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 September 30, 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	$	4,314,006	$	4,314,006	$	—	$	—
Agencies	507,903		—		507,903		—
Municipal	1,629		—		1,629		—
Non-U.S. government	379,154		—		379,154		—
Non-U.S. government-backed corporate	263,170		—		263,170		—
Corporate	3,453,222		—		3,453,222		—
Agency mortgage-backed	1,248,722		—		1,248,722		—
Non-agency mortgage-backed	261,850		—		261,850		—
Commercial mortgage-backed	406,268		—		406,268		—
Asset-backed	550,304		—		550,304		—
Total fixed maturity investments	11,386,228		4,314,006		7,072,222		—
Short term investments	4,116,156		—		4,116,156		—
Equity investments trading	379,422		379,422		—		—
Other investments
Catastrophe bonds	659,466		—		659,466		—
Private equity investments (1)	266,048		—		—		74,210
Senior secured bank loan funds (1)	24,567		—		—		—
Hedge funds (1)	12,028		—		—		—
Total other investments	962,109		—		659,466		74,210
Other assets and (liabilities)
Assumed and ceded (re)insurance contracts (2)	6,219		—		—		6,219
Derivatives (3)	18,565		212		18,353		—
Total other assets and (liabilities)	24,784		212		18,353		6,219
	$	16,868,699	$	4,693,640	$	11,866,197	$	80,429




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.

The Company’s fixed maturity investments are primarily priced using pricing services, such as index providers and pricing vendors, as well as broker quotations. In general, the pricing vendors provide pricing for a high volume of liquid securities that are actively traded. For securities that do not trade on an 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 September 30, 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 (December 31, 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 September 30, 2019, the Company’s agency fixed maturity investments had a weighted average yield to maturity of 2.0% and a weighted average credit quality of AA (December 31, 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 September 30, 2019, the Company’s municipal fixed maturity investments had a weighted average yield to maturity of 3.0% and a weighted average credit quality of AA (December 31, 2018 - 4.8% and A, respectively). The Company’s municipal fixed maturity investments are primarily priced by pricing services. When evaluating these securities, the pricing services gather information regarding the security from third-party sources such as trustees, paying agents or issuers. 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 over widely accepted market benchmarks.

Level 2 - At September 30, 2019, the Company’s non-U.S. government fixed maturity investments had a weighted average yield to maturity of 1.7% and a weighted average credit quality of AAA (December 31, 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 September 30, 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 (December 31, 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 September 30, 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 A (December 31, 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 September 30, 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 4.7 years (December 31, 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 September 30, 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 non-investment grade and a weighted average life of 4.7 years (December 31, 2018 - 4.4%, non-investment grade and 4.7 years, respectively). The Company’s non-agency Alt-A fixed maturity investments held at September 30, 2019 had a weighted average yield to maturity of 3.7%, a weighted average credit quality of non-investment grade and a weighted average life of 6.6 years (December 31, 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 September 30, 2019, the Company’s commercial mortgage-backed fixed maturity investments had a weighted average yield to maturity of 2.5%, a weighted average credit quality of AAA, and a weighted average life of 5.6 years (December 31, 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 September 30, 2019, the Company’s asset-backed fixed maturity investments had a weighted average yield to maturity of 3.4%, a weighted average credit quality of AAA and a weighted average life of 3.3 years (December 31, 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 September 30, 2019, the Company’s short term investments had a weighted average yield to maturity of 1.7% and a weighted average credit quality of AAA (December 31, 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 September 30, 2019	Fair Value (Level 3)			Valuation Technique	Unobservable Inputs	Low		High		Weighted Average or Actual
Other investments
Private equity investment	$	10,455		External valuation model	Indicative pricing	$	—	$	105.12	$	104.55
Private equity investments	63,755			Internal valuation model	Liquidity discount	n/a		n/a		12.5		%
Total other investments	74,210
Other assets and (liabilities)
Assumed and ceded (re)insurance contracts	484			Internal valuation model	Bond price	$	100.32	$	106.08	$	103.49
					Liquidity discount	n/a		n/a		1.3		%
Assumed and ceded (re)insurance contracts	(9,242		)	Internal valuation model	Net undiscounted cash flows	n/a		n/a		$	(11,028	)
					Expected loss ratio	n/a		n/a		34.9		%
					Discount rate	n/a		n/a		1.6		%
Assumed and ceded (re)insurance contracts	14,977			Internal valuation model	Expected loss ratio	n/a		n/a		0.0		%

Total other assets and (liabilities)	6,219
Total other assets and (liabilities) measured at fair value on a recurring basis using Level 3 inputs	$	80,429

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 - July 1, 2019	$	74,810		$	7,942		$	82,752
Total realized and unrealized losses
Included in other income	(592		)	(1,188		)	(1,780		)
Total foreign exchange losses	(8		)	—			(8		)
Purchases	—			(535		)	(535		)
Balance - September 30, 2019	$	74,210		$	6,219		$	80,429



	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	1,790			(1,030		)	760
Total foreign exchange losses	(16		)	—			(16		)
Purchases	17,891			(4,382		)	13,509
Settlements	—			20			20
Amounts acquired (1)	—			19,970			19,970
Balance - September 30, 2019	$	74,210		$	6,219		$	80,429




	Other assets and (liabilities)
Balance - July 1, 2018	$	(2,018	)
Total realized and unrealized gains
Included in other income	1,754
Purchases	(9,668		)
Settlements	983
Balance - September 30, 2018	$	(8,949	)



	Other assets and (liabilities)
Balance - January 1, 2018	$	(2,952	)
Total realized and unrealized gains
Included in other income	2,399
Purchases	(9,379		)
Settlements	983
Balance - September 30, 2018	$	(8,949	)

Level 3 - At September 30, 2019, the Company’s other investments included a $10.5 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 September 30, 2019, the Company’s other investments included $63.8 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. These unobservable inputs in isolation can cause significant increases or decreases in fair value. The discount rates are applied to each of the comparable net tangible book value multiples which are used to determine fair value. The comparable net tangible book value multiples are observable and based on the trading multiples of public industry peers of the underlying entity. Generally, an increase in the liquidity discount rate would result in a decrease in the fair value of this private equity investment.

Level 3 - At September 30, 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 September 30, 2019, the Company had a $9.2 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, would result in an increase in the expected profit and ultimate fair value of these assumed and ceded (re)insurance contracts.

Level 3 - At September 30, 2019, the Company had a $15.0 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.

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:




	September 30, 2019		December 31, 2018
Other investments	$	962,109	$	784,933
Other assets	$	37,820	$	4,968
Other liabilities	$	31,601	$	13,327

Included in net investment income for the three and nine months ended September 30, 2019 were net unrealized gains of $5.1 million and net unrealized gains of $7.3 million, respectively, related to the changes in fair value of other investments (2018 – net unrealized gains of $9.1 million and $17.8 million, respectively). Included in other income (loss) for the three and nine months ended September 30, 2019 were net unrealized gains of $Nil and $Nil, respectively, related to the changes in the fair value of other assets and liabilities (2018 - net unrealized gains of $Nil and $Nil, respectively).

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

At September 30, 2019

Fair Value

Unfunded
Commitments

Redemption Frequency

Redemption
Notice Period (Minimum Days)

Redemption
Notice Period (Maximum Days)

Private equity investments

191,838

359,470

See below

Senior secured bank loan funds

24,567

7,400

See below

Hedge funds

12,028

—

See below

Total other investments measured using net asset valuations

228,433

366,870

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 September 30, 2019, the Company had $24.6 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.