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Fair Value Measurements

12 Months Ended

Dec. 31, 2019

12. FAIR VALUE MEASUREMENTS

Fair Value Hierarchy

Fair value is defined as the price at which to sell an asset or transfer a liability (i.e. the "exit price") in an orderly transaction between market participants. We use a fair value hierarchy that gives the highest priority to quoted prices in active markets and the lowest priority to unobservable data. The hierarchy is broken down into three levels as follows:


•	Level 1 - Valuations based on unadjusted quoted prices in active markets for identical assets or liabilities that we have the ability to access. Valuation adjustments and block discounts are not applied to Level 1 instruments.


•	Level 2 - Valuations based on quoted prices in active markets for similar assets or liabilities, quoted prices for identical assets or liabilities in inactive markets, or for which significant inputs are observable (e.g. interest rates, yield curves, prepayment speeds, default rates, loss severities, etc.) or can be corroborated by observable market data.


•	Level 3 - Valuations based on unobservable inputs where there is little or no market activity. Unadjusted third party pricing sources or management's assumptions and internal valuation models may be used to determine the fair values.

In addition, certain of our other investments are measured at fair value using net asset value ("NAV") per share (or its equivalent) as a practical expedient and have not been classified within the fair value hierarchy above. 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

Valuation Methodologies of Financial Instruments Measured at Fair Value

Fixed Maturity Investments

The fair values for all securities in the fixed maturity investments and funds held - directly managed portfolios are independently provided by the investment accounting service providers, investment managers and investment custodians, each of which utilize internationally recognized independent pricing services. We record the unadjusted price provided by the investment accounting service providers, investment managers or investment custodians and validate this price through a process that includes, but is not limited to: (i) comparison of prices against alternative pricing sources; (ii) quantitative analysis (e.g. comparing the quarterly return for each managed portfolio to its target benchmark); (iii) evaluation of methodologies used by external parties to estimate fair value, including a review of the inputs used for pricing; and (iv) comparing the price to our knowledge of the current investment market. Our internal price validation procedures and review of fair value methodology documentation provided by independent pricing services have not historically resulted in adjustment in the prices obtained from the pricing service.

The independent pricing services used by the investment accounting service providers, investment managers and investment custodians obtain actual transaction prices for securities that have quoted prices in active markets. Where we utilize single unadjusted broker-dealer quotes, they are generally provided by market makers or broker-dealers who are recognized as market participants in the markets for which they are providing the quotes. For determining the fair value of securities that are not actively traded, in general, pricing services use "matrix pricing" in which the independent pricing service uses observable market inputs including, but not limited to, reported trades, benchmark yields, broker-dealer quotes, interest rates, prepayment speeds, default rates and other such inputs as are available from market sources to determine a reasonable fair value. In addition, pricing services use valuation models, using observable data, such as an Option Adjusted Spread model, to develop prepayment and interest rate scenarios. The Option Adjusted Spread model is commonly used to estimate fair value for securities such as mortgage-backed and asset-backed securities.

The following describes the techniques generally used to determine the fair value of our fixed maturity investments by asset class, including the investments underlying the funds held - directly managed.

•

U.S. government and agency securities consist of securities issued by the U.S. Treasury and mortgage pass-through agencies such as the Federal National Mortgage Association, the Federal Home Loan Mortgage Corporation and other agencies. Non-U.S. government securities consist of bonds issued by non-U.S. governments and agencies along with supranational organizations. The significant inputs used to determine the fair value of these securities include the spread above the risk-free yield curve, reported trades and broker-dealer quotes. These are considered to be observable market inputs and, therefore, the fair values of these securities are classified as Level 2.

•

Corporate securities consist primarily of investment-grade debt of a wide variety of corporate issuers and industries. The fair values of these securities are determined using the spread above the risk-free yield curve, reported trades, broker-dealer quotes, benchmark yields, and industry and market indicators. These are considered observable market inputs and, therefore, the fair values of these securities are classified as Level 2. Where pricing is unavailable from pricing services, such as in periods of low trading activity or when transactions are not orderly, we obtain non-binding quotes from broker-dealers. Where significant inputs are unable to be corroborated with market observable information, we classify the securities as Level 3.


•	Municipal securities consist primarily of bonds issued by U.S.-domiciled state and municipal entities. The fair values of these securities are determined using the spread above the risk-free yield curve, reported trades, broker-dealer quotes and benchmark yields. These are considered observable market inputs and, therefore, the fair values of these securities are classified as Level 2.

•

Asset-backed securities consist primarily of investment-grade bonds backed by pools of loans with a variety of underlying collateral. Residential and commercial mortgage-backed securities include both agency and non-agency originated securities. Where pricing is unavailable from pricing services, we obtain non-binding quotes from broker-dealers. This is generally the case when there is a low volume of trading activity and current transactions are not orderly. The significant inputs used to determine the fair value of these securities include the spread above the risk-free yield curve, reported trades, benchmark yields, prepayment speeds and default rates. The fair values of these securities are classified as Level 2 if the significant inputs are

market observable. Where significant inputs are unable to be corroborated with market observable information, we classify the securities as Level 3.

Equities

Our investments in equities consist of a combination of publicly and privately traded investments. Our publicly traded equity investments in common and preferred stocks predominantly trade on major exchanges and are managed by our external advisors. Our publicly traded equities are widely diversified and there is no significant concentration in any specific industry. Our exchange-traded funds trade on major exchanges. We use an internationally recognized pricing service to estimate the fair value of our publicly traded equities and exchange-traded funds. We have categorized the majority of our publicly traded equity investments, other than preferred stock, and our exchange-traded funds as Level 1 investments because the fair values of these investments are based on unadjusted quoted prices in active markets for identical assets. One equity security is trading in an inactive market and, as a result has been classified as Level 2. The fair value estimates of our investments in publicly traded preferred stock are based on observable market data and, as a result, have been categorized as Level 2.

Our privately held equity investments in common and preferred stocks are direct investments in companies that we believe offer attractive risk adjusted returns and/or offer other strategic advantages. Each investment may have its own unique terms and conditions and there may be restrictions on disposals. The market for these investments is illiquid and there is no active market. We use a combination of cost, internal models, reported values from co-investors/managers and observable inputs, such as capital raises and capital transactions between new and existing shareholders to calculate the fair value of the privately held equity investments. The fair value estimates of our investments in privately held equities are based on unobservable market data and, as a result, have been categorized as Level 3.

Other investments, at fair value

We have ongoing due diligence processes with respect to the other investments carried at fair value in which we invest and their managers. These processes are designed to assist us in assessing the quality of information provided by, or on behalf of, each fund and in determining whether such information continues to be reliable or whether further review is warranted. Certain funds do not provide full transparency of their underlying holdings; however, we obtain the audited financial statements for funds annually, and regularly review and discuss the fund performance with the fund managers to corroborate the reasonableness of the reported net asset values ("NAV").

The use of NAV as an estimate of the fair value for investments in certain entities that calculate NAV is a permitted practical expedient. Due to the time lag in the NAV reported by certain fund managers we adjust the valuation for capital calls and distributions. Other investments measured at fair value using NAV as a practical expedient have not been classified in the fair value hierarchy. Other investments for which we do not use NAV as a practical expedient have been valued using prices from independent pricing services, investment managers and broker-dealers.

The following describes the techniques generally used to determine the fair value of our other investments.


•	For our investments in hedge funds, we measure fair value by obtaining the most recently available NAV as advised by the external fund manager or third-party administrator. The fair values of these investments are measured using the NAV as a practical expedient and therefore have not been categorized within the fair value hierarchy.

•

Our investments in fixed income funds and equity funds are valued based on a combination of prices from independent pricing services, external fund managers or third-party administrators. For the publicly available prices we have classified the investments as Level 2. For the non-publicly available prices we are using NAV as a practical expedient and therefore these have not been categorized within the fair value hierarchy.


•	For our investments in private equity funds, we measure fair value by obtaining the most recently available NAV from the external fund manager or third-party administrator. The fair values of these investments are measured using the NAV as a practical expedient and therefore have not been categorized within the fair value hierarchy.

•

We measure the fair value of our direct investment in CLO equities based on valuations provided by independent pricing services, our external CLO equity manager, and valuations provided by the broker or lead underwriter of the investment (the "broker"). Our CLO equity investments have been classified as Level 3 due to the use of unobservable inputs in the valuation and the limited number of relevant trades in secondary markets.

In providing valuations, the independent pricing service providers, CLO equity manager and brokers use observable and unobservable inputs. Of the significant unobservable market inputs used, the default and loss severity rates involve the most judgment and create the most sensitivity. A significant increase or decrease in either of these significant inputs in isolation would result in lower or higher fair value estimates for direct investments in CLO equities and, in general, a change in default rate assumptions will be accompanied by a directionally similar change in loss severity rate assumptions. Collateral spreads and estimated maturity dates are less subjective inputs because they are based on the historical average of actual spreads and the weighted average life of the current underlying portfolios, respectively. A significant increase or decrease in either of these significant inputs in isolation would result in higher or lower fair value estimates for direct investments in CLO equities. In general, these inputs have no significant interrelationship with each other or with default and loss severity rates.

On a quarterly basis, we receive the valuation from the independent pricing providers, external CLO manager and brokers and then review the underlying cash flows and key assumptions used by them. We review and update the significant unobservable inputs based on information obtained from secondary markets. These inputs are our responsibility and we assess the reasonableness of the inputs (and if necessary, update the inputs) through communicating with industry participants, monitoring of the transactions in which we participate (for example, to evaluate default and loss severity rate trends), and reviewing market conditions, historical results, and emerging trends that may impact future cash flows.

If valuations from the independent pricing service providers, external CLO equity manager or brokers are not available, we use an income approach based on certain observable and unobservable inputs to value these investments. An income approach is also used to corroborate the reasonableness of the valuations provided by the pricing providers, external manager and brokers. Where an income approach is followed, the valuation is based on available trade information, such as expected cash flows and market assumptions on default and loss severity rates. Other inputs used in the valuation process include asset spreads, loan prepayment speeds, collateral spreads and estimated maturity dates.


•	For our investments in the CLO equity funds, we measure fair value by obtaining the most recently available NAV as advised by the external fund manager or third party administrator. The fair value of these investments is measured using the NAV as a practical expedient and therefore have not been categorized within the fair value hierarchy.


•	For our investments in private credit funds, we measure fair value by obtaining the most recently available NAV from the external fund manager or third-party administrator. The fair values of these investments are measured using the NAV as a practical expedient and therefore have not been categorized within the fair value hierarchy.

•

Included within other is an investment in a real estate debt fund, for which we measure fair value by obtaining the most recently available NAV from the external fund manager or third-party administrator. The fair value of this investment is measured using the NAV as a practical expedient and therefore has not been categorized within the fair value hierarchy.

Insurance Contracts - Fair Value Option

The Company uses an internal model to calculate the fair value of the liability for losses and loss adjustment expenses and reinsurance balances recoverable on paid and unpaid losses for certain retroactive reinsurance contracts where we have elected the fair value option in our Non-life Run-off segment. The fair value was calculated as the aggregate of discounted cash flows plus a risk margin. The discounted cash flow approach uses (i) estimated nominal cash flows based upon an appropriate payment pattern developed in accordance with standard actuarial techniques and (ii) a discount rate based upon a high quality rated corporate bond plus a credit spread for non-performance risk. The model uses corporate bond rates across the yield curve depending on the estimated timing of the future cash flows and specific to the currency of the risk. The risk margin was calculated using the present value of the cost of capital. The cost of capital approach uses (i) projected capital requirements, (ii) multiplied by the risk cost of capital representing the return required for non-hedgeable risk based upon the weighted average cost of capital less investment income and (iii) discounted using the weighted average cost of capital.

Derivative Instruments

The fair values of our foreign currency exchange contracts, as described in Note 7 - "Derivatives and Hedging Instruments" are classified as Level 2. The fair values are based upon prices in active markets for identical contracts.

Level 3 Measurements and Changes in Leveling

Transfers into or out of levels are recorded at their fair values as of the end of the reporting period, consistent with the date of determination of fair value.

Investments

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			Privately-held Equities			Other Investments			Total
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			Privately-held Equities			Other Investments			Total
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

Net realized and unrealized gains related to Level 3 assets in the table above are included in net realized and unrealized (losses) gains in our consolidated statements of earnings.

The securities transferred from Level 2 to Level 3 were transferred due to insufficient market observable inputs for the valuation of the specific assets. The transfers from Level 3 to Level 2 were based upon obtaining market observable information regarding the valuations of the specific assets.

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)
CLO equities	$87.6	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
Privately held equity investments	268.8	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.

Insurance Contracts - Fair Value Option

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

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

The fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses may increase or decrease due to changes in the corporate bond rate, the credit spread for non-performance risk, the risk cost of capital, the weighted average cost of capital and the estimated payment pattern as described below:

•

An increase in the corporate bond rate or credit spread for non-performance risk would result in a decrease in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses. Conversely, a decrease in the corporate bond rate or credit spread for non-performance risk would result in an increase in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses.

•

An increase in the weighted average cost of capital would result in an increase in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses. Conversely, a decrease in the weighted average cost of capital would result in a decrease in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses.


•	An increase in the risk cost of capital would result in an increase in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses. Conversely, a decrease in the risk cost of capital would result in a decrease in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses.

•

The duration of the liability and recoverable is adjusted every period to reflect actual net payments during the period and expected future payments. An acceleration of the estimated payment pattern, a decrease in duration, would result in an increase in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses. Conversely, a deceleration of the estimated payment pattern, an increase in duration, would result in a decrease in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses.

In addition, the estimate of the capital required to support the liabilities is based upon current industry standards for capital adequacy. If the required capital per unit of risk increases, then the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses would increase. Conversely, a decrease in required capital would result in a decrease in the fair value of the liability for losses and LAE and reinsurance balances recoverable on paid and unpaid losses.

Disclosure of Fair Values for Financial Instruments Carried at Cost

Senior Notes

As of December 31, 2019, our 4.50% Senior Notes due 2022 (the "2022 Senior Notes") and our 4.95% Senior Notes due 2029 (the "2029 Senior Notes" and, together with the 2022 Senior Notes, the "Senior Notes") were carried at amortized cost of $348.6 million and $493.6 million, respectively, while the fair value based on observable market pricing from a third party pricing service was $362.5 million and $537.4 million, respectively. The Senior Notes are classified as Level 2.

Insurance Contracts

Disclosure of fair value of amounts relating to insurance contracts is not required, except those for which we elected the fair value option, as described above.

Remaining Assets and Liabilities

Our remaining assets and liabilities were generally carried at cost or amortized cost, which due to their short-term nature approximates fair value as of December 31, 2019 and 2018.

- Definition

The entire disclosure for the fair value of financial instruments (as defined), including financial assets and financial liabilities (collectively, as defined), and the measurements of those instruments as well as disclosures related to the fair value of non-financial assets and liabilities. Such disclosures about the financial instruments, assets, and liabilities would include: (1) the fair value of the required items together with their carrying amounts (as appropriate); (2) for items for which it is not practicable to estimate fair value, disclosure would include: (a) information pertinent to estimating fair value (including, carrying amount, effective interest rate, and maturity, and (b) the reasons why it is not practicable to estimate fair value; (3) significant concentrations of credit risk including: (a) information about the activity, region, or economic characteristics identifying a concentration, (b) the maximum amount of loss the entity is exposed to based on the gross fair value of the related item, (c) policy for requiring collateral or other security and information as to accessing such collateral or security, and (d) the nature and brief description of such collateral or security; (4) quantitative information about market risks and how such risks are managed; (5) for items measured on both a recurring and nonrecurring basis information regarding the inputs used to develop the fair value measurement; and (6) for items presented in the financial statement for which fair value measurement is elected: (a) information necessary to understand the reasons for the election, (b) discussion of the effect of fair value changes on earnings, (c) a description of [similar groups] items for which the election is made and the relation thereof to the balance sheet, the aggregate carrying value of items included in the balance sheet that are not eligible for the election; (7) all other required (as defined) and desired information.

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