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Investment Securities

12 Months Ended

Dec. 31, 2019

Investments, Debt and Equity Securities [Abstract]

Investments Securities

White Mountains’s portfolio of investment securities held for general investment purposes consists of fixed maturity investments, short-term investments, common equity securities and other long-term investments, which are substantially all classified as trading securities. Trading securities are reported at fair value as of the balance sheet date. Net realized and unrealized investment gains (losses) on trading securities are reported in pre-tax revenues.

White Mountains’s fixed maturity investments are generally valued using industry standard pricing methodologies. Key inputs include benchmark yields, benchmark securities, reported trades, issuer spreads, bids, offers, credit ratings and prepayment speeds. Income on mortgage and asset-backed securities is recognized using an effective yield based on anticipated prepayments and the estimated economic life of the securities. When actual prepayments differ significantly from anticipated prepayments, the estimated economic life is recalculated and the remaining unamortized premium or discount is amortized prospectively over the remaining economic life.

Realized investment gains (losses) resulting from sales of investment securities are accounted for using the specific identification method. Premiums and discounts on all fixed maturity investments are amortized or accreted to income over the anticipated life of the investment. Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year. Short-term investments are carried at amortized or accreted cost, which approximated fair value as of as of December 31, 2019 and 2018.

Other long-term investments consist primarily of unconsolidated entities, Kudu’s Participation Contracts, private equity funds, hedge funds, ILS funds and private debt instruments.

Net Investment Income

White Mountains’s net investment income is comprised primarily of interest income associated with White Mountains’s fixed maturity investments and short-term investments and dividend income from its common equity securities and other long-term investments.

The following table presents pre-tax net investment income for 2019, 2018 and 2017:



	Year Ended December 31,
Millions	2019			2018			2017
Fixed maturity investments	$	32.4		$	35.1		$	44.9
Short-term investments	5.0			8.0			1.8
Common equity securities	13.5			15.1			10.6
Other long-term investments	30.1			3.8			1.2
Total investment income	81.0			62.0			58.5
Third-party investment expenses	(1.3		)	(3.0		)	(2.5		)
Net investment income, pre-tax	$	79.7		$	59.0		$	56.0

Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for 2019, 2018 and 2017:



	Year Ended December 31,
Millions	2019			2018			2017
Net realized investment gains (losses), pre-tax ⁽¹⁾	$	96.6		$	(12.9	)	$	24.1
Net unrealized investment gains (losses), pre-tax ⁽²⁾	336.6			(95.4		)	109.2
Net realized and unrealized investment gains (losses), pre-tax	433.2			(108.3		)	133.3
Income tax (expense) benefit attributable to net realized and unrealized investment gains (losses)	(87.0		)	18.2			(12.9		)
Net realized and unrealized investment gains (losses), after-tax	$	346.2		$	(90.1	)	$	120.4

⁽¹⁾ Excludes $67.5 realized gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”

⁽²⁾ Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”

For the years ended December 31, 2019, 2018 and 2017, all of White Mountains’s net realized and unrealized investment gains (losses) were recorded in the consolidated statements of operations. There were no investment gains (losses) recorded in other comprehensive income.

Net Realized Investment Gains (Losses)

The following tables present net realized investment gains (losses) for the years ended 2019, 2018 and 2017:



	Year Ended December 31, 2019
Millions	Net Realized Gains			Net Foreign Exchange Gains (Losses)		Total Net Realized Gains Reflected in Earnings
Fixed maturity investments	$	4.9		$	—	$	4.9
Short-term investments	.2			—		.2
Common equity securities	85.9			—		85.9
Other long-term investments ⁽¹⁾	5.6			—		5.6
Net realized investment gains, pre-tax	96.6			—		96.6
Income tax expense attributable to net realized investment gains	(10.6		)	—		(10.6		)
Net realized investment gains, after-tax	$	86.0		$	—	$	86.0



	Year Ended December 31, 2018
Millions	Net Realized (Losses) Gains			Net Foreign Exchange Gains (Losses)			Total Net Realized (Losses) Gains Reflected in Earnings
Fixed maturity investments	$	(29.8	)	$	18.2		$	(11.6	)
Short-term investments	(.8		)	—			(.8		)
Common equity securities	6.6			—			6.6
Other long-term investments	.1			(7.2		)	(7.1		)
Net realized investment (losses) gains, pre-tax	(23.9		)	11.0			(12.9		)
Income tax benefit attributable to net realized investment (losses) gains	9.1			—			9.1
Net realized investment (losses) gains, after-tax	$	(14.8	)	$	11.0		$	(3.8	)



	Year Ended December 31, 2017
Millions	Net Realized (Losses) Gains			Net Foreign Exchange Gains (Losses)			Total Net Realized Gains (Losses) Reflected in Earnings
Fixed maturity investments	$	(1.6	)	$	4.1		$	2.5
Short-term investments	(.3		)	—			(.3		)
Common equity securities	18.1			6.0			24.1
Other long-term investments	19.1			(21.3		)	(2.2		)
Net realized investment gains (losses), pre-tax	35.3			(11.2		)	24.1
Income tax expense attributable to net realized investment gains (losses)	(8.9		)	—			(8.9		)
Net realized investment gains (losses), after-tax	$	26.4		$	(11.2	)	$	15.2

White Mountains recognized gross realized investment gains of $104.0 million, $49.4 million and $61.5 million and gross realized investment losses of $7.4 million, $62.3 million and $37.4 million on sales of investment securities during 2019, 2018 and 2017

Net Unrealized Investment Gains (Losses)

The following tables present net unrealized investment gains (losses) and changes in the carrying value of investments measured at fair value for the years ended 2019, 2018 and 2017:



	Year Ended December 31, 2019
Millions	Net Unrealized Gains			Net Foreign Exchange Losses			Total Net Unrealized Gains Reflected in Earnings
Fixed maturity investments	$	38.6		$	—		$	38.6
Common equity securities	109.8			—			109.8
Other long-term investments ⁽¹⁾	188.5			(.3		)	188.2
Net unrealized investment gains (losses), pre-tax	336.9			(.3		)	336.6
Income tax expense attributable to net unrealized investment gains	(76.4		)	—			(76.4		)
Net unrealized investment gains (losses), after-tax	$	260.5		$	(.3	)	$	260.2

⁽¹⁾ Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”



	Year Ended December 31, 2018
Millions	Net Unrealized (Losses) Gains			Net Foreign Exchange (Losses) Gains			Total Net Unrealized (Losses) Gains Reflected in Earnings
Fixed maturity investments	$	(8.3	)	$	(14.8	)	$	(23.1	)
Common equity securities	(105.5		)	—			(105.5		)
Other long-term investments	30.2			3.0			33.2
Net unrealized investment losses, pre-tax	(83.6		)	(11.8		)	(95.4		)
Income tax benefit attributable to net unrealized investment losses	9.1			—			9.1
Net unrealized investment losses, after-tax	$	(74.5	)	$	(11.8	)	$	(86.3	)



	Year Ended December 31, 2017
Millions	Net Unrealized Gains (Losses)			Net Foreign Exchange Gains (Losses)			Total Net Unrealized Gains (Losses) Reflected in Earnings
Fixed maturity investments	$	13.8		$	12.7		$	26.5
Common equity securities	99.3			—			99.3
Other long-term investments	(15.6		)	(1.0		)	(16.6		)
Net unrealized investment gains, pre-tax	97.5			11.7			109.2
Income tax expense attributable to net unrealized investment gains	(4.0		)	—			(4.0		)
Net unrealized investment gains, after-tax	$	93.5		$	11.7		$	105.2

The following table presents total gains (losses) included in earnings attributable to net unrealized investment gains (losses) for Level 3 investments for the years ended December 31, 2019, 2018 and 2017 for investments held as of December 31, 2019, 2018 and 2017:



	Year Ended December 31,
Millions	2019		2018		2017
Other long-term investments	$	181.9	$	22.6	$	(15.4	)

Investment Holdings

The following tables present the cost or amortized cost, gross unrealized investment gains (losses) and carrying values of White Mountains’s fixed maturity investments as of December 31, 2019 and 2018.



	December 31, 2019
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Carrying Value
U.S. Government and agency obligations	$	231.7	$	1.0	$	(.2	)	$	232.5
Debt securities issued by corporations	454.9		12.5		(.2		)	467.2
Municipal obligations	284.7		12.5		(.1		)	297.1
Mortgage and asset-backed securities	206.6		2.7		(.3		)	209.0
Total fixed maturity investments	$	1,177.9	$	28.7	$	(.8	)	$	1,205.8



	December 31, 2018
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Carrying Value
U.S. Government and agency obligations	$	154.0	$	.1	$	(.9	)	$	153.2
Debt securities issued by corporations	519.0		1.0		(9.5		)	510.5
Municipal obligations	279.0		2.4		(1.1		)	280.3
Mortgage and asset-backed securities	136.1		.1		(2.7		)	133.5
Total fixed maturity investments	$	1,088.1	$	3.6	$	(14.2	)	$	1,077.5

The weighted average duration of White Mountains’s fixed income portfolio was approximately 2.8 years when including short-term investments and approximately 3.3 years when excluding short-term investments as of December 31, 2019.

The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of December 31, 2019. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.



	December 31, 2019
Millions	Cost or Amortized Cost		Carrying Value
Due in one year or less	$	190.0	$	190.8
Due after one year through five years	481.6		489.3
Due after five years through ten years	165.3		173.2
Due after ten years	134.4		143.5
Mortgage and asset-backed securities	206.6		209.0
Total	$	1,177.9	$	1,205.8

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency losses, and carrying values of White Mountains’s common equity securities and other long-term investments as of December 31, 2019 and 2018:



	December 31, 2019
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Net Foreign Currency Losses			Carrying Value
Common equity securities	$	553.3	$	130.6	$	—		$	—		$	683.9
Other long-term investments	$	667.4	$	255.2	$	(64.1	)	$	(2.2	)	$	856.3



	December 31, 2018
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Net Foreign Currency Losses			Carrying Value
Common equity securities	$	904.7	$	51.0	$	(30.1	)	$	—		$	925.6
Other long-term investments	$	330.3	$	52.2	$	(54.9	)	$	(2.0	)	$	325.6

Proceeds from the sales and maturities of investments, excluding short-term investments, totaled $1.0 billion, $2.2 billion and $2.8 billion for the years ended December 31, 2019, 2018 and 2017.

Investments Held on Deposit or as Collateral

As of December 31, 2019 and 2018, investments of $319.9 million and $254.3 million, were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM. White Mountains’s insurance subsidiaries are required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $9.9 million and $6.1 million as of December 31, 2019 and 2018.

Fair Value Measurements as of December 31, 2019

Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (“observable inputs”) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (“unobservable inputs”). Quoted prices in active markets for identical assets or liabilities have the highest priority (“Level 1”), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (“Level 2”) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (“Level 3”). As of December 31, 2019 and 2018, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 71% and 87% of the investment portfolio. See Note 1 — “Basis of Presentation and Significant Accounting Policies”.

Fair Value Measurements by Level

The following tables present White Mountains’s fair value measurements for investments as of December 31, 2019 and 2018 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, foreign governments, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations and common equity securities by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated these asset classes into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate and S&P 500 indices.



	December 31, 2019
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	232.5	$	232.5	$	—	$	—
Debt securities issued by corporations:
Financials	144.8		—		144.8		—
Industrial	59.0		—		59.0		—
Healthcare	52.6		—		52.6		—
Consumer	50.9		—		50.9		—
Energy	44.9		—		44.9		—
Technology	41.2		—		41.2		—
Communications	31.3		—		31.3		—
Utilities	25.0		—		25.0		—
Materials	17.5		—		17.5		—
Total debt securities issued by corporations	467.2		—		467.2		—

Municipal obligations	297.1		—		297.1		—
Mortgage and asset-backed securities	209.0		—		209.0		—
Total fixed maturity investments	1,205.8		232.5		973.3		—

Short-term investments ⁽¹⁾	201.2		189.4		11.8		—

Common equity securities:

Exchange traded funds ⁽²⁾	536.4		521.6		14.8		—
Other ⁽³⁾	147.5		25.9		121.5		0.1
Total common equity securities	683.9		547.5		136.3		0.1
Other long-term investments	654.0		—		—		654.0
Other long-term investments — NAV⁽⁴⁾	202.3		—		—		—
Total investments	$	2,947.2	$	969.4	$	1,121.4	$	654.1

⁽¹⁾Short-term investments are measured at amortized cost, which approximates fair value.

⁽²⁾ ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement.

⁽³⁾Primarily consists of two investments in unit trusts that predominantly invest in international equities and an open-end mutual fund that invests in domestic large-cap companies.

⁽⁴⁾ Consists of private equity funds, one hedge fund and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.



	December 31, 2018
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	153.2	$	153.2	$	—	$	—

Debt securities issued by corporations:
Financials	143.4		—		143.4		—
Consumer	68.5		—		68.5		—
Technology	60.5		—		60.5		—
Energy	57.6		—		57.6		—
Healthcare	55.0		—		55.0		—
Industrial	47.6		—		47.6		—
Communications	31.8		—		31.8		—
Materials	26.3		—		26.3		—
Utilities	19.8		—		19.8		—
Total debt securities issued by corporations	510.5		—		510.5		—

Municipal obligations	280.3		—		280.3		—
Mortgage and asset-backed securities	133.5		—		133.5		—
Total fixed maturity investments	1,077.5		153.2		924.3		—

Short-term investments ⁽¹⁾	214.2		204.4		9.8		—

Common equity securities:
Exchange traded funds ⁽²⁾	675.3		617.0		58.3		—
Healthcare	14.0		14.0		—		—
Financials	13.5		13.5		—		—
Communications	12.7		12.7		—		—
Industrial	11.4		11.4		—		—
Technology	7.4		7.4		—		—
Consumer	6.2		6.2		—		—
Energy	4.1		4.1		—		—
Materials	3.1		3.1		—		—
Other ⁽³⁾	177.9		—		177.9		—
Total common equity securities	925.6		689.4		236.2		—
Other long-term investments	138.7		—		—		138.7
Other long-term investments — NAV ⁽⁴⁾	186.9		—		—		—
Total investments	$	2,542.9	$	1,047.0	$	1,170.3	$	138.7

⁽¹⁾Short-term investments are measured at amortized cost, which approximates fair value.

⁽²⁾ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement.

⁽³⁾Consists of two investments in unit trusts that predominantly invest in international equities.

⁽⁴⁾Consists of private equity funds, one hedge fund, White Mountains’s non-controlling equity interest in Kudu prior to consolidation and one unconsolidated entity for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.

Debt Securities Issued by Corporations

The following table presents the ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2019 and 2018:



	Fair Value at December 31,
Millions	2019		2018
AAA	$	9.5	$	8.9
AA	73.9		88.7
A	288.5		270.5
BBB	95.3		142.4
Debt securities issued by corporations ⁽¹⁾	$	467.2	$	510.5


⁽¹⁾	Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc

Mortgage and Asset-backed Securities

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of December 31, 2019 and 2018:



	December 31, 2019						December 31, 2018
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	88.6	$	88.6	$	—	$	53.6	$	53.6	$	—
FHLMC	60.5		60.5		—		38.1		38.1		—
GNMA	30.8		30.8		—		23.7		23.7		—
Total agency ⁽¹⁾	179.9		179.9		—		115.4		115.4		—
Total mortgage-backed securities	179.9		179.9		—		115.4		115.4		—
Other asset-backed securities:
Vehicle receivables	15.1		15.1		—		9.2		9.2		—
Credit card receivables	14.0		14.0		—		8.9		8.9		—
Total other asset-backed securities	29.1		29.1		—		18.1		18.1		—
Total mortgage and asset-backed securities	$	209.0	$	209.0	$	—	$	133.5	$	133.5	$	—


⁽¹⁾	Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).

Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of December 31, 2019 and 2018:



	Carrying Value at
Millions	December 31, 2019		December 31, 2018
Kudu’s Participation Contracts ⁽¹⁾⁽²⁾	$	266.5	$	—
MediaAlpha ⁽¹⁾⁽³⁾	180.0		—
PassportCard/DavidShield ⁽¹⁾	90.0		75.0
Elementum ⁽¹⁾	55.1		—
Other unconsolidated entities ⁽¹⁾⁽⁴⁾	31.2		60.0
Kudu ⁽⁵⁾	—		30.7
Total unconsolidated entities ⁽¹⁾	622.8		165.7
Private equity funds and hedge funds	161.1		146.1
Insurance-linked securities funds	41.2		—
Other	31.2		13.8
Total other long-term investments	$	856.3	$	325.6

⁽¹⁾See Fair Value Measurements by Level table.

⁽²⁾ Includes Kudu’s non-controlling equity interests in the form of revenue and earnings participation contracts. As of December 31, 2019, White Mountains consolidates Kudu. See Note 2 — “Significant Transactions”.

⁽³⁾ The MediaAlpha Transaction was completed on February 26, 2019. See Note 2 — “Significant Transactions”.

⁽⁴⁾Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities.

⁽⁵⁾ Includes White Mountains’s non-controlling equity interest in Kudu prior to consolidation. See Note 2 — “Significant Transactions”.

Private Equity Funds and Hedge Funds

White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the NAV of the funds. As of December 31, 2019, White Mountains held investments in 12 private equity funds and one hedge fund. The largest investment in a single fund was $54.6 million as of December 31, 2019 and $54.3 million as of December 31, 2018.

The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of December 31, 2019 and 2018:



	December 31, 2019				December 31, 2018
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments

Private equity funds
Manufacturing/Industrial	$	57.7	$	4.1	$	42.9	$	10.5
Aerospace/Defense/Government	33.8		23.3		27.6		34.9
Financial services	15.0		22.8		8.3		13.6
Direct lending	—		—		13.0		17.7
Total private equity funds	106.5		50.2		91.8		76.7

Hedge funds
Long/short banks and financial	54.6		—		54.3		—
Total hedge funds	54.6		—		54.3		—
Total private equity funds and hedge funds included in other long-term investments	$	161.1	$	50.2	$	146.1	$	76.7

Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period.

The following table presents investments in private equity funds that were subject to lock-up periods as of December 31, 2019:



Millions	1 – 3 years		3 – 5 years		5 – 10 years		>10 years		Total
Private equity funds — expected lock-up period remaining	$	4.8	$	51.9	$	40.2	$	9.6	$	106.5

Investors in private equity funds are generally subject to indemnification obligations outside of the capital commitment period and prior to the winding up of the fund. As of December 31, 2019 and 2018, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds.

Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. As of December 31, 2019, White Mountains held one active hedge fund with a fair value of $54.6 million. The hedge fund is subject to a semi-annual restriction on redemptions and an advance notice period requirement of 45 days. On February 13, 2020, White Mountains submitted a notice to redeem its full interest in the hedge fund as of March 31, 2020 and expects to receive the proceeds, subject to any audit holdback, in the second quarter of 2020.

Insurance-Linked Securities Funds

White Mountains’s other long-term investments include ILS funds. The fair value of these investments are generally estimated using the NAV of the funds. As of December 31, 2019, White Mountains held investments in three ILS funds with a fair value of $41.2 million. Also as of December 31, 2019, White Mountains had made an in-transit cash contribution of $4.8 million, which was recorded within other assets, in support of its remaining $10.0 million commitment to invest $50.0 million in ILS funds managed by Elementum. The cash was invested in the ILS fund on January 1, 2020 and will be recorded within other long-term investments in the first quarter of 2020

Investments in ILS funds are generally subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. From time to time, natural catastrophe, liquidity, market or other events will occur that make the determination of fair value for underlying investments in an ILS fund less certain due to the potential for loss development. In such circumstances, the impacted investments may be subject to additional lock-up provisions.

As of December 31, 2019, White Mountains holds one ILS fund subject to a lock-up period that expires on June 1, 2020. White Mountains’s ILS funds are subject to monthly and annual restrictions on redemptions and advance redemption notice period requirements that range between 30 and 90 days. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period.

Rollforward of Fair Value Measurements by Level

White Mountains uses quoted market prices where available as the inputs to estimate fair value for its investments in active markets. Such measurements are considered to be either Level 1 or Level 2 measurements, depending on whether the quoted market price inputs are for identical securities (Level 1) or similar securities (Level 2). Level 3 measurements for fixed maturity investments, common equity securities and other long-term investments as of December 31, 2019 and 2018 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities.

The following tables present the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2019 and 2018:



							Level 3 Investments					Other Long-term Investments Measured at NAV ⁽³⁾
Millions	Level 1 Investments			Level 2 Investments			Common Equity Securities		Other Long-term Investments⁽²⁾			Other Long-term Investments Measured at NAV ⁽³⁾			Total
Balance at December 31, 2018	$	842.6		$	1,160.5		$	—	$	138.7		$	186.9		$	2,328.7		⁽¹⁾
Net realized and unrealized gains	163.0			76.1			—		181.2			12.7			433.0			⁽²⁾⁴⁾
Amortization/accretion	.2			(1.8		)	—		—			—			(1.6		)
Purchases	165.3			404.5			.1		185.4			110.8			866.1
Sales	(391.1		)	(529.7		)	—		—			(29.5		)	(950.3		)
Effect of Kudu Transaction	—			—			—		141.8			(71.7		)	70.1
Transfers in	—			—			—		10.9			4.0			14.9
Transfers out	—			—			—		(4.0		)	(10.9		)	(14.9		)
Balance at December 31, 2019	$	780.0		$	1,109.6		$	.1	$	654.0		$	202.3		$	2,746.0		⁽¹⁾

⁽¹⁾Excludes carrying value of $201.2 and $214.2 as of December 31, 2019 and 2018 classified as short-term investments.


⁽²⁾	Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions”.

⁽³⁾Includes private equity funds, hedge funds, ILS funds and unconsolidated entities for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies”.

⁽⁴⁾ Excludes realized and unrealized losses associated with short-term investments of $0.2 for the year ended December 31, 2019.



							Level 3 Investments		Other Long-term Investments Measured at NAV ⁽³⁾
Millions	Level 1 Investments			Level 2 Investments			Other Long- term Investments		Other Long-term Investments Measured at NAV ⁽³⁾			Total
Balance at December 31, 2017	$	890.4		$	2,105.4		$	77.2	$	135.3		$	3,208.3		⁽¹⁾⁽²⁾
Net realized and unrealized (losses) gains	(64.9		)	(64.4		)	16.2		13.3			(99.8		)	⁽⁴⁾
Amortization/accretion	.2			(2.7		)	—		—			(2.5		)
Purchases	514.7			783.8			45.3		50.5			1,394.3
Sales	(497.8		)	(1,661.6		)	—		(12.2		)	(2,171.6		)
Transfers in	—			—			—		—			—
Transfers out	—			—			—		—			—
Balance at December 31, 2018	$	842.6		$	1,160.5		$	138.7	$	186.9		$	2,328.7		⁽²⁾

⁽¹⁾Excludes carrying value of $(3.7) as of December 31, 2017 associated with foreign currency forward contracts.

⁽²⁾Excludes carrying value of $214.2 and $176.1 as of December 31, 2018 and 2017 classified as short-term investments.


⁽³⁾	Includes private equity funds, hedge funds and unconsolidated entities for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy See Note 1 — “Basis of Presentation and Significant Accounting Policies”.

⁽⁴⁾Excludes realized and unrealized losses associated with foreign currency forward contracts, foreign currency on cash and open trades and short-term investments of $3.5, $4.2 and $0.8 for the year ended December 31, 2018.

Fair Value Measurements — Transfers Between Levels - For Years Ended December 31, 2019 and 2018

Transfers between levels are recorded using the fair value measurement as of the end of the quarterly period in which the event or change in circumstance giving rise to the transfer occurred.

During 2019 and 2018, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements.

Significant Unobservable Inputs

The following tables present significant unobservable inputs used in estimating the fair value of other long-term investments, other than private equity funds, hedge funds and ILS funds, classified within Level 3 as of December 31, 2019 and 2018. The fair value of investments in private equity funds, hedge funds and ILS funds are generally estimated using the NAV of the funds.



$ in Millions	December 31, 2019
Description	Valuation Technique(s)	Fair Value ⁽¹⁾	Unobservable Inputs
			Discount Rate ⁽²⁾	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) ⁽²⁾
Kudu’s Participation Contracts	Discounted cash flow	$266.5	15% - 22%	6x - 12x
MediaAlpha	Discounted cash flow	$180.0	15%	4%
PassportCard/DavidShield	Discounted cash flow	$90.0	22%	4%
Elementum Holdings, L.P.	Discounted cash flow	$55.1	20%	4%
Private debt instruments	Discounted cash flow	$23.7	4% - 9%	N/A
All other	Discounted cash flow	$23.7	25% - 32%	4%

Compare.com	Estimated net realizable value	$2.5	Net asset value:	$2.5

⁽¹⁾Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

⁽²⁾Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.



$ in Millions	December 31, 2018
Description	Valuation Technique(s)	Fair Value ⁽¹⁾	Unobservable Inputs
			Discount Rate ⁽²⁾	Terminal Revenue Exit Multiple (x) ⁽²⁾
PassportCard/DavidShield	Discounted cash flow	$75.0	18%	1x
Compare.com	Discounted cash flow	$16.9	22%	3x
Private debt instrument	Discounted cash flow	$10.0	9%	N/A
All other	Discounted cash flow	$30.0	23%	2x - 4x

Galvanic Applied Sciences	Multiple of EBITDA	$3.1	EBITDA multiple:	6x

⁽¹⁾Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

⁽²⁾Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal revenue exit multiples in isolation would result in higher (lower) fair value measurements.