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Investment Securities

12 Months Ended

Dec. 31, 2022

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, its investment in MediaAlpha 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 fair value, which approximated amortized cost, as of December 31, 2022 and 2021.

Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits, 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, dividend income from common equity securities, distributions from its investment in MediaAlpha and distributions from other long-term investments.

The following table presents pre-tax net investment income for the years ended December 31, 2022, 2021 and 2020:


	Year Ended December 31,
Millions	2022		2021		2020
Fixed maturity investments	$	41.4	$	28.8	$	29.0
Short-term investments	16.4		.6		1.1
Common equity securities	1.6		.1		6.6
Investment in MediaAlpha	—		—		59.9

Other long-term investments	68.1		56.3		35.6
Amount attributable to TPC Providers	(1.0)		(1.0)		—
Total investment income	126.5		84.8		132.2
Third-party investment expenses	(2.1)		(2.3)		(1.2)
Net investment income, pre-tax	$	124.4	$	82.5	$	131.0

Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for the years ended December 31, 2022, 2021 and 2020:


	Year Ended December 31,
Millions	2022		2021		2020
Realized investment gains (losses)
Fixed maturity investments	$	(11.9)	$	3.9	$	10.9
Short-term investments	(1.4)		(.1)		.4
Common equity securities	—		.4		137.2
Investment in MediaAlpha	—		160.3		63.8
Other long-term investments	128.4		(7.7)		(25.2)
Net realized investment gains (losses)	115.1		156.8		187.1

Unrealized investment gains (losses)
Fixed maturity investments	(168.4)		(42.2)		27.5
Short-term investments	(1.1)		—		—
Common equity securities	(7.1)		14.9		(130.6)
Investment in MediaAlpha	(93.0)		(540.6)		622.2
Other long-term investments	(43.8)		172.7		10.6
Net unrealized investment gains (losses)	(313.4)		(395.2)		529.7
Net realized and unrealized investment gains (losses), before amount attributable to TPC providers (1)	(198.3)		(238.4)		716.8
Amount attributable to TPC Providers	6.8		(7.7)		—
Net realized and unrealized investment gains (losses)	$	(191.5)	$	(246.1)	$	716.8

Fixed maturity and short-term investments
Net realized and unrealized investment gains (losses)	$	(182.8)	$	(38.4)	$	38.8
Less: net realized and unrealized gains (losses) on investment securities sold during the period	(2.9)		(8.4)		(8.7)
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	$	(179.9)	$	(30.0)	$	47.5

Common equity securities and investment in MediaAlpha
Net realized and unrealized investment gains (losses) on common equity securities	$	(7.1)	$	15.3	$	6.6
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(93.0)		(380.3)		686.0
Total net realized and unrealized investment gains (losses)	(100.1)		(365.0)		692.6
Less: net realized and unrealized gains (losses) on investment securities sold during the period	—		20.3		38.3
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	$	(100.1)	$	(385.3)	$	654.3

(1) For 2022, 2021 and 2020, includes $(29.3), $(7.7) and $4.0 of net realized and unrealized investment gains (losses) related to foreign currency exchange.

For the years ended December 31, 2022, 2021 and 2020, 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.

White Mountains recognized gross realized investment gains of $129.9 million, $212.3 million and $214.4 million and gross realized investment losses of $14.8 million, $55.5 million and $27.3 million on sales of investment securities for the years ending December 31, 2022, 2021 and 2020.

The following table presents the total net unrealized gains (losses) attributable to Level 3 investments for the years ended December 31, 2022, 2021 and 2020 for investments held at the end of the period.


	Year Ended December 31,
Millions	2022		2021		2020

Total net unrealized investment gains on other long-term investments held at the end of period, pre-tax (1)	$	56.5	$	98.9	$	276.0

(1) For 2020, includes $278.7 of unrealized investment gains from White Mountains’s investment in MediaAlpha.

Proceeds from the sales and maturities of investments, excluding short-term investments, totaled $0.5 billion, $0.8 billion and $1.4 billion for the years ended December 31, 2022, 2021 and 2020.

Investment Holdings

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses) and carrying values of White Mountains’s fixed maturity investments as of December 31, 2022 and 2021.


	December 31, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	216.6	$	—	$	(10.2)	$	—	$	206.4
Debt securities issued by corporations	1,098.3		.6		(78.3)		(1.8)		1,018.8
Municipal obligations	281.6		.4		(23.4)		—		258.6
Mortgage and asset-backed securities	288.7		—		(34.5)		—		254.2
Collateralized loan obligations	190.8		.1		(6.0)		(2.0)		182.9
Total fixed maturity investments	$	2,076.0	$	1.1	$	(152.4)	$	(3.8)	$	1,920.9


	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
U.S. Government and agency obligations	$	212.1	$	.5	$	(1.1)	$	—	$	211.5
Debt securities issued by corporations	993.3		8.7		(8.7)		(.4)		992.9
Municipal obligations	276.4		16.8		(1.3)		—		291.9
Mortgage and asset-backed securities	277.2		2.9		(2.5)		—		277.6
Collateralized loan obligations	136.5		—		(.4)		(1.1)		135.0


Total fixed maturity investments	$	1,895.5	$	28.9	$	(14.0)	$	(1.5)	$	1,908.9

The weighted average duration of White Mountains’s fixed income portfolio was 2.3 years, including short-term investments, and 3.4 years, excluding short-term investments, as of December 31, 2022.

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, 2022. 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, 2022
Millions	Cost or Amortized Cost		Carrying Value
Due in one year or less	$	204.8	$	201.2
Due after one year through five years	914.0		853.2
Due after five years through ten years	374.4		337.4
Due after ten years	103.3		92.0
Mortgage and asset-backed securities and collateralized loan obligations	479.5		437.1

Total fixed maturity investments	$	2,076.0	$	1,920.9

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of common equity securities, White Mountains’s investment in MediaAlpha and other long-term investments as of December 31, 2022 and 2021:


	December 31, 2022
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value

Common equity securities	$	660.6	$	26.7	$	(8.4)	$	(10.5)	$	668.4
Investment in MediaAlpha	$	—	$	168.6	$	—	$	—	$	168.6


Other long-term investments	$	1,340.8	$	271.1	$	(107.1)	$	(16.8)	$	1,488.0


	December 31, 2021
Millions	Cost or Amortized Cost		Gross Unrealized Gains		Gross Unrealized Losses		Net Foreign Currency Gains (Losses)		Carrying Value
Common equity securities	$	236.3	$	16.1	$	—	$	(1.3)	$	251.1
Investment in MediaAlpha	$	—	$	261.6	$	—	$	—	$	261.6

Other long-term investments	$	1,186.7	$	239.0	$	(44.1)	$	(3.8)	$	1,377.8

Fair Value Measurements

As of December 31, 2022 and 2021, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 72% and 68% 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, 2022 and 2021 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, 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 by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class 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.


	December 31, 2022
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	206.4	$	206.4	$	—	$	—

Debt securities issued by corporations:
Financials	291.2		—		291.2		—
Consumer	191.9		—		191.9		—
Technology	123.7		—		123.7		—
Healthcare	121.3		—		121.3		—
Industrial	115.4		—		115.4		—
Utilities	73.8		—		73.8		—
Communications	47.9		—		47.9		—
Energy	33.9		—		33.9		—
Materials	19.7		—		19.7		—

Total debt securities issued by corporations	1,018.8		—		1,018.8		—

Municipal obligations	258.6		—		258.6		—
Mortgage and asset-backed securities	254.2		—		254.2		—

Collateralized loan obligations	182.9		—		182.9		—
Total fixed maturity investments	1,920.9		206.4		1,714.5		—

Short-term investments	924.1		924.1		—		—
Common equity securities

Exchange-trade funds	333.8		333.8		—		—
Other (1)	334.6		—		334.6		—
Total common equity securities	668.4		333.8		334.6		—
Investment in MediaAlpha	168.6		168.6		—		—












Other long-term investments	926.4		—		14.8		911.6
Other long-term investments — NAV (2)	561.6		—		—		—
Total other long-term investments	1,488.0		—		14.8		911.6
Total investments	$	5,170.0	$	1,632.9	$	2,063.9	$	911.6

(1) Consist of investments in listed funds that predominantly invest in international equities.

(2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured using NAV as a practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.


	December 31, 2021
Millions	Fair Value		Level 1		Level 2		Level 3
Fixed maturity investments:
U.S. Government and agency obligations	$	211.5	$	211.5	$	—	$	—

Debt securities issued by corporations:
Financials	264.2		—		264.2		—
Consumer	178.1		—		178.1		—
Technology	117.9		—		117.9		—
Industrial	112.9		—		112.9		—
Healthcare	112.8		—		112.8		—
Utilities	70.9		—		70.9		—
Communications	56.0		—		56.0		—
Energy	48.0		—		48.0		—
Materials	32.1		—		32.1		—

Total debt securities issued by corporations	992.9		—		992.9		—

Municipal obligations	291.9		—		291.9		—
Mortgage and asset-backed securities	277.6		—		277.6		—
Collateralized loan obligations	135.0		—		135.0		—


Total fixed maturity investments	1,908.9		211.5		1,697.4		—

Short-term investments	465.9		465.9		—		—
Common equity securities (1)	251.1		—		251.1		—

Investment in MediaAlpha	261.6		261.6		—		—
















Other long-term investments	895.3		—		4.7		890.6
Other long-term investments — NAV (2)	482.5		—		—		—
Total other long-term investments	1,377.8		—		4.7		890.6
Total investments	$	4,265.3	$	939.0	$	1,953.2	$	890.6

(1) Consists of investments in listed funds that predominantly invest in international equities.

Investments Held on Deposit or as Collateral

As of December 31, 2022 and 2021, investments of $500.5 million and $479.5 million, were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM.

HG Global is required to maintain an interest reserve account in connection with its senior notes issued in 2022. As of December 31, 2022, the interest reserve account, which is included in short-term investments, is $31.2 million. See Note 7 — “Debt”.

BAM is 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 $4.6 million and $4.8 million as of December 31, 2022 and 2021.

Lloyd’s trust deposits are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. As of December 31, 2022 and 2021, Ark held Lloyd’s trust deposits with a fair value of $137.4 million and $113.8 million.

The underwriting capacity of a member of Lloyd’s must be supported by providing a deposit (“Funds at Lloyd’s”) in the form of cash, securities or letters of credit in an amount determined by Lloyd’s. The amount of such deposit is calculated for each member through the completion of an annual capital adequacy exercise. These requirements allow Lloyd’s to evaluate that each member has sufficient assets to meet its underwriting liabilities plus a required solvency margin. As of December 31, 2022 and 2021, the fair value of Ark’s Funds at Lloyd’s investment deposits totaled $319.2 million and $342.8 million.

As at December 31, 2022 and 2021, Ark has $90.3 million and $50.0 million of short-term investments pledged as collateral under uncommitted stand by letters of credit. See Note 7 — “Debt”.

As of December 31, 2022, short-term investments of $203.7 million were held in a collateral trust account required to be maintained in relation to WM Outrigger Re’s reinsurance agreement with GAIL.

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 December 31, 2022 and 2021:


	Fair Value at December 31,
Millions	2022		2021
AAA	$	11.3	$	12.0
AA	96.0		85.0
A	567.9		490.4
BBB	337.7		396.8


Other	5.9		8.7
Debt securities issued by corporations (1)	$	1,018.8	$	992.9

(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 and Collateralized Loan Obligations

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of December 31, 2022 and 2021:


	December 31, 2022						December 31, 2021
Millions	Fair Value		Level 2		Level 3		Fair Value		Level 2		Level 3
Mortgage-backed securities:
Agency:
FNMA	$	124.5	$	124.5	$	—	$	125.4	$	125.4	$	—
FHLMC	78.8		78.8		—		90.5		90.5		—
GNMA	28.3		28.3		—		40.1		40.1		—
Total agency (1)	231.6		231.6		—		256.0		256.0		—
Non-agency: Residential	.3		.3		—		.5		.5		—

Total non-agency	.3		.3		—		.5		.5		—
Total mortgage-backed securities	231.9		231.9		—		256.5		256.5		—
Other asset-backed securities:
Credit card receivables	11.9		11.9		—		12.3		12.3		—
Vehicle receivables	10.4		10.4		—		8.8		8.8		—

Total other asset-backed securities	22.3		22.3		—		21.1		21.1		—
Total mortgage and asset-backed securities	254.2		254.2		—		277.6		277.6		—
Collateralized loan obligations:	182.9		182.9		—		135.0		135.0		—
Total mortgage and asset-backed securities and collateralized loan obligations	$	437.1	$	437.1	$	—	$	412.6	$	412.6	$	—

(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).

As of December 31, 2022, White Mountains’s investment portfolio included $182.9 million of collateralized loan obligations that are within the senior tranches of their respective fund securitization structures. All of White Mountains’s collateral loan obligations were rated AAA or AA as of December 31, 2022.

Investment in MediaAlpha

Following the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and is presented as a separate line item on the balance sheet.

At the December 31, 2022 closing price of $9.95 per share, the fair value of White Mountains’s investment in MediaAlpha was $168.6 million. See Note 2 — “Significant Transactions”.

Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of December 31, 2022 and 2021:


	Fair Value at December 31,
Millions	2022		2021
Kudu’s Participation Contracts	$	695.9	$	669.5
PassportCard/DavidShield	135.0		120.0
Elementum Holdings L.P.	30.0		45.0
Other unconsolidated entities (1)	37.2		34.4
Total unconsolidated entities	898.1		868.9
Private equity funds and hedge funds	197.8		153.8
Bank loan fund	174.8		163.0
Lloyd’s trust deposits	137.4		113.8
ILS funds	49.3		51.9
Private debt instruments	9.6		14.1
Other	21.0		12.3
Total other long-term investments	$	1,488.0	$	1,377.8

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

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, 2022, White Mountains held investments in 16 private equity funds and two hedge funds. The largest investment in a single private equity fund or hedge fund was $49.0 million as of December 31, 2022 and $31.3 million as of December 31, 2021.

The following table presents the fair value of investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of December 31, 2022 and 2021:


	December 31, 2022				December 31, 2021
Millions	Fair Value		Unfunded Commitments		Fair Value		Unfunded Commitments

Private equity funds
Aerospace/Defense/Government	$	59.4	$	37.5	$	69.8	$	11.8
Financial services	77.1		54.3		67.7		29.3
Real estate	4.1		2.5		4.3		2.9



Total private equity funds	140.6		94.3		141.8		44.0

Hedge funds
Long/short equity financials and business services	49.0		—		—		—
European small/mid cap	8.2		—		12.0		—
Total hedge funds	57.2		—		12.0		—
Total private equity funds and hedge funds included in other long-term investments	$	197.8	$	94.3	$	153.8	$	44.0

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, 2022:


Millions	1 – 3 years		3 – 5 years		5 – 10 years		>10 years		Total
Private equity funds — expected lock-up period remaining	$	4.2	$	18.8	$	113.9	$	3.7	$	140.6

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, 2022 and 2021, 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. Advance notice requirements for redemptions from White Mountains’s hedge fund investments range from 45 to 90 days. One of White Mountains’s hedge fund investments also limits redemptions to every second anniversary following the date of the initial investment.

Bank Loan Fund

White Mountains’s other long-term investments include a bank loan fund with a fair value of $174.8 million as of December 31, 2022. The fair value of this investment is estimated using the NAV of the fund. The bank loan fund’s investment objective is to provide, on an unleveraged basis, high current income consistent with preservation of capital and low duration. The bank loan fund primarily invests in a broad portfolio of U.S. dollar-denominated, non-investment grade, floating-rate senior secured loans and may invest in other financial instruments, such as secured and unsecured corporate debt, credit default swaps, reverse repurchase agreements, synthetic indices and cash and cash equivalents.

The investment in the bank loan fund is subject to 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. White Mountains may redeem all or a portion of its bank loan fund investment as of any calendar month-end upon 15 calendar days advanced written notice.

Lloyd’s Trust Deposits

White Mountains’s other long-term investments include Lloyd’s trust deposits, which consist of non-U.K. deposits and Canadian comingled pooled funds. The Lloyd’s trust deposits invest primarily in short-term government securities, agency securities and corporate bonds held in trusts that are managed by Lloyd's of London. These investments are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. The fair value of the Lloyd’s trust deposits is generally estimated using the NAV of the funds. As of December 31, 2022, White Mountains held Lloyd’s trust deposits with a fair value of $137.4 million.

Insurance-Linked Securities Funds

White Mountains’s other long-term investments include ILS fund investments. The fair value of these investments is generally estimated using the NAV of the funds. As of December 31, 2022, White Mountains held investments in ILS funds with a fair value of $49.3 million. During the fourth quarter of 2022, White Mountains agreed to invest an additional $100.0 million into ILS funds beginning in 2023. White Mountains pre-funded $70.0 million of this investment as of December 31, 2022, which has been recorded as a receivable within other assets.

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 ILS funds less certain due to the potential for loss development. In such circumstances, the impacted investments may be subject to additional lock-up provisions.

ILS funds are typically 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.

Rollforward of Level 3 Investments

Level 3 measurements as of December 31, 2022 and 2021 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 table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the years ended December 31, 2022 and 2021:


Level 3 Investments
Millions	Other Long-term Investments			Other Long-term Investments
Balance at December 31, 2021	$	890.6	Balance at December 31, 2020	$	614.2
Net realized and unrealized gains	60.4		Net realized and unrealized gains	117.3
Amortization/accretion	—		Amortization/accretion	—
Purchases	129.8		Purchases	225.4
Sales	(169.2)		Sales	(75.9)
Effect of Ark Transaction	—		Effect of Ark Transaction	9.6
Transfers in	—		Transfers in	—
Transfers out	—		Transfers out	—
Balance at December 31, 2022	$	911.6	Balance at December 31, 2021	$	890.6

Fair Value Measurements — Transfers Between Levels - For Years Ended December 31, 2022 and 2021

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 2022 and 2021, 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 2022 and 2021, 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 White Mountains’s other long-term investments classified within Level 3 as of December 31, 2022 and 2021. The tables below exclude $41.1 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds.

$ in Millions

December 31, 2022

Description

Valuation Technique(s) (1)

Fair Value (2)

Unobservable Inputs

Discount Rate (6)

Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)

Kudu’s Participation Contracts (3)(4)(5)

Discounted cash flow

$695.9

18% - 25%

7x - 16x

PassportCard/DavidShield

Discounted cash flow

$135.0

24%

Elementum Holdings, L.P.

Discounted cash flow

$30.0

21%

Private debt instruments

Discounted cash flow

$9.6

11%

N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

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

(3) 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. The weighted average discount rate and weighted average terminal cash flow exit multiple applied to Kudu’s Participation Contracts is 21% and 11.8x.

(4) In 2022, Kudu deployed a total of $99.8 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, Pennybacker Capital Management and TK Partners.

(5) As of December 31, 2022, two of Kudu’s Participation Contracts with a total fair value of $189.0 were valued using a probability weighted expected return method, which takes into account factors such as a discounted cash flow analysis, the expected value to be received in a pending sales transaction and the likelihood that a sales transaction will take place.

(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, 2021

Description

Valuation Technique(s) (1)

Fair Value (2)

Unobservable Inputs

Discount Rate (6)

Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6)

Kudu’s Participation Contracts (3)(4)(5)

Discounted cash flow

$669.5

18% - 23%

7x - 13x

PassportCard/DavidShield

Discounted cash flow

$120.0

23%

Elementum Holdings, L.P.

Discounted cash flow

$45.0

17%

Private debt instruments

Discounted cash flow

$9.4

N/A

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.

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

(4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management.

(5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which takes into account factors such as a discounted cash flow analysis, the expected value to be received in a pending sales transaction and the likelihood that a sales transaction will take place.