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Investment Securities

6 Months Ended

Jun. 30, 2020

Investments, Debt and Equity Securities [Abstract]

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 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 June 30, 2020 and December 31, 2019.

Other long-term investments consist primarily of unconsolidated entities, including Kudu’s non-controlling equity interests in the form of revenue and earnings participation contracts (“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 the three and six months ended June 30, 2020 and 2019:



	Three Months Ended						Six Months Ended
	June 30,						June 30,
Millions	2020			2019			2020			2019
Fixed maturity investments	$	7.3		$	8.3		$	15.4		$	16.4
Short-term investments	.1			1.3			.9			2.6
Common equity securities	2.2			2.9			6.0			8.3
Other long-term investments	10.3			8.8			20.8			10.4
Total investment income	19.9			21.3			43.1			37.7
Third-party investment expenses	(.3		)	(.3		)	(.6		)	(.7		)
Net investment income, pre-tax	$	19.6		$	21.0		$	42.5		$	37.0

Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for the three and six months ended June 30, 2020 and 2019:



	Three Months Ended					Six Months Ended
	June 30,					June 30,
Millions	2020		2019			2020			2019
Fixed maturity investments	$	30.0	$	16.9		$	32.2		$	38.0
Short-term investments	—		.3			.4			.3
Common equity securities	98.3		27.8			(42.5		)	139.1
Other long-term investments ^{(1) (2)}	24.6		$	(9.8	)	6.1			103.4
Net realized and unrealized investment gains (losses)	152.9		35.2			(3.8		)	280.8
Less: net gains (losses) on investment securities sold during the period	2.2		.2			(6.5		)	12.4
Net realized and unrealized investment gains on investment securities held at the end of the period	$	150.7	$	35.0		$	2.7		$	268.4

⁽¹⁾For the six months ended June 30, 2019, excludes $67.5 of realized gain and includes $114.7 of unrealized investment gain associated with the

MediaAlpha Transaction, which are both 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⁾For the three months ended June 30, 2020 and 2019, includes $0.4 and $0.3 of realized and unrealized investment gains related to foreign currency exchange. For the six months ended June 30, 2020 and 2019, there were no realized and unrealized investment gains related to foreign currency exchange.

The following table presents total gains (losses) included in earnings attributable to net unrealized investment gains (losses) for Level 3 investments for the three and six months ended June 30, 2020 and 2019 for investments still held at the end of the period:



	Three Months Ended					Six Months Ended
	June 30,					June 30,
Millions	2020		2019			2020		2019
Other long-term investments	$	25.3	$	(14.0	)	$	15.9	$	100.0
Total net unrealized investment gains (losses), pre-tax - Level 3 investments	$	25.3	$	(14.0	)	$	15.9	$	100.0

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 June 30, 2020 and December 31, 2019:



	June 30, 2020
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Carrying Value
U.S. Government and agency obligations	$	195.5	$	4.9	$	—		$	200.4
Debt securities issued by corporations	480.2		26.1		(.5		)	505.8
Municipal obligations	248.3		16.7		(.2		)	264.8
Mortgage and asset-backed securities	213.2		7.4		—			220.6
Total fixed maturity investments	$	1,137.2	$	55.1	$	(.7	)	$	1,191.6



	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

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 June 30, 2020 and December 31, 2019:



	June 30, 2020
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses			Net Foreign Currency Losses			Carrying Value
Common equity securities	$	502.8	$	69.3	$	(4.9	)	$	—		$	567.2
Other long-term investments	$	677.9	$	289.6	$	(67.1	)	$	(2.3	)	$	898.1



	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

Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of June 30, 2020 and December 31, 2019:



	Carrying Value at
Millions	June 30, 2020		December 31, 2019
Kudu’s Participation Contracts ⁽¹⁾	$	315.6	$	266.5
MediaAlpha ⁽¹⁾	225.0		180.0
PassportCard/DavidShield ⁽¹⁾	95.0		90.0
Elementum Holdings L.P. ⁽¹⁾	55.1		55.1
Other unconsolidated entities ⁽¹⁾⁽²⁾	31.9		33.7
Total unconsolidated entities ⁽¹⁾	722.6		625.3
Private equity funds and hedge funds	105.9		161.1
Insurance-linked securities funds	52.1		41.2
Private debt investments ⁽³⁾	17.5		28.7
Total other long-term investments	$	898.1	$	856.3

⁽¹⁾See Fair Value Measurements by Level table.

⁽²⁾Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities and Simple Agreement for Future Equity (“SAFE”) investments.

⁽³⁾ Includes $4.6 and $5.0 in private debt investments carried at fair value as of June 30. 2020 and amortized cost as of December 31, 2019.

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 net asset value (“NAV”) of the funds. As of June 30, 2020, White Mountains held investments in thirteen private equity funds. The largest investment in a single private equity fund or hedge fund was $23.1 million as of June 30, 2020 and $54.6 million as of December 31, 2019.

In the first quarter of 2020, White Mountains submitted a notice to redeem its sole hedge fund having a fair value of $45.6 million. The bulk of the redemption proceeds, subject to customary audit holdbacks, were received in April 2020 and the remaining balance is expected to be received in April 2021.

The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of June 30, 2020 and December 31, 2019:



	June 30, 2020				December 31, 2019
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments
Private equity funds
Aerospace/Defense/Government	$	44.8	$	15.7	$	33.8	$	23.3
Manufacturing/Industrial	43.8		4.0		57.7		4.1
Financial services	17.3		24.7		15.0		22.8
Total private equity funds	105.9		44.4		106.5		50.2
Hedge funds
Long/short banks and financials	—		—		54.6		—
Total hedge funds	—		—		54.6		—
Total private equity funds and hedge funds included in other long-term investments	$	105.9	$	44.4	$	161.1	$	50.2

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 June 30, 2020:



Millions	1 – 3 years	3 – 5 years	5 – 10 years	>10 years	Total
Private equity funds — expected lock-up period remaining	$4.7	$40.4	$56.7	$4.1	$105.9

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 June 30, 2020 and December 31, 2019, 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.

Insurance-Linked Securities Funds

White Mountains’s other long-term investments include ILS funds. The fair value of these investments is generally estimated using the NAV of the funds. As of June 30, 2020, White Mountains held investments in four ILS funds with a fair value of $52.1 million.

Investments in ILS funds are generally subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, non-renewal clauses, 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.

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 redemption remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period.

In the first quarter of 2020, White Mountains invested in an ILS fund that requires shareholders to make additional capital commitments annually equal to their existing capital commitment, unless a non-renewal notice is provided on or before September 15 of each calendar year. The notice of non-renewal constitutes a redemption request. Fund proceeds become available on the last calendar day of the month when the last underlying fund investment has fully matured or been commuted, which is typically three years from the initial investment in the fund.

Fair Value Measurements as of June 30, 2020

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 June 30, 2020 and December 31, 2019, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 68% and 71% of the investment portfolio.

Fair Value Measurements by Level

The following tables present White Mountains’s fair value measurements for investments as of June 30, 2020 and December 31, 2019 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.



	June 30, 2020
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	200.4	$	200.4	$	—	$	—

Debt securities issued by corporations:
Financials	151.9		—		151.9		—
Industrial	61.1		—		61.1		—
Technology	57.6		—		57.6		—
Consumer	55.6		—		55.6		—
Healthcare	43.3		—		43.3		—
Communications	40.9		—		40.9		—
Energy	34.3		—		34.3		—
Materials	32.1		—		32.1		—
Utilities	29.0		—		29.0		—
Total debt securities issued by corporations	505.8		—		505.8		—

Municipal obligations	264.8		—		264.8		—
Mortgage and asset-backed securities	220.6		—		220.6		—
Total fixed maturity investments	1,191.6		200.4		991.2		—

Short-term investments ⁽¹⁾	117.6		114.5		3.1		—

Common equity securities:
Exchange traded funds	442.4		442.4		—		—
Other ⁽²⁾	124.8		22.3		102.4		.1
Total common equity securities	567.2		464.7		102.4		.1

Other long-term investments	740.1		—		—		740.1
Other long-term investments — NAV ⁽³⁾	158.0		—		—		—
Total investments	$	2,774.5	$	779.6	$	1,096.7	$	740.2

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

⁽²⁾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.

⁽³⁾ Consists of private equity funds 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, 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		.1
Total common equity securities	683.9		547.5		136.3		.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.

Debt Securities Issued by Corporations

The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of June 30, 2020 and December 31, 2019:



	Fair Value at
Millions	June 30, 2020		December 31, 2019
AAA	$	8.3	$	9.5
AA	53.6		73.9
A	314.1		288.5
BBB	128.1		95.3
BB	1.7		—
Debt securities issued by corporations ⁽¹⁾	$	505.8	$	467.2


⁽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 June 30, 2020 and December 31, 2019:



	June 30, 2020						December 31, 2019
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	87.4	$	87.4	$	—	$	88.6	$	88.6	$	—
FHLMC	68.1		68.1		—		60.5		60.5		—
GNMA	42.2		42.2		—		30.8		30.8		—
Total agency ⁽¹⁾	197.7		197.7		—		179.9		179.9		—
Total mortgage-backed securities	197.7		197.7		—		179.9		179.9		—
Other asset-backed securities:
Vehicle receivables	11.5		11.5		—		15.1		15.1		—
Credit card receivables	11.4		11.4		—		14.0		14.0		—
Total other asset-backed securities	22.9		22.9		—		29.1		29.1		—
Total mortgage and asset-backed securities	$	220.6	$	220.6	$	—	$	209.0	$	209.0	$	—


⁽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).

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 June 30, 2020 and 2019 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 three months ended June 30, 2020 and 2019:



							Level 3 Investments					Other Long-term Investments Measured at NAV ⁽²⁾
Millions	Level 1 Investments			Level 2 Investments			Common Equity Securities		Other Long-term Investments			Other Long-term Investments Measured at NAV ⁽²⁾			Total
Balance at December 31, 2019	$	780.0		$	1,109.6		$	.1	$	654.0		$	202.3		$	2,746.0		⁽¹⁾
Net realized and unrealized (losses) gains	(13.9		)	3.6			—		15.6			(9.5		)	(4.2		)	⁽³⁾
Amortization/Accretion	—			(1.9		)	—		—			—			(1.9		)
Purchases	113.0			214.2			—		78.6			21.2			427.0
Sales	(214.0		)	(231.9		)	—		(8.1		)	(56.0		)	(510.0		)
Transfers in	—			—			—		—			—			—
Transfers out	—			—			—		—			—			—
Balance at June 30, 2020	$	665.1		$	1,093.6		$	.1	$	740.1		$	158.0		$	2,656.9		⁽¹⁾

⁽¹⁾Excludes carrying value of $117.6 and $201.2 as of June 30, 2020 and December 31, 2019 classified as short-term investments.

⁽²⁾Includes private equity funds, hedge funds and ILS funds 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”.

⁽³⁾ Excludes realized and unrealized gains associated with short-term investments of $0.4 for the six months ended June 30, 2020.



							Level 3 Investments		Other Long-term Investments Measured at NAV ^(3,5)
Millions	Level 1 Investments			Level 2 Investments			Other Long-term Investments		Other Long-term Investments Measured at NAV ^(3,5)			Total
Balance at December 31, 2018	$	842.6		$	1,160.5		$	138.7	$	186.9		$	2,328.7		⁽¹⁾
Net realized and unrealized gains	115.2			62.0			100.0		3.4			280.6			^{(2, 4)}
Amortization/Accretion	.1			(.7		)	—		—			(.6		)
Purchases	70.1			232.0			136.7		102.5			541.3
Sales	(343.5		)	(319.7		)	—		(3.8		)	(667.0		)
Transfers in	—			—			82.6		—			82.6
Transfers out	—			—			—		(82.6		)	(82.6		)
Balance at June 30, 2019	$	684.5		$	1,134.1		$	458.0	$	206.4		$	2,483.0		⁽¹⁾

⁽¹⁾Excludes carrying value of $187.1 and $214.2 as of June 30, 2019 and December 31, 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 and ILS funds 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 six months ended June 30, 2019.

⁽⁵⁾Transfer includes $71.7 associated with the Kudu Transaction. See Note 2 — “Significant Transactions”.

Fair Value Measurements — Transfers Between Levels - Six-months ended June 30, 2020 and 2019

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 the first six months of 2020 and 2019, 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.

During the first six months of 2020 and 2019, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 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 June 30, 2020 and December 31, 2019. 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	June 30, 2020
Description	Valuation Technique(s)	Fair Value ⁽⁵⁾	Unobservable Inputs
			Discount Rate ⁽²⁾⁽⁶⁾	Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) ⁽⁶⁾
Kudu’s Participation Contracts ⁽¹⁾⁽²⁾	Discounted cash flow	$315.6	18% - 23%	6x - 12x
MediaAlpha	Discounted cash flow	$225.0	14%	4%
PassportCard/DavidShield ⁽³⁾	Discounted cash flow	$95.0	23%	4%
Elementum Holdings, L.P.	Discounted cash flow	$55.1	19%	4%
Private debt instruments	Discounted cash flow	$17.5	6% - 12%	N/A
All other	Discounted cash flow	$15.7	24%	4%

Noblr, Inc.	Share price of recent transaction	$8.7	Share price:	$2.17
Zillion Insurance Services, Inc.⁽⁴⁾	Recent transaction	$5.0	Transaction price:	$5.0
Compare.com	Estimated net realizable value	$2.5	Net realizable value:	$2.5

⁽¹⁾During the six months ended June 30, 2020, Kudu deployed a total of $57.4 in new Kudu Participation Contracts, including Creation Investments Capital Management and Sequoia Financial Group.

⁽²⁾Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values.

⁽³⁾During the three months ended June 30, 2020, White Mountains made an additional $15.0 investment in PassportCard/DavidShield. See Note 2 - “Significant Transactions”.

⁽⁴⁾During the three months ended June 30, 2020, White Mountains made an additional $2.5 investment in Zillion Insurance Services, Inc.

⁽⁵⁾ Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

⁽⁶⁾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, 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%

Noblr, Inc.	Share price of recent transaction	$5.0	Share price:	$2.17
Zillion Insurance Services, Inc.	Recent transaction	$2.5	Transaction price:	$2.5
Compare.com	Estimated net realizable value	$2.5	Net realizable 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.