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Fair Value Disclosures (Tables)

6 Months Ended

May 31, 2022

Schedule of Assets and Liabilities Measured on Recurring Basis at Fair Value

The following is a summary of our financial assets and liabilities that are accounted for at fair value on a recurring basis, excluding Investments at fair value based on net asset value ("NAV") of $1.31 billion and $1.03 billion at May 31, 2022 and November 30, 2021, respectively, by level within the fair value hierarchy (in thousands):


	May 31, 2022
	Level 1		Level 2		Level 3		Counterparty and Cash Collateral Netting (1)		Total
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	3,867,049	$	157,414	$	200,961	$	—	$	4,225,424
Corporate debt securities	—		3,231,505		20,813		—		3,252,318
Collateralized debt obligations and collateralized loan obligations	—		323,627		49,858		—		373,485
U.S. government and federal agency securities	2,549,972		32,268		—		—		2,582,240
Municipal securities	—		630,483		—		—		630,483
Sovereign obligations	1,061,291		1,001,175		—		—		2,062,466
Residential mortgage-backed securities	—		1,591,820		1,059		—		1,592,879
Commercial mortgage-backed securities	—		343,744		1,870		—		345,614
Other asset-backed securities	—		202,509		84,778		—		287,287
Loans and other receivables	—		2,824,872		137,752		—		2,962,624
Derivatives	9,495		3,100,255		26,919		(2,728,569)		408,100
Investments at fair value	—		4,311		163,844		—		168,155
FXCM term loan	—		—		51,880		—		51,880

Total financial instruments owned, at fair value, excluding investments at fair value based on NAV	$	7,487,807	$	13,443,983	$	739,734	$	(2,728,569)	$	18,942,955

Loans to and investments in associated companies	$	—	$	1,795	$	14,795	$	—	$	16,590
Securities received as collateral, at fair value	$	1,322	$	—	$	—	$	—	$	1,322









Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	$	1,801,924	$	32,488	$	3,749	$	—	$	1,838,161
Corporate debt securities	—		2,308,815		401		—		2,309,216
U.S. government and federal agency securities	3,471,943		—		—		—		3,471,943

Sovereign obligations	1,371,769		902,107		—		—		2,273,876
Residential mortgage-backed securities	—		1,010		—		—		1,010
Commercial mortgage-backed securities	—		—		385		—		385
Loans	—		2,465,974		18,283		—		2,484,257
Derivatives	2,172		4,066,790		101,916		(2,884,689)		1,286,189
Total financial instruments sold, not yet purchased, at fair value	$	6,647,808	$	9,777,184	$	124,734	$	(2,884,689)	$	13,665,037


Other secured financings	$	—	$	—	$	2,362	$	—	$	2,362
Long-term debt	$	—	$	877,667	$	739,353	$	—	$	1,617,020
Obligation to return securities received as collateral, at fair value	$	1,322	$	—	$	—	$	—	$	1,322


	November 30, 2021
	Level 1		Level 2		Level 3		Counterparty and Cash Collateral Netting (1)		Total
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	2,737,255	$	257,318	$	87,647	$	—	$	3,082,220
Corporate debt securities	—		3,836,341		11,803		—		3,848,144
Collateralized debt obligations and collateralized loan obligations	—		579,518		31,946		—		611,464
U.S. government and federal agency securities	3,045,295		68,784		—		—		3,114,079
Municipal securities	—		509,559		—		—		509,559
Sovereign obligations	899,086		654,199		—		—		1,553,285
Residential mortgage-backed securities	—		1,168,246		1,477		—		1,169,723
Commercial mortgage-backed securities	—		196,419		2,333		—		198,752
Other asset-backed securities	—		337,022		93,524		—		430,546
Loans and other receivables	—		3,363,050		135,239		—		3,498,289
Derivatives	4,429		3,861,551		10,248		(3,305,756)		570,472
Investments at fair value	—		11,369		154,373		—		165,742
FXCM term loan	—		—		50,455		—		50,455
Total financial instruments owned, at fair value, excluding investments at fair value based on NAV	$	6,686,065	$	14,843,376	$	579,045	$	(3,305,756)	$	18,802,730


Loans to and investments in associated companies	$	—	$	—	$	30,842	$	—	$	30,842
Securities received as collateral, at fair value	$	7,289	$	—	$	—	$	—	$	7,289

Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	$	1,671,696	$	19,654	$	4,635	$	—	$	1,695,985
Corporate debt securities	—		2,111,777		482		—		2,112,259
U.S. government and federal agency securities	2,457,420		—		—		—		2,457,420
Sovereign obligations	935,801		593,040		—		—		1,528,841
Residential mortgage-backed securities	—		719		—		—		719
Commercial mortgage-backed securities	—		—		210		—		210
Loans	—		2,476,087		15,770		—		2,491,857
Derivatives	1,815		5,034,544		78,017		(3,702,200)		1,412,176
Total financial instruments sold, not yet purchased, at fair value	$	5,066,732	$	10,235,821	$	99,114	$	(3,702,200)	$	11,699,467


Other secured financings	$	—	$	76,883	$	25,905	$	—	$	102,788
Long-term debt	$	—	$	961,866	$	881,732	$	—	$	1,843,598
Obligation to return securities received as collateral, at fair value	$	7,289	$	—	$	—	$	—	$	7,289

(1)Represents counterparty and cash collateral netting across the levels of the fair value hierarchy for positions with the same counterparty.

Investments Measured at Fair Value Based on Net Asset Value

The following tables present information about our investments in entities that have the characteristics of an investment company (in thousands):


	Fair Value (1)		Unfunded Commitments
May 31, 2022
Equity Long/Short Hedge Funds (2)	$	482,004	$	—
Equity Funds (3)	57,760		41,191
Commodity Fund (4)	25,461		—
Multi-asset Funds (5)	418,397		—
Other Funds (6)	321,378		15,963
Total	$	1,305,000	$	57,154

November 30, 2021
Equity Long/Short Hedge Funds (2)	$	466,231	$	—
Equity Funds (3)	46,030		17,815
Commodity Fund (4)	24,401		—
Multi-asset Funds (5)	390,224		—
Other Funds (6)	99,054		36,090
Total	$	1,025,940	$	53,905

(1)Where fair value is calculated based on NAV, fair value has been derived from each of the funds' capital statements.

(2)This category includes investments in hedge funds that invest, long and short, primarily in both public and private equity securities in domestic and international markets. At May 31, 2022 and November 30, 2021, approximately 63% and 74%, respectively, of the fair value of investments are redeemable quarterly with 90 days prior written notice on December 31, 2021. At May 31, 2022 and November 30, 2021, approximately 32% and 21%, respectively, of the fair value of investments in this category cannot be redeemed because these investments include restrictions that do not allow for redemption before November 30, 2023. The remaining investments are redeemable quarterly with 60 days prior written notice.

(3)The investments in this category include investments in equity funds that invest in the equity of various U.S. and foreign private companies in a broad range of industries. These investments cannot be redeemed; instead distributions are received through the liquidation of the underlying assets of the funds, which are primarily expected to be liquidated in approximately one to thirteen years.

(4)This category includes investments in a hedge fund that invests, long and short, primarily in commodities. These investments are redeemable quarterly with 60 days prior written notice.

(5)This category includes investments in hedge funds that invest, long and short, primarily in multi-asset securities in domestic and international markets in both the public and private sectors. At May 31, 2022 and November 30, 2021, investments representing approximately 77% and 78%, respectively, of the fair value of investments are redeemable monthly with 60 days prior written notice. At May 31, 2022 and November 30, 2021, approximately 16% and 22%, respectively, of the fair value of investments in this category are redeemable quarterly with 90 days prior written notice. At May 31, 2022, the remaining investments cannot be redeemed because these investments include restrictions that do not allow for redemption before April 1, 2024.

(6)This category includes investments in a fund that invests in short-term trade receivables and payables that are expected to generally be outstanding between 90 to 120 days and short-term credit instruments. This category also includes investments in a fund that invests in distressed and special situations long and short credit strategies across sectors and asset types. Investments in this category are redeemable quarterly with 90 days prior written notice.

Summary of Changes in Fair Value of Financial Assets and Liabilities Classified as Level 3

The following is a summary of changes in fair value of our financial assets and liabilities that have been categorized within Level 3 of the fair value hierarchy for the three months ended May 31, 2022 (in thousands):


	Balance, February 28, 2022		Total gains/ losses (realized and unrealized) (1)		Purchases		Sales		Settlements		Issuances		Net transfers into (out of) Level 3		Balance, May 31, 2022		Changes in unrealized gains/losses included in earnings relating to instruments still held at May 31, 2022 (1)
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	113,922	$	35,581	$	67,540	$	(13,415)	$	—	$	—	$	(2,667)	$	200,961	$	35,361
Corporate debt securities	42,358		3,550		38,141		(47,025)		(12,604)		—		(3,607)		20,813		(849)
CDOs and CLOs	45,219		877		13,264		(28,037)		(1,466)		—		20,001		49,858		(1,798)

Sovereign obligations	23		—		—		—		—		—		(23)		—		—
Residential mortgage-backed securities	1,186		(47)		—		—		(80)		—		—		1,059		(17)
Commercial mortgage-backed securities	3,732		(439)		—		—		—		—		(1,423)		1,870		—
Other asset-backed securities	62,382		(781)		21,501		(1,688)		(12,296)		—		15,660		84,778		(1,065)
Loans and other receivables	137,942		(3,764)		15,598		(23,603)		(108)		—		11,687		137,752		(4,764)
Investments at fair value	169,508		1,576		37		—		(7,277)		—		—		163,844		1,576
FXCM term loan	50,335		1,545		—		—		—		—		—		51,880		1,545
Loans to and investments in associated companies	22,480		(7,685)		—		—		—		—		—		14,795		—


Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	5,666		(234)		(1,533)		—		—		—		(150)		$	3,749	(350)
Corporate debt securities	7,308		(3,588)		(16,091)		14,584		—		—		(1,812)		401		5
Sovereign obligations	1,159		—		—		—		—		—		(1,159)		—		—
Commercial mortgage-backed securities	315		—		—		70		—		—		—		385		—
Loans	11,541		10		(1,911)		1,089		—		—		7,554		18,283		119
Net derivatives (2)	47,770		(9,100)		(1,559)		—		(8,262)		—		46,148		74,997		9,903
Other secured financings	32,377		—		—		—		(30,015)		—		—		2,362		—
Long-term debt (1)	794,460		(146,261)		—		—		(4,950)		76,443		19,661		739,353		114,362

(1)Realized and unrealized gains/losses are primarily reported in Principal transactions revenues in the Consolidated Statements of Operations. Changes in instrument-specific credit risk related to structured notes within Long-term debt are included in the Consolidated Statements of Comprehensive Income (Loss), net of tax. Changes in unrealized gains/losses included in other comprehensive income (loss) for instruments still held at May 31, 2022 were gains of $31.9 million during the three months ended May 31, 2022.

(2)Net derivatives represent Financial instruments owned, at fair value - Derivatives and Financial instruments sold, not yet purchased, at fair value - Derivatives.


	Balance, February 28, 2021		Total gains/ losses (realized and unrealized) (1)		Purchases		Sales		Settlements		Issuances		Net transfers into (out of) Level 3		Balance, May 31, 2021		Changes in unrealized gains/losses included in earnings relating to instruments still held at May 31, 2021 (1)
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	102,065	$	7,997	$	448	$	(24,561)	$	—	$	—	$	502	$	86,451	$	(4,971)
Corporate debt securities	6,811		1,292		4,116		(5,870)		(132)		—		1,768		7,985		963
CDOs and CLOs	33,199		7,478		4,287		(37,324)		(1,203)		—		20,124		26,561		2,888


Residential mortgage-backed securities	21,692		205		—		—		(612)		—		(15,252)		6,033		(36)
Commercial mortgage-backed securities	2,671		201		—		—		(1,696)		—		—		1,176		(824)
Other asset-backed securities	60,594		3,575		12,835		(1,099)		(14,408)		—		9,058		70,555		819
Loans and other receivables	149,084		2,814		26,948		(8,070)		(156)		—		19,792		190,412		706
Investments at fair value	219,541		26,775		6,634		(17,085)		(5,031)		—		—		230,834		11,318
FXCM term loan	62,132		(2,977)		—		—		—		—		—		59,155		(2,977)
Loans to and investments in associated companies	39,397		(2,110)		—		—		—		—		—		37,287		(2,110)


Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	$	4,443	$	42	$	(23)	$	—	$	—	$	—	$	—	$	4,462	$	(40)
Corporate debt securities	1,571		(22)		(665)		27		—		—		16		927		(38)

Commercial mortgage-backed securities	35		—		(35)		35		—		—		—		35		—
Loans	14,916		(7)		(637)		6,330		44		—		(257)		20,389		(167)
Net derivatives (2)	305,506		(8,965)		(36)		33,715		593		—		(103,755)		227,058		8,372
Other secured financings	2,168		—		—		—		—		325		—		2,493		—
Long-term debt (1)	723,115		15,986		—		—		—		28,565		27,432		795,098		3,057

(1)Realized and unrealized gains/losses are primarily reported in Principal transactions revenues in the Consolidated Statements of Operations. Changes in instrument specific credit risk related to structured notes within long-term debt are included in the Consolidated Statements of Comprehensive Income (Loss), net of tax. Changes in unrealized gains/losses included in other comprehensive income (loss) for instruments still held at May 31, 2021 were losses of $19.0 million during the three months ended May 31, 2021.

(2)Net derivatives represent Financial instruments owned, at fair value - Derivatives and Financial instruments sold, not yet purchased, at fair value - Derivatives.

The following is a summary of changes in fair value of our financial assets and liabilities that have been categorized within Level 3 of the fair value hierarchy for the six months ended May 31, 2022 (in thousands):


	Balance, November 30, 2021		Total gains/ losses (realized and unrealized) (1)		Purchases		Sales		Settlements		Issuances		Net transfers into (out of) Level 3		Balance, May 31, 2022		Changes in unrealized gains/losses included in earnings relating to instruments still held at May 31, 2022 (1)
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	87,647	$	36,463	$	69,837	$	(13,839)	$	—	$	—	$	20,853	$	200,961	$	36,204
Corporate debt securities	11,803		5,631		9,465		(18,345)		(9)		—		12,268		20,813		2,381
CDOs and CLOs	31,946		254		31,245		(37,305)		(5,033)		—		28,751		49,858		(1,304)


Residential mortgage-backed securities	1,477		(111)		—		(204)		(103)		—		—		1,059		(57)
Commercial mortgage-backed securities	2,333		(463)		—		—		—		—		—		1,870		(29)
Other asset-backed securities	93,524		835		37,795		(17,238)		(22,812)		—		(7,326)		84,778		1,324
Loans and other receivables	135,239		(9,814)		29,962		(25,983)		(229)		—		8,577		137,752		(9,726)
Investments at fair value	154,373		33,310		14,286		—		(14,718)		—		(23,407)		163,844		33,380
FXCM term loan	50,455		1,425		—		—		—		—		—		51,880		1,425
Loans to and investments in associated companies	30,842		(16,047)		—		—		—		—		—		14,795		—


Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	$	4,635	$	(3,592)	$	(2,344)	$	5,050	$	—	$	—	$	—	$	3,749	$	3,009
Corporate debt securities	482		(11)		(70)		—		—		—		—		401		5

Commercial mortgage-backed securities	210		—		—		175		—		—		—		385		—
Loans	15,770		(15)		(12,315)		10,194		(87)		—		4,736		18,283		104
Net derivatives (2)	67,769		(88,018)		(1,559)		—		—		21,024		75,781		74,997		86,050
Other secured financings	25,905		—		—		—		(23,543)		—		—		2,362		—
Long-term debt (1)	881,732		(240,698)		—		—		—		100,195		(1,876)		739,353		175,615

(1)Realized and unrealized gains/losses are primarily reported in Principal transactions revenues in the Consolidated Statements of Operations. Changes in instrument-specific credit risk related to structured notes within Long-term debt are included in the Consolidated Statements of Comprehensive Income (Loss), net of tax. Changes in unrealized gains/losses included in other comprehensive income (loss) for instruments still held at May 31, 2022 were gains of $65.1 million during the six months ended May 31, 2022.

(2)Net derivatives represent Financial instruments owned, at fair value - Derivatives and Financial instruments sold, not yet purchased, at fair value - Derivatives.


	Balance, November 30, 2020		Total gains/ losses (realized and unrealized) (1)		Purchases		Sales		Settlements		Issuances		Net transfers into (out of) Level 3		Balance, May 31, 2021		Changes in unrealized gains/ losses included in earnings relating to instruments still held at May 31, 2021 (1)
Assets:
Financial instruments owned, at fair value:
Corporate equity securities	$	75,904	$	11,299	$	8,288	$	(37,297)	$	—	$	—	$	28,257	$	86,451	$	(3,683)
Corporate debt securities	23,146		2,466		4,370		(5,960)		(132)		—		(15,905)		7,985		1,492
CDOs and CLOs	17,972		10,616		16,510		(35,251)		(1,427)		—		18,141		26,561		6,808


Residential mortgage-backed securities	21,826		33		799		(784)		(1,126)		—		(14,715)		6,033		88
Commercial mortgage-backed securities	2,003		158		1,119		(393)		(1,696)		—		(15)		1,176		(740)
Other asset-backed securities	79,995		6,373		34,476		(27,647)		(26,465)		—		3,823		70,555		1,158
Loans and other receivables	134,636		17,580		37,431		(50,556)		(273)		—		51,594		190,412		14,146
Investments at fair value	213,946		103,032		11,489		(47,244)		(8,573)		—		(41,816)		230,834		80,099
FXCM term loan	59,455		(300)		—		—		—		—		—		59,155		(300)
Loans to and investments in associated companies	40,185		(2,898)		—		—		—		—		—		37,287		(2,898)


Liabilities:
Financial instruments sold, not yet purchased, at fair value:
Corporate equity securities	$	4,434	$	64	$	(23)	$	—	$	—	$	—	$	(13)	$	4,462	$	(62)
Corporate debt securities	141		1,349		(563)		—		—		—		—		927		(414)

Commercial mortgage-backed securities	35		—		(35)		35		—		—		—		35		—
Loans	16,635		1,441		(6,872)		8,817		—		—		368		20,389		(884)
Net derivatives (2)	26,017		16,813		(82)		66,304		506		—		117,500		227,058		(17,358)
Other secured financings	1,543		—		—		—		—		950		—		2,493		—
Long-term debt (1)	676,028		41,064		—		—		—		50,295		27,711		795,098		20,565

(1)Realized and unrealized gains/losses are primarily reported in Principal transactions revenues in the Consolidated Statements of Operations. Changes in instrument-specific credit risk related to structured notes within long-term debt are included in the Consolidated Statements of Comprehensive Income (Loss), net of tax. Changes in unrealized gains (losses) included in other comprehensive income (loss) for instruments still held at May 31, 2021 were losses of $61.6 million during the six months ended May 31, 2021.

(2)Net derivatives represent Financial instruments owned, at fair value - Derivatives and Financial instruments sold, not yet purchased, at fair value - Derivatives.

Quantitative Information About Significant Unobservable Inputs Used in Level 3 Fair Value Measurements

The tables below present information on the valuation techniques, significant unobservable inputs and their ranges for our financial assets and liabilities, subject to threshold levels related to the market value of the positions held, measured at fair value on a recurring basis with a significant Level 3 balance. The range of unobservable inputs could differ significantly across different firms given the range of products across different firms in the financial services sector. The inputs are not representative of the inputs that could have been used in the valuation of any one financial instrument (i.e., the input used for valuing one financial instrument within a particular class of financial instruments may not be appropriate for valuing other financial instruments within that given class). Additionally, the ranges of inputs presented below should not be construed to represent uncertainty regarding the fair values of our financial instruments; rather, the range of inputs is reflective of the differences in the underlying characteristics of the financial instruments in each category.

For certain categories, we have provided a weighted average of the inputs allocated based on the fair values of the financial instruments comprising the category. We do not believe that the range or weighted average of the inputs is indicative of the reasonableness of uncertainty of our Level 3 fair values. The range and weighted average are driven by the individual financial instruments within each category and their relative distribution in the population. The disclosed inputs when compared with the inputs as disclosed in other periods should not be expected to necessarily be indicative of changes in our estimates of unobservable inputs for a particular financial instrument as the population of financial instruments comprising the category will vary from period to period based on purchases and sales of financial instruments during the period as well as transfers into and out of Level 3 each period.


May 31, 2022
	Fair Value (in thousands)		Valuation Technique	Significant Unobservable Input(s)	Input/Range				Weighted Average
Financial instruments owned, at fair value
Corporate equity securities	$	200,961
Non-exchange-traded securities			Market approach	Price	$1		to	$366	$80
			Volatility benchmarking	Volatility	50	%	to	70%	60	%

Corporate debt securities	$	20,813	Market approach	Price	$23				—
				EBITDA multiple	3.3				—
			Scenario analysis	Estimated recovery percentage	6%				—

CDOs and CLOs	$	49,858	Discounted cash flows	Constant prepayment rate	20%				—
				Constant default rate	2%				—
				Loss severity	70%				—
				Discount rate/yield	10	%	to	22%	19	%
			Market approach	Price	$69		to	$102	$92


Commercial mortgage- backed securities	$	1,870	Scenario analysis	Estimated recovery percentage	81%				—






Other asset-backed securities	$	66,623	Discounted cash flows	Constant default rate	2%				—
				Loss severity	88%				—
				Discount rate/yield	5	%	to	17%	12	%
				Cumulative loss rate	5	%	to	21%	17	%
				Duration (years)	0.8 years		to	1.6 years	1.3 years
			Market approach	Price	$37				—

Loans and other receivables	$	137,752	Market approach	Price	$7		to	$136	$108
			Scenario analysis	Estimated recovery percentage	5	%	to	94%	35	%

Derivatives	$	18,755
Equity Options			Volatility benchmarking	Volatility	53%				—
Interest rate swaps			Market approach	Basis points upfront	2.8		to	11.1	6.7

Investments at fair value	$	158,312
Private equity securities			Market approach	Price	$1		to	$15,852	$548
				EBITDA multiple	15.7				—
			Discounted cash flows	Discount rate/yield	10	%	to	14%	12	%
			Scenario analysis	Discount rate/yield	12%				—

Investment in FXCM	$	51,880
Term loan			Discounted cash flows	Term based on the pay off (years)	0 months		to	1.7 years	1.7 years

Loans to and investments in associated companies
Non-exchange-traded warrants	$	14,795	Market approach	Underlying stock price	$723				—
				Underlying stock price	€11		to	€14	€13
				Volatility	25	%	to	49%	30	%



Financial instruments sold, not yet purchased, at fair value
Corporate equity securities	$	3,749
Non-exchange-traded securities			Market approach	Price	$1				—

Loans	$	18,283	Market approach	Price	$91				—
			Scenario analysis	Estimated recovery percentage	5%				—

Derivatives	$	97,612
Equity options			Volatility benchmarking	Volatility	29	%	to	63%	49	%
Interest rate swaps			Market approach	Basis points upfront	2.8		to	11.1	6.7
Total return swaps				Price	$99				—

Other secured financings	$	2,362	Scenario analysis	Estimated recovery percentage	13	%	to	36%	29	%

Long-term debt
Structured notes	$	739,353	Market approach	Price	$52		to	$108	$75
				Price	€60		to	€102	€80


November 30, 2021
	Fair Value (in thousands)		Valuation Technique	Significant Unobservable Input(s)	Input/Range				Weighted Average

Financial instruments owned, at fair value
Corporate equity securities	$	86,961
Non-exchange-traded securities			Market approach	Price	$1		to	$366	$183
			Volatility benchmarking	Volatility	40	%	to	53%	45	%

Corporate debt securities	$	11,803	Market approach	Price	$13		to	$100	$86

CDOs and CLOs	$	31,944	Discounted cash flows	Constant prepayment rate	20%				—
				Constant default rate	2%				—
				Loss severity	25	%	to	30%	26	%
				Discount rate/yield	8	%	to	19%	16	%
			Market approach	Price	$86		to	$103	$93

Commercial mortgage- backed securities	$	2,333	Scenario analysis	Estimated recovery percentage	81%				—






Other asset-backed securities	$	86,099	Discounted cash flows	Constant prepayment rate	0	%	to	35%	31	%
				Constant default rate	2	%	to	4%	4	%
				Loss severity	60	%	to	85%	55	%
				Discount rate/yield	3	%	to	16%	10	%
				Cumulative loss rate	7	%	to	20%	14	%
				Duration (years)	0.7 years		to	1.4 years	1.1 years
			Market approach	Price	$37		to	$100	$94

Loans and other receivables	$	134,015	Market approach	Price	$31		to	$101	$54
			Scenario analysis	Estimated recovery percentage	9	%	to	100%	76	%

Derivatives	$	6,501
Equity options			Volatility benchmarking	Volatility	46%				—
Interest rate swaps			Market approach	Basis points upfront	0.1		to	8.7	3.3
Total return swaps				Price	$100				—

Investments at fair value	$	128,152
Private equity securities			Market approach	Price	$1		to	$152	$32
				EBITDA multiple	16.9				—
				Revenue multiple	4.9		to	5.1	5.0
			Scenario analysis	Estimated recovery percentage	7%				—
				Discount rate/yield	13	%	to	21%	17	%
				Revenue growth	0%				—

Investment in FXCM	$	50,455
Term loan			Discounted cash flows	Term based on the pay off (years)	0 months		to	2.2 years	2.2 years

Loans to and investments in associated companies
Non-exchange-traded warrants	$	30,842	Market approach	Underlying stock price	$662				—
				Underlying stock price	€15		to	€18	€16
				Volatility	25	%	to	59%	31	%


Financial instruments sold, not yet purchased, at fair value
Corporate equity securities	$	4,635
Non-exchange-traded securities			Market approach	Price	$1				—

Loans	$	15,770	Market approach	Price	$31		to	$100	$43
			Scenario analysis	Estimated recovery percentage	50%				—

Derivatives	$	76,533
Equity options			Volatility benchmarking	Volatility	26	%	to	77%	40	%
Interest rate swaps			Market approach	Basis points upfront	0.1		to	8.7	3.1
Total return swaps				Price	$100				—

Other secured financings	$	25,905	Scenario analysis	Estimated recovery percentage	13	%	to	98%	92	%

Long-term debt
Structured notes	$	881,732	Market approach	Price	$76		to	$115	$94
				Price	€81		to	€113	€103

Summary of Gains (Losses) Due to Changes in Instrument Specific Credit Risk for Loans and Other Receivables and Loan Commitments Measured at Fair Value Under Fair Value Option

The following is a summary of gains (losses) due to changes in instrument-specific credit risk on loans, other receivables and debt instruments and gains (losses) due to other changes in fair value on long-term debt measured at fair value under the fair value option (in thousands):


	For the Three Months Ended May 31,				For the Six Months Ended May 31,
	2022		2021		2022		2021
Financial instruments owned, at fair value:
Loans and other receivables	$	(1,478)	$	15,520	$	(1,294)	$	23,259

Financial instruments sold, not yet purchased, at fair value:
Loans	$	(882)	$	(363)	$	(4,889)	$	(363)









Long-term debt:
Changes in instrument-specific credit risk (1)	$	42,886	$	(32,247)	$	94,133	$	(122,898)
Other changes in fair value (2)	161,381		6,846		255,932		86,113

(1) Changes in instrument-specific credit risk related to structured notes are included in the Consolidated Statements of Comprehensive Income (Loss), net of taxes.

(2) Other changes in fair value are included in Principal transactions revenues in the Consolidated Statements of Operations

Summary of Amount by Which Contractual Principal Exceeds Fair Value for Loans and Other Receivables Measured at Fair Value Under Fair Value Option

The following is a summary of the amounts by which contractual principal is greater than (less than) fair value for loans and other receivables, long-term debt and other secured financings measured at fair value under the fair value option (in thousands):


	May 31, 2022		November 30, 2021
Financial instruments owned, at fair value:
Loans and other receivables (1)	$	5,703,268	$	5,600,648

Loans and other receivables on nonaccrual status and/or 90 days or greater past due (1) (2)	143,521		64,203
Long-term debt	$	317,452	$	(38,391)
Other secured financings	$	2,913	$	3,432

(1) Interest income is recognized separately from other changes in fair value and is included in Interest income in the Consolidated Statements of Operations.

(2) Amounts include loans and other receivables 90 days or greater past due by which contractual principal exceeds fair value of $109.7 million and $19.7 million at May 31, 2022 and November 30, 2021, respectively