Fair Value Measurements (Tables)

12 Months Ended

Dec. 31, 2019

Fair Value Disclosures [Abstract]

Categorized Investments Recorded at Fair Value among Levels

We have categorized our assets and liabilities that are recorded at fair value on a recurring basis among levels based on the observability of inputs, or at fair value using NAV per share (or its equivalent) as follows:

	December 31, 2019
	Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)		Fair Value Based on NAV as Practical Expedient		Total Fair Value
Investments:
Fixed maturity investments:
U.S. government and agency	$	—	$	736,043	$	—	$	—	$	736,043
U.K. government	—		161,772		—		—		161,772
Other government	—		702,857		—		—		702,857
Corporate	—		5,697,067		—		—		5,697,067
Municipal	—		167,882		—		—		167,882
Residential mortgage-backed	—		471,836		—		—		471,836
Commercial mortgage-backed	—		900,029		—		—		900,029
Asset-backed	—		775,402		—		—		775,402
	$	—	$	9,612,888	$	—	$	—	$	9,612,888
Other assets included within funds held - directly managed	—		14,207		—		—		14,207
Equities:
Publicly traded equity investments	$	297,310	$	30,565	$	—	$	—	$	327,875
Exchange-traded funds	133,047		—		—		—		133,047
Privately held equity investments	—		—		268,799		—		268,799
	$	430,357	$	30,565	$	268,799	$	—	$	729,721
Other investments:
Hedge funds	$	—	$	—	$	—	$	1,121,904	$	1,121,904
Fixed income funds	—		398,143		—		82,896		481,039
Equity funds	—		111,040		—		299,109		410,149
Private equity funds	—		—		—		329,885		329,885
CLO equities	—		—		87,555		—		87,555
CLO equity funds	—		—		—		87,509		87,509
Other	—		34		314		6,031		6,379
	$	—	$	509,217	$	87,869	$	1,927,334	$	2,524,420
Total Investments	$	430,357	$	10,166,877	$	356,668	$	1,927,334	$	12,881,236
Cash and cash equivalents	$	173,892	$	222,191	$	—	$	—	$	396,083
Reinsurance balances recoverable on paid and unpaid losses:	$	—	$	—	$	695,518	$	—	$	695,518
Other Assets:
Derivatives qualifying as hedging	$	—	$	642	$	—	$	—	$	642
Derivatives not qualifying as hedges	$	—	$	1,369	$	—	$	—	$	1,369
Derivative instruments	$	—	$	2,011	$	—	$	—	$	2,011
Losses and LAE:	$	—	$	—	$	2,621,122	$	—	$	2,621,122
Other Liabilities:
Derivatives qualifying as hedging	$	—	$	11,452	$	—	$	—	$	11,452
Derivatives not qualifying as hedges	$	—	$	4,106	$	—	$	—	$	4,106
Derivative instruments	$	—	$	15,558	$	—	$	—	$	15,558

	December 31, 2018
	Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)		Fair Value Based on NAV as Practical Expedient		Total Fair Value
Investments:
Fixed maturity investments:
U.S. government and agency	$	—	$	510,245	$	—	$	—	$	510,245
U.K government	—		300,631		—		—		300,631
Other government	—		793,810		—		—		793,810
Corporate	—		4,802,454		37,386		—		4,839,840
Municipal	—		130,265		—		—		130,265
Residential mortgage-backed	—		773,557		—		—		773,557
Commercial mortgage-backed	—		705,674		7,389		—		713,063
Asset-backed	—		627,360		9,121		—		636,481
	$	—	$	8,643,996	$	53,896	$	—	$	8,697,892
Other assets included within funds held - directly managed	$	—	$	14,780	$	—	$	—	$	14,780
Equities:
Publicly traded equity investments	$	102,102	$	36,313	$	—	$	—	$	138,415
Privately held equity investments	—		—		228,710		—		228,710
	$	102,102	$	36,313	$	228,710	$	—	$	367,125
Other investments:
Hedge funds	$	—	$	—	$	—	$	852,584	$	852,584
Fixed income funds	—		290,864		—		112,994		403,858
Equity funds	—		100,440		—		233,241		333,681
Private equity funds	—		—		—		248,628		248,628
CLO equities	—		—		39,052		—		39,052
CLO equity funds	—		—		—		37,260		37,260
Private credit funds	—		—		—		33,381		33,381
Other	—		578		315		8,420		9,313
	$	—	$	391,882	$	39,367	$	1,526,508	$	1,957,757
Total Investments	$	102,102	$	9,086,971	$	321,973	$	1,526,508	$	11,037,554
Cash and cash equivalents	$	243,839	$	21,146	$	—	$	—	$	264,985
Reinsurance recoverable:	$	—	$	—	$	739,591	$	—	$	739,591
Other Assets:
Derivatives qualifying as hedging	$	—	$	1,615	$	—	$	—	$	1,615
Derivatives not qualifying as hedges	—		5,086		—		—		5,086
Derivative instruments	$	—	$	6,701	$	—	$	—	$	6,701
Losses and LAE:	$	—	$	—	$	2,874,055	$	—	$	2,874,055
Other Liabilities:
Derivatives qualifying as hedging	$	—	$	300	$	—	$	—	$	300
Derivatives not qualifying as hedges	—		683		—		—		683
Derivative instruments	$	—	$	983	$	—	$	—	$	983

Reconciliation of Beginning and Ending Balances for All Investments Measured at Fair Value on Recurring Basis

The following table presents a reconciliation of the beginning and ending balances for all investments measured at fair value on a recurring basis using Level 3 inputs during the years ended December 31, 2019 and 2018:

	2019
	Fixed maturity investments												Privately-held Equities			Other Investments			Total
	Corporate			Residential mortgage-backed			Commercial mortgage-backed			Asset-backed
Beginning fair value	$	37,386		$	—		$	7,389		$	9,121		$	228,710		$	39,367		$	321,973
Purchases	184			—			—			—			33,713			56,908			90,805
Sales	(3,520		)	—			(784		)	(5,088		)	(2,016		)	(590		)	(11,998		)
Total realized and unrealized gains (losses)	90			(1		)	64			241			8,392			(7,816		)	970
Transfer into Level 3 from Level 2	3,535			102			1,515			22,771			—			—			27,923
Transfer out of Level 3 into Level 2	(37,675		)	(101		)	(8,184		)	(27,045		)	—			—			(73,005		)
Ending fair value	$	—		$	—		$	—		$	—		$	268,799		$	87,869		$	356,668

	2018
	Fixed maturity investments												Privately-held Equities			Other Investments			Total
	Corporate			Residential mortgage-backed			Commercial mortgage-backed			Asset-backed
Beginning fair value	$	67,178		$	3,080		$	21,494		$	27,892		$	—		$	57,079		$	176,723
Purchases	14,391			—			3,749			46,074			227,000			13,173			304,387
Sales	(65,700		)	(1,184		)	(5,781		)	(49,020		)	—			(12,091		)	(133,776		)
Total realized and unrealized losses	(57		)	(28		)	(645		)	(1,843		)	(2		)	(18,794		)	(21,369		)
Transfer into Level 3 from Level 2	28,339			1,795			4,897			9,890			1,712			—			46,633
Transfer out of Level 3 into Level 2	(6,765		)	(3,663		)	(16,325		)	(23,872		)	—			—			(50,625		)
Ending fair value	$	37,386		$	—		$	7,389		$	9,121		$	228,710		$	39,367		$	321,973

The following table presents a reconciliation of the beginning and ending balances for all insurance contracts measured at fair value on a recurring basis using Level 3 inputs during the years ended December 31, 2019 and 2018:

	2019									2018
	Liability for losses and LAE			Reinsurance balances recoverable on paid and unpaid losses			Net			Liability for losses and LAE			Reinsurance balances recoverable on paid and unpaid losses			Net
Beginning fair value	$	2,874,055		$	739,591		$	2,134,464		$	1,794,669		$	542,224		$	1,252,445
Assumed business	9,218			—			9,218			1,890,061			372,780			1,517,281
Incurred losses and LAE:
Reduction in estimates of ultimate losses	(32,690		)	(2,958		)	(29,732		)	(108,429		)	(30,041		)	(78,388		)
Reduction in unallocated LAE	(19,915		)	—			(19,915		)	(20,656		)	—			(20,656		)
Change in fair value	160,630			43,449			117,181			27,845			21,181			6,664
Total incurred losses and LAE	108,025			40,491			67,534			(101,240		)	(8,860		)	(92,380		)
Paid losses	(416,770		)	(92,145		)	(324,625		)	(576,949		)	(148,175		)	(428,774		)
Effect of exchange rate movements	46,594			7,581			39,013			(132,486		)	(18,378		)	(114,108		)
Ending fair value	$	2,621,122		$	695,518		$	1,925,604		$	2,874,055		$	739,591		$	2,134,464

Changes in fair value in the table above are included in net incurred losses and LAE in our consolidated statements of earnings.

The following table presents the components of the net change in fair value for the years ended December 31, 2019, 2018 and 2017:

	2019		2018			2017
Changes in fair value due to changes in:
Duration	$	22,719	$	74,011		$	41,332
Corporate bond yield	94,462		(71,031		)	(11,076		)
Risk cost of capital	—		3,684			—
Change in fair value	$	117,181	$	6,664		$	30,256

Valuation Techniques and Inputs

Valuations Techniques and Inputs

The table below presents the quantitative information related to the fair value measurements for investments measured at fair value on a recurring basis using Level 3 inputs for the year ended December 31, 2019:

Qualitative Information about Level 3 Fair Value Measurements
	Fair Value at December 31, 2019	Valuation Techniques	Unobservable Input	Range (Average) (1)
	(in millions of U.S. dollars)
CLO equities	$87.6	Consensus pricing	Offered quotes	14-87 (48)
		Discounted Cash Flow method	Discount rate (%) (2) Recovery rate (3) Prepayment rate (4) Collateral reinvestment coupon floor (5)	10%-30% (19.5%) 50%-70% (60%) 20%-30% (25%) 1%
Privately held equity investments	268.8	Transactional value	Implied price at recent purchase transaction	13.50 - 13.85
		Cost as approximation of fair value	Cost as approximation of fair value

(1) The average represents the arithmetic average of the inputs and is not weighted by the relative fair value.

(2) Implied yields were determined from recent market color of comparable subordinated notes, as well as unique characteristics for each investment.

(3) For collateral which has already defaulted, a recovery rate equal to the current market value of the collateral was assumed.

(4) An assumed constant prepayment rate (CPR) was applied to the CLOs. CPRs are the annualized percentage of loans in the collateral pool that prepay.

(5) It was assumed that the collateral manager would reinvest into collateral with a similar weighted-average spread and a similar ratings composition to the current collateral pool.

Reconciliation of Beginning and Ending Balances for All Investments Measured at Fair Value on Recurring Basis

The following table presents a reconciliation of the beginning and ending balances for all insurance contracts measured at fair value on a recurring basis using Level 3 inputs during the years ended December 31, 2019 and 2018:

	2019									2018
	Liability for losses and LAE			Reinsurance balances recoverable on paid and unpaid losses			Net			Liability for losses and LAE			Reinsurance balances recoverable on paid and unpaid losses			Net
Beginning fair value	$	2,874,055		$	739,591		$	2,134,464		$	1,794,669		$	542,224		$	1,252,445
Assumed business	9,218			—			9,218			1,890,061			372,780			1,517,281
Incurred losses and LAE:
Reduction in estimates of ultimate losses	(32,690		)	(2,958		)	(29,732		)	(108,429		)	(30,041		)	(78,388		)
Reduction in unallocated LAE	(19,915		)	—			(19,915		)	(20,656		)	—			(20,656		)
Change in fair value	160,630			43,449			117,181			27,845			21,181			6,664
Total incurred losses and LAE	108,025			40,491			67,534			(101,240		)	(8,860		)	(92,380		)
Paid losses	(416,770		)	(92,145		)	(324,625		)	(576,949		)	(148,175		)	(428,774		)
Effect of exchange rate movements	46,594			7,581			39,013			(132,486		)	(18,378		)	(114,108		)
Ending fair value	$	2,621,122		$	695,518		$	1,925,604		$	2,874,055		$	739,591		$	2,134,464

Changes in fair value in the table above are included in net incurred losses and LAE in our consolidated statements of earnings.

The following table presents the components of the net change in fair value for the years ended December 31, 2019, 2018 and 2017:

	2019		2018			2017
Changes in fair value due to changes in:
Duration	$	22,719	$	74,011		$	41,332
Corporate bond yield	94,462		(71,031		)	(11,076		)
Risk cost of capital	—		3,684			—
Change in fair value	$	117,181	$	6,664		$	30,256

Quantitative Information

Below is a summary of the quantitative information regarding the significant observable and unobservable inputs used in the internal model to determine fair value on a recurring basis as of December 31, 2019 and 2018:

		2019	2018
Valuation Technique	Unobservable (U) and Observable (O) Inputs	Weighted Average	Weighted Average
Internal model	Corporate bond yield (O)	A rated	A rated
Internal model	Credit spread for non-performance risk (U)	0.2%	0.2%
Internal model	Risk cost of capital (U)	5.1%	5.0%
Internal model	Weighted average cost of capital (U)	8.5%	8.5%
Internal model	Duration - liability (U)	7.82 years	7.33 years
Internal model	Duration - reinsurance balances recoverable on paid and unpaid losses (U)	8.68 years	7.98 years