The use of fair value to measure certain assets and liabilities with resulting unrealized gains or losses is pervasive within the Company’s consolidated financial statements. Fair value is defined under accounting guidance currently applicable to the Company to be the price that would be received upon the sale of an asset or paid to transfer a liability in an orderly transaction between open market participants at the measurement date. The Company recognizes the change in unrealized gains and losses arising from changes in fair value in its consolidated statements of operations.

FASB ASC Topic Fair Value Measurements and Disclosures prescribes a fair value hierarchy that prioritizes the inputs to the respective valuation techniques used to measure fair value. The hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets or liabilities (Level 1) and the lowest priority to valuation techniques that use at least one significant input that is unobservable (Level 3). The three levels of the fair value hierarchy are described below:

In certain cases, the inputs used to measure fair value may fall into different levels of the fair value hierarchy. In such cases, the level in the fair value hierarchy within which the fair value measurement in its entirety falls has been determined based on the lowest level input that is significant to the fair value measurement of the asset or liability. The Company’s assessment of the significance of a particular input to the fair value measurement in its entirety requires judgment, and the Company considers factors specific to the asset or liability.

In order to determine if a market is active or inactive for a security, the Company considers a number of factors, including, but not limited to, the spread between what a seller is asking for a security and what a buyer is bidding for the same security, the volume of trading activity for the security in question, the price of the security compared to its par value (for fixed maturity investments), and other factors that may be indicative of market activity.

Below is a summary of the assets and liabilities that are measured at fair value on a recurring basis and also represents the carrying amount on the Company’s consolidated balance sheets:




At December 31, 2019	Total		Quoted Prices in Active Markets for Identical Assets (Level 1)			Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Fixed maturity investments
U.S. treasuries	$	4,467,345	$	4,467,345		$	—	$	—
Agencies	343,031		—			343,031		—
Non-U.S. government	497,392		—			497,392		—
Non-U.S. government-backed corporate	321,356		—			321,356		—
Corporate	3,075,660		—			3,075,660		—
Agency mortgage-backed	1,148,499		—			1,148,499		—
Non-agency mortgage-backed	294,604		—			294,604		—
Commercial mortgage-backed	468,698		—			468,698		—
Asset-backed	555,070		—			555,070		—
Total fixed maturity investments	11,171,655		4,467,345			6,704,310		—
Short term investments	4,566,277		—			4,566,277		—
Equity investments trading	436,931		436,931			—		—
Other investments
Catastrophe bonds	781,641		—			781,641		—
Private equity investments (1)	271,047		—			—		74,634
Senior secured bank loan funds (1)	22,598		—			—		—
Hedge funds (1)	12,091		—			—		—
Total other investments	1,087,377		—			781,641		74,634
Other assets and (liabilities)
Assumed and ceded (re)insurance contracts (2)	4,731		—			—		4,731
Derivatives (3)	16,937		(1,020		)	17,957		—
Total other assets and (liabilities)	21,668		(1,020		)	17,957		4,731
	$	17,283,908	$	4,903,256		$	12,070,185	$	79,365




At December 31, 2018	Total			Quoted Prices in Active Markets for Identical Assets (Level 1)		Significant Other Observable Inputs (Level 2)		Significant Unobservable Inputs (Level 3)
Fixed maturity investments
U.S. treasuries	$	3,331,411		$	3,331,411	$	—	$	—
Agencies	174,883			—		174,883		—
Municipal	6,854			—		6,854		—
Non-U.S. government	279,818			—		279,818		—
Non-U.S. government-backed corporate	160,063			—		160,063		—
Corporate	2,450,244			—		2,450,244		—
Agency mortgage-backed	817,880			—		817,880		—
Non-agency mortgage-backed	278,680			—		278,680		—
Commercial mortgage-backed	282,294			—		282,294		—
Asset-backed	306,743			—		306,743		—
Total fixed maturity investments	8,088,870			3,331,411		4,757,459		—
Short term investments	2,586,520			—		2,586,520		—
Equity investments trading	310,252			310,252		—		—
Other investments
Catastrophe bonds	516,571			—		516,571		—
Private equity investments (1)	242,647			—		—		54,545
Senior secured bank loan funds (1)	14,482			—		—		—
Hedge funds (1)	11,233			—		—		—
Total other investments	784,933			—		516,571		54,545
Other assets and (liabilities)
Assumed and ceded (re)insurance contracts (2)	(8,359		)	—		—		(8,359		)
Derivatives (3)	12,399			484		11,915		—
Total other assets and (liabilities)	4,040			484		11,915		(8,359		)
	$	11,774,615		$	3,642,147	$	7,872,465	$	46,186

Fixed maturity investments included in Level 1 consist of the Company’s investments in U.S. treasuries. Fixed maturity investments included in Level 2 are agencies, municipal, non-U.S. government, non-U.S. government-backed corporate, corporate, agency mortgage-backed, non-agency mortgage-backed, commercial mortgage-backed and asset-backed.

exchange, the pricing services generally utilize market data and other observable inputs in matrix pricing models to determine month end prices. Observable inputs include benchmark yields, reported trades, broker-dealer quotes, issuer spreads, bids, offers, reference data and industry and economic events. Index pricing generally relies on market traders as the primary source for pricing; however, models are also utilized to provide prices for all index eligible securities. The models use a variety of observable inputs such as benchmark yields, transactional data, dealer runs, broker-dealer quotes and corporate actions. Prices are generally verified using third-party data. Securities which are priced by an index provider are generally included in the index.

In general, broker-dealers value securities through their trading desks based on observable inputs. The methodologies include mapping securities based on trade data, bids or offers, observed spreads, and performance on newly issued securities. Broker-dealers also determine valuations by observing secondary trading of similar securities. Prices obtained from broker quotations are considered non-binding, however they are based on observable inputs and by observing secondary trading of similar securities obtained from active, non-distressed markets.

Level 1 - At December 31, 2019, the Company’s U.S. treasuries fixed maturity investments were primarily priced by pricing services and had a weighted average yield to maturity of 1.7% and a weighted average credit quality of AA (2018 - 2.5% and AA, respectively). When pricing these securities, the pricing services utilize daily data from many real time market sources, including active broker-dealers. Certain data sources are regularly reviewed for accuracy to attempt to ensure the most reliable price source is used for each issue and maturity date.

Level 2 - At December 31, 2019, the Company’s agency fixed maturity investments had a weighted average yield to maturity of 2.1% and a weighted average credit quality of AA (2018 - 3.0% and AA, respectively). The issuers of the Company’s agency fixed maturity investments primarily consist of the Federal National Mortgage Association, the Federal Home Loan Mortgage Corporation and other agencies. Fixed maturity investments included in agencies are primarily priced by pricing services. When evaluating these securities, the pricing services gather information from market sources and integrate other observations from markets and sector news. Evaluations are updated by obtaining broker-dealer quotes and other market information including actual trade volumes, when available. The fair value of each security is individually computed using analytical models which incorporate option adjusted spreads and other daily interest rate data.

Level 2 - At December 31, 2019, the Company did not hold any material positions in municipal fixed maturity investments. At December 31, 2018, the Company’s municipal fixed maturity investments had a weighted average yield to maturity of 4.8% and a weighted average credit quality of A. The Company’s municipal fixed maturity investments were primarily priced by pricing services. When evaluating these securities, the pricing services gathered information regarding the security from third-party sources such as trustees, paying agents or issuers. Evaluations were updated by obtaining broker-dealer quotes and other market information including actual trade volumes, when available. The pricing services also considered the specific terms and conditions of the securities, including any specific features which may have influenced risk. In certain instances, securities were individually evaluated using a spread over widely accepted market benchmarks.

Level 2 - At December 31, 2019, the Company’s non-U.S. government fixed maturity investments had a weighted average yield to maturity of 1.6% and a weighted average credit quality of AA (2018 - 2.7% and AAA, respectively). The issuers of securities in this sector are non-U.S. governments and their respective agencies as well as supranational organizations. Securities held in these sectors are primarily priced by

pricing services that employ proprietary discounted cash flow models to value the securities. Key quantitative inputs for these models are daily observed benchmark curves for treasury, swap and high issuance credits. The pricing services then apply a credit spread for each security which is developed by in-depth and real time market analysis. For securities in which trade volume is low, the pricing services utilize data from more frequently traded securities with similar attributes. These models may also be supplemented by daily market and credit research for international markets.

Level 2 - At December 31, 2019, the Company’s non-U.S. government-backed corporate fixed maturity investments had a weighted average yield to maturity of 2.0% and a weighted average credit quality of AA (2018 - 2.8% and AA, respectively). Non-U.S. government-backed corporate fixed maturity investments are primarily priced by pricing services that employ proprietary discounted cash flow models to value the securities. Key quantitative inputs for these models are daily observed benchmark curves for treasury, swap and high issuance credits. The pricing services then apply a credit spread to the respective curve for each security which is developed by in-depth and real time market analysis. For securities in which trade volume is low, the pricing services utilize data from more frequently traded securities with similar attributes. These models may also be supplemented by daily market and credit research for international markets.

Level 2 - At December 31, 2019, the Company’s corporate fixed maturity investments principally consisted of U.S. and international corporations and had a weighted average yield to maturity of 3.0% and a weighted average credit quality of BBB (2018 - 4.9% and BBB, respectively). The Company’s corporate fixed maturity investments are primarily priced by pricing services. When evaluating these securities, the pricing services gather information from market sources regarding the issuer of the security and obtain credit data, as well as other observations, from markets and sector news. Evaluations are updated by obtaining broker-dealer quotes and other market information including actual trade volumes, when available. The pricing services also consider the specific terms and conditions of the securities, including any specific features which may influence risk. In certain instances, securities are individually evaluated using a spread which is added to the U.S. treasury curve or a security specific swap curve as appropriate.

Level 2 - At December 31, 2019, the Company’s agency mortgage-backed fixed maturity investments included agency residential mortgage-backed securities with a weighted average yield to maturity of 2.5%, a weighted average credit quality of AA and a weighted average life of 4.9 years (2018 - 3.5%, AA and 7.1 years, respectively). The Company’s agency mortgage-backed fixed maturity investments are primarily priced by pricing services using a mortgage pool specific model which utilizes daily inputs from the active to-be-announced market which is very liquid, as well as the U.S. treasury market. The model also utilizes additional information, such as the weighted average maturity, weighted average coupon and other available pool level data which is provided by the sponsoring agency. Valuations are also corroborated with daily active market quotes.

Level 2 - The Company’s non-agency mortgage-backed fixed maturity investments include non-agency prime, non-agency Alt-A and other non-agency residential mortgage-backed securities. At December 31, 2019, the Company’s non-agency prime residential mortgage-backed fixed maturity investments had a weighted average yield to maturity of 3.3%, a weighted average credit quality of BBB, and a weighted average life of 4.8 years (2018 - 4.4%, non-investment grade and 4.7 years, respectively). The Company’s non-agency Alt-A fixed maturity investments held at December 31, 2019 had a weighted average yield to maturity of 3.8%, a weighted average credit quality of non-investment grade and a weighted average life of 6.3 years (2018 - 4.7%, non-investment grade and 6.3 years, respectively). Securities held in these sectors are primarily priced by pricing services using an option adjusted spread model or other relevant models, which principally utilize inputs including benchmark yields, available trade information or broker quotes, and issuer spreads. The pricing services also review collateral prepayment speeds, loss severity and delinquencies among other collateral performance indicators for the securities valuation, when applicable.

Level 2 - At December 31, 2019, the Company’s commercial mortgage-backed fixed maturity investments had a weighted average yield to maturity of 2.6%, a weighted average credit quality of AAA, and a weighted average life of 5.7 years (2018 - 3.6%, AAA and 5.0 years, respectively). Securities held in these sectors are primarily priced by pricing services. The pricing services apply dealer quotes and other available trade information such as bids and offers, prepayment speeds which may be adjusted for the underlying collateral or current price data, the U.S. treasury curve and swap curve as well as cash settlement. The pricing services discount the expected cash flows for each security held in this sector using a spread adjusted benchmark yield based on the characteristics of the security.

Level 2 - At December 31, 2019, the Company’s asset-backed fixed maturity investments had a weighted average yield to maturity of 3.3%, a weighted average credit quality of AAA and a weighted average life of 3.2 years (2018 - 4.3%, AAA and 3.2 years, respectively). The underlying collateral for the Company’s asset-backed fixed maturity investments primarily consists of bank loans, student loans, credit card receivables, auto loans and other receivables. Securities held in these sectors are primarily priced by pricing services. The pricing services apply dealer quotes and other available trade information such as bids and offers, prepayment speeds which may be adjusted for the underlying collateral or current price data, the U.S. treasury curve and swap curve as well as cash settlement. The pricing services determine the expected cash flows for each security held in this sector using historical prepayment and default projections for the underlying collateral and current market data. In addition, a spread is applied to the relevant benchmark and used to discount the cash flows noted above to determine the fair value of the securities held in this sector.

Level 2 - At December 31, 2019, the Company’s short term investments had a weighted average yield to maturity of 1.6% and a weighted average credit quality of AAA (2018 - 2.1% and AAA, respectively). The fair value of the Company’s portfolio of short term investments is generally determined using amortized cost which approximates fair value and, in certain cases, in a manner similar to the Company’s fixed maturity investments noted above.

Level 1 - The fair value of the Company’s portfolio of equity investments, classified as trading is primarily priced by pricing services, reflecting the closing price quoted for the final trading day of the period. When pricing these securities, the pricing services utilize daily data from many real time market sources, including applicable securities exchanges. All data sources are regularly reviewed for accuracy to attempt to ensure the most reliable price source was used for each security.

Level 1 and Level 2 - Other assets and liabilities include certain derivatives entered into by the Company. The fair value of these transactions includes certain exchange traded futures contracts which are considered Level 1, and foreign currency contracts and certain credit derivatives, determined using standard industry valuation models and considered Level 2, as the inputs to the valuation model are based on observable market inputs. For credit derivatives, these inputs include credit spreads, credit ratings of the underlying referenced security, the risk free rate and the contract term. For foreign currency contracts, these inputs include spot rates and interest rate curves.

Below is a summary of quantitative information regarding the significant unobservable inputs (Level 3) used in determining the fair value of assets and liabilities measured at fair value on a recurring basis:




At December 31, 2019	Fair Value (Level 3)			Valuation Technique	Unobservable Inputs	Low			High			Weighted Average or Actual

Other investments
Private equity investment	$	10,327		External valuation model	Manager pricing	$	103.20		$	103.77		$	103.20
Private equity investments	64,307			Internal valuation model	Discount rate	8.0		%	10.0		%	9.0		%
					Liquidity discount	n/a			n/a			15.0		%
Total other investments	74,634
Other assets and (liabilities)
Assumed and ceded (re)insurance contracts	501			Internal valuation model	Bond price	$	100.29		$	106.26		$	103.58
					Liquidity discount	n/a			n/a			1.3		%
Assumed and ceded (re)insurance contracts	(8,767		)	Internal valuation model	Net undiscounted cash flows	n/a			n/a			$	(11,179	)
					Expected loss ratio	n/a			n/a			33.1		%
					Discount rate	n/a			n/a			1.7		%
Assumed and ceded (re)insurance contracts	12,997			Internal valuation model	Expected loss ratio	n/a			n/a			0.0		%
Total other assets and (liabilities)	4,731
Total other assets and (liabilities) measured at fair value on a recurring basis using Level 3 inputs	$	79,365

Below is a reconciliation of the beginning and ending balances, for the periods shown, of assets and liabilities measured at fair value on a recurring basis using Level 3 inputs. Interest and dividend income are included in net investment income and are excluded from the reconciliation.




	Other investments		Other assets and (liabilities)			Total
Balance - January 1, 2019	$	54,545	$	(8,359	)	$	46,186
Total realized and unrealized gains (losses)
Included in other income	2,126		(2,347		)	(221		)
Total foreign exchange gains	5		—			5
Purchases	17,958		(4,553		)	13,405
Settlements	—		20			20
Amounts acquired (1)	—		19,970			19,970
Balance - December 31, 2019	$	74,634	$	4,731		$	79,365




	Other investments		Other assets and (liabilities)			Total
Balance - January 1, 2018	$	—	$	(2,952	)	$	(2,952	)
Total realized and unrealized gains
Included in other income	—		2,901			2,901
Purchases	54,545		(9,291		)	45,254
Settlements	—		983			983
Balance - December 31, 2018	$	54,545	$	(8,359	)	$	46,186

Level 3 - At December 31, 2019, the Company’s other investments included a $10.3 million private equity investment which is recorded at fair value, with the fair value obtained through the receipt of an indicative pricing obtained from the insurance manager of the security. The Company considers the price obtained to be unobservable, as there is little, if any, market activity for this security. This unobservable input in isolation can cause significant increases or decreases in fair value. Generally, an increase in the indicative pricing would result in an increase in the fair value of this private equity investment.

Level 3 - At December 31, 2019, the Company’s other investments included $64.3 million of private equity investments which are recorded at fair value, with the fair value obtained through the use of internal valuation models. The Company measured the fair value of these investments using multiples of net tangible book value of the underlying entity. The significant unobservable inputs used in the fair value measurement of these investments are liquidity discount rates applied to each of the net tangible book value multiples used in the internal valuation models, and discount rates applied to the expected cash flows of the underlying entity in various scenarios. These unobservable inputs in isolation can cause significant increases or decreases in fair value. Generally, an increase in the liquidity discount rate or discount rates would result in a decrease in the fair value of these private equity investments.

Level 3 - At December 31, 2019, the Company had a $0.5 million net asset related to an assumed reinsurance contract accounted for at fair value, with the fair value obtained through the use of an internal valuation model. The inputs to the internal valuation model are principally based on indicative pricing obtained from independent brokers and pricing vendors for similarly structured marketable securities. The most significant unobservable inputs include prices for similar marketable securities and a liquidity premium. The Company considers the prices for similar securities to be unobservable, as there is little, if any market activity for these similar assets. In addition, the Company has estimated a liquidity premium that would be required if the Company attempted to effectively exit its position by executing a short sale of these securities. Generally, an increase in the prices for similar marketable securities or a decrease in the liquidity premium would result in an increase in the expected profit and ultimate fair value of this assumed reinsurance contract.

Level 3 - At December 31, 2019, the Company had a $8.8 million net liability related to assumed and ceded (re)insurance contracts accounted for at fair value, with the fair value obtained through the use of an internal valuation model. The inputs to the internal valuation model are principally based on proprietary data as observable market inputs are generally not available. The most significant unobservable inputs include the assumed and ceded expected net cash flows related to the contracts, including the expected premium, acquisition expenses and losses; the expected loss ratio and the relevant discount rate used to present value the net cash flows. The contract period and acquisition expense ratio are considered an observable input as each is defined in the contract. Generally, an increase in the net expected cash flows and expected term of the contract and a decrease in the discount rate, expected loss ratio or acquisition expense ratio,

Level 3 - At December 31, 2019, the Company had a $13.0 million net asset related to assumed and ceded (re)insurance contracts accounted for at fair value, with the fair value obtained through the use of internal valuation models. The inputs to the models are primarily based on the unexpired period of risk and an evaluation of the probability of loss. The fair value of the contracts are sensitive to loss-triggering events. In the event of a loss, the Company would adjust the fair value of the contract to account for a recovery or liability in accordance with the contract terms and the estimate of exposure under the contract. The inputs for the contracts are based on management’s evaluation and are unobservable.

The Company uses various financial instruments in the normal course of its business. The Company’s insurance contracts are excluded from the fair value of financial instruments accounting guidance, unless the Company elects the fair value option, and therefore, are not included in the amounts discussed herein. The carrying values of cash and cash equivalents, accrued investment income, receivables for investments sold, certain other assets, payables for investments purchased, certain other liabilities, and other financial instruments not included herein approximated their fair values.

The fair value of the Company’s debt obligations is determined using indicative market pricing obtained from third-party service providers, which the Company considers Level 2 in the fair value hierarchy. There have been no changes during the period in the Company’s valuation technique used to determine the fair value of the Company’s debt obligations. Refer to “Note 9. Debt and Credit Facilities” for additional information related to the Company’s debt obligations.

The Company has elected to account for certain financial assets and financial liabilities at fair value using the guidance under FASB ASC Topic Financial Instruments as the Company believes it represents the most meaningful measurement basis for these assets and liabilities. Below is a summary of the balances the Company has elected to account for at fair value:




	2019		2018
Other investments	$	1,087,377	$	784,933
Other assets	$	32,944	$	4,968
Other liabilities	$	28,213	$	13,327

Included in net investment income for 2019 was net unrealized gains of $12.2 million related to the changes in fair value of other investments (2018 – losses of $8.3 million, 2017 – gains of $24.7 million). Included in other income for 2019 were net unrealized gains of $Nil related to the changes in the fair value of other assets and liabilities (2018 – $Nil, 2017 – $Nil).

The table below shows the Company’s portfolio of other investments measured using net asset valuations as a practical expedient:

At December 31, 2019

Fair Value

Unfunded
Commitments

Redemption Frequency

Redemption
Notice Period (Minimum Days)

Redemption
Notice Period (Maximum Days)

Private equity investments

196,413

351,028

See below

Senior secured bank loan funds

22,598

8,702

See below

Hedge funds

12,091

—

See below

Total other investments measured using net asset valuations

231,102

359,730

Private equity investments – A significant portion of the Company’s investments in private equity investments include alternative asset limited partnerships (or similar corporate structures) that invest in certain private equity asset classes including U.S. and global leveraged buyouts, mezzanine investments, distressed securities, real estate, and oil, gas and power. The Company generally has no right to redeem its interest in any of these private equity investments in advance of dissolution of the applicable private equity investment. Instead, the nature of these investments is that distributions are received by the Company in connection with the liquidation of the underlying assets of the respective private equity investment. It is estimated that the majority of the underlying assets of the limited partnerships would liquidate over 7 to 10 years from inception of the respective limited partnership.

Senior secured bank loan funds – At December 31, 2019 the Company had $22.6 million invested in closed end funds which invest primarily in loans. The Company has no right to redeem its investment in these funds. It is estimated that the majority of the underlying assets in these closed end funds would begin to liquidate over 4 to 5 years from inception of the applicable fund.