sep. 30, 2022	Dec. 31, 2022	Sep. 01, 2022	Jan. 31, 2020	Jul. 31, 2012
Guarantor Obligations [Line Items]
Percentage of risk premium ceded	60.00%					60.00%
Insurance-linked securities, term				12 years	12 years
Insurance-linked securities, callable term				5 years	5 years
Debt	$ 615.5	$ 420.9				$ 615.5
HG Global
Guarantor Obligations [Line Items]
Collateral held in supplement trust	833.9	852.0				833.9
Collateral trusts, investments and cash	457.7	481.7				457.7
BAM
Guarantor Obligations [Line Items]
Surplus notes	364.6	364.6				364.6
Interest receivable	11.6	5.7				11.6
HG Global
Guarantor Obligations [Line Items]
Surplus notes	$ 503.0					$ 503.0				$ 503.0
Percentage of par value of policy reinsured	15.00%					15.00%
Percent over a target trust balance						102.00%
Supplement trust target	$ 603.0					$ 603.0
HG Global | Series A BAM Surplus Note
Guarantor Obligations [Line Items]
Assets Held-in-trust	$ 574.5	601.8				$ 574.5
HG Global | BAM | Maximum
Guarantor Obligations [Line Items]
Aggregate losses on ceded business									$ 125.0
HG Re
Guarantor Obligations [Line Items]
Percentage of par value of policy reinsured	15.00%					15.00%
Assets Held-in-trust	$ 259.4	250.2				$ 259.4
BAM
Guarantor Obligations [Line Items]
Principal	98,619.0	89,196.5	$ 805.5			98,619.0		$ 42.5
BAM | HG Global
Guarantor Obligations [Line Items]
Interest receivable	166.4	157.6				166.4
BAM | Surplus Note
Guarantor Obligations [Line Items]
Repayments of unsecured debt		33.8
Accrued interest payment on surplus notes		9.8
BAM | Surplus Note | HG Global
Guarantor Obligations [Line Items]
Debt	$ 364.6	364.6				$ 364.6
BAM | Supplemental Trust
Guarantor Obligations [Line Items]
Repayments of unsecured debt		23.6
Accrued interest payment on surplus notes		$ 0.4
BAM | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Basis spread on variable rate						3.00%
BAM | Fixed interest rate | Surplus Note
Guarantor Obligations [Line Items]
Derivative, fixed interest rate (as a percent)	8.00%					8.00%
BAM | Forecast | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Effective percentage							3.20%
BAM | Fidus Re Ltd.
Guarantor Obligations [Line Items]
Secured debt				$ 150.0	$ 100.0
Aggregate losses on ceded business				135.0	165.0
Premium receivable, Premium expected to be collected				150.0	100.0
Percentage of quota share reinsurance agreement	100.00%		100.00%
BAM | Fidus Re Ltd. | 2018 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						28.00%
BAM | Fidus Re Ltd. | 2021 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						33.00%
BAM | Fidus Re Ltd. | Maximum
Guarantor Obligations [Line Items]
Aggregate losses on ceded business				$ 301.7	$ 276.1
Fidus Re Ltd. | BAM
Guarantor Obligations [Line Items]
Losses above retention, percentage of liability				90.00%	90.00%

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Municipal Bond Guarantee Insurance - Schedule of Municipal Bond Guarantee Insured Obligations (Details) - BAM $ in Millions	9 Months Ended	12 Months Ended
	Sep. 30, 2022 USD ($) Contract	Dec. 31, 2021 USD ($) Contract	Sep. 01, 2022 USD ($)	Jan. 31, 2021 USD ($)
Guarantor Obligations [Line Items]
Contracts outstanding | Contract	13,094	12,350
Remaining weighted average contract period outstanding (in years)	10 years 9 months 18 days	10 years 9 months 18 days
Principal	$ 98,619.0	$ 89,196.5	$ 42.5	$ 805.5
Interest	47,595.0	41,486.5
Total debt service outstanding	146,214.0	130,683.0
Total gross unearned insurance premiums	$ 286.7	$ 266.3

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Municipal Bond Guarantee Insurance - Schedule of Municipal Guarantee Insurance Contracts, Premium Received Over Contract Period (Details) - BAM - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Guarantor Obligations [Line Items]
October 1, 2022 - December 31, 2022	$ 6.9
January 1, 2023 - March 31, 2023	6.8
April 1, 2023 - June 30, 2023	6.7
July 1, 2023 - September 30, 2023	6.6
October 1, 2023 - December 31, 2023	6.4
Total 2023	26.5
2024	24.9
2025	23.2
2026	21.6
2027	20.1
2028 and thereafter	163.5
Total gross unearned insurance premiums	$ 286.7	$ 266.3

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Municipal Bond Guarantee Insurance - Schedule of Net Written Premiums (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earned premiums:
Net earned premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
HG/BAM
Written premiums:
Direct	18.4	12.8	44.9	34.5
Assumed	1.3	0.0	1.3	4.5
Net written premiums	19.7	12.8	46.2	39.0
Earned premiums:
Direct	6.5	5.9	22.0	16.8
Assumed	0.6	0.8	4.0	2.8
Net earned premiums	$ 7.1	$ 6.7	$ 26.0	$ 19.6

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Earnings Per Share - Basic and Diluted Earnings Per Share from Continuing Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Less: total income (loss) from discontinued operations, net of tax	893.1	5.3	903.2	(5.1)
Net (income) loss from discontinued operations attributable to non-controlling interests	(0.1)	0.0	(0.7)	1.1
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(4.8)	(376.7)	(150.1)	(304.2)
Allocation of losses (earnings) to participating restricted common shares	0.1	4.6	1.8	3.5
Basic and diluted earnings (losses) per share numerators	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Basic and diluted earnings per share (in dollars) - continuing operations:
Distributed earnings - dividends declared and paid (in usd per share)	$ 0	$ 0	$ 1.00	$ 1.00
Undistributed (losses) earnings (in usd per share)	(1.66)	(121.90)	(51.73)	(99.16)
Continuing operations (in usd per share)	(1.66)	(121.90)	(50.73)	(98.16)
Continuing operations (in usd per share)	$ (1.66)	$ (121.90)	$ (50.73)	$ (98.16)

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Earnings Per Share - Undistributed Net Earnings From Continuing Operations (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earnings Per Share [Abstract]
Net income (losses) attributable to White Mountains’s common shareholders, net of restricted common share amounts	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Dividends declared net of restricted common share amounts	0.0	0.0	(3.0)	(3.1)
Total undistributed net earnings (losses), net of restricted common share amounts	$ (4.7)	$ (372.1)	$ (151.3)	$ (303.8)

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Employee Share-Based Incentive Compensation Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended		36 Months Ended
	Sep. 30, 2022 USD ($) shares	Sep. 30, 2021 USD ($) shares	Sep. 30, 2022 USD ($) shares	Sep. 30, 2021 USD ($) shares	Dec. 31, 2021 USD ($) shares	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Dec. 31, 2020 USD ($)
Performance Share | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Vesting period			3 years
Performance cycle period			3 years
New grants (in shares) | shares	0	0	13,225	13,475	750
Additional compensation cost that would be recognized if all outstanding performance shares vested | $	$ 41.2		$ 41.2
Performance Share | Minimum | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Share-based compensation arrangement by share-based payment award, multiplier			0
Performance Share | Maximum | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Share-based compensation arrangement by share-based payment award, multiplier			2
Restricted Stock
Share-based compensation arrangement by share-based payment award
Vesting period			34 months
Restricted Stock | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Additional compensation cost that would be recognized if all outstanding performance shares vested | $	$ 19.2	$ 19.4	$ 19.2	$ 19.4	$ 15.9	$ 23.0	$ 23.2	$ 15.2
Issued (in shares) | shares	0	0	13,225	13,475

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Employee Share-Based Incentive Compensation Plans - Performance Shares (Details) - Performance Share - W T M Incentive Plan - USD ($) $ in Millions	1 Months Ended		3 Months Ended		9 Months Ended		36 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Target Performance Shares Outstanding
Beginning of period (in shares)			39,449	41,252	40,828	42,458
Shares paid (in shares)			0	(219)	(14,625)	(14,336)
New grants (in shares)			0	0	13,225	13,475	750
Forfeitures and cancellations (in shares)			0	205	21	769
Expense recognized (in shares)			0	0	0	0
End of period (in shares)			39,449	40,828	39,449	40,828	40,828
Accrued Expense
Beginning of period			$ 41.2	$ 45.7	$ 42.2	$ 56.3
Shares paid			0.0	(0.6)	(26.4)	(35.2)
New grants			0.0	0.0	0.0	0.0
Forfeitures and cancellations			(0.1)	0.2	(0.2)	0.4
Expense recognized			11.9	(6.5)	37.4	17.3
End of period			$ 53.0	$ 38.8	$ 53.0	$ 38.8	$ 42.2
Range Of Performance Cycle Current Year
Accrued Expense
Percentage of target payout - minimum actual	172.00%
Range Of Performance Cycle Previous Year
Accrued Expense
Percentage of target payout - minimum actual		200.00%

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Employee Share-Based Incentive Compensation Plans - Performance Shares Granted Under the WTM Incentive Plan (Details) - Performance Share - W T M Incentive Plan - USD ($) $ in Millions	Sep. 30, 2022	Jun. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Dec. 31, 2020
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	40,050
Assumed forfeitures (in shares)	(601)
Total target performance shares outstanding (in shares)	39,449	39,449	40,828	40,828	41,252	42,458
Accrued Expense	$ 53.8
Assumed forfeitures	(0.8)
Total Accrued Expense	$ 53.0	$ 41.2	$ 42.2	$ 38.8	$ 45.7	$ 56.3
2020 – 2022
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,350
Accrued Expense	$ 31.9
2021 – 2023
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,475
Accrued Expense	$ 14.7
2022 – 2024
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,225
Accrued Expense	$ 7.2

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Employee Share-Based Incentive Compensation Plans - Restricted Shares (Details) - W T M Incentive Plan - Restricted Stock - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Restricted Shares
Beginning of period (in shares)	38,350	38,280	37,850	43,105
Issued (in shares)	0	0	13,225	13,475
Vested (in shares)	0	(219)	(12,725)	(17,936)
Forfeited (in shares)	0	(211)	0	(794)
Expense recognized (in shares)	0	0	0	0
End of period (in shares)	38,350	37,850	38,350	37,850
Unamortized Issue Date Fair Value
Beginning of period	$ 23.0	$ 23.2	$ 15.9	$ 15.2
Issued	0.0	0.0	13.8	16.1
Vested	0.0	0.0	0.0	0.0
Forfeited	0.0	(0.2)	0.0	(0.8)
Expense recognized	(3.8)	(3.6)	(10.5)	(11.1)
End of period	$ 19.2	$ 19.4	$ 19.2	$ 19.4

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Leases - Narrative (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Leases [Abstract]
ROU lease assets	$ 24.5	$ 28.1
Operating lease liabilities	$ 26.5	$ 30.0

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Leases - Schedule of Lease Cost (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Leases [Abstract]
Lease cost	$ 1.9	$ 1.9	$ 5.9	$ 4.8
Less: sublease income	0.2	0.1	0.5	0.3
Net lease cost	$ 1.7	$ 1.8	$ 5.4	$ 4.5

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Leases - Schedule of Future Minimum Payments on Operating Leases (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Leases [Abstract]
Remainder of 2022	$ 1.7
2023	8.1
2024	7.1
2025	4.9
2026	2.6
Thereafter	5.0
Total undiscounted lease payments	29.4
Less: present value adjustment	2.9
Operating lease liabilities	$ 26.5	$ 30.0

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Leases - Schedule of Right-of-Use Assets and Lease Liabilities (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Lessee, Lease, Description [Line Items]
ROU lease assets	$ 24.5	$ 28.1
Lease liabilities	$ 26.5	$ 30.0
Operating lease, weighted average incremental borrowing rate, percent	4.10%	4.00%
HG/BAM
Lessee, Lease, Description [Line Items]
ROU lease assets	$ 6.2	$ 7.6
Lease liabilities	6.7	8.1
Ark
Lessee, Lease, Description [Line Items]
ROU lease assets	6.6	7.0
Lease liabilities	6.6	7.0
Asset Management (Kudu)
Lessee, Lease, Description [Line Items]
ROU lease assets	5.9	6.4
Lease liabilities	6.8	7.1
Other Operations
Lessee, Lease, Description [Line Items]
ROU lease assets	5.8	7.1
Lease liabilities	$ 6.4	$ 7.8

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Non-controlling Interests (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 158.3	$ 156.6
Total Non-Controlling Excluding Reciprocals
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 318.4	$ 280.6
HG Global
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	3.10%	3.10%
Total non-controlling interests	$ (0.3)	$ 8.9
Ark
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	28.00%	28.00%
Total non-controlling interests	$ 217.1	$ 230.7
Asset Management (Kudu)
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	10.70%	0.70%
Total non-controlling interests	$ 80.8	$ 12.4
NSM Insurance Group
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	0.00%	3.50%
Total non-controlling interests	$ 0.0	$ 16.7
Other
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 20.8	$ 11.9
BAM
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	100.00%	100.00%
Total non-controlling interests	$ (160.1)	$ (124.0)

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Segment Information - Narrative (Details)	9 Months Ended
	Sep. 30, 2022 segment
Segment Reporting [Abstract]
Number of operating segments	4

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Segment Information - Financial Information for White Mountain's Segments (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Segment Reporting Information [Line Items]
Earned insurance premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Net investment income	33.9	19.5	79.6	57.2
Net realized and unrealized investment gains (losses)	(29.4)	30.5	(141.9)	91.2
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7.0
Other revenues	40.9	31.9	103.4	68.1
Total revenues	383.2	(92.4)	720.3	353.4
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	76.5	56.7	184.4	130.9
Cost of sales	25.0	24.0	68.8	45.9
General and administrative expenses	87.1	51.9	258.4	215.5
Amortization of other intangible assets	1.4	2.0	3.4	3.1
Interest expense	10.5	4.4	27.5	14.8
Total expenses	414.2	268.2	998.7	658.0
Pre-tax income (loss) from continuing operations	(31.0)	(360.6)	(278.4)	(304.6)
Financial Guarantee (HG Global/BAM)
Segment Reporting Information [Line Items]
Earned insurance premiums	7.1	6.7	26.0	19.6
Net investment income	5.7	4.4	15.1	13.2
Net realized and unrealized investment gains (losses)	(38.8)	(4.0)	(114.0)	(15.6)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	1.3	0.3	3.7	0.9
Total revenues	(24.7)	7.4	(69.2)	18.1
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	1.7	3.0	9.5	6.5
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	15.8	12.4	49.5	42.7
Amortization of other intangible assets	0.0	0.0	0.0	0.0
Interest expense	2.0	0.0	5.4	0.0
Total expenses	19.5	15.4	64.4	49.2
Pre-tax income (loss) from continuing operations	(44.2)	(8.0)	(133.6)	(31.1)
Ark
Segment Reporting Information [Line Items]
Earned insurance premiums	346.1	213.4	757.8	435.8
Net investment income	4.9	0.6	9.7	1.8
Net realized and unrealized investment gains (losses)	(14.4)	0.3	(76.5)	10.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	6.6	3.4	10.1	9.4
Total revenues	343.2	217.7	701.1	457.3
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	74.8	53.7	174.9	124.4
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	26.9	21.8	79.8	84.4
Amortization of other intangible assets	0.0	0.0	0.0	0.0
Interest expense	3.7	2.1	10.6	4.5
Total expenses	319.1	206.8	721.5	461.1
Pre-tax income (loss) from continuing operations	24.1	10.9	(20.4)	(3.8)
Asset Management (Kudu)
Segment Reporting Information [Line Items]
Earned insurance premiums	0.0	0.0	0.0	0.0
Net investment income	14.8	9.5	41.2	26.1
Net realized and unrealized investment gains (losses)	41.1	18.9	45.8	62.5
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0.0	0.0	0.0	0.0
Commission revenues	0.0	0.0	0.0	0.0
Other revenues	0.0	0.1	0.0	0.2
Total revenues	55.9	28.5	87.0	88.8
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	0.0	0.0	0.0	0.0
Cost of sales	0.0	0.0	0.0	0.0
General and administrative expenses	4.5	3.3	10.2	9.0
Amortization of other intangible assets	0.0	0.0	0.2	0.2
Interest expense	4.2	1.9	10.3	9.2
Total expenses	8.7	5.2	20.7	18.4
Pre-tax income (loss) from continuing operations	47.2	23.3	66.3	70.4
Other Operations
Segment Reporting Information [Line Items]
Earned insurance premiums	0.0	0.0	0.0	0.0
Net investment income	8.5	5.0	13.6	16.1
Net realized and unrealized investment gains (losses)	(17.3)	15.3	2.8	34.0
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7.0
Other revenues	33.0	28.1	89.6	57.6
Total revenues	8.8	(346.0)	1.4	(210.8)
Loss and loss adjustment expenses	0.0	0.0	0.0	0.0
Insurance and reinsurance acquisition expenses	0.0	0.0	0.0	0.0
Cost of sales	25.0	24.0	68.8	45.9
General and administrative expenses	39.9	14.4	118.9	79.4
Amortization of other intangible assets	1.4	2.0	3.2	2.9
Interest expense	0.6	0.4	1.2	1.1
Total expenses	66.9	40.8	192.1	129.3
Pre-tax income (loss) from continuing operations	$ (58.1)	$ (386.8)	$ (190.7)	$ (340.1)

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Equity-Method Eligible Investments - Carrying Values of Equity Method Eligible Investments Recorded within Other Long-Term Investments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021	May 07, 2020	May 06, 2020
Investments in unconsolidated affiliates
Other long-term investments	$ 1,622.7	$ 1,377.8
Kudu investments
Investments in unconsolidated affiliates
Other long-term investments	$ 813.2	$ 669.5
Kudu investments | Minimum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	4.10%	3.20%
Kudu investments | Maximum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	33.00%	32.00%
Marketing Technology (MediaAlpha)
Investments in unconsolidated affiliates
Ownership interest (as a percent)	27.40%	28.00%
Other long-term investments	$ 148.2	$ 261.6
PassportCard/DavidShield
Investments in unconsolidated affiliates
Ownership interest (as a percent)	53.80%	53.80%	53.80%	50.00%
Other long-term investments	$ 132.0	$ 120.0
Elementum Holdings, L.P.
Investments in unconsolidated affiliates
Ownership interest (as a percent)	29.70%	29.70%
Other long-term investments	$ 45.0	$ 45.0
Other
Investments in unconsolidated affiliates
Other long-term investments	102.7	109.3
Equity Method Investments
Investments in unconsolidated affiliates
Other long-term investments	$ 27.7	$ 17.8

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Equity-Method Eligible Investments - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Equity Method Investee
Schedule of Equity Method Investments [Line Items]
Proceeds from dividends received	$ 16.1	$ 13.0	$ 42.9	$ 37.7

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Equity-Method Eligible Investments - Equity Method Investments Financial Data (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Total assets	$ 7,545.0		$ 7,545.0		$ 7,000.7
Total liabilities	3,678.7		3,678.7		3,296.0
Total revenues	383.2	$ (92.4)	720.3	$ 353.4
Net income (loss)	888.2	(371.4)	752.4	(308.2)
Marketing Technology (MediaAlpha)
Schedule of Equity Method Investments [Line Items]
Total assets	265.2		265.2		289.8
Total liabilities	333.6		333.6		$ 351.4
Total revenues	89.0	152.7	335.1	483.7
Total expenses	110.2	157.0	379.2	488.2
Net income (loss)	$ (21.2)	$ (4.3)	$ (44.1)	$ (4.5)

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Fair Value of Financial Instruments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 615.5	$ 420.9
Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	253.5	218.2
Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	35.6
Fair Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	146.1	0.0
Fair Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	26.2	27.6
Fair Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	149.4	162.8
Fair Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	265.5	246.8
Fair Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Fair Value	36.8	17.7
Carrying Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	146.4	0.0
Carrying Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	30.0	30.0
Carrying Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	150.0	155.9
Carrying Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	260.4	218.2
Carrying Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 35.6	$ 16.8

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Held for Sale and Discontinued Operations - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2018	Dec. 31, 2021	Dec. 31, 2020
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group			$ 886.8	$ 18.7
Other Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Liability related to sale	$ 0.0		0.0			$ 495.3
Assets held for sale - Other	0.0		0.0			$ 16.1
Sirius Group
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group	$ 0.0	$ 0.0	$ 0.0	18.7	$ 17.3
Discontinued Operations, Disposed of by Sale | Sirius Group
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group				17.6
Liability related to sale							$ 18.7
Net (income) loss from discontinued operations attributable to non-controlling interests				$ 1.1

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Held for Sale and Discontinued Operations - Financial Statement Disclosure (Details) - USD ($) $ in Millions		3 Months Ended		9 Months Ended		12 Months Ended
	Aug. 01, 2022	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2018	Dec. 31, 2021	Dec. 31, 2020
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net income (loss) from discontinued operations, net of tax - NSM Group		$ 6.3	$ 5.3	$ 16.4	$ (23.8)
Net gain (loss) from sale of discontinued operations, net of tax				886.8	18.7
Total income (loss) from discontinued operations, net of tax		(893.1)	(5.3)	(903.2)	5.1
Net (income) loss from discontinued operations attributable to non-controlling interests		(0.1)	0.0	(0.7)	1.1
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group		0.7	(2.2)	(5.2)	0.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group		2.9	0.0	2.9	0.0
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations				38.7	40.3
Net cash provided from (used for) investing activities				7.1	(54.6)
Net cash used from (used for) financing activities				(17.5)	13.8
Net change in cash during the period				98.0	99.4
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)				147.7	84.6
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)		245.7	184.0	245.7	184.0
Restricted cash balance		8.9	4.0	8.9	4.0		$ 4.5	$ 0.0
Interest paid				(10.9)	(5.3)
Net income tax payments				3.2	2.1
NSM Insurance Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		886.8	0.0	886.8	0.0
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)				143.9	0.0
Sirius Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		0.0	0.0	0.0	18.7	$ 17.3
Discontinued Operations, Held-for-sale | NSM Insurance Group
Disposal Group, Including Discontinued Operation, Balance Sheet Disclosures [Abstract]
Short-term investments, at fair value							7.8
Cash (restricted $89.2)							111.6
Restricted cash							89.2
Premiums and commissions receivable							85.0
Goodwill and other intangible assets							725.4
Other assets							59.2
Total assets held for sale							989.0
Debt							272.1
Premiums payable							135.9
Contingent consideration							6.8
Other liabilities							80.5
Total liabilities held for sale							495.3
Net assets held for sale							493.7
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Commission revenues		26.6	67.0	176.9	194.6
Other revenues		7.0	15.3	48.1	46.8
Total revenues - NSM Group		33.6	82.3	225.0	241.4
General and administrative expenses		15.7	48.9	126.8	142.4
Broker commission expenses		8.2	20.4	52.9	60.9
Change in fair value of contingent consideration		0.0	0.6	0.1	0.8
Amortization of other intangible assets		0.0	8.2	9.1	25.0
Loss on assets held for sale		0.0	0.0	0.0	(28.7)
Interest expense		1.6	5.9	12.1	17.7
Total expenses - NSM Group		25.5	84.0	201.0	275.5
Pre-tax income (loss) from discontinued operations - NSM Group		8.1	(1.7)	24.0	(34.1)
Income tax (expense) benefit		(1.8)	7.0	(7.6)	10.3
Net income (loss) from discontinued operations, net of tax - NSM Group		6.3	5.3	16.4	(23.8)
Net gain (loss) from sale of discontinued operations, net of tax		886.8	0.0	886.8	0.0
Total income (loss) from discontinued operations, net of tax		893.1	5.3	903.2	(5.1)
Net (income) loss from discontinued operations attributable to non-controlling interests		(0.2)	0.0	(0.8)	1.1
Total income (loss) from discontinued operations attributable to White Mountains’s common shareholders		892.9	5.3	902.4	(4.0)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group		0.7	(1.7)	(5.2)	0.9
Comprehensive income (loss) from discontinued operations		896.5	3.6	900.1	(3.1)
Other comprehensive income (loss) from discontinued operations attributable to non-controlling interests		(0.1)	0.0	0.2	(0.1)
Comprehensive income (loss) from discontinued operations attributable to White Mountains’s common shareholders		896.4	3.6	900.3	(3.2)
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations				38.7	40.3
Net cash provided from (used for) investing activities				7.1	(54.6)
Net cash used from (used for) financing activities				(17.5)	13.8
Effect of exchange rate changes on cash				4.0	0.6
Net change in cash during the period				32.3	0.1
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)				111.6	126.6
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)				(143.9)	0.0
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)		0.0	126.7	0.0	126.7
Restricted cash balance		0.0	92.2	0.0	92.2		$ 89.2	78.4
Interest paid				(12.0)	(16.6)
Net income tax payments				0.0	0.0
Discontinued Operations, Held-for-sale | Sirius Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		0.0	0.0	0.0	18.7
Discontinued Operations, Disposed of by Sale | NSM Insurance Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Loss on assets held for sale	$ (875.7)
Net gain (loss) from sale of discontinued operations, net of tax	886.8
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	$ 2.9
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Restricted cash balance		$ 105.1	$ 0.0	$ 105.1	0.0
Discontinued Operations, Disposed of by Sale | Sirius Group
Disposal Group, Including Discontinued Operation, Balance Sheet Disclosures [Abstract]
Total liabilities held for sale								$ 18.7
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax					$ 17.6

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Held for Sale and Discontinued Operations - Earnings Per Share for Discontinued Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss)	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(4.8)	(376.7)	(150.1)	(304.2)
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders	(893.1)	(5.3)	(903.2)	5.1
Allocation of earnings to participating restricted common shares	0.1	4.6	1.8	3.5
Basic and diluted earnings (losses) per share numerators	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)
Discontinued Operations
Basic and diluted earnings per share numerators (in millions):
Net income (loss)	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(23.6)	(389.2)	(252.3)	(356.8)
Less: net (income) loss from continuing operations attributable to non-controlling interests	18.8	12.5	102.2	52.6
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders	893.0	5.3	902.5	(4.0)
Allocation of earnings to participating restricted common shares	(11.8)	(0.1)	(10.8)	0.0
Basic and diluted earnings (losses) per share numerators	$ 881.2	$ 5.2	$ 891.7	$ (4.0)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000.0)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)