White Mountains Insurance (WTM) 10-Q 9 May 23 2023 Q1 Quarterly report Financial data

Cover Page

Cover Page - shares	3 Months Ended
	Mar. 31, 2023	May 05, 2023
Cover [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Mar. 31, 2023
Document Transition Report	false
Entity File Number	1-8993
Entity Registrant Name	WHITE MOUNTAINS INSURANCE GROUP, LTD
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	94-2708455
Entity Address, Address Line One	23 South Main Street, Suite 3B
Entity Address, City or Town	Hanover,
Entity Address, State or Province	NH
Entity Address, Postal Zip Code	03755-2053
City Area Code	603
Local Phone Number	640-2200
Title of 12(b) Security	Common Shares, par value $1.00 per share
Trading Symbol	WTM
Security Exchange Name	NYSE
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Common Stock, Shares Outstanding (in shares)		2,563,384
Entity Central Index Key	0000776867
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2023
Document Fiscal Period Focus	Q1
Amendment Flag	false

CONSOLIDATED BALANCE SHEETS

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Investments
Other long-term investments	$ 1,643	$ 1,488
Total assets	7,959.1	7,389.3
Liabilities
Debt	556.3	575.2
Total liabilities	3,866.3	3,454.3
White Mountains’s common shareholders’ equity
White Mountains’s common shares at $1 par value per share—authorized 50,000,000 shares; issued and outstanding 2,564,484 and 2,572,156 shares	2.6	2.6
Paid-in surplus	535.2	536
Retained earnings	3,367.3	3,211.8
Accumulated other comprehensive income (loss), after-tax:
Net unrealized gains (losses) from foreign currency translation and interest rate swap	(2.7)	(3.5)
Total White Mountains’s common shareholders’ equity	3,902.4	3,746.9
Noncontrolling interests	190.4	188.1
Total equity	4,092.8	3,935
Total liabilities and equity	7,959.1	7,389.3
Financial Guarantee (HG Global/BAM)
Investments
Fixed maturity investments, at fair value	924.8	909.9
Short-term investments, at fair value	65.9	65.9
Total investments	990.7	975.8
Cash	4.8	18.2
Insurance premiums receivable	6.3	6.6
Deferred acquisition costs	36.9	36
Other assets	21.6	21.9
Total assets	1,060.3	1,058.5
Liabilities
Unearned insurance premiums	299.8	298.3
Debt	146.6	146.5
Accrued incentive compensation	12.1	28
Other liabilities	30.1	29
Total liabilities	488.6	501.8
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Investments
Fixed maturity investments, at fair value	765	772.8
Common equity securities, at fair value	340.4	334.6
Short-term investments, at fair value	553.7	484.6
Other long-term investments	393.9	373.6
Total investments	2,053	1,965.6
Cash	132.6	101.5
Reinsurance recoverables	570.6	595.3
Insurance premiums receivable	909.7	544.1
Deferred acquisition costs	208.5	127.2
Goodwill and other intangible assets	292.5	292.5
Other assets	71.5	65.2
Total assets	4,238.4	3,691.4
Liabilities
Loss and loss adjustment expense reserves	1,345.6	1,296.5
Unearned insurance premiums	1,123.5	623.2
Debt	184.5	183.7
Reinsurance payable	193	251.1
Contingent consideration	42.9	45.3
Other liabilities	143.8	122.3
Total liabilities	3,033.3	2,522.1
Asset Management (Kudu)
Investments
Other long-term investments	683.2	695.9
Cash	36.6	101.4
Accrued investment income	19.1	12.4
Goodwill and other intangible assets	8.5	8.6
Other assets	20.6	7.6
Total assets	768	825.9
Liabilities
Debt	191.6	208.3
Other liabilities	54.8	65
Total liabilities	246.4	273.3
Other Operations
Investments
Fixed maturity investments, at fair value	266.1	238.2
Common equity securities, at fair value	357.4	333.8
Short-term investments, at fair value	264.6	373.6
Investment in MediaAlpha, at fair value	253.8	168.6
Other long-term investments	565.9	418.5
Total investments	1,707.8	1,532.7
Cash	28.7	33.9
Goodwill and other intangible assets	75.2	91.3
Other assets	80.7	155.6
Total assets	1,892.4	1,813.5
Liabilities
Debt	33.6	36.7
Accrued incentive compensation	40	86.1
Other liabilities	24.4	34.3
Total liabilities	$ 98	$ 157.1

CONSOLIDATED BALANCE SHEETS (Pa

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Common shares, par value per share (in dollars per share)	$ 1	$ 1
Common shares, authorized shares (in shares)	50,000,000	50,000,000
Common shares, issued shares (in shares)	2,564,484	2,572,156
Common shares, outstanding shares (in shares)	2,564,484	2,572,156
Asset Management (Kudu)
Restricted cash	$ 13	$ 12.2

CONSOLIDATED STATEMENTS OF OPER

CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Revenues:
Earned insurance premiums	$ 262.8	$ 202.8
Net investment income	39	20.6
Net realized and unrealized investment gains (losses)	112.9	(8.4)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	85.2	18.8
Commission revenues	3.3	2.9
Other revenues	28.7	23.7
Total revenues	531.9	260.4
Expenses:
Loss and loss adjustment expenses	147.8	122
Acquisition expenses	62.5	52.9
Cost of sales	13.9	21.4
General and administrative expenses	96	69.9
Change in fair value of contingent consideration	(2.4)	2.1
Interest expense	15	6.9
Total expenses	332.8	275.2
Net income (loss) from continuing operations	187.2	(12.1)
Net income (loss) from discontinued operations, net of tax	0	3.7
Net income (loss)	187.2	(8.4)
Net (income) loss attributable to noncontrolling interests	(7.7)	41.8
Net income (loss) attributable to White Mountains’s common shareholders	179.5	33.4
Pre-tax income (loss) from continuing operations	199.1	(14.8)
Income tax (expense) benefit	(11.9)	2.7
Financial Guarantee (HG Global/BAM)
Revenues:
Earned insurance premiums	7.7	8.4
Net investment income	7.2	4.6
Net realized and unrealized investment gains (losses)	17	(45.1)
Other revenues	0.8	0.8
Total revenues	32.7	(31.3)
Expenses:
Acquisition expenses	2.7	3
General and administrative expenses	17.3	16.3
Interest expense	4.5	0
Total expenses	24.5	19.3
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Revenues:
Earned insurance premiums	255.1	194.4
Net investment income	10.6	1.6
Net realized and unrealized investment gains (losses)	24.5	(17.5)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha		0
Commission revenues		0
Other revenues	(2.7)	(2.8)
Total revenues	287.5	175.7
Expenses:
Loss and loss adjustment expenses	147.8	122
Acquisition expenses	59.8	49.9
Cost of sales		0
General and administrative expenses	35.2	21
Change in fair value of contingent consideration	(2.4)	2.1
Interest expense	5	3.8
Total expenses	245.4	198.8
Pre-tax income (loss) from continuing operations		(23.1)
Asset Management (Kudu)
Revenues:
Earned insurance premiums	0	0
Net investment income	14.2	12.6
Net realized and unrealized investment gains (losses)	29.6	22.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0
Commission revenues	0	0
Other revenues	0	0
Total revenues	43.8	34.9
Expenses:
Loss and loss adjustment expenses	0	0
Acquisition expenses	0	0
Cost of sales	0	0
General and administrative expenses	3.8	2.8
Change in fair value of contingent consideration	0	0
Interest expense	4.7	2.8
Total expenses	8.5	5.6
Pre-tax income (loss) from continuing operations	35.3	29.3
Other Operations
Revenues:
Earned insurance premiums	0	0
Net investment income	7	1.8
Net realized and unrealized investment gains (losses)	41.8	31.9
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	85.2	18.8
Commission revenues	3.3	2.9
Other revenues	30.6	25.7
Total revenues	167.9	81.1
Expenses:
Loss and loss adjustment expenses	0	0
Acquisition expenses	0	0
Cost of sales	13.9	21.4
General and administrative expenses	39.7	29.8
Change in fair value of contingent consideration	0	0
Interest expense	0.8	0.3
Total expenses	54.4	51.5
Pre-tax income (loss) from continuing operations	$ 113.5	$ 29.6

CONSOLIDATED STATEMENTS OF COMP

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (Unaudited) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Statement of Comprehensive Income [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders	$ 179.5	$ 33.4
Other comprehensive income (loss), net of tax	1.2	(0.4)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group	0	(1.9)
Comprehensive income (loss)	180.7	31.1
Other comprehensive (income) loss attributable to noncontrolling interests	(0.4)	0.2
Comprehensive income (loss) attributable to White Mountains’s common shareholders	$ 180.3	$ 31.3
Basic earnings (loss) per share
Income (Loss) from Continuing Operations, Per Basic Share	$ 69.83	$ 9.90
Discontinued operations (in usd per share)	0	1.20
Total consolidated operations (in usd per share)	69.83	11.10
Diluted earnings (loss) per share
Continuing operations (in usd per share)	69.83	9.90
Discontinued operations (in usd per share)	0	1.20
Total consolidated operations (in usd per share)	69.83	11.10
Dividends declared and paid per White Mountains’s common share	$ 1	$ 1

CONSOLIDATED STATEMENTS OF CHAN

CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY (Unaudited) - USD ($) $ in Millions	Total	Total	Common shares and paid-in surplus	Retained earnings	AOCI, after tax	Non-controlling interest	Total Equity	BAM Non-controlling interest	BAM Total Equity
Beginning Balances at Dec. 31, 2021		$ 3,548.1	$ 588.9	$ 2,957.5	$ 1.7	$ 156.6	$ 3,704.7
Increase (Decrease) in Shareholders' Equity
Net income (loss)	$ (8.4)	33.4		33.4		(41.8)	(8.4)
Other comprehensive income (loss), net of tax	(0.4)	(0.2)			(0.2)	(0.2)	(0.4)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group		(1.9)			(1.9)		(1.9)
Comprehensive income (loss)	31.1	31.3		33.4	(2.1)	(42)	(10.7)
Dividends declared on common shares		(3)		(3)			(3)
Dividends to noncontrolling interests						(0.6)	(0.6)
Issuances of common shares		0.8	0.8				0.8
Repurchases and retirements of common shares		(39)	(7.3)	(31.7)			(39)
BAM member surplus contribution, net of tax								$ 12.3	$ 12.3
Amortization of restricted share awards		2.9	2.9				2.9
Recognition of equity-based compensation expense of subsidiaries		1.2	1.2			0.2	1.4
Net contributions and dilution from other noncontrolling interests		(0.2)	(0.2)			0.7	0.5
Ending Balances at Mar. 31, 2022		3,542.1	586.3	2,956.2	(0.4)	127.2	3,669.3
Beginning Balances at Dec. 31, 2022	3,935	3,746.9	538.6	3,211.8	(3.5)	188.1	3,935
Increase (Decrease) in Shareholders' Equity
Net income (loss)	187.2	179.5		179.5		7.7	187.2
Other comprehensive income (loss), net of tax	1.2	0.8			0.8	0.4	1.2
Comprehensive income (loss)	180.7	180.3		179.5	0.8	8.1	188.4
Dividends declared on common shares		(2.6)		(2.6)			(2.6)
Dividends to noncontrolling interests						(7.2)	(7.2)
Issuances of common shares		0.1	0.1				0.1
Repurchases and retirements of common shares		(25.3)	(3.9)	(21.4)			(25.3)
BAM member surplus contribution, net of tax								$ 11.8	$ 11.8
Amortization of restricted share awards		3.1	3.1				3.1
Recognition of equity-based compensation expense of subsidiaries		0.4	0.4			0.2	0.6
Net contributions and dilution from other noncontrolling interests		(0.5)	(0.5)			(1.2)	(1.7)
Disposition of noncontrolling interests						(9.4)	(9.4)
Ending Balances at Mar. 31, 2023	$ 4,092.8	$ 3,902.4	$ 537.8	$ 3,367.3	$ (2.7)	$ 190.4	$ 4,092.8

CONSOLIDATED STATEMENTS OF CASH

CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Cash flows from operations:
Net income (loss)	$ 187.2	$ (8.4)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses	(112.9)	8.4
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	(85.2)	(18.8)
Deferred income tax expense (benefit)	(3.6)	5.7
Amortization of restricted share awards	3.1	2.9
Amortization (accretion) and depreciation	(2.4)	4.3
Net (income) loss from discontinued operation, net of tax - NSM Group	0	(3.7)
Other operating items:
Net change in reinsurance recoverables	24.7	16
Net change in insurance premiums receivable	(365.3)	(343.6)
Net change in deferred acquisition costs	(82.2)	(71.6)
Net change in loss and loss adjustment expense reserves	49.1	104.9
Net change in unearned insurance premiums	501.8	388.2
Net change in reinsurance payable	(58.1)	(75.2)
Net change in restricted cash	0.8	0
Proceeds from Kudu’s Participation Contracts sold	62.9	0
Contributions to Kudu’s Participation Contracts	(30.9)	0
Net change in other assets and liabilities	(3.4)	(55)
Net cash provided from (used for) operations - continuing operations	85.6	(45.9)
Net cash provided from (used for) operations - NSM Group discontinued operations (Note 19)	0	4.4
Net cash provided from (used for) operations	85.6	(41.5)
Cash flows from investing activities:
Net change in short-term investments	47.6	136.7
Sales of fixed maturity investments	54.6	86.5
Maturities, calls and paydowns of fixed maturity investments	66.8	39
Distributions and redemptions of other long-term investments	2	39.8
Purchases of fixed maturity investments	(127.6)	(115)
Purchases of common equity securities	0	(38)
Purchases of other long-term investments	(146.1)	(21.4)
Net other investing activities	(11.2)	4.9
Net cash provided from (used for) investing activities - continuing operations	(96.6)	132.5
Net cash provided from (used for) investing activities - NSM Group discontinued operations (Note 19)	0	7.3
Net cash provided from (used for) investing activities	(96.6)	139.8
Cash flows from financing activities:
Draw down of debt and revolving line of credit	0	2
Repayment of debt and revolving line of credit	(20)	(1.3)
Cash dividends paid to common shareholders	(2.6)	(3)
Common shares repurchased	(25.3)	(39)
Net contributions from (distributions to) other noncontrolling interests	(1.7)	0.4
Net (contributions to) distributions from discontinued operations	0	9.7
BAM member surplus contributions	11.8	12.3
Fidus Re premium payments	(3.5)	(1.9)
Net cash provided from (used for) financing activities - continuing operations	(41.3)	(20.8)
Net cash provided from (used for) financing activities - NSM Group discontinued operations (Note 19)	0	(10.3)
Net cash provided from (used for) financing activities	(41.3)	(31.1)
Net change in cash during the period	(52.3)	65.8
Cash balances at beginning of period (includes restricted cash balances of $12.2 and $4.5 and excludes discontinued operations cash balances of $0.0 and $111.6)	255	147.7
Cash balances at end of period (includes restricted cash balances of $13.0 and $4.5 and excludes discontinued operations cash balances of $0.0 and $113.6)	202.7	213.5
Supplemental cash flows information:
Interest paid	(5.8)	(5.5)
Net income tax payments	(17.8)	(0.3)
Other Operations
Cash flows from investing activities:
Proceeds from the sale of Other Businesses, net of cash sold of $0.8 and $0.0	17.3	0
Marketing Technology (MediaAlpha)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	$ (85.2)	$ (18.8)

CONSOLIDATED STATEMENTS OF CA_2

CONSOLIDATED STATEMENTS OF CASH FLOWS (Parenthetical) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Restricted cash balance	$ 13	$ 4.5
Discontinued operations cash balance	202.7	213.5
Other Operations
Cash sold in subsidiary transaction	0.8	0
Discontinued Operations, Held-for-sale | NSM Insurance Group
Restricted cash balance		90.2
Discontinued operations cash balance	$ 0	$ 113.6

Basis of Presentation and Signi

Basis of Presentation and Significant Accounting Policies	3 Months Ended
	Mar. 31, 2023
Accounting Policies [Abstract]
Basis of Presentation and Significant Accounting Policies	Basis of Presentation and Significant Accounting Policies Basis of Presentation White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”) is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report. The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of the Company, its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates. These interim financial statements include all adjustments considered necessary by management to fairly state the financial position, results of operations and cash flows of White Mountains. These interim financial statements may not be indicative of financial results for the full year and should be read in conjunction with the Company’s 2022 Annual Report on Form 10-K. Reportable Segments As of March 31, 2023, White Mountains conducted its operations through three reportable segments: (1) HG Global/BAM, (2) Ark/WM Outrigger, and (3) Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations. White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the Company’s chief operating decision makers and its Board of Directors. See Note 14 — “Segment Information.” The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (collectively, “HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively with HG Global, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM (the “BAM Surplus Notes”). As of March 31, 2023 and December 31, 2022, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a variable interest entity (“VIE”) for which White Mountains is the primary beneficiary. BAM’s results are all attributed to noncontrolling interests. The Ark/WM Outrigger segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”) and Outrigger Re Ltd. Segregated Account 2023-1 (“WM Outrigger Re”) (collectively with Ark, “Ark/WM Outrigger”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, specialty, marine & energy, casualty and accident & health. Ark underwrites select coverages through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”) and its wholly-owned subsidiary Group Ark Insurance Limited (“GAIL”). White Mountains acquired a controlling ownership interest in Ark on January 1, 2021 (the “Ark Transaction”). As of March 31, 2023 and December 31, 2022, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within results of operations and other comprehensive income for the three months ended March 31, 2022 are shown net of amounts relating to the TPC Providers’ share of the Syndicates’ results, including investment results. During the fourth quarter of 2022, Ark sponsored the formation of Outrigger Re Ltd., a Bermuda company registered as a special purpose insurer and segregated accounts company, to provide collateralized reinsurance protection on Ark’s Bermuda global property catastrophe excess of loss portfolio written in calendar year 2023. Outrigger Re Ltd. issued non-voting redeemable preference shares on behalf of four segregated accounts to White Mountains and unrelated third party investors. White Mountains consolidates the results of its segregated account, WM Outrigger Re, in its financial statements. See Note 2 — “Significant Transactions.” As of March 31, 2023 and December 31, 2022, White Mountains owned 100.0% of WM Outrigger Re’s preferred equity. The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions generally are structured as minority preferred equity stakes with distribution rights, typically tied to gross revenues and designed to generate immediate cash yields. As of March 31, 2023 and December 31, 2022, White Mountains owned 89.2% and 89.3% of Kudu’s basic units outstanding (76.1% and 76.1% on a fully diluted, fully converted basis). White Mountains’s Other Operations consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC (“WM Capital”), its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/ DavidShield”), Elementum Holdings LP (“Elementum”), certain other consolidated and unconsolidated entities (“Other Operating Businesses”) and certain other assets. Discontinued Operations On August 1, 2022, White Mountains Holdings (Luxembourg) S.à r.l. (“WTM Holdings Seller”), an indirect wholly owned subsidiary of White Mountains, completed the sale of White Mountains Catskill Holdings, Inc. and NSM Insurance HoldCo, LLC (“NSM” and, collectively with White Mountains Catskill Holdings, Inc., the “NSM Group”) to Riser Merger Sub, Inc., an affiliate of The Carlyle Group Inc. (the “NSM Transaction”), pursuant to the terms of the securities purchase agreement dated as of May 9, 2022. See Note 2 — “Significant Transactions. ” NSM is a full-service managing general agent (“MGA”) and program administrator with delegated binding authorities for specialty property and casualty insurance. As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.” Significant Accounting Policies Refer to the Company’s 2022 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies.

Significant Transactions

Significant Transactions	3 Months Ended
	Mar. 31, 2023
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Significant Transactions	Significant Transactions NSM On August 1, 2022, the NSM Transaction closed. White Mountains received $1.4 billion in net cash proceeds at closing and recognized a net transaction gain of $875.7 million, which was comprised of $886.8 million of net gain from sale of discontinued operations and $2.9 million of comprehensive income related to the recognition of foreign currency translation gains (losses) from the sale, partially offset by $14.0 million of compensation and other costs related to the transaction recorded in Other Operations. WM Outrigger Re During the fourth quarter of 2022, Ark sponsored the formation of Outrigger Re Ltd., a Bermuda company registered as a special purpose insurer and segregated accounts company, to provide reinsurance capacity to Ark. On December 20, 2022, Outrigger Re Ltd. issued $250.0 million of non-voting redeemable preference shares on behalf of four segregated accounts to White Mountains and unrelated third party investors. Upon issuance of the preference shares, Outrigger Re Ltd. entered into collateralized quota share agreements with GAIL to provide reinsurance protection on Ark’s Bermuda global property catastrophe excess of loss portfolio written in calendar year 2023. The proceeds from the issuance of the preference shares were deposited into collateral trust accounts to fund any potential obligations under the reinsurance agreements with GAIL. Outrigger Re Ltd.’s obligations under the reinsurance agreements with GAIL are subject to an aggregate limit equal to the assets in the collateral trusts at any point in time. The terms of the reinsurance agreements are renewable upon the mutual agreement of Ark and the applicable preference shareholder. White Mountains purchased 100% of the preference shares issued by its segregated account, WM Outrigger Re, for $205.0 million. White Mountains consolidates WM Outrigger Re’s results in its financial statements. WM Outrigger Re’s quota share reinsurance agreement with GAIL eliminates in White Mountains’s consolidated financial statements. Kudu On May 26, 2022, Kudu raised $114.5 million of equity capital (the “Kudu Transaction”) from Massachusetts Mutual Life Insurance Company (“Mass Mutual”), White Mountains and Kudu management. Mass Mutual, White Mountains and Kudu management contributed $64.1 million, $50.0 million and $0.4 million at a pre-money valuation of 1.3x, or $114.0 million above the December 31, 2021 equity value of Kudu’s go-forward portfolio of revenue and earnings participation contracts (“Participation Contracts”). The go-forward portfolio of Kudu’s Participation Contracts excluded $54.3 million of enterprise value as of December 31, 2021 relating to two portfolio companies that had announced sale transactions prior to the capital raise. As a result of the Kudu Transaction, White Mountains’s basic ownership of Kudu decreased from 99.1% to 89.3%.

Investment Securities

Investment Securities	3 Months Ended
	Mar. 31, 2023
Investments, Debt and Equity Securities [Abstract]
Investment Securities	Investment Securities 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 March 31, 2023 and December 31, 2022. 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, insurance-linked securities (“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 three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Fixed maturity investments $ 14.5 $ 8.2 Short-term investments 9.7 .1 Common equity securities 1.3 — Other long-term investments 14.1 13.2 Amount attributable to TPC Providers — (.5) Total investment income 39.6 21.0 Third-party investment expenses (.6) (.4) Net investment income, pre-tax $ 39.0 $ 20.6 Net Realized and Unrealized Investment Gains (Losses) The following table presents net realized and unrealized investment gains (losses) for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Realized investment gains (losses) Fixed maturity investments $ (.1) $ (1.1) Short-term investments (.4) (.2) Other long-term investments 47.2 18.7 Net realized investment gains (losses) 46.7 17.4 Unrealized investment gains (losses) Fixed maturity investments 29.7 (79.5) Short-term investments 1.2 .2 Common equity securities 29.4 1.0 Investment in MediaAlpha 85.2 18.8 Other long-term investments 5.9 50.4 Net unrealized investment gains (losses) 151.4 (9.1) Net realized and unrealized investment gains (losses), before amount attributable to TPC providers (1) 198.1 8.3 Amount attributable to TPC Providers — 2.1 Net realized and unrealized investment gains (losses) $ 198.1 $ 10.4 Fixed maturity and short-term investments Net realized and unrealized investment gains (losses) $ 30.4 $ (80.6) Less: net realized and unrealized gains (losses) on investment 1.8 (1.0) Net unrealized investment gains (losses) recognized during the period on $ 28.6 $ (79.6) Common equity securities and investment in MediaAlpha Net realized and unrealized investment gains (losses) on common $ 29.4 $ 1.0 Net realized and unrealized investment gains (losses) from 85.2 18.8 Total net realized and unrealized investment gains (losses) 114.6 19.8 Less: net realized and unrealized gains (losses) on investment — — Net unrealized investment gains (losses) recognized during the period on $ 114.6 $ 19.8 (1) For the three months ended March 31, 2023 and 2022, includes $5.4 and $2.6 of realized and unrealized investment gains related to foreign currency exchange. The following table presents total net unrealized gains (losses) attributable to Level 3 investments for the three months ended March 31, 2023 and 2022 for investments still held at the end of the period: Three Months Ended March 31, Millions 2023 2022 Total net unrealized investment gains on other long-term investments held at the $ 37.0 $ 27.2 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 March 31, 2023 and December 31, 2022: March 31, 2023 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 245.7 $ .1 $ (8.0) $ — $ 237.8 Debt securities issued by corporations 1,073.9 1.3 (63.1) (1.7) 1,010.4 Municipal obligations 280.0 — (17.0) — 263.0 Mortgage and asset-backed securities 289.5 — (30.7) — 258.8 Collateralized loan obligations 192.1 .1 (5.2) (1.1) 185.9 Total fixed maturity investments $ 2,081.2 $ 1.5 $ (124.0) $ (2.8) $ 1,955.9 December 31, 2022 Millions Cost or Gross Gross Net Foreign Carrying 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 The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of March 31, 2023. 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. March 31, 2023 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 223.8 $ 219.2 Due after one year through five years 943.6 891.9 Due after five years through ten years 338.8 314.2 Due after ten years 93.4 85.9 Mortgage and asset-backed securities and collateralized loan obligations 481.6 444.7 Total fixed maturity investments $ 2,081.2 $ 1,955.9 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 March 31, 2023 and December 31, 2022: March 31, 2023 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 660.6 $ 48.0 $ (2.8) $ (8.0) $ 697.8 Investment in MediaAlpha $ — $ 253.8 $ — $ — $ 253.8 Other long-term investments $ 1,489.7 $ 264.3 $ (96.2) $ (14.8) $ 1,643.0 December 31, 2022 Millions Cost or Gross Gross Net Foreign Carrying 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 Fair Value Measurements 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). See Note 17 — “Fair Value of Financial Instruments.” As of March 31, 2023 and December 31, 2022, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 70% and 72% of the investment portfolio. Fair Value Measurements by Level The following tables present White Mountains’s fair value measurements for investments as of March 31, 2023 and December 31, 2022 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. March 31, 2023 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 237.8 $ 237.8 $ — $ — Debt securities issued by corporations: Financials 281.9 — 281.9 — Consumer 194.9 — 194.9 — Healthcare 124.8 — 124.8 — Technology 123.3 — 123.3 — Industrial 119.8 — 119.8 — Utilities 64.0 — 64.0 — Communications 45.2 — 45.2 — Energy 36.4 — 36.4 — Materials 20.1 — 20.1 — Total debt securities issued by corporations 1,010.4 — 1,010.4 — Municipal obligations 263.0 — 263.0 — Mortgage and asset-backed securities 258.8 — 258.8 — Collateralized loan obligations 185.9 — 185.9 — Total fixed maturity investments 1,955.9 237.8 1,718.1 — Short-term investments 884.2 878.4 5.8 — Common equity securities: Exchange-traded funds 357.4 357.4 — — Other (1) 340.4 — 340.4 — Total common equity securities 697.8 357.4 340.4 — Investment in MediaAlpha 253.8 253.8 — — Other long-term investments 970.2 — 15.5 954.7 Other long-term investments — NAV (2) 672.8 — — — Total other long-term investments 1,643.0 — 15.5 954.7 Total investments $ 5,434.7 $ 1,727.4 $ 2,079.8 $ 954.7 (1) Consists 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, 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 — Healthcare 121.3 — 121.3 — Technology 123.7 — 123.7 — 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-traded 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) Consists 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. Investments Held on Deposit or as Collateral As of March 31, 2023 and December 31, 2022, investments of $517.5 million and $500.5 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 March 31, 2023 and December 31, 2022, the fair value of the interest reserve account, which was included in short-term investments, was $31.6 million and $31.2 million. See Note 7 - “Debt.” BAM is required to maintain deposits with certain insurance regulatory agencies in order to maintain its insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $4.6 million as of both March 31, 2023 and December 31, 2022. 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 March 31, 2023 and December 31, 2022, Ark held Lloyd’s trust deposits with a fair value of $148.7 million and $137.4 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 whether each member has sufficient assets to meet its underwriting liabilities plus a required solvency margin. As of March 31, 2023 and December 31, 2022, the fair value of Ark’s Funds at Lloyd’s investment deposits totaled $326.3 million and $319.2 million. As of March 31, 2023 and December 31, 2022, Ark held additional investments on deposit or as collateral for insurance regulators and reinsurance counterparties of $263.3 million and $257.0 million. As of March 31, 2023 and December 31, 2022, Ark had $144.1 million and $90.3 million of short-term investments pledged as collateral under uncommitted standby letters of credit. See Note 7 — “Debt.” As of March 31, 2023 and December 31, 2022, short-term investments of $206.0 million and $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 March 31, 2023 and December 31, 2022: Fair Value at Millions March 31, 2023 December 31, 2022 AAA $ 11.4 $ 11.3 AA 95.9 96.0 A 558.8 567.9 BBB 338.0 337.7 Other 6.3 5.9 Debt securities issued by corporations (1) $ 1,010.4 $ 1,018.8 (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 March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 129.7 $ 129.7 $ — $ 124.5 $ 124.5 $ — FHLMC 81.2 81.2 — 78.8 78.8 — GNMA 33.0 33.0 — 28.3 28.3 — Total agency (1) 243.9 243.9 — 231.6 231.6 — Non-agency: Residential .3 .3 — .3 .3 — Total non-agency .3 .3 — .3 .3 — Total mortgage-backed securities 244.2 244.2 — 231.9 231.9 — Other asset-backed securities: Credit card receivables 4.4 4.4 — 11.9 11.9 — Vehicle receivables 10.2 10.2 — 10.4 10.4 — Total other asset-backed securities 14.6 14.6 — 22.3 22.3 — Total mortgage and asset-backed securities 258.8 258.8 — 254.2 254.2 — Collateralized loan obligations 185.9 185.9 — 182.9 182.9 — Total mortgage and asset-backed securities $ 444.7 $ 444.7 $ — $ 437.1 $ 437.1 $ — (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 March 31, 2023, White Mountains’s investment portfolio included $185.9 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 March 31, 2023. Investment in MediaAlpha In 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). 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. As of March 31, 2023, White Mountains owned 16.9 million shares, representing a 26.8% basic ownership interest (24.3% o n a fully diluted, fully converted bas is). See Note 16 — “Equity Method Eligible Investments.” At this current level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $6.60 per share increase or decrease in White Mountains’s book value per share. At the March 31, 2023 closing price of $14.98 per share, the fair value of White Mountains’s investment in MediaAlpha was $253.8 million. Other Long-Term Investments The following table presents the carrying values of White Mountains’s other long-term investments as of March 31, 2023 and December 31, 2022: Fair Value at Millions March 31, 2023 December 31, 2022 Kudu’s Participation Contracts $ 683.2 $ 695.9 PassportCard/DavidShield 140.0 135.0 Elementum Holdings, L.P. 30.0 30.0 Other unconsolidated entities (1) 87.5 37.2 Total unconsolidated entities 940.7 898.1 Private equity funds and hedge funds 218.5 197.8 Bank loan fund 179.5 174.8 Lloyd’s trust deposits 148.7 137.4 ILS funds 123.6 49.3 Private debt instruments 10.1 9.6 Other 21.9 21.0 Total other long-term investments $ 1,643.0 $ 1,488.0 (1) Includes White Mountains’s noncontrolling equity interests in certain private common equity securities, 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 March 31, 2023, White Mountains held investments in seventeen private equity funds and two hedge funds. The largest investment in a single private equity fund or hedge fund was $49.9 million as of March 31, 2023 and $49.0 million and December 31, 2022. 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 March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 78.0 $ 37.5 $ 59.4 $ 37.5 Financial services 77.3 52.6 77.1 54.3 Real estate 4.1 2.5 4.1 2.5 Total private equity funds 159.4 92.6 140.6 94.3 Hedge funds Long/short equity financials and business services 49.8 — 49.0 — European small/mid cap 9.3 — 8.2 — Total hedge funds 59.1 — 57.2 — Total private equity funds and hedge funds included in other long-term investments $ 218.5 $ 92.6 $ 197.8 $ 94.3 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 March 31, 2023: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $4.1 $18.6 $132.3 $4.4 $159.4 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 March 31, 2023 and December 31, 2022, 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 $179.5 million and $174.8 million as of March 31, 2023 and 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 March 31, 2023 and December 31, 2022, White Mountains held Lloyd’s trust deposits with a fair value of $148.7 million and $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 March 31, 2023 and December 31, 2022, White Mountains held investments in ILS funds with a fair value of $123.6 million and $49.3 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 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, or until the underlying investment has fully matured or been commuted. Rollforward of Level 3 Investments Level 3 measurements as of March 31, 2023 and 2022 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 three months ended March 31, 2023 and 2022: Level 3 Investments Millions Other Long-term Other Long-term Balance at December 31, 2022 $ 911.6 Balance at December 31, 2021 $ 890.6 Net realized and unrealized gains 35.1 Net realized and unrealized gains 26.8 Amortization/accretion — Amortization/accretion — Purchases and contributions 117.0 Purchases and contributions — Sales and distributions (109.0) Sales and distributions (31.7) Transfers in — Transfers in — Transfers out — Transfers out — Balance at March 31, 2023 $ 954.7 Balance at March 31, 2022 $ 885.7 Fair Value Measurements — Transfers Between Levels - Three months ended March 31, 2023 and 2022 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 three months ended March 31, 2023 and 2022, 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 three months ended March 31, 2023 and 2022, 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 March 31, 2023 and December 31, 2022. The tables below exclude $91.8 million and $41.1 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 March 31, 2023 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (5) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (5) Kudu’s Participation Contracts (3)(4) Discounted cash flow $683.2 18% - 25% 7x - 22x PassportCard/DavidShield Discounted cash flow $140.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $30.0 20% 4% Private debt instruments Discounted cash flow $9.7 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 12.7x. (4) In 2023, Kudu deployed a total of $30.9 into new and existing Participation Contracts. (5) 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, 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% 4% Elementum Holdings, L.P. Discounted cash flow $30.0 21% 4% 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 Participation Contracts. (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 sale 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.

Goodwill and Other Intangible A

Goodwill and Other Intangible Assets	3 Months Ended
	Mar. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract]
Goodwill and Other Intangible Assets	Goodwill and Other Intangible Assets White Mountains accounts for business combinations using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any noncontrolling interest in the acquired entities at their acquisition date fair values. Goodwill represents the excess of the amount paid to acquire businesses over the fair value of identifiable net assets at the date of acquisition. The estimated acquisition date fair values, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date. The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill as of March 31, 2023 and December 31, 2022: $ in Millions Weighted Average Economic March 31, 2023 December 31, 2022 Acquisition Date Fair Value Accumulated Amortization Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Net Carrying Value Goodwill: Ark N/A $ 116.8 $ — $ 116.8 $ 116.8 $ — $ 116.8 Kudu N/A 7.6 — 7.6 7.6 7.6 Other Operations N/A 44.4 — 44.4 52.1 — 52.1 Total goodwill 168.8 — 168.8 176.5 — 176.5 Other intangible assets: Ark Underwriting capacity N/A 175.7 — 175.7 175.7 — 175.7 Kudu Trade names 7 2.2 1.3 .9 2.2 1.2 1.0 Other Operations Trade names 13.3 13.3 2.6 10.7 17.9 3.0 14.9 Customer relationships 11.0 24.8 7.0 17.8 29.5 7.5 22.0 Other 12.1 2.8 .5 2.3 2.8 .5 2.3 Subtotal 40.9 10.1 30.8 50.2 11.0 39.2 Total other intangible assets 218.8 11.4 207.4 228.1 12.2 215.9 Total goodwill and other intangible assets $ 387.6 $ 11.4 376.2 $ 404.6 $ 12.2 392.4 Intangible Assets Valuation Methods The goodwill recognized for the entities shown above is attributed to expected future cash flows. The acquisition date fair values of other intangible assets with finite lives are estimated using income approach techniques, which use future expected cash flows to develop a discounted present value amount. The multi-period-excess-earnings method estimates fair value using the present value of the incremental after-tax cash flows attributable solely to the other intangible asset over its remaining life. This approach was used to estimate the fair value of other intangible assets associated with the underwriting capacity and customer relationships. The relief-from-royalty method was used to estimate fair value for other intangible assets that relate to rights that could be obtained via a license from a third-party owner. Under this method, the fair value is estimated using the present value of license fees avoided by owning rather than leasing the asset. This technique was used to estimate the fair value of trade names and other intangible assets. The with-or-without method estimates the fair value of other intangible assets that provide an incremental benefit. Under this method, the fair value of the other intangible asset is calculated by comparing the value of the entity with and without the other intangible asset. This approach was used to estimate the fair value of favorable lease terms. On at least an annual basis beginning no later than the interim period included in the one-year anniversary of an acquisition, White Mountains evaluates goodwill and other intangible assets for potential impairment. Between annual evaluations, White Mountains considers changes in circumstances or events subsequent to the most recent evaluation that may indicate that an impairment may exist and, if necessary will perform an interim review for potential impairment. During the three months ended March 31, 2023 and 2022, White Mountains did not recognize any impairments to goodwill and other intangible assets. Rollforward of Goodwill and Other Intangible Assets The following table presents the change in goodwill and other intangible assets for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, 2023 2022 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 176.5 $ 215.9 $ 392.4 $ 142.3 $ 198.2 $ 340.5 Dispositions (1) (6.7) (6.9) (13.6) — — — Measurement period adjustments (2) (1.0) — (1.0) — — — Amortization — (1.6) (1.6) — (1.0) (1.0) Ending balance $ 168.8 $ 207.4 $ 376.2 $ 142.3 $ 197.2 $ 339.5 (1) Relates to a disposition within Other Operations. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended March 31, 2023 adjustments relate to an acquisition within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with this acquisition during 2022 had not yet been finalized as of the end of the period.

Loss and Loss Adjustment Expens

Loss and Loss Adjustment Expense Reserves	3 Months Ended
	Mar. 31, 2023
Insurance Loss Reserves [Abstract]
Loss and Loss Adjustment Expense Reserves	Loss and Loss Adjustment Expense Reserves P&C Insurance and Reinsurance The following table summarizes the loss and loss adjustment expense (“LAE”) reserve activity of the Ark/WM Outrigger segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Gross beginning balance $ 1,296.5 $ 894.7 Less: beginning reinsurance recoverable on unpaid losses (1) (505.0) (428.9) Net loss and LAE reserves 791.5 465.8 Loss and LAE incurred relating to: Current year losses 139.2 125.7 Prior year losses 8.6 (3.7) Net incurred losses and LAE 147.8 122.0 Loss and LAE paid relating to: Current year losses (4.0) (.6) Prior year losses (87.7) (39.4) Net paid loss and LAE (91.7) (40.0) Change in TPC Providers’ participation (2) 145.4 57.5 Foreign currency translation and other adjustments to loss and LAE 3.7 (1.7) Net ending balance 996.7 603.6 Plus: ending reinsurance recoverable on unpaid losses (3) 348.9 396.0 Gross ending balance $ 1,345.6 $ 999.6 (1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $145.4 and $276.8 as of December 31, 2022 and 2021. (2) Amount represents the impact to net loss and LAE reserves due to a change in the TPC Providers’ participation related to the annual reinsurance to close process. (3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $0.0 and $207.3 as of March 31, 2023 and 2022. For the three months ended March 31, 2023, the Ark/WM Outrigger segment recognized $8.6 million of net unfavorable prior year loss reserve development at Ark, driven primarily by Winter Storm Elliot. For the three months ended March 31, 2022, the Ark/WM Outrigger segment recognized $3.7 million of net favorable prior year loss reserve development at Ark, driven primarily by the property line of business. Impact of Third-Party Capital For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by TPC Providers using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. A reinsurance to close (“RITC”) agreement is generally put in place after the third year of operations for a year of account such that the outstanding loss and LAE reserves, including future development thereon, are reinsured into the next year of account. As a result, and in combination with the changing participation provided by TPC Providers, Ark’s participation on outstanding loss and LAE reserves reinsured into the next year of account may change, perhaps significantly. During the first quarter of 2023, an RITC agreement was executed such that the outstanding loss and LAE reserves for claims arising out of the 2020 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 42.8%, were reinsured into the 2021 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 0.0%. During the first quarter of 2022, an RITC agreement was executed such that the outstanding loss and LAE reserves for claims arising out of the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%, were reinsured into the 2020 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 42.8%. Municipal Bond Guarantee Insurance HG Re and BAM do not have any outstanding loss and LAE reserves related to BAM’s municipal bond guarantee insurance business.

Third-Party Reinsurance

Third-Party Reinsurance	3 Months Ended
	Mar. 31, 2023
Reinsurance Disclosures [Abstract]
Third-Party Reinsurance	Third-Party Reinsurance P&C Insurance and Reinsurance In the normal course of business, Ark may seek to limit losses that may arise from catastrophes or other events by reinsuring certain risks with third-party reinsurers. Ark remains liable for risks reinsured in the event that the reinsurer does not honor its obligations under reinsurance contracts. The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for the Ark/WM Outrigger segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Written premiums: Direct $ 246.2 $ 230.9 Assumed 563.2 402.2 Gross written premiums 809.4 633.1 Ceded (195.2) (1) (89.3) Net written premiums $ 614.2 $ 543.8 Earned premiums: Direct $ 150.4 $ 138.7 Assumed 162.1 106.6 Gross earned premiums 312.5 245.3 Ceded (57.4) (2) (50.9) Net earned premiums $ 255.1 $ 194.4 Losses and LAE: Gross $ 162.4 $ 183.1 Ceded (14.6) (3) (61.1) Net losses and LAE $ 147.8 $ 122.0 (1) The ceded written premiums exclude $44.1 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (2) The ceded earned premiums exclude $5.2 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (3) The ceded loss and LAE exclude $0.2 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. The following table presents the Ark/WM Outrigger segment’s reinsurance recoverables as of March 31, 2023 and December 31, 2022: Millions March 31, 2023 December 31, 2022 Reinsurance recoverables on unpaid losses $ 348.9 (1) $ 505.0 (3) Reinsurance recoverables on paid losses 23.1 31.1 Ceded unearned premiums 198.6 (2) 59.2 Reinsurance recoverables $ 570.6 $ 595.3 (1) The reinsurance recoverables on unpaid losses exclude $0.2 ceded by Ark to WM Outrigger Re as of March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (2) The ceded unearned premiums exclude $38.9 ceded by Ark to WM Outrigger Re as of March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (3) The reinsurance recoverables on unpaid losses include $145.4 attributable to TPC Providers as of December 31, 2022, which are collateralized. As reinsurance contracts do not relieve Ark of its obligation to its policyholders, Ark seeks to reduce the credit risk associated with reinsurance balances by avoiding over-reliance on specific reinsurers through the application of concentration limits and thresholds. Ark is selective with its reinsurers, placing reinsurance with only those reinsurers having a strong financial condition. Ark monitors the financial strength of its reinsurers on an ongoing basis. The following table presents the Ark/WM Outrigger segment’s gross and net reinsurance recoverables by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) ratings as of March 31, 2023: $ in Millions As of March 31, 2023 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 173.8 $ — $ 173.8 64.7 % A- to A 77.9 — 77.9 29.0 B++ or lower and not rated 120.3 103.2 17.1 6.3 Total $ 372.0 $ 103.2 $ 268.8 100.0 % (1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good). Reinsurance Contracts Accounted for as Deposits Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), which is accounted for using the deposit method and recorded within other assets. Ark earns an annual crediting rate of 3.0%, which is recorded within other revenue. As of March 31, 2023, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.6 million. Municipal Bond Guarantee Insurance See Note 10 — “Municipal Bond Guarantee Insurance” for third-party reinsurance balances and reinsurance contracts accounted for as deposits related to White Mountains’s financial guarantee business.

Debt

Debt	3 Months Ended
	Mar. 31, 2023
Debt Disclosure [Abstract]
Debt	Debt The following table presents White Mountains’s debt outstanding as of March 31, 2023 and December 31, 2022: $ in Millions March 31, 2023 Effective (1) December 31, 2022 Effective (1) HG Global Senior Notes $ 150.0 11.0% $ 150.0 8.9% Unamortized discount and issuance cost (3.4) (3.5) HG Global Senior Notes, carrying value 146.6 146.5 Ark 2007 Subordinated Notes, carrying value 30.0 30.0 Ark 2021 Subordinated Notes Tranche 1 42.0 41.3 Ark 2021 Subordinated Notes Tranche 2 47.0 47.0 Ark 2021 Subordinated Notes Tranche 3 70.0 70.0 Unamortized issuance cost (4.5) (4.6) Ark 2021 Subordinated Notes, carrying value 154.5 153.7 Total Ark Subordinated Notes, carrying value 184.5 10.3% 183.7 7.6% Kudu Credit Facility 198.3 8.7% 215.2 6.1% Unamortized issuance cost (6.7) (6.9) Kudu Credit Facility, carrying value 191.6 208.3 Other Operations debt 34.3 8.5% 37.4 6.6% Unamortized issuance cost (.7) (.7) Other Operations debt, carrying value 33.6 36.7 Total debt $ 556.3 $ 575.2 (1) Effective rate includes the effect of the amortization of debt issuance costs and, where applicable, the original issue discount. HG Global Senior Notes On April 29, 2022, HG Global received the proceeds from the issuance of its $150.0 million face value floating rate secured senior notes (the “HG Global Senior Notes”). The HG Global Senior Notes, which mature in April 2032, accrue interest at a floating rate equal to the three-month Secured Overnight Financing Rate (“SOFR”) plus 6.3% per annum. Subsequent to the five-year anniversary of the funding date, absent the occurrence of an early amortization trigger event, HG Global will be required to make payments of principal on a quarterly basis totaling $15.0 million annually. Upon the occurrence of an early amortization trigger event, HG Global is required to use all available cash flow to repay the notes. Early amortization trigger events include scenarios in which HG Re is effectively in runoff. HG Global has the option to redeem, in whole or in part, the HG Global Senior Notes after the five-year anniversary of the funding date at the outstanding principal amount plus accrued interest. On June 16, 2022, HG entered into an interest rate cap agreement, effective on July 25, 2022, to limit its exposure to the risk of interest rate increases on the HG Global Senior Notes. The notional amount of the interest rate cap is $150.0 million and the termination date is July 25, 2025. See Note 9 — “Derivatives.” The HG Global Senior Notes require HG Global to maintain an interest reserve account of eight times the interest accrued for the most recent quarterly interest period. As of March 31, 2023, the fair value of the interest reserve account, which is included in short-term investments, is $31.6 million. The HG Global Senior Notes are secured by the capital stock and other equity interests of HG Global’s subsidiaries, the interest reserve account, and all cash and non-cash proceeds from such collateral. The HG Global Senior Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings. If the payment of principal and interest under the HG Global Senior Notes becomes subject to tax withholding on behalf of a relevant governmental authority for certain indemnified taxes, the HG Global Senior Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The HG Global Senior Notes require the payment of additional interest of 1.0% per annum if the HG Global Senior Notes receive a non-investment grade rating or are no longer rated. As of March 31, 2023, the HG Global Senior Notes had an investment grade rating. As of March 31, 2023, the HG Global Senior Notes had an outstanding balance of $150.0 million. Ark Subordinated Notes In March 2007, GAIL issued $30.0 million face value of floating rate unsecured junior subordinated deferrable interest notes to Alesco Preferred Funding XII Ltd., Alesco Preferred Funding XIII Ltd. and Alesco Preferred Funding XIV Ltd (the “Ark 2007 Subordinated Notes”). The Ark 2007 Subordinated Notes, which mature in June 2037, accrue interest at a floating rate equal to the three-month U.S. London Inter-Bank Offered Rate (“LIBOR”) plus 4.6% per annum. As of March 31, 2023, the Ark 2007 Subordinated Notes had an outstanding balance of $30.0 million. In the third quarter of 2021, GAIL issued $163.3 million face value floating rate unsecured subordinated notes at par in three separate transactions for proceeds of $157.8 million, net of debt issuance costs (collectively, the “Ark 2021 Subordinated Notes”). The Ark 2021 Subordinated Notes were issued in private placement offerings that were exempt from the registration requirements of the Securities Act of 1933. On July 13, 2021, Ark issued €39.1 million ($46.3 million based upon the foreign exchange spot rate as of the date of the transaction) face value floating rate unsecured subordinated notes (“Ark 2021 Subordinated Notes Tranche 1”). The Ark 2021 Subordinated Notes Tranche 1, which mature in July 2041, accrue interest at a floating rate equal to the three-month Euro Interbank Offered Rate (“EURIBOR”) plus 5.75% per annum. On August 11, 2021, Ark issued $47.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Subordinated Notes Tranche 2”). The Ark 2021 Subordinated Notes Tranche 2, which mature in August 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 5.75% per annum. On September 8, 2021, Ark issued $70.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Subordinated Notes Tranche 3”). The Ark 2021 Subordinated Notes Tranche 3, which mature in September 2041, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 6.1% per annum. On the ten-year anniversary of the issue dates, the interest rate for the Ark 2021 Subordinated Notes will increase by 1.0% per annum. Ark has the option to redeem, in whole or in part, the Ark 2021 Subordinated Notes ahead of contractual maturity at the outstanding principal amounts plus accrued interest at the ten-year anniversary or any subsequent interest payment date. All payments of principal and interest under the Ark 2021 Subordinated Notes are conditional upon GAIL’s solvency and compliance with the enhanced capital requirements of the Bermuda Monetary Authority (“BMA”). The deferral of payments of principal and interest under these conditions does not constitute a default by Ark and does not give the noteholders any rights to accelerate repayment of the Ark 2021 Subordinated Notes or take any enforcement action under the Ark 2021 Subordinated Notes. If the payments of principal and interest under the Ark 2021 Subordinated Notes become subject to tax withholding on behalf of Bermuda or any political subdivision there, the Ark 2021 Subordinated Notes require the payment of additional amounts such that the amount received by the noteholders is the same as would have been received absent the tax withholding being imposed. The Ark 2021 Subordinated Notes Tranche 3 require the payment of additional interest of 1.0% per annum upon the occurrence of a premium load event until such event is remedied. Premium load events include the failure to meet payment obligations of the Ark 2021 Subordinated Notes Tranche 3 when due, failure of GAIL to maintain an investment grade credit rating, failure to maintain 120% of GAIL’s Bermuda solvency capital requirement, failure of GAIL to maintain a debt to capital ratio below 40%, late filing of GAIL’s or Ark’s financial information, and making a restricted payment or distribution on GAIL’s common stock or other securities that rank junior or pari passu with the Ark 2021 Subordinated Notes Tranche 3 when a different premium load event exists or will be caused by the restricted payment. As of March 31, 2023, there were no premium load events. As of March 31, 2023, the Ark 2021 Subordinated Notes Tranche 1 had an outstanding balance of €39.1 million ($42.0 million based upon the foreign exchange spot rate as of March 31, 2023), the Ark 2021 Subordinated Notes Tranche 2 had an outstanding balance of $47.0 million, and the Ark 2021 Subordinated Notes Tranche 3 had an outstanding balance of $70.0 million. The Ark Subordinated Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings. Ark Standby Letter of Credit Facilities In December 2021, Ark entered into two uncommitted secured standby letter of credit facility agreements to support the continued growth and expansion of its GAIL insurance and reinsurance operations. The standby letter of credit facility agreements were executed with ING Bank N.V., London Branch (the “ING LOC Facility”) with capacity of $50.0 million on an uncollateralized basis and with Citibank Europe Plc (the “Citibank LOC Facility”) with capacity of $100.0 million on a collateralized basis. In September 2022, Ark entered into an additional uncommitted standby letter of credit facility agreement with Lloyds Bank Corporate Markets PLC (the “Lloyds LOC Facility”) with capacity of $50.0 million on a collateralized basis. As of March 31, 2023, the ING LOC Facility was undrawn. As of March 31, 2023, the Citibank LOC Facility had an outstanding balance of $92.3 million and short-term investments pledged as collateral of $106.3 million. As of March 31, 2023, the Lloyds LOC Facility had an outstanding balance of $35.0 million and short-term investments pledged as collateral of $37.8 million. Ark’s uncommitted secured standby letter of credit facility agreements contain various representations, warranties and covenants that White Mountains considers to be customary for such borrowings. Kudu Credit Facility On March 23, 2021, Kudu entered into a secured revolving credit facility (the “Kudu Credit Facility”) with Mass Mutual to repay its prior credit facility and to fund new investments and related transaction expenses. The maximum borrowing capacity of the Kudu Credit Facility is $300.0 million. The Kudu Credit Facility matures on March 23, 2036. Interest on the Kudu Credit Facility accrues at a floating interest rate equal to the greater of the three month LIBOR or 0.25% plus, in each case, 4.30%. The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of March 31, 2023, the interest reserve account had a balance of $13.0 million. The Kudu Credit Facility requires Kudu to maintain a ratio of the outstanding balance to the sum of the fair market value of Kudu’s Participation Contracts and cash held in certain accounts (the “LTV Percentage”) of less than 50% in years 0-3, 40% in years 4-6, 25% in years 7-8, 15% in years 9-10, and 0% thereafter. As of March 31, 2023, Kudu had a 28.8% LTV Percentage. Kudu may borrow undrawn balances within the initial three-year availability period, subject to customary terms and conditions, to the extent the amount borrowed under the Kudu Credit Facility does not exceed the borrowing base, which is equal to 35% of the fair value of Kudu’s qualifying Participation Contracts. When considering the fair value of Kudu’s qualifying Participation Contracts as of March 31, 2023, the available undrawn balance was $47.4 million. The following table presents the change in debt under the Kudu Credit Facility for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Kudu Credit Facility Beginning balance $ 215.2 $ 225.4 Term loans Borrowings — — Repayments (16.9) — Ending balance $ 198.3 $ 225.4 The Kudu Credit Facility is secured by all property of the loan parties and contains various affirmative and negative covenants that White Mountains considers to be customary for such borrowings. Other Operations Debt As of March 31, 2023, White Mountains’s Other Operations had debt with an outstanding balance of $34.3 million, which consisted of four secured credit facilities (collectively, “Other Operations debt”). Compliance At March 31, 2023, White Mountains was in compliance, in all material respects, with all of the covenants under its debt instruments.

Income Taxes

Income Taxes	3 Months Ended
	Mar. 31, 2023
Income Tax Disclosure [Abstract]
Income Taxes	Income Taxes The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law such that taxes are imposed, the Bermuda Exempted Undertakings Tax Protection Act of 1966 states that the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035. The Company has subsidiaries and branches that operate in various other jurisdictions around the world and are subject to tax in the jurisdictions in which they operate. As of March 31, 2023, the primary jurisdictions in which the Company’s subsidiaries and branches were subject to tax include Ireland, Israel, Luxembourg, the United Kingdom and the United States. White Mountains’s income tax expense related to pre-tax income from continuing operations for the three months ended March 31, 2023 represented an effective tax rate of 6.0%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by full year forecasted income in jurisdictions with lower tax rates than the United States. White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the three months ended March 31, 2022 represented an effective tax rate of 18.2%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by income in jurisdictions with lower tax rates than the United States and a decrease in the full valuation allowance on net deferred tax assets in certain U.S. operations within Other Operations, partially offset by an increase in the full valuation allowance at BAM and state income taxes. On April 1, 2023, the U.K. corporate tax rate increased from 19.0% to 25.0%. On August 16, 2022, the U.S. enacted the Inflation Reduction Act (the “IRA”). White Mountains has evaluated the tax provisions of the IRA, the most significant of which relate to the corporate alternative minimum tax and the tax on share repurchases, and does not expect the legislation to have a material impact on the results of its operations. In arriving at the effective tax rate for the three months ended March 31, 2023 and 2022, White Mountains forecasted all income and expense items including the change in unrealized investment gains (losses) and realized investment gains (losses) for the years ending December 31, 2023 and 2022. White Mountains records a valuation allowance against deferred tax assets if it becomes more likely than not that all or a portion of a deferred tax asset will not be realized. Changes in valuation allowances from period to period are included in income tax expense in the period of change. In determining whether or not a valuation allowance, or change therein, is warranted, White Mountains considers factors such as prior earnings history, expected future earnings, carryback and carryforward periods and strategies that if executed would result in the realization of a deferred tax asset. With few exceptions, White Mountains is no longer subject to U.S. federal, state, or non-U.S. income tax examinations by tax authorities for years before 2017.

Derivatives

Derivatives	3 Months Ended
	Mar. 31, 2023
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivatives	Derivatives HG Global Interest Rate Cap On June 16, 2022, HG entered into an interest rate cap agreement, effective on July 25, 2022, to limit its exposure to the risk of interest rate increases on the HG Global Senior Notes. The notional amount of the interest rate cap is $150.0 million and the termination date is July 25, 2025. HG paid initial premiums of $3.3 million for the interest rate cap. Under the terms of the interest rate cap agreement, if the current three-month SOFR rate at the measurement date exceeds 3.5%, HG will receive payments from the counterparty equal to the difference between the three-month SOFR rate on the determination date and 3.5%, multiplied by the notional amount of the cap based on the number of days in the quarter. As of March 31, 2023, the three-month SOFR rate was 4.9%. HG accounts for the interest rate cap as a derivative at fair value, with changes in fair value recognized in current period earnings within interest expense. For the three months ended March 31, 2023, White Mountains recognized a loss of $0.7 million related to the change in fair value on the interest rate cap within interest expense. For the three months ended March 31, 2023, White Mountains received a payment of $0.2 million related to the periodic settlement of the interest rate cap. As of March 31, 2023 and December 31, 2022, the estimated fair value of the interest rate cap recorded in other assets was $3.4 million and $4.1 million. White Mountains classifies the interest rate cap as a Level 2 measurement.

Municipal Bond Guarantee Insura

Municipal Bond Guarantee Insurance	3 Months Ended
	Mar. 31, 2023
Guarantees [Abstract]
Municipal Bond Guarantee Insurance	Municipal Bond Guarantee Insurance HG Global was established to fund the startup of BAM, a mutual municipal bond insurer. HG Global, together with its subsidiaries, provided the initial capitalization of BAM through the purchase of $503.0 million of the BAM Surplus Notes. Reinsurance Treaties FLRT BAM is a party to a first loss reinsurance treaty (“FLRT”) with HG Re under which HG Re provides first loss protection up to 15%-of-par outstanding on each municipal bond insured by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. In return, BAM cedes approximately 60% of the risk premium charged for insuring the municipal bond, which is net of a ceding commission. The FLRT is a perpetual agreement with terms that can be renegotiated after a specified period of time. During 2021, BAM and HG Re agreed that the terms may be renegotiated at the end of 2024, and each subsequent five-year period thereafter. Fidus Re BAM is party to a collateralized financial guarantee excess of loss reinsurance agreement that serves to increase BAM’s claims paying resources and is provided by Fidus Re Ltd. (“Fidus Re”). In 2018, Fidus Re was initially capitalized by the issuance of $100.0 million of insurance-linked securities (the “Fidus Re 2018 Agreement”), which have an initial term of 12 years and are callable five years after the date of issuance. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. Under the Fidus Re 2018 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $165.0 million on a portion of BAM’s financial guarantee portfolio (the “2018 Covered Portfolio”) up to a total reimbursement of $100.0 million. The Fidus Re 2018 Agreement does not provide coverage for losses in excess of $276.1 million. The 2018 Covered Portfolio consists of approximately 26% of BAM’s gross par outstanding as of March 31, 2023. In 2021, Fidus Re issued an additional $150.0 million of insurance-linked securities (the “Fidus Re 2021 Agreement”), which have an initial term of 12 years and are callable five years after the date of issuance. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. Under the Fidus Re 2021 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $135.0 million on a portion of BAM’s financial guarantee portfolio (the “2021 Covered Portfolio”) up to a total reimbursement of $150.0 million. The Fidus Re 2021 Agreement does not provide coverage for losses in excess of $301.7 million. The 2021 Covered Portfolio consists of approximately 31% of BAM’s gross par outstanding as of March 31, 2023. In 2022, Fidus Re issued an additional $150.0 million of insurance linked securities (the “Fidus Re 2022 Agreement”), which have an initial term of 12 years and are callable seven years after the date of issuance. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. Under the Fidus Re 2022 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $110.0 million on a portion of BAM’s financial guarantee portfolio (the “2022 Covered Portfolio”) up to a total reimbursement of $150.0 million. The Fidus Re 2022 Agreement does not provide coverage for losses in excess of $276.7 million. The 2022 Covered Portfolio consists of approximately 32% of BAM’s gross par outstanding as of March 31, 2023. The Fidus Re agreements are accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as they do not meet the risk transfer requirements necessary to be accounted for as reinsurance. XOLT In January 2020, BAM entered into an excess of loss reinsurance agreement (the “XOLT”) with HG Re. Under the XOLT, HG Re provides last dollar protection for exposures on municipal bonds insured by BAM in excess of the New York State Department of Financial Services (“NYDFS”) single issuer limits. As of March 31, 2023, the XOLT is subject to an aggregate limit equal to the lesser of $125.0 million or the assets held in the supplemental collateral trust (the “Supplemental Trust”) at any point in time. The agreement is accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as the agreement does not meet the risk transfer requirements necessary to be accounted for as reinsurance. Collateral Trusts HG Re’s obligations under the FLRT are subject to an aggregate limit equal to the assets in two collateral trusts, the Supplemental Trust and the Regulation 114 Trust (together, the “Collateral Trusts”), at any point in time. On a monthly basis, BAM deposits cash equal to ceded premiums, net of ceding commissions, due to HG Re under the FLRT directly into the Regulation 114 Trust. The Regulation 114 Trust target balance is equal to HG Re’s unearned premiums and unpaid loss and LAE reserves, if any. If, at the end of any quarter, the Regulation 114 Trust balance is below the target balance, funds will be withdrawn from the Supplemental Trust and deposited into the Regulation 114 Trust in an amount equal to the shortfall. If, at the end of any quarter, the Regulation 114 Trust balance is above 102% of the target balance, funds will be withdrawn from the Regulation 114 Trust and deposited into the Supplemental Trust. The Regulation 114 Trust balance as of March 31, 2023 and December 31, 2022 was $300.8 million and $288.6 million. The Supplemental Trust target balance is $603.0 million, less the amount of cash and securities in the Regulation 114 Trust in excess of its target balance (the “Supplemental Trust Target Balance”). If, at the end of any quarter, the Supplemental Trust balance exceeds the Supplemental Trust Target Balance, such excess may be distributed to HG Re. The distribution will be made first as an assignment of accrued interest on the BAM Surplus Notes and second in cash and/or fixed income securities. As the BAM Surplus Notes are repaid over time, the BAM Surplus Notes will be replaced in the Supplemental Trust by cash and fixed income securities. The Supplemental Trust balance as of March 31, 2023 and December 31, 2022 was $579.9 million and $568.3 million. As of March 31, 2023 and December 31, 2022, the Collateral Trusts held assets of $880.7 million and $856.9 million, which included $520.6 million and $503.3 million of cash and investments, $340.0 million and $340.0 million of BAM Surplus Notes and $20.1 million and $13.6 million of interest receivable on the BAM Surplus Notes. BAM Surplus Notes Through 2024, the interest rate on the BAM Surplus Notes is a variable rate equal to the one-year U.S. Treasury rate plus 300 basis points, set annually. During 2023, the interest rate on the BAM Surplus Notes is 7.7%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. Under its agreements with HG Global, BAM is required to seek regulatory approval to pay principal and interest on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS. In December 2022, BAM made a $36.0 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $24.6 million was a repayment of principal held in the Supplemental Trust, $1.0 million was a payment of accrued interest held in the Supplemental Trust and $10.4 million was a payment of accrued interest held outside the Supplemental Trust. During the three months ended March 31, 2023 and 2022, BAM made no repayments of the BAM Surplus Notes or accrued interest. As of March 31, 2023 and December 31, 2022, the principal balance on the BAM Surplus Notes was $340.0 million for both periods and total interest receivable on the BAM Surplus Notes was $164.5 million and $157.9 million. Insured Obligations and Premiums The following table presents a schedule of BAM’s insured obligations as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Contracts outstanding 13,607 13,382 Remaining weighted average contract period (in years) 10.8 10.8 Contractual debt service outstanding (in millions): Principal $ 101,785.7 $ 99,996.9 Interest 49,801.9 48,880.6 Total debt service outstanding $ 151,587.6 $ 148,877.5 Gross unearned insurance premiums (in millions) $ 299.8 $ 298.3 The following table presents a schedule of BAM’s future premium revenues as of March 31, 2023: Millions March 31, 2023 April 1, 2023 - December 31, 2023 $ 20.9 January 1, 2024 - March 31, 2024 6.8 April 1, 2024 - June 30, 2024 6.7 July 1, 2024 - September 30, 2024 6.5 October 1, 2024 - December 31, 2024 6.4 Total 2024 26.4 2025 24.7 2026 23.1 2027 21.5 2028 19.8 2029 and thereafter 163.4 Total gross unearned insurance premiums $ 299.8 The following table presents a schedule of written premiums and earned premiums included in the HG Global/BAM segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Written premiums: Direct $ 9.2 $ 9.4 Assumed — — Gross written premiums (1) $ 9.2 $ 9.4 Earned premiums: Direct $ 7.0 $ 7.6 Assumed .7 .8 Gross earned premiums (1) $ 7.7 $ 8.4 (1) There are no ceded premium amounts in the periods presented, and gross earned premiums are equivalent to net written premiums and net earned premiums.

Earnings Per Share

Earnings Per Share	3 Months Ended
	Mar. 31, 2023
Earnings Per Share [Abstract]
Earnings Per Share	Earnings Per Share White Mountains calculates earnings per share using the two-class method, which allocates earnings between common shares and unvested restricted common shares. Both classes of shares participate equally in dividends and earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares. The following table presents the Company’s computation of earnings per share from continuing operations for the three months ended March 31, 2023 and 2022. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended March 31, 2023 2022 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 179.5 $ 33.4 Less: total income (loss) from discontinued operations, net of tax (1) — 3.7 Less: net (income) loss from discontinued operations attributable — (.1) Net income (loss) from continuing operations attributable to 179.5 29.8 Allocation of (earnings) losses to participating restricted common shares (2) (2.2) (.3) Basic and diluted earnings (losses) per share numerators $ 177.3 $ 29.5 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,569.9 3,006.2 Average unvested restricted common shares (3) (31.1) (29.6) Basic earnings (losses) per share denominator 2,538.8 2,976.6 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,569.9 3,006.2 Average unvested restricted common shares (3) (31.1) (29.6) Diluted earnings (losses) per share denominator 2,538.8 2,976.6 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ 1.00 $ 1.00 Undistributed earnings (losses) 68.83 8.90 Basic and diluted earnings (losses) per share $ 69.83 $ 9.90 (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group. See Note 19 — “Held for Sale and Discontinued Operations. ” (2) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (3) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.” The following table presents the undistributed net earnings (losses) from continuing operations for the three months ended March 31, 2023 and 2022. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended March 31, Millions 2023 2022 Undistributed net earnings - continuing operations: Net income (loss) attributable to White Mountains’s common $ 177.3 $ 29.5 Dividends declared, net of restricted common share amounts (1) (2.5) (3.0) Total undistributed net earnings (losses), net of restricted common share amounts $ 174.8 $ 26.5 (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities.

Employee Share-Based Incentive

Employee Share-Based Incentive Compensation Plans	3 Months Ended
	Mar. 31, 2023
Share-Based Payment Arrangement [Abstract]
Employee Share-Based Incentive Compensation Plans	Employee Share-Based Incentive Compensation Plans White Mountains’s share-based incentive compensation plans are designed to incentivize key employees to maximize shareholder value over long periods of time. White Mountains believes that this is best pursued by utilizing a pay-for-performance program that closely aligns the financial interests of management with those of its shareholders while rewarding appropriate risk taking. White Mountains accomplishes this by emphasizing variable long-term compensation that is contingent on performance over a number of years rather than fixed entitlements. White Mountains expenses all its share-based compensation. As a result, White Mountains’s calculation of its owners’ returns includes the expense of all outstanding share-based compensation awards. White Mountains’s Long-Term Incentive Plan (the “WTM Incentive Plan”) provides for grants of various types of share-based and non-share-based incentive awards to key employees and directors of White Mountains. As of March 31, 2023 and 2022, White Mountains’s share-based incentive compensation awards consist of performance shares and restricted shares. Performance Shares Performance shares are designed to reward employees for meeting company-wide performance targets. Performance shares are conditional grants of a specified maximum number of common shares or an equivalent amount of cash. Awards generally vest at the end of a three-year service period, are subject to the attainment of pre-specified performance goals, and are valued based on the market value of common shares at the time awards are paid. Performance shares earned under the WTM Incentive Plan are typically paid in cash but may be paid in common shares. Compensation expense is recognized for the vested portion of the awards over the related service periods. The level of payout ranges from zero to two times the number of shares initially granted, depending on White Mountains’s financial performance. Performance shares become payable at the conclusion of a performance cycle (typically three years) if pre-defined financial targets are met. The performance measures used for determining performance share payouts are growth in White Mountains’s adjusted book value per share and intrinsic value per share. Intrinsic value per share is generally calculated by adjusting adjusted book value per share for differences between the adjusted book value of certain assets and liabilities and White Mountains’s estimate of their underlying intrinsic values. The following table presents the performance share activity for the three months ended March 31, 2023 and 2022 for performance shares granted under the WTM Incentive Plan: Three Months Ended March 31, 2023 2022 $ in Millions Target Performance Accrued Target Performance Accrued Beginning of period 39,449 $ 67.5 40,828 $ 42.2 Shares paid (1) (13,350) (40.8) (14,625) (26.4) New grants 10,895 — 13,075 — Forfeitures and cancellations (2) 37 .4 24 .3 Expense recognized — 9.3 — 5.8 End of period 37,031 $ 36.4 39,302 $ 21.9 (1) WTM performance share payments in 2023 for the 2020-2022 performance cycle, which were paid in March 2023 at 200% of target. WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP. During the three months ended March 31, 2023, White Mountains granted 10,895 performance shares for the 2023-2025 performance cycle. During the three months ended March 31, 2022, White Mountains granted 13,075 performance shares for the 2022-2024 performance cycle. For the 2020-2022 performance cycle, all performance shares earned were settled in cash. For the 2019-2021 performance cycle, the Company issued common shares for 750 performance shares earned, and all other performance shares earned were settled in cash. If the outstanding performance shares had vested on March 31, 2023, the total additional compensation cost to be recognized would have been $44.6 million, based on accrual factors as of March 31, 2023 (common share price and payout assumptions). The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of March 31, 2023 for each performance cycle: March 31, 2023 $ in Millions Target Performance Accrued Performance cycle: 2021 – 2023 13,475 $ 22.6 2022 – 2024 13,225 14.0 2023 – 2025 10,895 .4 Sub-total 37,595 37.0 Assumed forfeitures (564) (.6) Total 37,031 $ 36.4 Restricted Shares Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards under the WTM Incentive Plan for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, 2023 2022 $ in Millions Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,350 $ 15.5 37,850 $ 15.9 Issued 10,895 16.0 13,075 13.6 Vested (11,650) — (12,725) — Forfeited — — — — Expense recognized — (3.2) — (3.0) End of period 37,595 $ 28.3 38,200 $ 26.5

Noncontrolling Interests

Noncontrolling Interests	3 Months Ended
	Mar. 31, 2023
Noncontrolling Interest [Abstract]
Noncontrolling Interests	Noncontrolling Interests Noncontrolling interests consist of the ownership interests of noncontrolling shareholders in consolidated entities and are presented separately on the balance sheet. The following table presents the balance of noncontrolling interests included in White Mountains’s total equity and the related percentage of each consolidated entity’s total equity owned by noncontrolling shareholders as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 $ in Millions Noncontrolling Percentage (1) Noncontrolling Equity Noncontrolling Percentage (1) Noncontrolling Equity Noncontrolling interests, excluding BAM HG Global 3.1 % $ (.3) 3.1 % $ (.6) Ark 28.0 % 251.3 28.0 % 247.9 Kudu 10.8 % 81.3 10.8 % 75.1 Other various 10.3 various 20.4 Total, excluding BAM 342.6 342.8 BAM 100.0 % (152.2) 100.0 % (154.7) Total noncontrolling interests $ 190.4 $ 188.1 (1) The noncontrolling percentage represents the basic ownership interests held by noncontrolling shareholders with the exception of HG Global, for which the noncontrolling percentage represents the preferred share ownership held by noncontrolling shareholders.

Segment Information

Segment Information	3 Months Ended
	Mar. 31, 2023
Segment Reporting [Abstract]
Segment Information	Segment Information As of March 31, 2023, White Mountains conducted its operations through three reportable segments: (1) HG Global/BAM, (2) Ark/WM Outrigger, and (3) Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations. White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the chief operating decision makers and the Board of Directors. Significant intercompany transactions among White Mountains’s segments have been eliminated herein. During the fourth quarter of 2022, Ark sponsored the formation of Outrigger Re Ltd. to provide reinsurance protection on Ark’s Bermuda global property catastrophe excess of loss portfolio written in calendar year 2023. White Mountains consolidates its segregated account of Outrigger Re Ltd., WM Outrigger Re, in its financial statements. WM Outrigger Re’s quota share reinsurance agreement with GAIL eliminates in White Mountains’s consolidated financial statements. WM Outrigger Re exclusively provides reinsurance protection to Ark. As a result, WM Outrigger Re was aggregated with Ark within the Ark/WM Outrigger segment starting in 2023. See Note 2 — “Significant Transactions.” As a result of the NSM Transaction, the results of operations for NSM, previously reported as a segment, have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations.” Prior period amounts have been reclassified to conform to the current period’s presentation. The following tables present the financial information for White Mountains’s segments for the three months ended March 31, 2023 and 2022: Millions HG Global/BAM Ark/WM Outrigger HG Global BAM (1) Ark WM Outrigger Re Kudu Other Operations Total Three Months Ended March 31, 2023 Earned insurance premiums $ 6.4 $ 1.3 $ 249.9 $ 5.2 $ — $ — $ 262.8 Net investment income 4.0 3.2 8.4 2.2 14.2 7.0 39.0 Net investment income (expense) - 6.6 (6.6) — — — — — Net realized and unrealized investment 7.9 9.1 24.5 — 29.6 41.8 112.9 Net realized and unrealized investment gains — — — — — 85.2 85.2 Commission revenues — — — — — 3.3 3.3 Other revenues — .8 (2.7) — — 30.6 28.7 Total revenues 24.9 7.8 280.1 7.4 43.8 167.9 531.9 Loss and loss adjustment expenses — — 147.6 .2 — — 147.8 Acquisition expenses 1.8 .9 58.9 .9 — — 62.5 Cost of sales — — — — — 13.9 13.9 General and administrative expenses 1.1 16.2 35.1 .1 3.8 39.7 96.0 Change in fair value of contingent — — (2.4) — — — (2.4) Interest expense 4.5 — 5.0 — 4.7 .8 15.0 Total expenses 7.4 17.1 244.2 1.2 8.5 54.4 332.8 Pre-tax income (loss) from continuing operations $ 17.5 $ (9.3) $ 35.9 $ 6.2 $ 35.3 $ 113.5 $ 199.1 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. Millions HG Global/BAM Ark/WM Outrigger Other Operations HG Global BAM (1) Ark Kudu Total Three Months Ended March 31, 2022 Earned insurance premiums $ 6.9 $ 1.5 $ 194.4 $ — $ — $ 202.8 Net investment income 2.1 2.5 1.6 12.6 1.8 20.6 Net investment income (expense) - 2.9 (2.9) — — — — Net realized and unrealized investment gains (losses) (23.5) (21.6) (17.5) 22.3 31.9 (8.4) Net realized and unrealized investment gains — — — — 18.8 18.8 Commission revenues — — — — 2.9 2.9 Other revenues .1 .7 (2.8) — 25.7 23.7 Total revenues (11.5) (19.8) 175.7 34.9 81.1 260.4 Losses and loss adjustment expenses — — 122.0 — — 122.0 Acquisition expenses 2.6 .4 49.9 — — 52.9 Cost of sales — — — — 21.4 21.4 General and administrative expenses .7 15.6 21.0 2.8 29.8 69.9 Change in fair value of contingent consideration — — 2.1 — — 2.1 Interest expense — — 3.8 2.8 .3 6.9 Total expenses 3.3 16.0 198.8 5.6 51.5 275.2 Pre-tax income (loss) from continuing operations $ (14.8) $ (35.8) $ (23.1) $ 29.3 $ 29.6 $ (14.8)

Variable Interest Entities

Variable Interest Entities	3 Months Ended
	Mar. 31, 2023
Variable Interest Entity, Not Primary Beneficiary, Disclosures [Abstract]
Variable Interest Entities	Variable Interest Entities BAM BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. However, the equity at risk funded by BAM’s members is not sufficient to fund its operations without the additional financial support provided by the BAM Surplus Notes and accordingly, White Mountains has determined that BAM is a VIE. Pursuant to the FLRT, BAM’s underwriting guidelines may only be amended with the consent of HG Re. In addition, HG Holdings Ltd, a subsidiary of HG Global, has the right to designate two directors for election to BAM’s Board of Directors. As a result, we have determined that White Mountains is the primary beneficiary and is required to consolidate BAM’s results in its financial statements. Since BAM is owned by its members, its equity and results of operations are included in noncontrolling interests. HG Re’s obligations under the FLRT are subject to an aggregate limit equal to the assets in the Collateral Trusts at any point in time. WM Outrigger Re White Mountains has determined that Outrigger Re Ltd. and WM Outrigger Re are VIEs. White Mountains is not the primary beneficiary of Outrigger Re Ltd. or the other segregated accounts. White Mountains is the primary beneficiary of WM Outrigger Re, as it has both the power to direct the activities that most significantly impact WM Outrigger Re’s economic performance and the obligation to absorb losses, or the right to receive returns, that could potentially be significant to WM Outrigger Re. As a result, White Mountains consolidates WM Outrigger Re’s results in its financial statements. The assets of WM Outrigger Re can only be used to settle the liabilities of WM Outrigger Re, and there is no recourse to the Company for any creditors of WM Outrigger Re. PassportCard/DavidShield As of March 31, 2023, White Mountains’s ownership interest in PassportCard/DavidShield was 53.8%. White Mountains has determined that both PassportCard and DavidShield are VIEs but that White Mountains is not the primary beneficiary and therefore does not consolidate either PassportCard or DavidShield. The governance structures for both PassportCard and DavidShield were designed to give White Mountains and its co-investor equal power to make the decisions that most significantly impact operations. White Mountains does not have the unilateral power to direct the operations of PassportCard or DavidShield and does not hold a controlling financial interest. White Mountains’s ownership interest gives White Mountains the ability to exert significant influence over the significant financial and operating activities of PassportCard/DavidShield. Accordingly, White Mountains’s investment in PassportCard/DavidShield meets the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard/DavidShield. Changes in the fair value of PassportCard/DavidShield are recorded in net realized and unrealized investment gains (losses). As of March 31, 2023, White Mountains’s maximum exposure to loss on its equity investment in PassportCard/DavidShield and the non-interest-bearing loan to its partner is the total carrying value of $149.7 million. Elementum As of March 31, 2023, White Mountains’s ownership interest in Elementum was 26.6%. White Mountains has determined that Elementum is a VIE but that White Mountains is not the primary beneficiary and therefore does not consolidate Elementum. White Mountains’s ownership interest gives White Mountains the ability to exert significant influence over the significant financial and operating activities of Elementum. Accordingly, Elementum meets the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in Elementum. Changes in the fair value of Elementum are recorded in net realized and unrealized investment gains (losses). As of March 31, 2023, White Mountains’s maximum exposure to loss on its limited partnership interest in Elementum is the carrying value of $30.0 million. Limited Partnerships White Mountains’s investments in limited partnerships are generally considered VIEs because the limited partnership interests do not have substantive kick-out rights or participating rights. White Mountains does not have the unilateral power to direct the operations of these limited partnerships, and therefore White Mountains is not the primary beneficiary and does not consolidate the limited partnerships. White Mountains has taken the fair value option for its investments in limited partnerships, which are generally measured at NAV as a practical expedient. As of March 31, 2023, White Mountains’s maximum exposure to loss on its investments in limited partnerships is the carrying value of $159.4 million.

Equity-Method Eligible Investme

Equity-Method Eligible Investments	3 Months Ended
	Mar. 31, 2023
Equity Method Investments and Joint Ventures [Abstract]
Equity-Method Eligible Investments	Equity Method Eligible Investments White Mountains’s equity method eligible investments include Kudu’s Participation Contracts, White Mountains’s investment in MediaAlpha, PassportCard/DavidShield, Elementum Holdings, L.P. and certain other unconsolidated entities, private equity funds and hedge funds in which White Mountains has the ability to exert significant influence over the investee’s operating and financial policies. The following table presents the ownership interests and carrying values of White Mountains’s equity method eligible investments as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 $ in Millions Ownership Interest (1) Carrying Value Ownership Interest (1) Carrying Value Kudu’s Participation Contracts (1) 4.1% - 30.0% $ 683.2 4.1% - 30.0% $ 695.9 Investment in MediaAlpha 26.8% 253.8 27.1% 168.6 PassportCard/DavidShield 53.8% 140.0 53.8% 135.0 Elementum Holdings, L.P. 26.6% 30.0 29.7% 30.0 Other equity method eligible investments, at fair value Under 50.0% 180.8 Under 50.0% 84.4 Other equity method eligible investments, at fair value 50.0% and over 10.5 50.0% and over — (1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are noncontrolling equity interests in the form of revenue and earnings participation contracts. For the three months ended March 31, 2023 and 2022, White Mountains received dividend and income distributions from equity method eligible investments of $7.7 million and $13.1 million, which were recorded within net investment income in the consolidated statements of operations.

Fair Value of Financial Instrum

Fair Value of Financial Instruments	3 Months Ended
	Mar. 31, 2023
Fair Value Disclosures [Abstract]
Fair Value of Financial Instruments	Fair Value of Financial Instruments White Mountains records its financial instruments at fair value with the exception of debt obligations, which are recorded as debt at face value less unamortized original issue discount. See Note 7 — “Debt.” The following table presents the fair value and carrying value of these financial instruments as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Carrying Value Fair Value Carrying Value HG Global Senior Notes $ 158.8 $ 146.6 $ 155.7 $ 146.5 Ark 2007 Subordinated Notes $ 29.2 $ 30.0 $ 28.4 $ 30.0 Ark 2021 Subordinated Notes $ 165.5 $ 154.5 $ 163.1 $ 153.7 Kudu Credit Facility $ 208.2 $ 191.6 $ 223.9 $ 208.3 Other Operations debt $ 35.4 $ 33.6 $ 38.2 $ 36.7 The fair value estimates for the HG Global Senior Notes, Ark 2007 Subordinated Notes, Ark 2021 Subordinated Notes, Kudu Credit Facility and Other Operations debt have been determined based on a discounted cash flow approach and are considered to be Level 3 measurements. For the fair value level measurements associated with White Mountains’s investment securities. See Note 3 — “Investment Securities.” For the fair value level measurements associated with White Mountains’s derivative instruments. See Note 9 — “Derivatives.”

Commitments and Contingencies

Commitments and Contingencies	3 Months Ended
	Mar. 31, 2023
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	Commitments and Contingencies Legal Contingencies White Mountains, and the insurance industry in general, is routinely subject to claims related litigation and arbitration in the normal course of business, as well as litigation and arbitration that do not arise from, nor are directly related to, claims activity. White Mountains’s estimates of the costs of settling matters routinely encountered in claims activity are reflected in the reserves for unpaid loss and LAE. See Note 5 — “Losses and Loss Adjustment Expense Reserves.”

Held for Sale and Discontinued

Held for Sale and Discontinued Operations	3 Months Ended
	Mar. 31, 2023
Discontinued Operations and Disposal Groups [Abstract]
Held for Sale and Discontinued Operations	Held for Sale and Discontinued Operations NSM On August 1, 2022, White Mountains closed the NSM Transaction. See Note 2 — “Significant Transactions.” As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. Net Income (Loss) from Discontinued Operations The following table summarizes the results of operations, including related income taxes associated with the businesses classified as discontinued operations for the three months ended March 31, 2022: Millions Three Months Ended Revenues Commission revenues $ 70.1 Other revenues 18.4 Total revenues 88.5 Expenses General and administrative expenses 54.0 Broker commission expenses 20.6 Change in fair value of contingent consideration .1 Amortization of other intangible assets 9.1 Interest expense 2.1 Total expenses 85.9 Pre-tax income (loss) from discontinued operations 2.6 Income tax (expense) benefit 1.1 Net income (loss) from discontinued operations, net of tax 3.7 Net (income) loss from discontinued operations attributable to noncontrolling interests (.1) Total income (loss) from discontinued operations attributable to White 3.6 Other comprehensive income (loss) from discontinued operations, net of tax (1.9) Comprehensive income (loss) from discontinued operations 1.7 Other comprehensive income (loss) from discontinued operations attributable to .1 Comprehensive income (loss) from discontinued operations attributable to $ 1.8 Net Change in Cash from Discontinued Operations The following table summarizes the net change in cash associated with the businesses classified as discontinued operations for the three months ended March 31, 2022: Millions Three Months Ended Net cash provided from (used for) operations $ 4.4 Net cash provided from (used for) investing activities 7.3 Net cash used from (used for) financing activities (10.3) Effect of exchange rate changes on cash .6 Net change in cash during the period 2.0 Cash balances at beginning of period (includes restricted cash of $89.2) 111.6 Cash balances at end of period (includes restricted cash of $90.2 ) 113.6 Supplemental cash flows information: Interest paid $ (2.9) Net income tax payments $ — Earnings Per Share from Discontinued Operations White Mountains calculates earnings per share using the two-class method, which allocates earnings between common and unvested restricted common shares. Both classes of shares participate equally in earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares. Diluted earnings per share amounts are also impacted by the net effect of potentially dilutive common shares outstanding. The following table presents the Company’s computation of earnings per share for discontinued operations for the three months ended March 31, 2022: Three Months Ended Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 33.4 Less: net income (loss) from continuing operations (12.1) Less: net (income) loss from continuing operations attributable to noncontrolling 41.9 Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders (1) 3.6 Allocation of earnings to participating restricted common shares (2) — Basic and diluted earnings per share numerators (3) $ 3.6 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,006.2 Average unvested restricted common shares (4) (29.6) Basic earnings per share denominator 2,976.6 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,006.2 Average unvested restricted common shares (4) (29.6) Diluted earnings per share denominator 2,976.6 Basic and diluted earnings (losses) per share (in dollars) - discontinued operations: $ 1.20 (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group (2) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (3) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three months ended March 31, 2022. (4) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

Basis of Presentation and Sig_2

Basis of Presentation and Significant Accounting Policies (Policies)	3 Months Ended
	Mar. 31, 2023
Accounting Policies [Abstract]
Basis of Presentation	Basis of Presentation White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”) is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report. The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of the Company, its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.
Reportable Segments	Reportable Segments As of March 31, 2023, White Mountains conducted its operations through three reportable segments: (1) HG Global/BAM, (2) Ark/WM Outrigger, and (3) Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations. White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the Company’s chief operating decision makers and its Board of Directors. See Note 14 — “Segment Information.” The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (collectively, “HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively with HG Global, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM (the “BAM Surplus Notes”). As of March 31, 2023 and December 31, 2022, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a variable interest entity (“VIE”) for which White Mountains is the primary beneficiary. BAM’s results are all attributed to noncontrolling interests. The Ark/WM Outrigger segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”) and Outrigger Re Ltd. Segregated Account 2023-1 (“WM Outrigger Re”) (collectively with Ark, “Ark/WM Outrigger”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, specialty, marine & energy, casualty and accident & health. Ark underwrites select coverages through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”) and its wholly-owned subsidiary Group Ark Insurance Limited (“GAIL”). White Mountains acquired a controlling ownership interest in Ark on January 1, 2021 (the “Ark Transaction”). As of March 31, 2023 and December 31, 2022, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% after taking account of management’s equity incentives). The remaining shares are owned by current and former employees. In the future, management rollover shareholders could earn additional shares in Ark if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts with Ark’s corporate member. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. Captions within results of operations and other comprehensive income for the three months ended March 31, 2022 are shown net of amounts relating to the TPC Providers’ share of the Syndicates’ results, including investment results. During the fourth quarter of 2022, Ark sponsored the formation of Outrigger Re Ltd., a Bermuda company registered as a special purpose insurer and segregated accounts company, to provide collateralized reinsurance protection on Ark’s Bermuda global property catastrophe excess of loss portfolio written in calendar year 2023. Outrigger Re Ltd. issued non-voting redeemable preference shares on behalf of four segregated accounts to White Mountains and unrelated third party investors. White Mountains consolidates the results of its segregated account, WM Outrigger Re, in its financial statements. See Note 2 — “Significant Transactions.” As of March 31, 2023 and December 31, 2022, White Mountains owned 100.0% of WM Outrigger Re’s preferred equity. The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset and wealth managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions generally are structured as minority preferred equity stakes with distribution rights, typically tied to gross revenues and designed to generate immediate cash yields. As of March 31, 2023 and December 31, 2022, White Mountains owned 89.2% and 89.3% of Kudu’s basic units outstanding (76.1% and 76.1% on a fully diluted, fully converted basis). White Mountains’s Other Operations consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC (“WM Capital”), its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/ DavidShield”), Elementum Holdings LP (“Elementum”), certain other consolidated and unconsolidated entities (“Other Operating Businesses”) and certain other assets.
Discontinued Operations	Discontinued Operations On August 1, 2022, White Mountains Holdings (Luxembourg) S.à r.l. (“WTM Holdings Seller”), an indirect wholly owned subsidiary of White Mountains, completed the sale of White Mountains Catskill Holdings, Inc. and NSM Insurance HoldCo, LLC (“NSM” and, collectively with White Mountains Catskill Holdings, Inc., the “NSM Group”) to Riser Merger Sub, Inc., an affiliate of The Carlyle Group Inc. (the “NSM Transaction”), pursuant to the terms of the securities purchase agreement dated as of May 9, 2022. See Note 2 — “Significant Transactions. ” NSM is a full-service managing general agent (“MGA”) and program administrator with delegated binding authorities for specialty property and casualty insurance. As a result of the NSM Transaction, the assets and liabilities of NSM Group have been presented in the balance sheet as held for sale for periods prior to the closing of the transaction, and the results of operations for NSM Group have been classified as discontinued operations in the statements of operations and comprehensive income through the closing of the transaction. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued Operations.”

Investment Securities (Tables)

Investment Securities (Tables)	3 Months Ended
	Mar. 31, 2023
Investments, Debt and Equity Securities [Abstract]
Pre-tax net investment income	The following table presents pre-tax net investment income for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Fixed maturity investments $ 14.5 $ 8.2 Short-term investments 9.7 .1 Common equity securities 1.3 — Other long-term investments 14.1 13.2 Amount attributable to TPC Providers — (.5) Total investment income 39.6 21.0 Third-party investment expenses (.6) (.4) Net investment income, pre-tax $ 39.0 $ 20.6
Schedule of net realized and unrealized investment gains and losses	The following table presents net realized and unrealized investment gains (losses) for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Realized investment gains (losses) Fixed maturity investments $ (.1) $ (1.1) Short-term investments (.4) (.2) Other long-term investments 47.2 18.7 Net realized investment gains (losses) 46.7 17.4 Unrealized investment gains (losses) Fixed maturity investments 29.7 (79.5) Short-term investments 1.2 .2 Common equity securities 29.4 1.0 Investment in MediaAlpha 85.2 18.8 Other long-term investments 5.9 50.4 Net unrealized investment gains (losses) 151.4 (9.1) Net realized and unrealized investment gains (losses), before amount attributable to TPC providers (1) 198.1 8.3 Amount attributable to TPC Providers — 2.1 Net realized and unrealized investment gains (losses) $ 198.1 $ 10.4 Fixed maturity and short-term investments Net realized and unrealized investment gains (losses) $ 30.4 $ (80.6) Less: net realized and unrealized gains (losses) on investment 1.8 (1.0) Net unrealized investment gains (losses) recognized during the period on $ 28.6 $ (79.6) Common equity securities and investment in MediaAlpha Net realized and unrealized investment gains (losses) on common $ 29.4 $ 1.0 Net realized and unrealized investment gains (losses) from 85.2 18.8 Total net realized and unrealized investment gains (losses) 114.6 19.8 Less: net realized and unrealized gains (losses) on investment — — Net unrealized investment gains (losses) recognized during the period on $ 114.6 $ 19.8 (1) For the three months ended March 31, 2023 and 2022, includes $5.4 and $2.6 of realized and unrealized investment gains related to foreign currency exchange.
Net unrealized investment gains (losses) for Level 3 investments	The following table presents total net unrealized gains (losses) attributable to Level 3 investments for the three months ended March 31, 2023 and 2022 for investments still held at the end of the period: Three Months Ended March 31, Millions 2023 2022 Total net unrealized investment gains on other long-term investments held at the $ 37.0 $ 27.2
Investment holdings, equity securities, convertible fixed maturities and other long-term investments	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 March 31, 2023 and December 31, 2022: March 31, 2023 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 245.7 $ .1 $ (8.0) $ — $ 237.8 Debt securities issued by corporations 1,073.9 1.3 (63.1) (1.7) 1,010.4 Municipal obligations 280.0 — (17.0) — 263.0 Mortgage and asset-backed securities 289.5 — (30.7) — 258.8 Collateralized loan obligations 192.1 .1 (5.2) (1.1) 185.9 Total fixed maturity investments $ 2,081.2 $ 1.5 $ (124.0) $ (2.8) $ 1,955.9 December 31, 2022 Millions Cost or Gross Gross Net Foreign Carrying 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 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 March 31, 2023 and December 31, 2022: March 31, 2023 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 660.6 $ 48.0 $ (2.8) $ (8.0) $ 697.8 Investment in MediaAlpha $ — $ 253.8 $ — $ — $ 253.8 Other long-term investments $ 1,489.7 $ 264.3 $ (96.2) $ (14.8) $ 1,643.0 December 31, 2022 Millions Cost or Gross Gross Net Foreign Carrying 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
Schedule of fixed maturity investment holdings	The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of March 31, 2023. 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. March 31, 2023 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 223.8 $ 219.2 Due after one year through five years 943.6 891.9 Due after five years through ten years 338.8 314.2 Due after ten years 93.4 85.9 Mortgage and asset-backed securities and collateralized loan obligations 481.6 444.7 Total fixed maturity investments $ 2,081.2 $ 1,955.9
Fair value measurements by level, investment securities	The following tables present White Mountains’s fair value measurements for investments as of March 31, 2023 and December 31, 2022 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. March 31, 2023 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 237.8 $ 237.8 $ — $ — Debt securities issued by corporations: Financials 281.9 — 281.9 — Consumer 194.9 — 194.9 — Healthcare 124.8 — 124.8 — Technology 123.3 — 123.3 — Industrial 119.8 — 119.8 — Utilities 64.0 — 64.0 — Communications 45.2 — 45.2 — Energy 36.4 — 36.4 — Materials 20.1 — 20.1 — Total debt securities issued by corporations 1,010.4 — 1,010.4 — Municipal obligations 263.0 — 263.0 — Mortgage and asset-backed securities 258.8 — 258.8 — Collateralized loan obligations 185.9 — 185.9 — Total fixed maturity investments 1,955.9 237.8 1,718.1 — Short-term investments 884.2 878.4 5.8 — Common equity securities: Exchange-traded funds 357.4 357.4 — — Other (1) 340.4 — 340.4 — Total common equity securities 697.8 357.4 340.4 — Investment in MediaAlpha 253.8 253.8 — — Other long-term investments 970.2 — 15.5 954.7 Other long-term investments — NAV (2) 672.8 — — — Total other long-term investments 1,643.0 — 15.5 954.7 Total investments $ 5,434.7 $ 1,727.4 $ 2,079.8 $ 954.7 (1) Consists 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, 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 — Healthcare 121.3 — 121.3 — Technology 123.7 — 123.7 — 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-traded 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) Consists 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.
Debt securities issued by corporations, credit ratings	The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of March 31, 2023 and December 31, 2022: Fair Value at Millions March 31, 2023 December 31, 2022 AAA $ 11.4 $ 11.3 AA 95.9 96.0 A 558.8 567.9 BBB 338.0 337.7 Other 6.3 5.9 Debt securities issued by corporations (1) $ 1,010.4 $ 1,018.8 (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-backed, asset-backed securities	The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 129.7 $ 129.7 $ — $ 124.5 $ 124.5 $ — FHLMC 81.2 81.2 — 78.8 78.8 — GNMA 33.0 33.0 — 28.3 28.3 — Total agency (1) 243.9 243.9 — 231.6 231.6 — Non-agency: Residential .3 .3 — .3 .3 — Total non-agency .3 .3 — .3 .3 — Total mortgage-backed securities 244.2 244.2 — 231.9 231.9 — Other asset-backed securities: Credit card receivables 4.4 4.4 — 11.9 11.9 — Vehicle receivables 10.2 10.2 — 10.4 10.4 — Total other asset-backed securities 14.6 14.6 — 22.3 22.3 — Total mortgage and asset-backed securities 258.8 258.8 — 254.2 254.2 — Collateralized loan obligations 185.9 185.9 — 182.9 182.9 — Total mortgage and asset-backed securities $ 444.7 $ 444.7 $ — $ 437.1 $ 437.1 $ — (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).
Schedule of carrying values for other long-term investments	The following table presents the carrying values of White Mountains’s other long-term investments as of March 31, 2023 and December 31, 2022: Fair Value at Millions March 31, 2023 December 31, 2022 Kudu’s Participation Contracts $ 683.2 $ 695.9 PassportCard/DavidShield 140.0 135.0 Elementum Holdings, L.P. 30.0 30.0 Other unconsolidated entities (1) 87.5 37.2 Total unconsolidated entities 940.7 898.1 Private equity funds and hedge funds 218.5 197.8 Bank loan fund 179.5 174.8 Lloyd’s trust deposits 148.7 137.4 ILS funds 123.6 49.3 Private debt instruments 10.1 9.6 Other 21.9 21.0 Total other long-term investments $ 1,643.0 $ 1,488.0 (1) Includes White Mountains’s noncontrolling equity interests in certain private common equity securities, preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments.
Other long-term investments	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 March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 78.0 $ 37.5 $ 59.4 $ 37.5 Financial services 77.3 52.6 77.1 54.3 Real estate 4.1 2.5 4.1 2.5 Total private equity funds 159.4 92.6 140.6 94.3 Hedge funds Long/short equity financials and business services 49.8 — 49.0 — European small/mid cap 9.3 — 8.2 — Total hedge funds 59.1 — 57.2 — Total private equity funds and hedge funds included in other long-term investments $ 218.5 $ 92.6 $ 197.8 $ 94.3
Fair value of private equity funds subject to lock-up periods	The following table presents investments in private equity funds that were subject to lock-up periods as of March 31, 2023: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $4.1 $18.6 $132.3 $4.4 $159.4
Rollforward of fair value investments by level	The following table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the three months ended March 31, 2023 and 2022: Level 3 Investments Millions Other Long-term Other Long-term Balance at December 31, 2022 $ 911.6 Balance at December 31, 2021 $ 890.6 Net realized and unrealized gains 35.1 Net realized and unrealized gains 26.8 Amortization/accretion — Amortization/accretion — Purchases and contributions 117.0 Purchases and contributions — Sales and distributions (109.0) Sales and distributions (31.7) Transfers in — Transfers in — Transfers out — Transfers out — Balance at March 31, 2023 $ 954.7 Balance at March 31, 2022 $ 885.7
Schedule of significant unobservable inputs used in estimating the fair value of investment securities	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 March 31, 2023 and December 31, 2022. The tables below exclude $91.8 million and $41.1 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 March 31, 2023 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (5) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (5) Kudu’s Participation Contracts (3)(4) Discounted cash flow $683.2 18% - 25% 7x - 22x PassportCard/DavidShield Discounted cash flow $140.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $30.0 20% 4% Private debt instruments Discounted cash flow $9.7 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 12.7x. (4) In 2023, Kudu deployed a total of $30.9 into new and existing Participation Contracts. (5) 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, 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% 4% Elementum Holdings, L.P. Discounted cash flow $30.0 21% 4% 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 Participation Contracts. (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 sale 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.

Goodwill and Other Intangible_2

Goodwill and Other Intangible Assets (Tables)	3 Months Ended
	Mar. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract]
Schedule of Intangible Assets and Goodwill	The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill as of March 31, 2023 and December 31, 2022: $ in Millions Weighted Average Economic March 31, 2023 December 31, 2022 Acquisition Date Fair Value Accumulated Amortization Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Net Carrying Value Goodwill: Ark N/A $ 116.8 $ — $ 116.8 $ 116.8 $ — $ 116.8 Kudu N/A 7.6 — 7.6 7.6 7.6 Other Operations N/A 44.4 — 44.4 52.1 — 52.1 Total goodwill 168.8 — 168.8 176.5 — 176.5 Other intangible assets: Ark Underwriting capacity N/A 175.7 — 175.7 175.7 — 175.7 Kudu Trade names 7 2.2 1.3 .9 2.2 1.2 1.0 Other Operations Trade names 13.3 13.3 2.6 10.7 17.9 3.0 14.9 Customer relationships 11.0 24.8 7.0 17.8 29.5 7.5 22.0 Other 12.1 2.8 .5 2.3 2.8 .5 2.3 Subtotal 40.9 10.1 30.8 50.2 11.0 39.2 Total other intangible assets 218.8 11.4 207.4 228.1 12.2 215.9 Total goodwill and other intangible assets $ 387.6 $ 11.4 376.2 $ 404.6 $ 12.2 392.4 The following table presents the change in goodwill and other intangible assets for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, 2023 2022 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 176.5 $ 215.9 $ 392.4 $ 142.3 $ 198.2 $ 340.5 Dispositions (1) (6.7) (6.9) (13.6) — — — Measurement period adjustments (2) (1.0) — (1.0) — — — Amortization — (1.6) (1.6) — (1.0) (1.0) Ending balance $ 168.8 $ 207.4 $ 376.2 $ 142.3 $ 197.2 $ 339.5 (1) Relates to a disposition within Other Operations. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended March 31, 2023 adjustments relate to an acquisition within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with this acquisition during 2022 had not yet been finalized as of the end of the period.

Loss and Loss Adjustment Expe_2

Loss and Loss Adjustment Expense Reserves (Tables)	3 Months Ended
	Mar. 31, 2023
Insurance Loss Reserves [Abstract]
Schedule of Liability for Unpaid Claims and Claims Adjustment Expense	The following table summarizes the loss and loss adjustment expense (“LAE”) reserve activity of the Ark/WM Outrigger segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Gross beginning balance $ 1,296.5 $ 894.7 Less: beginning reinsurance recoverable on unpaid losses (1) (505.0) (428.9) Net loss and LAE reserves 791.5 465.8 Loss and LAE incurred relating to: Current year losses 139.2 125.7 Prior year losses 8.6 (3.7) Net incurred losses and LAE 147.8 122.0 Loss and LAE paid relating to: Current year losses (4.0) (.6) Prior year losses (87.7) (39.4) Net paid loss and LAE (91.7) (40.0) Change in TPC Providers’ participation (2) 145.4 57.5 Foreign currency translation and other adjustments to loss and LAE 3.7 (1.7) Net ending balance 996.7 603.6 Plus: ending reinsurance recoverable on unpaid losses (3) 348.9 396.0 Gross ending balance $ 1,345.6 $ 999.6 (1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $145.4 and $276.8 as of December 31, 2022 and 2021. (2) Amount represents the impact to net loss and LAE reserves due to a change in the TPC Providers’ participation related to the annual reinsurance to close process. (3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $0.0 and $207.3 as of March 31, 2023 and 2022.

Third-Party Reinsurance (Tables

Third-Party Reinsurance (Tables)	3 Months Ended
	Mar. 31, 2023
Reinsurance Disclosures [Abstract]
Effects of Reinsurance	The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for the Ark/WM Outrigger segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Written premiums: Direct $ 246.2 $ 230.9 Assumed 563.2 402.2 Gross written premiums 809.4 633.1 Ceded (195.2) (1) (89.3) Net written premiums $ 614.2 $ 543.8 Earned premiums: Direct $ 150.4 $ 138.7 Assumed 162.1 106.6 Gross earned premiums 312.5 245.3 Ceded (57.4) (2) (50.9) Net earned premiums $ 255.1 $ 194.4 Losses and LAE: Gross $ 162.4 $ 183.1 Ceded (14.6) (3) (61.1) Net losses and LAE $ 147.8 $ 122.0 (1) The ceded written premiums exclude $44.1 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (2) The ceded earned premiums exclude $5.2 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (3) The ceded loss and LAE exclude $0.2 ceded by Ark to WM Outrigger Re for the three months ended March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. The following table presents the Ark/WM Outrigger segment’s reinsurance recoverables as of March 31, 2023 and December 31, 2022: Millions March 31, 2023 December 31, 2022 Reinsurance recoverables on unpaid losses $ 348.9 (1) $ 505.0 (3) Reinsurance recoverables on paid losses 23.1 31.1 Ceded unearned premiums 198.6 (2) 59.2 Reinsurance recoverables $ 570.6 $ 595.3 (1) The reinsurance recoverables on unpaid losses exclude $0.2 ceded by Ark to WM Outrigger Re as of March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (2) The ceded unearned premiums exclude $38.9 ceded by Ark to WM Outrigger Re as of March 31, 2023, which eliminate in White Mountains’s consolidated financial statements. (3) The reinsurance recoverables on unpaid losses include $145.4 attributable to TPC Providers as of December 31, 2022, which are collateralized. The following table presents the Ark/WM Outrigger segment’s gross and net reinsurance recoverables by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) ratings as of March 31, 2023: $ in Millions As of March 31, 2023 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 173.8 $ — $ 173.8 64.7 % A- to A 77.9 — 77.9 29.0 B++ or lower and not rated 120.3 103.2 17.1 6.3 Total $ 372.0 $ 103.2 $ 268.8 100.0 % (1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good).

Debt (Tables)

Debt (Tables)	3 Months Ended
	Mar. 31, 2023
Debt Disclosure [Abstract]
Schedule of debt outstanding	The following table presents White Mountains’s debt outstanding as of March 31, 2023 and December 31, 2022: $ in Millions March 31, 2023 Effective (1) December 31, 2022 Effective (1) HG Global Senior Notes $ 150.0 11.0% $ 150.0 8.9% Unamortized discount and issuance cost (3.4) (3.5) HG Global Senior Notes, carrying value 146.6 146.5 Ark 2007 Subordinated Notes, carrying value 30.0 30.0 Ark 2021 Subordinated Notes Tranche 1 42.0 41.3 Ark 2021 Subordinated Notes Tranche 2 47.0 47.0 Ark 2021 Subordinated Notes Tranche 3 70.0 70.0 Unamortized issuance cost (4.5) (4.6) Ark 2021 Subordinated Notes, carrying value 154.5 153.7 Total Ark Subordinated Notes, carrying value 184.5 10.3% 183.7 7.6% Kudu Credit Facility 198.3 8.7% 215.2 6.1% Unamortized issuance cost (6.7) (6.9) Kudu Credit Facility, carrying value 191.6 208.3 Other Operations debt 34.3 8.5% 37.4 6.6% Unamortized issuance cost (.7) (.7) Other Operations debt, carrying value 33.6 36.7 Total debt $ 556.3 $ 575.2 (1) Effective rate includes the effect of the amortization of debt issuance costs and, where applicable, the original issue discount. The following table presents the change in debt under the Kudu Credit Facility for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Kudu Credit Facility Beginning balance $ 215.2 $ 225.4 Term loans Borrowings — — Repayments (16.9) — Ending balance $ 198.3 $ 225.4

Municipal Bond Guarantee Insu_2

Municipal Bond Guarantee Insurance (Tables)	3 Months Ended
	Mar. 31, 2023
Guarantees [Abstract]
Schedule of Municipal Bond Guarantee Insured Obligations	The following table presents a schedule of BAM’s insured obligations as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Contracts outstanding 13,607 13,382 Remaining weighted average contract period (in years) 10.8 10.8 Contractual debt service outstanding (in millions): Principal $ 101,785.7 $ 99,996.9 Interest 49,801.9 48,880.6 Total debt service outstanding $ 151,587.6 $ 148,877.5 Gross unearned insurance premiums (in millions) $ 299.8 $ 298.3
Financial Guarantee Insurance Contracts, Premium Received over Contract Period	The following table presents a schedule of BAM’s future premium revenues as of March 31, 2023: Millions March 31, 2023 April 1, 2023 - December 31, 2023 $ 20.9 January 1, 2024 - March 31, 2024 6.8 April 1, 2024 - June 30, 2024 6.7 July 1, 2024 - September 30, 2024 6.5 October 1, 2024 - December 31, 2024 6.4 Total 2024 26.4 2025 24.7 2026 23.1 2027 21.5 2028 19.8 2029 and thereafter 163.4 Total gross unearned insurance premiums $ 299.8
Schedule of Gross Written Premiums	The following table presents a schedule of written premiums and earned premiums included in the HG Global/BAM segment for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, Millions 2023 2022 Written premiums: Direct $ 9.2 $ 9.4 Assumed — — Gross written premiums (1) $ 9.2 $ 9.4 Earned premiums: Direct $ 7.0 $ 7.6 Assumed .7 .8 Gross earned premiums (1) $ 7.7 $ 8.4 (1) There are no ceded premium amounts in the periods presented, and gross earned premiums are equivalent to net written premiums and net earned premiums.

Earnings Per Share (Tables)

Earnings Per Share (Tables)	3 Months Ended
	Mar. 31, 2023
Earnings Per Share [Abstract]
Computation of earnings per share	The following table presents the Company’s computation of earnings per share from continuing operations for the three months ended March 31, 2023 and 2022. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended March 31, 2023 2022 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 179.5 $ 33.4 Less: total income (loss) from discontinued operations, net of tax (1) — 3.7 Less: net (income) loss from discontinued operations attributable — (.1) Net income (loss) from continuing operations attributable to 179.5 29.8 Allocation of (earnings) losses to participating restricted common shares (2) (2.2) (.3) Basic and diluted earnings (losses) per share numerators $ 177.3 $ 29.5 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,569.9 3,006.2 Average unvested restricted common shares (3) (31.1) (29.6) Basic earnings (losses) per share denominator 2,538.8 2,976.6 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,569.9 3,006.2 Average unvested restricted common shares (3) (31.1) (29.6) Diluted earnings (losses) per share denominator 2,538.8 2,976.6 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ 1.00 $ 1.00 Undistributed earnings (losses) 68.83 8.90 Basic and diluted earnings (losses) per share $ 69.83 $ 9.90 (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group. See Note 19 — “Held for Sale and Discontinued Operations. ” (2) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (3) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”
Schedule of Undistributed Net Earnings (Losses) from Continuing Operations	The following table presents the undistributed net earnings (losses) from continuing operations for the three months ended March 31, 2023 and 2022. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended March 31, Millions 2023 2022 Undistributed net earnings - continuing operations: Net income (loss) attributable to White Mountains’s common $ 177.3 $ 29.5 Dividends declared, net of restricted common share amounts (1) (2.5) (3.0) Total undistributed net earnings (losses), net of restricted common share amounts $ 174.8 $ 26.5 (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities.

Employee Share-Based Incentiv_2

Employee Share-Based Incentive Compensation Plans (Tables)	3 Months Ended
	Mar. 31, 2023
Share-Based Payment Arrangement [Abstract]
Summary of performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan	The following table presents the performance share activity for the three months ended March 31, 2023 and 2022 for performance shares granted under the WTM Incentive Plan: Three Months Ended March 31, 2023 2022 $ in Millions Target Performance Accrued Target Performance Accrued Beginning of period 39,449 $ 67.5 40,828 $ 42.2 Shares paid (1) (13,350) (40.8) (14,625) (26.4) New grants 10,895 — 13,075 — Forfeitures and cancellations (2) 37 .4 24 .3 Expense recognized — 9.3 — 5.8 End of period 37,031 $ 36.4 39,302 $ 21.9 (1) WTM performance share payments in 2023 for the 2020-2022 performance cycle, which were paid in March 2023 at 200% of target. WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP.
Share-based Compensation, Performance Shares Award Outstanding Activity	The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of March 31, 2023 for each performance cycle: March 31, 2023 $ in Millions Target Performance Accrued Performance cycle: 2021 – 2023 13,475 $ 22.6 2022 – 2024 13,225 14.0 2023 – 2025 10,895 .4 Sub-total 37,595 37.0 Assumed forfeitures (564) (.6) Total 37,031 $ 36.4
Summary of restricted shares activity	Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards under the WTM Incentive Plan for the three months ended March 31, 2023 and 2022: Three Months Ended March 31, 2023 2022 $ in Millions Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,350 $ 15.5 37,850 $ 15.9 Issued 10,895 16.0 13,075 13.6 Vested (11,650) — (12,725) — Forfeited — — — — Expense recognized — (3.2) — (3.0) End of period 37,595 $ 28.3 38,200 $ 26.5

Noncontrolling Interests (Table

Noncontrolling Interests (Tables)	3 Months Ended
	Mar. 31, 2023
Noncontrolling Interest [Abstract]
Non-controlling Interests	The following table presents the balance of noncontrolling interests included in White Mountains’s total equity and the related percentage of each consolidated entity’s total equity owned by noncontrolling shareholders as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 $ in Millions Noncontrolling Percentage (1) Noncontrolling Equity Noncontrolling Percentage (1) Noncontrolling Equity Noncontrolling interests, excluding BAM HG Global 3.1 % $ (.3) 3.1 % $ (.6) Ark 28.0 % 251.3 28.0 % 247.9 Kudu 10.8 % 81.3 10.8 % 75.1 Other various 10.3 various 20.4 Total, excluding BAM 342.6 342.8 BAM 100.0 % (152.2) 100.0 % (154.7) Total noncontrolling interests $ 190.4 $ 188.1 (1) The noncontrolling percentage represents the basic ownership interests held by noncontrolling shareholders with the exception of HG Global, for which the noncontrolling percentage represents the preferred share ownership held by noncontrolling shareholders.

Segment Information (Tables)

Segment Information (Tables)	3 Months Ended
	Mar. 31, 2023
Segment Reporting [Abstract]
Schedule of Financial Information for White Mountains' Segments	The following tables present the financial information for White Mountains’s segments for the three months ended March 31, 2023 and 2022: Millions HG Global/BAM Ark/WM Outrigger HG Global BAM (1) Ark WM Outrigger Re Kudu Other Operations Total Three Months Ended March 31, 2023 Earned insurance premiums $ 6.4 $ 1.3 $ 249.9 $ 5.2 $ — $ — $ 262.8 Net investment income 4.0 3.2 8.4 2.2 14.2 7.0 39.0 Net investment income (expense) - 6.6 (6.6) — — — — — Net realized and unrealized investment 7.9 9.1 24.5 — 29.6 41.8 112.9 Net realized and unrealized investment gains — — — — — 85.2 85.2 Commission revenues — — — — — 3.3 3.3 Other revenues — .8 (2.7) — — 30.6 28.7 Total revenues 24.9 7.8 280.1 7.4 43.8 167.9 531.9 Loss and loss adjustment expenses — — 147.6 .2 — — 147.8 Acquisition expenses 1.8 .9 58.9 .9 — — 62.5 Cost of sales — — — — — 13.9 13.9 General and administrative expenses 1.1 16.2 35.1 .1 3.8 39.7 96.0 Change in fair value of contingent — — (2.4) — — — (2.4) Interest expense 4.5 — 5.0 — 4.7 .8 15.0 Total expenses 7.4 17.1 244.2 1.2 8.5 54.4 332.8 Pre-tax income (loss) from continuing operations $ 17.5 $ (9.3) $ 35.9 $ 6.2 $ 35.3 $ 113.5 $ 199.1 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. Millions HG Global/BAM Ark/WM Outrigger Other Operations HG Global BAM (1) Ark Kudu Total Three Months Ended March 31, 2022 Earned insurance premiums $ 6.9 $ 1.5 $ 194.4 $ — $ — $ 202.8 Net investment income 2.1 2.5 1.6 12.6 1.8 20.6 Net investment income (expense) - 2.9 (2.9) — — — — Net realized and unrealized investment gains (losses) (23.5) (21.6) (17.5) 22.3 31.9 (8.4) Net realized and unrealized investment gains — — — — 18.8 18.8 Commission revenues — — — — 2.9 2.9 Other revenues .1 .7 (2.8) — 25.7 23.7 Total revenues (11.5) (19.8) 175.7 34.9 81.1 260.4 Losses and loss adjustment expenses — — 122.0 — — 122.0 Acquisition expenses 2.6 .4 49.9 — — 52.9 Cost of sales — — — — 21.4 21.4 General and administrative expenses .7 15.6 21.0 2.8 29.8 69.9 Change in fair value of contingent consideration — — 2.1 — — 2.1 Interest expense — — 3.8 2.8 .3 6.9 Total expenses 3.3 16.0 198.8 5.6 51.5 275.2 Pre-tax income (loss) from continuing operations $ (14.8) $ (35.8) $ (23.1) $ 29.3 $ 29.6 $ (14.8)
Schedule of Reconciliation of Revenue from Segments to Consolidated

Equity-Method Eligible Invest_2

Equity-Method Eligible Investments (Tables)	3 Months Ended
	Mar. 31, 2023
Equity Method Investments and Joint Ventures [Abstract]
Equity Method Investments	The following table presents the ownership interests and carrying values of White Mountains’s equity method eligible investments as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 $ in Millions Ownership Interest (1) Carrying Value Ownership Interest (1) Carrying Value Kudu’s Participation Contracts (1) 4.1% - 30.0% $ 683.2 4.1% - 30.0% $ 695.9 Investment in MediaAlpha 26.8% 253.8 27.1% 168.6 PassportCard/DavidShield 53.8% 140.0 53.8% 135.0 Elementum Holdings, L.P. 26.6% 30.0 29.7% 30.0 Other equity method eligible investments, at fair value Under 50.0% 180.8 Under 50.0% 84.4 Other equity method eligible investments, at fair value 50.0% and over 10.5 50.0% and over — (1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are noncontrolling equity interests in the form of revenue and earnings participation contracts.

Fair Value of Financial Instr_2

Fair Value of Financial Instruments (Tables)	3 Months Ended
	Mar. 31, 2023
Fair Value Disclosures [Abstract]
Summary of the fair value and carrying value of financial instruments	The following table presents the fair value and carrying value of these financial instruments as of March 31, 2023 and December 31, 2022: March 31, 2023 December 31, 2022 Millions Fair Value Carrying Value Fair Value Carrying Value HG Global Senior Notes $ 158.8 $ 146.6 $ 155.7 $ 146.5 Ark 2007 Subordinated Notes $ 29.2 $ 30.0 $ 28.4 $ 30.0 Ark 2021 Subordinated Notes $ 165.5 $ 154.5 $ 163.1 $ 153.7 Kudu Credit Facility $ 208.2 $ 191.6 $ 223.9 $ 208.3 Other Operations debt $ 35.4 $ 33.6 $ 38.2 $ 36.7

Held for Sale and Discontinue_2

Held for Sale and Discontinued Operations (Tables)	3 Months Ended
	Mar. 31, 2023
Discontinued Operations and Disposal Groups [Abstract]
Schedule of Discontinued Operations	The following table summarizes the results of operations, including related income taxes associated with the businesses classified as discontinued operations for the three months ended March 31, 2022: Millions Three Months Ended Revenues Commission revenues $ 70.1 Other revenues 18.4 Total revenues 88.5 Expenses General and administrative expenses 54.0 Broker commission expenses 20.6 Change in fair value of contingent consideration .1 Amortization of other intangible assets 9.1 Interest expense 2.1 Total expenses 85.9 Pre-tax income (loss) from discontinued operations 2.6 Income tax (expense) benefit 1.1 Net income (loss) from discontinued operations, net of tax 3.7 Net (income) loss from discontinued operations attributable to noncontrolling interests (.1) Total income (loss) from discontinued operations attributable to White 3.6 Other comprehensive income (loss) from discontinued operations, net of tax (1.9) Comprehensive income (loss) from discontinued operations 1.7 Other comprehensive income (loss) from discontinued operations attributable to .1 Comprehensive income (loss) from discontinued operations attributable to $ 1.8 Net Change in Cash from Discontinued Operations The following table summarizes the net change in cash associated with the businesses classified as discontinued operations for the three months ended March 31, 2022: Millions Three Months Ended Net cash provided from (used for) operations $ 4.4 Net cash provided from (used for) investing activities 7.3 Net cash used from (used for) financing activities (10.3) Effect of exchange rate changes on cash .6 Net change in cash during the period 2.0 Cash balances at beginning of period (includes restricted cash of $89.2) 111.6 Cash balances at end of period (includes restricted cash of $90.2 ) 113.6 Supplemental cash flows information: Interest paid $ (2.9) Net income tax payments $ — Three Months Ended Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 33.4 Less: net income (loss) from continuing operations (12.1) Less: net (income) loss from continuing operations attributable to noncontrolling 41.9 Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders (1) 3.6 Allocation of earnings to participating restricted common shares (2) — Basic and diluted earnings per share numerators (3) $ 3.6 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,006.2 Average unvested restricted common shares (4) (29.6) Basic earnings per share denominator 2,976.6 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,006.2 Average unvested restricted common shares (4) (29.6) Diluted earnings per share denominator 2,976.6 Basic and diluted earnings (losses) per share (in dollars) - discontinued operations: $ 1.20 (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group (2) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (3) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three months ended March 31, 2022. (4) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans.”

Basis of Presentation and Sig_3

Basis of Presentation and Significant Accounting Policies (Details) $ in Millions	3 Months Ended
	Mar. 31, 2023 USD ($) segment	Dec. 31, 2022	Jul. 31, 2012 USD ($)
Basis of Presentation
Number of reportable segments | segment	3
Ark
Basis of Presentation
Percent of shares outstanding	12.50%
Ark | Ark
Basis of Presentation
Ownership interest (as a percent)	72%	72%
Asset Management (Kudu)
Basis of Presentation
Ownership interest (as a percent)	89.20%	89.30%
Fully diluted ownership interest (as a percent)	76.10%	76.10%
Preferred Stock | HG Global
Basis of Presentation
Ownership interest (as a percent)	96.90%	96.90%
Preferred Stock | Outrigger Re
Basis of Presentation
Ownership interest (as a percent)	100%	100%
Common equity securities | HG Global
Basis of Presentation
Ownership interest (as a percent)	88.40%	88.40%
HG Global
Basis of Presentation
Percentage of par value of policy reinsured	15%
Surplus notes | $	$ 503		$ 503
Ark | Ark
Basis of Presentation
Fully diluted ownership interest (as a percent)	63%	63%

Significant Transactions - NSM

Significant Transactions - NSM (Details) - Discontinued Operations, Disposed of by Sale - NSM Insurance Group $ in Millions	Aug. 01, 2022 USD ($)
Other Significant Noncash Transactions [Line Items]
Transaction value	$ 1,400
Gain on transaction	875.7
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group	886.8
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9
Compensation and other costs	$ 14

Significant Transactions - Outr

Significant Transactions - Outrigger Re (Details) - USD ($) $ in Millions		3 Months Ended
	Dec. 20, 2022	Dec. 31, 2022
Outrigger Re
Other Significant Transactions [Line Items]
Issuance of redeemable preference shares	$ 250
Outrigger Re
Other Significant Transactions [Line Items]
Ownership interest after all transactions (as a percent)		100%
Purchase price		$ 205

Significant Transactions - Kudu

Significant Transactions - Kudu (Details) $ in Millions		12 Months Ended
	May 26, 2022 USD ($)	Dec. 31, 2021 USD ($)	May 25, 2022
Asset Management (Kudu)
Other Significant Noncash Transactions [Line Items]
Basic ownership	89.30%		99.10%
Asset Management (Kudu)
Other Significant Noncash Transactions [Line Items]
Pre-money valuation	1.3
Pre-money valuation, amount	$ 114
Enterprise value excluded		$ 54.3
Mass Mutual
Other Significant Noncash Transactions [Line Items]
Equity capital raised	64.1
White Mountains
Other Significant Noncash Transactions [Line Items]
Equity capital raised	50
Kudu Investment Management, LLC
Other Significant Noncash Transactions [Line Items]
Equity capital raised	0.4
Asset Management (Kudu)
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 114.5

Investment Securities - Schedul

Investment Securities - Schedule of Interest Income on Fixed Maturity Investments (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Schedule of Investments [Line Items]
Total investment income	$ (39.6)	$ (21)
Third-party investment expenses	(0.6)	(0.4)
Net investment income	39	20.6
Fixed maturity investments
Schedule of Investments [Line Items]
Total investment income	(14.5)	(8.2)
Short-term investments
Schedule of Investments [Line Items]
Total investment income	(9.7)	(0.1)
Common equity securities
Schedule of Investments [Line Items]
Total investment income	(1.3)	0
Other long-term investments
Schedule of Investments [Line Items]
Total investment income	(14.1)	(13.2)
TPC Providers
Schedule of Investments [Line Items]
Total investment income	$ 0	$ (0.5)

Investment Securities - Net Rea

Investment Securities - Net Realized and Unrealized Investment Gains (Losses) (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	$ 46.7	$ 17.4
Net unrealized investment gains (losses)	151.4	(9.1)
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	85.2	18.8
Gain (loss) on investments, exchange rate effect	5.4	2.6
Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment gains (losses)	198.1	10.4
Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(0.1)	(1.1)
Net unrealized investment gains (losses)	29.7	(79.5)
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(0.4)	(0.2)
Net unrealized investment gains (losses)	1.2	0.2
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses)	29.4	1
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	29.4	1
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses)	85.2	18.8
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	85.2	18.8
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	47.2	18.7
Net unrealized investment gains (losses)	5.9	50.4
Net realized and unrealized investment (losses) gains
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	198.1	8.3
TPC Providers
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	0	2.1
Fixed maturity and short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	30.4	(80.6)
Net realized and unrealized investment gains (losses)	1.8	(1)
Fixed maturity and short-term investments | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	28.6	(79.6)
Common equity securities and investment in MediaAlpha
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	114.6	19.8
Net realized and unrealized investment gains (losses)	0	0
Common equity securities and investment in MediaAlpha | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) recognized during the period on investment securities held at the end of the period	$ 114.6	$ 19.8

Investment Securities - Investm

Investment Securities - Investment gains (losses) for Level 3 (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains on other long-term investments held at the end of the period, pre-tax	$ 37	$ 27.2

Investment Securities - Inves_2

Investment Securities - Investment Holdings Fixed Maturity Table (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 245.7	$ 216.6
Gross Unrealized Gains	0.1	0
Gross Unrealized Losses	(8)	(10.2)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	237.8	206.4
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,073.9	1,098.3
Gross Unrealized Gains	1.3	0.6
Gross Unrealized Losses	(63.1)	(78.3)
Net Foreign Currency Gains (Losses)	(1.7)	(1.8)
Carrying Value	1,010.4	1,018.8
Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	280	281.6
Gross Unrealized Gains	0	0.4
Gross Unrealized Losses	(17)	(23.4)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	263	258.6
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	289.5	288.7
Gross Unrealized Gains	0	0
Gross Unrealized Losses	(30.7)	(34.5)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	258.8	254.2
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	192.1	190.8
Gross Unrealized Gains	0.1	0.1
Gross Unrealized Losses	(5.2)	(6)
Net Foreign Currency Gains (Losses)	(1.1)	(2)
Carrying Value	185.9	182.9
Total fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	2,081.2	2,076
Gross Unrealized Gains	1.5	1.1
Gross Unrealized Losses	(124)	(152.4)
Net Foreign Currency Gains (Losses)	(2.8)	(3.8)
Carrying Value	$ 1,955.9	$ 1,920.9

Investment Securities - Cost an

Investment Securities - Cost and Amortized Cost Maturity Schedule (Details) $ in Millions	Mar. 31, 2023 USD ($)
Cost or Amortized Cost
Total fixed maturity investments	$ 2,081.2
Carrying Value
Total fixed maturity investments	1,955.9
Fixed Maturities and Convertible Fixed Maturities Excluding Mortgage Backed Securities
Cost or Amortized Cost
Due in one year or less	223.8
Due after one year through five years	943.6
Due after five years through ten years	338.8
Due after ten years	93.4
Carrying Value
Due in one year or less	219.2
Due after one year through five years	891.9
Due after five years through ten years	314.2
Due after ten years	85.9
Mortgage and asset-backed securities
Cost or Amortized Cost
Mortgage and asset-backed securities and collateralized loan obligations	481.6
Carrying Value
Mortgage and asset-backed securities and collateralized loan obligations	$ 444.7

Investment Securities - Inves_3

Investment Securities - Investment Holding Common Equities/ Other Investments/ MediaAlpha (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Mar. 31, 2023	Dec. 31, 2022
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 660.6	$ 660.6
Gross Unrealized Gains	48	26.7
Gross Unrealized Losses	(2.8)	(8.4)
Net Foreign Currency Gains (Losses)	(8)	(10.5)
Common equity securities, at fair value	697.8	668.4
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	0	0
Gross Unrealized Gains	253.8	168.6
Gross Unrealized Losses	0	0
Net Foreign Currency Gains (Losses)	0	0
Common equity securities, at fair value	253.8	168.6
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,489.7	1,340.8
Gross Unrealized Gains	264.3	271.1
Gross Unrealized Losses	(96.2)	(107.1)
Net Foreign Currency Gains (Losses)	(14.8)	(16.8)
Common equity securities, at fair value	$ 1,643	$ 1,488

Investment Securities - Fair Va

Investment Securities - Fair Value Measurements (Details)	3 Months Ended	12 Months Ended
	Mar. 31, 2023	Dec. 31, 2022
Investments, Debt and Equity Securities [Abstract]
Percentage of investments recorded at fair value	70%	72%

Investment Securities - Fair _2

Investment Securities - Fair Value Measurement by Level (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022	Mar. 31, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 1,643	$ 1,488
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,010.4	1,018.8
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Level 3 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	954.7	911.6	$ 885.7	$ 890.6
Fair value measured on a recurring basis
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	5,434.7	5,170
Other long-term investments	1,643	1,488
Fair value measured on a recurring basis | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	253.8	168.6
Fair value measured on a recurring basis | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	237.8	206.4
Fair value measured on a recurring basis | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,010.4	1,018.8
Fair value measured on a recurring basis | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	281.9	291.2
Fair value measured on a recurring basis | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	194.9	191.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	124.8	121.3
Fair value measured on a recurring basis | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	123.3	123.7
Fair value measured on a recurring basis | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	119.8	115.4
Fair value measured on a recurring basis | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	64	73.8
Fair value measured on a recurring basis | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	45.2	47.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	36.4	33.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	20.1	19.7
Fair value measured on a recurring basis | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	263	258.6
Fair value measured on a recurring basis | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Fair value measured on a recurring basis | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Fair value measured on a recurring basis | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,955.9	1,920.9
Fair value measured on a recurring basis | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	884.2	924.1
Fair value measured on a recurring basis | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	697.8	668.4
Fair value measured on a recurring basis | Common equity securities | Exchange traded funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	357.4	333.8
Fair value measured on a recurring basis | Common equity securities | Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	340.4	334.6
Fair value measured on a recurring basis | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	970.2	926.4
Fair value measured on a recurring basis | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	672.8	561.6
Fair value measured on a recurring basis | Level 1
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,727.4	1,632.9
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 1 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	253.8	168.6
Fair value measured on a recurring basis | Level 1 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	237.8	206.4
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	237.8	206.4
Fair value measured on a recurring basis | Level 1 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	878.4	924.1
Fair value measured on a recurring basis | Level 1 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	357.4	333.8
Fair value measured on a recurring basis | Level 1 | Common equity securities | Exchange traded funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	357.4	333.8
Fair value measured on a recurring basis | Level 1 | Common equity securities | Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 1 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 2
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	2,079.8	2,063.9
Other long-term investments	15.5	14.8
Fair value measured on a recurring basis | Level 2 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 2 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,010.4	1,018.8
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	281.9	291.2
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	194.9	191.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	124.8	121.3
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	123.3	123.7
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	119.8	115.4
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	64	73.8
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	45.2	47.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	36.4	33.9
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	20.1	19.7
Fair value measured on a recurring basis | Level 2 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	263	258.6
Fair value measured on a recurring basis | Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Fair value measured on a recurring basis | Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Fair value measured on a recurring basis | Level 2 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,718.1	1,714.5
Fair value measured on a recurring basis | Level 2 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	5.8	0
Fair value measured on a recurring basis | Level 2 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	340.4	334.6
Fair value measured on a recurring basis | Level 2 | Common equity securities | Exchange traded funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 2 | Common equity securities | Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	340.4	334.6
Fair value measured on a recurring basis | Level 2 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	15.5	14.8
Fair value measured on a recurring basis | Level 2 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 3
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	954.7	911.6
Other long-term investments	954.7	911.6
Fair value measured on a recurring basis | Level 3 | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 3 | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	0	0
Fair value measured on a recurring basis | Level 3 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Common equity securities | Exchange traded funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Common equity securities | Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	954.7	911.6
Fair value measured on a recurring basis | Level 3 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 0	$ 0

Investment Securities - Inves_4

Investment Securities - Investments Held on Deposit or as Collateral (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	$ 517.5	$ 500.5
Assets held by insurance regulators	4.6	4.6
Other long-term investments	1,643	1,488
Outrigger Re | Cash and Short Term Investments
Debt and Equity Securities, FV-NI [Line Items]
Investment owned, balance	206	203.7
HG Global Senior Notes | Secured Debt
Debt and Equity Securities, FV-NI [Line Items]
Interest reserve account	31.6	31.2
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	148.7	137.4
Additional Investments, Insurance Regulators and Reinsurance Counterparties | Asset Pledged as Collateral
Debt and Equity Securities, FV-NI [Line Items]
Investments pledged as collateral	263.3	257
Short-term investments | Asset Pledged as Collateral
Debt and Equity Securities, FV-NI [Line Items]
Investments pledged as collateral	144.1	90.3
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 326.3	$ 319.2

Investment Securities - Debt se

Investment Securities - Debt securities issued by corporation (Details) - Debt securities issued by corporations - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 1,010.4	$ 1,018.8
AAA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.4	11.3
AA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	95.9	96
A
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	558.8	567.9
BBB
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	338	337.7
Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 6.3	$ 5.9

Investment Securities - Mortgag

Investment Securities - Mortgage-backed Asset Securities Table (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 244.2	$ 231.9
Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	14.6	22.3
Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	444.7	437.1
Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	244.2	231.9
Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	14.6	22.3
Level 2 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	258.8	254.2
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9	182.9
Level 2 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	444.7	437.1
Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Level 3 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
FNMA | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	129.7	124.5
FNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	129.7	124.5
FNMA | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
FHLMC | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	81.2	78.8
FHLMC | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	81.2	78.8
FHLMC | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
GNMA | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	33	28.3
GNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	33	28.3
GNMA | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Non-agency: Residential | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.3	0.3
Non-agency: Residential | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.3	0.3
Non-agency: Residential | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Total non-agency | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.3	0.3
Total non-agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.3	0.3
Total non-agency | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Credit card receivables | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	4.4	11.9
Credit card receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	4.4	11.9
Credit card receivables | Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Vehicle receivables | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	10.2	10.4
Vehicle receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	10.2	10.4
Vehicle receivables | Level 3 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Collateralized mortgage obligations | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	185.9
Total agency | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	243.9	231.6
Total agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	243.9	231.6
Total agency | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 0	$ 0

Investment Securities - Inves_5

Investment Securities - Investment in MediaAlpha textual (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
	Mar. 31, 2023	Dec. 31, 2022
Marketing Technology (MediaAlpha)
Subsidiary, Sale of Stock [Line Items]
Ownership interest (as a percent)	26.80%	27.10%
Share price (in usd per share)	$ 14.98
Investment in MediaAlpha, at fair value	$ 253.8
Marketing Technology (MediaAlpha)
Subsidiary, Sale of Stock [Line Items]
Investment owned (in shares)	16.9
Fully diluted ownership interest (as a percent)	24.30%
Marketing Technology (MediaAlpha) | IPO
Subsidiary, Sale of Stock [Line Items]
Increase in investment owned (in dollars per share)	$ 1
Increase in book value per share (in dollars per share)	$ 6.60

Investment Securities - Other l

Investment Securities - Other long-term investments (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 1,643	$ 1,488
Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	683.2	695.9
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	140	135
Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	30	30
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	87.5	37.2
Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	940.7	898.1
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	218.5	197.8
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	179.5	174.8
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	148.7	137.4
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	123.6	49.3
Private debt instruments
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	10.1	9.6
Other
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 21.9	$ 21

Investment Securities - Hedge F

Investment Securities - Hedge Funds and Private Equity Funds (Details) $ in Millions	3 Months Ended
	Mar. 31, 2023 USD ($) fund	Mar. 31, 2022 USD ($)	Dec. 31, 2022 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Investments in trading securities | $	$ 30.9	$ 0
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments | fund	17
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments | fund	2
Total private equity funds and hedge funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Largest single fund investment | $	$ 49.9		$ 49

Investment Securities - Fair _3

Investment Securities - Fair Value of Hedge Funds and Private Equity Funds (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Total private equity funds and hedge funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 218.5	$ 197.8
Unfunded Commitments	92.6	94.3
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	159.4	140.6
Unfunded Commitments	92.6	94.3
Private equity funds | Aerospace/Defense/Government
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	78	59.4
Unfunded Commitments	37.5	37.5
Private equity funds | Financial services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	77.3	77.1
Unfunded Commitments	52.6	54.3
Private equity funds | Real estate
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	4.1	4.1
Unfunded Commitments	2.5	2.5
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	59.1	57.2
Unfunded Commitments	0	0
Hedge funds | Long/short equity financials and business services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	49.8	49
Unfunded Commitments	0	0
Hedge funds | European small/mid cap
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	9.3	8.2
Unfunded Commitments	$ 0	$ 0

Investment Securities - Inves_6

Investment Securities - Investments In Private Equity Funds Subject to Lock-Up Periods (Details) - Private equity funds $ in Millions	Mar. 31, 2023 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 159.4
1 – 3 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	4.1
3 – 5 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	18.6
5 – 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	132.3
Greater than 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 4.4

Investment Securities - Lloyd's

Investment Securities - Lloyd's Trust Deposits, Bank Loan Fund, and Insurance-Linked Securities Funds (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Dec. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 1,643	$ 1,488
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	179.5	174.8
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	148.7	137.4
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 123.6	$ 49.3
Minimum | Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	45 days
Minimum | ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	30 days
Maximum | Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days
Maximum | ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days

Investment Securities - Rollfor

Investment Securities - Rollforward of Fair Value Measurements by Level (Details) - Other long-term investments - Level 3 Investments - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	$ 911.6	$ 890.6
Net realized and unrealized gains	35.1	26.8
Amortization/accretion	0	0
Purchases and contributions	117	0
Sales and distributions	(109)	(31.7)
Transfers in	0	0
Transfers out	0	0
Ending balance	$ 954.7	$ 885.7

Investment Securities - Signifi

Investment Securities - Significant Unobservable Inputs (Details) $ in Millions	3 Months Ended		12 Months Ended
	Mar. 31, 2023 USD ($)	Mar. 31, 2022 USD ($)	Dec. 31, 2022 USD ($)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities	$ 30.9	$ 0
Kudu investments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, pretax discount rate			0.21
Cash flow exit multiple, pretax			11.8
Kudu investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	18%		18%
Kudu investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	25%		25%
Kudu investments | Terminal Multiple | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal cash flow exit multiple	7		7
Kudu investments | Terminal Multiple | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal cash flow exit multiple	22		16
Kudu Participation Contracts | Asset Management (Kudu)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities			$ 99.8
Kudu Participation Contracts | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, pretax discount rate	0.21
Cash flow exit multiple, pretax	12.7
Level 3 | Other long-term investments | Recent Transaction
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 91.8		41.1
Level 3 | Kudu investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	683.2		695.9
Level 3 | Kudu investments | Standard Poors NR Rating | Probability weighted expected return method
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value			189
Level 3 | PassportCard/DavidShield | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 140		$ 135
Level 3 | PassportCard/DavidShield | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	23%		24%
Level 3 | PassportCard/DavidShield | Measurement Input, Long-term Revenue Growth Rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate	4%		4%
Level 3 | Elementum Holdings, L.P. | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 30		$ 30
Level 3 | Elementum Holdings, L.P. | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	20%		21%
Level 3 | Elementum Holdings, L.P. | Measurement Input, Long-term Revenue Growth Rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate	4%		4%
Level 3 | Private debt instruments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 9.7		$ 9.6
Level 3 | Private debt instruments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	11%		11%
Level 3 | Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities	$ 30.9

Goodwill and Other Intangible_3

Goodwill and Other Intangible Assets - Schedule of Acquisition Date Fair Values, Accumulated Amortization and Net Carrying Values for Other Intangibles Assets and Goodwill, By Company (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Dec. 31, 2022
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	$ 168.8	$ 176.5
Goodwill	168.8	176.5
Total Equity Including Noncontrolling Interest
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, accumulated amortization	11.4	12.2
Total goodwill and other intangible assets	387.6	404.6
Total goodwill and other intangible assets	376.2	392.4
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	218.8	228.1
Other intangible assets, accumulated amortization	11.4	12.2
Other intangible assets, net carrying value	207.4	215.9
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	116.8	116.8
Goodwill	116.8	116.8
Indefinite-Lived Intangible Assets (Excluding Goodwill)	175.7	175.7
Asset Management (Kudu)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	7.6	7.6
Goodwill	$ 7.6	7.6
Asset Management (Kudu) | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	7 years
Other intangible assets, acquisition date fair value	$ 2.2	2.2
Other intangible assets, accumulated amortization	1.3	1.2
Other intangible assets, net carrying value	0.9	1
Other Operations
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	44.4	52.1
Goodwill	44.4	52.1
Other intangible assets, acquisition date fair value	40.9	50.2
Other intangible assets, accumulated amortization	10.1	11
Other intangible assets, net carrying value	30.8	39.2
Total goodwill and other intangible assets	$ 75.2	91.3
Other Operations | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	13 years 3 months 18 days
Other intangible assets, acquisition date fair value	$ 13.3	17.9
Other intangible assets, accumulated amortization	2.6	3
Other intangible assets, net carrying value	$ 10.7	14.9
Other Operations | Customer relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	11 years
Other intangible assets, acquisition date fair value	$ 24.8	29.5
Other intangible assets, accumulated amortization	7	7.5
Other intangible assets, net carrying value	$ 17.8	22
Other Operations | Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	12 years 1 month 6 days
Other intangible assets, acquisition date fair value	$ 2.8	2.8
Other intangible assets, accumulated amortization	0.5	0.5
Other intangible assets, net carrying value	$ 2.3	$ 2.3

Goodwill and Other Intangible_4

Goodwill and Other Intangible Assets - Narrative (Details) - USD ($)	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Impairments to goodwill and other intangibles	$ 0	$ 0

Goodwill and Other Intangible_5

Goodwill and Other Intangible Assets - Schedule of Goodwill and Other Intangible Assets Rollforward (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance	$ 176.5
Goodwill, ending balance	168.8
Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance	176.5	$ 142.3
Dispositions	(6.7)	0
Measurement period adjustments	(1)	0
Amortization of other intangible assets	0	0
Goodwill, ending balance	168.8	142.3
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets (excluding goodwill), beginning balance	215.9	198.2
Dispositions	(6.9)	0
Measurement period adjustments	0	0
Amortization of other intangible assets	(1.6)	(1)
Other intangible assets (excluding goodwill), ending balance	207.4	197.2
Total Goodwill and Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, gross (including goodwill), beginning balance	392.4	340.5
Dispositions	(13.6)	0
Measurement period adjustments	(1)	0
Amortization of other intangible assets	(1.6)	(1)
Other intangible assets, gross (including goodwill), ending balance	$ 376.2	$ 339.5

Loss and Loss Adjustment Expe_3

Loss and Loss Adjustment Expense Reserves (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
TPC Providers | Ark
Loss and LAE paid relating to:
Percent of underwriting capital provided by third parties				0%	42.80%	58.30%
Ark
Loss and LAE paid relating to:
Reinsurance recoverables	$ 570.6		$ 595.3
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance	1,296.5	$ 894.7
Less: beginning reinsurance recoverable on unpaid losses	(505)	(428.9)
Net loss and LAE reserves	791.5	465.8
Loss and LAE incurred relating to:
Current year losses	139.2	125.7
Prior year losses	8.6	(3.7)
Net incurred losses and LAE	147.8	122
Loss and LAE paid relating to:
Current year losses	(4)	(0.6)
Prior year losses	(87.7)	(39.4)
Net paid loss and LAE	(91.7)	(40)
Change in TPC providers’ participation	145.4	57.5
Foreign currency translation and other adjustments to loss and LAE reserves	3.7	(1.7)
Net ending balance	996.7	603.6
Plus: ending reinsurance recoverable on unpaid losses	348.9	396
Gross ending balance	1,345.6	999.6
Reinsurance recoverables	570.6		$ 595.3
P&C Insurance and Reinsurance (Ark/WM Outrigger) | TPC Providers
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Less: beginning reinsurance recoverable on unpaid losses	(145.4)	(276.8)
Loss and LAE paid relating to:
Reinsurance recoverables		$ 207.3
P&C Insurance and Reinsurance (Ark/WM Outrigger) | TPC Providers | Ark
Loss and LAE paid relating to:
Reinsurance recoverables	$ 0

Third-Party Reinsurance - Effec

Third-Party Reinsurance - Effects of Reinsurance (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Earned premiums:
Net earned premiums	$ 262.8	$ 202.8
Ark
Written premiums:
Direct	246.2	230.9
Assumed	563.2	402.2
Gross written premiums	809.4	633.1
Ceded	(195.2)	(89.3)
Net written premiums	614.2	543.8
Earned premiums:
Direct	150.4	138.7
Assumed	162.1	106.6
Gross earned premiums	312.5	245.3
Ceded	(57.4)	(50.9)
Net earned premiums	255.1	194.4
Losses and LAE:
Policyholder Benefits and Claims Incurred, Assumed	162.4	183.1
Policyholder Benefits and Claims Incurred, Ceded	(14.6)	(61.1)
Policyholder Benefits and Claims Incurred, Net, Total	147.8	$ 122
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Written premiums:
Ceded	(44.1)
Earned premiums:
Ceded	(5.2)
Losses and LAE:
Policyholder Benefits and Claims Incurred, Ceded	$ (0.2)

Third-Party Reinsurance - Reins

Third-Party Reinsurance - Reinsurance Recoverables (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Ark
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses	$ 348.9	$ 505
Reinsurance recoverables on paid losses	23.1	31.1
Ceded unearned premiums	198.6	59.2
Reinsurance recoverables	$ 570.6	595.3
Ark | Third Point Re
Reinsurance [Line Items]
Annual crediting rate	3%
Carrying value of investment	$ 20.6
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses	0.2
Ceded unearned premiums	$ (38.9)
TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses		$ 145.4

Third-Party Reinsurance - Remai

Third-Party Reinsurance - Remaining Gross and Net Reinsurance Recoverables (Details) - All Entities Except TCP Providers - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Reinsurance [Line Items]
Reinsurance recoverables		$ 372
Reinsurance Recoverables, Collateral		103.2
Net Reinsurance Recoverables		$ 268.8
Percent of reinsurance recoverables from insurers that are collateralized		100%
A+ or better
Reinsurance [Line Items]
Reinsurance recoverables	$ 173.8
Reinsurance Recoverables, Collateral	0
Net Reinsurance Recoverables	$ 173.8
Percent of reinsurance recoverables from insurers that are collateralized	64.70%
A- to A
Reinsurance [Line Items]
Reinsurance recoverables	$ 77.9
Reinsurance Recoverables, Collateral	0
Net Reinsurance Recoverables	$ 77.9
Percent of reinsurance recoverables from insurers that are collateralized	29%
B++ or lower and not rated
Reinsurance [Line Items]
Reinsurance recoverables	$ 120.3
Reinsurance Recoverables, Collateral	103.2
Net Reinsurance Recoverables	$ 17.1
Percent of reinsurance recoverables from insurers that are collateralized	6.30%

Debt - Summary of Debt Outstand

Debt - Summary of Debt Outstanding (Details) € in Millions, $ in Millions	Mar. 31, 2023 USD ($)	Mar. 31, 2023 EUR (€)	Dec. 31, 2022 USD ($)	Mar. 31, 2022 USD ($)	Dec. 31, 2021 USD ($)
Debt Instrument
Total debt	$ 556.3		$ 575.2
Ark Subordinated Debt
Debt Instrument
Unamortized issuance cost	(4.5)		(4.6)
Ark 2007 Subordinated Notes, carrying value | Ark Subordinated Debt
Debt Instrument
Amount borrowed	30		30
Ark 2021 Subordinated Notes Tranche 1
Debt Instrument
Amount borrowed | €		€ 39.1
Ark 2021 Subordinated Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	42		41.3
Ark 2021 Subordinated Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	47		47
Ark 2021 Subordinated Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	70		70
Ark 2021 Notes | Ark Subordinated Debt
Debt Instrument
Total debt	$ 154.5		$ 153.7
Ark
Debt Instrument
Effective percentage	10.30%	10.30%	7.60%
Ark | Ark Subordinated Debt
Debt Instrument
Total debt	$ 184.5		$ 183.7
Kudu Credit Facility | Asset Management (Kudu)
Debt Instrument
Total debt	191.6		208.3
Other Debt | Other
Debt Instrument
Total debt	$ 33.6		$ 36.7
HG Senior Notes
Debt Instrument
Effective percentage	11%	11%	8.90%
Secured Debt | HG Senior Notes
Debt Instrument
Amount borrowed	$ 150		$ 150
Unamortized issuance cost	(3.4)		(3.5)
Total debt	146.6		146.5
Term Loan | Kudu Credit Facility
Debt Instrument
Amount borrowed	198.3		215.2
Unamortized issuance cost	$ (6.7)		$ (6.9)
Effective percentage	8.70%	8.70%	6.10%
Term Loan | Kudu Credit Facility | Asset Management (Kudu)
Debt Instrument
Total debt	$ 198.3		$ 215.2	$ 225.4	$ 225.4
Term Loan | Other Operations
Debt Instrument
Amount borrowed	34.3		37.4
Unamortized issuance cost	$ (0.7)		$ (0.7)
Effective percentage	8.50%	8.50%	6.60%

Debt - Narrative (Details)

Debt - Narrative (Details) € in Millions

1 Months Ended

3 Months Ended

Apr. 29, 2022 USD ($)

Sep. 08, 2021 USD ($)

Sep. 30, 2021 USD ($)

Aug. 31, 2021

Jul. 31, 2021

Mar. 31, 2007 USD ($)

Mar. 31, 2023 USD ($) credit_facility

Sep. 30, 2021 USD ($)

Mar. 31, 2023 EUR (€) credit_facility

Dec. 31, 2022 USD ($)

Sep. 30, 2022 USD ($)

Jun. 16, 2022 USD ($)

Aug. 11, 2021 USD ($)

Jul. 13, 2021 USD ($)

Jul. 13, 2021 EUR (€)

Debt Instrument

Debt

$ 556,300,000

$ 575,200,000

Debt covenant, maximum loan to value percent, period one

50%

50%

Debt covenant, maximum loan to value percent, period two

40%

40%

Debt covenant, maximum loan to value percent, period three

25%

25%

Debt covenant, maximum loan to value percent, period four

15%

15%

Debt covenant, maximum loan to value percent, period five

0%

0%

Debt covenant, maximum loan to value percent

28.80%

28.80%

Short-term investments | Asset Pledged as Collateral

Debt Instrument

Investments pledged as collateral

$ 144,100,000

90,300,000

HG Global | Interest Rate Cap

Debt Instrument

Notional amount

$ 150,000,000

Unsecured Subordinated Debt | Group Ark Insurance Limited

Debt Instrument

Borrowings

$ 157,800,000

Unsecured Subordinated Debt | Group Ark Insurance Limited | Ark

Debt Instrument

Notes issued

$ 163,300,000

$ 163,300,000

HG Global Senior Notes | Secured Debt

Debt Instrument

Borrowings

$ 150,000,000

Annual payments

15,000,000

Interest reserve account

$ 31,600,000

31,200,000

Additional interest rate

1%

HG Global Senior Notes | Secured Debt | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate

Debt Instrument

Basis spread on variable rate

6.30%

Ark 2007 Subordinated Notes, carrying value | Ark Subordinated Debt

Debt Instrument

Outstanding balance

$ 30,000,000

30,000,000

Ark 2007 Subordinated Notes, carrying value | Junior Notes | Ark

Debt Instrument

Face value

$ 30,000,000

Debt

30,000,000

Ark 2007 Subordinated Notes, carrying value | Junior Notes | USD-LIBOR | Ark

Debt Instrument

Basis spread on variable rate

4.60%

Ark 2021 Subordinated Notes Tranche 1

Debt Instrument

Outstanding balance | €

€ 39.1

Ark 2021 Subordinated Notes Tranche 1 | Ark Subordinated Debt

Debt Instrument

Outstanding balance

42,000,000

41,300,000

Ark 2021 Subordinated Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited

Debt Instrument

Notes issued

$ 46,300,000

€ 39.1

Ark 2021 Subordinated Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited | EURIBOR

Debt Instrument

Basis spread on variable rate

5.75%

Ark 2021 Subordinated Notes Tranche 2 | Ark Subordinated Debt

Debt Instrument

Outstanding balance

47,000,000

47,000,000

Ark 2021 Subordinated Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited

Debt Instrument

Notes issued

$ 47,000,000

Ark 2021 Subordinated Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR

Debt Instrument

Basis spread on variable rate

5.75%

Ark 2021 Subordinated Notes Tranche 3 | Ark Subordinated Debt

Debt Instrument

Outstanding balance

70,000,000

70,000,000

Ark 2021 Subordinated Notes Tranche 3 | Unsecured Subordinated Debt | Group Ark Insurance Limited

Debt Instrument

Additional interest rate

1%

Notes issued

$ 70,000,000

Solvency capital requirement

120%

Debt to capital requirement

40%

Ark 2021 Subordinated Notes Tranche 3 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR

Debt Instrument

Basis spread on variable rate

6.10%

ING LOC Facility | Secured Debt | Ark | Letter of Credit | Uncollateralized

Debt Instrument

Total commitment under revolving credit facility

50,000,000

Citibank LOC Facility | Short-term investments | Asset Pledged as Collateral

Debt Instrument

Investments pledged as collateral

106,300,000

Citibank LOC Facility | Secured Debt

Debt Instrument

Line of credit

92,300,000

Citibank LOC Facility | Secured Debt | Ark | Letter of Credit | Collateral Pledged

Debt Instrument

Total commitment under revolving credit facility

100,000,000

Lloyds LOC Facility | Short-term investments | Asset Pledged as Collateral

Debt Instrument

Investments pledged as collateral

37,800,000

Lloyds LOC Facility | Secured Debt

Debt Instrument

Line of credit

35,000,000

Lloyds LOC Facility | Secured Debt | Ark | Letter of Credit | Collateral Pledged

Debt Instrument

Total commitment under revolving credit facility

$ 50,000,000

Kudu Bank Facility | Asset Management (Kudu)

Debt Instrument

Total commitment under revolving credit facility

$ 300,000,000

Kudu Bank Facility | Revolving Credit Facility

Debt Instrument

Effective percentage

0.25%

0.25%

Kudu Bank Facility | Revolving Credit Facility | London Interbank Offered Rate (LIBOR)

Debt Instrument

Basis spread on variable rate

4.30%

Kudu Bank Facility | Line of Credit | Asset Management (Kudu)

Debt Instrument

Interest reserve

$ 13,000,000

Kudu Bank Facility | Term Loan | Asset Management (Kudu)

Debt Instrument

Percentage of borrowing base

35%

35%

Remaining borrowing capacity under revolving credit facility

$ 47,400,000

Other Operations | Term Loan

Debt Instrument

Outstanding balance

$ 34,300,000

$ 37,400,000

Effective percentage

8.50%

8.50%

6.60%

Secured credit facilities | credit_facility

4

4

Debt - Schedule of the Change i

Debt - Schedule of the Change in Debt (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Debt Instrument
Beginning balance	$ 575.2
Repayments	(20)	$ (1.3)
Ending balance	556.3
Asset Management (Kudu) | Kudu Credit Facility
Debt Instrument
Beginning balance	208.3
Ending balance	191.6
Asset Management (Kudu) | Term Loan | Kudu Credit Facility
Debt Instrument
Beginning balance	215.2	225.4
Borrowings	0	0
Repayments	(16.9)	0
Ending balance	$ 198.3	$ 225.4

Income Taxes (Details)

Income Taxes (Details)	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation, percent	6%	18.20%

Derivatives (Details)

Derivatives (Details) - HG Global - Interest Rate Cap - USD ($)		3 Months Ended
	Jun. 16, 2022	Mar. 31, 2023	Dec. 31, 2022
Derivative [Line Items]
Notional amount	$ 150,000,000
Premiums paid	$ 3,300,000
Derivative, fair value, net		$ 3,400,000	$ 4,100,000
Proceeds from Periodic Settlement of Derivatives		200,000
Interest Expense
Derivative [Line Items]
Change in fair value of derivative instruments		$ 700,000
Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Derivative [Line Items]
Derivative, cap interest rate	3.50%
3-month variable rate		4.90%

Municipal Bond Guarantee Insu_3

Municipal Bond Guarantee Insurance - Narrative (Details) - USD ($)	1 Months Ended	3 Months Ended			12 Months Ended
	Mar. 31, 2023	Mar. 31, 2023	Dec. 31, 2022	Mar. 31, 2022	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2018	Jan. 01, 2025	Dec. 31, 2023	Mar. 31, 2021	Jun. 30, 2018	Jul. 31, 2012
Guarantor Obligations [Line Items]
Percentage of risk premium ceded	60%	60%
Insurance-linked securities, term					12 years	12 years	12 years
Insurance-linked securities, callable term					7 years	5 years	5 years
HG Global
Guarantor Obligations [Line Items]
Collateral held in supplement trust	$ 880,700,000	$ 880,700,000	$ 856,900,000		$ 856,900,000
Collateral trusts, investments and cash	520,600,000	520,600,000	503,300,000		503,300,000
BAM
Guarantor Obligations [Line Items]
Surplus notes	340,000,000	340,000,000	340,000,000		340,000,000
Interest receivable	20,100,000	20,100,000	13,600,000		13,600,000
Series A BAM Surplus Note | BAM
Guarantor Obligations [Line Items]
Interest receivable	164,500,000	164,500,000	157,900,000		157,900,000
HG Global
Guarantor Obligations [Line Items]
Surplus notes	$ 503,000,000	$ 503,000,000										$ 503,000,000
Percentage of par value of policy reinsured	15%	15%
Percent over a target trust balance		102%
Supplement trust target	$ 603,000,000	$ 603,000,000
HG Global | Series A BAM Surplus Note
Guarantor Obligations [Line Items]
Assets Held-in-trust	579,900,000	$ 579,900,000	568,300,000		568,300,000
HG Global | BAM | Maximum
Guarantor Obligations [Line Items]
Reinsurance, Excess Retention, Amount Reinsured, Per Life	$ 125,000,000
HG Re
Guarantor Obligations [Line Items]
Percentage of par value of policy reinsured	15%	15%
Assets Held-in-trust	$ 300,800,000	$ 300,800,000	288,600,000		288,600,000
BAM | Surplus Note
Guarantor Obligations [Line Items]
Repayments of unsecured debt		$ 0	36,000,000	$ 0
Accrued interest payment on surplus notes			10,400,000		10,400,000
BAM | Supplemental Trust
Guarantor Obligations [Line Items]
Repayments of unsecured debt			24,600,000
Accrued interest payment on surplus notes			1,000,000		1,000,000
BAM | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Basis spread on variable rate		3%
BAM | Forecast | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Effective percentage									7.70%
BAM | Forecast | Fixed interest rate | Surplus Note
Guarantor Obligations [Line Items]
Derivative, fixed interest rate (as a percent)								8%
BAM | Fidus Re Ltd.
Guarantor Obligations [Line Items]
Secured debt			$ 150,000,000		150,000,000					$ 150,000,000	$ 100,000,000
Reinsurance, Limit on Total Reimbursement					150,000,000	$ 150,000,000	$ 100,000,000
Percentage of financial guaranty policies covered		32%
BAM | Fidus Re Ltd. | 2018 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered		26%
BAM | Fidus Re Ltd. | 2021 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered		31%
BAM | Fidus Re Ltd. | Maximum
Guarantor Obligations [Line Items]
Reinsurance, Excess Retention, Amount Reinsured, Per Life					276,700,000	301,700,000	276,100,000
BAM | Fidus Re Ltd. | Minimum
Guarantor Obligations [Line Items]
Reinsurance, Excess Retention, Amount Reinsured, Per Life					$ 110,000,000	$ 135,000,000	$ 165,000,000
Fidus Re Ltd. | BAM
Guarantor Obligations [Line Items]
Percentage of par value of policy reinsured					90%	90%	90%

Municipal Bond Guarantee Insu_4

Municipal Bond Guarantee Insurance - Schedule of Municipal Bond Guarantee Insured Obligations (Details) - BAM $ in Millions	3 Months Ended	12 Months Ended
	Mar. 31, 2023 USD ($) Contract	Dec. 31, 2022 USD ($) Contract
Guarantor Obligations [Line Items]
Contracts outstanding | Contract	13,607	13,382
Remaining weighted average contract period (in years)	10 years 9 months 18 days	10 years 9 months 18 days
Principal	$ 101,785.7	$ 99,996.9
Interest	49,801.9	48,880.6
Total debt service outstanding	151,587.6	148,877.5
Total gross unearned insurance premiums	$ 299.8	$ 298.3

Municipal Bond Guarantee Insu_5

Municipal Bond Guarantee Insurance - Schedule of Municipal Guarantee Insurance Contracts, Premium Received Over Contract Period (Details) - BAM - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Guarantor Obligations [Line Items]
April 1, 2023 - December 31, 2023	$ 20.9
January 1, 2024 - March 31, 2024	6.8
April 1, 2024 - June 30, 2024	6.7
July 1, 2024 - September 30, 2024	6.5
October 1, 2024 - December 31, 2024	6.4
Total 2024	26.4
2025	24.7
2026	23.1
2027	21.5
2028	19.8
2029 and thereafter	163.4
Total gross unearned insurance premiums	$ 299.8	$ 298.3

Municipal Bond Guarantee Insu_6

Municipal Bond Guarantee Insurance - Schedule of Net Written Premiums (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Earned premiums:
Net earned premiums	$ 262.8	$ 202.8
HG/BAM
Written premiums:
Direct	9.2	9.4
Assumed	0	0
Net written premiums	9.2	9.4
Earned premiums:
Direct	7	7.6
Assumed	0.7	0.8
Net earned premiums	$ 7.7	$ 8.4

Earnings Per Share - Basic and

Earnings Per Share - Basic and Diluted Earnings Per Share from Continuing Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders	$ 179.5	$ 33.4
Less: total income (loss) from discontinued operations, net of tax	0	3.7
Net (income) loss from discontinued operations attributable to noncontrolling interests	0	(0.1)
Net income (loss) from continuing operations attributable to White Mountains’s common shareholders	179.5	29.8
Allocation of losses (earnings) to participating restricted common shares	(2.2)	(0.3)
Basic and diluted earnings (losses) per share numerators	$ 177.3	$ 29.5
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,569,900	3,006,200
Average unvested restricted common shares	(31,100)	(29,600)
Basic earnings (losses) per share denominator (in shares)	2,538,800	2,976,600
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,569,900	3,006,200
Average unvested restricted common shares	(31,100)	(29,600)
Diluted earnings (losses) per share denominator	2,538,800	2,976,600
Basic and diluted earnings per share (in dollars) - continuing operations:
Distributed earnings - dividends declared and paid (in usd per share)	$ 1	$ 1
Undistributed earnings (losses)	68.83	8.90
Continuing operations (in usd per share)	69.83	9.90
Basic and diluted earnings (losses) per share	$ 69.83	$ 9.90

Earnings Per Share - Undistribu

Earnings Per Share - Undistributed Net Earnings From Continuing Operations (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Earnings Per Share [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders, net of restricted common share amounts	$ 177.3	$ 29.5
Dividends declared net of restricted common share amounts	(2.5)	(3)
Total undistributed net earnings (losses), net of restricted common share amounts	$ 174.8	$ 26.5

Employee Share-Based Incentiv_3

Employee Share-Based Incentive Compensation Plans - Narrative (Details) $ in Millions	3 Months Ended		36 Months Ended
	Mar. 31, 2023 USD ($) shares	Mar. 31, 2022 USD ($) shares	Dec. 31, 2021 USD ($) shares	Dec. 31, 2022 USD ($)
Performance Share | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Vesting period	3 years
Performance cycle period	3 years
New grants (in shares) | shares	10,895	13,075	750
Additional compensation cost that would be recognized if all outstanding performance shares vested	$ 44.6
Performance Share | Minimum | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Share-based compensation arrangement by share-based payment award, multiplier	0
Performance Share | Maximum | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Share-based compensation arrangement by share-based payment award, multiplier	2
Restricted Stock
Share-based compensation arrangement by share-based payment award
Vesting period	34 months
Additional compensation cost that would be recognized if all outstanding performance shares vested	$ 28.3	$ 26.5
Restricted Stock | W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Additional compensation cost that would be recognized if all outstanding performance shares vested			$ 15.9	$ 15.5
Issued (in shares) | shares	10,895	13,075

Employee Share-Based Incentiv_4

Employee Share-Based Incentive Compensation Plans - Performance Shares (Details) - USD ($) $ in Millions	1 Months Ended		3 Months Ended		36 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Mar. 31, 2023	Mar. 31, 2022	Dec. 31, 2021
Performance Share
Target Performance Shares Outstanding
End of period (in shares)	37,031		37,031
Accrued Expense
End of period	$ 36.4		$ 36.4
Performance Share | W T M Incentive Plan
Target Performance Shares Outstanding
Beginning of period (in shares)			39,449	40,828
Shares paid (in shares)			(13,350)	(14,625)
New grants (in shares)			10,895	13,075	750
Forfeitures and cancellations (in shares)			37	24
Expense recognized (in shares)			0	0
End of period (in shares)					40,828
Accrued Expense
Beginning of period			$ 67.5	$ 42.2
Shares paid			(40.8)	(26.4)
New grants			0	0
Forfeitures and cancellations			0.4	0.3
Expense recognized			$ 9.3	$ 5.8
End of period					$ 42.2
Performance Share | W T M Incentive Plan | Range Of Performance Cycle Current Year
Accrued Expense
Percentage of target payout - minimum actual	200%
Performance Share | W T M Incentive Plan | Range Of Performance Cycle Previous Year
Accrued Expense
Percentage of target payout - minimum actual		172%
W T M Incentive Plan
Target Performance Shares Outstanding
End of period (in shares)	37,031	39,302	37,031	39,302
Accrued Expense
End of period	$ 36.4	$ 21.9	$ 36.4	$ 21.9

Employee Share-Based Incentiv_5

Employee Share-Based Incentive Compensation Plans - Performance Shares Granted Under the WTM Incentive Plan (Details) - Performance Share - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	37,595
Total target performance shares outstanding (in shares)	37,031
Accrued Expense	$ 37
Total Accrued Expense	$ 36.4
W T M Incentive Plan
Share-based compensation arrangement by share-based payment award
Assumed forfeitures (in shares)	(564)
Total target performance shares outstanding (in shares)		39,449	40,828
Assumed forfeitures	$ (0.6)
Total Accrued Expense		$ 67.5	$ 42.2
W T M Incentive Plan | 2021 – 2023
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,475
Accrued Expense	$ 22.6
W T M Incentive Plan | 2022 – 2024
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,225
Accrued Expense	$ 14
W T M Incentive Plan | 2023 – 2025
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	10,895
Accrued Expense	$ 0.4

Employee Share-Based Incentiv_6

Employee Share-Based Incentive Compensation Plans - Restricted Shares (Details) - Restricted Stock - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Restricted Shares
End of period (in shares)	37,595	38,200
Unamortized Issue Date Fair Value
End of period	$ 28.3	$ 26.5
W T M Incentive Plan
Restricted Shares
Beginning of period (in shares)	38,350	37,850
Issued (in shares)	10,895	13,075
Vested (in shares)	(11,650)	(12,725)
Forfeited (in shares)	0	0
Expense recognized (in shares)	0	0
Unamortized Issue Date Fair Value
Beginning of period	$ 15.5	$ 15.9
Issued	16	13.6
Vested	0	0
Forfeited	0	0
Expense recognized	$ (3.2)	$ (3)

Noncontrolling Interests (Detai

Noncontrolling Interests (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Noncontrolling Interest [Line Items]
Noncontrolling Equity	$ 190.4	$ 188.1
Total, excluding BAM
Noncontrolling Interest [Line Items]
Noncontrolling Equity	$ 342.6	$ 342.8
HG Global
Noncontrolling Interest [Line Items]
Noncontrolling Percentage	3.10%	3.10%
Noncontrolling Equity	$ (0.3)	$ (0.6)
Ark
Noncontrolling Interest [Line Items]
Noncontrolling Percentage	28%	28%
Noncontrolling Equity	$ 251.3	$ 247.9
Asset Management (Kudu)
Noncontrolling Interest [Line Items]
Noncontrolling Percentage	10.80%	10.80%
Noncontrolling Equity	$ 81.3	$ 75.1
Other
Noncontrolling Interest [Line Items]
Noncontrolling Equity	$ 10.3	$ 20.4
BAM
Noncontrolling Interest [Line Items]
Noncontrolling Percentage	100%	100%
Noncontrolling Equity	$ (152.2)	$ (154.7)

Segment Information - Narrative

Segment Information - Narrative (Details)	3 Months Ended
	Mar. 31, 2023 segment
Segment Reporting [Abstract]
Number of operating segments	3

Segment Information - Financial

Segment Information - Financial Information for White Mountain's Segments (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Segment Reporting Information [Line Items]
Earned insurance premiums	$ 262.8	$ 202.8
Net investment income	39	20.6
Net investment income (expense) - BAM Surplus Note interest	0	0
Net realized and unrealized investment gains (losses)	112.9	(8.4)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	85.2	18.8
Commission revenues	3.3	2.9
Other revenues	28.7	23.7
Total revenues	531.9	260.4
Loss and loss adjustment expenses	147.8	122
Acquisition expenses	62.5	52.9
Cost of sales	13.9	21.4
General and administrative expenses	96	69.9
Change in fair value of contingent consideration	(2.4)	2.1
Interest expense	15	6.9
Total expenses	332.8	275.2
Pre-tax income (loss) from continuing operations	199.1	(14.8)
Financial Guarantee (HG Global/BAM)
Segment Reporting Information [Line Items]
Earned insurance premiums	7.7	8.4
Net investment income	7.2	4.6
Net realized and unrealized investment gains (losses)	17	(45.1)
Other revenues	0.8	0.8
Total revenues	32.7	(31.3)
Acquisition expenses	2.7	3
General and administrative expenses	17.3	16.3
Interest expense	4.5	0
Total expenses	24.5	19.3
Financial Guarantee (HG Global/BAM) | HG Global
Segment Reporting Information [Line Items]
Earned insurance premiums	6.4	6.9
Net investment income	4	2.1
Net investment income (expense) - BAM Surplus Note interest	6.6	2.9
Net realized and unrealized investment gains (losses)	7.9	(23.5)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0
Commission revenues	0	0
Other revenues	0	0.1
Total revenues	24.9	(11.5)
Loss and loss adjustment expenses	0	0
Acquisition expenses	1.8	2.6
Cost of sales	0	0
General and administrative expenses	1.1	0.7
Change in fair value of contingent consideration	0	0
Interest expense	4.5	0
Total expenses	7.4	3.3
Pre-tax income (loss) from continuing operations	17.5	(14.8)
Financial Guarantee (HG Global/BAM) | BAM
Segment Reporting Information [Line Items]
Earned insurance premiums	1.3	1.5
Net investment income	3.2	2.5
Net investment income (expense) - BAM Surplus Note interest	(6.6)	(2.9)
Net realized and unrealized investment gains (losses)	9.1	(21.6)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0
Commission revenues	0	0
Other revenues	0.8	0.7
Total revenues	7.8	(19.8)
Loss and loss adjustment expenses	0	0
Acquisition expenses	0.9	0.4
Cost of sales	0	0
General and administrative expenses	16.2	15.6
Change in fair value of contingent consideration	0	0
Interest expense	0	0
Total expenses	17.1	16
Pre-tax income (loss) from continuing operations	(9.3)	(35.8)
P&C Insurance and Reinsurance (Ark/WM Outrigger)
Segment Reporting Information [Line Items]
Earned insurance premiums	255.1	194.4
Net investment income	10.6	1.6
Net investment income (expense) - BAM Surplus Note interest		0
Net realized and unrealized investment gains (losses)	24.5	(17.5)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha		0
Commission revenues		0
Other revenues	(2.7)	(2.8)
Total revenues	287.5	175.7
Loss and loss adjustment expenses	147.8	122
Acquisition expenses	59.8	49.9
Cost of sales		0
General and administrative expenses	35.2	21
Change in fair value of contingent consideration	(2.4)	2.1
Interest expense	5	3.8
Total expenses	245.4	198.8
Pre-tax income (loss) from continuing operations		(23.1)
P&C Insurance and Reinsurance (Ark/WM Outrigger) | Ark
Segment Reporting Information [Line Items]
Earned insurance premiums	249.9
Net investment income	8.4
Net investment income (expense) - BAM Surplus Note interest	0
Net realized and unrealized investment gains (losses)	24.5
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0
Commission revenues	0
Other revenues	(2.7)
Total revenues	280.1
Loss and loss adjustment expenses	147.6
Acquisition expenses	58.9
Cost of sales	0
General and administrative expenses	35.1
Change in fair value of contingent consideration	(2.4)
Interest expense	5
Total expenses	244.2
Pre-tax income (loss) from continuing operations	35.9
P&C Insurance and Reinsurance (Ark/WM Outrigger) | Outrigger Re
Segment Reporting Information [Line Items]
Earned insurance premiums	5.2
Net investment income	2.2
Net investment income (expense) - BAM Surplus Note interest	0
Net realized and unrealized investment gains (losses)	0
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0
Commission revenues	0
Other revenues	0
Total revenues	7.4
Loss and loss adjustment expenses	0.2
Acquisition expenses	0.9
Cost of sales	0
General and administrative expenses	0.1
Change in fair value of contingent consideration	0
Interest expense	0
Total expenses	1.2
Pre-tax income (loss) from continuing operations	6.2
Asset Management (Kudu)
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0
Net investment income	14.2	12.6
Net investment income (expense) - BAM Surplus Note interest	0	0
Net realized and unrealized investment gains (losses)	29.6	22.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0
Commission revenues	0	0
Other revenues	0	0
Total revenues	43.8	34.9
Loss and loss adjustment expenses	0	0
Acquisition expenses	0	0
Cost of sales	0	0
General and administrative expenses	3.8	2.8
Change in fair value of contingent consideration	0	0
Interest expense	4.7	2.8
Total expenses	8.5	5.6
Pre-tax income (loss) from continuing operations	35.3	29.3
Other Operations
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0
Net investment income	7	1.8
Net investment income (expense) - BAM Surplus Note interest	0	0
Net realized and unrealized investment gains (losses)	41.8	31.9
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	85.2	18.8
Commission revenues	3.3	2.9
Other revenues	30.6	25.7
Total revenues	167.9	81.1
Loss and loss adjustment expenses	0	0
Acquisition expenses	0	0
Cost of sales	13.9	21.4
General and administrative expenses	39.7	29.8
Change in fair value of contingent consideration	0	0
Interest expense	0.8	0.3
Total expenses	54.4	51.5
Pre-tax income (loss) from continuing operations	$ 113.5	$ 29.6

Variable Interest Entities (Det

Variable Interest Entities (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Limited Partnerships and Insurance-Linked Securities Funds
Variable Interest Entity [Line Items]
Fair Value	$ 159.4
DavidShield
Variable Interest Entity [Line Items]
Ownership interest (as a percent)	53.80%
PassportCard/DavidShield
Variable Interest Entity [Line Items]
Ownership interest (as a percent)	53.80%	53.80%
Other investments	$ 149.7
Elementum Holdings, L.P.
Variable Interest Entity [Line Items]
Ownership interest (as a percent)	26.60%	29.70%
Other investments	$ 30

Equity-Method Eligible Invest_3

Equity-Method Eligible Investments - Carrying Values of Equity Method Eligible Investments Recorded within Other Long-Term Investments (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Investments in unconsolidated affiliates
Other long-term investments	$ 1,643	$ 1,488
Kudu investments
Investments in unconsolidated affiliates
Other long-term investments	$ 683.2	$ 695.9
Kudu investments | Minimum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	4.10%	4.10%
Kudu investments | Maximum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	30%	30%
Marketing Technology (MediaAlpha)
Investments in unconsolidated affiliates
Ownership interest (as a percent)	26.80%	27.10%
Other long-term investments	$ 253.8	$ 168.6
PassportCard/DavidShield
Investments in unconsolidated affiliates
Ownership interest (as a percent)	53.80%	53.80%
Other long-term investments	$ 140	$ 135
Elementum Holdings, L.P.
Investments in unconsolidated affiliates
Ownership interest (as a percent)	26.60%	29.70%
Other long-term investments	$ 30	$ 30
Other
Investments in unconsolidated affiliates
Other long-term investments	180.8	84.4
Equity Method Investments
Investments in unconsolidated affiliates
Other long-term investments	$ 10.5	$ 0

Equity-Method Eligible Invest_4

Equity-Method Eligible Investments - Narrative (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Equity Method Investee
Schedule of Equity Method Investments [Line Items]
Proceeds from dividends received	$ 7.7	$ 13.1

Fair Value of Financial Instr_3

Fair Value of Financial Instruments (Details) - USD ($) $ in Millions	Mar. 31, 2023	Dec. 31, 2022
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 556.3	$ 575.2
Fair Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	158.8	155.7
Fair Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	29.2	28.4
Fair Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	165.5	163.1
Fair Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	208.2	223.9
Fair Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Fair Value	35.4	38.2
Carrying Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	146.6	146.5
Carrying Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	30	30
Carrying Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	154.5	153.7
Carrying Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	191.6	208.3
Carrying Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 33.6	$ 36.7

Held for Sale and Discontinue_3

Held for Sale and Discontinued Operations - Financial Statement Disclosure (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Dec. 31, 2022	Dec. 31, 2021
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net income (loss) from discontinued operations, net of tax	$ 0	$ 3.7
Net (income) loss from discontinued operations attributable to noncontrolling interests	0	(0.1)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group	0	(1.9)
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations	0	4.4
Net cash provided from (used for) investing activities	0	7.3
Net cash used from (used for) financing activities	0	(10.3)
Net change in cash during the period	(52.3)	65.8
Cash balances at beginning of period (includes restricted cash balances of $12.2 and $4.5 and excludes discontinued operations cash balances of $0.0 and $111.6)	255	147.7
Cash balances at end of period (includes restricted cash balances of $13.0 and $4.5 and excludes discontinued operations cash balances of $0.0 and $113.6)	202.7	213.5
Restricted cash balance	13	4.5	$ 12.2	$ 4.5
Interest paid	(5.8)	(5.5)
Net income tax payments	17.8	0.3
Discontinued Operations, Held-for-sale | NSM Insurance Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Commission revenues		70.1
Other revenues		18.4
Total revenues		88.5
General and administrative expenses		54
Broker commission expenses		20.6
Change in fair value of contingent consideration		0.1
Amortization of other intangible assets		9.1
Interest expense		2.1
Total expenses		85.9
Pre-tax income (loss) from discontinued operations		2.6
Income tax (expense) benefit		1.1
Net income (loss) from discontinued operations, net of tax		3.7
Net (income) loss from discontinued operations attributable to noncontrolling interests		(0.1)
Total income (loss) from discontinued operations attributable to White Mountains’s common shareholders		3.6
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group		(1.9)
Comprehensive income (loss) from discontinued operations		1.7
Other comprehensive income (loss) from discontinued operations attributable to noncontrolling interests		0.1
Comprehensive income (loss) from discontinued operations attributable to White Mountains’s common shareholders		1.8
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations		4.4
Net cash provided from (used for) investing activities		7.3
Net cash used from (used for) financing activities		(10.3)
Effect of exchange rate changes on cash		0.6
Net change in cash during the period		2
Cash balances at beginning of period (includes restricted cash balances of $12.2 and $4.5 and excludes discontinued operations cash balances of $0.0 and $111.6)	0	111.6
Cash balances at end of period (includes restricted cash balances of $13.0 and $4.5 and excludes discontinued operations cash balances of $0.0 and $113.6)	$ 0	113.6
Restricted cash balance		90.2		$ 89.2
Interest paid		(2.9)
Net income tax payments		$ 0

Held for Sale and Discontinue_4

Held for Sale and Discontinued Operations - Earnings Per Share for Discontinued Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Basic and diluted earnings per share numerators (in millions):
Net Income (Loss) Available to Common Stockholders, Basic, Total	$ 179.5	$ 33.4
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	179.5	29.8
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders	0	(3.7)
Allocation of earnings to participating restricted common shares	(2.2)	(0.3)
Basic and diluted earnings (losses) per share numerators	$ 177.3	$ 29.5
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period	2,569,900	3,006,200
Average unvested restricted common shares	(31,100)	(29,600)
Basic earnings (losses) per share denominator (in shares)	2,538,800	2,976,600
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period	2,569,900	3,006,200
Average unvested restricted common shares	(31,100)	(29,600)
Diluted earnings (losses) per share denominator	2,538,800	2,976,600
Discontinued operations (in usd per share)	$ 0	$ 1.20
Discontinued operations (in usd per share)	$ 0	$ 1.20
Discontinued Operations
Basic and diluted earnings per share numerators (in millions):
Net Income (Loss) Available to Common Stockholders, Basic, Total		$ 33.4
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent		(12.1)
Less: net (income) loss from continuing operations attributable to noncontrolling interests		41.9
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders		3.6
Allocation of earnings to participating restricted common shares		0
Basic and diluted earnings (losses) per share numerators		$ 3.6
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period		3,006,200
Average unvested restricted common shares		(29,600)
Basic earnings (losses) per share denominator (in shares)		2,976,600
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period		3,006,200
Average unvested restricted common shares		(29,600)
Diluted earnings (losses) per share denominator		2,976,600
Discontinued operations (in usd per share)		$ 1.20