3. Fair Value

(a) Fair Value of Financial Instrument Assets

The fair value hierarchy prioritizes the inputs to valuation techniques used to measure fair value by maximizing the use of observable inputs and minimizing the use of unobservable inputs by requiring that the most observable inputs be used when available. Observable inputs are inputs that market participants would use in pricing an asset or liability based on market data obtained from sources independent of the Company. Unobservable inputs are inputs that reflect the Company’s assumptions about what market participants would use in pricing the asset or liability based on the best information available in the circumstances. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement.

The Company determines the appropriate level in the hierarchy for each financial instrument that it measures at fair value. In determining fair value, the Company uses various valuation approaches, including market, income and cost approaches. The hierarchy is broken down into three levels based on the observability of inputs as follows:


•	Level 1 inputs—Unadjusted, quoted prices in active markets for identical assets or liabilities that the Company has the ability to access.

The Company’s financial instruments that it measures at fair value using Level 1 inputs generally include: equities listed on a major exchange and exchange traded derivatives, including futures that are actively traded.


•	Level 2 inputs—Quoted prices in active markets for similar assets or liabilities, quoted prices for identical or similar assets or liabilities in inactive markets and significant directly or indirectly observable inputs, other than quoted prices, used in industry accepted models.

The Company’s financial instruments that it measures at fair value using Level 2 inputs generally include: U.S. government issued bonds; U.S. government sponsored enterprises bonds; U.S. state, territory and municipal entities bonds; non-U.S. sovereign government, supranational and government related bonds; investment grade and high yield corporate bonds; asset-backed securities; mortgage-backed securities; short-term investments; certain common and preferred equities; notes and loans receivable; foreign exchange forward contracts and over-the-counter derivatives such as foreign currency option contracts, interest rate swaps and TBAs.


•	Level 3 inputs—Unobservable inputs.

The Company’s financial instruments that it measures at fair value using Level 3 inputs generally include: inactively traded fixed maturities including U.S. state, territory and municipal bonds; special purpose financing asset-backed bonds; unlisted or private equities; certain other mutual fund or exchange traded fund equities; privately placed corporate loans, notes and loan receivables and notes securitizations included in other invested assets; and certain other derivatives, including inactively traded weather derivatives, longevity insurance-linked securities and total return swaps included in other invested assets.

The Company’s financial instruments measured at fair value include investments and the segregated investment portfolio underlying the funds held–directly managed account (see Notes 5 and 6). At December 31, 2017 and 2016, the Company’s financial instruments measured at fair value were classified between Levels 1, 2 and 3 as follows (in thousands of U.S. dollars):



December 31, 2017	Quoted prices in active markets for identical assets (Level 1)		Significant other observable inputs (Level 2)			Significant unobservable inputs (Level 3)			Total
Fixed maturities
U.S. government and government sponsored enterprises	$	—	$	2,205,964		$	—		$	2,205,964
U.S. states, territories and municipalities	—		561,505			128,806			690,311
Non-U.S. sovereign government, supranational and government related	—		1,750,770			—			1,750,770
Corporate bonds	—		6,128,636			—			6,128,636
Asset-backed securities	—		30,965			20,738			51,703
Residential mortgage-backed securities	—		1,822,725			—			1,822,725
Other mortgage-backed securities	—		4,750			—			4,750
Fixed maturities	$	—	$	12,505,315		$	149,544		$	12,654,859
Short-term investments	$	—	$	4,400		$	—		$	4,400
Equities
Finance	$	11,115	$	1		$	21,926		$	33,042
Industrials	16,534		—			—			16,534
Technology	1,990		—			10,961			12,951
Insurance	—		7,558			—			7,558
Communications	3,215		—			—			3,215
Consumer cyclical	2,170		—			—			2,170
Consumer noncyclical	897		—			—			897
Other	3,493		—			—			3,493
Mutual funds and exchange traded funds	—		—			558,736			558,736
Equities	$	39,414	$	7,559		$	591,623		$	638,596
Other invested assets
Derivative assets
Foreign exchange forward contracts	$	—	$	8,559		$	—		$	8,559
Futures contracts	3,367		—			—			3,367
Insurance-linked securities	—		—			11,985			11,985
Total return swaps	—		—			2,505			2,505
TBAs	—		391			—			391
Other
Corporate loans	—		—			205,331			205,331
Notes and loan receivables and notes securitization	—		3,425			108,563			111,988
Private equities	—		—			331,932			331,932
Derivative liabilities
Foreign exchange forward contracts	—		(20,328		)	—			(20,328		)
Total return swaps	—		—			(3,269		)	(3,269		)
Interest rate swaps	—		(12,298		)	—			(12,298		)
TBAs	—		(591		)	—			(591		)
Other invested assets	$	3,367	$	(20,842	)	$	657,047		$	639,572
Funds held–directly managed
U.S. government and government sponsored enterprises	$	—	$	161,023		$	—		$	161,023
Non-U.S. sovereign government, supranational and government related	—		95,812			—			95,812
Corporate bonds	—		41,090			—			41,090
Short-term investments	—		453			—			453
Other invested assets	—		—			2,067			2,067
Funds held–directly managed	$	—	$	298,378		$	2,067		$	300,445
Total	$	42,781	$	12,794,810		$	1,400,281		$	14,237,872



December 31, 2016	Quoted prices in active markets for identical assets (Level 1)		Significant other observable inputs (Level 2)			Significant unobservable inputs (Level 3)			Total
Fixed maturities
U.S. government and government sponsored enterprises	$	—	$	3,541,433		$	—		$	3,541,433
U.S. states, territories and municipalities	—		560,728			123,827			684,555
Non-U.S. sovereign government, supranational and government related	—		1,136,034			—			1,136,034
Corporate	—		5,705,522			—			5,705,522
Asset-backed securities	—		24,709			99,351			124,060
Residential mortgage-backed securities	—		2,240,897			—			2,240,897
Fixed maturities	$	—	$	13,209,323		$	223,178		$	13,432,501
Short-term investments	$	—	$	21,697		$	—		$	21,697
Equities
Finance	$	973	$	4,960		$	20,934		$	26,867
Technology	—		—			9,800			9,800
Insurance	—		1,800			—			1,800
Consumer noncyclical	6		—			—			6
Mutual funds and exchange traded funds	—		—			153			153
Equities	$	979	$	6,760		$	30,887		$	38,626
Other invested assets
Derivative assets
Foreign exchange forward contracts	$	—	$	5,263		$	—		$	5,263
Insurance-linked securities	—		—			10,130			10,130
Total return swaps	—		—			1,989			1,989
TBAs	—		1,369			—			1,369
Other
Notes and loan receivables and notes securitization	—		1,500			141,693			143,193
Private equities	—		—			305,729			305,729
Derivative liabilities
Foreign exchange forward contracts	—		(7,142		)	—			(7,142		)
Insurance-linked securities	—		—			(97		)	(97		)
Total return swaps	—		—			(3,217		)	(3,217		)
Interest rate swaps	—		(13,403		)	—			(13,403		)
TBAs	—		(185		)	—			(185		)
Other invested assets	$	—	$	(12,598	)	$	456,227		$	443,629
Funds held–directly managed
U.S. government and government sponsored enterprises	$	—	$	171,975		$	—		$	171,975
Non-U.S. sovereign government, supranational and government related	—		104,512			—			104,512
Corporate bonds	—		71,365			—			71,365
Short-term investments	—		1,603			—			1,603
Other invested assets	—		—			4,540			4,540
Funds held–directly managed	$	—	$	349,455		$	4,540		$	353,995
Total	$	979	$	13,574,637		$	714,832		$	14,290,448

The increase in equities at December 31, 2017 compared to December 31, 2016 was primarily due to a $500 million investment in two Exor managed public equity funds (see Note 19). The increase in other assets at December 31, 2017 compared to December 31, 2016 was primarily due to a $207 million investment in privately placed corporate loans.

At December 31, 2017 and 2016, the aggregate carrying amounts of items included in Other invested assets that the Company did not measure at fair value were $746 million and $632 million, respectively, which related to the Company’s investments that are accounted for using the cost method of accounting or equity method of accounting.

In addition to the investments underlying the funds held–directly managed account held at fair value of $300 million and $354 million at December 31, 2017 and 2016, respectively, the funds held–directly managed account also included cash and cash equivalents, carried at fair value, of $74 million and $76 million, respectively, and accrued investment income of $3 million and $4 million, respectively. At December 31, 2017 and 2016, the aggregate carrying amounts of items included in the funds held–directly managed account that the Company did not measure at fair value were $47 million and $77 million, respectively, which primarily related to other assets and liabilities held by Colisée Re related to the underlying business, which are carried at cost (see Note 5).

At December 31, 2017 and 2016, substantially all of the accrued investment income in the Consolidated Balance Sheets relate to the Company’s investments and the investments underlying the funds held–directly managed account for which the fair value option was elected.

During the years ended December 31, 2017 and 2016, there were no transfers between Level 1 and Level 2.

Disclosures about the fair value of financial instruments that the Company does not measure at fair value exclude insurance contracts and certain other financial instruments. At December 31, 2017 and 2016, the fair values of financial instrument assets recorded in the Consolidated Balance Sheets not described above approximate their carrying values.

The reconciliations of the beginning and ending balances for all financial instruments measured at fair value using Level 3 inputs for the years ended December 31, 2017 and 2016, were as follows (in thousands of U.S. dollars):



For the year ended December 31, 2017	Balance at beginning of year		Realized and unrealized investment gains (losses) included in net income			Purchases and issuances ⁽¹⁾		Settlements and sales ⁽²⁾			Net transfers into (out of) Level 3		Balance at end of year		Change in unrealized investment gains (losses) relating to assets held at end of year
Fixed maturities
U.S. states, territories and municipalities	$	123,827	$	5,804		$	—	$	(825	)	$	—	$	128,806	$	5,804
Asset-backed securities	99,351		3,300			1,360		(83,273		)	—		20,738		1,316
Fixed maturities	$	223,178	$	9,104		$	1,360	$	(84,098	)	$	—	$	149,544	$	7,120
Equities
Finance	$	20,934	$	992		$	—	$	—		$	—	$	21,926	$	992
Technology	9,800		1,611			—		(450		)	—		10,961		1,611
Mutual funds and exchange traded funds	153		51,476			507,250		(143		)	—		558,736		51,486
Equities	$	30,887	$	54,079		$	507,250	$	(593	)	$	—	$	591,623	$	54,089
Other invested assets
Derivatives, net	$	8,805	$	5,977		$	1,793	$	(5,354	)	$	—	$	11,221	$	3,231
Corporate loans	—		(709		)	206,700		(660		)	—		205,331		(695		)
Notes and loan receivables and notes securitization	141,693		2,744			2,040		(37,914		)	—		108,563		6,977
Private equities	305,729		29,942			17,572		(21,311		)	—		331,932		27,533
Other invested assets	$	456,227	$	37,954		$	228,105	$	(65,239	)	$	—	$	657,047	$	37,046
Funds held–directly managed	$	4,540	$	(516	)	$	495	$	(2,452	)	$	—	$	2,067	$	(629	)
Total	$	714,832	$	100,621		$	737,210	$	(152,382	)	$	—	$	1,400,281	$	97,626


(1)	Purchases and issuances of derivatives include issuances of $2 million.


(2)	Settlements and sales of equities include sales of $1 million.



For the year ended December 31, 2016	Balance at beginning of year		Realized and unrealized investment (losses) gains included in net income			Purchases and issuances ⁽¹⁾		Settlements and sales ⁽²⁾			Net transfers into (out of) Level 3		Balance at end of year		Change in unrealized investment (losses) gains relating to assets held at end of year
Fixed maturities
U.S. states, territories and municipalities	$	138,847	$	(14,240	)	$	—	$	(780	)	$	—	$	123,827	$	(14,240	)
Asset-backed securities	369,699		21			191,048		(461,417		)	—		99,351		(4,628		)
Fixed maturities	$	508,546	$	(14,219	)	$	191,048	$	(462,197	)	$	—	$	223,178	$	(18,868	)
Equities
Finance	$	22,760	$	3,438		$	—	$	(5,264	)	$	—	$	20,934	$	3,211
Technology	8,207		1,143			450		—			—		9,800		1,143
Communications	1,985		209			—		(2,194		)	—		—		55
Mutual funds and exchange traded funds	4,604		(242		)	—		(4,209		)	—		153		14
Equities	$	37,556	$	4,548		$	450	$	(11,667	)	$	—	$	30,887	$	4,423
Other invested assets
Derivatives, net	$	5,351	$	(3,314	)	$	2,256	$	4,512		$	—	$	8,805	$	(1,772	)
Notes and loan receivables and notes securitization	125,922		2,599			71,828		(58,656		)	—		141,693		2,278
Annuities and residuals	8,436		262			—		(8,698		)	—		—		—
Private equities	71,298		6,764			236,022		(8,355		)	—		305,729		2,827
Other invested assets	$	211,007	$	6,311		$	310,106	$	(71,197	)	$	—	$	456,227	$	3,333
Funds held–directly managed	$	10,146	$	1,698		$	1,011	$	(8,315	)	$	—	$	4,540	$	1,678
Total	$	767,255	$	(1,662	)	$	502,615	$	(553,376	)	$	—	$	714,832	$	(9,434	)


(1)	There were no issuances included in the purchases and issuances amounts above.


(2)	Settlements and sales of fixed maturities, equities, other invested assets and funds held–directly managed include sales of $276 million, $12 million, $43 million and $8 million, respectively.

The significant unobservable inputs used in the valuation of financial instruments measured at fair value using Level 3 inputs at December 31, 2017 and 2016 were as follows (fair value in thousands of U.S. dollars):



December 31, 2017	Fair value			Valuation techniques	Unobservable inputs	Range (Weighted average)
Fixed maturities
U.S. states, territories and municipalities	$	128,806		Discounted cash flow	Credit spreads	0.2% – 10.2% (4.7%)
Asset-backed securities	20,738			Discounted cash flow	Credit spreads	4.7% (4.7%)
Equities
Finance	21,926			Weighted market comparables	Net income multiple	16.7 (16.7)
				Weighted market comparables	Tangible book value multiple	2.0 (2.0)
					Liquidity discount	25.0% (25.0%)
					Comparable return	4.1% (4.1%)
Technology	10,961			Reported market value	Tangible book value multiple	100.0% (100.0%)
Other invested assets
Total return swaps, net	(764		)	Discounted cash flow	Credit spreads	2.4% – 30.8% (18.5%)
Insurance-linked securities – longevity swaps	11,962			Discounted cash flow	Credit spreads	1.7% (1.7%)
Notes and loan receivables	102,907			Discounted cash flow	Credit spreads	3.9% – 39.3% (6.1%)
Notes and loan receivables	4,265			Discounted cash flow	Credit spreads	17.5% (17.5%)
Notes and loan receivables				Discounted cash flow	Gross revenue/fair value	1.1 (1.1)
Notes securitization	1,391			Discounted cash flow	Credit spreads	1.5% (1.5%)
Private equity – direct	3,011			Discounted cash flow and market multiples	Tangible book value multiple	0.8 (0.8)
				Discounted cash flow and market multiples	Recoverability of intangible assets	0% (0%)
Private equity funds	12,559			Reported market value	Net asset value, as reported	100.0% (100.0%)
				Reported market value	Market adjustments	-0.7% (-0.7%)
Private equity – other	24,241			Discounted cash flow	Effective yield	3.8% (3.8%)
Funds held–directly managed
Other invested assets	2,067			Reported market value	Net asset value, as reported	100.0% (100.0%)
				Reported market value	Market adjustments	0% (0%)



December 31, 2016	Fair value			Valuation techniques	Unobservable inputs	Range (Weighted average)
Fixed maturities
U.S. states, territories and municipalities	$	123,827		Discounted cash flow	Credit spreads	1.5% – 10.5% (6.3%)
Asset-backed securities	99,351			Discounted cash flow	Credit spreads	4.1% – 18.5% (14.9%)
Equities
Finance	20,934			Weighted market comparables	Net income multiple	20.3 (20.3)
				Weighted market comparables	Tangible book value multiple	1.9 (1.9)
					Liquidity discount	25.0% (25.0%)
					Comparable return	36.9% (36.9%)

Technology	9,800			Reported market value	Tangible book value multiple	100.0% (100.0%)
Other invested assets
Total return swaps, net	(1,228		)	Discounted cash flow	Credit spreads	2.9% – 29.4% (19.3%)
Insurance-linked securities – longevity swaps	9,218			Discounted cash flow	Credit spreads	2.6% (2.6%)
Notes and loan receivables	131,176			Discounted cash flow	Credit spreads	4.2% – 24.4% (5.2%)
Notes and loan receivables	8,953			Discounted cash flow	Credit spreads	17.5% (17.5%)
Notes and loan receivables				Discounted cash flow	Gross revenue/fair value	1.2 (1.2)
Notes securitization	1,564			Discounted cash flow	Credit spreads	3.3% (3.3%)
Private equity – direct	5,019			Discounted cash flow and weighted market comparables	Net income multiple	8.6 (8.6)
					Tangible book value multiple	2.0 (2.0)
					Recoverability of intangible assets	0% (0%)
Private equity funds	11,064			Reported market value	Net asset value, as reported	100.0% (100.0%)
				Reported market value	Market adjustments	-0.7% (-0.7%)
Private equity – other	29,949			Discounted cash flow	Effective yield	5.8% (5.8%)
Funds held–directly managed
Other invested assets	4,540			Reported market value	Net asset value, as reported	100.0% (100.0%)
				Reported market value	Market adjustments	0% (0%)

The tables above do not include financial instruments that are measured using unobservable inputs (Level 3) where the unobservable inputs were obtained from external sources and used without adjustment. These financial instruments include mutual fund and exchange traded funds investments (included within equities), certain private equity funds (included within private equities), privately placed corporate loans (included within other invested assets) and certain derivatives (included within other invested assets).

The Company has established a Valuation Committee which is responsible for determining the Company’s invested asset valuation procedures, reviewing significant changes in the fair value measurements of securities classified as Level 3 and ensuring that there is an appropriate independent peer analysis, on at least an annual basis, on the fair value measurements of significant securities that are classified as Level 3. The Valuation Committee is comprised of members of the Company’s senior management team. The Company’s Group Enterprise Risk Management Financial Risk Policy which covers, amongst other items, invested asset valuation.

Changes in the fair value of the Company’s financial instruments subject to the fair value option during the years ended December 31, 2017, 2016 and 2015 were as follows (in thousands of U.S. dollars):



	2017			2016			2015
Fixed maturities and short-term investments	$	124,033		$	(90,334	)	$	(276,776	)
Equities	60,460			(14,850		)	(187,561		)
Other invested assets	28,144			11,066			(1,835		)
Funds held–directly managed	(5,612		)	(721		)	(6,323		)
Total	$	207,025		$	(94,839	)	$	(472,495	)

Substantially all of the above changes in fair value are included in the Consolidated Statements of Operations under the caption Net realized and unrealized investment gains (losses).

The following methods and assumptions were used by the Company in estimating the fair value of each class of financial instrument recorded in the Consolidated Balance Sheets. There have been no material changes in the Company’s valuation techniques during the periods presented.

Fixed maturities

•

U.S. government and government sponsored enterprises—U.S. government and government sponsored enterprises securities consist primarily of bonds issued by the U.S. Treasury and corporate debt securities issued by government sponsored enterprises and federally owned or established corporations. These securities are generally priced by independent pricing services. The independent pricing services may use actual transaction prices for securities that have been actively traded. For securities that have not been actively traded, each pricing source has its own proprietary method to determine the fair value, which may incorporate option adjusted spreads (OAS), interest rate data and market news. The Company generally classifies these securities in Level 2.

•

U.S. states, territories and municipalities—U.S. states, territories and municipalities securities consist primarily of bonds issued by U.S. states, territories and municipalities and the Federal Home Loan Mortgage Corporation. These securities are generally priced by independent pricing services using the techniques described for U.S. government and government sponsored enterprises above. The Company generally classifies these securities in Level 2. Certain of the bonds that are issued by municipal housing authorities and the Federal Home Loan Mortgage Corporation are not actively traded and are priced based on internal models using unobservable inputs. Accordingly, the Company classifies these securities in Level 3. The significant unobservable input used in the fair value measurement of these U.S. states, territories and municipalities securities classified as Level 3 is credit spreads. A significant increase (decrease) in credit spreads in isolation could result in a significantly lower (higher) fair value measurement.

•

Non-U.S. sovereign government, supranational and government related—Non-U.S. sovereign government, supranational and government related securities consist primarily of bonds issued by non-U.S. national governments and their agencies, non-U.S. regional governments and supranational organizations. These securities are generally priced by independent pricing services using the techniques described for U.S. government and government sponsored enterprises above. The Company generally classifies these securities in Level 2.

•

Corporate—Corporate securities consist primarily of bonds issued by U.S. and foreign corporations covering a variety of industries and issuing countries. Corporate securities also include real estate investment trusts, catastrophe bonds, longevity and mortality bonds and government guarantee corporate debt. These securities are generally priced by independent pricing services and brokers. The pricing provider incorporates information including credit spreads, interest rate data and market news into the valuation of each security. The Company generally classifies these securities in Level 2. When a corporate security is inactively traded or the valuation model uses unobservable inputs, the Company classifies the security in Level 3.

•

Asset-backed securities—Asset-backed securities primarily consist of bonds issued by U.S. and foreign corporations that are predominantly backed by student loans, automobile loans, credit card receivables, equipment leases, and special purpose financing. With the exception of special purpose financing securities, these asset-backed securities are generally priced by independent pricing services and brokers. The pricing provider applies dealer quotes and other available trade information, prepayment speeds, yield curves and credit spreads to the valuation. The Company generally classifies these securities in Level 2. Special purpose financing securities are generally inactively traded and are priced based on valuation models using unobservable inputs. The Company generally classifies these securities in Level 3. The significant unobservable input used in the fair value measurement of these asset-backed securities classified as Level 3 is credit spreads. A significant increase (decrease) in credit spreads in isolation could result in a significantly lower (higher) fair value measurement.

•

Residential mortgage-backed securities—Residential mortgage-backed securities primarily consist of bonds issued by the Government National Mortgage Association, the Federal National Mortgage Association, the Federal Home Loan Mortgage Corporation, as well as private, non-agency issuers. These residential mortgage-backed securities are generally priced by independent pricing services and brokers. When current market trades are not available, the pricing provider or the Company will employ proprietary models with observable inputs including other trade information, prepayment speeds, yield curves and credit spreads. The Company generally classifies these securities in Level 2.

•

Other mortgage-backed securities—Other mortgage-backed securities primarily consist of commercial mortgage-backed securities. These securities are generally priced by independent pricing services and brokers. The pricing provider applies dealer quotes and other available trade information, prepayment speeds, yield curves and credit spreads to the valuation. The Company generally classifies these securities in Level 2.

In general, the methods employed by the independent pricing services to determine the fair value of the securities that have not been actively traded primarily involve the use of “matrix pricing” in which the independent pricing source applies the credit spread for a comparable security that has traded recently to the current yield curve to determine a reasonable fair value. The Company generally uses one pricing source per security and uses a pricing service ranking to consistently select the most appropriate pricing service in instances where it receives multiple quotes on the same security. When fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Most of the Company’s fixed maturities are priced from the pricing services or dealer quotes. The Company will typically not make adjustments to prices received from pricing services or dealer quotes; however, in instances where the quoted external price for a security uses significant unobservable inputs, the Company will classify that security as Level 3. The methods used to develop and substantiate the unobservable inputs used are based on the Company’s valuation policy and are dependent upon the facts and circumstances surrounding the individual investments which are generally transaction specific. The Company’s inactively traded fixed maturities are classified as Level 3. For all fixed maturity investments, the bid price is used for estimating fair value.

To validate prices, the Company compares the fair value estimates to its knowledge of the current market and will investigate prices that it considers not to be representative of fair value. The Company also reviews an internally generated fixed maturity price validation report which converts prices received for fixed maturity investments from the independent pricing sources and from broker-dealers quotes and plots OAS and duration on a sector and rating basis. The OAS is calculated using established algorithms developed by an independent risk analytics platform vendor. The OAS on the fixed maturity price validation report are compared for securities in a similar sector and having a similar rating, and outliers are identified and investigated for price reasonableness. In addition, the Company completes quantitative analyses to compare the performance of each fixed maturity investment portfolio to the performance of an appropriate benchmark, with significant differences identified and investigated.

Short-term investments

Short-term investments are valued in a manner similar to the Company’s fixed maturity investments and are generally classified in Level 2.

Equities

Equity securities include U.S. and foreign common and preferred stocks, real estate investment trusts, mutual funds and exchange traded funds. Equities, real estate investment trusts and exchange traded funds are generally classified in Level 1 as the Company uses prices received from independent pricing sources based on quoted prices in active markets. Equities classified as Level 2 are generally mutual funds invested in fixed income securities, where the net asset value of the fund is provided on a daily basis, and certain common and preferred equities. Equities classified as Level 3 are generally mutual funds invested in securities other than the common stock of publicly traded companies, where the net asset value is not provided on a daily basis, and inactively traded common stocks. The significant unobservable inputs used in the fair value measurement of inactively traded common stocks classified as Level 3 include market return information, weighted using management’s judgment, from comparable selected publicly traded companies in the same industry, in a similar region and of a similar size, including net income multiples, tangible book value multiples, comparable returns, revenue multiples, adjusted earnings multiples and projected return on equity ratios. Significant increases (decreases) in any of these inputs could result in a significantly higher (lower) fair value measurement. Significant unobservable inputs used in measuring the fair value measurement of inactively traded common stocks also include a liquidity discount. A significant increase (decrease) in the liquidity discount could result in a significantly lower (higher) fair value measurement.

To validate prices, the Company completes quantitative analyses to compare the performance of each equity investment portfolio to the performance of an appropriate benchmark, with significant differences identified and investigated.

Other invested assets

The Company’s exchange traded derivatives, such as futures, are generally classified as Level 1 as their fair values are quoted prices in active markets. The Company’s foreign exchange forward contracts, foreign currency option contracts, interest rate swaps and TBAs are generally classified as Level 2 within the fair value hierarchy and are priced by independent pricing services.

Included in the Company’s Level 3 classification, in general, are certain inactively traded derivatives, including weather derivative insurance-linked securities and total return swaps; corporate loans; notes and loan receivables and notes securitizations; and private equities. For Level 3 instruments, the Company will generally (i) receive a price based on a manager’s or trustee’s valuation for the asset; (ii) develop an internal discounted cash flow model to measure fair value; or (iii) use market return information, adjusted if necessary and weighted using management’s judgment, from comparable selected publicly traded equity funds in a similar region and of a similar size. Where the Company receives prices from the manager or trustee, these prices are based on the manager’s or trustee’s estimate of fair value for the assets and are generally audited on an annual basis. Where the Company develops its own discounted cash flow models, the inputs will be specific to the asset in question, based on appropriate historical information, adjusted as necessary, and using appropriate discount rates. The significant unobservable inputs used in the fair value measurement of other invested assets classified as Level 3 include credit spreads, gross revenue to fair value ratios, net income multiples, effective yields, tangible book value multiples and other valuation ratios. Significant increases (decreases) in any of these inputs in isolation could result in a significantly lower (higher) fair value measurement. Significant unobservable inputs used in the fair value measurement of other invested assets classified as Level 3 also include an assessment of the recoverability of intangible assets and market return information, weighted using management’s judgment, from comparable selected publicly traded companies in the same industry, in a similar region and of a similar size. Significant increases (decreases) in these inputs in isolation could result in a significantly higher (lower) fair value measurement. As part of the Company’s modeling to determine the fair value of an investment, the Company considers counterparty credit risk as an input to the model, however, the majority of the Company’s counterparties are investment grade rated institutions and the failure of any one counterparty would not have a significant impact on the Company’s consolidated financial statements.

To validate prices, the Company will compare them to benchmarks, where appropriate, or to the business results generally within that asset class and specifically to those particular assets.

Funds held–directly managed

The segregated investment portfolio underlying the funds held–directly managed account is comprised of fixed maturities, short-term investments and other invested assets which are fair valued on a basis consistent with the methods described above. Substantially all fixed maturities and short-term investments within the funds held–directly managed account are classified as Level 2 within the fair value hierarchy.

The other invested assets within the segregated investment portfolio underlying the funds held–directly managed account, which are classified as Level 3 investments, are primarily real estate mutual fund investments carried at fair value. For the real estate mutual fund investments, the Company receives a price based on the real estate fund manager’s valuation for the asset and further adjusts the price, if necessary, based on appropriate current information on the real estate market. A significant increase (decrease) to the adjustment to the real estate fund manager’s valuation could result in a significantly lower (higher) fair value measurement.

To validate prices within the segregated investment portfolio underlying the funds held–directly managed account, the Company utilizes the methods described above.

See Note 5 further details regarding Funds held–directly managed.

(b) Fair Value of Financial Instrument Liabilities

At December 31, 2017 and 2016, the carrying values of financial instrument liabilities recorded in the Consolidated Balance Sheets approximate their fair values, with the exception of the long-term debt related to senior notes and capital efficient notes (CENts). The fair value of the debt related to senior notes as of December 31, 2017 and 2016 was calculated based on discounted cash flow models using observable market yields and contractual cash flows based on the aggregate principal amount outstanding. The fair value of the debt related to CENts as of December 31, 2017 was calculated based on market data valuation models using observable inputs based on the aggregate principal amount outstanding of the intercompany debt.

See Note 10 for further details related to the Company's debt, including the carrying values and fair values.

At December 31, 2017 and 2016, the Company’s debt related to the senior notes and CENts was classified as Level 2 in the fair value hierarchy.

Disclosures about the fair value of financial instrument liabilities exclude insurance contracts and certain other financial instruments.