FAIR VALUE OF FINANCIAL INSTRUMENTS (Tables)

6 Months Ended

Jun. 30, 2016

Fair Value Disclosures [Abstract]

Schedule of carrying value and estimated fair value, as well as the respective hierarchy classifications, of the financial assets and liabilities that are not carried at estimated fair value

The following table presents the carrying value and estimated fair value, as well as the respective hierarchy classifications, of the Company’s financial assets and liabilities that are not carried at estimated fair value on a recurring basis as of June 30, 2016 (amounts in thousands): 

	As of June 30, 2016				Fair Value Hierarchy
	Carrying Amount		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:
Cash, restricted cash, and cash equivalents	$	1,137,465	$	1,137,465	$	1,137,465	$	—	$	—
Liabilities:
Senior notes	412,229		393,113		393,113		—		—
Junior subordinated notes	249,309		193,300		—		—		193,300

The following table presents the carrying value and estimated fair value, as well as the respective hierarchy classifications, of the Company’s financial assets and liabilities that are not carried at estimated fair value on a recurring basis as of December 31, 2015 (amounts in thousands): 

	As of December 31, 2015				Fair Value Hierarchy
	Carrying Amount		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:
Cash, restricted cash, and cash equivalents	$	807,496	$	807,496	$	807,496	$	—	$	—
Liabilities:
Senior notes	413,006		394,390		394,390		—		—
Junior subordinated notes	248,498		216,757		—		—		216,757

Schedule of fair value of financial assets and liabilities measured on a recurring basis

The following table presents information about the Company’s assets and liabilities measured at fair value on a recurring basis as of June 30, 2016, and indicates the fair value hierarchy of the valuation techniques utilized by the Company to determine such fair value (amounts in thousands):

	Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable  Inputs (Level 3)		Balance as of June 30, 2016
Assets:
Securities:
Corporate debt securities	$	—	$	27,867	$	149,372	$	177,239
Residential mortgage-backed securities	—		—		45,800		45,800
Total securities	—		27,867		195,172		223,039
Corporate loans	—		3,690,982		200,841		3,891,823
Equity investments, at estimated fair value	43,047		51,885		123,374		218,306
Interests in joint ventures and partnerships, at estimated fair value	—		—		758,321		758,321
Derivatives:
Foreign exchange forward contracts and options	—		26,781		2,189		28,970
Warrants	—		—		2,120		2,120
Options	—		—		2,112		2,112
Total derivatives	—		26,781		6,421		33,202
Total	$	43,047	$	3,797,515	$	1,284,129	$	5,124,691
Liabilities:
Collateralized loan obligation secured notes	$	—	$	4,055,722	$	—	$	4,055,722
Collateralized loan obligation secured notes to affiliates	—		63,624		—		63,624
Derivatives:
Interest rate swaps	—		59,063		—		59,063
Foreign exchange forward contracts and options	—		4,308		537		4,845
Total derivatives	—		63,371		537		63,908
Total	$	—	$	4,182,717	$	537	$	4,183,254

The following table presents information about the Company’s assets and liabilities measured at fair value on a recurring basis as of December 31, 2015, and indicates the fair value hierarchy of the valuation techniques utilized by the Company to determine such fair value (amounts in thousands):

	Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)		Balance as of December 31, 2015
Assets:
Securities:
Corporate debt securities	$	—	$	172,912	$	194,986	$	367,898
Residential mortgage-backed securities	—		—		49,621		49,621
Total securities	—		172,912		244,607		417,519
Corporate loans	—		4,889,876		298,734		5,188,610
Equity investments, at estimated fair value	40,765		75,533		146,648		262,946
Interests in joint ventures and partnerships, at estimated fair value	—		—		888,408		888,408
Derivatives:							0
Foreign exchange forward contracts and options	—		37,120		3,637		40,757
Options	—		—		95		95
Total derivatives	—		37,120		3,732		40,852
Total	$	40,765	$	5,175,441	$	1,582,129	$	6,798,335
Liabilities:
Collateralized loan obligation secured notes	$	—	$	4,843,746	$	—	$	4,843,746
Derivatives:
Interest rate swaps	—		41,743		—		41,743
Foreign exchange forward contracts and options	—		1,399		750		2,149
Total derivatives	—		43,142		750		43,892
Total	$	—	$	4,886,888	$	750	$	4,887,638

Schedule of additional information about assets and liabilities, including derivatives, that are measured at fair value on a recurring basis

The following table presents additional information about assets and liabilities, including derivatives that are measured at fair value on a recurring basis for which the Company has utilized Level 3 inputs to determine fair value, for the three months ended June 30, 2016 (amounts in thousands):

	Assets
	Corporate Debt Securities			Residential Mortgage- Backed Securities			Corporate Loans			Equity Investments, at Estimated Fair Value			Interests in Joint Ventures and Partnerships			Foreign Exchange Options, Net			Warrants			Options
Beginning balance as of April 1, 2016	$	150,068		$	47,714		$	296,982		$	138,563		$	748,329		$	1,841		$	—		$	498
Total gains or losses (for the period):
Included in earnings(1)	(667		)	748			(44,943		)	(17,377		)	947			(189		)	(165		)	1,614
Transfers into Level 3	—			—			—			—			—			—						—
Transfers out of Level 3	—			—			—			—			—			—						—
Purchases	—			—			997			—			45,756			—						—
Sales				—			(26,685		)	(5,130		)	—			—						—
Settlements	(29		)	(2,662		)	(25,510		)	7,318			(36,711		)	—			2,285			—
Ending balance as of June 30, 2016	$	149,372		$	45,800		$	200,841		$	123,374		$	758,321		$	1,652		$	2,120		$	2,112
Change in unrealized gains or losses for the period included in earnings for assets held at the end of the reporting period(1)	$	(667	)	$	748		$	(44,943	)	$	(17,377	)	$	947		$	(189	)	$	(165	)	$	1,614

(1) Amounts are included in net realized and unrealized gain (loss) on investments or net realized and unrealized gain (loss) on derivatives and foreign exchange in the condensed consolidated statements of operations.

The following table presents additional information about assets and liabilities, including derivatives that are measured at fair value on a recurring basis for which the Company has utilized Level 3 inputs to determine fair value, for the six months ended June 30, 2016 (amounts in thousands):

	Assets
	Corporate Debt Securities			Residential Mortgage- Backed Securities			Corporate Loans			Equity Investments, at Estimated Fair Value			Interests in Joint Ventures and Partnerships			Foreign Exchange Options, Net			Warrants			Options
Beginning balance as of January 1, 2016	$	194,986		$	49,621		$	298,734		$	146,648		$	888,408		$	2,887		$	—		$	95
Total gains or losses (for the period):
Included in earnings(1)	(45,549		)	1,080			(51,770		)	(25,462		)	(79,748		)	(1,235		)	(165		)	2,017
Transfers into Level 3	—			—			—			—			—			—						—
Transfers out of Level 3	—			—			—			—			—			—						—
Purchases	—			—			3,303			—			59,823			—						—
Sales				—			(26,685		)	(5,130		)	—			—						—
Settlements	(65		)	(4,901		)	(22,741		)	7,318			(110,162		)	—			2,285			—
Ending balance as of June 30, 2016	$	149,372		$	45,800		$	200,841		$	123,374		$	758,321		$	1,652		$	2,120		$	2,112
Change in unrealized gains or losses for the period included in earnings for assets held at the end of the reporting period(1)	$	(45,549	)	$	1,076		$	(51,770	)	$	(25,462	)	$	(79,748	)	$	(1,235	)	$	(165	)	$	2,017

(1) Amounts are included in net realized and unrealized gain (loss) on investments or net realized and unrealized gain (loss) on derivatives and foreign exchange in the condensed consolidated statements of operations.

The following table presents additional information about assets and liabilities, including derivatives, that are measured at fair value on a recurring basis for which the Company has utilized Level 3 inputs to determine fair value, for the three months ended June 30, 2015 (amounts in thousands):

	Assets
	Corporate Debt Securities			Residential Mortgage- Backed Securities			Corporate Loans			Equity Investments, at Estimated Fair Value		Interests in Joint Ventures and Partnerships			Warrants			Options
Beginning balance as of April 1, 2015	$	307,911		$	53,935		$	336,186		$	103,319	$	719,290		$	521		$	4,309
Total gains or losses (for the period):
Included in earnings(1)	(7,763		)	1,239			(2,278		)	2,213		12,204			(110		)	(1,399		)
Transfers into Level 3	—			—			—			—		—			—			—
Transfers out of Level 3	—			—			—			—		—			—			—
Purchases	—			—			10,999			—		13,830			—			—
Sales	(76,366		)	—			—			—		—			—			—
Settlements	2,109			(2,785		)	(3,860		)	61,347		(5,727		)	—			—
Ending balance as of June 30, 2015	$	225,891		$	52,389		$	341,047		$	166,879	$	739,597		$	411		$	2,910
Change in unrealized gains or losses for the period included in earnings for assets held at the end of the reporting period(1)	$	(11,907	)	$	43		$	(2,374	)	$	2,213	$	12,204		$	(110	)	$	(1,399	)

(1) Amounts are included in net realized and unrealized gain (loss) on investments or net realized and unrealized gain (loss) on derivatives and foreign exchange in the condensed consolidated statements of operations.

The following table presents additional information about assets and liabilities, including derivatives, that are measured at fair value on a recurring basis for which the Company has utilized Level 3 inputs to determine fair value, for the six months ended June 30, 2015 (amounts in thousands):

	Assets																					Liabilities
	Corporate Debt Securities			Residential Mortgage- Backed Securities			Corporate Loans			Equity Investments, at Estimated Fair Value			Interests in Joint Ventures and Partnerships			Warrants			Options			Collateralized Loan Obligation Secured Notes
Beginning balance as of January 1, 2015	$	317,034		$	55,184		$	347,077		$	81,719		$	718,772		$	—		$	5,212		$	5,501,099
Total gains or losses (for the period):
Included in earnings(1)	(11,759		)	3,015			(58,048		)	(21,114		)	(20,158		)	(2,001		)	(2,302		)	—
Transfers into Level 3	—			—			—			—			—			—			—			—
Transfers out of Level 3(2)	—			—			—			—			—			—			—			(5,501,099		)
Purchases	—			—			12,307			—			49,367			—			—			—
Sales	(80,579		)	—			(25,511		)	—			—			—			—			—
Settlements	1,195			(5,810		)	65,222			106,274			(8,384		)	2,412			—			—
Ending balance as of June 30, 2015	$	225,891		$	52,389		$	341,047		$	166,879		$	739,597		$	411		$	2,910		$	—
Change in unrealized gains or losses for the period included in earnings for assets held at the end of the reporting period(1)	$	(14,418	)	$	196		$	(57,161	)	$	(20,418	)	$	(19,982	)	$	(2,001	)	$	(2,302	)	$	—

(1) Amounts are included in net realized and unrealized gain (loss) on investments or net realized and unrealized gain (loss) on derivatives and foreign exchange in the condensed consolidated statements of operations. Amounts for collateralized loan obligation secured notes, which represent liabilities measured at fair value, are included in net realized and unrealized loss on debt in the condensed consolidated statements of operations.

(2) CLO secured notes were transferred out of Level 3 due to the adoption of accounting guidance effective January 1, 2015, whereby the debt obligations of the Company's consolidated CLOs were measured on the basis of the estimated fair value of the financial assets of the CLOs. As such, as of June 30, 2015, these debt obligations were classified as Level 2. Refer to Note 2 to these condensed consolidated financial statements for further discussion.

Summary of valuation techniques used for assets and liabilities, measured at fair value and categorized within level 3

The following table presents additional information about valuation techniques and inputs used for assets and liabilities, including derivatives, that are measured at fair value and categorized within Level 3 as of June 30, 2016 (dollar amounts in thousands): 

	Balance as of June 30, 2016		Valuation Techniques(1)	Unobservable Inputs(2)	Weighted Average(3)	Range	Impact to Valuation from an Increase  in Input(4)
Assets:
Corporate debt securities	$	149,372	Yield analysis	Yield	12%	7% - 14%	Decrease
				Net leverage	10x	9x-10x	Decrease
				EBITDA multiple	8x	7x - 9x	Increase
				Discount margin	1250	1250bps	Decrease
			Market comparables	LTM EBITDA multiple	6x	6x	Increase
Residential mortgage – backed securities	$	45,800	Discounted cash flows	Probability of default	1%	0% - 2%	Decrease
				Loss severity	43%	35% - 50%	Decrease
				Constant prepayment rate	16%	12% - 20%	(5	)
Corporate loans	$	200,841	Yield Analysis	Yield	20%	4% - 198%	Decrease
				Net leverage	9x	1x - 18x	Decrease
				EBITDA multiple	9x	7x - 12x	Increase
Equity investments, at estimated fair value(6)	$	123,374	Inputs to both market comparables and discounted cash flow	Illiquidity discount	11%	0% - 15%	Decrease
				Weight ascribed to market comparables	25%	0% - 100%	(7	)
				Weight ascribed to discounted cash flows	75%	0% - 100%	(8	)
			Market comparables	LTM EBITDA multiple	9x	0x - 13x	Increase
				Forward EBITDA multiple	7x	3x - 11x	Increase

			Discounted cash flows	Weighted average cost of capital	9%	7% - 14%	Decrease
				LTM EBITDA exit multiple	9x	2x - 10x	Increase
Interests in joint ventures and partnerships(9)	$	758,321	Inputs to both market comparables and discounted cash flow	Weight ascribed to market comparables	37%	0% - 100%	(7	)
				Weight ascribed to discounted cash flows	63%	0% - 100%	(8	)
			Market comparables	LTM EBITDA multiple	5x	1x- 9x	Increase
				Capitalization Rate	7%	6% - 12%	Decrease
			Discounted cash flows	Weighted average cost of capital	10%	7% - 24%	Decrease
				LTM EBITDA exit multiple	10x	10x
				Average price per BOE(10)	$25.06	$16.07-$33.15	Increase
			Yield analysis	Yield	15%	15%	Decrease
				Net leverage	2x	2x	Decrease
				EBITDA multiple	7x	7x	Increase
Foreign exchange options, net	$	1,652	Option pricing model	Forward and spot rates	11,500	6 - 13,500	(11	)
Options(12)	$	2,112	Inputs to both market comparables and discounted cash flow	Illiquidity discount	10%	10%	Decrease
				Weight ascribed to market comparables	50%	50%	(7	)
				Weight ascribed to discounted cash flows	50%	50%	(8	)
	,		Market comparables	LTM EBITDA multiple	11x	11x	Increase
				Forward EBITDA multiple	8x	8x	Increase
			Discounted cash flows	Weighted average cost of capital	15%	15%	Decrease
				LTM EBITDA exit multiple	5x	5x	Increase

(1) For the assets that have more than one valuation technique, the Company may rely on the techniques individually or in aggregate based on a weight ascribed to each one ranging from 0-100%. When determining the weighting ascribed to each valuation methodology, the Company considers, among other factors, the availability of direct market comparables, the applicability of a discounted cash flow analysis and the expected hold period and manner of realization for the investment. These factors can result in different weightings among the investments and in certain instances, may result in up to a 100% weighting to a single methodology. Broker quotes obtained for valuation purposes are reviewed by the Company through other valuation techniques.

(2) In determining certain of these inputs, management evaluates a variety of factors including economic conditions, industry and market developments; market valuations of comparable companies; and company specific developments including exit strategies and realization opportunities.

(3) Weighted average amounts are based on the estimated fair values.

(4) Unless otherwise noted, this column represents the directional change in the fair value of the Level 3 investments that would result from an increase to the corresponding unobservable input. A decrease to the unobservable input would have the opposite effect. Significant increases and decreases in these inputs in isolation could result in significantly higher or lower fair value measurements.

(5) The impact of changes in prepayment speeds may have differing impacts depending on the seniority of the instrument. Generally, an increase in the constant prepayment speed will positively impact the overall valuation of traditional mortgage assets. In contrast, an increase in the constant prepayment rate will negatively impact the overall valuation of interest-only strips.

(6) When determining the illiquidity discount to be applied to equity investments, at estimated fair value, the Company seeks to take a uniform approach across its portfolio and generally applies a minimum 5% discount to all private equity investments carried at estimated fair value. The Company then evaluates such investments to determine if factors exist that could make it more challenging to monetize the investment and, therefore, justify applying a higher illiquidity discount. These factors generally include the salability of the investment, whether the issuer is undergoing significant restructuring activity or similar factors, as well as characteristics about the issuer including its size and/or whether it is experiencing, or expected to experience, a significant decline in earnings. Depending on the applicability of these factors, the Company determines the amount of any incremental illiquidity discount to be applied above the 5% minimum, and during the time the Company holds the investment, the illiquidity discount may be increased or decreased, from time to time, based on changes to these factors. The amount of illiquidity discount applied at any time requires considerable judgment about what a market participant would consider and is based on the facts and circumstances of each individual investment. Accordingly, the illiquidity discount ultimately considered by a market participant upon the realization of any investment may be higher or lower than that estimated by the Company in its valuations. Of the total equity investments, at estimated fair value, $47.8 million was valued solely using a market comparables technique.

(7) The directional change from an increase in the weight ascribed to the market comparables approach would increase the fair value of the Level 3 investments if the market comparables approach results in a higher valuation than the discounted cash flow approach. The opposite would be true if the market comparables approach results in a lower valuation than the discounted cash flow approach.

(8) The directional change from an increase in the weight ascribed to the discounted cash flow approach would increase the fair value of the Level 3 investments if the discounted cash flow approach results in a higher valuation than the market comparables approach. The opposite would be true if the discounted cash flow approach results in a lower valuation than the market comparables approach.

(9) Inputs exclude an asset that was valued using an independent third party valuation firm. Of the total interest in joint ventures and partnerships, $59.6 million was valued solely using a discounted cash flow technique, while $7.8 million was valued solely using a market comparables technique and $21.4 million was valued solely using a yield analysis.

(10) Natural resources assets with an estimated fair value of $98.4 million as of June 30, 2016 were valued using commodity prices. Commodity prices may be measured using a common volumetric equivalent where one barrel of oil equivalent (‘‘BOE’’) is determined using the ratio of six thousand cubic feet of natural gas to one barrel of oil, condensate or natural gas liquids. The price per BOE is provided to show the aggregate of all price inputs for these investments over a common volumetric equivalent although the valuations for specific investments may use price inputs specific to the asset for purposes of our valuations. The discounted cash flows include forecasted production of liquids (oil, condensate, and natural gas liquids) and natural gas with a forecasted revenue ratio of approximately 45% liquids and 55% natural gas.

(11) Inputs include forward rates for investments in Chinese Yuan and Indian Rupees.

(12) The total options were valued using 50% a discount cash flow technique and 50% a market comparables technique.

The table above excludes warrants of $2.1 million, comprised of equity-like securities in a company that were valued using an independent third party valuation firm primarily based on the contractual agreement and public disclosures of the expected sale value.

The following table presents additional information about valuation techniques and inputs used for assets, including derivatives, that are measured at fair value and categorized within Level 3 as of December 31, 2015 (dollar amounts in thousands):

	Balance as of December 31, 2015		Valuation Techniques(1)	Unobservable Inputs(2)	Weighted Average(3)	Range	Impact to Valuation from an Increase in Input(4)
Assets:
Corporate debt securities	$	194,986	Yield analysis	Yield	23%	6% - 31%	Decrease
				Net leverage	10x	10x-12x	Decrease
				EBITDA multiple	7x	7x - 10x	Increase
				Discount margin	750	750bps	Decrease
Residential mortgage – backed securities	$	49,621	Discounted cash flows	Probability of default	1%	0% - 3%	Decrease
				Loss severity	40%	35% - 45%	Decrease
				Constant prepayment rate	15%	12% - 18%	(5	)
Corporate loans	$	298,734	Yield Analysis	Yield	11%	3% - 18%	Decrease
				Net leverage	7x	1x - 19x	Decrease
				EBITDA multiple	9x	6x - 15x	Increase
Equity investments, at estimated fair value(6)	$	146,648	Inputs to market comparables, discounted cash flow and broker quotes	Illiquidity discount	11%	0% - 15%	Decrease
				Weight ascribed to market comparables	52%	0% - 100%	(7	)
				Weight ascribed to discounted cash flows	42%	0% - 100%	(8	)
				Weight ascribed to broker quotes	6%	0% - 100%	(9	)
			Market comparables	LTM EBITDA multiple	8x	4x - 13x	Increase
				Forward EBITDA multiple	8x	3x - 11x	Increase
			Discounted cash flows	Weighted average cost of capital	9%	7% - 14%	Decrease
				LTM EBITDA exit multiple	8x	0x - 9x	Increase
			Broker quotes	Offered quotes	4	0 - 5	Increase
Interests in joint ventures and partnerships(10)	$	888,408	Inputs to both market comparables and discounted cash flow	Weight ascribed to market comparables	43%	0% - 100%	(7	)
				Weight ascribed to discounted cash flows	57%	0% - 100%	(8	)
			Market comparables	LTM EBITDA multiple	5x	1x - 9x	Decrease
			Discounted cash flows	Weighted average cost of capital	8%	6% - 20%	Decrease
				Average price per BOE(11)	$20.61	$14.33 - $23.22	Increase
			Yield analysis	Yield	16%	16%	Decrease
				Net leverage	2x	2x	Decrease
				EBITDA multiple	8x	8x	Increase
Foreign exchange options, net	$	2,887	Option pricing model	Forward and spot rates	11,500	6 -14,000	(12	)
Options(13)	$	95	Inputs to both market comparables and discounted cash flow	Illiquidity discount	10%	10%	Decrease
				Weight ascribed to market comparables	50%	50%	(7	)
				Weight ascribed to discounted cash flows	50%	50%	(8	)
	,		Market comparables	LTM EBITDA multiple	9x	9x	Increase
				Forward EBITDA multiple	8x	8x	Increase
			Discounted cash flows	Weighted average cost of capital	14%	14%	Decrease
				LTM EBITDA exit multiple	8x	8x	Increase

(1) For the assets that have more than one valuation technique, the Company may rely on the techniques individually or in aggregate based on a weight ascribed to each one ranging from 0-100%. When determining the weighting ascribed to each valuation methodology, the Company considers, among other factors, the availability of direct market comparables, the applicability of a discounted cash flow analysis and the expected hold period and manner of realization for the investment. These factors can result in different weightings among the investments and in certain instances, may result in up to a 100% weighting to a single methodology. Broker quotes obtained for valuation purposes are reviewed by the Company through other valuation techniques.

(2) In determining certain of these inputs, management evaluates a variety of factors including economic conditions, industry and market developments; market valuations of comparable companies; and company specific developments including exit strategies and realization opportunities.

(3) Weighted average amounts are based on the estimated fair values.

(4) Unless otherwise noted, this column represents the directional change in the fair value of the Level 3 investments that would result from an increase to the corresponding unobservable input. A decrease to the unobservable input would have the opposite effect. Significant increases and decreases in these inputs in isolation could result in significantly higher or lower fair value measurements.

(5) The impact of changes in prepayment speeds may have differing impacts depending on the seniority of the instrument. Generally, an increase in the constant prepayment speed will positively impact the overall valuation of traditional mortgage assets. In contrast, an increase in the constant prepayment rate will negatively impact the overall valuation of interest-only strips.

(6) When determining the illiquidity discount to be applied to equity investments, at estimated fair value, the Company seeks to take a uniform approach across its portfolio and generally applies a minimum 5% discount to all private equity investments carried at estimated fair value. The Company then evaluates such investments to determine if factors exist that could make it more challenging to monetize the investment and, therefore, justify applying a higher illiquidity discount. These factors generally include the salability of the investment, whether the issuer is undergoing significant restructuring activity or similar factors, as well as characteristics about the issuer including its size and/or whether it is experiencing, or expected to experience, a significant decline in earnings. Depending on the applicability of these factors, the Company determines the amount of any incremental illiquidity discount to be applied above the 5% minimum, and during the time the Company holds the investment, the illiquidity discount may be increased or decreased, from time to time, based on changes to these factors. The amount of illiquidity discount applied at any time requires considerable judgment about what a market participant would consider and is based on the facts and circumstances of each individual investment. Accordingly, the illiquidity discount ultimately considered by a market participant upon the realization of any investment may be higher or lower than that estimated by the Company in its valuations. Of the total equity investments, at estimated fair value, $6.4 million was valued solely using broker quotes, while $11.3 million was valued solely using a market comparables technique.

(7) The directional change from an increase in the weight ascribed to the market comparables approach would increase the fair value of the Level 3 investments if the market comparables approach results in a higher valuation than the discounted cash flow approach and broker quotes, if applicable. The opposite would be true if the market comparables approach results in a lower valuation than the discounted cash flow approach and broker quotes, if applicable.

(8) The directional change from an increase in the weight ascribed to the discounted cash flow approach would increase the fair value of the Level 3 investments if the discounted cash flow approach results in a higher valuation than the market comparables approach and broker quotes, if applicable. The opposite would be true if the discounted cash flow approach results in a lower valuation than the market comparables approach and broker quotes, if applicable.

(9) The directional change from an increase in the weight ascribed to broker quotes would increase the fair value of the Level 3 investments if the broker quotes results in a higher valuation than the market comparables and discounted cash flow approaches, if applicable. The opposite would be true if the broker quotes results in a lower valuation than the market comparables and discounted cash flow approaches, if applicable.

(10) Inputs exclude an asset that was valued using an independent third party valuation firm. Of the total interest in joint ventures and partnerships, $164.4 million was valued solely using a discounted cash flow technique, while $98.9 million was valued solely using a market comparables technique and $17.5 million was valued solely using a yield analysis.

(11) Natural resources assets with an estimated fair value of $114.1 million as of December 31, 2015 were valued using commodity prices. Commodity prices may be measured using a common volumetric equivalent where one barrel of oil equivalent (‘‘BOE’’) is determined using the ratio of six thousand cubic feet of natural gas to one barrel of oil, condensate or natural gas liquids. The price per BOE is provided to show the aggregate of all price inputs for these investments over a common volumetric equivalent although the valuations for specific investments may use price inputs specific to the asset for purposes of our valuations. The discounted cash flows include forecasted production of liquids (oil, condensate, and natural gas liquids) and natural gas with a forecasted revenue ratio of approximately 25% liquids and 75% natural gas.

(12) Inputs include forward rates for investments in Chinese Yuan and Indian Rupees.

(13) The total options were valued using 50% a discount cash flow technique and 50% a market comparables technique.