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 quarterly period ended March 31, 2021
Or
☐	TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934

Commission file number:  001-16209

 

ARCH CAPITAL GROUP LTD.

(Exact name of registrant as specified in its charter)

Bermuda				98-0374481
(State or other jurisdiction of incorporation or organization)				(I.R.S. Employer Identification No.)
Waterloo House, Ground Floor
100 Pitts Bay Road,	Pembroke	HM 08,	Bermuda	(441)	278-9250
(Address of principal executive offices)				(Registrant’s telephone number, including area code)

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

Title of each class	Trading Symbol (s)	Name of each exchange on which registered
Common shares, $0.0011 par value per share	ACGL	NASDAQ	Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share	ACGLP	NASDAQ	Stock Market
Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share	ACGLO	NASDAQ	Stock Market

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 ☑     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 ☑     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 ☑ 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. ☐

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

As of April 30, 2021, there were 403,619,081 common shares, $0.0011 par value per share, of the registrant outstanding.

ARCH CAPITAL GROUP LTD.

INDEX TO FORM 10-Q

		Page No.
	PART I
	Financial Information	2
Item 1.	Consolidated Financial Statements	4
Item 2.	Management’s Discussion and Analysis of Financial Condition and Results of Operations	37
Item 3.	Quantitative and Qualitative Disclosures About Market Risk	61
Item 4.	Controls and Procedures	61
	PART II
	Other Information	62
Item 1.	Legal Proceedings	62
Item 1A.	Risk Factors	62
Item 2.	Unregistered Sales of Equity Securities and Use of Proceeds	63
Item 3.	Defaults Upon Senior Securities	63
Item 4.	Mine Safety Disclosures	63
Item 5.	Other Information	63
Item 6.	Exhibits	64
	Signatures	65

ARCH CAPITAL  1 2021 FIRST QUARTER FORM 10-Q

PART I.  FINANCIAL INFORMATION

Cautionary Note Regarding Forward-Looking Statements 

The Private Securities Litigation Reform Act of 1995 (“PSLRA”) provides a “safe harbor” for forward-looking statements. This report or any other written or oral statements made by or on behalf of us may include forward-looking statements, which reflect our current views with respect to future events and financial performance. All statements other than statements of historical fact included in or incorporated by reference in this report are forward-looking statements. Forward-looking statements, for purposes of the PSLRA or otherwise, can generally be identified by the use of forward-looking terminology such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe” or “continue” and similar statements of a future or forward-looking nature or their negative or variations or similar terminology.

Forward-looking statements involve our current assessment of risks and uncertainties. Actual events and results may differ materially from those expressed or implied in these statements. Important factors that could cause actual events or results to differ materially from those indicated in such statements are discussed below and elsewhere in this report and in our periodic reports filed with the Securities and Exchange Commission (the “SEC”), and include:

•our ability to successfully implement our business strategy during “soft” as well as “hard” markets;

•acceptance of our business strategy, security and financial condition by rating agencies and regulators, as well as by brokers and our insureds and reinsureds;

•our ability to consummate acquisitions and integrate the business we have acquired or may acquire into our existing operations;

•our ability to maintain or improve our ratings, which may be affected by our ability to raise additional equity or debt financings, by ratings agencies’ existing or new policies and practices, as well as other factors described herein;

•general economic and market conditions (including inflation, interest rates, unemployment, housing prices, foreign currency exchange rates, prevailing credit terms and the depth and duration of a recession, including those resulting from COVID-19) and conditions specific to the reinsurance and insurance markets in which we operate;

•competition, including increased competition, on the basis of pricing, capacity (including alternative sources of capital), coverage terms, or other factors;

•developments in the world’s financial and capital markets and our access to such markets;

•our ability to successfully enhance, integrate and maintain operating procedures (including information technology) to effectively support our current and new business;

•the loss of key personnel;

•material differences between actual and expected assessments for guaranty funds and mandatory pooling arrangements;

•accuracy of those estimates and judgments utilized in the preparation of our financial statements, including those related to revenue recognition, insurance and other reserves, reinsurance recoverables, investment valuations, intangible assets, bad debts, income taxes, contingencies and litigation, and any determination to use the deposit method of accounting;

•greater than expected loss ratios on business written by us and adverse development on claim and/or claim expense liabilities related to business written by our insurance and reinsurance subsidiaries;

•the adequacy of the Company’s loss reserves;

•severity and/or frequency of losses;

•greater frequency or severity of unpredictable natural and man-made catastrophic events;

•claims for natural or man-made catastrophic events or severe economic events in our insurance, reinsurance and mortgage businesses could cause large losses and substantial volatility in our results of operations;

•the effect of climate change on our business;

•the effect of contagious disease (including COVID-19) on our business;

•acts of terrorism, political unrest and other hostilities or other unforecasted and unpredictable events;

ARCH CAPITAL  2 2021 FIRST QUARTER FORM 10-Q

•availability to us of reinsurance to manage our gross and net exposures and the cost of such reinsurance;

•the failure of reinsurers, managing general agents, third party administrators or others to meet their obligations to us;

•the timing of loss payments being faster or the receipt of reinsurance recoverables being slower than anticipated by us;

•our investment performance, including legislative or regulatory developments that may adversely affect the fair value of our investments;

•changes in general economic conditions, including sovereign debt concerns or downgrades of U.S. securities by credit rating agencies, which could affect our business, financial condition and results of operations;

•changes in the method for determining the London Inter-bank Offered Rate (“LIBOR”) and the potential replacement of LIBOR;

•the volatility of our shareholders’ equity from foreign currency fluctuations, which could increase due to us not matching portions of our projected liabilities in foreign currencies with investments in the same currencies;

•changes in accounting principles or policies or in our application of such accounting principles or policies;

•changes in the political environment of certain countries in which we operate or underwrite business;

•a disruption caused by cyber-attacks or other technology breaches or failures on us or our business partners and service providers, which could negatively impact our business and/or expose us to litigation;

•statutory or regulatory developments, including as to tax matters and insurance and other regulatory matters such as the adoption of proposed legislation that would affect Bermuda-headquartered companies and/or Bermuda-based insurers or reinsurers and/or changes in regulations or tax laws applicable to us, our subsidiaries, brokers or customers, including the Tax Cuts and Jobs Act of 2017; and

•the other matters set forth under Item 1A “Risk Factors”, Item 7 “Management’s Discussion and Analysis of Financial Condition and Results of Operations” and other sections of our Annual Report on Form 10-K for the year ended December 31, 2020, as well as the other factors set forth in our other documents on file with the SEC, and management’s response to any of the aforementioned factors.

All subsequent written and oral forward-looking statements attributable to us or persons acting on our behalf are expressly qualified in their entirety by these cautionary statements. The foregoing review of important factors should not be construed as exhaustive and should be read in conjunction with other cautionary statements that are included herein or elsewhere. We undertake no obligation to publicly update or revise any forward-looking statement, whether as a result of new information, future events or otherwise. 

ARCH CAPITAL  3 2021 FIRST QUARTER FORM 10-Q

ITEM 1. CONSOLIDATED FINANCIAL STATEMENTS

	Page No.
Report of Independent Registered Public Accounting Firm	5
Consolidated Balance Sheets
March 31, 2021 (unaudited) and December 31, 2020	6
Consolidated Statements of Income
For the three month periods ended March 31, 2021 and 2020 (unaudited)	7
Consolidated Statements of Comprehensive Income
For the three month periods ended March 31, 2021 and 2020 (unaudited)	8
Consolidated Statements of Changes in Shareholders’ Equity
For the three month periods ended March 31, 2021 and 2020 (unaudited)	9
Consolidated Statements of Cash Flows
For the three month periods ended March 31, 2021 and 2020 (unaudited)	10
Notes to Consolidated Financial Statements (unaudited)
Note 1 - Basis of Presentation and Recent Accounting Pronouncements	11
Note 2 - Share Transactions	11
Note 3 - Earnings Per Common Share	12
Note 4 - Segment Information	13
Note 5 - Reserve for Losses and Loss Adjustment Expenses	16
Note 6 - Allowance for Expected Credit Losses	17
Note 7 - Investment Information	19
Note 8 - Fair Value	25
Note 9 - Derivative Instruments	30
Note 10 - Commitments and Contingencies	31
Note 11 - Variable Interest Entities and Noncontrolling Interests	31
Note 12 - Other Comprehensive Income (Loss)	35
Note 13 - Income Taxes	36
Note 14 - Legal Proceedings	36
Note 15 - Transactions with Related Parties	36

ARCH CAPITAL  4 2021 FIRST QUARTER FORM 10-Q

Report of Independent Registered Public Accounting Firm

To the Board of Directors and Shareholders of Arch Capital Group Ltd.

Results of Review of Interim Financial Statements

We have reviewed the accompanying consolidated balance sheet of Arch Capital Group Ltd. and its subsidiaries (the “Company”) as of March 31, 2021, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and the consolidated statements of cash flows for the three-month periods ended March 31, 2021 and 2020, including the related notes (collectively referred to as the “interim financial statements”). Based on our reviews, we are not aware of any material modifications that should be made to the accompanying interim financial statements for them to be in conformity with accounting principles generally accepted in the United States of America.

We have previously audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States) (PCAOB), the consolidated balance sheet of the Company as of December 31, 2020, and the related consolidated statements of income, comprehensive income, changes in shareholders’ equity, and cash flows for the year then ended (not presented herein), and in our report dated February 26, 2021, we expressed an unqualified opinion on those consolidated financial statements. In our opinion, the information set forth in the accompanying consolidated balance sheet as of December 31, 2020, is fairly stated, in all material respects, in relation to the consolidated balance sheet from which it has been derived.

Basis for Review Results

These interim financial statements are the responsibility of the Company’s management. We are a public accounting firm registered with the PCAOB and are required to be independent with respect to the Company in accordance with the U.S. federal securities laws and the applicable rules and regulations of the Securities and Exchange Commission and the PCAOB. We conducted our review in accordance with the standards of the PCAOB. A review of interim financial information consists principally of applying analytical procedures and making inquiries of persons responsible for financial and accounting matters. It is substantially less in scope than an audit conducted in accordance with the standards of the PCAOB, the objective of which is the expression of an opinion regarding the financial statements taken as a whole. Accordingly, we do not express such an opinion.

/s/ PricewaterhouseCoopers LLP

New York, NY

May 6, 2021

ARCH CAPITAL  5 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

(U.S. dollars in thousands, except share data)

	(Unaudited)
	March 31, 2021		December 31, 2020
Assets
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $18,447,720 and $18,143,305; net of allowance for credit losses: $3,830 and $2,397 )	$	18,723,035	$	18,717,825
Short-term investments available for sale, at fair value (amortized cost: $1,269,312 and $1,924,292; net of allowance for credit losses: $0 and $0)	1,269,631		1,924,922
Collateral received under securities lending, at fair value (amortized cost: $143,886 and $301,089)	143,894		301,096
Equity securities, at fair value	1,532,906		1,444,830
Other investments (portion measured at fair value: $3,935,354 and $3,824,796)	4,435,354		4,324,796
Investments accounted for using the equity method	2,256,327		2,047,889
Total investments	28,361,147		28,761,358
Cash	941,951		906,448
Accrued investment income	101,108		103,299
Securities pledged under securities lending, at fair value (amortized cost: $142,129 and $294,493)	140,949		294,912
Investment in operating affiliates	739,783		129,291
Premiums receivable (net of allowance for credit losses: $36,111 and $37,781)	2,618,175		2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $10,872 and $11,636)	4,041,076		4,500,802
Contractholder receivables (net of allowance for credit losses: $5,853 and $8,638)	1,919,655		1,986,924
Ceded unearned premiums	1,406,489		1,234,075
Deferred acquisition costs	919,740		790,708
Receivable for securities sold	199,424		92,743
Goodwill and intangible assets	679,509		692,863
Other assets	2,135,261		1,724,288
Total assets	$	44,204,267	$	43,282,297
Liabilities
Reserve for losses and loss adjustment expenses	$	16,443,952	$	16,513,929
Unearned premiums	5,549,127		4,838,965
Reinsurance balances payable	919,125		683,263
Contractholder payables	1,925,508		1,995,562
Collateral held for insured obligations	222,245		215,581
Senior notes	2,861,417		2,861,113
Revolving credit agreement borrowings	155,687		155,687
Securities lending payable	143,886		301,089
Payable for securities purchased	386,453		218,779
Other liabilities	1,565,861		1,510,888
Total liabilities	30,173,261		29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests	57,670		58,548
Shareholders' Equity
Non-cumulative preferred shares	780,000		780,000
Common shares ($0.0011 par, shares issued: 581,226,408 and 579,000,841)	645		643
Additional paid-in capital	2,014,741		1,977,794
Retained earnings	12,790,216		12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	205,827		488,895
Common shares held in treasury, at cost (shares: 177,913,031 and 172,280,199)	(2,694,957)		(2,503,909)
Total shareholders' equity available to Arch	13,096,472		13,105,886
Non-redeemable noncontrolling interests	876,864		823,007
Total shareholders' equity	13,973,336		13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$	44,204,267	$	43,282,297

See Notes to Consolidated Financial Statements

ARCH CAPITAL 6 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF INCOME

(U.S. dollars in thousands, except share data)

	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Revenues
Net premiums earned	$	1,948,422	$	1,744,444
Net investment income	98,856		145,153
Net realized gains (losses)	142,461		(366,960)
Other underwriting income	6,110		6,852
Equity in net income (loss) of investment funds accounted for using the equity method	71,686		(4,209)
Other income (loss)	(1,741)		32
Total revenues	2,265,794		1,525,312
Expenses
Losses and loss adjustment expenses	1,203,100		1,115,419
Acquisition expenses	304,481		247,283
Other operating expenses	261,033		234,544
Corporate expenses	25,384		20,796
Amortization of intangible assets	14,402		16,631
Interest expense	38,346		32,555
Net foreign exchange (gains) losses	(20,063)		(72,671)
Total expenses	1,826,683		1,594,557
Income (loss) before income taxes and income (loss) from operating affiliates	439,111		(69,245)
Income tax expense	(38,860)		(27,945)
Income (loss) from operating affiliates	75,457		8,516
Net income (loss)	$	475,708	$	(88,674)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	$	427,753	$	133,714
Net income per common share and common share equivalent
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32
Weighted average common shares and common share equivalents outstanding
Basic	400,807,895		403,892,161
Diluted	409,223,253		414,033,570

See Notes to Consolidated Financial Statements

ARCH CAPITAL 7 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME

(U.S. dollars in thousands)

	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Comprehensive Income
Net income (loss)	$	475,708	$	(88,674)
Other comprehensive income (loss), net of deferred income tax
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(261,750)		(57,287)
Reclassification of net realized (gains) losses, included in net income (loss)	2,697		(121,229)
Foreign currency translation adjustments	(28,584)		(44,689)
Comprehensive income (loss)	188,071		(311,879)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Other comprehensive (income) loss attributable to noncontrolling interests	4,570		33,058
Comprehensive income (loss) available to Arch	$	155,089	$	(46,030)

See Notes to Consolidated Financial Statements

ARCH CAPITAL 8 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CHANGES IN SHAREHOLDERS’ EQUITY

(U.S. dollars in thousands)

	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Non-cumulative preferred shares
Balance at beginning and end of period	$	780,000	$	780,000
Common shares
Balance at beginning of period	643		638
Common shares issued, net	2		4
Balance at end of period	645		642
Additional paid-in capital
Balance at beginning of period	1,977,794		1,889,683
Amortization of share-based compensation	40,573		28,050
Other changes	(3,626)		3,754
Balance at end of period	2,014,741		1,921,487
Retained earnings
Balance at beginning of period	12,362,463		11,021,006
Cumulative effect of an accounting change (1)	—		(22,452)
Balance at beginning of period, as adjusted	12,362,463		10,998,554
Net income (loss)	475,708		(88,674)
Net (income) loss attributable to noncontrolling interests	(37,552)		232,791
Preferred share dividends	(10,403)		(10,403)
Balance at end of period	12,790,216		11,132,268
Accumulated other comprehensive income (loss), net of deferred income tax
Balance at beginning of period	488,895		212,091
Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax:
Balance at beginning of period	501,295		258,486
Unrealized holding gains (losses) during period, net of reclassification adjustment	(259,053)		(178,516)
Unrealized holding gains (losses) during period attributable to noncontrolling interests	4,469		33,179
Balance at end of period	246,711		113,149
Foreign currency translation adjustments, net of deferred income tax:
Balance at beginning of period	(12,400)		(46,395)
Foreign currency translation adjustments	(28,584)		(44,689)
Foreign currency translation adjustments attributable to noncontrolling interests	100		(121)
Balance at end of period	(40,884)		(91,205)
Balance at end of period	205,827		21,944
Common shares held in treasury, at cost
Balance at beginning of period	(2,503,909)		(2,406,047)
Shares repurchased for treasury	(191,048)		(83,050)
Balance at end of period	(2,694,957)		(2,489,097)
Total shareholders’ equity available to Arch	13,096,472		11,367,244
Non-redeemable noncontrolling interests	876,864		492,785
Total shareholders’ equity	$	13,973,336	$	11,860,029

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

See Notes to Consolidated Financial Statements

ARCH CAPITAL 9 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF CASH FLOWS

(U.S. dollars in thousands)

	(Unaudited)
	Three Months Ended
	March 31,
	2021		2020
Operating Activities
Net income (loss)	$	475,708	$	(88,674)
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(161,007)		362,964
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(135,939)		29,034
Amortization of intangible assets	14,402		16,631
Share-based compensation	40,812		28,549
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	560,153		506,057
Unearned premiums, net of ceded unearned premiums	560,035		392,802
Premiums receivable	(608,250)		(418,457)
Deferred acquisition costs	(126,701)		(75,135)
Reinsurance balances payable	240,206		79,807
Other items, net	(96,574)		(223,124)
Net cash provided by (used for) operating activities	762,845		610,454
Investing Activities
Purchases of fixed maturity investments	(11,530,968)		(11,965,995)
Purchases of equity securities	(309,419)		(760,683)
Purchases of other investments	(430,961)		(228,471)
Proceeds from sales of fixed maturity investments	10,917,134		11,723,123
Proceeds from sales of equity securities	284,986		266,301
Proceeds from sales, redemptions and maturities of other investments	323,591		216,131
Proceeds from redemptions and maturities of fixed maturity investments	421,042		198,356
Net settlements of derivative instruments	47,660		195,488
Net (purchases) sales of short-term investments	589,175		(11,777)
Change in cash collateral related to securities lending	—		55,001
Purchase of operating affiliate	(546,349)		—
Purchases of fixed assets	(12,490)		(8,470)
Other	(246,590)		42,500
Net cash provided by (used for) investing activities	(493,189)		(278,496)
Financing Activities
Purchases of common shares under share repurchase program	(179,266)		(75,486)
Proceeds from common shares issued, net	(10,008)		(4,527)
Proceeds from borrowings	—		16,300
Change in cash collateral related to securities lending	—		(55,001)
Third party investment in non-redeemable noncontrolling interests	15,971		(2,867)
Dividends paid to redeemable noncontrolling interests	(948)		(1,181)
Other	(1,948)		(1,331)
Preferred dividends paid	(10,403)		(10,403)
Net cash provided by (used for) financing activities	(186,602)		(134,496)
Effects of exchange rate changes on foreign currency cash and restricted cash	(6,084)		(30,723)
Increase (decrease) in cash and restricted cash	76,970		166,739
Cash and restricted cash, beginning of year	1,290,544		903,698
Cash and restricted cash, end of period	$	1,367,514	$	1,070,437

See Notes to Consolidated Financial Statements

ARCH CAPITAL 10 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

1.    Basis of Presentation and Recent Accounting Pronouncements

General

Arch Capital Group Ltd. (“Arch Capital”) is a public listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements include the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. See note 11.

Basis of Presentation

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation. 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 at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2020 (“2020 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated

balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.

2.    Share Transactions

Share-Based Compensation

During the 2021 first quarter, the Company granted 1,218,465 stock options, 685,104 performance share awards (“PSAs”) and units (“PSUs”) and 1,168,577 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2021 first quarter were approximately $9.20, $37.38 and $35.82 per share, respectively. Such values are being amortized over the respective substantive vesting period.

During the 2020 first quarter, the Company granted 1,116,073 stock options, 557,204 PSAs and PSUs and 910,879 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2020 first quarter were approximately $8.14, $44.17 and $42.36 per share, respectively. Such values are being amortized over the respective substantive vesting period.

ARCH CAPITAL  11 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Share Repurchases 

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 394.5 million common shares for an aggregate purchase price of $4.23 billion. For the three months ended March 31, 2021, Arch Capital repurchased 5.3 million shares under the share repurchase program with an aggregate purchase price of $179.3 million. Arch Capital repurchased 2.6 million shares

under the share repurchase program with an aggregate purchase price of $75.5 million during the three months ended March 31, 2020. At March 31, 2021, $737.3 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

3.    Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:

	Three Months Ended
	March 31,
	2021		2020
Numerator:
Net income (loss)	$	475,708	$	(88,674)
Amounts attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	$	427,753	$	133,714
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	400,807,895		403,892,161
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,230,794		2,275,473
Stock options (1)	6,184,564		7,865,936
Weighted average common shares and common share equivalents outstanding — diluted	409,223,253		414,033,570
Earnings per common share:
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

4.    Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: construction and national accounts; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).

The mortgage segment includes the Company’s U.S. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.

The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:

	Three Months Ended
	March 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,415,886		$	1,471,060		$	391,246		$	3,277,293		$	216,523		$	3,397,206
Premiums ceded	(421,047)			(471,948)			(56,051)			(948,147)			(37,212)			(888,749)
Net premiums written	994,839			999,112			335,195			2,329,146			179,311			2,508,457
Change in unearned premiums	(175,365)			(354,212)			1,122			(528,455)			(31,580)			(560,035)
Net premiums earned	819,474			644,900			336,317			1,800,691			147,731			1,948,422
Other underwriting income (loss)	—			(1,198)			6,897			5,699			411			6,110
Losses and loss adjustment expenses	(535,747)			(484,870)			(63,689)			(1,084,306)			(118,794)			(1,203,100)
Acquisition expenses	(128,222)			(118,025)			(30,082)			(276,329)			(28,152)			(304,481)
Other operating expenses	(137,113)			(60,514)			(49,131)			(246,758)			(14,275)			(261,033)
Underwriting income (loss)	$	18,392		$	(19,707)		$	200,312		198,997			(13,079)			185,918
Net investment income										78,729			20,127			98,856
Net realized gains (losses)										101,336			41,125			142,461
Equity in net income (loss) of investment funds accounted for using the equity method										71,686			—			71,686
Other income (loss)										(1,741)			—			(1,741)
Corporate expenses (2)										(23,468)			—			(23,468)
Transaction costs and other (2)										(1,201)			(715)			(1,916)
Amortization of intangible assets										(14,402)			—			(14,402)
Interest expense										(34,197)			(4,149)			(38,346)
Net foreign exchange gains (losses)										21,505			(1,442)			20,063
Income (loss) before income taxes and income (loss) from operating affiliates										397,244			41,867			439,111
Income tax (expense) benefit										(38,852)			(8)			(38,860)
Income (loss) from operating affiliates										75,457			—			75,457
Net income (loss)										433,849			41,859			475,708
Amounts attributable to redeemable noncontrolling interests										117			(972)			(855)
Amounts attributable to nonredeemable noncontrolling interests										—			(36,697)			(36,697)
Net income (loss) available to Arch										433,966			4,190			438,156
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	423,563		$	4,190		$	427,753
Underwriting Ratios
Loss ratio	65.4		%	75.2		%	18.9		%	60.2		%	80.4		%	61.7		%
Acquisition expense ratio	15.6		%	18.3		%	8.9		%	15.3		%	19.1		%	15.6		%
Other operating expense ratio	16.7		%	9.4		%	14.6		%	13.7		%	9.7		%	13.4		%
Combined ratio	97.7		%	102.9		%	42.4		%	89.2		%	109.2		%	90.7		%
Goodwill and intangible assets	$	276,211		$	17,807		$	377,841		$	671,859		$	7,650		$	679,509

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

ARCH CAPITAL  14 2021 FIRST QUARTER FORM 10-Q

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

	Three Months Ended
	March 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,207,645		$	1,122,519		$	368,945		$	2,698,537		$	234,902		$	2,832,830
Premiums ceded	(378,897)			(325,339)			(44,327)			(747,991)			(48,202)			(695,584)
Net premiums written	828,748			797,180			324,618			1,950,546			186,700			2,137,246
Change in unearned premiums	(112,829)			(253,720)			20,408			(346,141)			(46,661)			(392,802)
Net premiums earned	715,919			543,460			345,026			1,604,405			140,039			1,744,444
Other underwriting income (loss)	—			2,120			4,599			6,719			133			6,852
Losses and loss adjustment expenses	(507,108)			(430,069)			(67,566)			(1,004,743)			(110,676)			(1,115,419)
Acquisition expenses	(107,337)			(79,606)			(38,536)			(225,479)			(21,804)			(247,283)
Other operating expenses	(129,649)			(45,297)			(45,896)			(220,842)			(13,702)			(234,544)
Underwriting income (loss)	$	(28,175)		$	(9,392)		$	197,627		160,060			(6,010)			154,050
Net investment income										113,028			32,125			145,153
Net realized gains (losses)										(72,109)			(294,851)			(366,960)
Equity in net income (loss) of investment funds accounted for using the equity method										(4,209)			—			(4,209)
Other income (loss)										32			—			32
Corporate expenses (2)										(18,201)			—			(18,201)
Transaction costs and other (2)										(2,595)			—			(2,595)
Amortization of intangible assets										(16,631)			—			(16,631)
Interest expense										(25,245)			(7,310)			(32,555)
Net foreign exchange gains (losses)										63,307			9,364			72,671
Income (loss) before income taxes and income (loss) from operating affiliates										197,437			(266,682)			(69,245)
Income tax (expense) benefit										(27,945)			—			(27,945)
Income (loss) from operating affiliates										8,516			—			8,516
Net income (loss)										178,008			(266,682)			(88,674)
Amounts attributable to redeemable noncontrolling interests										(57)			(1,096)			(1,153)
Amounts attributable to nonredeemable noncontrolling interests										—			233,944			233,944
Net income (loss) available to Arch										177,951			(33,834)			144,117
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	167,548		$	(33,834)		$	133,714
Underwriting Ratios
Loss ratio	70.8		%	79.1		%	19.6		%	62.6		%	79.0		%	63.9		%
Acquisition expense ratio	15.0		%	14.6		%	11.2		%	14.1		%	15.6		%	14.2		%
Other operating expense ratio	18.1		%	8.3		%	13.3		%	13.8		%	9.8		%	13.4		%
Combined ratio	103.9		%	102.0		%	44.1		%	90.5		%	104.4		%	91.5		%
Goodwill and intangible assets	$	268,296		$	2,516		$	426,988		$	697,800		$	7,650		$	705,450

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

5.    Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Three Months Ended
	March 31,
	2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,244,772		1,134,442
Prior years	(41,672)		(19,023)
Total net incurred losses and loss adjustment expenses	1,203,100		1,115,419
Retroactive reinsurance transactions (1)	(183,893)		60,635
Net foreign exchange (gains) losses	(46,877)		(142,573)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(58,984)		(41,260)
Prior years	(585,118)		(561,947)
Total net paid losses and loss adjustment expenses	(644,102)		(603,207)
Net reserve for losses and loss adjustment expenses at end of period	12,527,302		10,239,466
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114
Reserve for losses and loss adjustment expenses at end of period	$	16,443,952	$	14,309,580

(1)     During 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

2021 First Quarter

During the 2021 first quarter, the Company recorded net favorable development on prior year loss reserves of $41.7 million, which consisted of $4.1 million favorable development from the insurance segment, $26.8 million from the reinsurance segment and $10.9 million from the mortgage segment, partially offset by $0.1 million unfavorable from the ‘other’ segment.

The insurance segment’s net favorable development of $4.1 million, or 0.5 loss ratio points, for the 2021 first quarter consisted of $25.0 million of net favorable development in short-tailed and $20.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $14.6 million of favorable development from property (excluding marine), primarily from the 2019 and 2020 accident years (i.e., the year in which a loss occurred), $8.0 million of favorable development in lenders products, primarily from the 2020 accident year, and $2.5

million of favorable development in travel and accident, primarily from the 2020 accident year. Net adverse development in medium-tailed lines included $10.8 million of adverse development in program business, primarily from the 2016 to 2020 accident years, $6.0 million of adverse development in professional liability business, primarily from the 2019 accident year, and $5.0 million of adverse development in surety, primarily from the 2019 accident year.

The reinsurance segment’s net favorable development of $26.8 million, or 4.2 loss ratio points, for the 2021 first quarter consisted of net favorable development in short-tailed, medium-tailed and long-tailed lines. Net favorable development of $17.5 million in short-tailed lines reflected $23.3 million of favorable development related to property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), and $16.6 million of favorable development from other specialty,

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

primarily from the 2018 and 2019 underwriting years, partially offset by $22.5 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $9.3 million in medium and long-tailed lines reflected favorable development in casualty across most underwriting years.

The mortgage segment’s net favorable development was $10.9 million, or 3.2 loss ratio points, for the 2021 first quarter, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.

2020 First Quarter

During the 2020 first quarter, the Company recorded net favorable development on prior year loss reserves of $19.0 million, which consisted of $1.1 million from the insurance segment, $11.6 million from the reinsurance segment, $6.1 million from the mortgage segment and $0.2 million from the ‘other’ segment.

The insurance segment’s net favorable development of $1.1 million, or 0.2 loss ratio points, for the 2020 first quarter consisted of $3.9 million of net favorable development in short-tailed lines, $7.9 million of net adverse development in medium-tailed lines and $5.2 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across 2018 and prior accident years. Net adverse development in medium-tailed lines included $13.2 million of adverse development in contract binding business across most accident years, partially offset by $5.1 million of favorable development in professional liability business. Net favorable development in longer-tailed lines primarily related to construction business driven by the 2017 accident year.

The reinsurance segment’s net favorable development of $11.6 million, or 2.1 loss ratio points, for the 2020 first quarter consisted of $21.5 million of net favorable development in short-tailed and medium-tailed lines and net adverse development of $9.9 million in long-tailed lines. Net favorable development in short-tailed and medium-tailed lines reflected $11.9 million of favorable development in other specialty lines across most underwriting years and $10.5 million of favorable development from property catastrophe business, primarily from the 2015 to 2019 underwriting years. Such amounts were partially offset by $4.3 million of adverse development in property other than property catastrophe business, driven by the 2018 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty reserves from various underwriting years.

The mortgage segment’s net favorable development was $6.1 million, or 1.8 loss ratio points, for the 2020 first quarter. The 2020 first quarter development was primarily driven by subrogation recoveries on second lien and student loan business.

6.    Allowance for Expected Credit Losses

Premiums Receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,670)
Balance at end of period	$	2,618,175	$	36,111
December 31, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(764)
Balance at end of period	$	4,041,076	$	10,872
December 31, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			(1,738)
Balance at end of period	$	4,500,802	$	11,636

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

(1)    At March 31, 2021 and December 31, 2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(2,785)
Balance at end of period	$	1,919,655	$	5,853
December 31, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			1,975
Balance at end of period	$	1,986,924	$	8,638

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

7.    Investment Information

At March 31, 2021, total investable assets of $29.1 billion included $26.3 billion held by the Company and $2.7 billion attributable to Watford.

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses (2)		Cost or Amortized Cost
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	8,072,883	$	242,832	$	(83,961)	$	(2,569)	$	7,916,581
Mortgage backed securities	571,071		7,066		(11,165)		(325)		575,495
Municipal bonds	457,329		19,942		(4,814)		(2)		442,203
Commercial mortgage backed securities	255,373		2,755		(1,721)		(5)		254,344
U.S. government and government agencies	5,042,208		15,102		(30,545)		—		5,057,651
Non-U.S. government securities	2,425,882		127,886		(19,267)		(51)		2,317,314
Asset backed securities	2,028,441		18,817		(4,962)		(878)		2,015,464
Total	18,853,187		434,400		(156,435)		(3,830)		18,579,052
Short-term investments	1,269,631		920		(601)		—		1,269,312
Total	$	20,122,818	$	435,320	$	(157,036)	$	(3,830)	$	19,848,364
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

ARCH CAPITAL  19 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	3,253,030	$	(82,735)	$	15,894	$	(1,226)	$	3,268,924	$	(83,961)
Mortgage backed securities	383,760		(10,271)		20,648		(894)		404,408		(11,165)
Municipal bonds	90,634		(4,737)		1,827		(77)		92,461		(4,814)
Commercial mortgage backed securities	39,863		(759)		23,421		(962)		63,284		(1,721)
U.S. government and government agencies	3,920,377		(30,545)		—		—		3,920,377		(30,545)
Non-U.S. government securities	911,609		(18,433)		16,841		(834)		928,450		(19,267)
Asset backed securities	502,300		(2,391)		142,331		(2,571)		644,631		(4,962)
Total	9,101,573		(149,871)		220,962		(6,564)		9,322,535		(156,435)
Short-term investments	95,579		(601)		—		—		95,579		(601)
Total	$	9,197,152	$	(150,472)	$	220,962	$	(6,564)	$	9,418,114	$	(157,036)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

At March 31, 2021, on a lot level basis, approximately 4,610 security lots out of a total of approximately 11,360 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.1 million. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $0.9 million.

ARCH CAPITAL  20 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

	March 31, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	381,212	$	370,798	$	348,200	$	339,951
Due after one year through five years	11,124,344		10,918,279		10,629,959		10,340,819
Due after five years through 10 years	4,052,472		4,008,520		4,881,564		4,654,754
Due after 10 years	440,274		436,152		482,180		448,139
	15,998,302		15,733,749		16,341,903		15,783,663
Mortgage backed securities	571,071		575,495		630,001		626,368
Commercial mortgage backed securities	255,373		254,344		389,900		384,254
Asset backed securities	2,028,441		2,015,464		1,634,804		1,627,384
Total (1)	$	18,853,187	$	18,579,052	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities Lending Agreements

The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.

The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At March 31, 2021, the fair value of the cash collateral received on securities lending was nil and the fair value of security collateral received was $143.9 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was nil, and the fair value of security collateral received was $301.1 million.

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
March 31, 2021
U.S. government and government agencies	$	16,397	$	—	$	102,743	$	—	$	119,140
Corporate bonds	13,724		—		—		—		13,724
Equity securities	11,022		—		—		—		11,022
Total	$	41,143	$	—	$	102,743	$	—	$	143,886
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	143,886
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

ARCH CAPITAL  21 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Equity Securities, at Fair Value

At March 31, 2021, the Company held $1.5 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.

Other Investments

The following table summarizes the Company’s other investments and other investable assets:

	March 31, 2021		December 31, 2020
Fixed maturities	$	900,304	$	843,354
Other investments	2,318,185		2,331,885
Short-term investments	623,930		557,008
Equity securities	92,935		92,549
Investments accounted for using the fair value option	$	3,935,354	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,435,354	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	March 31, 2021		December 31, 2020
Term loan investments	$	1,187,752	$	1,231,731
Lending	606,207		572,636
Credit related funds	79,355		90,780
Energy	78,500		65,813
Investment grade fixed income	142,630		138,646
Infrastructure	152,352		165,516
Private equity	52,064		48,750
Real estate	19,325		18,013
Total	$	2,318,185	$	2,331,885

Investments Accounted For Using the Equity Method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	March 31, 2021		December 31, 2020
Credit related funds	$	818,344	$	740,060
Equities	357,641		343,058
Real estate	292,424		258,518
Lending	199,913		179,629
Private equity	288,657		235,289
Infrastructure	179,225		175,882
Energy	120,123		115,453
Total	$	2,256,327	$	2,047,889

Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund’s net assets which may otherwise hinder the general partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.

Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company has determined that it is not required to consolidate these investments because it is not the primary beneficiary of the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:

	March 31, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,256,327		2,047,889
Investments accounted for using the fair value option (2)	196,087		184,720
Total	$	2,452,414	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at March 31, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $36.1 million at March 31, 2021, compared to $35.6 million at December 31, 2020.

ARCH CAPITAL  22 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Net Investment Income

The components of net investment income were derived from the following sources:

	March 31,
	2021		2020
Three Months Ended
Fixed maturities	$	90,626	$	114,847
Term loans	14,728		23,170
Equity securities	5,650		6,007
Short-term investments	607		4,896
Other (1)	14,355		19,406
Gross investment income	125,966		168,326
Investment expenses	(27,110)		(23,173)
Net investment income	$	98,856	$	145,153

(1)    Includes income distributions from investment funds and other items.

Net Realized Gains (Losses)

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	March 31,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	65,002	$	178,200
Gross losses on investment sales	(62,998)		(31,968)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	16,553		(127,666)
Other investments	46,855		(307,800)
Equity securities	2,065		(4,909)
Short-term investments	736		(8,681)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	37,849		(539)
Net unrealized gains (losses) on equity securities still held at reporting date	19,708		(175,566)
Allowance for credit losses:
Investments related	(1,648)		(9,320)
Underwriting related	5,268		(3,270)
Net impairment losses	—		(533)
Derivative instruments (1)	36,116		127,189
Other	(23,045)		(2,097)
Net realized gains (losses)	$	142,461	$	(366,960)

(1)    See note 9 for information on the Company’s derivative instruments.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded $71.7 million of equity in net income related to investment funds accounted for using the equity method in the 2021 first quarter, compared to loss of $4.2 million for the 2020 first quarter. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. At March 31, 2021 the Company’s carrying value in Coface was $604.6 million.

ARCH CAPITAL  23 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
March 31, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	182		—		2,421		2,603
Additions (reductions) for previously recognized expected credit losses	(382)		(9)		(540)		(931)
Reductions due to disposals	(83)		—		(156)		(239)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,207	$	2	$	2,621	$	3,830
December 31, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		634
Additions for current-period provision for expected credit losses	2,942		67		7,644		10,653
Additions (reductions) for previously recognized expected credit losses	(1,398)		6		(5,638)		(7,030)
Reductions due to disposals	(571)		(62)		(1,227)		(1,860)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,490	$	11	$	896	$	2,397

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.

The following table details the value of the Company’s restricted assets:

	March 31, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	4,815,120	$	4,643,334
Third party agreements	3,366,016		3,083,324
Deposits with U.S. regulatory authorities	819,444		827,552
Deposits with non-U.S. regulatory authorities	330,197		179,099
Total restricted assets	$	9,330,777	$	8,733,309

In addition, Watford maintains secured credit facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of March 31, 2021 and December 31, 2020, Watford held $1.0 billion and $954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	March 31, 2021		December 31, 2020
Cash	$	941,951	$	906,448
Restricted cash (included in ‘other assets’)	$	425,563	$	384,096
Cash and restricted cash	$	1,367,514	$	1,290,544

ARCH CAPITAL  24 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

8.    Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).

The levels in the hierarchy are defined as follows:

Level 1:	Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets
Level 2:	Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument
Level 3:	Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but

is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the average number of prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at March 31, 2021.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $25.9 billion of financial assets and liabilities measured at fair value at March 31, 2021, approximately $146.9 million, or 0.6%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, were priced using non-binding broker-dealer quotes or modeled valuations.

Fixed maturities

The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs

ARCH CAPITAL  25 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value.

The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:

•U.S. government and government agencies — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.

•Corporate bonds — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Mortgage-backed securities — valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Municipal bonds — valuations provided by independent pricing services, with all prices provided

through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

•Commercial mortgage-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Non-U.S. government securities — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Asset-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Certain

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ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Other investments

The Company’s other investments include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within level 2.

Contingent consideration liabilities

Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at March 31, 2021:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,072,883	$	—	$	8,072,870	$	13
Mortgage backed securities	571,071		—		571,071		—
Municipal bonds	457,329		—		457,329		—
Commercial mortgage backed securities	255,373		—		255,373		—
U.S. government and government agencies	5,042,208		4,949,217		92,991		—
Non-U.S. government securities	2,425,882		—		2,425,882		—
Asset backed securities	2,028,441		—		2,024,969		3,472
Total	18,853,187		4,949,217		13,900,485		3,485
Short-term investments	1,269,631		1,252,535		17,096		—
Equity securities, at fair value	1,543,703		1,476,504		24,087		43,112
Derivative instruments (4)	156,160		—		156,160		—
Residential mortgage loans	5,693		—		5,693		—
Fair value option:
Corporate bonds	724,316		—		723,327		989
Non-U.S. government bonds	23,996		—		23,996		—
Mortgage backed securities	2,828		—		2,828		—
Commercial mortgage backed securities	1,225		—		1,225		—
Asset backed securities	147,666		—		147,666		—
U.S. government and government agencies	273		164		109		—
Short-term investments	623,930		482,869		141,061		—
Equity securities	92,935		21,512		247		71,176
Other investments	1,078,505		31,268		979,307		67,930
Other investments measured at net asset value (2)	1,239,680
Total	3,935,354		535,813		2,019,766		140,095
Total assets measured at fair value	$	25,763,728	$	8,214,069	$	16,123,287	$	186,692
Liabilities measured at fair value:
Contingent consideration liabilities	$	(465)	$	—	$	—	$	(465)
Securities sold but not yet purchased (3)	(34,097)		—		(34,097)		—
Derivative instruments (4)	(98,103)		—		(98,103)		—
Total liabilities measured at fair value	$	(132,665)	$	—	$	(132,200)	$	(465)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Contingent Consideration Liabilities
Three Months Ended March 31, 2021
Balance at beginning of period	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(68)		—		4		248		2,188		904		—
Included in other comprehensive income	114		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		7,365		—		193		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(6,786)		—		—		—
Settlements	—		—		—		—		—		—		(4)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Three Months Ended March 31, 2020
Balance at beginning of period	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	9		7		—		(27)		1,921		(3,721)		(54)
Included in other comprehensive income	(22)		(5,416)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		21		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(17,175)		—		—		—
Settlements	(1,357)		(1,462)		—		—		—		—		85
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

Financial Instruments Disclosed, But Not Carried, At Fair Value

The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at March 31, 2021, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At March 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.4 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 billion. The fair values of the senior notes were obtained from a third party pricing service and are based on observable market inputs. As such, the fair values of the senior notes are classified within Level 2.

9.    Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements. 

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives		Liability Derivatives		Notional Value (1)
March 31, 2021
Futures contracts (2)	$	85,379	$	(54,615)	$	7,116,745
Foreign currency forward contracts (2)	17,898		(29,887)		2,190,031
TBAs (3)	—		—		—
Other (2)	52,883		(13,601)		6,324,926
Total	$	156,160	$	(98,103)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
TBAs (3)	—		—		—
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(1)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

(2)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(3)    The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

The Company did not hold any derivatives which were designated as hedging instruments at March 31, 2021 or December 31, 2020.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.

At March 31, 2021, asset derivatives and liability derivatives of $148.4 million and $98.1 million, respectively, were subject to a master netting agreement, compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. The remaining derivatives included in the preceding table were not subject to a master netting agreement.

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as	March 31,
hedging instruments:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	47,438	$	95,944
Foreign currency forward contracts	(22,071)		(10,870)
TBAs	—		745
Other (1)	10,749		41,370
Total	$	36,116	$	127,189

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

10.    Commitments and Contingencies

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.3 billion at March 31, 2021, compared to $2.1 billion at December 31, 2020.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $1.0 million for the three months ended March 31, 2021, compared to $6.6 million for the 2020 period.

11.    Variable Interest Entities and Noncontrolling Interests

Watford

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of March 31, 2021, the Company owns approximately 10.3% of Watford’s outstanding common equity. The Company also owns $35.0 million in aggregate principal amount of Watford

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Watford’s preference shares.

Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford. As such, the results of Watford are included in the Company’s consolidated financial statements.

The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital has assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The transaction is expected to close in the second quarter of 2021 and remains subject to customary closing conditions. Shareholder approval has been obtained and regulatory approvals are ongoing. Upon closing of the transaction, Watford will be wholly owned by Greysbridge and Greysbridge will be owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC.

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	March 31,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,880,768	$	1,790,385
Fixed maturities available for sale, at fair value	627,387		655,249
Equity securities, at fair value	62,314		52,410
Cash	236,164		211,451
Accrued investment income	14,325		14,679
Premiums receivable	252,523		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	291,485		286,590
Ceded unearned premiums	113,180		122,339
Deferred acquisition costs	62,224		53,705
Receivable for securities sold	68,076		37,423
Goodwill and intangible assets	7,650		7,650
Other assets	87,358		75,801
Total assets of consolidated VIE	$	3,703,454	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,568,243	$	1,519,583
Unearned premiums	426,975		407,714
Reinsurance balances payable	77,041		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,757		172,689
Payable for securities purchased	59,230		25,881
Other liabilities	214,103		193,494
Total liabilities of consolidated VIE	$	2,674,036	$	2,538,317
Redeemable noncontrolling interests	$	52,421	$	52,398

(1)    Includes in “other investments” on the Company’s balance sheet.

For the three months ended March 31, 2021, Watford generated $7.0 million of cash provided by operating activities, $21.4 million of cash provided by investing activities and $1.0 million of cash used for financing activities, compared to $24.6 million of cash provided by operating activities, $35.7 million of cash used for investing activities and $12.3 million of cash provided by financing activities for the three months ended March 31, 2020.

Non-redeemable noncontrolling interests

The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately 90% at March 31, 2021. The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

The following table sets forth activity in the non-redeemable noncontrolling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	21,730		(123)
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	36,697		(233,944)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,570)		(33,058)
Balance, end of period	$	876,864	$	492,785

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Redeemable noncontrolling interests

The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Watford Preference Shares were issued at a discounted amount of $24.50 per share. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

The following table sets forth activity in the redeemable non-controlling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	58,548	$	55,404
Accretion of preference share issuance costs	23		23
Other	(901)		(51)
Balance, end of period	$	57,670	$	55,376

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	March 31,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(36,697)	$	233,944
Amounts attributable to redeemable noncontrolling interests	(855)		(1,153)
Net (income) loss attributable to noncontrolling interests	$	(37,552)	$	232,791

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NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreement benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			March 31, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(306)	$	1,152	$	846	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(1,081)		2,885		1,804		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	66,747		(32)		62		30		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,604)		4,277		2,673		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,117)		7,991		6,874		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(780)		6,577		5,797		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(898)		6,047		5,149		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(908)		8,034		7,126		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	132,881		(58)		294		236		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	368,797		(370)		6,077		5,707		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(433)		9,527		9,094		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	321,393		(23)		5,969		5,946		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		—		4,767		4,767		—		—		—		—
Total	$	4,200,317	$	(7,610)	$	63,659	$	56,049	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

ARCH CAPITAL  34 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

12.    Other Comprehensive Income (Loss)

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended
Details About	Line Item That Includes	March 31,
AOCI Components	Reclassification	2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	2,004	$	146,232
	Provision for credit losses	(1,647)		(9,320)
	Other-than-temporary impairment losses	—		(533)
	Total before tax	357		136,379
	Income tax (expense) benefit	(3,054)		(15,150)
	Net of tax	$	(2,697)	$	121,229

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended March 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(294,360)	$	(32,610)	$	(261,750)
Less reclassification of net realized gains (losses) included in net income	357		3,054		(2,697)
Foreign currency translation adjustments	(28,415)		169		(28,584)
Other comprehensive income (loss)	$	(323,132)	$	(35,495)	$	(287,637)
Three Months Ended March 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(63,451)	$	(6,164)	$	(57,287)
Less reclassification of net realized gains (losses) included in net income	136,379		15,150		121,229
Foreign currency translation adjustments	(45,424)		(735)		(44,689)
Other comprehensive income (loss)	$	(245,254)	$	(22,049)	$	(223,205)

ARCH CAPITAL  35 2021 FIRST QUARTER FORM 10-Q

ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

13.    Income Taxes

The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 7.6% for the three months ended March 31, 2021, compared to (46.0%) for the 2020 period. The Company’s prior year effective tax rate was impacted by significant portion of realized losses generated in lower tax jurisdictions.

The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

The Company had a net deferred tax asset of $48.1 million at March 31, 2021, compared to a net deferred tax asset of $15.7 million at December 31, 2020. The change is primarily a result of market value fluctuations in the investment portfolio. In addition, the Company paid $7.1 million and $7.4 million of income taxes for the three months ended March 31, 2021 and 2020, respectively.

14.    Legal Proceedings

The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of March 31, 2021, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

15.    Transactions with Related Parties

In the 2019 fourth quarter, Barbican, a wholly owned subsidiary of the Company, entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of nil and $275.0 million, respectively, at March 31, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020.

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021.

Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.

ARCH CAPITAL  36 2021 FIRST QUARTER FORM 10-Q

ITEM 2.     MANAGEMENT’S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF OPERATIONS

The following is a discussion and analysis of our financial condition and results of operations. This should be read in conjunction with our consolidated financial statements included in Item 1 of this report and also our Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our Annual Report on Form 10-K for the year ended December 31, 2020 (“2020 Form 10-K”). In addition, readers should review “Risk Factors” set forth in Item 1A of Part I of our 2020 Form 10-K and “ITEM 1A—Risk Factors” of this Form 10-Q. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Arch Capital Group Ltd. (“Arch Capital” and, together with its subsidiaries, “Arch”, “we” or “us”) is a publicly listed Bermuda exempted company with approximately $15.8 billion in capital at March 31, 2021 and, through operations in Bermuda, the United States, Europe, Canada, Australia and Hong Kong, writes insurance, reinsurance and mortgage insurance on a worldwide basis.

CURRENT OUTLOOK

Our three primary areas of focus for 2021 are to continue our growth in the sectors where rates allow for returns that are substantially more than our cost of capital, to optimize our mortgage insurance book as it transitions from forbearance to recovery on its way back to normalcy in the next few quarters, and to actively manage our investments and capital to enhance our returns over the long run.

From an operating perspective, the 2021 first quarter reflected the benefits of attractive pricing in almost all of our insurance markets. As a result, we currently expect the next several quarters to continue to show improved underwriting margins, partially due to the compounding of rate-on-rate increases and the rebalancing of our mix. Importantly, the market is showing discipline in maintaining its momentum and the recent catastrophic losses are likely to keep upward pressure on rates.

Consequently, these rate improvements have enabled us to continue to expand writings in our property casualty segments. In the insurance segment, our rate increases for the first quarter averaged over 11%, representing the fifth consecutive quarter of rate increases in excess of loss cost trends. In reinsurance, we estimate that our effective rate change was roughly 8%. We continue to write a portion of our overall book in catastrophe-exposed business, which has the potential to increase the volatility of our operating results.

The extent to which COVID-19 continues to impact our business, results of operations and financial results depends on numerous evolving factors including, but not limited to the duration of COVID-19, the extent to which it will impact macroeconomic conditions, the speed of the anticipated recovery and governmental, business and individual reactions to the pandemic. During the first quarter of 2021, we did not make any significant changes to our 2020 COVID-19 related loss reserves.

For our U.S. primary mortgage operations, reported delinquencies were 3.86% at March 31, 2021, compared to 4.19% at December 31, 2020. Delinquencies continue to be better than our expectations at the beginning of the COVID-19 pandemic but delinquency rates remain at elevated levels, reflecting the impact of the recession and forbearance programs under the CARES Act to borrowers experiencing a hardship. Forbearance allows for mortgage payments to be suspended for up to 360 days or longer along with a suspension of foreclosures and evictions. See “Results of Operations—Mortgage Segment” for further details on our mortgage operations.

In the first quarter, our U.S. primary mortgage operations saw new insurance written of $27 billion, around 60% above the same period last year. The refinancing boom that began last year has resulted in significant turnover in our insurance in force and lower persistency. However, if mortgage rates continue to rise, we would expect persistency to gradually return to the longer-term range of 75%. Outside of the U.S., we increased our writings in Australia as the housing market remains strong there. We like the long-term opportunity in Australia as demonstrated by our announcement in March to acquire Westpac's LMI business. The agreement allows us to free up capital even as we build our Australian presence and diversify our earning streams at attractive risk-adjusted returns.

We remain committed to providing solutions across many offerings as the marketplace evolves, including the mortgage credit risk transfer programs initiated by government sponsored enterprises, or “GSEs.” In addition, we enter into aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda and issue mortgage insurance linked notes, increasing our protection for mortgage tail risk. The Bellemeade structures provide approximately $4.3 billion of aggregate reinsurance coverage at March 31, 2021.

ARCH CAPITAL  37 2021 FIRST QUARTER FORM 10-Q

FINANCIAL MEASURES

Management uses the following three key financial indicators in evaluating our performance and measuring the overall growth in value generated for Arch Capital’s common shareholders:

Book Value per Share

Book value per share represents total common shareholders’ equity available to Arch divided by the number of common shares outstanding. Management uses growth in book value per share as a key measure of the value generated for our common shareholders each period and believes that book value per share is the key driver of Arch Capital’s share price over time. Book value per share is impacted by, among other factors, our underwriting results, investment returns and share repurchase activity, which has an accretive or dilutive impact on book value per share depending on the purchase price.

Book value per share was $30.54 at March 31, 2021, compared to $30.31 at December 31, 2020 and $26.10 at March 31, 2020. The 0.8% increase in book value per share for the 2021 first quarter reflected the impact of a high level of catastrophic loss activity and the impact of rising interest rates on our fixed income portfolio. Results for the 2021 first quarter reflected a one-time gain of $74.5 million realized from the Company’s recent acquisition of a 29.5% stake in Coface, a global trade credit insurer. The 17.0% increase in book value per share over the trailing twelve months reflected strong underwriting results and investment returns.

Operating Return on Average Common Equity

Operating return on average common equity (“Operating ROAE”) represents annualized after-tax operating income available to Arch common shareholders divided by the average of beginning and ending common shareholders’ equity available to Arch during the period. After-tax operating income available to Arch common shareholders, a non-GAAP financial measure as defined in Regulation G, represents net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings) equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and income taxes. Management uses Operating ROAE as a key measure of the return generated to common shareholders. See “Comment on Non-GAAP Financial Measures.”

Our Operating ROAE was 7.8% for the 2021 first quarter, compared to 7.1% for the 2020 first quarter. The ratios for

both periods reflected the impact of a high level of catastrophic loss activity and low yields on investments.

Total Return on Investments

Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. The following table summarizes our total return compared to the benchmark return against which we measured our portfolio during the periods. See “Comment on Non-GAAP Financial Measures.”

	Arch Portfolio		Benchmark Return
Pre-tax total return (before investment expenses):
2021 First Quarter	(0.18)	%	(0.51)	%
2020 First Quarter	(0.86)	%	(4.55)	%

Total return for the 2021 first quarter reflected the impact of rising interest rates on our fixed income portfolio. We continue to maintain a short duration on our portfolio of 2.71 years at March 31, 2021.

The benchmark return index is a customized combination of indices intended to approximate a target portfolio by asset mix and average credit quality while also matching the approximate estimated duration and currency mix of our insurance and reinsurance liabilities. Although the estimated duration and average credit quality of this index will move as the duration and rating of its constituent securities change, generally we do not adjust the composition of the benchmark return index except to incorporate changes to the mix of liability currencies and durations noted above. The benchmark return index should not be interpreted as expressing a preference for or aversion to any particular sector or sector weight. The index is intended solely to provide, unlike many master indices that change based on the size of their constituent indices, a relatively stable basket of investable indices. At March 31, 2021, the benchmark return index had an average credit quality of “Aa1” by Moody’s Investors Service (“Moody’s”), and an estimated duration of 3.14 years.

ARCH CAPITAL  38 2021 FIRST QUARTER FORM 10-Q

The benchmark return index included weightings to the following indices:

	%
ICE BoAML 1-5 Year A - AAA U.S. Corporate Index	13.00	%
ICE BoAML 5-10 Year A - AAA U.S. Corporate Index	11.00
ICE BoAML 1-5 Year U.S. Treasury Index	11.00
MSCI ACWI Net Total Return USD Index	9.30
ICE BoAML 1-10 Year BBB U.S. Corporate Index	5.00
JPM CLOIE Investment Grade	5.00
S&P/LSTA Leveraged Loan Total Return Index	4.965
ICE BoAML U.S. Mortgage Backed Securities Index	4.00
ICE BoAML AAA US Fixed Rate CMBS	4.00
ICE BoAML 1-5 Year U.K. Gilt Index	4.00
ICE BoAML German Government 1-10 Year Index	3.50
ICE BoAML 0-3 Year U.S. Treasury Index	3.25
ICE BoAML 5-10 Year U.S. Treasury Index	3.00
ICE BoAML 1-10 Year U.S. Municipal Securities Index	3.00
Bloomberg Barclays ABS Aaa Index	3.00
ICE BoAML 1-5 Year Australia Government Index	2.75
ICE BoAML U.S. High Yield Constrained Index	2.50
ICE BoAML 1-5 Year Canada Government Index	2.00
ICE BofA CCC and Lower US High Yield Constrained Index	1.38
Bloomberg Barclays Global High Yield Index	1.38
S&P DJ Global ex-US Select Real Estate Securities Net Index	0.825
FTSE Nareit All Mortgage Capped Index Total Return USD	0.825
Bloomberg Barclays CMBS: Erisa Eligible Unhedged USD	0.825
ICE BoAML 15+ Year Canada Government Index	0.50
Total	100.00	%

COMMENT ON NON-GAAP FINANCIAL MEASURES

Throughout this filing, we present our operations in the way we believe will be the most meaningful and useful to investors, analysts, rating agencies and others who use our financial information in evaluating the performance of our company. This presentation includes the use of after-tax operating income available to Arch common shareholders, which is defined as net income available to Arch common shareholders, excluding net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other and income taxes, and the use of annualized operating return on average common equity. The presentation of after-tax operating income available to Arch common shareholders and annualized operating return on average common equity are non-GAAP financial measures as defined in Regulation G. The reconciliation of such measures to net income available to Arch common shareholders and annualized return on average common equity (the most directly comparable

GAAP financial measures) in accordance with Regulation G is included under “Results of Operations” below.

We believe that net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other in any particular period are not indicative of the performance of, or trends in, our business. Although net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method and net foreign exchange gains or losses are an integral part of our operations, the decision to realize investment gains or losses, the recognition of the change in the carrying value of investments accounted for using the fair value option in net realized gains or losses, the recognition of net impairment losses, the recognition of equity in net income or loss of investment funds accounted for using the equity method and the recognition of foreign exchange gains or losses are independent of the insurance underwriting process and result, in large part, from general economic and financial market conditions. Furthermore, certain users of our financial information believe that, for many companies, the timing of the realization of investment gains or losses is largely opportunistic. In addition, changes in the allowance for credit losses and net impairment losses recognized in earnings on the Company’s investments represent other-than-temporary declines in expected recovery values on securities without actual realization. The use of the equity method on certain of our investments in certain funds that invest in fixed maturity securities is driven by the ownership structure of such funds (either limited partnerships or limited liability companies). In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on our proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). This method of accounting is different from the way we account for our other fixed maturity securities and the timing of the recognition of equity in net income or loss of investment funds accounted for using the equity method may differ from gains or losses in the future upon sale or maturity of such investments. Transaction costs and other include advisory, financing, legal, severance, incentive compensation and other transaction costs related to acquisitions. We believe that transaction costs and other, due to their non-recurring nature, are not indicative of the performance of, or trends in, our business performance. Due to these reasons, we exclude net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other from the calculation of after-tax operating income available to Arch common shareholders.

We believe that showing net income available to Arch common shareholders exclusive of the items referred to above reflects the underlying fundamentals of our business

ARCH CAPITAL  39 2021 FIRST QUARTER FORM 10-Q

since we evaluate the performance of and manage our business to produce an underwriting profit. In addition to presenting net income available to Arch common shareholders, we believe that this presentation enables investors and other users of our financial information to analyze our performance in a manner similar to how management analyzes performance. We also believe that this measure follows industry practice and, therefore, allows the users of financial information to compare our performance with our industry peer group. We believe that the equity analysts and certain rating agencies which follow us and the insurance industry as a whole generally exclude these items from their analyses for the same reasons.

Our segment information includes the presentation of consolidated underwriting income or loss and a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. Such measures represent the pre-tax profitability of our underwriting operations and include net premiums earned plus other underwriting income, less losses and loss adjustment expenses, acquisition expenses and other operating expenses. Other operating expenses include those operating expenses that are incremental and/or directly attributable to our individual underwriting operations. Underwriting income or loss does not incorporate items included in our corporate (non-underwriting) segment. While these measures are presented in note 4, “Segment Information,” of the notes accompanying our consolidated financial statements, they are considered non-GAAP financial measures when presented elsewhere on a consolidated basis. The reconciliations of underwriting income or loss to income before income taxes (the most directly comparable GAAP financial measure) on a consolidated basis and a subtotal before the contribution from the ‘other’ segment, in accordance with Regulation G, is shown in note 4, “Segment Information” to our consolidated financial statements.

We measure segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangibles and, accordingly, investment income and other non-underwriting related items are not allocated to each underwriting segment. For the ‘other’ segment, performance is measured based on net income or loss.

Along with consolidated underwriting income, we provide a subtotal of underwriting income or loss before the contribution from the ‘other’ segment. The ‘other’ segment includes the results of Watford Holdings Ltd. Watford Holdings Ltd. is the parent of Watford Re Ltd., a multi-line Bermuda reinsurance company (together with Watford Holdings Ltd., “Watford”). Pursuant to generally accepted accounting principles, Watford is considered a variable

interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate the results of Watford in our consolidated financial statements, although we only own approximately 10% of Watford’s common equity. Watford’s own management and board of directors are responsible for its results and profitability. In addition, we do not guarantee or provide credit support for Watford. Since Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. Our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. We believe that presenting certain information excluding the ‘other’ segment enables investors and other users of our financial information to analyze our performance in a manner similar to how our management analyzes performance.

Our presentation of segment information includes the use of a current year loss ratio which excludes favorable or adverse development in prior year loss reserves. This ratio is a non-GAAP financial measure as defined in Regulation G. The reconciliation of such measure to the loss ratio (the most directly comparable GAAP financial measure) in accordance with Regulation G is shown on the individual segment pages. Management utilizes the current year loss ratio in its analysis of the underwriting performance of each of our underwriting segments.

Total return on investments includes investment income, equity in net income or loss of investment funds accounted for using the equity method, net realized gains and losses (excluding changes in the allowance for credit losses on non-investment related financial assets) and the change in unrealized gains and losses generated by Arch’s investment portfolio. Total return is calculated on a pre-tax basis and before investment expenses, excludes amounts reflected in the ‘other’ segment, and reflects the effect of financial market conditions along with foreign currency fluctuations. In addition, total return incorporates the timing of investment returns during the periods. There is no directly comparable GAAP financial measure for total return. Management uses total return on investments as a key measure of the return generated to Arch common shareholders, and compares the return generated by our investment portfolio against benchmark returns during the periods.

ARCH CAPITAL  40 2021 FIRST QUARTER FORM 10-Q

RESULTS OF OPERATIONS

The following table summarizes our consolidated financial data, including a reconciliation of net income or loss available to Arch common shareholders to after-tax operating income or loss available to Arch common shareholders. Each line item reflects the impact of our percentage ownership of Watford’s common equity during such period.

	Three Months Ended
	March 31,
	2021		2020
Net income available to Arch common shareholders	$	427,753	$	133,714
Net realized (gains) losses	(105,551)		109,364
Equity in net (income) loss of investment funds accounted for using the equity method	(71,686)		4,209
Net foreign exchange (gains) losses	(21,332)		(64,491)
Transaction costs and other	1,274		2,595
Income tax expense (1)	9,311		4,365
After-tax operating income available to Arch common shareholders	$	239,769	$	189,756
Beginning common shareholders’ equity	$	12,325,886	$	10,717,371
Ending common shareholders’ equity	12,316,472		10,587,244
Average common shareholders’ equity	$	12,321,179	$	10,652,308
Annualized return on average common equity %	13.9		5.0
Annualized operating return on average common equity %	7.8		7.1

(1) Income tax expense on net realized gains or losses, equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses and transaction costs and other reflects the relative mix reported by jurisdiction and the varying tax rates in each jurisdiction.

Segment Information

We classify our businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — corporate (non-underwriting) and ‘other.’ Our insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to our chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for our three underwriting segments based on underwriting income or loss. We do not manage our assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

We determined our reportable segments using the management approach described in accounting guidance

regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of our consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

Insurance Segment

The following tables set forth our insurance segment’s underwriting results:

	Three Months Ended March 31,
	2021			2020			%  Change
Gross premiums written	$	1,415,886		$	1,207,645		17.2
Premiums ceded	(421,047)			(378,897)
Net premiums written	994,839			828,748			20.0
Change in unearned premiums	(175,365)			(112,829)
Net premiums earned	819,474			715,919			14.5
Other underwriting income (loss)	—			—
Losses and loss adjustment expenses	(535,747)			(507,108)
Acquisition expenses	(128,222)			(107,337)
Other operating expenses	(137,113)			(129,649)
Underwriting income (loss)	$	18,392		$	(28,175)		165.3
Underwriting Ratios							% Point Change
Loss ratio	65.4		%	70.8		%	(5.4)
Acquisition expense ratio	15.6		%	15.0		%	0.6
Other operating expense ratio	16.7		%	18.1		%	(1.4)
Combined ratio	97.7		%	103.9		%	(6.2)

The insurance segment consists of our insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

•Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs).

•Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks.

•Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing.

ARCH CAPITAL  41 2021 FIRST QUARTER FORM 10-Q

•Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis.

•Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure.

•Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and standalone terrorism are also offered.

•Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups.

•Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1,000 companies and smaller transaction business programs.

Premiums Written.

The following tables set forth our insurance segment’s net premiums written by major line of business:

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	170,498	17.1	$	127,585	15.4
Professional lines	238,246		23.9	169,118		20.4
Programs	158,401		15.9	112,532		13.6
Construction and national accounts	134,792		13.5	115,999		14.0
Excess and surplus casualty	85,593		8.6	65,419		7.9
Travel, accident and health	92,306		9.3	126,046		15.2
Lenders products	34,860		3.5	33,292		4.0
Other	80,143		8.1	78,757		9.5
Total	$	994,839	100.0	$	828,748	100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the insurance segment in the 2021 first quarter were 17.2% higher than in the 2020 first quarter, while net premiums written were 20.0% higher. The higher level of net premiums written reflected increases across most lines of business, due in part to new business opportunities, rate increases and growth in existing accounts, partially offset by a decrease in travel business, reflecting the ongoing impact of the COVID-19 global pandemic.

Net Premiums Earned.

The following tables set forth our insurance segment’s net premiums earned by major line of business:

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Property, energy, marine and aviation	$	157,259	19.2	$	111,183	15.5
Professional lines	199,671		24.4	151,700		21.2
Programs	112,840		13.8	108,878		15.2
Construction and national accounts	102,671		12.5	99,700		13.9
Excess and surplus casualty	75,367		9.2	65,097		9.1
Travel, accident and health	49,666		6.1	77,375		10.8
Lenders products	40,081		4.9	25,343		3.5
Other	81,919		10.0	76,643		10.7
Total	$	819,474	100.0	$	715,919	100.0

ARCH CAPITAL  42 2021 FIRST QUARTER FORM 10-Q

Net premiums written are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months. Net premiums earned in the 2021 first quarter were 14.5% higher than in the 2020 first quarter. Net premiums earned reflect changes in net premiums written over the previous five quarters.

Losses and Loss Adjustment Expenses.

The table below shows the components of the insurance segment’s loss ratio:

	Three Months Ended
	March 31,
	2021		2020
Current year	65.9	%	71.0	%
Prior period reserve development	(0.5)	%	(0.2)	%
Loss ratio	65.4	%	70.8	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The insurance segment’s current year loss ratio in the 2021 first quarter was 5.1 points lower than in the 2020 first quarter. The 2021 first quarter loss ratio reflected 5.1 points of current year catastrophic activity, primarily from winter storms Uri and Viola, compared to 6.9 points of catastrophic activity for the 2020 first quarter, which included 5.0 points for exposure to the COVID-19 global pandemic.

Prior Period Reserve Development.

The insurance segment’s net favorable development was $4.1 million, or 0.5 points, for the 2021 first quarter, compared to $1.1 million, or 0.2 points, for the 2020 first quarter. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the insurance segment’s prior year reserve development.

Underwriting Expenses.

2021 First Quarter versus 2020 Period. The insurance segment’s underwriting expense ratio was 32.3% in the 2021 first quarter, compared to 33.1% in the 2020 first quarter, with the decrease primarily due to growth in net premiums earned.

Reinsurance Segment 

The following tables set forth our reinsurance segment’s underwriting results:

	Three Months Ended March 31,
	2021			2020			%  Change
Gross premiums written	$	1,471,060		$	1,122,519		31.0
Premiums ceded	(471,948)			(325,339)
Net premiums written	999,112			797,180			25.3
Change in unearned premiums	(354,212)			(253,720)
Net premiums earned	644,900			543,460			18.7
Other underwriting income (loss)	(1,198)			2,120
Losses and loss adjustment expenses	(484,870)			(430,069)
Acquisition expenses	(118,025)			(79,606)
Other operating expenses	(60,514)			(45,297)
Underwriting income (loss)	$	(19,707)		$	(9,392)		(109.8)
Underwriting Ratios							% Point Change
Loss ratio	75.2		%	79.1		%	(3.9)
Acquisition expense ratio	18.3		%	14.6		%	3.7
Other operating expense ratio	9.4		%	8.3		%	1.1
Combined ratio	102.9		%	102.0		%	0.9

The reinsurance segment consists of our reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include:

•Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business.

•Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs.

•Other specialty: provides coverage to ceding company clients for proportional motor and other lines, including surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and political risk.

•Property catastrophe: provides protection for most catastrophic losses that are covered in the underlying policies written by reinsureds, including hurricane, earthquake, flood, tornado, hail and fire, and coverage for other perils on a case-by-case basis. Property catastrophe reinsurance provides coverage on an excess of loss basis when aggregate losses and loss adjustment expense from a single occurrence or aggregation of losses from a covered peril exceed the retention specified in the contract.

ARCH CAPITAL  43 2021 FIRST QUARTER FORM 10-Q

•Property excluding property catastrophe: provides coverage for both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss treaty basis and on a facultative basis. In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis.

•Other: includes life reinsurance business on both a proportional and non-proportional basis, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance.

Premiums Written.

The following tables set forth our reinsurance segment’s net premiums written by major line of business:

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	292,833	29.3	$	158,924	19.9
Property catastrophe	117,207		11.7	89,092		11.2
Other specialty	284,331		28.5	284,952		35.7
Casualty	218,256		21.8	190,880		23.9
Marine and aviation	61,638		6.2	49,785		6.2
Other	24,847		2.5	23,547		3.0
Total	$	999,112	100.0	$	797,180	100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the reinsurance segment in the 2021 first quarter were 31.0% higher than in the 2020 first quarter, while net premiums written were 25.3% higher. Premiums written for the reinsurance segment in the 2020 first quarter were affected by the presence of an $88 million loss portfolio transfer contract, written and fully earned in the period in the other specialty line of business. Absent this transaction, gross and net premiums written would have been higher than in the 2020 first quarter by 42.2% and 40.8%, respectively. The growth in net premiums written reflected increases in most lines of business, mainly due to rate increases and new business.

Net Premiums Earned.

The following tables set forth our reinsurance segment’s net premiums earned by major line of business:

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Property excluding property catastrophe	$	187,782	29.1	$	112,652	20.7
Property catastrophe	88,011		13.6	53,000		9.8
Other specialty	163,898		25.4	203,385		37.4
Casualty	149,031		23.1	135,071		24.9
Marine and aviation	40,108		6.2	24,858		4.6
Other	16,070		2.5	14,494		2.7
Total	$	644,900	100.0	$	543,460	100.0

Net premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Excluding the loss portfolio transfer contract, net premiums earned by the reinsurance segment in the 2021 first quarter were 41.5% higher than in the 2020 first quarter, and reflect changes in net premiums written over the previous five quarters.

Other Underwriting Income (Loss).

Other underwriting income for the 2021 first quarter was a loss of $1.2 million, compared to a gain of $2.1 million for the 2020 first quarter.

Losses and Loss Adjustment Expenses.

The table below shows the components of the reinsurance segment’s loss ratio:

	Three Months Ended
	March 31,
	2021		2020
Current year	79.4	%	81.2	%
Prior period reserve development	(4.2)	%	(2.1)	%
Loss ratio	75.2	%	79.1	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The reinsurance segment’s current year loss ratio in the 2021 first quarter was 1.8 points lower than in the 2020 first quarter. The 2021 first quarter loss ratio reflected 24.7 points of current year catastrophic activity, including winter storms Uri and Viola as well as other minor global events. The 2020 first quarter included 12.7 points of catastrophic activity, included 9.3 points for exposure to the COVID-19 pandemic.

ARCH CAPITAL  44 2021 FIRST QUARTER FORM 10-Q

Prior Period Reserve Development.

The reinsurance segment’s net favorable development was $26.8 million, or 4.2 points, for the 2021 first quarter, compared to $11.6 million, or 2.1 points, for the 2020 first quarter. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the reinsurance segment’s prior year reserve development.

Underwriting Expenses.

2021 First Quarter versus 2020 Period. The underwriting expense ratio for the reinsurance segment was 27.7% in the 2021 first quarter, compared to 22.9% in the 2020 first quarter. The 2020 first quarter ratio reflected a 4.4 point benefit related to the loss portfolio transfer contract and changes in mix of business.

Mortgage Segment 

Our mortgage operations include U.S. and international mortgage insurance and reinsurance operations as well as participation in GSE credit risk-sharing transactions. Our mortgage group includes direct mortgage insurance in the U.S. primarily through Arch Mortgage Insurance Company, United Guaranty Residential Insurance Company and Arch Mortgage Guaranty Company (together, “Arch MI U.S.”); mortgage reinsurance by Arch Reinsurance Ltd. (“Arch Re Bermuda”) to mortgage insurers on both a proportional and non-proportional basis globally; direct mortgage insurance in Europe through Arch Insurance (EU) Designated Activity Company (“Arch Insurance EU”); in Hong Kong through Arch MI Asia Limited (“Arch MI Asia”); in Australia through Arch LMI Pty Ltd (“Arch LMI”) and participation in various GSE credit risk-sharing products primarily through Arch Re Bermuda.

The following tables set forth our mortgage segment’s underwriting results.

	Three Months Ended March 31,
	2021			2020			% Change
Gross premiums written	$	391,246		$	368,945		6.0
Premiums ceded	(56,051)			(44,327)
Net premiums written	335,195			324,618			3.3
Change in unearned premiums	1,122			20,408
Net premiums earned	336,317			345,026			(2.5)
Other underwriting income	6,897			4,599
Losses and loss adjustment expenses	(63,689)			(67,566)
Acquisition expenses	(30,082)			(38,536)
Other operating expenses	(49,131)			(45,896)
Underwriting income	$	200,312		$	197,627		1.4
Underwriting Ratios							% Point Change
Loss ratio	18.9		%	19.6		%	(0.7)
Acquisition expense ratio	8.9		%	11.2		%	(2.3)
Other operating expense ratio	14.6		%	13.3		%	1.3
Combined ratio	42.4		%	44.1		%	(1.7)

Premiums Written.

The following tables set forth our mortgage segment’s net premiums written by underwriting location (i.e., where the business is underwritten):

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	247,529	73.8	$	264,108	81.4
Other	87,666		26.2	60,510		18.6
Total	$	335,195	100.0	$	324,618	100.0

2021 First Quarter versus 2020 Period. Gross premiums written by the mortgage segment in the 2021 first quarter were 6.0% higher than in the 2020 first quarter, while net premiums written were 3.3% higher, primarily reflecting growth in Australian single premium mortgage insurance, partially offset by a lower level of U.S. primary mortgage insurance in force on monthly premium policies.

The persistency rate, which represents the percentage of mortgage insurance in force at the beginning of a 12-month period that remains in force at the end of such period, was 54.1% for the Arch MI U.S. portfolio of mortgage insurance policies at March 31, 2021, reflecting the higher level of mortgage refinancing activity, compared to 58.7% at December 31, 2020.

ARCH CAPITAL  45 2021 FIRST QUARTER FORM 10-Q

The following tables provide details on the new insurance written (“NIW”) generated by Arch MI U.S. NIW represents the original principal balance of all loans that received coverage during the period.

(U.S. Dollars in millions)	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Total new insurance written (NIW) (1)	$	27,019		$	16,778
Credit quality (FICO):
>=740	$	17,818	65.9	$	10,069	60.0
680-739	8,418		31.2	5,787		34.5
620-679	783		2.9	922		5.5
Total	$	27,019	100.0	$	16,778	100.0
Loan-to-value (LTV):
95.01% and above	$	1,608	6.0	$	1,668	9.9
90.01% to 95.00%	12,288		45.5	7,199		42.9
85.01% to 90.00%	8,312		30.8	5,329		31.8
85.00% and below	4,811		17.8	2,582		15.4
Total	$	27,019	100.0	$	16,778	100.0
Monthly vs. single:
Monthly	$	24,989	92.5	$	15,692	93.5
Single	2,030		7.5	1,086		6.5
Total	$	27,019	100.0	$	16,778	100.0
Purchase vs. refinance:
Purchase	$	20,505	75.9	$	12,299	73.3
Refinance	6,514		24.1	4,479		26.7
Total	$	27,019	100.0	$	16,778	100.0

(1)Represents the original principal balance of all loans that received coverage during the period.

Net Premiums Earned.

The following tables set forth our mortgage segment’s net premiums earned by underwriting location:

	Three Months Ended March 31,
	2021			2020
	Amount		%	Amount		%
Underwriting location:
United States	$	262,550	78.1	$	289,162	83.8
Other	73,767		21.9	55,864		16.2
Total	$	336,317	100.0	$	345,026	100.0

2021 First Quarter versus 2020 Period. Net premiums earned for the 2021 first quarter were 2.5% lower than in the 2020 first quarter, and reflected a decrease in U.S. primary mortgage insurance in force, partially offset by an increase in earnings from Australian single premium policy terminations.

Other Underwriting Income.

Other underwriting income, which is primarily related to GSE credit risk-sharing transactions was $6.9 million for the 2021 first quarter, compared to $4.6 million for the 2020 first quarter.

Losses and Loss Adjustment Expenses.

The table below shows the components of the mortgage segment’s loss ratio:

	Three Months Ended
	March 31,
	2021		2020
Current year	22.1	%	21.4	%
Prior period reserve development	(3.2)	%	(1.8)	%
Loss ratio	18.9	%	19.6	%

Current Year Loss Ratio.

2021 First Quarter versus 2020 Period. The mortgage segment’s current year loss ratio was 0.7 points higher in the 2021 first quarter than in the 2020 first quarter. The 2021 first quarter loss ratio reflected continued elevated new delinquency rates, primarily due to financial stress related to the COVID-19 pandemic.

For both the 2021 and 2020 periods, incurred losses were due, in part, to financial stress from the COVID-19 pandemic. Segregating estimated losses due to COVID-19 from the overall mortgage segment estimated losses would require knowledge of the number of delinquencies specifically attributable to COVID-19. As this analysis cannot be performed accurately, the Company is not reporting COVID-19 provisions separately from its overall loss provisions.

Prior Period Reserve Development.

The mortgage segment’s net favorable development was $10.9 million, or 3.2 points, for the 2021 first quarter, compared to $6.1 million, or 1.8 points, for the 2020 first quarter. See note 5, “Reserve for Losses and Loss Adjustment Expenses,” to our consolidated financial statements for information about the mortgage segment’s prior year reserve development.

Underwriting Expenses.

2021 First Quarter versus 2020 Period. The underwriting expense ratio for the mortgage segment was 23.5% in the 2021 first quarter, compared to 24.5% in the 2020 first quarter, with the decrease reflecting lower acquisition expenses on U.S. primary mortgage insurance and to a lesser extent international business.

Corporate (Non-Underwriting) Segment

The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, items related to our non-cumulative preferred shares, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets

ARCH CAPITAL  46 2021 FIRST QUARTER FORM 10-Q

and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment. See note 1, “Basis of Presentation and Recent Accounting Pronouncements,” to our consolidated financial statements for information about the change in presentation of income or loss from operating affiliates.

Net Investment Income.

The components of net investment income were derived from the following sources:

	Three Months Ended
	March 31,
	2021		2020
Fixed maturities	$	79,017	$	101,763
Equity securities	5,650		5,630
Short-term investments	644		3,385
Other (1)	15,559		20,479
Gross investment income	100,870		131,257
Investment expenses (2)	(22,141)		(18,229)
Net investment income	$	78,729	$	113,028

(1)    Amounts include dividends and other distributions on investment funds, term loan investments, funds held balances, cash balances and other items.

(2)    Investment expenses were approximately 0.35% of average invested assets for the 2021 first quarter, consistent with 0.35% for the 2020 first quarter.

The lower level of net investment income for the 2021 first quarter primarily related to lower yields available in the financial market. The pre-tax investment income yield, calculated based on amortized cost and on an annualized basis, was 1.31% for the 2021 first quarter, compared to 2.20% for the 2020 first quarter.

Corporate Expenses.

Corporate expenses were $23.5 million for the 2021 first quarter, compared to $18.2 million for the 2020 first quarter. The increase in corporate expenses was primarily due to higher incentive compensation costs.

Transaction Costs and Other.

Transaction costs and other were $1.2 million for the 2021 first quarter, compared to $2.6 million for the 2020 first quarter. Amounts in the 2021 and 2020 periods are primarily related to acquisitions activity for the respective period.

Amortization of Intangible Assets.

Amortization of intangible assets for the 2021 first quarter was $14.4 million, compared to $16.6 million for the 2020 first quarter. Amounts in 2021 and 2020 primarily related to

amortization of finite-lived intangible assets. See the consolidated financial statements contained in our 2020 Form 10-K for disclosures on our amortization pattern.

Interest Expense.

Interest expense was $34.2 million for the 2021 first quarter, compared to the $25.2 million for the 2020 first quarter. The higher level of interest expense mainly resulted from the issuance of $1.0 billion of 3.635% senior notes in June 2020.

Net Realized Gains or Losses.

We recorded net realized gains of $101.3 million for the 2021 first quarter, compared to net realized losses of $72.1 million for the 2020 first quarter. Currently, our portfolio is actively managed to maximize total return within certain guidelines. The effect of financial market movements on the investment portfolio will directly impact net realized gains and losses as the portfolio is adjusted and rebalanced. Net realized gains or losses from the sale of fixed maturities primarily results from our decisions to reduce credit exposure, to change duration targets, to rebalance our portfolios or due to relative value determinations.

Net realized gains or losses also include realized and unrealized contract gains and losses on our derivative instruments, changes in the fair value of assets accounted for using the fair value option and in the fair value of equities, along with changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings. See note 7, “Investment Information—Net Realized Gains (Losses),” to our consolidated financial statements for additional information. See note 7, “Investment Information—Allowance for Credit Losses,” to our consolidated financial statements for additional information.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method.

We recorded $71.7 million of equity in net income related to investment funds accounted for using the equity method in the 2021 first quarter, compared to a loss of $4.2 million for the 2020 first quarter. Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Investment funds accounted for using the equity method totaled $2.3 billion at March 31, 2021, compared to $2.0 billion at December 31, 2020. See note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements for additional information.

Net Foreign Exchange Gains or Losses.

Net foreign exchange gains for the 2021 first quarter were $21.5 million, compared to net foreign exchange gains for the 2020 first quarter of $63.3 million. Amounts in both periods

ARCH CAPITAL  47 2021 FIRST QUARTER FORM 10-Q

were primarily unrealized and resulted from the effects of revaluing our net insurance liabilities required to be settled in foreign currencies at each balance sheet date.

Income Tax Expense.

Our income tax provision on income (loss) before income taxes, including income (loss) from operating affiliates, resulted in an expense of 8.2% for the 2021 first quarter, compared to 13.6% for the 2020 first quarter. Such amounts exclude the results of the ‘other’ segment. Our effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

Income (loss) from operating affiliates.

We recorded $75.5 million of net income from our operating affiliates in the 2021 first quarter, compared to $8.5 million for the 2020 first quarter. Results for the 2021 first quarter reflected a one-time gain of $74.5 million realized from the Company’s acquisition of 29.5% of the common equity in Coface, a global trade credit insurer. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years.

Other Segment 

The ‘other’ segment includes the results of Watford. Pursuant to generally accepted accounting principles, Watford is considered a variable interest entity and we concluded that we are the primary beneficiary of Watford. As such, we consolidate the results of Watford in our consolidated financial statements, although we only own approximately 10% of Watford’s common equity. See note 11, “Variable Interest Entities and Noncontrolling Interests,” and note 4, “Segment Information,” to our consolidated financial statements for additional information on Watford.

CRITICAL ACCOUNTING POLICIES,

ESTIMATES AND RECENT ACCOUNTING PRONOUNCEMENTS

Critical accounting policies, estimates and recent accounting pronouncements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020 Form 10-K, updated where applicable in the notes accompanying our consolidated financial statements, including note 1, “Basis of Presentation and Recent Accounting Pronouncements.”

FINANCIAL CONDITION

Investable Assets 

At March 31, 2021, total investable assets held by Arch were $26.3 billion, excluding the $2.7 billion included in the ‘other’ segment (i.e., attributable to Watford).

Investable Assets Held by Arch 

The following table summarizes the fair value of the investable assets held by Arch:

Investable assets (1):	Estimated Fair Value			% of Total
March 31, 2021
Fixed maturities (2)	$	18,627,372		70.7
Short-term investments (2)	1,409,960			5.4
Cash	705,787			2.7
Equity securities (2)	1,507,029			5.7
Other investments (2)	1,527,999			5.8
Other investable assets (3)	500,000			1.9
Investments accounted for using the equity method	2,256,327			8.6
Securities transactions entered into but not settled at the balance sheet date	(195,875)			(0.7)
Total investable assets held by Arch	$	26,338,599		100.0
Average effective duration (in years)	2.71
Average S&P/Moody’s credit ratings (4)	AA-/Aa3
Embedded book yield (5)	1.59		%
December 31, 2020
Fixed maturities (2)	$	18,771,296		69.9
Short-term investments (2)	2,063,240			7.7
Cash	694,997			2.6
Equity securities (2)	1,436,104			5.3
Other investments (2)	1,480,347			5.5
Other investable assets (3)	500,000			1.9
Investments accounted for using the equity method	2,047,889			7.6
Securities transactions entered into but not settled at the balance sheet date	(137,578)			(0.5)
Total investable assets held by Arch	$	26,856,295		100.0
Average effective duration (in years)	3.01
Average S&P/Moody’s credit ratings (4)	AA/Aa2
Embedded book yield (5)	1.56		%

(1)In securities lending transactions, we receive collateral in excess of the fair value of the securities pledged. For purposes of this table, we have excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value.

(2)Includes investments carried as available for sale, at fair value and at fair value under the fair value option.

(3)Represents participation interests in a receivable of a reverse repurchase agreement.

(4)Average credit ratings on our investment portfolio on securities with ratings by Standard & Poor’s Rating Services (“S&P”) and Moody’s Investors Service (“Moody’s”).

(5)Before investment expenses.

ARCH CAPITAL  48 2021 FIRST QUARTER FORM 10-Q

At March 31, 2021, approximately $18.1 billion, or 68.8%, of total investable assets held by Arch were internally managed, compared to $19.2 billion, or 71.4%, at December 31, 2020.

The following table summarizes our fixed maturities and fixed maturities pledged under securities lending agreements (“Fixed Maturities”) by type:

	Estimated Fair Value		% of Total
March 31, 2021
Corporate bonds	$	8,233,771	44.2
Residential mortgage backed securities	558,584		3.0
Municipal bonds	455,550		2.4
Commercial mortgage backed securities	256,598		1.4
U.S. government and government agencies	4,876,796		26.2
Non-U.S. government securities	2,287,921		12.3
Asset backed securities	1,958,152		10.5
Total	$	18,627,372	100.0
December 31, 2020
Corporate bonds	$	8,039,745	42.8
Residential mortgage backed securities	616,619		3.3
Municipal bonds	492,734		2.6
Commercial mortgage backed securities	390,990		2.1
U.S. government and government agencies	5,354,863		28.5
Non-U.S. government securities	2,310,157		12.3
Asset backed securities	1,566,188		8.3
Total	$	18,771,296	100.0

The following table provides the credit quality distribution of our Fixed Maturities. For individual fixed maturities, S&P ratings are used. In the absence of an S&P rating, ratings from Moody’s are used, followed by ratings from Fitch Ratings.

	Estimated Fair Value		% of Total
March 31, 2021
U.S. government and gov’t agencies (1)	$	5,432,191	29.2
AAA	3,145,642		16.9
AA	2,069,764		11.1
A	3,878,113		20.8
BBB	2,829,202		15.2
BB	622,448		3.3
B	331,144		1.8
Lower than B	57,659		0.3
Not rated	261,209		1.4
Total	$	18,627,372	100.0
December 31, 2020
U.S. government and gov’t agencies (1)	$	5,963,758	31.8
AAA	3,117,046		16.6
AA	2,063,738		11.0
A	3,760,280		20.0
BBB	2,699,201		14.4
BB	574,189		3.1
B	268,095		1.4
Lower than B	54,795		0.3
Not rated	270,194		1.4
Total	$	18,771,296	100.0

(1)Includes U.S. government-sponsored agency residential mortgage-backed securities and agency commercial mortgage-backed securities.

The following table provides information on the severity of the unrealized loss position as a percentage of amortized cost for all Fixed Maturities which were in an unrealized loss position:

Severity of gross unrealized losses:	Estimated Fair Value		Gross Unrealized Losses		% of Total Gross Unrealized Losses
March 31, 2021
0-10%	$	9,047,946	$	(139,904)	93.0
10-20%	58,325		(7,860)		5.2
20-30%	8,556		(2,095)		1.4
Greater than 30%	193		(570)		0.4
Total	$	9,115,020	$	(150,429)	100.0
December 31, 2020
0-10%	$	3,583,981	$	(55,542)	79.4
10-20%	95,495		(12,183)		17.4
20-30%	1,061		(406)		0.6
Greater than 30%	1,249		(1,785)		2.6
Total	$	3,681,786	$	(69,916)	100.0

ARCH CAPITAL  49 2021 FIRST QUARTER FORM 10-Q

The following table summarizes our top ten exposures to fixed income corporate issuers by fair value at March 31, 2021, excluding guaranteed amounts and covered bonds:

	Estimated Fair Value		Credit Rating (1)
JPMorgan Chase & Co.	$	389,799	A-/A2
Bank of America Corporation	312,603		A-/A2
Wells Fargo & Company	237,410		BBB+/A2
Citigroup Inc.	231,573		BBB+/A3
Morgan Stanley	214,190		BBB+/A1
The Goldman Sachs Group, Inc.	174,407		BBB+/A2
Nestlé S.A.	158,152		AA-/Aa3
Apple Inc.	131,135		AA+/Aa1
Chevron Corporation	110,767		AA-/Aa2
AT&T Inc.	103,918		BBB/Baa2
Total	$	2,063,954

(1)Average credit ratings as assigned by S&P and Moody’s, respectively.

The following table provides information on our structured securities, which includes residential mortgage-backed securities (“RMBS”), commercial mortgage-backed securities (“CMBS”) and asset-backed securities (“ABS”):

	Agencies		Investment Grade		Below Investment Grade		Total
Mar 31, 2021
RMBS	$	525,144	$	1,627	$	31,813	$	558,584
CMBS	30,251		201,132		25,215		256,598
ABS	—		1,765,074		193,078		1,958,152
Total	$	555,395	$	1,967,833	$	250,106	$	2,773,334
Dec 31, 2020
RMBS	$	584,499	$	4,102	$	28,018	$	616,619
CMBS	24,396		342,491		24,103		390,990
ABS	—		1,403,137		163,051		1,566,188
Total	$	608,895	$	1,749,730	$	215,172	$	2,573,797

The following table summarizes our equity securities, which include investments in exchange traded funds:

	March 31, 2021		December 31, 2020
Equities (1)	$	782,747	$	676,437
Exchange traded funds
Fixed income (2)	235,606		341,139
Equity and other (3)	488,676		418,528
Total	$	1,507,029	$	1,436,104

(1)Primarily in consumer non-cyclical, consumer cyclical, technology, communications and financial stocks at March 31, 2021.

(2)Primarily in corporate, MBS and municipal strategies at March 31, 2021.

(3)Primarily in utilities, large cap stocks and foreign equities at March 31, 2021.

The following table summarizes our other investments and other investable assets:

	March 31, 2021		December 31, 2020
Lending	$	606,207	$	572,636
Term loan investments	397,566		380,193
Energy	78,500		65,813
Credit related funds	79,355		90,780
Investment grade fixed income	142,630		138,646
Infrastructure	152,352		165,516
Private equity	52,064		48,750
Real estate	19,325		18,013
Total fair value option	$	1,527,999	$	1,480,347
Other investable assets	$	500,000	$	500,000
Total other investments	$	2,027,999	$	1,980,347

For details on our investments accounted for using the equity method, see note 7, “Investment Information—Investments Accounted For Using the Equity Method,” to our consolidated financial statements.

Our investment strategy allows for the use of derivative instruments. We utilize various derivative instruments such as futures contracts to enhance investment performance, replicate investment positions or manage market exposures and duration risk that would be allowed under our investment guidelines if implemented in other ways. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures related to derivatives.

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. See note 8, “Fair Value,” to our consolidated financial statements for a summary of our financial assets and liabilities measured at fair value, segregated by level in the fair value hierarchy.

ARCH CAPITAL  50 2021 FIRST QUARTER FORM 10-Q

Investable Assets in the ‘Other’ Segment

Investable assets in the ‘other’ segment are managed by Watford. The board of directors of Watford establishes its investment policies and guidelines. A significant amount of Watford’s investments are accounted for using the fair value option with changes in the carrying value of such investments recorded in net realized gains or losses.

The following table summarizes investable assets in the ‘other’ segment:

	March 31, 2021		December 31, 2020
Investments accounted for using the fair value option:
Other investments	$	790,186	$	851,538
Fixed maturities	539,688		455,163
Short-term investments	483,601		418,690
Equity securities	67,295		64,994
Total	1,880,770		1,790,385
Fixed maturities available for sale, at fair value	586,431		613,503
Equity securities, at fair value	62,314		52,410
Cash	236,164		211,451
Securities sold but not yet purchased	(34,097)		(21,679)
Securities transactions entered into but not settled at the balance sheet date	8,846		11,542
Total investable assets included in ‘other’ segment	$	2,740,428	$	2,657,612

Reinsurance

The effects of reinsurance on written and earned premiums and losses and loss adjustment expenses (“LAE”) with unaffiliated reinsurers were as follows:

	Three Months Ended
	March 31,
	2021		2020
Premiums written:
Direct	$	1,892,245	$	1,688,798
Assumed	1,504,961		1,144,032
Ceded	(888,749)		(695,584)
Net	$	2,508,457	$	2,137,246
Premiums earned:
Direct	$	1,712,925	$	1,545,825
Assumed	947,614		761,074
Ceded	(712,117)		(562,455)
Net	$	1,948,422	$	1,744,444
Losses and LAE:
Direct	$	985,933	$	985,083
Assumed	667,311		545,869
Ceded	(450,144)		(415,533)
Net	$	1,203,100	$	1,115,419

See note 6, “Allowance for Expected Credit Losses,” to our consolidated financial statements for information about our reinsurance recoverables and related allowance for credit losses.

Bellemeade Re

We have entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, we will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. We will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage generally decreases over a ten-year period as the underlying covered mortgages amortize, unless provisional call options embedded within certain of the Bellemeade Agreements are executed or if pre-defined delinquency triggering events occur.

The following table summarizes the respective coverages and retentions at March 31, 2021:

			March 31, 2021
	Initial Coverage at Issuance		Current Coverage		Remaining Retention, Net
Bellemeade 2017-1 Ltd. (1)	$	368,114	$	145,573	$	124,281
Bellemeade 2018-1 Ltd. (2)	374,460		250,095		121,963
Bellemeade 2018-2 Ltd. (3)	653,278		66,747		303,766
Bellemeade 2018-3 Ltd. (4)	506,110		302,563		125,226
Bellemeade 2019-1 Ltd. (5)	341,790		219,256		104,221
Bellemeade 2019-2 Ltd. (6)	621,022		398,316		158,732
Bellemeade 2019-3 Ltd. (7)	700,920		528,084		178,241
Bellemeade 2019-4 Ltd. (8)	577,267		468,737		114,325
Bellemeade 2020-1 Ltd. (9)	528,540		141,262		750,797
Bellemeade 2020-2 Ltd. (10)	449,167		380,888		235,372
Bellemeade 2020-3 Ltd. (11)	451,816		451,816		167,556
Bellemeade 2020-4 Ltd. (12)	337,013		337,013		142,435
Bellemeade 2021-1 Ltd. (13)	643,577		643,577		169,634
Total	$	6,553,074	$	4,333,927	$	2,696,549

(1)    Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.

(2)    Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.

(3)    Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.

(4)    Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.

(5)    Issued in March 2019, covering in-force policies primarily issued between 2005-2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.

(6)    Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.

(7)    Issued in July 2019, covering in-force policies issued in 2016.

ARCH CAPITAL  51 2021 FIRST QUARTER FORM 10-Q

(8)    Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

(9)     Issued in June 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $450 million was directly funded by Bellemeade 2020-1 Ltd. with an additional $79 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(10)    Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(11)    Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(12) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

(13) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

Reserve for Losses and Loss Adjustment Expenses 

We establish reserve for losses and loss adjustment expenses (“Loss Reserves”) which represent estimates involving actuarial and statistical projections, at a given point in time, of our expectations of the ultimate settlement and administration costs of losses incurred. Estimating Loss Reserves is inherently difficult. We utilize actuarial models as well as available historical insurance industry loss ratio experience and loss development patterns to assist in the establishment of Loss Reserves. Actual losses and loss adjustment expenses paid will deviate, perhaps substantially, from the reserve estimates reflected in our financial statements.

At March 31, 2021 and December 31, 2020, our Loss Reserves, net of unpaid losses and loss adjustment expenses recoverable, by type and by operating segment were as follows:

	March 31, 2021		December 31, 2020
Insurance segment:
Case reserves	$	1,998,483	$	2,051,640
IBNR reserves	4,036,207		3,889,823
Total net reserves	6,034,690		5,941,463
Reinsurance segment:
Case reserves	1,503,315		1,560,523
Additional case reserves	368,458		280,472
IBNR reserves	2,351,015		2,253,953
Total net reserves	4,222,788		4,094,948
Mortgage segment:
Case reserves	688,005		631,921
IBNR reserves	277,739		271,702
Total net reserves	965,744		903,623
Other segment:
Case reserves	588,036		566,587
Additional case reserves	39,312		32,321
IBNR reserves	676,732		660,132
Total net reserves	1,304,080		1,259,040
Total:
Case reserves	4,777,839		4,810,671
Additional case reserves	407,770		312,793
IBNR reserves	7,341,693		7,075,610
Total net reserves	$	12,527,302	$	12,199,074

At March 31, 2021 and December 31, 2020, the insurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	March 31, 2021		December 31, 2020
Insurance segment:
Professional lines (1)	$	1,457,723	$	1,482,820
Construction and national accounts	1,433,994		1,395,067
Excess and surplus casualty (2)	833,272		816,495
Programs	733,193		699,354
Property, energy, marine and aviation	506,565		517,692
Travel, accident and health	86,135		98,910
Lenders products	56,964		48,946
Other (3)	926,844		882,179
Total net reserves	$	6,034,690	$	5,941,463

(1)Includes professional liability, executive assurance and healthcare business.

(2)Includes casualty and contract binding business.

(3)Includes alternative markets, excess workers’ compensation and surety business.

ARCH CAPITAL  52 2021 FIRST QUARTER FORM 10-Q

At March 31, 2021 and December 31, 2020, the reinsurance segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	March 31, 2021		December 31, 2020
Reinsurance segment:
Casualty (1)	$	1,937,311	$	1,995,849
Other specialty (2)	942,302		917,178
Property excluding property catastrophe	628,305		594,033
Marine and aviation	201,813		204,205
Property catastrophe	396,878		268,858
Other (3)	116,179		114,825
Total net reserves	$	4,222,788	$	4,094,948

(1)Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.

(2)Includes non-excess motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.

(3)Includes life, casualty clash and other.

At March 31, 2021 and December 31, 2020, the mortgage segment’s Loss Reserves by major line of business, net of unpaid losses and loss adjustment expenses recoverable, were as follows:

	March 31, 2021		December 31, 2020
U.S. primary mortgage insurance (1)	$	700,169	$	649,748
Other	265,575		253,875
Total net reserves	$	965,744	$	903,623

(1)    At March 31, 2021, 29.1% represents policy years 2011 and prior and the remainder from later policy years. At December 31, 2020 , 28.3% of total net reserves represent policy years 2011 and prior and the remainder from later policy years.

Mortgage Operations Supplemental Information

The mortgage segment’s insurance in force (“IIF”) and risk in force (“RIF”) were as follows at March 31, 2021 and December 31, 2020:

(U.S. Dollars in millions)	March 31, 2021			December 31, 2020
	Amount		%	Amount		%
Insurance In Force (IIF) (1):
U.S. primary mortgage insurance	$	276,179	64.7	$	280,579	66.2
Mortgage reinsurance	31,699		7.4	31,220		7.4
Other (2)	119,138		27.9	111,740		26.4
Total	$	427,016	100.0	$	423,539	100.0
Risk In Force (RIF) (3):
U.S. primary mortgage insurance	$	69,234	89.9	$	70,522	90.5
Mortgage reinsurance	2,214		2.9	2,226		2.9
Other (2)	5,573		7.2	5,146		6.6
Total	$	77,021	100.0	$	77,894	100.0

(1)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance.

(2)Includes GSE credit risk-sharing transactions and international insurance business.

(3)Represents the aggregate dollar amount of each insured mortgage loan’s current principal balance multiplied by the insurance coverage percentage specified in the policy for insurance policies issued and after contract limits and/or loss ratio caps for credit risk-sharing or reinsurance transactions.

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at March 31, 2021:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2011 and prior	$	13,569	4.9	$	3,086	4.5	11.16	%
2012	2,769		1.0	734		1.1	3.17	%
2013	6,522		2.4	1,817		2.6	3.17	%
2014	7,250		2.6	1,993		2.9	3.96	%
2015	12,971		4.7	3,495		5.0	3.64	%
2016	21,354		7.7	5,718		8.3	4.66	%
2017	20,826		7.5	5,413		7.8	5.46	%
2018	22,856		8.3	5,794		8.4	6.98	%
2019	40,743		14.8	10,157		14.7	4.72	%
2020	100,435		36.4	24,460		35.3	0.91	%
2021	26,884		9.7	6,567		9.5	0.03	%
Total	$	276,179	100.0	$	69,234	100.0	3.86	%

(1)Represents the ending percentage of loans in default.

ARCH CAPITAL  53 2021 FIRST QUARTER FORM 10-Q

The IIF and RIF for our U.S. primary mortgage insurance business by policy year were as follows at December 31, 2020:

(U.S. Dollars in millions)	IIF			RIF			Delinquency
	Amount		%	Amount		%	Rate (1)
Policy year:
2011 and prior	$	14,588	5.2	$	3,327	4.7	11.36	%
2012	3,651		1.3	992		1.4	2.98	%
2013	7,546		2.7	2,107		3.0	3.30	%
2014	8,261		2.9	2,273		3.2	4.06	%
2015	15,032		5.4	4,048		5.7	3.72	%
2016	24,958		8.9	6,648		9.4	4.77	%
2017	24,748		8.8	6,413		9.1	5.52	%
2018	27,304		9.7	6,918		9.8	6.76	%
2019	48,304		17.2	12,001		17.0	4.61	%
2020	106,187		37.8	25,795		36.6	0.76	%
Total	$	280,579	100.0	$	70,522	100.0	4.19	%

(1)Represents the ending percentage of loans in default.

The following tables provide supplemental disclosures on risk in force for our U.S. primary mortgage insurance business at March 31, 2021 and December 31, 2020:

(U.S. Dollars in millions)	March 31, 2021				December 31, 2020
	Amount			%	Amount			%
Credit quality (FICO):
>=740	$	40,230		58.1	$	40,774		57.8
680-739	24,006			34.7	24,498			34.7
620-679	4,607			6.7	4,837			6.9
<620	391			0.6	413			0.6
Total	$	69,234		100.0	$	70,522		100.0
Weighted average FICO score	744				743
Loan-to-value (LTV):
95.01% and above	$	8,310		12.0	$	8,643		12.3
90.01% to 95.00%	37,193			53.7	37,877			53.7
85.01% to 90.00%	19,648			28.4	20,013			28.4
85.00% and below	4,083			5.9	3,989			5.7
Total	$	69,234		100.0	$	70,522		100.0
Weighted average LTV	92.8		%		92.8		%
Total RIF, net of external reinsurance	$	55,503			$	56,658

(U.S. Dollars in millions)	March 31, 2021			December 31, 2020
	Amount		%	Amount		%
Total RIF by State:
Texas	$	5,569	8.0	$	5,636	8.0
California	5,343		7.7	5,261		7.5
Florida	3,544		5.1	3,632		5.2
Georgia	2,929		4.2	2,959		4.2
Illinois	2,728		3.9	2,762		3.9
North Carolina	2,610		3.8	2,622		3.7
Virginia	2,458		3.6	2,526		3.6
Minnesota	2,452		3.5	2,520		3.6
Massachusetts	2,434		3.5	2,464		3.5
Washington	2,154		3.1	2,220		3.1
Other	37,013		53.5	37,920		53.8
Total	$	69,234	100.0	$	70,522	100.0

The following table provides supplemental disclosures for our U.S. primary mortgage insurance business related to insured loans and loss metrics:

(U.S. Dollars in thousands, except policy, loan and claim count)	Three Months Ended
	March 31,
	2021			2020
Roll-forward of insured loans in default:
Beginning delinquent number of loans	52,234			20,163
New notices	10,990			9,419
Cures	(16,131)			(10,541)
Paid claims	(179)			(627)
Ending delinquent number of loans (1)	46,914			18,414
Ending number of policies in force (1)	1,214,245			1,293,799
Delinquency rate (1)	3.86		%	1.42		%
Losses:
Number of claims paid	179			627
Total paid claims	$	6,882		$	26,038
Average per claim	$	38.4		$	41.5
Severity (2)	82.0		%	92.8		%
Average case reserve per default (in thousands)	$	15.2		$	14.4

(1)Includes first lien primary and pool policies.

(2)Represents total paid claims divided by RIF of loans for which claims were paid.

The risk to capital ratio, which represents total current (non-delinquent) risk in force, net of reinsurance, divided by total statutory capital, for Arch MI U.S. was approximately 8.7 to 1 at March 31, 2021, compared to 9.3 to 1 at December 31, 2020.

ARCH CAPITAL  54 2021 FIRST QUARTER FORM 10-Q

Shareholders’ Equity and Book Value per Share

The following table presents the calculation of book value per share:

(U.S. dollars in thousands, except  share data)	March 31, 2021		December 31, 2020
Total shareholders’ equity available to Arch	$	13,096,472	$	13,105,886
Less preferred shareholders’ equity	780,000		780,000
Common shareholders’ equity available to Arch	$	12,316,472	$	12,325,886
Common shares and common share equivalents outstanding, net of treasury shares (1)	403,313,377		406,720,642
Book value per share	$	30.54	$	30.31

(1)Excludes the effects of 18,608,462 and 17,839,333 stock options and 1,015,055 and 1,153,784 restricted stock units outstanding at March 31, 2021 and December 31, 2020, respectively.

LIQUIDITY

This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions with Watford.

Liquidity is a measure of our ability to access sufficient cash flows to meet the short-term and long-term cash requirements of our business operations.

Arch Capital is a holding company whose assets primarily consist of the shares in its subsidiaries. Generally, Arch Capital depends on its available cash resources, liquid investments and dividends or other distributions from its subsidiaries to make payments, including the payment of debt service obligations and operating expenses it may incur and any dividends or liquidation amounts with respect to our preferred and common shares.

For the three months ended March 31, 2021, Arch Capital received dividends of $207.9 million from Arch Re Bermuda, our Bermuda-based reinsurer and insurer, which can pay approximately $3.5 billion to Arch Capital during the remainder of 2021 without providing an affidavit to the Bermuda Monetary Authority (“BMA”).

We expect that our liquidity needs, including our anticipated (re)insurance obligations and operating and capital expenditure needs, for the next twelve months, will be met by funds generated from underwriting activities and investment income, as well as by our balance of cash, short-term

investments, proceeds on the sale or maturity of our investments, and our credit facilities.

Cash Flows

The following table summarizes our cash flows from operating, investing and financing activities, excluding amounts related to the ‘other’ segment (i.e., Watford). See note 11, “Variable Interest Entities and Noncontrolling Interests,” for cash flows related to Watford.

	Three Months Ended
	March 31,
	2021		2020
Total cash provided by (used for):
Operating activities	$	755,928	$	585,956
Investing activities	(498,658)		(242,766)
Financing activities	(201,625)		(146,856)
Effects of exchange rate changes on foreign currency cash	(3,387)		(23,738)
Increase (decrease) in cash and restricted cash	$	52,258	$	172,596

•Cash provided by operating activities for the three months ended March 31, 2021 reflected a higher level of premiums collected than in the 2020 period.

•Cash used for investing activities for the three months ended March 31, 2021 was higher than in the 2020 period. Activity for the three months ended March 31, 2021 reflected our $546.3 million purchase of a 29.5% interest in Coface.

•Cash used for financing activities for the three months ended March 31, 2021 was higher than cash used in the 2020 period, reflecting $179.3 million of repurchases under our share repurchase program, compared to $75.5 million of repurchases in the 2020 period.

ARCH CAPITAL  55 2021 FIRST QUARTER FORM 10-Q

CAPITAL RESOURCES

This section does not include information specific to Watford. We do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions with Watford.

The following table provides an analysis of our capital structure:

(U.S. dollars in thousands, except  share data)	Mar 31, 2021		Dec 31, 2020
Senior notes	$	2,723,660	$	2,723,423
Shareholders’ equity available to Arch:
Series E non-cumulative preferred shares	$	450,000	$	450,000
Series F non-cumulative preferred shares	330,000		330,000
Common shareholders’ equity	12,316,472		12,325,886
Total	$	13,096,472	$	13,105,886
Total capital available to Arch	$	15,820,132	$	15,829,309
Debt to total capital (%)	17.2		17.2
Preferred to total capital (%)	4.9		4.9
Debt and preferred to total capital (%)	22.1		22.1

Arch MI U.S. is required to maintain compliance with the GSEs requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” The financial requirements require an eligible mortgage insurer’s available assets, which generally include only the most liquid assets of an insurer, to meet or exceed “minimum required assets” as of each quarter end. Minimum required assets are calculated from PMIERs tables with several risk dimensions (including origination year, original loan-to-value and original credit score of performing loans, and the delinquency status of non-performing loans) and are subject to a minimum amount. Arch MI U.S. satisfied the PMIERs’ financial requirements as of March 31, 2021 with an estimated PMIER sufficiency ratio of 190%, compared to 173% at December 31, 2020.

Arch Capital, through its subsidiaries, provides financial support to certain of its insurance subsidiaries and affiliates, through certain reinsurance arrangements beneficial to the ratings of such subsidiaries. Historically, our insurance, reinsurance and mortgage insurance subsidiaries have entered into separate reinsurance arrangements with Arch Re Bermuda covering individual lines of business. The

reinsurance agreements between our U.S.-based property casualty insurance and reinsurance subsidiaries and Arch Re Bermuda were canceled on a cutoff basis as of January 1, 2018. In 2019, certain reinsurance agreements between our insurance subsidiaries and Arch Re Bermuda were reinstated.

GUARANTOR INFORMATION

The below table provides a description of our senior notes payable at March 31, 2021, excluding amounts attributable to the ‘other’ segment (i.e., Watford):

	Interest		Principal		Carrying
Issuer/Due	(Fixed)		Amount		Amount
Arch Capital:
May 1, 2034	7.350	%	$	300,000	$	297,396
June 30, 2050	3.635	%	1,000,000		988,554
Arch-U.S.:
Nov. 1, 2043 (1)	5.144	%	500,000		494,973
Arch Finance:
Dec. 15, 2026 (1)	4.011	%	500,000		497,314
Dec. 15, 2046 (1)	5.031	%	450,000		445,423
Total			$	2,750,000	$	2,723,660

(1)Fully and unconditionally guaranteed by Arch Capital.

Our senior notes were issued by Arch Capital, Arch Capital Group (U.S.) Inc. (“Arch-U.S.”) and Arch Capital Finance LLC (“Arch Finance”). Arch-U.S. is a wholly-owned subsidiary of Arch Capital and Arch Finance is a wholly-owned finance subsidiary of Arch-U.S. Our 2034 senior notes and 2050 senior notes issued by Arch Capital are unsecured and unsubordinated obligations of Arch Capital and ranked equally with all of its existing and future unsecured and unsubordinated indebtedness. The 2043 senior notes issued by Arch-U.S. are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital. The 2026 senior notes and 2046 senior notes issued by Arch Finance are unsecured and unsubordinated obligations of Arch Finance and Arch Capital and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital.

Arch-U.S. and Arch Finance depend on their available cash resources, liquid investments and dividends or other distributions from their subsidiaries or affiliates to make payments, including the payment of debt service obligations and operating expenses they may incur.

ARCH CAPITAL  56 2021 FIRST QUARTER FORM 10-Q

The following tables present condensed financial information for Arch Capital (parent guarantor) and Arch-U.S. (subsidiary issuer):

	March 31, 2021				December 31, 2020
	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Assets
Total investments	$	357	$	345,224	$	172	$	396,547
Cash	8,920		11,051		18,932		11,368
Investment in operating affiliates	7,408		—		7,731		—
Due from subsidiaries and affiliates	—		200,742		—		201,515
Other assets	12,824		57,607		10,659		34,405
Total assets	$	29,509	$	614,624	$	37,494	$	643,835
Liabilities
Senior notes	1,285,950		494,973		1,285,867		494,944
Due to subsidiaries and affiliates	—		507,045		—		586,805
Other liabilities	34,586		57,889		23,270		41,876
Total liabilities	$	1,320,536	$	1,059,907	$	1,309,137	$	1,123,625
Non-cumulative preferred shares	$	780,000	—		$	780,000	—

	Three Months Ended				Year Ended
	March 31, 2021				December 31, 2020
	Arch Capital		Arch-U.S.		Arch Capital		Arch-U.S.
Revenues
Net investment income	$	432	$	2,608	$	53	$	18,084
Net realized gains (losses)	—		55,108		(2,110)		26,096
Equity in net income (loss) of investments accounted for using the equity method	—		(336)		—		2,507
Total revenues	432		57,380		(2,057)		46,687
Expenses
Corporate expenses	23,315		1,586		65,566		7,227
Interest expense	14,683		11,801		40,445		47,566
Net foreign exchange (gains) losses	1		—		3		—
Total expenses	37,999		13,387		106,014		54,793
Income (loss) before income taxes and income (loss) from operating affiliates	(37,567)		43,993		(108,071)		(8,106)
Income tax (expense) benefit	—		(8,896)		—		2,689
Income (loss) from operating affiliates	(171)		—		(437)		—
Net income available to Arch	(37,738)		35,097		(108,508)		(5,417)
Preferred dividends	(10,403)		—		(41,612)		—
Net income available to Arch common shareholders	$	(48,141)	$	35,097	$	(150,120)	$	(5,417)

ARCH CAPITAL  57 2021 FIRST QUARTER FORM 10-Q

SHARE REPURCHASE PROGRAM

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. For the three months ended March 31, 2021, Arch Capital repurchased 5.3 million shares under the share repurchase program with an aggregate purchase price of $179.3 million. Since the inception of the share repurchase program through March 31, 2021, Arch Capital has repurchased 394.5 million common shares for an aggregate purchase price of $4.23 billion. At March 31, 2021, approximately $737.3 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

CATASTROPHIC EVENTS AND SEVERE ECONOMIC EVENTS

We have large aggregate exposures to natural and man-made catastrophic events, pandemic events like COVID-19 and severe economic events. Natural catastrophes can be caused by various events, including hurricanes, floods, windstorms, earthquakes, hailstorms, tornadoes, explosions, severe winter weather, fires, droughts and other natural disasters. Man-made catastrophic events may include acts of war, acts of terrorism and political instability. Catastrophes can also cause losses in non-property business such as mortgage insurance, workers’ compensation or general liability. In addition to the nature of property business, we believe that economic and geographic trends affecting insured property, including inflation, property value appreciation and geographic concentration, tend to generally increase the size of losses from catastrophic events over time.

Our models employ both proprietary and vendor-based systems and include cross-line correlations for property, marine, offshore energy, aviation, workers compensation and personal accident. We seek to limit the probable maximum pre-tax loss to a specific level for severe catastrophic events. Currently, we seek to limit our 1-in-250 year return period net probable maximum loss from a severe catastrophic event in any geographic zone to approximately 25% of tangible shareholders’ equity available to Arch (total shareholders’ equity available to Arch less goodwill and intangible assets). We reserve the right to change this threshold at any time.

Based on in-force exposure estimated as of April 1, 2021, our modeled peak zone catastrophe exposure was a windstorm affecting the Northeastern U.S., with a net probable maximum pre-tax loss of $778 million, followed by windstorms affecting the Florida Tri-County and the Gulf of

Mexico regions with net probable maximum pre-tax losses of $765 and $702 million, respectively. Our exposures to other perils, such as U.S. earthquake and international events, were less than the exposures arising from U.S. windstorms and hurricanes. As of April 1, 2021, our modeled peak zone earthquake exposure (San Francisco earthquake) represented approximately 76% of our peak zone catastrophe exposure, and our modeled peak zone international exposure (UK windstorm) was substantially less than both our peak zone windstorm and earthquake exposures.

Effective January 1, 2021, our insurance operations had in effect a reinsurance program which provided coverage for certain property-catastrophe related losses equal to $276 million in excess of various retentions per occurrence.

We also have significant exposure to losses due to mortgage defaults resulting from severe economic events in the future. For our U.S. mortgage insurance business, we have developed a proprietary risk model (“Realistic Disaster Scenario” or “RDS”) that simulates the maximum loss resulting from a severe economic downturn impacting the housing market. The RDS models the collective impact of adverse conditions for key economic indicators, the most significant of which is a decline in home prices. The RDS model projects paths of future home prices, unemployment rates, income levels and interest rates and assumes correlation across states and geographic regions. The resulting future performance of our in-force portfolio is then estimated under the economic stress scenario, reflecting loan and borrower information.

Currently, we seek to limit our modeled RDS loss from a severe economic event to approximately 25% of tangible shareholders’ equity available to Arch. We reserve the right to change this threshold at any time. Based on in-force exposure estimated as of April 1, 2021, our modeled RDS loss was approximately 6% of tangible shareholders’ equity available to Arch.

Net probable maximum loss estimates are net of expected reinsurance recoveries, before income tax and before excess reinsurance reinstatement premiums. RDS loss estimates are net of expected reinsurance recoveries and before income tax. Catastrophe loss estimates are reflective of the zone indicated and not the entire portfolio. Since hurricanes and windstorms can affect more than one zone and make multiple landfalls, our catastrophe loss estimates include clash estimates from other zones. Our catastrophe loss estimates and RDS loss estimates do not represent our maximum exposures and it is highly likely that our actual incurred losses would vary materially from the modeled estimates. There can be no assurances that we will not suffer pre-tax losses greater than 25% of our tangible shareholders’ equity from one or more catastrophic events or severe economic events due to several factors. These factors include the inherent uncertainties in

ARCH CAPITAL  58 2021 FIRST QUARTER FORM 10-Q

estimating the frequency and severity of such events and the margin of error in making such determinations resulting from potential inaccuracies and inadequacies in the data provided by clients and brokers, the modeling techniques and the application of such techniques or as a result of a decision to change the percentage of shareholders' equity exposed to a single catastrophic event or severe economic event. In addition, actual losses may increase if our reinsurers fail to meet their obligations to us or the reinsurance protections purchased by us are exhausted or are otherwise unavailable. See “Risk Factors—Risks Relating to Our Industry” and “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Catastrophic Events and Severe Economic Events” in our 2020 Form 10-K.

OFF-BALANCE SHEET ARRANGEMENTS

Off-balance sheet arrangements are discussed in Management’s Discussion and Analysis of Financial Condition and Results of Operations contained in our 2020 Form 10-K.

MARKET SENSITIVE INSTRUMENTS AND RISK MANAGEMENT

In accordance with the SEC’s Financial Reporting Release No. 48, we performed a sensitivity analysis to determine the effects that market risk exposures could have on the future earnings, fair values or cash flows of our financial instruments as of March 31, 2021. Market risk represents the risk of changes in the fair value of a financial instrument and is comprised of several components, including liquidity, basis and price risks. We have not included Watford in the following analyses as we do not guarantee or provide credit support for Watford, and our financial exposure to Watford is limited to our investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

An analysis of material changes in market risk exposures at March 31, 2021 that affect the quantitative and qualitative disclosures presented in our 2020 Form 10-K (see section captioned “Management’s Discussion and Analysis of Financial Condition and Results of Operations—Market Sensitive Instruments and Risk Management”) were as follows: 

Investment Market Risk

Fixed Income Securities. We invest in interest rate sensitive securities, primarily debt securities. We consider the effect of interest rate movements on the fair value of our fixed maturities, fixed maturities pledged under securities lending agreements, short-term investments and certain of our other investments, equity securities and investment funds

accounted for using the equity method which invest in fixed income securities (collectively, “Fixed Income Securities”) and the corresponding change in unrealized appreciation. As interest rates rise, the fair value of our Fixed Income Securities falls, and the converse is also true. Based on historical observations, there is a low probability that all interest rate yield curves would shift in the same direction at the same time. Furthermore, at times interest rate movements in certain credit sectors exhibit a much lower correlation to changes in U.S. Treasury yields. Accordingly, the actual effect of interest rate movements may differ materially from the amounts set forth in the following tables.

The following table summarizes the effect that an immediate, parallel shift in the interest rate yield curve would have had on our Fixed Income Securities:

(U.S. dollars in  billions)	Interest Rate Shift in Basis Points
	-100			-50			—		+50			+100
Mar 31, 2021
Total fair value	$	24.99		$	24.68		$	24.36	$	24.04		$	23.73
Change from base	2.6		%	1.3		%			(1.3)		%	(2.6)		%
Change in unrealized value	$	0.63		$	0.32				$	(0.32)		$	(0.63)
Dec 31, 2020
Total fair value	$	25.82		$	25.44		$	25.07	$	24.69		$	24.31
Change from base	3.0		%	1.5		%			(1.5)		%	(3.0)		%
Change in unrealized value	$	0.75		$	0.38				$	(0.38)		$	(0.75)

In addition, we consider the effect of credit spread movements on the market value of our Fixed Income Securities and the corresponding change in unrealized value. As credit spreads widen, the fair value of our Fixed Income Securities falls, and the converse is also true. In periods where the spreads on our Fixed Income Securities are much higher than their historical average due to short-term market dislocations, a parallel shift in credit spread levels would result in a much more pronounced change in unrealized value.

ARCH CAPITAL  59 2021 FIRST QUARTER FORM 10-Q

The following table summarizes the effect that an immediate, parallel shift in credit spreads in a static interest rate environment would have had on our Fixed Income Securities:

(U.S. dollars in  billions)	Credit Spread Shift in Percentage Points
	-100			-50			—		+50			+100
Mar 31, 2021
Total fair value	$	24.87		$	24.61		$	24.36	$	24.12		$	23.85
Change from base	2.1		%	1.0		%			(1.0)		%	(2.1)		%
Change in unrealized value	$	0.51		$	0.24				$	(0.24)		$	(0.51)
Dec 31, 2020
Total fair value	$	25.54		$	25.32		$	25.07	$	24.82		$	24.59
Change from base	1.9		%	1.0		%			(1.0)		%	(1.9)		%
Change in unrealized value	$	0.48		$	0.25				$	(0.25)		$	(0.48)

Another method that attempts to measure portfolio risk is Value-at-Risk (“VaR”). VaR measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. The 1-year 95th percentile parametric VaR reported herein estimates that 95% of the time, the portfolio loss in a one-year horizon would be less than or equal to the calculated number, stated as a percentage of the measured portfolio’s initial value. The VaR is a variance-covariance based estimate, based on linear sensitivities of a portfolio to a broad set of systematic market risk factors and idiosyncratic risk factors mapped to the portfolio exposures. The relationships between the risk factors are estimated using historical data, and the most recent data points are generally given more weight. As of March 31, 2021, our portfolio’s VaR was estimated to be 3.9% compared to an estimated 4.3% at December 31, 2020. In periods where the volatility of the risk factors mapped to our portfolio’s exposures is higher due to market conditions, the resulting VaR is higher than in other periods.

Equity Securities. At March 31, 2021 and December 31, 2020, the fair value of our investments in equity securities (excluding securities included in Fixed Income Securities above) totaled $1.3 billion and $1.1 billion, respectively. These investments are exposed to price risk, which is the potential loss arising from decreases in fair value. An immediate hypothetical 10% decline in the value of each position would reduce the fair value of such investments by approximately $127.1 million and $109.5 million at March 31, 2021 and December 31, 2020, respectively, and would have decreased book value per share by approximately $0.32 and $0.27, respectively. An immediate hypothetical 10% increase in the value of each position would increase the fair value of such investments by approximately $127.1 million and $109.5 million at March 31, 2021 and December 31, 2020, respectively, and would have increased book value per share by approximately $0.32 and $0.27, respectively.

Investment-Related Derivatives. At March 31, 2021, the notional value of all derivative instruments (excluding to-be-announced mortgage backed securities which are included in the fixed income securities analysis above and foreign currency forward contracts which are included in the foreign currency exchange risk analysis below) was $13.1 billion, compared to $8.6 billion at December 31, 2020. If the underlying exposure of each investment-related derivative held at March 31, 2021 depreciated by 100 basis points, it would have resulted in a reduction in net income of approximately $131.4 million, and a decrease in book value per share of approximately $0.33 per share, compared to $85.7 million and $0.21 per share, respectively, on investment-related derivatives held at December 31, 2020. If the underlying exposure of each investment-related derivative held at March 31, 2021 appreciated by 100 basis points, it would have resulted in an increase in net income of approximately $131.4 million, and an increase in book value per share of approximately $0.33 per share, compared to $85.7 million and $0.21 per share, respectively, on investment-related derivatives held at December 31, 2020. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional disclosures concerning derivatives.

For further discussion on investment activity, please refer to “Financial Condition—Investable Assets.”

Foreign Currency Exchange Risk

Foreign currency rate risk is the potential change in value, income and cash flow arising from adverse changes in foreign currency exchange rates. Through our subsidiaries and branches located in various foreign countries, we conduct our insurance and reinsurance operations in a variety of local currencies other than the U.S. Dollar. We generally hold investments in foreign currencies which are intended to mitigate our exposure to foreign currency fluctuations in our net insurance liabilities. We may also utilize foreign currency forward contracts and currency options as part of our investment strategy. See note 9, “Derivative Instruments,” to our consolidated financial statements for additional information.

ARCH CAPITAL  60 2021 FIRST QUARTER FORM 10-Q

The following table provides a summary of our net foreign currency exchange exposures, as well as foreign currency derivatives in place to manage these exposures:

(U.S. dollars in thousands, except  per share data)	March 31, 2021		December 31, 2020
Net assets (liabilities), denominated in foreign currencies, excluding shareholders’ equity and derivatives	$	(30,221)	$	(309,968)
Shareholders’ equity denominated in foreign currencies (1)	704,173		695,355
Net foreign currency forward contracts outstanding (2)	477,734		1,108,161
Net exposures denominated in foreign currencies	$	1,151,686	$	1,493,548
Pre-tax impact of a hypothetical 10% appreciation of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	(115,169)	$	(149,355)
Book value per share	$	(0.29)	$	(0.37)
Pre-tax impact of a hypothetical 10% decline of the U.S. Dollar against foreign currencies:
Shareholders’ equity	$	115,169	$	149,355
Book value per share	$	0.29	$	0.37

(1)    Represents capital contributions held in the foreign currencies of our operating units.

(2)    Represents the net notional value of outstanding foreign currency forward contracts.

Although we generally attempt to match the currency of our projected liabilities with investments in the same currencies, from time to time we may elect to over or underweight one or more currencies, which could increase our exposure to foreign currency fluctuations and increase the volatility of our shareholders’ equity. Historical observations indicate a low probability that all foreign currency exchange rates would shift against the U.S. Dollar in the same direction and at the same time and, accordingly, the actual effect of foreign currency rate movements may differ materially from the amounts set forth above. For further discussion on foreign exchange activity, please refer to “Results of Operations.”

Effects of Inflation

We do not believe that inflation has had a material effect on our consolidated results of operations, except insofar as inflation may affect our reserve for losses and loss adjustment expenses and interest rates. The potential exists, after a catastrophe loss or pandemic events like COVID-19, for the development of inflationary pressures in a local economy. The anticipated effects of inflation on us are considered in our catastrophe loss models. The actual effects of inflation on our results cannot be accurately known until claims are ultimately settled.

OTHER FINANCIAL INFORMATION

The consolidated financial statements as of March 31, 2021 have been reviewed by PricewaterhouseCoopers LLP, the registrant's independent public accountants, whose report is included as an exhibit to this filing. The report of PricewaterhouseCoopers LLP states that they did not audit and they do not express an opinion on that unaudited financial information. Accordingly, the degree of reliance on their report on such information should be restricted in light of the limited nature of the review procedures applied. PricewaterhouseCoopers LLP is not subject to the liability provisions of Section 11 of the Securities Act of 1933 for their report on the unaudited financial information because that report is not a "report" or a "part" of the registration statement prepared or certified by PricewaterhouseCoopers LLP within the meaning of Sections 7 and 11 of the Securities Act of 1933.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

Reference is made to the information appearing above under the subheading “Market Sensitive Instruments and Risk Management” under the caption “Management’s Discussion and Analysis of Financial Condition and Results of Operations,” which information is hereby incorporated by reference. 

ITEM 4. CONTROLS AND PROCEDURES

Evaluation of Disclosure Controls and Procedures

In connection with the filing of this Form 10-Q, our management, including the Chief Executive Officer and Chief Financial Officer, conducted an evaluation of the effectiveness of disclosure controls and procedures pursuant to applicable Exchange Act Rules as of the end of the period covered by this report. Based on that evaluation, the Chief Executive Officer and Chief Financial Officer concluded that the disclosure controls and procedures were effective as of the end of and during the period covered by this report with respect to information being recorded, processed, summarized and reported within time periods specified in the SEC’s rules and forms and with respect to timely communication to them and other members of management responsible for preparing periodic reports of all material information required to be disclosed in this report as it relates to Arch Capital and its consolidated subsidiaries.

We continue to enhance our operating procedures and internal controls to effectively support our business and our

ARCH CAPITAL  61 2021 FIRST QUARTER FORM 10-Q

regulatory and reporting requirements. Our management does not expect that our disclosure controls or our internal controls will prevent all errors and all fraud. A control system, no matter how well conceived and operated, can provide only reasonable, not absolute, assurance that the objectives of the control system are met. Further, the design of a control system must reflect the fact that there are resource constraints, and the benefits of controls must be considered relative to their costs. As a result of the inherent limitations in all control systems, no evaluation of controls can provide absolute assurance that all control issues and instances of fraud, if any, within the company have been detected. These inherent limitations include the realities that judgments in decision-making can be faulty, and that breakdowns can occur because of simple error or mistake. Additionally, controls can be circumvented by the individual acts of some persons or by collusion of two or more people. The design of any system of controls also is based in part upon certain assumptions about the likelihood of future events, and there can be no assurance that any design will succeed in achieving its stated goals under all potential future conditions; over time, controls may become inadequate because of changes in conditions, or the degree of compliance with the policies or procedures may deteriorate. As a result of the inherent limitations in a cost-effective control system, misstatement due to error or fraud may occur and not be detected. Accordingly, our disclosure controls and procedures are designed to provide reasonable, not absolute, assurance that the disclosure controls and procedures are met.

Changes in Internal Controls Over Financial Reporting

There have been no changes in internal control over financial reporting that occurred during the quarter ended March 31, 2021 that have materially affected, or are reasonably likely to materially affect, internal control over financial reporting. We have not experienced any material impact to our internal controls over financial reporting despite the fact that most of our employees are working remotely due to the COVID-19. We are continually monitoring and assessing COVID-19 situation on our internal controls to minimize the impact on their design and operating effectiveness.

PART II.  OTHER INFORMATION

ITEM 1. LEGAL PROCEEDINGS

We, in common with the insurance industry in general, are subject to litigation and arbitration in the normal course of our business. As of March 31, 2021, we were not a party to any litigation or arbitration which is expected by management to have a material adverse effect on our results of operations and financial condition and liquidity.

ITEM 1A. RISK FACTORS

There were no material changes from the risk factors previously disclosed in our Annual Report on Form 10-K for the year ended December 31, 2020.

ARCH CAPITAL  62 2021 FIRST QUARTER FORM 10-Q

ITEM 2. UNREGISTERED SALES OF EQUITY SECURITIES AND USE OF PROCEEDS

The following table summarizes our purchases of common shares for the 2021 first quarter:

	Issuer Purchases of Equity Securities
Period	Total Number of Shares Purchased (1)	Average Price Paid per Share		Total Number of Shares Purchased as Part of Publicly Announced Plans or Programs	Approximate Dollar Value of Shares that  May Yet be Purchased Under the Plan or Programs (2)
1/1/2021 - 1/31/2021	714,177	$	32.50	—	$	893,591
2/1/2021 - 2/28/2021	4,107,493	33.81		—	$	761,583
3/1/2021 - 3/31/2021	811,162	35.73		—	$	737,262
Total	5,632,832	$	33.92	—

(1)Represents repurchases by Arch Capital of shares, from time to time, from employees in order to facilitate the payment of withholding taxes on restricted shares granted and the exercise of stock appreciation rights. We purchased these shares at their fair value, as determined by reference to the closing price of our common shares on the day the restricted shares vested or the stock appreciation rights were exercised.

(2)Remaining amount available at March 31, 2021 under Arch Capital’s share repurchase authorization, under which repurchases may be effected from time to time in open market or privately negotiated transactions through December 31, 2021.

ITEM 3. DEFAULTS UPON SENIOR SECURITIES

None.

ITEM 4. MINE SAFETY DISCLOSURES

Not applicable.

ITEM 5. OTHER INFORMATION

In accordance with Section 10a(i)(2) of the Securities Exchange Act of 1934, as amended, we are responsible for disclosing non-audit services to be provided by our independent auditor, PricewaterhouseCoopers LLP, which are approved by the Audit Committee of our board of directors. During the 2021 first quarter, the Audit Committee approved engagements of PricewaterhouseCoopers LLP for permitted non-audit services, which consisted of tax consulting services, tax compliance services and other accounting consulting services.

ARCH CAPITAL  63 2021 FIRST QUARTER FORM 10-Q

ITEM 6. EXHIBITS

		Incorporated by Reference
Exhibit Number	Exhibit Description	Form	Original Number	Date Filed	Filed Herewith
10.1	Second Amendment to Third Amended and Restated Arch Capital Group Ltd. Incentive Compensation Plan				X
15	Accountants’ Awareness Letter (regarding unaudited interim financial information)				X
31.1	Certification of Chief Executive Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002				X
31.2	Certification of Chief Financial Officer pursuant to Section 302 of the Sarbanes-Oxley Act of 2002				X
32.1	Certification of Chief Executive Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002				X
32.2	Certification of Chief Financial Officer pursuant to Section 906 of the Sarbanes-Oxley Act of 2002				X
101.INS	XBRL Instance Document
101.SCH	XBRL Taxonomy Extension Schema Document
101.CAL	XBRL Taxonomy Extension Calculation Linkbase Document
101.DEF	XBRL Taxonomy Extension Definition Linkbase Document
101.LAB	XBRL Taxonomy Extension Label Linkbase Document
101.PRE	XBRL Taxonomy Extension Presentation Linkbase Document

ARCH CAPITAL  64 2021 FIRST QUARTER FORM 10-Q

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.

	ARCH CAPITAL GROUP LTD.
	(REGISTRANT)
	/s/ Marc Grandisson
Date: May 6, 2021	Marc Grandisson
	Chief Executive Officer (Principal Executive Officer)
	/s/ François Morin
Date: May 6, 2021	François Morin
	Executive Vice President, Chief Financial Officer (Principal Financial and Accounting Officer) and Treasurer

ARCH CAPITAL  65 2021 FIRST QUARTER FORM 10-Q

EX-10.1

    Exhibit 10.1

SECOND AMENDMENT TO THIRD AMENDED AND RESTATED

ARCH CAPITAL GROUP LTD. INCENTIVE COMPENSATION PLAN

The Third Amended and Restated Arch Capital Group Ltd. Incentive Compensation Plan is amended, effective as of February 26, 2021, by adding the following paragraph as a new second paragraph in Section 5.3 (with the existing second paragraph thereof becoming the third paragraph of Section 5.3):

“Notwithstanding the foregoing, unless otherwise determined by the Committee, in the event an Eligible Employee who has been selected to participate in the Plan for a Plan Year dies during the Plan Year, a pro-rata portion (based on the number of days during the Plan Year elapsed through the date of death) of the Eligible Employee’s Target Bonus Opportunity for the Plan Year will be paid in a single lump sum in cash to the Eligible Employee’s Beneficiary on the date determined by the Company (which date shall not be later than March 15 of the following Plan Year). Such Eligible Employee (and his or her Beneficiaries) shall not be entitled to any additional amounts in respect of such Plan Year. For purposes of this Plan, “Beneficiary” means the person, persons, trust or trusts which have been designated by an Eligible Employee in his or her most recent written beneficiary designation filed with the Company to receive the benefits specified under this Plan upon the death of the Eligible Employee, or, if there is no designated Beneficiary or surviving designated Beneficiary, then the person, persons, trust or trusts entitled by will or the laws of descent and distribution to receive such benefits.”

EX-15

Exhibit 15

May 6, 2021

Securities and Exchange Commission

100 F Street, N.E.

Washington, DC 20549

Commissioners:

We are aware that our report dated May 6, 2021, on our review of interim financial information of Arch Capital Group Ltd., which appears in this Quarterly Report on Form 10-Q, is incorporated by reference in the Registration Statements on Form S-3 (No. 333-250869) and in the Registration Statements on Form S-8 (Nos. 333-224783, 333-211193, 333-142835, 333-181308 and 333- 203993) of Arch Capital Group Ltd.

Very truly yours,

/s/ PricewaterhouseCoopers LLP

New York, NY

EX-31.1

Exhibit 31.1

Certification

of Chief Executive Officer

Pursuant to Section 302 of the

Sarbanes-Oxley Act of 2002

I, Marc Grandisson, certify that:

1.    I have reviewed this quarterly report on Form 10-Q of Arch Capital Group Ltd.;

2.    Based on my knowledge, this 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 the 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 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 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 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.

Date:	May 6, 2021
By:	/s/ Marc Grandisson
Name:	Marc Grandisson
Title:	Chief Executive Officer

EX-31.2

Exhibit 31.2

Certification

of Chief Financial Officer

Pursuant to Section 302 of the

Sarbanes-Oxley Act of 2002

I, François Morin, certify that:

1.     I have reviewed this quarterly report on Form 10-Q of Arch Capital Group Ltd.;

2.     Based on my knowledge, this 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 the 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 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 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 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.

Date:	May 6, 2021
By:	/s/ François Morin
Name:	François Morin
Title:	Executive Vice President, Chief Financial Officer and Treasurer

EX-32.1

Exhibit 32.1

Certification Pursuant to Chapter 63, Title 18 United States Code §1350

As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

    In connection with the Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending March 31, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Marc Grandisson, as Chief Executive Officer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)    the Report fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; and

(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	May 6, 2021
By:	/s/ Marc Grandisson
Name:	Marc Grandisson
Title:	Chief Executive Officer

A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.

EX-32.2

Exhibit 32.2

Certification Pursuant to Chapter 63, Title 18 United States Code §1350

As Adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

    In connection with the Quarterly Report of Arch Capital Group Ltd. (the “Company”) on Form 10-Q for the period ending March 31, 2021 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), François Morin, as Executive Vice President, Chief Financial Officer and Treasurer of the Company, certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)    the Report fully complies with the requirements of section 13(a) of the Securities Exchange Act of 1934; and

(2)    the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:	May 6, 2021
By:	/s/ François Morin
Name:	François Morin
Title:	Executive Vice President, Chief Financial Officer and Treasurer

A signed original of this written statement required by Section 906 or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Arch Capital Group Ltd. and will be retained by Arch Capital Group Ltd. and furnished to the Securities and Exchange Commission or its staff upon request.

XML

Document and Entity Information - shares	3 Months Ended
	Mar. 31, 2021	Apr. 30, 2021
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Mar. 31, 2021
Document Transition Report	false
Entity File Number	001-16209
Entity Registrant Name	ARCH CAPITAL GROUP LTD.
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	98-0374481
Entity Address, Address Line One	Waterloo House, Ground Floor
Entity Address, Address Line Two	100 Pitts Bay Road,
Entity Address, City or Town	Pembroke
Entity Address, Postal Zip Code	HM 08,
Entity Address, Country	BM
City Area Code	(441)
Local Phone Number	278-9250
Entity Listings [Line Items]
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		403,619,081
Document Fiscal Period Focus	Q1
Document Fiscal Year Focus	2021
Current Fiscal Year End Date	--12-31
Entity Central Index Key	0000947484
Amendment Flag	false
Common shares
Entity Listings [Line Items]
Title of 12(b) Security	Common shares, $0.0011 par value per share
Trading Symbol	ACGL
Security Exchange Name	NASDAQ
Depositary Series E Preferred Stock
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1000th interest in a 5.25% Series E preferred share
Trading Symbol	ACGLP
Security Exchange Name	NASDAQ
Depositary Series F Preferred Stock
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1000th interest in a 5.45% Series F preferred share
Trading Symbol	ACGLO
Security Exchange Name	NASDAQ

XML

Unaudited Consolidated Balance Sheets - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $18,447,720 and $18,143,305; net of allowance for credit losses: $3,830 and $2,397 )	$ 18,723,035	$ 18,717,825
Short-term investments available for sale, at fair value (amortized cost: $1,269,312 and $1,924,292; net of allowance for credit losses: $0 and $0)	1,269,631	1,924,922
Collateral received under securities lending, at fair value (amortized cost: $143,886 and $301,089)	143,894	301,096
Equity securities, at fair value	1,532,906	1,444,830
Other investments (portion measured at fair value: $3,935,354 and $3,824,796)	4,435,354	4,324,796
Investments accounted for using the equity method	2,256,327	2,047,889
Total investments	28,361,147	28,761,358
Cash	941,951	906,448
Accrued investment income	101,108	103,299
Securities pledged under securities lending, at fair value (amortized cost: $142,129 and $294,493)	140,949	294,912
Investment in operating affiliates	739,783	129,291
Premiums receivable (net of allowance for credit losses: $36,111 and $37,781)	2,618,175	2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $10,872 and $11,636)	4,041,076	4,500,802
Contractholder receivables (net of allowance for credit losses: $5,853 and $8,638)	1,919,655	1,986,924
Ceded unearned premiums	1,406,489	1,234,075
Deferred acquisition costs	919,740	790,708
Receivable for securities sold	199,424	92,743
Goodwill and intangible assets	679,509	692,863
Other assets	2,135,261	1,724,288
Total assets	44,204,267	43,282,297
Liabilities
Reserve for losses and loss adjustment expenses	16,443,952	16,513,929
Unearned premiums	5,549,127	4,838,965
Reinsurance balances payable	919,125	683,263
Contractholder payables	1,925,508	1,995,562
Collateral held for insured obligations	222,245	215,581
Senior notes	2,861,417	2,861,113
Revolving credit agreement borrowings	155,687	155,687
Securities lending payable	143,886	301,089
Payable for securities purchased	386,453	218,779
Other liabilities	1,565,861	1,510,888
Total liabilities	30,173,261	29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests	57,670	58,548
Shareholders' Equity
Non-cumulative preferred shares	780,000	780,000
Common shares ($0.0011 par, shares issued: 581,226,408 and 579,000,841)	645	643
Additional paid-in capital	2,014,741	1,977,794
Retained earnings	12,790,216	12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	205,827	488,895
Common shares held in treasury, at cost (shares: 177,913,031 and 172,280,199)	(2,694,957)	(2,503,909)
Total shareholders' equity available to Arch	13,096,472	13,105,886
Non-redeemable noncontrolling interests	876,864	823,007
Total shareholders' equity	13,973,336	13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$ 44,204,267	$ 43,282,297

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Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Mar. 31, 2021		Dec. 31, 2020
Fixed maturities available for sale, at amortized cost	$ 18,447,720		$ 18,143,305
Allowance for credit losses on investments	3,830		2,397
Short-term investments available for sale, at amortized cost	1,269,312		1,924,292
Collateral received under securities lending, at amortized cost	143,886		301,089
Other investments measured at fair value	3,935,354		3,824,796
Securities pledged under securities lending, at amortized cost	142,129		294,493
Allowance for credit losses on premiums receivable	36,111		37,781
Allowance for credit losses on reinsurance recoverable	10,872		11,636
Allowance for credit losses on contractholder receivable	$ 5,853		$ 8,638
Common shares, par value per share	$ 0.0011		$ 0.0011
Common shares issued (shares)	581,226,408		579,000,841
Common shares held in treasury (shares)	177,913,031		172,280,199
Fixed maturities
Allowance for credit losses on investments	$ 3,830		$ 2,397
Short-term investments
Allowance for credit losses on investments	0	[1]	0
Short-term investments available for sale, at amortized cost	$ 1,269,312		$ 1,924,292

[1] Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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Unaudited Consolidated Statements of Income - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Revenues
Net premiums earned	$ 1,948,422	$ 1,744,444
Net investment income	98,856	145,153
Net realized gains (losses)	142,461	(366,960)
Other underwriting income	6,110	6,852
Equity in net income (loss) of investment funds accounted for using the equity method	71,686	(4,209)
Other income (loss)	(1,741)	32
Total revenues	2,265,794	1,525,312
Expenses
Losses and loss adjustment expenses	1,203,100	1,115,419
Acquisition expenses	304,481	247,283
Other operating expenses	261,033	234,544
Corporate expenses	25,384	20,796
Amortization of intangible assets	14,402	16,631
Interest expense	38,346	32,555
Net foreign exchange (gains) losses	(20,063)	(72,671)
Total expenses	1,826,683	1,594,557
Income (loss) before income taxes and income (loss) from operating affiliates	439,111	(69,245)
Income tax expense	(38,860)	(27,945)
Income (loss) from operating affiliates	75,457	8,516
Net income (loss)	475,708	(88,674)
Net (income) loss attributable to noncontrolling interests	(37,552)	232,791
Net income (loss) available to Arch	438,156	144,117
Preferred dividends	(10,403)	(10,403)
Net income (loss) available to Arch common shareholders	$ 427,753	$ 133,714
Net income per common share and common share equivalent
Basic (per share)	$ 1.07	$ 0.33
Diluted (per share)	$ 1.05	$ 0.32
Weighted average common shares and common share equivalents outstanding
Basic (shares)	400,807,895	403,892,161
Diluted (shares)	409,223,253	414,033,570

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Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Comprehensive Income
Net income (loss)	$ 475,708	$ (88,674)
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(261,750)	(57,287)
Reclassification of net realized (gains) losses, included in net income (loss)	2,697	(121,229)
Foreign currency translation adjustments	(28,584)	(44,689)
Comprehensive income (loss)	188,071	(311,879)
Net (income) loss attributable to noncontrolling interests	(37,552)	232,791
Other comprehensive (income) loss attributable to noncontrolling interests	4,570	33,058
Comprehensive income (loss) available to Arch	$ 155,089	$ (46,030)

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Unaudited Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Retained earnings Cumulative effect of an accounting change	Retained earnings Balance at beginning of period, as adjusted	Accumulated other comprehensive income (loss), net of deferred income tax	Unrealized appreciation (decline) in value of available-for-sale securities, net of deferred income tax	Foreign currency translation adjustments, net of deferred income tax	Common shares held in treasury, at cost
Balance at beginning of period at Dec. 31, 2019		$ 780,000	$ 638	$ 1,889,683	$ 11,021,006	$ (22,452)	$ 10,998,554	$ 212,091	$ 258,486	$ (46,395)	$ (2,406,047)
Common shares issued, net			4
Amortization of share-based compensation				28,050
Other changes				3,754
Net income (loss)	$ (88,674)				(88,674)
Net (income) loss attributable to noncontrolling interests	232,791				232,791
Preferred share dividends	(10,403)				(10,403)
Unrealized holding gains (losses) during period, net of reclassification adjustment									(178,516)
Unrealized holding gains (losses) during period attributable to noncontrolling interests									33,179
Foreign currency translation adjustments	(44,689)									(44,689)
Foreign currency translation adjustments attributable to noncontrolling interests										(121)
Shares repurchased for treasury	(75,500)										(83,050)
Balance at end of period at Mar. 31, 2020	11,367,244	780,000	642	1,921,487	11,132,268			21,944	113,149	(91,205)	(2,489,097)
Non-redeemable noncontrolling interests, end of period at Mar. 31, 2020	492,785
Total shareholders’ equity at Mar. 31, 2020	11,860,029
Balance at beginning of period at Dec. 31, 2020	13,105,886	780,000	643	1,977,794	12,362,463	$ 0	$ 12,362,463	488,895	501,295	(12,400)	(2,503,909)
Common shares issued, net			2
Amortization of share-based compensation				40,573
Other changes				(3,626)
Net income (loss)	475,708				475,708
Net (income) loss attributable to noncontrolling interests	(37,552)				(37,552)
Preferred share dividends	(10,403)				(10,403)
Unrealized holding gains (losses) during period, net of reclassification adjustment									(259,053)
Unrealized holding gains (losses) during period attributable to noncontrolling interests									4,469
Foreign currency translation adjustments	(28,584)									(28,584)
Foreign currency translation adjustments attributable to noncontrolling interests										100
Shares repurchased for treasury	(179,300)										(191,048)
Balance at end of period at Mar. 31, 2021	13,096,472	$ 780,000	$ 645	$ 2,014,741	$ 12,790,216			$ 205,827	$ 246,711	$ (40,884)	$ (2,694,957)
Non-redeemable noncontrolling interests, end of period at Mar. 31, 2021	876,864
Total shareholders’ equity at Mar. 31, 2021	$ 13,973,336
Accounting Standards Update	us-gaap:AccountingStandardsUpdate201613Member

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Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Operating Activities
Net income (loss)	$ 475,708	$ (88,674)
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	(161,007)	362,964
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	(135,939)	29,034
Amortization of intangible assets	14,402	16,631
Share-based compensation	40,812	28,549
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	560,153	506,057
Unearned premiums, net of ceded unearned premiums	560,035	392,802
Premiums receivable	(608,250)	(418,457)
Deferred acquisition costs	(126,701)	(75,135)
Reinsurance balances payable	240,206	79,807
Other items, net	(96,574)	(223,124)
Net cash provided by (used for) operating activities	762,845	610,454
Investing Activities
Purchases of fixed maturity investments	(11,530,968)	(11,965,995)
Purchases of equity securities	(309,419)	(760,683)
Purchases of other investments	(430,961)	(228,471)
Proceeds from sales of fixed maturity investments	10,917,134	11,723,123
Proceeds from sales of equity securities	284,986	266,301
Proceeds from sales, redemptions and maturities of other investments	323,591	216,131
Proceeds from redemptions and maturities of fixed maturity investments	421,042	198,356
Net settlements of derivative instruments	47,660	195,488
Net (purchases) sales of short-term investments	589,175	(11,777)
Change in cash collateral related to securities lending	0	55,001
Purchase of operating affiliate	(546,349)	0
Purchases of fixed assets	(12,490)	(8,470)
Other	(246,590)	42,500
Net cash provided by (used for) investing activities	(493,189)	(278,496)
Financing Activities
Purchases of common shares under share repurchase program	(179,266)	(75,486)
Proceeds from common shares issued, net	(10,008)	(4,527)
Proceeds from borrowings	0	16,300
Change in cash collateral related to securities lending	0	(55,001)
Third party investment in non-redeemable noncontrolling interests	15,971	(2,867)
Dividends paid to redeemable noncontrolling interests	(948)	(1,181)
Other	(1,948)	(1,331)
Preferred dividends paid	(10,403)	(10,403)
Net cash provided by (used for) financing activities	(186,602)	(134,496)
Effects of exchange rate changes on foreign currency cash and restricted cash	(6,084)	(30,723)
Increase (decrease) in cash and restricted cash	76,970	166,739
Cash and restricted cash, beginning of year	1,290,544	903,698
Cash and restricted cash, end of period	$ 1,367,514	$ 1,070,437

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Basis of Presentation and Recent Accounting Pronouncements

3 Months Ended

Mar. 31, 2021

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Basis of Presentation and Recent Accounting Pronouncements

Basis of Presentation and Recent Accounting Pronouncements

General

Arch Capital Group Ltd. (“Arch Capital”) is a public listed Bermuda exempted company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly-owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. The Company’s consolidated financial statements include the results of Watford Holdings Ltd. and its wholly owned subsidiaries (“Watford”). Watford is a multi-line Bermuda reinsurance company. Watford’s own management and board of directors are responsible for its results and profitability. See note 11.

Basis of Presentation

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation. 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 at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2020 (“2020 Form 10-K”), including the Company’s audited consolidated financial statements and related notes.

The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated

balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Recent Accounting Pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.

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Share Transactions

3 Months Ended

Mar. 31, 2021

Stockholders' Equity Note [Abstract]

Share Transactions

Share Transactions

Share-Based Compensation

During the 2021 first quarter, the Company granted 1,218,465 stock options, 685,104 performance share awards (“PSAs”) and units (“PSUs”) and 1,168,577 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2021 first quarter were approximately $9.20, $37.38 and $35.82 per share, respectively. Such values are being amortized over the respective substantive vesting period.

During the 2020 first quarter, the Company granted 1,116,073 stock options, 557,204 PSAs and PSUs and 910,879 restricted shares and units to certain employees. The stock options were valued at the grant date using the Black-Scholes option pricing model. The weighted average grant-date fair value of the stock options, PSAs/PSUs and restricted shares and units granted during the 2020 first quarter were approximately $8.14, $44.17 and $42.36 per share, respectively. Such values are being amortized over the respective substantive vesting period.

Share Repurchases 

The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 394.5 million common shares for an aggregate purchase price of $4.23 billion. For the three months ended March 31, 2021, Arch Capital repurchased 5.3 million shares under the share repurchase program with an aggregate purchase price of $179.3 million. Arch Capital repurchased 2.6 million shares

under the share repurchase program with an aggregate purchase price of $75.5 million during the three months ended March 31, 2020. At March 31, 2021, $737.3 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations.

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Earnings Per Common Share

3 Months Ended

Mar. 31, 2021

Earnings Per Share [Abstract]

Earnings Per Common Share

Earnings Per Common Share

The following table sets forth the computation of basic and diluted earnings per common share:

	Three Months Ended
	March 31,
	2021		2020
Numerator:
Net income (loss)	$	475,708	$	(88,674)
Amounts attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	$	427,753	$	133,714
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	400,807,895		403,892,161
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,230,794		2,275,473
Stock options (1)	6,184,564		7,865,936
Weighted average common shares and common share equivalents outstanding — diluted	409,223,253		414,033,570
Earnings per common share:
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.

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Segment Information

3 Months Ended

Mar. 31, 2021

Segment Reporting [Abstract]

Segment Information

Segment Information

The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results.

The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the Chief Executive Officer of Arch Capital, the Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment.

The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: construction and national accounts; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business).

The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other).

The mortgage segment includes the Company’s U.S. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity.

The corporate (non-underwriting) segment results include net investment income, other income (loss), corporate expenses, transaction costs and other, interest expense, items related to the Company’s non-cumulative preferred shares, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investment funds accounted for using the equity method, net foreign exchange gains or losses, income or loss from operating affiliates and income taxes. Such amounts exclude the results of the ‘other’ segment.

The ‘other’ segment includes the results of Watford (see note 11). For the ‘other’ segment, performance is measured based on net income or loss.

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:

	Three Months Ended
	March 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,415,886		$	1,471,060		$	391,246		$	3,277,293		$	216,523		$	3,397,206
Premiums ceded	(421,047)			(471,948)			(56,051)			(948,147)			(37,212)			(888,749)
Net premiums written	994,839			999,112			335,195			2,329,146			179,311			2,508,457
Change in unearned premiums	(175,365)			(354,212)			1,122			(528,455)			(31,580)			(560,035)
Net premiums earned	819,474			644,900			336,317			1,800,691			147,731			1,948,422
Other underwriting income (loss)	—			(1,198)			6,897			5,699			411			6,110
Losses and loss adjustment expenses	(535,747)			(484,870)			(63,689)			(1,084,306)			(118,794)			(1,203,100)
Acquisition expenses	(128,222)			(118,025)			(30,082)			(276,329)			(28,152)			(304,481)
Other operating expenses	(137,113)			(60,514)			(49,131)			(246,758)			(14,275)			(261,033)
Underwriting income (loss)	$	18,392		$	(19,707)		$	200,312		198,997			(13,079)			185,918
Net investment income										78,729			20,127			98,856
Net realized gains (losses)										101,336			41,125			142,461
Equity in net income (loss) of investment funds accounted for using the equity method										71,686			—			71,686
Other income (loss)										(1,741)			—			(1,741)
Corporate expenses (2)										(23,468)			—			(23,468)
Transaction costs and other (2)										(1,201)			(715)			(1,916)
Amortization of intangible assets										(14,402)			—			(14,402)
Interest expense										(34,197)			(4,149)			(38,346)
Net foreign exchange gains (losses)										21,505			(1,442)			20,063
Income (loss) before income taxes and income (loss) from operating affiliates										397,244			41,867			439,111
Income tax (expense) benefit										(38,852)			(8)			(38,860)
Income (loss) from operating affiliates										75,457			—			75,457
Net income (loss)										433,849			41,859			475,708
Amounts attributable to redeemable noncontrolling interests										117			(972)			(855)
Amounts attributable to nonredeemable noncontrolling interests										—			(36,697)			(36,697)
Net income (loss) available to Arch										433,966			4,190			438,156
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	423,563		$	4,190		$	427,753
Underwriting Ratios
Loss ratio	65.4		%	75.2		%	18.9		%	60.2		%	80.4		%	61.7		%
Acquisition expense ratio	15.6		%	18.3		%	8.9		%	15.3		%	19.1		%	15.6		%
Other operating expense ratio	16.7		%	9.4		%	14.6		%	13.7		%	9.7		%	13.4		%
Combined ratio	97.7		%	102.9		%	42.4		%	89.2		%	109.2		%	90.7		%
Goodwill and intangible assets	$	276,211		$	17,807		$	377,841		$	671,859		$	7,650		$	679,509

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Three Months Ended
	March 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,207,645		$	1,122,519		$	368,945		$	2,698,537		$	234,902		$	2,832,830
Premiums ceded	(378,897)			(325,339)			(44,327)			(747,991)			(48,202)			(695,584)
Net premiums written	828,748			797,180			324,618			1,950,546			186,700			2,137,246
Change in unearned premiums	(112,829)			(253,720)			20,408			(346,141)			(46,661)			(392,802)
Net premiums earned	715,919			543,460			345,026			1,604,405			140,039			1,744,444
Other underwriting income (loss)	—			2,120			4,599			6,719			133			6,852
Losses and loss adjustment expenses	(507,108)			(430,069)			(67,566)			(1,004,743)			(110,676)			(1,115,419)
Acquisition expenses	(107,337)			(79,606)			(38,536)			(225,479)			(21,804)			(247,283)
Other operating expenses	(129,649)			(45,297)			(45,896)			(220,842)			(13,702)			(234,544)
Underwriting income (loss)	$	(28,175)		$	(9,392)		$	197,627		160,060			(6,010)			154,050
Net investment income										113,028			32,125			145,153
Net realized gains (losses)										(72,109)			(294,851)			(366,960)
Equity in net income (loss) of investment funds accounted for using the equity method										(4,209)			—			(4,209)
Other income (loss)										32			—			32
Corporate expenses (2)										(18,201)			—			(18,201)
Transaction costs and other (2)										(2,595)			—			(2,595)
Amortization of intangible assets										(16,631)			—			(16,631)
Interest expense										(25,245)			(7,310)			(32,555)
Net foreign exchange gains (losses)										63,307			9,364			72,671
Income (loss) before income taxes and income (loss) from operating affiliates										197,437			(266,682)			(69,245)
Income tax (expense) benefit										(27,945)			—			(27,945)
Income (loss) from operating affiliates										8,516			—			8,516
Net income (loss)										178,008			(266,682)			(88,674)
Amounts attributable to redeemable noncontrolling interests										(57)			(1,096)			(1,153)
Amounts attributable to nonredeemable noncontrolling interests										—			233,944			233,944
Net income (loss) available to Arch										177,951			(33,834)			144,117
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	167,548		$	(33,834)		$	133,714
Underwriting Ratios
Loss ratio	70.8		%	79.1		%	19.6		%	62.6		%	79.0		%	63.9		%
Acquisition expense ratio	15.0		%	14.6		%	11.2		%	14.1		%	15.6		%	14.2		%
Other operating expense ratio	18.1		%	8.3		%	13.3		%	13.8		%	9.8		%	13.4		%
Combined ratio	103.9		%	102.0		%	44.1		%	90.5		%	104.4		%	91.5		%
Goodwill and intangible assets	$	268,296		$	2,516		$	426,988		$	697,800		$	7,650		$	705,450

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

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Reserve for Losses and Loss Adjustment Expenses

3 Months Ended

Mar. 31, 2021

Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]

Reserve for losses and loss adjustment expenses

Reserve for Losses and Loss Adjustment Expenses

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Three Months Ended
	March 31,
	2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,244,772		1,134,442
Prior years	(41,672)		(19,023)
Total net incurred losses and loss adjustment expenses	1,203,100		1,115,419
Retroactive reinsurance transactions (1)	(183,893)		60,635
Net foreign exchange (gains) losses	(46,877)		(142,573)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(58,984)		(41,260)
Prior years	(585,118)		(561,947)
Total net paid losses and loss adjustment expenses	(644,102)		(603,207)
Net reserve for losses and loss adjustment expenses at end of period	12,527,302		10,239,466
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114
Reserve for losses and loss adjustment expenses at end of period	$	16,443,952	$	14,309,580

(1)     During 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

Development on Prior Year Loss Reserves

2021 First Quarter

During the 2021 first quarter, the Company recorded net favorable development on prior year loss reserves of $41.7 million, which consisted of $4.1 million favorable development from the insurance segment, $26.8 million from the reinsurance segment and $10.9 million from the mortgage segment, partially offset by $0.1 million unfavorable from the ‘other’ segment.

The insurance segment’s net favorable development of $4.1 million, or 0.5 loss ratio points, for the 2021 first quarter consisted of $25.0 million of net favorable development in short-tailed and $20.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $14.6 million of favorable development from property (excluding marine), primarily from the 2019 and 2020 accident years (i.e., the year in which a loss occurred), $8.0 million of favorable development in lenders products, primarily from the 2020 accident year, and $2.5

million of favorable development in travel and accident, primarily from the 2020 accident year. Net adverse development in medium-tailed lines included $10.8 million of adverse development in program business, primarily from the 2016 to 2020 accident years, $6.0 million of adverse development in professional liability business, primarily from the 2019 accident year, and $5.0 million of adverse development in surety, primarily from the 2019 accident year.

The reinsurance segment’s net favorable development of $26.8 million, or 4.2 loss ratio points, for the 2021 first quarter consisted of net favorable development in short-tailed, medium-tailed and long-tailed lines. Net favorable development of $17.5 million in short-tailed lines reflected $23.3 million of favorable development related to property other than property catastrophe business, primarily from the 2016 to 2019 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period), and $16.6 million of favorable development from other specialty,

primarily from the 2018 and 2019 underwriting years, partially offset by $22.5 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $9.3 million in medium and long-tailed lines reflected favorable development in casualty across most underwriting years.

The mortgage segment’s net favorable development was $10.9 million, or 3.2 loss ratio points, for the 2021 first quarter, primarily driven by favorable development in the credit risk transfer and international portfolios. Subrogation recoveries on second lien and student loan business also contributed.

2020 First Quarter

During the 2020 first quarter, the Company recorded net favorable development on prior year loss reserves of $19.0 million, which consisted of $1.1 million from the insurance segment, $11.6 million from the reinsurance segment, $6.1 million from the mortgage segment and $0.2 million from the ‘other’ segment.

The insurance segment’s net favorable development of $1.1 million, or 0.2 loss ratio points, for the 2020 first quarter consisted of $3.9 million of net favorable development in short-tailed lines, $7.9 million of net adverse development in medium-tailed lines and $5.2 million of net favorable development in long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across 2018 and prior accident years. Net adverse development in medium-tailed lines included $13.2 million of adverse development in contract binding business across most accident years, partially offset by $5.1 million of favorable development in professional liability business. Net favorable development in longer-tailed lines primarily related to construction business driven by the 2017 accident year.

The reinsurance segment’s net favorable development of $11.6 million, or 2.1 loss ratio points, for the 2020 first quarter consisted of $21.5 million of net favorable development in short-tailed and medium-tailed lines and net adverse development of $9.9 million in long-tailed lines. Net favorable development in short-tailed and medium-tailed lines reflected $11.9 million of favorable development in other specialty lines across most underwriting years and $10.5 million of favorable development from property catastrophe business, primarily from the 2015 to 2019 underwriting years. Such amounts were partially offset by $4.3 million of adverse development in property other than property catastrophe business, driven by the 2018 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty reserves from various underwriting years.

The mortgage segment’s net favorable development was $6.1 million, or 1.8 loss ratio points, for the 2020 first quarter. The 2020 first quarter development was primarily driven by subrogation recoveries on second lien and student loan business.

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Allowance for Expected Credit Losses

3 Months Ended

Mar. 31, 2021

Credit Loss [Abstract]

Allowance for expected credit losses

Allowance for Expected Credit Losses

Premiums Receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,670)
Balance at end of period	$	2,618,175	$	36,111
December 31, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Reinsurance Recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(764)
Balance at end of period	$	4,041,076	$	10,872
December 31, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			(1,738)
Balance at end of period	$	4,500,802	$	11,636

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

(1)    At March 31, 2021 and December 31, 2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder Receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(2,785)
Balance at end of period	$	1,919,655	$	5,853
December 31, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			1,975
Balance at end of period	$	1,986,924	$	8,638

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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Investment Information

3 Months Ended

Mar. 31, 2021

Disclosure Investment Information [Abstract]

Investment Information

Investment Information

At March 31, 2021, total investable assets of $29.1 billion included $26.3 billion held by the Company and $2.7 billion attributable to Watford.

Available For Sale Investments

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses (2)		Cost or Amortized Cost
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	8,072,883	$	242,832	$	(83,961)	$	(2,569)	$	7,916,581
Mortgage backed securities	571,071		7,066		(11,165)		(325)		575,495
Municipal bonds	457,329		19,942		(4,814)		(2)		442,203
Commercial mortgage backed securities	255,373		2,755		(1,721)		(5)		254,344
U.S. government and government agencies	5,042,208		15,102		(30,545)		—		5,057,651
Non-U.S. government securities	2,425,882		127,886		(19,267)		(51)		2,317,314
Asset backed securities	2,028,441		18,817		(4,962)		(878)		2,015,464
Total	18,853,187		434,400		(156,435)		(3,830)		18,579,052
Short-term investments	1,269,631		920		(601)		—		1,269,312
Total	$	20,122,818	$	435,320	$	(157,036)	$	(3,830)	$	19,848,364
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	3,253,030	$	(82,735)	$	15,894	$	(1,226)	$	3,268,924	$	(83,961)
Mortgage backed securities	383,760		(10,271)		20,648		(894)		404,408		(11,165)
Municipal bonds	90,634		(4,737)		1,827		(77)		92,461		(4,814)
Commercial mortgage backed securities	39,863		(759)		23,421		(962)		63,284		(1,721)
U.S. government and government agencies	3,920,377		(30,545)		—		—		3,920,377		(30,545)
Non-U.S. government securities	911,609		(18,433)		16,841		(834)		928,450		(19,267)
Asset backed securities	502,300		(2,391)		142,331		(2,571)		644,631		(4,962)
Total	9,101,573		(149,871)		220,962		(6,564)		9,322,535		(156,435)
Short-term investments	95,579		(601)		—		—		95,579		(601)
Total	$	9,197,152	$	(150,472)	$	220,962	$	(6,564)	$	9,418,114	$	(157,036)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

At March 31, 2021, on a lot level basis, approximately 4,610 security lots out of a total of approximately 11,360 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $1.1 million. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $0.9 million.

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

	March 31, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	381,212	$	370,798	$	348,200	$	339,951
Due after one year through five years	11,124,344		10,918,279		10,629,959		10,340,819
Due after five years through 10 years	4,052,472		4,008,520		4,881,564		4,654,754
Due after 10 years	440,274		436,152		482,180		448,139
	15,998,302		15,733,749		16,341,903		15,783,663
Mortgage backed securities	571,071		575,495		630,001		626,368
Commercial mortgage backed securities	255,373		254,344		389,900		384,254
Asset backed securities	2,028,441		2,015,464		1,634,804		1,627,384
Total (1)	$	18,853,187	$	18,579,052	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities Lending Agreements

The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan from the Company.

The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At March 31, 2021, the fair value of the cash collateral received on securities lending was nil and the fair value of security collateral received was $143.9 million. At December 31, 2020, the fair value of the cash collateral received on securities lending was nil, and the fair value of security collateral received was $301.1 million.

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
March 31, 2021
U.S. government and government agencies	$	16,397	$	—	$	102,743	$	—	$	119,140
Corporate bonds	13,724		—		—		—		13,724
Equity securities	11,022		—		—		—		11,022
Total	$	41,143	$	—	$	102,743	$	—	$	143,886
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	143,886
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Equity Securities, at Fair Value

At March 31, 2021, the Company held $1.5 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors.

Other Investments

The following table summarizes the Company’s other investments and other investable assets:

	March 31, 2021		December 31, 2020
Fixed maturities	$	900,304	$	843,354
Other investments	2,318,185		2,331,885
Short-term investments	623,930		557,008
Equity securities	92,935		92,549
Investments accounted for using the fair value option	$	3,935,354	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,435,354	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	March 31, 2021		December 31, 2020
Term loan investments	$	1,187,752	$	1,231,731
Lending	606,207		572,636
Credit related funds	79,355		90,780
Energy	78,500		65,813
Investment grade fixed income	142,630		138,646
Infrastructure	152,352		165,516
Private equity	52,064		48,750
Real estate	19,325		18,013
Total	$	2,318,185	$	2,331,885

Investments Accounted For Using the Equity Method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	March 31, 2021		December 31, 2020
Credit related funds	$	818,344	$	740,060
Equities	357,641		343,058
Real estate	292,424		258,518
Lending	199,913		179,629
Private equity	288,657		235,289
Infrastructure	179,225		175,882
Energy	120,123		115,453
Total	$	2,256,327	$	2,047,889

Certain of the Company’s other investments are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund’s net assets which may otherwise hinder the general partner or investment manager’s ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification.

Limited Partnership Interests

In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company has determined that it is not required to consolidate these investments because it is not the primary beneficiary of the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment.

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:

	March 31, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,256,327		2,047,889
Investments accounted for using the fair value option (2)	196,087		184,720
Total	$	2,452,414	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at March 31, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $36.1 million at March 31, 2021, compared to $35.6 million at December 31, 2020.

Net Investment Income

The components of net investment income were derived from the following sources:

	March 31,
	2021		2020
Three Months Ended
Fixed maturities	$	90,626	$	114,847
Term loans	14,728		23,170
Equity securities	5,650		6,007
Short-term investments	607		4,896
Other (1)	14,355		19,406
Gross investment income	125,966		168,326
Investment expenses	(27,110)		(23,173)
Net investment income	$	98,856	$	145,153

(1)    Includes income distributions from investment funds and other items.

Net Realized Gains (Losses)

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	March 31,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	65,002	$	178,200
Gross losses on investment sales	(62,998)		(31,968)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	16,553		(127,666)
Other investments	46,855		(307,800)
Equity securities	2,065		(4,909)
Short-term investments	736		(8,681)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	37,849		(539)
Net unrealized gains (losses) on equity securities still held at reporting date	19,708		(175,566)
Allowance for credit losses:
Investments related	(1,648)		(9,320)
Underwriting related	5,268		(3,270)
Net impairment losses	—		(533)
Derivative instruments (1)	36,116		127,189
Other	(23,045)		(2,097)
Net realized gains (losses)	$	142,461	$	(366,960)

(1)    See note 9 for information on the Company’s derivative instruments.

Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method

The Company recorded $71.7 million of equity in net income related to investment funds accounted for using the equity method in the 2021 first quarter, compared to loss of $4.2 million for the 2020 first quarter. In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the market value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds.

Investments in Operating Affiliates

Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface and Premia Holdings Ltd. (“Premia”) and are generally recorded on a three month lag.

In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. At March 31, 2021 the Company’s carrying value in Coface was $604.6 million.

Allowance for Expected Credit Losses

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
March 31, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	182		—		2,421		2,603
Additions (reductions) for previously recognized expected credit losses	(382)		(9)		(540)		(931)
Reductions due to disposals	(83)		—		(156)		(239)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,207	$	2	$	2,621	$	3,830
December 31, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		634
Additions for current-period provision for expected credit losses	2,942		67		7,644		10,653
Additions (reductions) for previously recognized expected credit losses	(1,398)		6		(5,638)		(7,030)
Reductions due to disposals	(571)		(62)		(1,227)		(1,860)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,490	$	11	$	896	$	2,397

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Restricted Assets

The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K.

The following table details the value of the Company’s restricted assets:

	March 31, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	4,815,120	$	4,643,334
Third party agreements	3,366,016		3,083,324
Deposits with U.S. regulatory authorities	819,444		827,552
Deposits with non-U.S. regulatory authorities	330,197		179,099
Total restricted assets	$	9,330,777	$	8,733,309

In addition, Watford maintains secured credit facilities to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of March 31, 2021 and December 31, 2020, Watford held $1.0 billion and $954.6 million, respectively, in pledged assets to collateralize the credit facility mentioned above.

Reconciliation of Cash and Restricted Cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	March 31, 2021		December 31, 2020
Cash	$	941,951	$	906,448
Restricted cash (included in ‘other assets’)	$	425,563	$	384,096
Cash and restricted cash	$	1,367,514	$	1,290,544

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Fair Value

3 Months Ended

Mar. 31, 2021

Fair Value Disclosures [Abstract]

Fair Value

Fair Value

Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority).

The levels in the hierarchy are defined as follows:

Level 1:	Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets
Level 2:	Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument
Level 3:	Inputs to the valuation methodology are unobservable and significant to the fair value measurement

Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others.

The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but

is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the average number of prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used (i.e., a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. The Company did not adjust any of the prices obtained from the independent pricing sources at March 31, 2021.

In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $25.9 billion of financial assets and liabilities measured at fair value at March 31, 2021, approximately $146.9 million, or 0.6%, were priced using non-binding broker-dealer quotes or modeled valuations. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, were priced using non-binding broker-dealer quotes or modeled valuations.

Fixed maturities

The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs

including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value.

The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class:

•U.S. government and government agencies — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2.

•Corporate bonds — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Mortgage-backed securities — valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

•Municipal bonds — valuations provided by independent pricing services, with all prices provided

through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2.

•Commercial mortgage-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Non-U.S. government securities — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2.

•Asset-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process.

Equity securities

The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Certain

equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3.

Other investments

The Company’s other investments include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities.

Derivative instruments

The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2.

Short-term investments

The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2.

Residential mortgage loans

The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities are classified within level 2.

Contingent consideration liabilities

Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to various Company’s acquisitions. Such amounts are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at March 31, 2021:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,072,883	$	—	$	8,072,870	$	13
Mortgage backed securities	571,071		—		571,071		—
Municipal bonds	457,329		—		457,329		—
Commercial mortgage backed securities	255,373		—		255,373		—
U.S. government and government agencies	5,042,208		4,949,217		92,991		—
Non-U.S. government securities	2,425,882		—		2,425,882		—
Asset backed securities	2,028,441		—		2,024,969		3,472
Total	18,853,187		4,949,217		13,900,485		3,485
Short-term investments	1,269,631		1,252,535		17,096		—
Equity securities, at fair value	1,543,703		1,476,504		24,087		43,112
Derivative instruments (4)	156,160		—		156,160		—
Residential mortgage loans	5,693		—		5,693		—
Fair value option:
Corporate bonds	724,316		—		723,327		989
Non-U.S. government bonds	23,996		—		23,996		—
Mortgage backed securities	2,828		—		2,828		—
Commercial mortgage backed securities	1,225		—		1,225		—
Asset backed securities	147,666		—		147,666		—
U.S. government and government agencies	273		164		109		—
Short-term investments	623,930		482,869		141,061		—
Equity securities	92,935		21,512		247		71,176
Other investments	1,078,505		31,268		979,307		67,930
Other investments measured at net asset value (2)	1,239,680
Total	3,935,354		535,813		2,019,766		140,095
Total assets measured at fair value	$	25,763,728	$	8,214,069	$	16,123,287	$	186,692
Liabilities measured at fair value:
Contingent consideration liabilities	$	(465)	$	—	$	—	$	(465)
Securities sold but not yet purchased (3)	(34,097)		—		(34,097)		—
Derivative instruments (4)	(98,103)		—		(98,103)		—
Total liabilities measured at fair value	$	(132,665)	$	—	$	(132,200)	$	(465)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Contingent Consideration Liabilities
Three Months Ended March 31, 2021
Balance at beginning of period	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(68)		—		4		248		2,188		904		—
Included in other comprehensive income	114		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		7,365		—		193		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(6,786)		—		—		—
Settlements	—		—		—		—		—		—		(4)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Three Months Ended March 31, 2020
Balance at beginning of period	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	9		7		—		(27)		1,921		(3,721)		(54)
Included in other comprehensive income	(22)		(5,416)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		21		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(17,175)		—		—		—
Settlements	(1,357)		(1,462)		—		—		—		—		85
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

Financial Instruments Disclosed, But Not Carried, At Fair Value

The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at March 31, 2021, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

At March 31, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.4 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 billion. The fair values of the senior notes were obtained from a third party pricing service and are based on observable market inputs. As such, the fair values of the senior notes are classified within Level 2.

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Derivative Instruments

3 Months Ended

Mar. 31, 2021

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Derivative Instruments

Derivative Instruments

The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements. 

In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed

securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy.

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives		Liability Derivatives		Notional Value (1)
March 31, 2021
Futures contracts (2)	$	85,379	$	(54,615)	$	7,116,745
Foreign currency forward contracts (2)	17,898		(29,887)		2,190,031
TBAs (3)	—		—		—
Other (2)	52,883		(13,601)		6,324,926
Total	$	156,160	$	(98,103)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
TBAs (3)	—		—		—
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(1)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

(2)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(3)    The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

The Company did not hold any derivatives which were designated as hedging instruments at March 31, 2021 or December 31, 2020.

The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure.

At March 31, 2021, asset derivatives and liability derivatives of $148.4 million and $98.1 million, respectively, were subject to a master netting agreement, compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. The remaining derivatives included in the preceding table were not subject to a master netting agreement.

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as	March 31,
hedging instruments:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	47,438	$	95,944
Foreign currency forward contracts	(22,071)		(10,870)
TBAs	—		745
Other (1)	10,749		41,370
Total	$	36,116	$	127,189

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

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Commitments and Contingencies

3 Months Ended

Mar. 31, 2021

Commitments and Contingencies Disclosure [Abstract]

Commitments and Contingencies

Commitments and Contingencies

Investment Commitments

The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $2.3 billion at March 31, 2021, compared to $2.1 billion at December 31, 2020.

Interest Paid

Interest paid on the Company’s senior notes and other borrowings were $1.0 million for the three months ended March 31, 2021, compared to $6.6 million for the 2020 period.

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Variable Interest Entities and Noncontrolling Interests

3 Months Ended

Mar. 31, 2021

Noncontrolling Interest [Abstract]

Variable Interest Entity and Noncontrolling Interests

Variable Interest Entities and Noncontrolling Interests

Watford

In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares, approximately 11% of Watford’s outstanding common equity. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of March 31, 2021, the Company owns approximately 10.3% of Watford’s outstanding common equity. The Company also owns $35.0 million in aggregate principal amount of Watford

Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Watford’s preference shares.

Watford is considered a VIE and the Company concluded that it is the primary beneficiary of Watford. As such, the results of Watford are included in the Company’s consolidated financial statements.

The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions.

In the 2020 fourth quarter, Arch Capital, Watford Holdings Ltd. and Greysbridge Ltd., a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”) pursuant to which, among other things, Arch Capital agreed to acquire all of the common shares of Watford Holdings Ltd. not owned by Arch for a cash purchase price of $35.00 per common share. Arch Capital has assigned its rights under the Merger Agreement to Greysbridge Holdings Ltd., a wholly-owned subsidiary of Arch Capital (“Greysbridge”). The transaction is expected to close in the second quarter of 2021 and remains subject to customary closing conditions. Shareholder approval has been obtained and regulatory approvals are ongoing. Upon closing of the transaction, Watford will be wholly owned by Greysbridge and Greysbridge will be owned 40% by Arch Re Bermuda, 30% by certain investment funds managed by Kelso & Company and 30% by certain investment funds managed by Warburg Pincus LLC.

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	March 31,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,880,768	$	1,790,385
Fixed maturities available for sale, at fair value	627,387		655,249
Equity securities, at fair value	62,314		52,410
Cash	236,164		211,451
Accrued investment income	14,325		14,679
Premiums receivable	252,523		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	291,485		286,590
Ceded unearned premiums	113,180		122,339
Deferred acquisition costs	62,224		53,705
Receivable for securities sold	68,076		37,423
Goodwill and intangible assets	7,650		7,650
Other assets	87,358		75,801
Total assets of consolidated VIE	$	3,703,454	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,568,243	$	1,519,583
Unearned premiums	426,975		407,714
Reinsurance balances payable	77,041		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,757		172,689
Payable for securities purchased	59,230		25,881
Other liabilities	214,103		193,494
Total liabilities of consolidated VIE	$	2,674,036	$	2,538,317
Redeemable noncontrolling interests	$	52,421	$	52,398

(1)    Includes in “other investments” on the Company’s balance sheet.

For the three months ended March 31, 2021, Watford generated $7.0 million of cash provided by operating activities, $21.4 million of cash provided by investing activities and $1.0 million of cash used for financing activities, compared to $24.6 million of cash provided by operating activities, $35.7 million of cash used for investing activities and $12.3 million of cash provided by financing activities for the three months ended March 31, 2020.

Non-redeemable noncontrolling interests

The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s common shares was approximately 90% at March 31, 2021. The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’

The following table sets forth activity in the non-redeemable noncontrolling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	21,730		(123)
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	36,697		(233,944)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,570)		(33,058)
Balance, end of period	$	876,864	$	492,785

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Redeemable noncontrolling interests

The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Watford Preference Shares were issued at a discounted amount of $24.50 per share. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income.

The following table sets forth activity in the redeemable non-controlling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	58,548	$	55,404
Accretion of preference share issuance costs	23		23
Other	(901)		(51)
Balance, end of period	$	57,670	$	55,376

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	March 31,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(36,697)	$	233,944
Amounts attributable to redeemable noncontrolling interests	(855)		(1,153)
Net (income) loss attributable to noncontrolling interests	$	(37,552)	$	232,791

Bellemeade Re

The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements.

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreement benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			March 31, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(306)	$	1,152	$	846	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(1,081)		2,885		1,804		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	66,747		(32)		62		30		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,604)		4,277		2,673		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,117)		7,991		6,874		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(780)		6,577		5,797		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(898)		6,047		5,149		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(908)		8,034		7,126		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	132,881		(58)		294		236		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	368,797		(370)		6,077		5,707		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(433)		9,527		9,094		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	321,393		(23)		5,969		5,946		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		—		4,767		4,767		—		—		—		—
Total	$	4,200,317	$	(7,610)	$	63,659	$	56,049	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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Other Comprehensive Income (Loss)

3 Months Ended

Mar. 31, 2021

Comprehensive Income Note Disclosure [Abstract]

Other Comprehensive Income (Loss)

Other Comprehensive Income (Loss)

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended
Details About	Line Item That Includes	March 31,
AOCI Components	Reclassification	2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	2,004	$	146,232
	Provision for credit losses	(1,647)		(9,320)
	Other-than-temporary impairment losses	—		(533)
	Total before tax	357		136,379
	Income tax (expense) benefit	(3,054)		(15,150)
	Net of tax	$	(2,697)	$	121,229

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended March 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(294,360)	$	(32,610)	$	(261,750)
Less reclassification of net realized gains (losses) included in net income	357		3,054		(2,697)
Foreign currency translation adjustments	(28,415)		169		(28,584)
Other comprehensive income (loss)	$	(323,132)	$	(35,495)	$	(287,637)
Three Months Ended March 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(63,451)	$	(6,164)	$	(57,287)
Less reclassification of net realized gains (losses) included in net income	136,379		15,150		121,229
Foreign currency translation adjustments	(45,424)		(735)		(44,689)
Other comprehensive income (loss)	$	(245,254)	$	(22,049)	$	(223,205)

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Income Taxes

3 Months Ended

Mar. 31, 2021

Income Tax Disclosure [Abstract]

Income Taxes

Income Taxes

The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 7.6% for the three months ended March 31, 2021, compared to (46.0%) for the 2020 period. The Company’s prior year effective tax rate was impacted by significant portion of realized losses generated in lower tax jurisdictions.

The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction.

The Company had a net deferred tax asset of $48.1 million at March 31, 2021, compared to a net deferred tax asset of $15.7 million at December 31, 2020. The change is primarily a result of market value fluctuations in the investment portfolio. In addition, the Company paid $7.1 million and $7.4 million of income taxes for the three months ended March 31, 2021 and 2020, respectively.

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Legal Proceedings	3 Months Ended
	Mar. 31, 2021
Disclosure Legal Proceedings [Abstract]
Legal Proceedings	Legal ProceedingsThe Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of March 31, 2021, the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

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Transactions With Related Parties

3 Months Ended

Mar. 31, 2021

Related Party Transactions [Abstract]

Transactions with related parties

Transactions with Related Parties

In the 2019 fourth quarter, Barbican, a wholly owned subsidiary of the Company, entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of nil and $275.0 million, respectively, at March 31, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020.

In the 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021.

Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,” for information about Watford.

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Basis of Presentation and Recent Accounting Pronouncements (Policies)

3 Months Ended

Mar. 31, 2021

Organization, Consolidation and Presentation of Financial Statements [Abstract]

Basis of accounting

The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). All significant intercompany transactions and balances have been eliminated in consolidation.

Use of estimates

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 at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.

Recent accounting pronouncements

Recently Issued Accounting Standards Adopted

The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements.

For information regarding additional accounting standards that the Company has not yet adopted, see note 3(r), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2020 Form 10-K

Reclassification of prior periods

The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 7.

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Earnings Per Common Share (Tables)

3 Months Ended

Mar. 31, 2021

Earnings Per Share [Abstract]

Schedule of computation of basic and diluted earnings per common share

The following table sets forth the computation of basic and diluted earnings per common share:

	Three Months Ended
	March 31,
	2021		2020
Numerator:
Net income (loss)	$	475,708	$	(88,674)
Amounts attributable to noncontrolling interests	(37,552)		232,791
Net income (loss) available to Arch	438,156		144,117
Preferred dividends	(10,403)		(10,403)
Net income (loss) available to Arch common shareholders	$	427,753	$	133,714
Denominator:
Weighted average common shares and common share equivalents outstanding — basic	400,807,895		403,892,161
Effect of dilutive common share equivalents:
Nonvested restricted shares	2,230,794		2,275,473
Stock options (1)	6,184,564		7,865,936
Weighted average common shares and common share equivalents outstanding — diluted	409,223,253		414,033,570
Earnings per common share:
Basic	$	1.07	$	0.33
Diluted	$	1.05	$	0.32

(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.

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Segment Information (Tables)

3 Months Ended

Mar. 31, 2021

Segment Reporting [Abstract]

Analysis of underwriting income or loss by segment and reconciliation to net income available to common shareholders

The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders:

	Three Months Ended
	March 31, 2021
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,415,886		$	1,471,060		$	391,246		$	3,277,293		$	216,523		$	3,397,206
Premiums ceded	(421,047)			(471,948)			(56,051)			(948,147)			(37,212)			(888,749)
Net premiums written	994,839			999,112			335,195			2,329,146			179,311			2,508,457
Change in unearned premiums	(175,365)			(354,212)			1,122			(528,455)			(31,580)			(560,035)
Net premiums earned	819,474			644,900			336,317			1,800,691			147,731			1,948,422
Other underwriting income (loss)	—			(1,198)			6,897			5,699			411			6,110
Losses and loss adjustment expenses	(535,747)			(484,870)			(63,689)			(1,084,306)			(118,794)			(1,203,100)
Acquisition expenses	(128,222)			(118,025)			(30,082)			(276,329)			(28,152)			(304,481)
Other operating expenses	(137,113)			(60,514)			(49,131)			(246,758)			(14,275)			(261,033)
Underwriting income (loss)	$	18,392		$	(19,707)		$	200,312		198,997			(13,079)			185,918
Net investment income										78,729			20,127			98,856
Net realized gains (losses)										101,336			41,125			142,461
Equity in net income (loss) of investment funds accounted for using the equity method										71,686			—			71,686
Other income (loss)										(1,741)			—			(1,741)
Corporate expenses (2)										(23,468)			—			(23,468)
Transaction costs and other (2)										(1,201)			(715)			(1,916)
Amortization of intangible assets										(14,402)			—			(14,402)
Interest expense										(34,197)			(4,149)			(38,346)
Net foreign exchange gains (losses)										21,505			(1,442)			20,063
Income (loss) before income taxes and income (loss) from operating affiliates										397,244			41,867			439,111
Income tax (expense) benefit										(38,852)			(8)			(38,860)
Income (loss) from operating affiliates										75,457			—			75,457
Net income (loss)										433,849			41,859			475,708
Amounts attributable to redeemable noncontrolling interests										117			(972)			(855)
Amounts attributable to nonredeemable noncontrolling interests										—			(36,697)			(36,697)
Net income (loss) available to Arch										433,966			4,190			438,156
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	423,563		$	4,190		$	427,753
Underwriting Ratios
Loss ratio	65.4		%	75.2		%	18.9		%	60.2		%	80.4		%	61.7		%
Acquisition expense ratio	15.6		%	18.3		%	8.9		%	15.3		%	19.1		%	15.6		%
Other operating expense ratio	16.7		%	9.4		%	14.6		%	13.7		%	9.7		%	13.4		%
Combined ratio	97.7		%	102.9		%	42.4		%	89.2		%	109.2		%	90.7		%
Goodwill and intangible assets	$	276,211		$	17,807		$	377,841		$	671,859		$	7,650		$	679,509

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

	Three Months Ended
	March 31, 2020
	Insurance			Reinsurance			Mortgage			Sub-Total			Other			Total
Gross premiums written (1)	$	1,207,645		$	1,122,519		$	368,945		$	2,698,537		$	234,902		$	2,832,830
Premiums ceded	(378,897)			(325,339)			(44,327)			(747,991)			(48,202)			(695,584)
Net premiums written	828,748			797,180			324,618			1,950,546			186,700			2,137,246
Change in unearned premiums	(112,829)			(253,720)			20,408			(346,141)			(46,661)			(392,802)
Net premiums earned	715,919			543,460			345,026			1,604,405			140,039			1,744,444
Other underwriting income (loss)	—			2,120			4,599			6,719			133			6,852
Losses and loss adjustment expenses	(507,108)			(430,069)			(67,566)			(1,004,743)			(110,676)			(1,115,419)
Acquisition expenses	(107,337)			(79,606)			(38,536)			(225,479)			(21,804)			(247,283)
Other operating expenses	(129,649)			(45,297)			(45,896)			(220,842)			(13,702)			(234,544)
Underwriting income (loss)	$	(28,175)		$	(9,392)		$	197,627		160,060			(6,010)			154,050
Net investment income										113,028			32,125			145,153
Net realized gains (losses)										(72,109)			(294,851)			(366,960)
Equity in net income (loss) of investment funds accounted for using the equity method										(4,209)			—			(4,209)
Other income (loss)										32			—			32
Corporate expenses (2)										(18,201)			—			(18,201)
Transaction costs and other (2)										(2,595)			—			(2,595)
Amortization of intangible assets										(16,631)			—			(16,631)
Interest expense										(25,245)			(7,310)			(32,555)
Net foreign exchange gains (losses)										63,307			9,364			72,671
Income (loss) before income taxes and income (loss) from operating affiliates										197,437			(266,682)			(69,245)
Income tax (expense) benefit										(27,945)			—			(27,945)
Income (loss) from operating affiliates										8,516			—			8,516
Net income (loss)										178,008			(266,682)			(88,674)
Amounts attributable to redeemable noncontrolling interests										(57)			(1,096)			(1,153)
Amounts attributable to nonredeemable noncontrolling interests										—			233,944			233,944
Net income (loss) available to Arch										177,951			(33,834)			144,117
Preferred dividends										(10,403)			—			(10,403)
Net income (loss) available to Arch common shareholders										$	167,548		$	(33,834)		$	133,714
Underwriting Ratios
Loss ratio	70.8		%	79.1		%	19.6		%	62.6		%	79.0		%	63.9		%
Acquisition expense ratio	15.0		%	14.6		%	11.2		%	14.1		%	15.6		%	14.2		%
Other operating expense ratio	18.1		%	8.3		%	13.3		%	13.8		%	9.8		%	13.4		%
Combined ratio	103.9		%	102.0		%	44.1		%	90.5		%	104.4		%	91.5		%
Goodwill and intangible assets	$	268,296		$	2,516		$	426,988		$	697,800		$	7,650		$	705,450

(1)    Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

(2)    Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

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Reserve for Losses and Loss Adjustment Expenses (Tables)

3 Months Ended

Mar. 31, 2021

Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]

Analysis of losses and loss adjustment expenses and reconciliation of beginning and ending reserve balances

The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses:

	Three Months Ended
	March 31,
	2021		2020
Reserve for losses and loss adjustment expenses at beginning of period	$	16,513,929	$	13,891,842
Unpaid losses and loss adjustment expenses recoverable	4,314,855		4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period	12,199,074		9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year	1,244,772		1,134,442
Prior years	(41,672)		(19,023)
Total net incurred losses and loss adjustment expenses	1,203,100		1,115,419
Retroactive reinsurance transactions (1)	(183,893)		60,635
Net foreign exchange (gains) losses	(46,877)		(142,573)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year	(58,984)		(41,260)
Prior years	(585,118)		(561,947)
Total net paid losses and loss adjustment expenses	(644,102)		(603,207)
Net reserve for losses and loss adjustment expenses at end of period	12,527,302		10,239,466
Unpaid losses and loss adjustment expenses recoverable	3,916,650		4,070,114
Reserve for losses and loss adjustment expenses at end of period	$	16,443,952	$	14,309,580

(1)     During 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

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Allowance for Expected Credit Losses (Tables)

3 Months Ended

Mar. 31, 2021

Credit Loss [Abstract]

Premiums receivable

The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables:

	Premium Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	2,064,586	$	37,781
Change for provision of expected credit losses (1)			(1,670)
Balance at end of period	$	2,618,175	$	36,111
December 31, 2020
Balance at beginning of period	$	1,778,717	$	21,003
Cumulative effect of accounting change (2)			6,539
Change for provision of expected credit losses (1)			10,239
Balance at end of period	$	2,064,586	$	37,781

(1)Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

(2)Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Reinsurance recoverables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables:

	Reinsurance Recoverables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	4,500,802	$	11,636
Change for provision of expected credit losses			(764)
Balance at end of period	$	4,041,076	$	10,872
December 31, 2020
Balance at beginning of period	$	4,346,816	$	1,364
Cumulative effect of accounting change (1)			12,010
Change for provision of expected credit losses			(1,738)
Balance at end of period	$	4,500,802	$	11,636

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Ceded credit risk

The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums):

	March 31,			December 31
	2021			2020
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$	4,041,076		$	4,500,802
% due from carriers with A.M. Best rating of “A-” or better	64.5		%	63.9		%
% due from all other carriers with no A.M. Best rating (1)	35.5		%	36.1		%
Largest balance due from any one carrier as % of total shareholders’ equity	1.7		%	1.8		%

(1)    At March 31, 2021 and December 31, 2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.

Contractholder receivables

The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables:

	Contract-holder Receivables, Net of Allowance		Allowance for Expected Credit Losses
March 31, 2021
Balance at beginning of period	$	1,986,924	$	8,638
Change for provision of expected credit losses			(2,785)
Balance at end of period	$	1,919,655	$	5,853
December 31, 2020
Balance at beginning of period	$	2,119,460	$	—
Cumulative effect of accounting change (1)			6,663
Change for provision of expected credit losses			1,975
Balance at end of period	$	1,986,924	$	8,638

(1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

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Investment Information (Tables)

3 Months Ended

Mar. 31, 2021

Disclosure Investment Information [Abstract]

Summary of fair value and cost or amortized cost of available for sale securities

The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale:

	Estimated Fair Value		Gross Unrealized Gains		Gross Unrealized Losses		Allowance for Expected Credit Losses (2)		Cost or Amortized Cost
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	8,072,883	$	242,832	$	(83,961)	$	(2,569)	$	7,916,581
Mortgage backed securities	571,071		7,066		(11,165)		(325)		575,495
Municipal bonds	457,329		19,942		(4,814)		(2)		442,203
Commercial mortgage backed securities	255,373		2,755		(1,721)		(5)		254,344
U.S. government and government agencies	5,042,208		15,102		(30,545)		—		5,057,651
Non-U.S. government securities	2,425,882		127,886		(19,267)		(51)		2,317,314
Asset backed securities	2,028,441		18,817		(4,962)		(878)		2,015,464
Total	18,853,187		434,400		(156,435)		(3,830)		18,579,052
Short-term investments	1,269,631		920		(601)		—		1,269,312
Total	$	20,122,818	$	435,320	$	(157,036)	$	(3,830)	$	19,848,364
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	7,856,571	$	414,247	$	(34,388)	$	(896)	$	7,477,608
Mortgage backed securities	630,001		8,939		(5,028)		(278)		626,368
Municipal bonds	494,522		27,291		(3,835)		(11)		471,077
Commercial mortgage backed securities	389,900		8,722		(2,954)		(122)		384,254
U.S. government and government agencies	5,557,077		22,612		(12,611)		—		5,547,076
Non-U.S. government securities	2,433,733		153,891		(8,060)		—		2,287,902
Asset backed securities	1,634,804		19,225		(10,715)		(1,090)		1,627,384
Total	18,996,608		654,927		(77,591)		(2,397)		18,421,669
Short-term investments	1,924,922		2,693		(2,063)		—		1,924,292
Total	$	20,921,530	$	657,620	$	(79,654)	$	(2,397)	$	20,345,961

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

(2)    Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

Summary of available for sale securities in a continual unrealized loss position

The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position:

	Less than 12 Months				12 Months or More				Total
	Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses		Estimated Fair Value		Gross Unrealized Losses
March 31, 2021
Fixed maturities (1):
Corporate bonds	$	3,253,030	$	(82,735)	$	15,894	$	(1,226)	$	3,268,924	$	(83,961)
Mortgage backed securities	383,760		(10,271)		20,648		(894)		404,408		(11,165)
Municipal bonds	90,634		(4,737)		1,827		(77)		92,461		(4,814)
Commercial mortgage backed securities	39,863		(759)		23,421		(962)		63,284		(1,721)
U.S. government and government agencies	3,920,377		(30,545)		—		—		3,920,377		(30,545)
Non-U.S. government securities	911,609		(18,433)		16,841		(834)		928,450		(19,267)
Asset backed securities	502,300		(2,391)		142,331		(2,571)		644,631		(4,962)
Total	9,101,573		(149,871)		220,962		(6,564)		9,322,535		(156,435)
Short-term investments	95,579		(601)		—		—		95,579		(601)
Total	$	9,197,152	$	(150,472)	$	220,962	$	(6,564)	$	9,418,114	$	(157,036)
December 31, 2020
Fixed maturities (1):
Corporate bonds	$	747,442	$	(33,086)	$	3,934	$	(1,302)	$	751,376	$	(34,388)
Mortgage backed securities	284,619		(4,788)		3,637		(240)		288,256		(5,028)
Municipal bonds	67,937		(3,835)		—		—		67,937		(3,835)
Commercial mortgage backed securities	126,624		(2,916)		2,655		(38)		129,279		(2,954)
U.S. government and government agencies	1,285,907		(12,611)		—		—		1,285,907		(12,611)
Non-U.S. government securities	543,844		(7,658)		2,441		(402)		546,285		(8,060)
Asset backed securities	634,470		(9,110)		57,737		(1,605)		692,207		(10,715)
Total	3,690,843		(74,004)		70,404		(3,587)		3,761,247		(77,591)
Short-term investments	97,920		(2,063)		—		—		97,920		(2,063)
Total	$	3,788,763	$	(76,067)	$	70,404	$	(3,587)	$	3,859,167	$	(79,654)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements

The contractual maturities of the Company’s fixed maturities are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.

	March 31, 2021				December 31, 2020
Maturity	Estimated Fair Value		Amortized Cost		Estimated Fair Value		Amortized Cost
Due in one year or less	$	381,212	$	370,798	$	348,200	$	339,951
Due after one year through five years	11,124,344		10,918,279		10,629,959		10,340,819
Due after five years through 10 years	4,052,472		4,008,520		4,881,564		4,654,754
Due after 10 years	440,274		436,152		482,180		448,139
	15,998,302		15,733,749		16,341,903		15,783,663
Mortgage backed securities	571,071		575,495		630,001		626,368
Commercial mortgage backed securities	255,373		254,344		389,900		384,254
Asset backed securities	2,028,441		2,015,464		1,634,804		1,627,384
Total (1)	$	18,853,187	$	18,579,052	$	18,996,608	$	18,421,669

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Securities lending transactions accounted for as secured borrowings, by significant investment category

The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements is as follows:

	Remaining Contractual Maturity of the Agreements
	Overnight and Continuous		Less than 30 Days		30-90 Days		90 Days or More		Total
March 31, 2021
U.S. government and government agencies	$	16,397	$	—	$	102,743	$	—	$	119,140
Corporate bonds	13,724		—		—		—		13,724
Equity securities	11,022		—		—		—		11,022
Total	$	41,143	$	—	$	102,743	$	—	$	143,886
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	143,886
December 31, 2020
U.S. government and government agencies	$	142,317	$	—	$	139,290	$	—	$	281,607
Corporate bonds	3,021		—		—		—		3,021
Equity securities	16,461		—		—		—		16,461
Total	$	161,799	$	—	$	139,290	$	—	$	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9									$	—
Amounts related to securities lending not included in offsetting disclosure in note 9									$	301,089

Summary of assets and liabilities accounted for using the fair value option

The following table summarizes the Company’s other investments and other investable assets:

	March 31, 2021		December 31, 2020
Fixed maturities	$	900,304	$	843,354
Other investments	2,318,185		2,331,885
Short-term investments	623,930		557,008
Equity securities	92,935		92,549
Investments accounted for using the fair value option	$	3,935,354	$	3,824,796
Other investable assets (1)	500,000		500,000
Total other investments	$	4,435,354	$	4,324,796

(1) Participation interests in a receivable of a reverse repurchase agreement.

Summary of other investments

The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy:

	March 31, 2021		December 31, 2020
Term loan investments	$	1,187,752	$	1,231,731
Lending	606,207		572,636
Credit related funds	79,355		90,780
Energy	78,500		65,813
Investment grade fixed income	142,630		138,646
Infrastructure	152,352		165,516
Private equity	52,064		48,750
Real estate	19,325		18,013
Total	$	2,318,185	$	2,331,885

Summary of investments accounted for using equity method

The following table summarizes the Company’s investments accounted for using the equity method, by strategy:

	March 31, 2021		December 31, 2020
Credit related funds	$	818,344	$	740,060
Equities	357,641		343,058
Real estate	292,424		258,518
Lending	199,913		179,629
Private equity	288,657		235,289
Infrastructure	179,225		175,882
Energy	120,123		115,453
Total	$	2,256,327	$	2,047,889

Summary of investments in limited partnership interests where the Company has a variable interest

The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet line item:

	March 31, 2021		December 31, 2020
Investments accounted for using the equity method (1)	2,256,327		2,047,889
Investments accounted for using the fair value option (2)	196,087		184,720
Total	$	2,452,414	$	2,232,609

(1)    Aggregate unfunded commitments were $2.0 billion at March 31, 2021, compared to $1.8 billion at December 31, 2020.

(2)    Aggregate unfunded commitments were $36.1 million at March 31, 2021, compared to $35.6 million at December 31, 2020.

Components of net investment income

The components of net investment income were derived from the following sources:

	March 31,
	2021		2020
Three Months Ended
Fixed maturities	$	90,626	$	114,847
Term loans	14,728		23,170
Equity securities	5,650		6,007
Short-term investments	607		4,896
Other (1)	14,355		19,406
Gross investment income	125,966		168,326
Investment expenses	(27,110)		(23,173)
Net investment income	$	98,856	$	145,153

(1)    Includes income distributions from investment funds and other items.

Summary of net realized gains (losses), excluding other-than-temporary impairment provisions

Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows:

	March 31,
	2021		2020
Three Months Ended
Available for sale securities:
Gross gains on investment sales	$	65,002	$	178,200
Gross losses on investment sales	(62,998)		(31,968)
Change in fair value of assets and liabilities accounted for using the fair value option:
Fixed maturities	16,553		(127,666)
Other investments	46,855		(307,800)
Equity securities	2,065		(4,909)
Short-term investments	736		(8,681)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period	37,849		(539)
Net unrealized gains (losses) on equity securities still held at reporting date	19,708		(175,566)
Allowance for credit losses:
Investments related	(1,648)		(9,320)
Underwriting related	5,268		(3,270)
Net impairment losses	—		(533)
Derivative instruments (1)	36,116		127,189
Other	(23,045)		(2,097)
Net realized gains (losses)	$	142,461	$	(366,960)

(1)    See note 9 for information on the Company’s derivative instruments.

Rollforward of the allowance for expected credit losses of securities classified as available for sale

The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale:

	Structured Securities (1)		Municipal Bonds		Corporate Bonds		Total
March 31, 2021
Balance at beginning of period	$	1,490	$	11	$	896	$	2,397
Additions for current-period provision for expected credit losses	182		—		2,421		2,603
Additions (reductions) for previously recognized expected credit losses	(382)		(9)		(540)		(931)
Reductions due to disposals	(83)		—		(156)		(239)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,207	$	2	$	2,621	$	3,830
December 31, 2020
Balance at beginning of period	$	—	$	—	$	—	$	—
Cumulative effect of accounting change (2)	517		—		117		634
Additions for current-period provision for expected credit losses	2,942		67		7,644		10,653
Additions (reductions) for previously recognized expected credit losses	(1,398)		6		(5,638)		(7,030)
Reductions due to disposals	(571)		(62)		(1,227)		(1,860)
Write-offs charged against the allowance	—		—		—		—
Balance at end of period	$	1,490	$	11	$	896	$	2,397

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Summary of restricted assets

The following table details the value of the Company’s restricted assets:

	March 31, 2021		December 31, 2020
Assets used for collateral or guarantees:
Affiliated transactions	$	4,815,120	$	4,643,334
Third party agreements	3,366,016		3,083,324
Deposits with U.S. regulatory authorities	819,444		827,552
Deposits with non-U.S. regulatory authorities	330,197		179,099
Total restricted assets	$	9,330,777	$	8,733,309

Reconciliation of cash and restricted cash

The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets:

	March 31, 2021		December 31, 2020
Cash	$	941,951	$	906,448
Restricted cash (included in ‘other assets’)	$	425,563	$	384,096
Cash and restricted cash	$	1,367,514	$	1,290,544

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Fair Value (Tables)

3 Months Ended

Mar. 31, 2021

Fair Value Disclosures [Abstract]

Fair value hierarchy

The following table presents the Company’s financial assets and liabilities measured at fair value by level at March 31, 2021:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	8,072,883	$	—	$	8,072,870	$	13
Mortgage backed securities	571,071		—		571,071		—
Municipal bonds	457,329		—		457,329		—
Commercial mortgage backed securities	255,373		—		255,373		—
U.S. government and government agencies	5,042,208		4,949,217		92,991		—
Non-U.S. government securities	2,425,882		—		2,425,882		—
Asset backed securities	2,028,441		—		2,024,969		3,472
Total	18,853,187		4,949,217		13,900,485		3,485
Short-term investments	1,269,631		1,252,535		17,096		—
Equity securities, at fair value	1,543,703		1,476,504		24,087		43,112
Derivative instruments (4)	156,160		—		156,160		—
Residential mortgage loans	5,693		—		5,693		—
Fair value option:
Corporate bonds	724,316		—		723,327		989
Non-U.S. government bonds	23,996		—		23,996		—
Mortgage backed securities	2,828		—		2,828		—
Commercial mortgage backed securities	1,225		—		1,225		—
Asset backed securities	147,666		—		147,666		—
U.S. government and government agencies	273		164		109		—
Short-term investments	623,930		482,869		141,061		—
Equity securities	92,935		21,512		247		71,176
Other investments	1,078,505		31,268		979,307		67,930
Other investments measured at net asset value (2)	1,239,680
Total	3,935,354		535,813		2,019,766		140,095
Total assets measured at fair value	$	25,763,728	$	8,214,069	$	16,123,287	$	186,692
Liabilities measured at fair value:
Contingent consideration liabilities	$	(465)	$	—	$	—	$	(465)
Securities sold but not yet purchased (3)	(34,097)		—		(34,097)		—
Derivative instruments (4)	(98,103)		—		(98,103)		—
Total liabilities measured at fair value	$	(132,665)	$	—	$	(132,200)	$	(465)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020:

			Estimated Fair Value Measurements Using:
	Estimated Fair Value		Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Assets measured at fair value (1):
Available for sale securities:
Fixed maturities:
Corporate bonds	$	7,856,571	$	—	$	7,856,558	$	13
Mortgage backed securities	630,001		—		630,001		—
Municipal bonds	494,522		—		494,522		—
Commercial mortgage backed securities	389,900		—		389,900		—
U.S. government and government agencies	5,557,077		5,463,356		93,721		—
Non-U.S. government securities	2,433,733		—		2,433,733		—
Asset backed securities	1,634,804		—		1,631,378		3,426
Total	18,996,608		5,463,356		13,529,813		3,439
Short-term investments	1,924,922		1,920,565		4,357		—
Equity securities, at fair value	1,460,959		1,401,653		17,291		42,015
Derivative instruments (4)	177,383		—		177,383		—
Fair value option:
Corporate bonds	651,294		—		650,309		985
Non-U.S. government bonds	35,263		—		35,263		—
Mortgage backed securities	3,282		—		3,282		—
Commercial mortgage backed securities	1,090		—		1,090		—
Asset backed securities	152,151		—		152,151		—
U.S. government and government agencies	274		164		110		—
Short-term investments	557,008		420,131		136,877		—
Equity securities	92,549		23,373		188		68,988
Other investments	1,134,229		51,149		1,015,977		67,103
Other investments measured at net asset value (2)	1,197,656
Total	3,824,796		494,817		1,995,247		137,076
Total assets measured at fair value	$	26,384,668	$	9,280,391	$	15,724,091	$	182,530
Liabilities measured at fair value:
Contingent consideration liabilities	$	(461)	$	—	$	—	$	(461)
Securities sold but not yet purchased (3)	(21,679)		—		(21,679)		—
Derivative instruments (4)	(108,705)		—		(108,705)		—
Total liabilities measured at fair value	$	(130,845)	$	—	$	(130,384)	$	(461)

(1)    In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

(2)    In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

(3)    Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

(4)    See note 9.

Rollforward of Level 3 investments

The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs:

	Assets												Liabilities
s	Available For Sale				Fair Value Option						Fair Value
	Structured Securities (1)		Corporate Bonds		Corporate Bonds		Other Investments		Equity Securities		Equity Securities		Contingent Consideration Liabilities
Three Months Ended March 31, 2021
Balance at beginning of period	$	3,426	$	13	$	985	$	67,103	$	68,988	$	42,015	$	(461)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	(68)		—		4		248		2,188		904		—
Included in other comprehensive income	114		—		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		—		7,365		—		193		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(6,786)		—		—		—
Settlements	—		—		—		—		—		—		(4)
Transfers in and/or out of Level 3	—		—		—		—		—		—		—
Balance at end of period	$	3,472	$	13	$	989	$	67,930	$	71,176	$	43,112	$	(465)
Three Months Ended March 31, 2020
Balance at beginning of period	$	5,216	$	8,851	$	932	$	68,817	$	58,094	$	55,889	$	(7,998)
Total gains or (losses) (realized/unrealized)
Included in earnings (2)	9		7		—		(27)		1,921		(3,721)		(54)
Included in other comprehensive income	(22)		(5,416)		—		—		—		—		—
Purchases, issuances, sales and settlements
Purchases	—		—		33		21		—		3,464		—
Issuances	—		—		—		—		—		—		—
Sales	—		—		—		(17,175)		—		—		—
Settlements	(1,357)		(1,462)		—		—		—		—		85
Transfers in and/or out of Level 3	—		—		—		2,984		—		—		—
Balance at end of period	$	3,846	$	1,980	$	965	$	54,620	$	60,015	$	55,632	$	(7,967)

(1)    Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

(2)    Gains or losses were included in net realized gains (losses).

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Derivative Instruments (Tables)

3 Months Ended

Mar. 31, 2021

Derivative Instruments and Hedging Activities Disclosure [Abstract]

Fair value and notional amount of derivatives

The following table summarizes information on the fair values and notional values of the Company’s derivative instruments:

	Estimated Fair Value
	Asset Derivatives		Liability Derivatives		Notional Value (1)
March 31, 2021
Futures contracts (2)	$	85,379	$	(54,615)	$	7,116,745
Foreign currency forward contracts (2)	17,898		(29,887)		2,190,031
TBAs (3)	—		—		—
Other (2)	52,883		(13,601)		6,324,926
Total	$	156,160	$	(98,103)
December 31, 2020
Futures contracts (2)	$	11,046	$	(4,496)	$	3,099,796
Foreign currency forward contracts (2)	52,716		(6,202)		1,656,729
TBAs (3)	—		—		—
Other (2)	113,621		(98,007)		5,763,919
Total	$	177,383	$	(108,705)

(1)    Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

(2)    The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

(3)    The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

Summary of net realized gains (losses) recorded in the consolidated statements of income

Realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in ‘net realized gains (losses)’ in the consolidated statements of income, as summarized in the following table:

Derivatives not designated as	March 31,
hedging instruments:	2021		2020
Three Months Ended
Net realized gains (losses):
Futures contracts	$	47,438	$	95,944
Foreign currency forward contracts	(22,071)		(10,870)
TBAs	—		745
Other (1)	10,749		41,370
Total	$	36,116	$	127,189

(1)    Includes realized gains and losses on swaps, options and other derivatives contracts.

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Variable Interest Entities and Noncontrolling Interests (Tables)

3 Months Ended

Mar. 31, 2021

Noncontrolling Interest [Abstract]

Carrying value of assets and liabilities of variable interest entity

The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported:

	March 31,		December 31,
	2021		2020
Assets
Investments accounted for using the fair value option (1)	$	1,880,768	$	1,790,385
Fixed maturities available for sale, at fair value	627,387		655,249
Equity securities, at fair value	62,314		52,410
Cash	236,164		211,451
Accrued investment income	14,325		14,679
Premiums receivable	252,523		224,377
Reinsurance recoverable on unpaid and paid losses and LAE	291,485		286,590
Ceded unearned premiums	113,180		122,339
Deferred acquisition costs	62,224		53,705
Receivable for securities sold	68,076		37,423
Goodwill and intangible assets	7,650		7,650
Other assets	87,358		75,801
Total assets of consolidated VIE	$	3,703,454	$	3,532,059
Liabilities
Reserve for losses and loss adjustment expenses	$	1,568,243	$	1,519,583
Unearned premiums	426,975		407,714
Reinsurance balances payable	77,041		63,269
Revolving credit agreement borrowings	155,687		155,687
Senior notes	172,757		172,689
Payable for securities purchased	59,230		25,881
Other liabilities	214,103		193,494
Total liabilities of consolidated VIE	$	2,674,036	$	2,538,317
Redeemable noncontrolling interests	$	52,421	$	52,398

(1)    Includes in “other investments” on the Company’s balance sheet.

Activity in non-redeemable noncontrolling interests

The following table sets forth activity in the non-redeemable noncontrolling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	823,007	$	762,777
Additional paid in capital attributable to noncontrolling interests	21,730		(123)
Repurchases attributable to non-redeemable noncontrolling interests (1)	—		(2,867)
Amounts attributable to noncontrolling interests	36,697		(233,944)
Other comprehensive income (loss) attributable to noncontrolling interests	(4,570)		(33,058)
Balance, end of period	$	876,864	$	492,785

(1) During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

Activity in redeemable noncontrolling interests

The following table sets forth activity in the redeemable non-controlling interests:

	March 31,
	2021		2020
Three Months Ended
Balance, beginning of period	$	58,548	$	55,404
Accretion of preference share issuance costs	23		23
Other	(901)		(51)
Balance, end of period	$	57,670	$	55,376

Portion of income or loss attributable to third party investors

The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below:

	March 31,
	2021		2020
Three Months Ended
Amounts attributable to non-redeemable noncontrolling interests	$	(36,697)	$	233,944
Amounts attributable to redeemable noncontrolling interests	(855)		(1,153)
Net (income) loss attributable to noncontrolling interests	$	(37,552)	$	232,791

Total assets and maximum exposure to loss associated with VIEs

The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreement benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions.

			March 31, 2021								December 31, 2020
			Maximum Exposure to Loss								Maximum Exposure to Loss
Bellemeade Entities (Issue Date)	Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total		Total VIE Assets		On-Balance Sheet (Asset) Liability		Off-Balance Sheet		Total
Bellemeade 2017-1 Ltd. (Oct-17)	$	145,573	$	(306)	$	1,152	$	846	$	145,573	$	(245)	$	844	$	599
Bellemeade 2018-1 Ltd. (Apr-18)	250,095		(1,081)		2,885		1,804		250,095		(903)		2,245		1,342
Bellemeade 2018-2 Ltd. (Aug-18)	66,747		(32)		62		30		108,395		(138)		280		142
Bellemeade 2018-3 Ltd. (Oct-18)	302,563		(1,604)		4,277		2,673		302,563		(1,320)		3,262		1,942
Bellemeade 2019-1 Ltd. (Mar-19)	219,256		(1,117)		7,991		6,874		219,256		(1,361)		8,461		7,100
Bellemeade 2019-2 Ltd. (Apr-19)	398,316		(780)		6,577		5,797		398,316		(730)		5,201		4,471
Bellemeade 2019-3 Ltd. (Jul-19)	528,084		(898)		6,047		5,149		528,084		(861)		5,079		4,218
Bellemeade 2019-4 Ltd. (Oct-19)	468,737		(908)		8,034		7,126		468,737		(890)		6,676		5,786
Bellemeade 2020-1 Ltd. (Jun-20) (1)	132,881		(58)		294		236		275,068		(178)		1,012		834
Bellemeade 2020-2 Ltd. (Sep-20) (2)	368,797		(370)		6,077		5,707		423,420		(556)		6,839		6,283
Bellemeade 2020-3 Ltd. (Nov-20) (3)	418,158		(433)		9,527		9,094		418,158		(631)		9,605		8,974
Bellemeade 2020-4 Ltd. (Dec-20) (4)	321,393		(23)		5,969		5,946		321,393		(156)		6,816		6,660
Bellemeade 2021-1 Ltd. (Mar-21) (5)	579,717		—		4,767		4,767		—		—		—		—
Total	$	4,200,317	$	(7,610)	$	63,659	$	56,049	$	3,859,058	$	(7,969)	$	56,320	$	48,351

(1)  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(2)  An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(3)  An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(4)  An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

(5)  An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

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Other Comprehensive Income (Loss) (Tables)

3 Months Ended

Mar. 31, 2021

Comprehensive Income Note Disclosure [Abstract]

Details about amounts reclassified from AOCI

The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss):

		Amounts Reclassified from AOCI
	Consolidated Statement of Income	Three Months Ended
Details About	Line Item That Includes	March 31,
AOCI Components	Reclassification	2021		2020
Unrealized appreciation on available-for-sale investments
	Net realized gains (losses)	$	2,004	$	146,232
	Provision for credit losses	(1,647)		(9,320)
	Other-than-temporary impairment losses	—		(533)
	Total before tax	357		136,379
	Income tax (expense) benefit	(3,054)		(15,150)
	Net of tax	$	(2,697)	$	121,229

Schedule of comprehensive income (loss)

	Before Tax Amount		Tax Expense (Benefit)		Net of Tax Amount
Three Months Ended March 31, 2021
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(294,360)	$	(32,610)	$	(261,750)
Less reclassification of net realized gains (losses) included in net income	357		3,054		(2,697)
Foreign currency translation adjustments	(28,415)		169		(28,584)
Other comprehensive income (loss)	$	(323,132)	$	(35,495)	$	(287,637)
Three Months Ended March 31, 2020
Unrealized appreciation (decline) in value of investments:
Unrealized holding gains (losses) arising during period	$	(63,451)	$	(6,164)	$	(57,287)
Less reclassification of net realized gains (losses) included in net income	136,379		15,150		121,229
Foreign currency translation adjustments	(45,424)		(735)		(44,689)
Other comprehensive income (loss)	$	(245,254)	$	(22,049)	$	(223,205)

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Share Transactions - Share-based compensation (Details) - $ / shares	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grants during period, options (shares)	1,218,465	1,116,073
Weighted average grant date fair value, options (per share)	$ 9.20	$ 8.14
Performance shares and units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grants during period, other than options (shares)	685,104	557,204
Weighted average grant date fair value, other than options (per share)	$ 37.38	$ 44.17
Restricted shares and units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grants during period, other than options (shares)	1,168,577	910,879
Weighted average grant date fair value, other than options (per share)	$ 35.82	$ 42.36

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Share Transactions - Share repurchases (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Class of Stock [Line Items]
Treasury stock, shares acquired (shares)	5.3	2.6
Shares repurchased for treasury	$ 179.3	$ 75.5
Common shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program	394.5
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 4,230.0
Remaining authorized repurchase amount	$ 737.3

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Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Numerator:
Net income (loss)		$ 475,708	$ (88,674)
Amounts attributable to noncontrolling interests		(37,552)	232,791
Net income available to Arch		438,156	144,117
Preferred dividends		(10,403)	(10,403)
Net income (loss) available to Arch common shareholders		$ 427,753	$ 133,714
Denominator:
Weighted average common shares outstanding — basic		400,807,895	403,892,161
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,230,794	2,275,473
Stock options	[1]	6,184,564	7,865,936
Weighted average common shares and common share equivalents outstanding — diluted		409,223,253	414,033,570
Earnings per common share:
Basic (per share)		$ 1.07	$ 0.33
Diluted (per share)		$ 1.05	$ 0.32
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		2,400,082	1,155,088

[1] Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 first quarter and 2020 first quarter, the number of stock options excluded were 2,400,082 and 1,155,088, respectively.

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Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended
		Mar. 31, 2021 USD ($) segment	Mar. 31, 2020 USD ($)	Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,397,206	$ 2,832,830
Premiums ceded		(888,749)	(695,584)
Net premiums written		2,508,457	2,137,246
Change in unearned premiums		(560,035)	(392,802)
Net premiums earned		1,948,422	1,744,444
Other underwriting income (loss)		6,110	6,852
Losses and loss adjustment expenses		(1,203,100)	(1,115,419)
Acquisition expenses		(304,481)	(247,283)
Other operating expenses		(261,033)	(234,544)
Underwriting income (loss)		185,918	154,050
Net investment income		98,856	145,153
Net realized gains (losses)		142,461	(366,960)
Equity in net income (loss) of investment funds accounted for using the equity method		71,686	(4,209)
Other income (loss)		(1,741)	32
Corporate expenses		(23,468)	(18,201)
Transaction costs and other		(1,916)	(2,595)
Amortization of intangible assets		(14,402)	(16,631)
Interest expense		(38,346)	(32,555)
Net foreign exchange gains (losses)		20,063	72,671
Income (loss) before income taxes and income (loss) from operating affiliates		439,111	(69,245)
Income tax expense (benefit)		(38,860)	(27,945)
Income (loss) from operating affiliates		75,457	8,516
Net income (loss)		475,708	(88,674)
Amounts attributable to redeemable noncontrolling interests		(855)	(1,153)
Amounts attributable to non-redeemable noncontrolling interests		(36,697)	233,944
Net income (loss) available to Arch		438,156	144,117
Preferred dividends		(10,403)	(10,403)
Net income (loss) available to Arch common shareholders		$ 427,753	$ 133,714
Underwriting Ratios
Loss ratio		61.70%	63.90%
Acquisition expense ratio		15.60%	14.20%
Other operating expense ratio		13.40%	13.40%
Combined ratio		90.70%	91.50%
Goodwill and intangible assets		$ 679,509	$ 705,450	$ 692,863
Other
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 216,523	234,902
Premiums ceded		(37,212)	(48,202)
Net premiums written		179,311	186,700
Change in unearned premiums		(31,580)	(46,661)
Net premiums earned		147,731	140,039
Other underwriting income (loss)		411	133
Losses and loss adjustment expenses		(118,794)	(110,676)
Acquisition expenses		(28,152)	(21,804)
Other operating expenses		(14,275)	(13,702)
Underwriting income (loss)		(13,079)	(6,010)
Net investment income		20,127	32,125
Net realized gains (losses)		41,125	(294,851)
Equity in net income (loss) of investment funds accounted for using the equity method		0	0
Other income (loss)		0	0
Corporate expenses	[2]	0	0
Transaction costs and other	[2]	(715)	0
Amortization of intangible assets		0	0
Interest expense		(4,149)	(7,310)
Net foreign exchange gains (losses)		(1,442)	9,364
Income (loss) before income taxes and income (loss) from operating affiliates		41,867	(266,682)
Income tax expense (benefit)		(8)	0
Income (loss) from operating affiliates		0	0
Net income (loss)		41,859	(266,682)
Amounts attributable to redeemable noncontrolling interests		(972)	(1,096)
Amounts attributable to non-redeemable noncontrolling interests		(36,697)	233,944
Net income (loss) available to Arch		4,190	(33,834)
Preferred dividends		0	0
Net income (loss) available to Arch common shareholders		$ 4,190	$ (33,834)
Underwriting Ratios
Loss ratio		80.40%	79.00%
Acquisition expense ratio		19.10%	15.60%
Other operating expense ratio		9.70%	9.80%
Combined ratio		109.20%	104.40%
Goodwill and intangible assets		$ 7,650	$ 7,650
Underwriting segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 3,277,293	2,698,537
Premiums ceded		(948,147)	(747,991)
Net premiums written		2,329,146	1,950,546
Change in unearned premiums		(528,455)	(346,141)
Net premiums earned		1,800,691	1,604,405
Other underwriting income (loss)		5,699	6,719
Losses and loss adjustment expenses		(1,084,306)	(1,004,743)
Acquisition expenses		(276,329)	(225,479)
Other operating expenses		(246,758)	(220,842)
Underwriting income (loss)		198,997	160,060
Net investment income		78,729	113,028
Net realized gains (losses)		101,336	(72,109)
Equity in net income (loss) of investment funds accounted for using the equity method		71,686	(4,209)
Other income (loss)		(1,741)	32
Corporate expenses	[2]	(23,468)	(18,201)
Transaction costs and other	[2]	(1,201)	(2,595)
Amortization of intangible assets		(14,402)	(16,631)
Interest expense		(34,197)	(25,245)
Net foreign exchange gains (losses)		21,505	63,307
Income (loss) before income taxes and income (loss) from operating affiliates		397,244	197,437
Income tax expense (benefit)		(38,852)	(27,945)
Income (loss) from operating affiliates		75,457	8,516
Net income (loss)		433,849	178,008
Amounts attributable to redeemable noncontrolling interests		117	(57)
Amounts attributable to non-redeemable noncontrolling interests		0	0
Net income (loss) available to Arch		433,966	177,951
Preferred dividends		(10,403)	(10,403)
Net income (loss) available to Arch common shareholders		$ 423,563	$ 167,548
Underwriting Ratios
Loss ratio		60.20%	62.60%
Acquisition expense ratio		15.30%	14.10%
Other operating expense ratio		13.70%	13.80%
Combined ratio		89.20%	90.50%
Goodwill and intangible assets		$ 671,859	$ 697,800
Underwriting segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,415,886	1,207,645
Premiums ceded		(421,047)	(378,897)
Net premiums written		994,839	828,748
Change in unearned premiums		(175,365)	(112,829)
Net premiums earned		819,474	715,919
Other underwriting income (loss)		0	0
Losses and loss adjustment expenses		(535,747)	(507,108)
Acquisition expenses		(128,222)	(107,337)
Other operating expenses		(137,113)	(129,649)
Underwriting income (loss)		$ 18,392	$ (28,175)
Underwriting Ratios
Loss ratio		65.40%	70.80%
Acquisition expense ratio		15.60%	15.00%
Other operating expense ratio		16.70%	18.10%
Combined ratio		97.70%	103.90%
Goodwill and intangible assets		$ 276,211	$ 268,296
Underwriting segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,471,060	1,122,519
Premiums ceded		(471,948)	(325,339)
Net premiums written		999,112	797,180
Change in unearned premiums		(354,212)	(253,720)
Net premiums earned		644,900	543,460
Other underwriting income (loss)		(1,198)	2,120
Losses and loss adjustment expenses		(484,870)	(430,069)
Acquisition expenses		(118,025)	(79,606)
Other operating expenses		(60,514)	(45,297)
Underwriting income (loss)		$ (19,707)	$ (9,392)
Underwriting Ratios
Loss ratio		75.20%	79.10%
Acquisition expense ratio		18.30%	14.60%
Other operating expense ratio		9.40%	8.30%
Combined ratio		102.90%	102.00%
Goodwill and intangible assets		$ 17,807	$ 2,516
Underwriting segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	391,246	368,945
Premiums ceded		(56,051)	(44,327)
Net premiums written		335,195	324,618
Change in unearned premiums		1,122	20,408
Net premiums earned		336,317	345,026
Other underwriting income (loss)		6,897	4,599
Losses and loss adjustment expenses		(63,689)	(67,566)
Acquisition expenses		(30,082)	(38,536)
Other operating expenses		(49,131)	(45,896)
Underwriting income (loss)		$ 200,312	$ 197,627
Underwriting Ratios
Loss ratio		18.90%	19.60%
Acquisition expense ratio		8.90%	11.20%
Other operating expense ratio		14.60%	13.30%
Combined ratio		42.40%	44.10%
Goodwill and intangible assets		$ 377,841	$ 426,988

[1] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

[2] Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’

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Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of period		$ 16,513,929	$ 13,891,842
Unpaid losses and loss adjustment expenses recoverable		4,314,855	4,082,650
Net reserve for losses and loss adjustment expenses at beginning of period		12,199,074	9,809,192
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,244,772	1,134,442
Prior years		(41,672)	(19,023)
Total net incurred losses and loss adjustment expenses		1,203,100	1,115,419
Retroactive reinsurance transaction	[1]	(183,893)	60,635
Net foreign exchange (gains) losses		(46,877)	(142,573)
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(58,984)	(41,260)
Prior years		(585,118)	(561,947)
Total net paid losses and loss adjustment expenses		(644,102)	(603,207)
Net reserve for losses and loss adjustment expenses at end of period		12,527,302	10,239,466
Unpaid losses and loss adjustment expenses recoverable		3,916,650	4,070,114
Reserve for losses and loss adjustment expenses at end of period		$ 16,443,952	$ 14,309,580

[1] During 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). During the 2020 first quarter, the Company entered into a reinsurance to close agreement of the 2017 and prior years of account previously covered by a third party arrangement.

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Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 41,672	$ 19,023
Underwriting segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 4,100	$ 1,100
Percentage of prior year development	0.50%	0.20%
Underwriting segments | Insurance | Short tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 25,000	$ 3,900
Underwriting segments | Insurance | Short tailed lines | Property insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	14,600
Underwriting segments | Insurance | Short tailed lines | Travel and accident
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	2,500
Underwriting segments | Insurance | Short tailed lines | Lenders products
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	8,000
Underwriting segments | Insurance | Medium tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(20,900)	(7,900)
Underwriting segments | Insurance | Medium tailed lines | Programs
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(10,800)
Underwriting segments | Insurance | Medium tailed lines | Professional liability
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(6,000)	5,100
Underwriting segments | Insurance | Medium tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(13,200)
Underwriting segments | Insurance | Medium tailed lines | Surety Line of Business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(5,000)
Underwriting segments | Insurance | Long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		5,200
Underwriting segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 26,800	$ 11,600
Percentage of prior year development	4.20%	2.10%
Underwriting segments | Reinsurance | Short tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 17,500
Underwriting segments | Reinsurance | Short tailed lines | Property catastrophe and property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	23,300
Underwriting segments | Reinsurance | Short tailed lines | Property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(22,500)
Underwriting segments | Reinsurance | Short tailed lines | Other specialty lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	16,600
Underwriting segments | Reinsurance | Short tailed and medium tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ 21,500
Underwriting segments | Reinsurance | Short tailed and medium tailed lines | Property catastrophe and property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(4,300)
Underwriting segments | Reinsurance | Short tailed and medium tailed lines | Property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		10,500
Underwriting segments | Reinsurance | Short tailed and medium tailed lines | Other specialty lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		11,900
Underwriting segments | Reinsurance | Medium tailed and long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	9,300
Underwriting segments | Reinsurance | Long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(9,900)
Underwriting segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 10,900	$ 6,100
Percentage of prior year development	3.20%	1.80%
Underwriting segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ (100)	$ 200

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Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended	12 Months Ended
		Mar. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 2,064,586	$ 1,778,717
Balance at end of period		2,618,175	2,064,586
Allowance for Expected Credit Losses
Balance at beginning of period		37,781	21,003
Cumulative effect of accounting change (1)	[1]		6,539
Change for provision of expected credit losses (1)	[2]	(1,670)	10,239
Balance at end of period		36,111	37,781
Write-offs charged against the allowance		$ 100	$ 2,800
Accounting Standards Update		us-gaap:AccountingStandardsUpdate201613Member

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

[2] Amounts deemed uncollectible are written-off in operating expenses. For the March 31, 2021 and as of December 31, 2020, amounts written off were $0.1 million and $2.8 million, respectively.

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Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands		3 Months Ended	12 Months Ended
		Mar. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 4,500,802	$ 4,346,816
Balance at end of period		4,041,076	4,500,802
Allowance for Expected Credit Losses
Balance at beginning of period		11,636	1,364
Cumulative effect of accounting change	[1]		12,010
Change for provision of expected credit losses		(764)	(1,738)
Balance at end of period		$ 10,872	$ 11,636

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

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Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		3 Months Ended	12 Months Ended
		Mar. 31, 2021	Dec. 31, 2020
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE		$ 4,041,076	$ 4,500,802
Reinsurance recoverable | Credit concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage		64.50%	63.90%
Reinsurance recoverable | Credit concentration risk | Not Rated
Ceded Credit Risk [Line Items]
Concentration risk percentage	[1]	35.50%	36.10%
Reinsurance recoverable | Credit concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage		92.00%	94.00%
Stockholders' equity | Reinsurer concentration risk
Ceded Credit Risk [Line Items]
Concentration risk percentage		1.70%	1.80%

[1] At March 31, 2021 and December 31, 2020 over 92% and 94% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively

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Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands		3 Months Ended	12 Months Ended
		Mar. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 1,986,924	$ 2,119,460
Balance at end of period		1,919,655	1,986,924
Allowance for Expected Credit Losses
Balance at beginning of period		8,638	0
Cumulative effect of accounting change	[1]		6,663
Change for provision of expected credit losses		(2,785)	1,975
Balance at end of period		$ 5,853	$ 8,638

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

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Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021		Dec. 31, 2020	Dec. 31, 2019
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		$ 18,723,035		$ 18,717,825
Estimated Fair Value		1,269,631		1,924,922
Estimated Fair Value		20,122,818		20,921,530
Gross Unrealized Gains		435,320		657,620
Gross Unrealized Losses		(157,036)		(79,654)
Allowance for expected credit losses		(3,830)		(2,397)	$ 0
Amortized cost		18,447,720		18,143,305
Cost		1,269,312		1,924,292
Cost or Amortized Cost		$ 19,848,364		20,345,961
Accounting Standards Update		us-gaap:AccountingStandardsUpdate201613Member
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	[1]	$ 18,853,187		18,996,608
Gross Unrealized Gains	[1]	434,400		654,927
Gross Unrealized Losses	[1]	(156,435)		(77,591)
Allowance for expected credit losses		(3,830)	[1],[2]	(2,397)
Amortized cost	[1]	18,579,052		18,421,669
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		8,072,883		7,856,571
Gross Unrealized Gains	[1]	242,832		414,247
Gross Unrealized Losses	[1]	(83,961)		(34,388)
Allowance for expected credit losses		(2,569)	[1],[2]	(896)
Amortized cost	[1]	7,916,581		7,477,608
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		571,071		630,001
Gross Unrealized Gains	[1]	7,066		8,939
Gross Unrealized Losses	[1]	(11,165)		(5,028)
Allowance for expected credit losses		(325)	[1],[2]	(278)
Amortized cost	[1]	575,495		626,368
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		457,329		494,522
Gross Unrealized Gains	[1]	19,942		27,291
Gross Unrealized Losses	[1]	(4,814)		(3,835)
Allowance for expected credit losses		(2)	[1],[2]	(11)
Amortized cost	[1]	442,203		471,077
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		255,373		389,900
Gross Unrealized Gains	[1]	2,755		8,722
Gross Unrealized Losses	[1]	(1,721)		(2,954)
Allowance for expected credit losses		(5)	[1],[2]	(122)
Amortized cost	[1]	254,344		384,254
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		5,042,208		5,557,077
Gross Unrealized Gains	[1]	15,102		22,612
Gross Unrealized Losses	[1]	(30,545)		(12,611)
Allowance for expected credit losses		0	[1],[2]	0
Amortized cost	[1]	5,057,651		5,547,076
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,425,882		2,433,733
Gross Unrealized Gains	[1]	127,886		153,891
Gross Unrealized Losses	[1]	(19,267)		(8,060)
Allowance for expected credit losses		(51)	[1],[2]	0
Amortized cost	[1]	2,317,314		2,287,902
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		2,028,441		1,634,804
Gross Unrealized Gains	[1]	18,817		19,225
Gross Unrealized Losses	[1]	(4,962)		(10,715)
Allowance for expected credit losses		(878)	[1],[2]	(1,090)
Amortized cost	[1]	2,015,464		1,627,384
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value		1,269,631		1,924,922
Gross Unrealized Gains		920		2,693
Gross Unrealized Losses		(601)		(2,063)
Allowance for expected credit losses		0	[2]	0
Cost		$ 1,269,312		$ 1,924,292

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

[2] Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

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Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		$ 9,197,152	$ 3,788,763
Estimated Fair Value - 12 Months or More		220,962	70,404
Estimated Fair Value		9,418,114	3,859,167
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(150,472)	(76,067)
Gross Unrealized Losses - 12 Months or More		(6,564)	(3,587)
Gross Unrealized Losses		(157,036)	(79,654)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	9,101,573	3,690,843
Estimated Fair Value - 12 Months or More	[1]	220,962	70,404
Estimated Fair Value	[1]	9,322,535	3,761,247
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(149,871)	(74,004)
Gross Unrealized Losses - 12 Months or More	[1]	(6,564)	(3,587)
Gross Unrealized Losses	[1]	(156,435)	(77,591)
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	3,253,030	747,442
Estimated Fair Value - 12 Months or More	[1]	15,894	3,934
Estimated Fair Value	[1]	3,268,924	751,376
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(82,735)	(33,086)
Gross Unrealized Losses - 12 Months or More	[1]	(1,226)	(1,302)
Gross Unrealized Losses	[1]	(83,961)	(34,388)
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	383,760	284,619
Estimated Fair Value - 12 Months or More	[1]	20,648	3,637
Estimated Fair Value	[1]	404,408	288,256
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(10,271)	(4,788)
Gross Unrealized Losses - 12 Months or More	[1]	(894)	(240)
Gross Unrealized Losses	[1]	(11,165)	(5,028)
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	90,634	67,937
Estimated Fair Value - 12 Months or More	[1]	1,827	0
Estimated Fair Value	[1]	92,461	67,937
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(4,737)	(3,835)
Gross Unrealized Losses - 12 Months or More	[1]	(77)	0
Gross Unrealized Losses	[1]	(4,814)	(3,835)
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	39,863	126,624
Estimated Fair Value - 12 Months or More	[1]	23,421	2,655
Estimated Fair Value	[1]	63,284	129,279
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(759)	(2,916)
Gross Unrealized Losses - 12 Months or More	[1]	(962)	(38)
Gross Unrealized Losses	[1]	(1,721)	(2,954)
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	3,920,377	1,285,907
Estimated Fair Value - 12 Months or More	[1]	0	0
Estimated Fair Value	[1]	3,920,377	1,285,907
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(30,545)	(12,611)
Gross Unrealized Losses - 12 Months or More	[1]	0	0
Gross Unrealized Losses	[1]	(30,545)	(12,611)
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	911,609	543,844
Estimated Fair Value - 12 Months or More	[1]	16,841	2,441
Estimated Fair Value	[1]	928,450	546,285
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(18,433)	(7,658)
Gross Unrealized Losses - 12 Months or More	[1]	(834)	(402)
Gross Unrealized Losses	[1]	(19,267)	(8,060)
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	[1]	502,300	634,470
Estimated Fair Value - 12 Months or More	[1]	142,331	57,737
Estimated Fair Value	[1]	644,631	692,207
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	[1]	(2,391)	(9,110)
Gross Unrealized Losses - 12 Months or More	[1]	(2,571)	(1,605)
Gross Unrealized Losses	[1]	(4,962)	(10,715)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months		95,579	97,920
Estimated Fair Value - 12 Months or More		0	0
Estimated Fair Value		95,579	97,920
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months		(601)	(2,063)
Gross Unrealized Losses - 12 Months or More		0	0
Gross Unrealized Losses		$ (601)	$ (2,063)

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

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Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Estimated Fair Value
Estimated Fair Value		$ 18,723,035	$ 18,717,825
Amortized Cost
Amortized cost		18,447,720	18,143,305
Fixed maturities
Estimated Fair Value
Due in one year or less		381,212	348,200
Due after one year through five years		11,124,344	10,629,959
Due after five years through 10 years		4,052,472	4,881,564
Due after 10 years		440,274	482,180
Single maturity date		15,998,302	16,341,903
Estimated Fair Value	[1]	18,853,187	18,996,608
Amortized Cost
Due in one year or less		370,798	339,951
Due after one year through five years		10,918,279	10,340,819
Due after five years through 10 years		4,008,520	4,654,754
Due after 10 years		436,152	448,139
Single maturity date		15,733,749	15,783,663
Amortized cost	[1]	18,579,052	18,421,669
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date		571,071	630,001
Estimated Fair Value		571,071	630,001
Amortized Cost
Securities without single maturity date		575,495	626,368
Amortized cost	[1]	575,495	626,368
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date		255,373	389,900
Estimated Fair Value		255,373	389,900
Amortized Cost
Securities without single maturity date		254,344	384,254
Amortized cost	[1]	254,344	384,254
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date		2,028,441	1,634,804
Estimated Fair Value		2,028,441	1,634,804
Amortized Cost
Securities without single maturity date		2,015,464	1,627,384
Amortized cost	[1]	$ 2,015,464	$ 1,627,384

[1] In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

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Investment Information - Securities lending agreements (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Disclosure Investment Information [Abstract]
Fair value of cash collateral received on securities lending	$ 0	$ 0
Fair value of non-cash collateral received on securities lending	143,900	301,100
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	143,886	301,089
Gross amount of recognized liabilities for securities lending in offsetting disclosure in note 9	0	0
Amounts related to securities lending not included in offsetting disclosure in note 9	143,886	301,089
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	119,140	281,607
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	13,724	3,021
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	11,022	16,461
Overnight and continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	41,143	161,799
Overnight and continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	16,397	142,317
Overnight and continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	13,724	3,021
Overnight and continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	11,022	16,461
Less than 30 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	102,743	139,290
30 - 90 days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	102,743	139,290
30 - 90 days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30 - 90 days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 days or more | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	$ 0	$ 0

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Investment Information - Other investments (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		$ 3,935,354	$ 3,824,796
Other investable assets	[1]	500,000	500,000
Other investments (portion measured at fair value: $3,935,354 and $3,824,796)		4,435,354	4,324,796
Fair value option | Fixed maturities
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		900,304	843,354
Fair value option | Other investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		2,318,185	2,331,885
Fair value option | Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		1,187,752	1,231,731
Fair value option | Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		606,207	572,636
Fair value option | Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		79,355	90,780
Fair value option | Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		78,500	65,813
Fair value option | Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		142,630	138,646
Fair value option | Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		152,352	165,516
Fair value option | Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		52,064	48,750
Fair value option | Other investments | Real estate
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		19,325	18,013
Fair value option | Short-term investments
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		623,930	557,008
Fair value option | Equity securities
Schedule Of Other Investments [Line Items]
Other investments measured at fair value		$ 92,935	$ 92,549

[1] Participation interests in a receivable of a reverse repurchase agreement

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Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 2,256,327	$ 2,047,889
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	818,344	740,060
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	357,641	343,058
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	292,424	258,518
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	199,913	179,629
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	288,657	235,289
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	179,225	175,882
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 120,123	$ 115,453

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Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 2,452,414	$ 2,232,609
Aggregate unfunded commitments		2,300,000	2,100,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	2,256,327	2,047,889
Aggregate unfunded commitments		2,000,000	1,800,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	196,087	184,720
Aggregate unfunded commitments		$ 36,100	$ 35,600

[1] Aggregate unfunded commitments were $2.0 billion at March 31, 2021, compared to $1.8 billion at December 31, 2020.

[2] Aggregate unfunded commitments were $36.1 million at March 31, 2021, compared to $35.6 million at December 31, 2020.

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Investment Information - Net investment income (Details) - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Net investment income:
Gross investment income		$ 125,966	$ 168,326
Investment expenses		(27,110)	(23,173)
Net investment income		98,856	145,153
Fixed maturities
Net investment income:
Gross investment income		90,626	114,847
Term loans
Net investment income:
Gross investment income		14,728	23,170
Equity securities
Net investment income:
Gross investment income		5,650	6,007
Short-term investments
Net investment income:
Gross investment income		607	4,896
Other
Net investment income:
Gross investment income	[1]	$ 14,355	$ 19,406

[1] Includes income distributions from investment funds and other items.

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Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		3 Months Ended		12 Months Ended
		Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 65,002	$ 178,200
Available for sale securities, gross losses on investment sales		(62,998)	(31,968)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		37,849	(539)
Net unrealized gains (losses) on equity securities still held at reporting date		19,708	(175,566)
Allowance for credit losses:
Allowance for credit losses - investment related		(2,603)		$ (10,653)
Allowance for credit losses - underwriting related		5,268	(3,270)
Net impairment losses		0	(533)
Derivative instruments	[1]	36,116	127,189
Other		(23,045)	(2,097)
Net realized gains (losses)		142,461	(366,960)
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		16,553	(127,666)
Allowance for credit losses:
Allowance for credit losses - investment related		(1,648)	(9,320)
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		46,855	(307,800)
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		2,065	(4,909)
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ 736	$ (8,681)

[1] See note 9 for information on the Company’s derivative instruments.

XML

Investment Information - Investment in operating affiliates (Details) € / shares in Units, € in Thousands, $ in Thousands	3 Months Ended
	Mar. 31, 2021 USD ($)	Mar. 31, 2021 EUR (€)	Mar. 31, 2020 USD ($)	Mar. 31, 2021 € / shares	Dec. 31, 2020 USD ($)
Schedule of Equity Method Investments [Line Items]
Payments to Acquire Interest in Subsidiaries and Affiliates	$ 546,349		$ 0
Investment in operating affiliates	739,783				$ 129,291
Income (loss) from operating affiliates	$ 75,457		$ 8,516
Operating Affiliates
Schedule of Equity Method Investments [Line Items]
Time lag for reporting	three	three
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.50%
Consideration paid per share | € / shares				€ 9.95
Payments to Acquire Interest in Subsidiaries and Affiliates	$ 546,000	€ 453,000
Investment in operating affiliates	604,600
Income (loss) from operating affiliates	74,500
Purchase Of Affiliate, Deferred Gain	$ 36,000
Purchase Of Operating Affiliate, Deferred Gain, Period Of Recognition	5 years	5 years

XML

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		3 Months Ended		12 Months Ended
		Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020
Allowance for expected credit losses
Balance at beginning of period		$ 2,397	$ 0	$ 0
Cumulative effect of accounting change	[1]			634
Additions for current-period provision for expected credit losses		2,603		10,653
Additions (reductions) for previously recognized expected credit losses		(931)		(7,030)
Reductions due to disposals		(239)		(1,860)
Write-offs charged against the allowance		0		0
Balance at end of period		$ 3,830		2,397
Accounting Standards Update		us-gaap:AccountingStandardsUpdate201613Member
Fixed maturities
Allowance for expected credit losses
Balance at beginning of period		$ 2,397
Additions for current-period provision for expected credit losses		1,648	9,320
Balance at end of period		3,830		2,397
Fixed maturities | Structured securities
Allowance for expected credit losses
Balance at beginning of period	[2]	1,490	0	0
Cumulative effect of accounting change	[1],[2]			517
Additions for current-period provision for expected credit losses	[2]	182		2,942
Additions (reductions) for previously recognized expected credit losses	[2]	(382)		(1,398)
Reductions due to disposals	[2]	(83)		(571)
Write-offs charged against the allowance	[2]	0		0
Balance at end of period		1,207		1,490	[2]
Fixed maturities | Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		11	0	0
Cumulative effect of accounting change	[1]			0
Additions for current-period provision for expected credit losses		0		67
Additions (reductions) for previously recognized expected credit losses		(9)		6
Reductions due to disposals		0		(62)
Write-offs charged against the allowance		0		0
Balance at end of period		2		11
Fixed maturities | Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		896	$ 0	0
Cumulative effect of accounting change	[1]			117
Additions for current-period provision for expected credit losses		2,421		7,644
Additions (reductions) for previously recognized expected credit losses		(540)		(5,638)
Reductions due to disposals		(156)		(1,227)
Write-offs charged against the allowance		0		0
Balance at end of period		$ 2,621		$ 896

[1] Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

[2] Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

XML

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Restricted Assets [Line Items]
Restricted assets	$ 9,330,777	$ 8,733,309
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,815,120	4,643,334
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	3,366,016	3,083,324
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	819,444	827,552
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	330,197	179,099
Watford Holdings Ltd
Restricted Assets [Line Items]
Assets pledged as collateral	$ 1,000,000	$ 954,600

XML

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020	Mar. 31, 2020	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Cash	$ 941,951	$ 906,448
Restricted cash (included in ‘other assets’)	425,563	384,096
Cash and restricted cash	$ 1,367,514	$ 1,290,544	$ 1,070,437	$ 903,698

XML

Investment Information - Narrative (Details) $ in Thousands	3 Months Ended
	Mar. 31, 2021 USD ($) lots	Mar. 31, 2020 USD ($)	Dec. 31, 2020 USD ($) lots
Narrative items:
Investable assets	$ 29,100,000
Equity in net (loss) income of investment funds accounted for using the equity method	71,686	$ (4,209)
Equity securities, at fair value	$ 1,532,906		$ 1,444,830
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	4,610		2,320
Total number of positions (lots) | lots	11,360		11,180
Largest single loss	$ 1,100		$ 900
Minimum
Narrative items:
Time lag for reporting	one
Maximum
Narrative items:
Time lag for reporting	three
Underwriting segments
Narrative items:
Investable assets	$ 26,300,000
Equity in net (loss) income of investment funds accounted for using the equity method	71,686	(4,209)
Other
Narrative items:
Investable assets	2,700,000
Equity in net (loss) income of investment funds accounted for using the equity method	$ 0	$ 0

XML

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Quoted Prices in Active Markets for Identical Assets (Level 1)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		$ 8,214,069	$ 9,280,391
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	4,949,217	5,463,356
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	4,949,217	5,463,356
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,252,535	1,920,565
Quoted Prices in Active Markets for Identical Assets (Level 1) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,476,504	1,401,653
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		535,813	494,817
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		164	164
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		482,869	420,131
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		21,512	23,373
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		31,268	51,149
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		16,123,287	15,724,091
Liabilities measured at fair value		(132,200)	(130,384)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(34,097)	(21,679)
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(98,103)	(108,705)
Significant Other Observable Inputs (Level 2) | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,693
Significant Other Observable Inputs (Level 2) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	13,900,485	13,529,813
Significant Other Observable Inputs (Level 2) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	8,072,870	7,856,558
Significant Other Observable Inputs (Level 2) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	571,071	630,001
Significant Other Observable Inputs (Level 2) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	457,329	494,522
Significant Other Observable Inputs (Level 2) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	255,373	389,900
Significant Other Observable Inputs (Level 2) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	92,991	93,721
Significant Other Observable Inputs (Level 2) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	2,425,882	2,433,733
Significant Other Observable Inputs (Level 2) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	2,024,969	1,631,378
Significant Other Observable Inputs (Level 2) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		17,096	4,357
Significant Other Observable Inputs (Level 2) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		24,087	17,291
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		156,160	177,383
Significant Other Observable Inputs (Level 2) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,019,766	1,995,247
Significant Other Observable Inputs (Level 2) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		723,327	650,309
Significant Other Observable Inputs (Level 2) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,828	3,282
Significant Other Observable Inputs (Level 2) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,225	1,090
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		109	110
Significant Other Observable Inputs (Level 2) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		23,996	35,263
Significant Other Observable Inputs (Level 2) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		147,666	152,151
Significant Other Observable Inputs (Level 2) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		141,061	136,877
Significant Other Observable Inputs (Level 2) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		247	188
Significant Other Observable Inputs (Level 2) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		979,307	1,015,977
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		186,692	182,530
Liabilities measured at fair value		(465)	(461)
Significant Unobservable Inputs (Level 3) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(465)	(461)
Significant Unobservable Inputs (Level 3) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0
Significant Unobservable Inputs (Level 3) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	3,485	3,439
Significant Unobservable Inputs (Level 3) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	13	13
Significant Unobservable Inputs (Level 3) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	3,472	3,426
Significant Unobservable Inputs (Level 3) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		43,112	42,015
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		140,095	137,076
Significant Unobservable Inputs (Level 3) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		989	985
Significant Unobservable Inputs (Level 3) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		71,176	68,988
Significant Unobservable Inputs (Level 3) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		67,930	67,103
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		25,763,728	26,384,668
Liabilities measured at fair value		(132,665)	(130,845)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(465)	(461)
Estimated Fair Value | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(34,097)	(21,679)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(98,103)	(108,705)
Estimated Fair Value | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,693
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		18,853,187	18,996,608
Estimated Fair Value | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		8,072,883	7,856,571
Estimated Fair Value | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		571,071	630,001
Estimated Fair Value | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		457,329	494,522
Estimated Fair Value | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		255,373	389,900
Estimated Fair Value | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,042,208	5,557,077
Estimated Fair Value | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,425,882	2,433,733
Estimated Fair Value | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,028,441	1,634,804
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,269,631	1,924,922
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,543,703	1,460,959
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		156,160	177,383
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,935,354	3,824,796
Estimated Fair Value | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		724,316	651,294
Estimated Fair Value | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,828	3,282
Estimated Fair Value | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,225	1,090
Estimated Fair Value | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		273	274
Estimated Fair Value | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		23,996	35,263
Estimated Fair Value | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		147,666	152,151
Estimated Fair Value | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		623,930	557,008
Estimated Fair Value | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		92,935	92,549
Estimated Fair Value | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,078,505	1,134,229
Estimated Fair Value | Fair value option | Other investments measured at net asset value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	$ 1,239,680	$ 1,197,656

[1] Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.

[2] In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See note 7, “—Securities Lending Agreements.”

[3] In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

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Fair Value - Rollforward of Level 3 assets and liabilities (Details) - Recurring - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Contingent consideration liability
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (461)	$ (7,998)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	(54)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	0
Settlements		(4)	85
Transfers in and/or out of Level 3		0	0
Balance at end of period		(465)	(7,967)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[2]	3,426	5,216
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[2]	(68)	9
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[2]	114	(22)
Purchases, issuances, sales and settlements
Purchases	[2]	0	0
Issuances	[2]	0	0
Sales	[2]	0	0
Settlements	[2]	0	(1,357)
Transfers in and/or out of Level 3	[2]	0	0
Balance at end of period	[2]	3,472	3,846
Available for sale | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		13	8,851
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	7
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	(5,416)
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	0
Settlements		0	(1,462)
Transfers in and/or out of Level 3		0	0
Balance at end of period		13	1,980
Fair value option | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		985	932
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	4	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	33
Issuances		0	0
Sales		0	0
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of period		989	965
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		67,103	68,817
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	248	(27)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		7,365	21
Issuances		0	0
Sales		(6,786)	(17,175)
Settlements		0	0
Transfers in and/or out of Level 3		0	2,984
Balance at end of period		67,930	54,620
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		68,988	58,094
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	2,188	1,921
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	0
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of period		71,176	60,015
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		42,015	55,889
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	904	(3,721)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		193	3,464
Issuances		0	0
Sales		0	0
Settlements		0	0
Transfers in and/or out of Level 3		0	0
Balance at end of period		$ 43,112	$ 55,632

[1] Gains or losses were included in net realized gains (losses).

[2] Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

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Fair Value - Narrative (Details) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 25,900,000	$ 26,500,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 146,900	$ 150,100
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.60%	0.60%
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Senior notes	$ 2,861,417	$ 2,861,113
Estimated fair value of senior notes	$ 3,400,000	$ 3,700,000

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Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020
Derivative offsetting
Derivative assets subject to master netting agreements		$ 148,400	$ 138,800
Derivative liabilities subject to master netting agreements		98,100	93,000
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		156,160	177,383
Liability derivatives - fair value		(98,103)	(108,705)
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	7,116,745	3,099,796
Not designated as hedging instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	85,379	11,046
Not designated as hedging instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(54,615)	(4,496)
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	2,190,031	1,656,729
Not designated as hedging instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	17,898	52,716
Not designated as hedging instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(29,887)	(6,202)
Not designated as hedging instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[1],[3]	0	0
Not designated as hedging instrument | TBAs | Fixed maturities available for sale
Derivative [Line Items]
Asset derivatives - fair value	[3]	0	0
Liability derivatives - fair value	[3]	0	0
Not designated as hedging instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	6,324,926	5,763,919
Not designated as hedging instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	52,883	113,621
Not designated as hedging instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (13,601)	$ (98,007)

[1] Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.

[2] The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

[3] The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

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Derivative Instruments - Summary of net realized gains (losses) recorded in the consolidated statements of income (Details) - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	$ 36,116	$ 127,189
Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		36,116	127,189
Futures contracts | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		47,438	95,944
Foreign currency forward contracts | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(22,071)	(10,870)
TBAs | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		0	745
Other | Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[2]	$ 10,749	$ 41,370

[1] See note 9 for information on the Company’s derivative instruments.

[2] Includes realized gains and losses on swaps, options and other derivatives contracts

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Commitments and Contingencies (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Investment commitments	$ 2,300.0		$ 2,100.0
Interest paid on senior notes and other borrowings	$ 1.0	$ 6.6

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Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ / shares in Units, $ in Thousands	1 Months Ended	3 Months Ended
	Mar. 31, 2014	Mar. 31, 2021	Dec. 31, 2020	Mar. 31, 2020
Variable Interest Entity [Line Items]
Net cash provided by (used for) operating activities		$ 762,845		$ 610,454
Net cash provided by (used for) investing activities		(493,189)		(278,496)
Net cash (used for) provided by financing activities		$ (186,602)		(134,496)
Watford Holdings Ltd
Variable Interest Entity [Line Items]
Business acquisition, share price (per share)			$ 35.00
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Initial investment contribution amount	$ 100,000
Number of shares acquired	2,500,000
Ownership percentage	11.00%	10.30%
Senior notes, face amount		$ 35,000
Senior notes, stated percentage		6.50%
Net cash provided by (used for) operating activities		$ 7,000		24,600
Net cash provided by (used for) investing activities		21,400		(35,700)
Net cash (used for) provided by financing activities		$ (1,000)		$ 12,300
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Watford Merger Transaction
Variable Interest Entity [Line Items]
Percentage ownership after merger transaction			40.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Kelso And Company
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners			30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Warburg Pincus LLC
Variable Interest Entity [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners			30.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd | Non-cumulative preferred shares
Variable Interest Entity [Line Items]
Ownership percentage		6.60%

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Variable Interest Entities and Noncontrolling Interests - Carrying amount of assets and liabilities of variable interest entity (Details) - USD ($) $ in Thousands		Mar. 31, 2021	Dec. 31, 2020	Mar. 31, 2020	Dec. 31, 2019
Variable Interest Entity [Line Items]
Other investments measured at fair value		$ 3,935,354	$ 3,824,796
Fixed maturities available for sale, at fair value		18,723,035	18,717,825
Equity securities, at fair value		1,532,906	1,444,830
Cash		941,951	906,448
Accrued investment income		101,108	103,299
Premiums receivable		2,618,175	2,064,586		$ 1,778,717
Reinsurance recoverable on unpaid and paid losses and LAE		4,041,076	4,500,802		4,346,816
Ceded unearned premiums		1,406,489	1,234,075
Deferred acquisition costs		919,740	790,708
Receivable for securities sold		199,424	92,743
Goodwill and intangible assets		679,509	692,863	$ 705,450
Other assets		2,135,261	1,724,288
Total VIE Assets		44,204,267	43,282,297
Reserve for losses and loss adjustment expenses		16,443,952	16,513,929	14,309,580	13,891,842
Unearned premiums		5,549,127	4,838,965
Reinsurance balances payable		919,125	683,263
Revolving credit agreement borrowings		155,687	155,687
Senior notes		2,861,417	2,861,113
Payable for securities purchased		386,453	218,779
Other liabilities		1,565,861	1,510,888
Total liabilities		30,173,261	29,294,856
Redeemable noncontrolling interests		57,670	58,548
Watford Holdings Ltd
Variable Interest Entity [Line Items]
Redeemable noncontrolling interests		57,670	58,548	$ 55,376	$ 55,404
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Variable Interest Entity [Line Items]
Other investments measured at fair value	[1]	1,880,768	1,790,385
Fixed maturities available for sale, at fair value		627,387	655,249
Equity securities, at fair value		62,314	52,410
Cash		236,164	211,451
Accrued investment income		14,325	14,679
Premiums receivable		252,523	224,377
Reinsurance recoverable on unpaid and paid losses and LAE		291,485	286,590
Ceded unearned premiums		113,180	122,339
Deferred acquisition costs		62,224	53,705
Receivable for securities sold		68,076	37,423
Goodwill and intangible assets		7,650	7,650
Other assets		87,358	75,801
Total VIE Assets		3,703,454	3,532,059
Reserve for losses and loss adjustment expenses		1,568,243	1,519,583
Unearned premiums		426,975	407,714
Reinsurance balances payable		77,041	63,269
Revolving credit agreement borrowings		155,687	155,687
Senior notes		172,757	172,689
Payable for securities purchased		59,230	25,881
Other liabilities	[1]	214,103	193,494
Total liabilities		2,674,036	2,538,317
Redeemable noncontrolling interests		$ 52,421	$ 52,398

[1] Includes in “other investments” on the Company’s balance sheet.

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Variable Interest Entities and Noncontrolling Interests - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands		3 Months Ended
		Mar. 31, 2021	Mar. 31, 2020
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		$ 823,007
Amounts attributable to noncontrolling interests		36,697	$ (233,944)
Other comprehensive (income) loss attributable to noncontrolling interests		(4,570)	(33,058)
Non-redeemable noncontrolling interests, end of period		876,864	492,785
Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		823,007	762,777
Additional paid in capital attributable to noncontrolling interests		21,730	(123)
Repurchases attributable to non-redeemable noncontrolling interests	[1]	0	(2,867)
Amounts attributable to noncontrolling interests		36,697	(233,944)
Other comprehensive (income) loss attributable to noncontrolling interests		(4,570)	(33,058)
Non-redeemable noncontrolling interests, end of period		$ 876,864	$ 492,785
Noncontrolling shareholders | Common shares | Watford Holdings Ltd
Noncontrolling Interest [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners		90.00%

[1] During 2020, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.

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Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	$ 58,548
Redeemable noncontrolling interests, end of period	57,670
Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	58,548	$ 55,404
Accretion of preference share issuance costs	23	23
Other	(901)	(51)
Redeemable noncontrolling interests, end of period	$ 57,670	$ 55,376
Cumulative redeemable preference shares | Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Par value per share			$ 0.01
Liquidation preference per share			25.00
Issue price per share			$ 24.50

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Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ (36,697)	$ 233,944
Dividends attributable to redeemable noncontrolling interests	(855)	(1,153)
Net (income) loss attributable to noncontrolling interests	$ (37,552)	$ 232,791

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Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Mar. 31, 2021		Dec. 31, 2020
Variable Interest Entity [Line Items]
Total VIE Assets		$ 44,204,267		$ 43,282,297
Maximum Exposure to Loss, Total		2,452,414		2,232,609
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		4,200,317		3,859,058
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(7,610)		(7,969)
Maximum Exposure to Loss - Off-Balance Sheet		63,659		56,320
Maximum Exposure to Loss, Total		56,049		48,351
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		145,573		145,573
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(306)		(245)
Maximum Exposure to Loss - Off-Balance Sheet		1,152		844
Maximum Exposure to Loss, Total		846		599
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		250,095		250,095
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,081)		(903)
Maximum Exposure to Loss - Off-Balance Sheet		2,885		2,245
Maximum Exposure to Loss, Total		1,804		1,342
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
Variable Interest Entity [Line Items]
Total VIE Assets		66,747		108,395
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(32)		(138)
Maximum Exposure to Loss - Off-Balance Sheet		62		280
Maximum Exposure to Loss, Total		30		142
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		302,563		302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,604)		(1,320)
Maximum Exposure to Loss - Off-Balance Sheet		4,277		3,262
Maximum Exposure to Loss, Total		2,673		1,942
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets		219,256		219,256
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,117)		(1,361)
Maximum Exposure to Loss - Off-Balance Sheet		7,991		8,461
Maximum Exposure to Loss, Total		6,874		7,100
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets		398,316		398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(780)		(730)
Maximum Exposure to Loss - Off-Balance Sheet		6,577		5,201
Maximum Exposure to Loss, Total		5,797		4,471
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets		528,084		528,084
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(898)		(861)
Maximum Exposure to Loss - Off-Balance Sheet		6,047		5,079
Maximum Exposure to Loss, Total		5,149		4,218
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets		468,737		468,737
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(908)		(890)
Maximum Exposure to Loss - Off-Balance Sheet		8,034		6,676
Maximum Exposure to Loss, Total		7,126		5,786
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[1]	132,881		275,068
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[1]	(58)		(178)
Maximum Exposure to Loss - Off-Balance Sheet	[1]	294		1,012
Maximum Exposure to Loss, Total	[1]	236		834
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd. (Jun-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		79,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[2]	368,797		423,420
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[2]	(370)		(556)
Maximum Exposure to Loss - Off-Balance Sheet	[2]	6,077		6,839
Maximum Exposure to Loss, Total	[2]	5,707		6,283
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		26,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[3]	418,158		418,158
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[3]	(433)		(631)
Maximum Exposure to Loss - Off-Balance Sheet	[3]	9,527		9,605
Maximum Exposure to Loss, Total	[3]	9,094		8,974
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd. (Nov-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		34,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20)
Variable Interest Entity [Line Items]
Total VIE Assets	[4]	321,393		321,393
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability	[4]	(23)		(156)
Maximum Exposure to Loss - Off-Balance Sheet	[4]	5,969		6,816
Maximum Exposure to Loss, Total	[4]	5,946		6,660
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd. (Dec-20) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		16,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21)
Variable Interest Entity [Line Items]
Total VIE Assets		579,717	[5]	0
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		0	[5]	0
Maximum Exposure to Loss - Off-Balance Sheet		4,767	[5]	0
Maximum Exposure to Loss, Total		4,767	[5]	$ 0
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd. (Mar-21) | Funded by directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage, Amount		$ 64,000

[1]  An additional $79 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table

[2] An additional $26 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[3] An additional $34 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[4] An additional $16 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table.

[5] An additional $64 million capacity was provided directly to Arch MI U.S. by a separate panel of reinsurers and is not reflected in this table

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Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		12 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (2,603)		$ (10,653)
Other-than-temporary impairment losses	0	$ (533)
Income (loss) before income taxes and income (loss) from operating affiliates	439,111	(69,245)
Income tax expense	(38,860)	(27,945)
Net of tax	438,156	144,117
Reclassification out of accumulated other comprehensive income | Unrealized appreciation on available-for-sale investments
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Net realized gains (losses)	2,004	146,232
Provision for credit losses	(1,647)	(9,320)
Other-than-temporary impairment losses	0	(533)
Income (loss) before income taxes and income (loss) from operating affiliates	357	136,379
Income tax expense	(3,054)	(15,150)
Net of tax	$ (2,697)	$ 121,229

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Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (294,360)	$ (63,451)
Less reclassification of net realized gains included in net income, before tax	357	136,379
Foreign currency translation adjustments, before tax	(28,415)	(45,424)
Other comprehensive income (loss), before tax	(323,132)	(245,254)
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(32,610)	(6,164)
Less reclassification of net realized gains included in net income, tax	3,054	15,150
Foreign currency translation adjustments, tax	169	(735)
Other comprehensive income (loss), tax	(35,495)	(22,049)
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(261,750)	(57,287)
Less reclassification of net realized gains included in net income, net of tax	(2,697)	121,229
Foreign currency translation adjustments, net of tax	(28,584)	(44,689)
Net current period other comprehensive income (loss)	$ (287,637)	$ (223,205)

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Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	(7.60%)	46.00%
Net deferred tax asset	$ 48,100		$ 15,700
Income taxes paid	$ 7,100	$ 7,400

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Transactions With Related Parties (Details) - USD ($) $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020	Dec. 31, 2020	Dec. 31, 2019
Related Party Transaction [Line Items]
Purchases of other investments	$ 430,961	$ 228,471
Reinsurance recoverable on unpaid and paid losses and LAE	4,041,076		$ 4,500,802	$ 4,346,816
Premia Holdings Ltd. | Barbican Group Holdings Limited
Related Party Transaction [Line Items]
Reinsurance recoverable on unpaid and paid losses and LAE	0		199,800
Funds held liability	275,000		$ 149,600
Legacy business, amount of liabilities transferred	$ 380,000