White Mountains Insurance (WTM) 10-Q 7 Nov 22 2022 Q3 Quarterly report Financial data

Cover Page

Cover Page - shares	9 Months Ended
	Sep. 30, 2022	Nov. 03, 2022
Cover [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Sep. 30, 2022
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
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)		2,576,232
Entity Central Index Key	0000776867
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2022
Document Fiscal Period Focus	Q3
Amendment Flag	false

CONSOLIDATED BALANCE SHEETS

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Investments
Other long-term investments	$ 1,622.7	$ 1,377.8
Total assets	7,545	7,000.7
Liabilities
Loss and loss adjustment expense reserves	1,329.4	894.7
Debt	615.5	420.9
Total liabilities	3,678.7	3,296
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 2,576,232 and 3,017,772 shares	2.6	3
Paid-in surplus	532.7	585.9
Retained earnings	3,175.9	2,957.5
Accumulated other comprehensive income (loss), after-tax:
Net unrealized gains (losses) from foreign currency translation and interest rate swap	(3.2)	1.7
Total White Mountains’s common shareholders’ equity	3,708	3,548.1
Non-controlling interests	158.3	156.6
Total equity	3,866.3	3,704.7
Total liabilities and equity	7,545	7,000.7
Financial Guarantee (HG Global/BAM)
Investments
Fixed maturity investments, at fair value	874.4	934.1
Short-term investments, at fair value	62.3	32.4
Total investments	936.7	966.5
Cash	17.3	19.8
Insurance premiums receivable	6.6	6.9
Deferred acquisition costs	34.9	33.1
Other assets	22.3	18.5
Total assets	1,017.8	1,044.8
Liabilities
Unearned insurance premiums	286.7	266.3
Debt	146.4	0
Accrued incentive compensation	21.6	24.7
Other liabilities	29.5	30.9
Total liabilities	484.2	321.9
P&C Insurance and Reinsurance (Ark)
Investments
Fixed maturity investments, at fair value	741.8	688.6
Common equity securities, at fair value	286.4	251.1
Short-term investments, at fair value	309.4	296.2
Other long-term investments	329.7	326.2
Total investments	1,667.3	1,562.1
Cash	123.4	67.8
Reinsurance recoverables	550.9	448.4
Insurance premiums receivable	698.6	416
Ceded unearned premiums	59.7	67.1
Deferred acquisition costs	151.4	108.2
Goodwill and other intangible assets	292.5	292.5
Other assets	62.9	64.9
Total assets	3,606.7	3,027
Liabilities
Loss and loss adjustment expense reserves	1,329.4	894.7
Unearned insurance premiums	781.3	495.9
Debt	180	185.9
Reinsurance payable	312.7	424.1
Contingent consideration	32.9	28
Other liabilities	107.6	93.8
Total liabilities	2,743.9	2,122.4
Asset Management (Kudu)
Investments
Other long-term investments	813.2	669.5
Cash	76.6	21.4
Accrued investment income	12.5	16.9
Goodwill and other intangible assets	8.7	8.9
Other assets	9.7	10.4
Total assets	920.7	727.1
Liabilities
Debt	253.5	218.2
Other liabilities	59.7	42.8
Total liabilities	313.2	261
Other Operations
Investments
Fixed maturity investments, at fair value	238.1	286.2
Common equity securities, at fair value	46.4	0
Short-term investments, at fair value	824.7	129.5
Investment in MediaAlpha, at fair value	148.2	261.6
Other long-term investments	479.8	382.1
Total investments	1,737.2	1,059.4
Cash	28.4	38.7
Goodwill and other intangible assets	92	39.1
Other assets	142.2	59.5
Assets held for sale - NSM	0	989
Assets held for sale - Other	0	16.1
Total assets	1,999.8	2,201.8
Liabilities
Debt	35.6	16.8
Accrued incentive compensation	67.2	48.5
Other liabilities	34.6	30.1
Liabilities held for sale - NSM Group	0	495.3
Total liabilities	$ 137.4	$ 590.7

CONSOLIDATED BALANCE SHEETS (Pa

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
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)	2,576,232	3,017,772
Common shares, outstanding shares (in shares)	2,576,232	3,017,772
Asset Management (Kudu)
Restricted cash	$ 8.9	$ 4.5

CONSOLIDATED STATEMENTS OF OPER

CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Revenues:
Earned insurance premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Net investment income	33.9	19.5	79.6	57.2
Net realized and unrealized investment gains (losses)	(29.4)	30.5	(141.9)	91.2
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7
Other revenues	40.9	31.9	103.4	68.1
Total revenues	383.2	(92.4)	720.3	353.4
Expenses:
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	76.5	56.7	184.4	130.9
Cost of sales	25	24	68.8	45.9
General and administrative expenses	87.1	51.9	258.4	215.5
Amortization of other intangible assets	1.4	2	3.4	3.1
Interest expense	10.5	4.4	27.5	14.8
Total expenses	414.2	268.2	998.7	658
Pre-tax income (loss) from continuing operations	(31)	(360.6)	(278.4)	(304.6)
Income tax (expense) benefit	7.4	(28.6)	26.1	(52.2)
Net income (loss) from continuing operations	(23.6)	(389.2)	(252.3)	(356.8)
Net income (loss) from discontinued operations, net of tax - NSM Group	6.3	5.3	16.4	(23.8)
Net gain (loss) from sale of discontinued operations, net of tax			886.8	18.7
Net income (loss)	869.5	(383.9)	650.9	(361.9)
Net (income) loss attributable to non-controlling interests	18.7	12.5	101.5	53.7
Net income (loss) attributable to White Mountains’s common shareholders	888.2	(371.4)	752.4	(308.2)
Sirius Group
Expenses:
Net gain (loss) from sale of discontinued operations, net of tax	0	0	0	18.7
NSM Insurance Group
Expenses:
Net gain (loss) from sale of discontinued operations, net of tax	886.8	0	886.8	0
Financial Guarantee (HG Global/BAM)
Revenues:
Earned insurance premiums	7.1	6.7	26	19.6
Net investment income	5.7	4.4	15.1	13.2
Net realized and unrealized investment gains (losses)	(38.8)	(4)	(114)	(15.6)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	1.3	0.3	3.7	0.9
Total revenues	(24.7)	7.4	(69.2)	18.1
Expenses:
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	1.7	3	9.5	6.5
Cost of sales	0	0	0	0
General and administrative expenses	15.8	12.4	49.5	42.7
Amortization of other intangible assets	0	0	0	0
Interest expense	2	0	5.4	0
Total expenses	19.5	15.4	64.4	49.2
Pre-tax income (loss) from continuing operations	(44.2)	(8)	(133.6)	(31.1)
P&C Insurance and Reinsurance (Ark)
Revenues:
Earned insurance premiums	346.1	213.4	757.8	435.8
Net investment income	4.9	0.6	9.7	1.8
Net realized and unrealized investment gains (losses)	(14.4)	0.3	(76.5)	10.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	6.6	3.4	10.1	9.4
Total revenues	343.2	217.7	701.1	457.3
Expenses:
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	74.8	53.7	174.9	124.4
Cost of sales	0	0	0	0
General and administrative expenses	26.9	21.8	79.8	84.4
Amortization of other intangible assets	0	0	0	0
Interest expense	3.7	2.1	10.6	4.5
Total expenses	319.1	206.8	721.5	461.1
Pre-tax income (loss) from continuing operations	24.1	10.9	(20.4)	(3.8)
Asset Management (Kudu)
Revenues:
Earned insurance premiums	0	0	0	0
Net investment income	14.8	9.5	41.2	26.1
Net realized and unrealized investment gains (losses)	41.1	18.9	45.8	62.5
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	0	0.1	0	0.2
Total revenues	55.9	28.5	87	88.8
Expenses:
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	4.5	3.3	10.2	9
Amortization of other intangible assets	0	0	0.2	0.2
Interest expense	4.2	1.9	10.3	9.2
Total expenses	8.7	5.2	20.7	18.4
Pre-tax income (loss) from continuing operations	47.2	23.3	66.3	70.4
Other Operations
Revenues:
Earned insurance premiums	0	0	0	0
Net investment income	8.5	5	13.6	16.1
Net realized and unrealized investment gains (losses)	(17.3)	15.3	2.8	34
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7
Other revenues	33	28.1	89.6	57.6
Total revenues	8.8	(346)	1.4	(210.8)
Expenses:
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	25	24	68.8	45.9
General and administrative expenses	39.9	14.4	118.9	79.4
Amortization of other intangible assets	1.4	2	3.2	2.9
Interest expense	0.6	0.4	1.2	1.1
Total expenses	66.9	40.8	192.1	129.3
Pre-tax income (loss) from continuing operations	$ (58.1)	$ (386.8)	$ (190.7)	$ (340.1)

CONSOLIDATED STATEMENTS OF COMP

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Statement of Comprehensive Income [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Other comprehensive income (loss), net of tax	(1.4)	0	(3)	(0.3)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group	0.7	(2.2)	(5.2)	0.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	0	2.9	0
Comprehensive income (loss)	890.4	(373.6)	747.1	(307.6)
Other comprehensive (income) loss attributable to non-controlling interests	(0.3)	0.2	0.4	0
Comprehensive income (loss) attributable to White Mountains’s common shareholders	$ 890.1	$ (373.4)	$ 747.5	$ (307.6)
Basic earnings (loss) per share
Continuing operations (in usd per share)	$ (1.66)	$ (121.90)	$ (50.73)	$ (98.16)
Discontinued operations (in usd per share)	308.59	1.72	304.97	(1.29)
Total consolidated operations (in usd per share)	306.93	(120.18)	254.24	(99.45)
Diluted earnings (loss) per share
Continuing operations (in usd per share)	(1.66)	(121.90)	(50.73)	(98.16)
Discontinued operations (in usd per share)	308.59	1.72	304.97	(1.29)
Total consolidated operations (in usd per share)	306.93	(120.18)	254.24	(99.45)
Dividends declared and paid per White Mountains’s common share (in usd per share)	$ 0	$ 0	$ 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, 2020		$ 3,906	$ 595.2	$ 3,311.2	$ (0.4)	$ (88.1)	$ 3,817.9
Increase (Decrease) in Shareholders' Equity
Net income (loss)	$ (361.9)	(308.2)		(308.2)		(53.7)	(361.9)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	0
Other comprehensive income (loss), net of tax	(0.3)	0.4			0.4		0.4
Comprehensive income (loss)	(307.6)	(307.8)		(308.2)	0.4	(53.7)	(361.5)
Dividends declared on common shares		(3.1)		(3.1)			(3.1)
Dividends to non-controlling interests						(1.8)	(1.8)
Issuances of common shares		1.7	1.7				1.7
Issuances of shares of non-controlling interests						6.1	6.1
Repurchases and retirements of common shares		(94.6)	(16.6)	(78)			(94.6)
BAM member surplus contribution, net of tax								$ 44.8	$ 44.8
Amortization of restricted share awards		11.1	11.1				11.1
Recognition of equity-based compensation expense of subsidiaries		2	2			0.3	2.3
Net contributions and dilution from other non-controlling interests		6.4	(7.2)	13.4	0.2	(5.3)	1.1
Acquisition of non-controlling interests						230.3	230.3
Ending Balances at Sep. 30, 2021		3,521.7	586.2	2,935.3	0.2	132.6	3,654.3
Beginning Balances at Jun. 30, 2021		3,978.2	597.2	3,378.6	2.4	129.8	4,108
Increase (Decrease) in Shareholders' Equity
Net income (loss)	(383.9)	(371.4)		(371.4)		(12.5)	(383.9)
Net change in foreign currency translation and other		(2.2)			(2.2)	(0.2)	(2.4)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	0
Other comprehensive income (loss), net of tax	0
Comprehensive income (loss)	(373.6)	(373.6)		(371.4)	(2.2)	(12.7)	(386.3)
Dividends to non-controlling interests						(0.6)	(0.6)
Repurchases and retirements of common shares		(87.1)	(15.2)	(71.9)			(87.1)
BAM member surplus contribution, net of tax								14.7	14.7
Amortization of restricted share awards		3.6	3.6				3.6
Recognition of equity-based compensation expense of subsidiaries		0.2	0.2				0.2
Net contributions and dilution from other non-controlling interests		0.4	0.4			1.4	1.8
Ending Balances at Sep. 30, 2021		3,521.7	586.2	2,935.3	0.2	132.6	3,654.3
Beginning Balances at Dec. 31, 2021	3,704.7	3,548.1	588.9	2,957.5	1.7	156.6	3,704.7
Increase (Decrease) in Shareholders' Equity
Net income (loss)	650.9	752.4		752.4		(101.5)	650.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	2.9			2.9		2.9
Other comprehensive income (loss), net of tax	(3)	(7.8)			(7.8)	(0.4)	(8.2)
Comprehensive income (loss)	747.1	747.5		752.4	(4.9)	(101.9)	645.6
Dividends declared on common shares		(3)		(3)			(3)
Dividends to non-controlling interests						(7.5)	(7.5)
Issuances of common shares		3	3				3
Issuances of shares of non-controlling interests						74.6	74.6
Repurchases and retirements of common shares		(610.5)	(89.2)	(521.3)			(610.5)
BAM member surplus contribution, net of tax								62.3	62.3
Amortization of restricted share awards		10.3	10.3				10.3
Recognition of equity-based compensation expense of subsidiaries		8.1	8.1			0.8	8.9
Net contributions and dilution from other non-controlling interests		4.5	14.2	(9.7)		(9.1)	(4.6)
Disposition of non-controlling interests						(17.5)	(17.5)
Ending Balances at Sep. 30, 2022	3,866.3	3,708	535.3	3,175.9	(3.2)	158.3	3,866.3
Beginning Balances at Jun. 30, 2022		3,323.3	603.2	2,725.1	(5)	168.7	3,492
Increase (Decrease) in Shareholders' Equity
Net income (loss)	869.5	888.2		888.2		(18.7)	869.5
Net change in foreign currency translation and other		(1.1)			(1.1)	0.3	(0.8)
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	2.9	2.9			2.9		2.9
Other comprehensive income (loss), net of tax	(1.4)
Comprehensive income (loss)	890.4	890		888.2	1.8	(18.4)	871.6
Dividends to non-controlling interests						(0.5)	(0.5)
Repurchases and retirements of common shares		(508.9)	(71.5)	(437.4)			(508.9)
BAM member surplus contribution, net of tax								$ 26	$ 26
Amortization of restricted share awards		3.8	3.8				3.8
Recognition of equity-based compensation expense of subsidiaries		0.4	0.4			0.2	0.6
Net contributions and dilution from other non-controlling interests		(0.6)	(0.6)			(0.2)	(0.8)
Disposition of non-controlling interests	(17.5)					(17.5)
Ending Balances at Sep. 30, 2022	$ 3,866.3	$ 3,708	$ 535.3	$ 3,175.9	$ (3.2)	$ 158.3	$ 3,866.3

CONSOLIDATED STATEMENTS OF CASH

CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Cash flows from operations:
Net income (loss)	$ 650.9	$ (361.9)
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net realized and unrealized investment (gains) losses	141.9	(91.2)
Net realized and unrealized investment (gains) losses from investment in MediaAlpha	113.3	325.5
Deferred income tax expense	22.1	36.7
Amortization of restricted share awards	10.3	11.1
Amortization and depreciation	7	13.6
Net (income) loss from discontinued operation, net of tax - NSM Group	(16.4)	23.8
Net gain (loss) from sale of discontinued operations, net of tax	(886.8)	(18.7)
Other operating items:
Net change in reinsurance recoverables	(102.5)	(32.3)
Net change in insurance premiums receivable	(282.3)	(245.7)
Net change in ceded unearned premiums	7.4	78.1
Net change in loss and loss adjustment expense reserves	434.7	194.9
Net change in unearned insurance premiums	305.8	290
Net change in deferred acquisition costs	(45)	(60)
Net change in reinsurance payable	(111.4)	(46.8)
Net change in restricted cash	4.4	4.5
Investments in Kudu Participation Contracts	(97.9)	(141.6)
Net change in other assets and liabilities, net	(37.3)	25.7
Net cash provided from (used for) operations - continuing operations	118.2	5.7
Net cash provided from (used for) operations - NSM Group discontinued operations (Note 19)	38.7	40.3
Net cash provided from (used for) operations	156.9	46
Cash flows from investing activities:
Net change in short-term investments	(735.4)	(83.7)
Sales of fixed maturity investments	212.4	215.9
Maturities, calls and paydowns of fixed maturity investments	107.3	144.6
Sales of common equity securities and investment in MediaAlpha	0	176.8
Distributions and redemptions of other long-term investments	55	98.2
Release of cash pre-funded/placed in escrow for Ark Transaction	0	646.3
Purchases of consolidated subsidiaries, net of cash acquired of $0.3 and $52.2	(67.9)	10.6
Purchases of other long-term investments	(136.9)	(206.5)
Purchases of common equity securities	(88)	(119.7)
Purchases of fixed maturity investments	(474.1)	(996)
Other investing activities, net	3.7	(1.3)
Net cash provided from (used for) investing activities - continuing operations	260.4	(114.8)
Net cash provided from (used for) investing activities - NSM Group discontinued operations (Note 19)	7.1	(54.6)
Net cash provided from (used for) investing activities	267.5	(169.4)
Cash flows from financing activities:
Draw down of debt and revolving line of credit	211.8	368.9
Repayment of debt and revolving line of credit	(10.5)	(94.8)
Cash dividends paid to the Company’s common shareholders	(3)	(3.1)
Common shares repurchased	(610.5)	(94.6)
Net distributions from non-controlling interest shareholders	(9.2)	1.1
Contributions from discontinued operations	11.6	0
Capital contributions from BAM members	62.3	44.8
Acquisition of subsidiary shares by non-controlling interest shareholders	74.6	6.1
Fidus Re premium payment	(5.6)	(6.9)
Other financing activities, net	(2.1)	(13)
Net cash provided from (used for) financing activities - continuing operations	(280.6)	208.5
Net cash provided from (used for) financing activities - NSM Group discontinued operations (Note 19)	(17.5)	13.8
Net cash provided from (used for) financing activities	(298.1)	222.3
Net change in cash during the period	98	99.4
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)	147.7	84.6
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)	245.7	184
Supplemental cash flows information:
Interest paid	(10.9)	(5.3)
Net income tax payments	(3.2)	(2.1)
NSM Insurance Group
Adjustments to reconcile net income to net cash provided from (used for) operations:
Net gain (loss) from sale of discontinued operations, net of tax	(886.8)	0
Cash flows from investing activities:
Proceeds from the sale of consolidated subsidiaries, net of cash sold	1,364.8	0
Other Operations
Cash flows from investing activities:
Proceeds from the sale of consolidated subsidiaries, net of cash sold	19.5	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	$ 113.3	$ 325.5

CONSOLIDATED STATEMENTS OF CA_2

CONSOLIDATED STATEMENTS OF CASH FLOWS (Parenthetical) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Cash acquired from acquisition	$ 0.3	$ 52.2
Restricted cash balance	8.9	4
Discontinued operations cash balance	245.7	184
NSM Insurance Group
Cash sold in subsidiary transaction	143.9	0
Other Operations
Cash sold in subsidiary transaction	0.5	0
Discontinued Operations, Held-for-sale | NSM Insurance Group
Cash sold in subsidiary transaction	(143.9)	0
Restricted cash balance	0	92.2
Discontinued operations cash balance	$ 0	$ 126.7

Basis of Presentation and Signi

Basis of Presentation and Significant Accounting Policies	9 Months Ended
	Sep. 30, 2022
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 2021 Annual Report on Form 10-K. Reportable Segments White Mountains has determined its reportable segments based on the nature of the underlying businesses, the manner in which the Company’s subsidiaries and affiliates are organized and managed and the organization of the financial information provided to the chief operating decision maker to assess performance and make decisions regarding allocation of resources. As of September 30, 2022, White Mountains’s reportable segments were HG Global/BAM, Ark and Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations. The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “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 September 30, 2022 and December 31, 2021, 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 for which White Mountains is the primary beneficiary. BAM’s results are all attributed to non-controlling interests. The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. 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”). See Note 2 — “Significant Transactions. ” As of September 30, 2022 and December 31, 2021, 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 are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results. 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 typically are structured as minority preferred equity stakes with distribution rights, generally tied to gross revenues and designed to generate strong, stable cash yields. As of September 30, 2022 and December 31, 2021, White Mountains owned 89.3% and 99.3% of the basic units outstanding (76.1% and 84.7% 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”), and 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 previously announced 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 of December 31, 2021, White Mountains owned 96.5% of the basic units outstanding of NSM (87.3% on a fully diluted, fully converted basis). 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 2021 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies.

Significant Transactions

Significant Transactions	9 Months Ended
	Sep. 30, 2022
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. 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 and in each case, 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 participation contracts. As of September 30, 2022, Kudu’s go-forward portfolio of participation contracts excludes $41.1 million of enterprise value 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%. Ark On October 1, 2020, White Mountains entered into a subscription and purchase agreement (the “Ark SPA”) with Ark and certain selling shareholders (collectively with Ark, the “Ark Sellers”). Under the terms of the Ark SPA, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and to purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020, White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the Ark Transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a credit facility agreement and $366.3 million placed in escrow. On January 1, 2021, White Mountains completed the Ark Transaction in accordance with the terms of the Ark SPA. As of September 30, 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. White Mountains recognized total assets acquired related to the Ark Transaction of $2.5 billion, including goodwill and other intangible assets of $292.5 million, and total liabilities of $1.7 billion, including contingent consideration of $22.5 million and non-controlling interest of $220.2 million. Ark incurred transaction costs of $25.3 million in the first quarter of 2021. In the third quarter of 2021, Ark issued $163.3 million of floating rate unsecured subordinated notes (the “Ark 2021 Subordinated Notes”) in three separate transactions. See Note 7 — “Debt.” In connection with the issuance of the Ark 2021 Subordinated Notes, White Mountains and Ark terminated White Mountains’s commitment to provide up to $200.0 million of additional equity capital to Ark in 2021. The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date: Millions As of January 1, 2021 Investments $ 594.3 Cash 52.0 (1) Reinsurance recoverables 433.4 Insurance premiums receivable 236.7 Ceded unearned premiums 170.2 Value of in-force business acquired 71.7 Other assets 88.9 Loss and loss adjustment expense reserves (696.0) Unearned insurance premiums (326.1) Debt (46.4) Ceded reinsurance payable (528.3) Other liabilities (25.9) Net tangible assets acquired 24.5 Goodwill 116.8 Other intangible assets - syndicate underwriting capacity 175.7 Deferred tax liability on other intangible assets (33.4) Net assets acquired $ 283.6 (1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction. The values of net tangible assets acquired and the resulting goodwill, other intangible assets and contingent consideration were recorded at fair value using Level 3 inputs. The majority of the tangible assets acquired and liabilities assumed were recorded at their carrying values, as their carrying values approximated their fair values due to their short-term nature. The fair values of goodwill, other intangible assets and the contingent consideration liability were internally estimated primarily based on the income approach. The income approach estimates fair value based on the present value of the cash flows that the assets are expected to generate in the future. White Mountains developed internal estimates for the expected future cash flows and discount rates used in the present value calculations. The value of in-force business acquired represents the estimated profits relating to the unexpired contracts, net of related prepaid reinsurance, at the acquisition date through the expiration date of the contracts. For the three and nine months ended September 30, 2022, Ark recognized $0.7 million and $6.8 million of amortization expense on the value of in-force business acquired. For the three and nine months ended September 30, 2021, Ark recognized $11.0 million and $54.9 million of amortization expense on the value of in-force business acquired. The value of the syndicate underwriting capacity intangible asset was estimated using net cash flows attributable to Ark’s rights to write business in the Lloyd’s market. The value of the in-force business acquired and the syndicate underwriting capacity were estimated using a discounted cash flow method. Significant inputs to the valuation models include estimates of growth in premium revenues, investment returns, claim costs, expenses and discount rates based on a weighted average cost of capital. In evaluating the fair value of Ark’s loss and loss adjustment expense reserves (“LAE”), White Mountains determined that the risk-free rate of interest was approximately equal to the risk factor reflecting the uncertainty within the reserves and that no adjustment was necessary. As of September 30, 2022 and December 31, 2021, Ark recognized total contingent consideration liabilities of $32.9 million and $28.0 million. Any future adjustments to contingent consideration liabilities will be recognized through pre-tax income (loss). For the three and nine months ended September 30, 2022, Ark recognized pre-tax expense of $2.7 million and $4.9 million for the change in the fair value of its contingent consideration liabilities. For both the three and nine months ended September 30, 2021, Ark recognized pre-tax expense of $1.5 million for the change in the fair value of its contingent consideration liabilities. MediaAlpha On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3.6 million shares at $19.00 per share ($17.67 per share net of underwriting fees) and received total proceeds of $63.8 million. White Mountains also received $55.0 million of net proceeds related to a dividend recapitalization at MediaAlpha. Subsequent to 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 White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet. On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160.3 million. As of September 30, 2022, White Mountains owned 16.9 million shares, representing a 27.4% basic ownership interest (25.0% fully-diluted/fully-converted basis). 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 September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 16 — “Equity-Method Eligible Investments.” PassportCard/DavidShield On January 24, 2018, White Mountains acquired a 50.0% ownership interest in DavidShield, its joint venture partner in PassportCard. DavidShield is an MGA that is the leading provider of expatriate medical insurance in Israel and uses the same card-based delivery system as PassportCard. As part of the transaction, White Mountains reorganized its equity stake in PassportCard so that White Mountains and its partner in DavidShield would each own 50.0% of both businesses. To facilitate the transaction, White Mountains provided financing to its partner in the form of a non-interest-bearing loan that is secured by the partner’s equity in PassportCard and DavidShield. The gross purchase price for the 50.0% interest in DavidShield was $41.8 million, or $28.3 million net of the financing provided for the restructuring. On May 7, 2020, White Mountains made an additional $15.0 million investment in PassportCard/DavidShield to support operations through the ongoing COVID-19 pandemic. The transaction increased White Mountains’s ownership interest from 50.0% to 53.8%, but had no impact on the governance structure of the companies, including White Mountains’s board representation or other investor rights. 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 the operations of PassportCard and DavidShield. Because White Mountains does not have the unilateral power to direct the operations of PassportCard or DavidShield, White Mountains does not hold a controlling financial interest in either PassportCard or DavidShield and does not consolidate either entity. White Mountains’s ownership interest gives White Mountains the opportunity to exert significant influence over the significant financial and operating activities of PassportCard and DavidShield. Accordingly, PassportCard and DavidShield meet the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard and DavidShield. Changes in the fair value of PassportCard and DavidShield are recorded in realized and unrealized investment gains. White Mountains’s maximum exposure to loss on its equity investment in PassportCard/DavidShield and the non-interest-bearing loan to its partner is limited to the total carrying value of $143.0 million.

Investment Securities

Investment Securities	9 Months Ended
	Sep. 30, 2022
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 September 30, 2022 and December 31, 2021. Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits, insurance-linked securities (“ILS”) funds and private debt investments. 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 and nine months ended September 30, 2022 and 2021: Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Fixed maturity investments $ 11.1 $ 8.2 $ 28.6 $ 21.9 Short-term investments 6.7 — 7.2 .5 Common equity securities .1 .1 .2 .1 Other long-term investments 17.1 12.0 45.9 37.1 Amount attributable to TPC Providers (.3) (.2) (.8) (.8) Total investment income 34.7 20.1 81.1 58.8 Third-party investment expenses (.8) (.6) (1.5) (1.6) Net investment income, pre-tax $ 33.9 $ 19.5 $ 79.6 $ 57.2 Net Realized and Unrealized Investment Gains (Losses) The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Realized investment gains (losses) Fixed maturity investments $ (4.9) $ 1.0 $ (10.8) $ 3.8 Short-term investments (.1) (.3) (.4) — Common equity securities — — — .4 Investment in MediaAlpha — — — 160.3 Other long-term investments 3.4 9.2 24.1 0.9 Net realized investment gains (losses) (1.6) 9.9 12.9 165.4 Unrealized investment gains (losses) Fixed maturity investments (58.8) (7.9) (192.9) (27.0) Short-term investments (2.1) — (2.6) — Common equity securities 4.3 1.6 (6.3) 7.3 Investment in MediaAlpha (18.6) (396.8) (113.3) (485.8) Other long-term investments 27.5 28.4 40.8 112.3 Net unrealized investment gains (losses) (47.7) (374.7) (274.3) (393.2) Net realized and unrealized investment gains (losses), before amount attributable to TPC providers (1) (49.3) (364.8) (261.4) (227.8) Amount attributable to TPC Providers 1.3 (1.7) 6.2 (6.5) Net realized and unrealized investment gains (losses) $ (48.0) $ (366.5) $ (255.2) $ (234.3) Fixed maturity and short-term investments Net realized and unrealized investment gains (losses) $ (65.9) $ (7.2) $ (206.7) $ (23.2) Less: net realized and unrealized gains (losses) on investment .1 (5.7) (3.0) (6.9) Net unrealized investment gains (losses) on investment $ (66.0) $ (1.5) $ (203.7) $ (16.3) Common equity securities and investment in MediaAlpha Net realized and unrealized investment gains (losses) on common $ 4.3 $ 1.6 $ (6.3) $ 7.7 Net realized and unrealized investment gains (losses) from (18.6) (396.8) (113.3) (325.5) Total net realized and unrealized investment gains (losses) (14.3) (395.2) (119.6) (317.8) Less: net realized and unrealized gains (losses) on investment — .4 — 20.3 Net unrealized investment gains (losses) on investment $ (14.3) $ (395.6) $ (119.6) $ (338.1) (1) For the three months ended September 30, 2022 and 2021, includes $(22.6) and $(7.0) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2022 and 2021, includes $(44.4) and $(7.4) of realized and unrealized investment gains (losses) related to foreign currency exchange. The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and nine months ended September 30, 2022 and 2021 for investments still held at the end of the period: Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Other long-term investments $ 40.8 $ 26.5 $ 57.7 $ 75.5 Total net unrealized investment gains, pre-tax - Level 3 investments $ 40.8 $ 26.5 $ 57.7 $ 75.5 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 September 30, 2022 and December 31, 2021: September 30, 2022 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 227.9 $ — $ (11.0) $ — $ 216.9 Debt securities issued by corporations 1,068.8 — (91.2) (3.1) 974.5 Municipal obligations 289.3 — (24.4) — 264.9 Mortgage and asset-backed securities 278.3 — (37.6) — 240.7 Collateralized loan obligations 169.7 — (7.6) (4.8) 157.3 Total fixed maturity investments $ 2,034.0 $ — $ (171.8) $ (7.9) $ 1,854.3 December 31, 2021 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 212.1 $ .5 $ (1.1) $ — $ 211.5 Debt securities issued by corporations 993.3 8.7 (8.7) (.4) 992.9 Municipal obligations 276.4 16.8 (1.3) — 291.9 Mortgage and asset-backed securities 277.2 2.9 (2.5) — 277.6 Collateralized loan obligations 136.5 — (.4) (1.1) 135.0 Total fixed maturity investments $ 1,895.5 $ 28.9 $ (14.0) $ (1.5) $ 1,908.9 The following table presents the cost or amortized cost and carrying values of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2022. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties. September 30, 2022 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 207.5 $ 203.8 Due after one year through five years 917.9 849.4 Due after five years through ten years 354.8 309.3 Due after ten years 105.8 93.8 Mortgage and asset-backed securities and collateralized loan obligations 448.0 398.0 Total fixed maturity investments $ 2,034.0 $ 1,854.3 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 September 30, 2022 and December 31, 2021: September 30, 2022 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 324.2 $ 32.7 $ (8.7) $ (15.4) $ 332.8 Investment in MediaAlpha $ — $ 148.2 $ — $ — $ 148.2 Other long-term investments $ 1,390.7 $ 345.0 $ (90.0) $ (23.0) $ 1,622.7 December 31, 2021 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 236.3 $ 16.1 $ — $ (1.3) $ 251.1 Investment in MediaAlpha $ — $ 261.6 $ — $ — $ 261.6 Other long-term investments $ 1,186.7 $ 239.0 $ (44.1) $ (3.8) $ 1,377.8 Fair Value Measurements 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 September 30, 2022 and December 31, 2021, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 69% and 68% of the investment portfolio. Fair Value Measurements by Level The following tables present White Mountains’s fair value measurements for investments as of September 30, 2022 and December 31, 2021 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate. September 30, 2022 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 216.9 $ 216.9 $ — $ — Debt securities issued by corporations: Financials 269.0 — 269.0 — Consumer 181.4 — 181.4 — Industrial 115.8 — 115.8 — Healthcare 114.3 — 114.3 — Technology 110.8 — 110.8 — Utilities 75.9 — 75.9 — Communications 49.1 — 49.1 — Energy 36.1 — 36.1 — Materials 22.1 — 22.1 — Total debt securities issued by corporations 974.5 — 974.5 — Municipal obligations 264.9 — 264.9 — Mortgage and asset-backed securities 240.7 — 240.7 — Collateralized loan obligations 157.3 — 157.3 — Total fixed maturity investments 1,854.3 216.9 1,637.4 — Short-term investments 1,196.4 1,196.4 — — Common equity securities (1) 332.8 46.4 286.4 — Investment in MediaAlpha 148.2 148.2 — — Other long-term investments 1,058.0 — 13.9 1,044.1 Other long-term investments — NAV (2) 564.7 — — — Total other long-term investments 1,622.7 — 13.9 1,044.1 Total investments $ 5,154.4 $ 1,607.9 $ 1,937.7 $ 1,044.1 (1) Consist of investments in exchange traded funds (“ETFs”) and 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 at net asset value (“NAV”) using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2021 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 211.5 $ 211.5 $ — $ — Debt securities issued by corporations: Financials 264.2 — 264.2 — Consumer 178.1 — 178.1 — Technology 117.9 — 117.9 — Industrial 112.9 — 112.9 — Healthcare 112.8 — 112.8 — Utilities 70.9 — 70.9 — Communications 56.0 — 56.0 — Energy 48.0 — 48.0 — Materials 32.1 — 32.1 — Total debt securities issued by corporations 992.9 — 992.9 — Municipal obligations 291.9 — 291.9 — Mortgage and asset-backed securities 277.6 — 277.6 — Collateralized loan obligations 135.0 — 135.0 — Total fixed maturity investments 1,908.9 211.5 1,697.4 — Short-term investments 465.9 465.9 — — Common equity securities (1) 251.1 — 251.1 — Investment in MediaAlpha 261.6 261.6 — — Other long-term investments 895.3 — 4.7 890.6 Other long-term investments — NAV (2) 482.5 — — — Total other long-term investments 1,377.8 — 4.7 890.6 Total investments $ 4,265.3 $ 939.0 $ 1,953.2 $ 890.6 (1) Consist of investments in listed funds that predominantly invest in international equities. (2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at NAV using the 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 September 30, 2022 and December 31, 2021, investments of $455.1 million and $479.5 million were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM. BAM is required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $4.6 million and $4.8 million as of September 30, 2022 and December 31, 2021. Lloyd’s trust deposits are generally required of Lloyd's syndicates to protect policyholders in non-U.K. markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. As of September 30, 2022 and December 31, 2021, Ark held Lloyd’s trust deposits with a fair value of $117.8 million and $113.8 million The underwriting capacity of a member of Lloyd’s must be supported by providing a deposit (“Funds at Lloyd’s”) in the form of cash, securities or letters of credit in an amount determined by Lloyd’s. The amount of such deposit is calculated for each member through the completion of an annual capital adequacy exercise. These requirements allow Lloyd’s to evaluate that each member has sufficient assets to meet its underwriting liabilities plus a required solvency margin. As of September 30, 2022 and December 31, 2021, the fair value of Ark’s Funds at Lloyd’s investment deposits totaled $311.4 million and $342.8 million. As of September 30, 2022 and December 31, 2021, Ark had $49.8 million and $50.0 million of short-term investments pledged as collateral under an uncommitted standby letter of credit. See Note 7 — “Debt.” 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 September 30, 2022 and December 31, 2021: Fair Value at Millions September 30, 2022 December 31, 2021 AAA $ 11.2 $ 12.0 AA 90.5 85.0 A 524.0 490.4 BBB 343.0 396.8 Other 5.8 8.7 Debt securities issued by corporations (1) $ 974.5 $ 992.9 (1) Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc. Mortgage and Asset-backed Securities and Collateralized Loan Obligations The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 114.1 $ 114.1 $ — $ 125.4 $ 125.4 $ — FHLMC 74.5 74.5 — 90.5 90.5 — GNMA 28.9 28.9 — 40.1 40.1 — Total agency (1) 217.5 217.5 — 256.0 256.0 — Non-agency: Residential .4 .4 — .5 .5 — Total non-agency .4 .4 — .5 .5 — Total mortgage-backed securities 217.9 217.9 — 256.5 256.5 — Other asset-backed securities: Credit card receivables 11.9 11.9 — 12.3 12.3 — Vehicle receivables 10.9 10.9 — 8.8 8.8 — Total other asset-backed securities 22.8 22.8 — 21.1 21.1 — Total mortgage and asset-backed securities 240.7 240.7 — 277.6 277.6 — Collateralized loan obligations 157.3 157.3 — 135.0 135.0 — Total mortgage and asset-backed securities and collateralized loan obligations $ 398.0 $ 398.0 $ — $ 412.6 $ 412.6 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC). As of September 30, 2022, White Mountains’s investment portfolio included $157.3 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 September 30, 2022. Investment in MediaAlpha Following the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and is presented as a separate line item on the balance sheet. At the September 30, 2022 closing price of $8.75 per share, the fair value of White Mountains’s investment in MediaAlpha was $148.2 million. See Note 2 — “Significant Transactions.” Other Long-Term Investments The following table presents the carrying values of White Mountains’s other long-term investments as of September 30, 2022 and December 31, 2021: Fair Value at Millions September 30, 2022 December 31, 2021 Kudu’s Participation Contracts $ 813.2 $ 669.5 PassportCard/DavidShield 132.0 120.0 Elementum Holdings, L.P. 45.0 45.0 Other unconsolidated entities (1) 37.0 34.4 Total unconsolidated entities 1,027.2 868.9 Private equity funds and hedge funds 239.8 153.8 Bank loan fund 155.7 163.0 Lloyd’s trust deposits 117.8 113.8 ILS funds 49.4 51.9 Private debt investments 13.0 14.1 Other 19.8 12.3 Total other long-term investments $ 1,622.7 $ 1,377.8 (1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, convertible preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments. Private Equity Funds and Hedge Funds White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the NAV of the funds. As of September 30, 2022, White Mountains held investments in 16 private equity funds and two hedge funds. The largest investment in a single private equity fund or hedge fund was $49.3 million and $31.3 million as of September 30, 2022 and December 31, 2021. The following table presents the fair value of investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 102.9 $ 45.1 $ 69.8 $ 11.8 Financial services 77.9 54.9 67.7 29.3 Real estate 4.3 2.5 4.3 2.9 Total private equity funds 185.1 102.5 141.8 44.0 Hedge funds Long/short equity financials and business services 49.3 — — — European small/mid cap 5.4 — 12.0 — Total hedge funds 54.7 — 12.0 — Total private equity funds and hedge funds included in other long-term investments $ 239.8 $ 102.5 $ 153.8 $ 44.0 Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period. The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2022: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $27.5 $19.0 $135.4 $3.2 $185.1 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 September 30, 2022 and December 31, 2021, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds. Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. Advance notice requirements for redemptions from White Mountains’s hedge funds 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 $155.7 million as of September 30, 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 September 30, 2022, White Mountains held Lloyd’s trust deposits with a fair value of $117.8 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 September 30, 2022, White Mountains held investments in ILS funds with a fair value of $49.4 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. One of the ILS funds in White Mountains’s portfolio requires shareholders to provide advance redemption notice on or before September 15 of each calendar year. Amounts requested for redemption in this fund remain subject to market fluctuation until the underlying investment has fully matured or been commuted, which may be up to a period of three years from the start of each calendar year. Rollforward of Level 3 Investments Level 3 measurements as of September 30, 2022 and 2021 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities. The following table presents the changes in White Mountains’s fair value measurements for Level 3 investments for the nine months ended September 30, 2022 and 2021: Level 3 Investments Millions Other Long-term Other Long-term Balance at December 31, 2021 $ 890.6 Balance at December 31, 2020 $ 614.2 Net realized and unrealized gains 57.3 Net realized and unrealized gains 79.0 Amortization/accretion — Amortization/accretion — Purchases 127.9 Purchases 143.6 Sales (31.7) Sales (31.9) Effect of Ark Transaction — Effect of Ark Transaction 9.6 Transfers in — Transfers in — Transfers out — Transfers out — Balance at September 30, 2022 $ 1,044.1 Balance at September 30, 2021 $ 814.5 Fair Value Measurements — Transfers Between Levels - Nine months ended September 30, 2022 and 2021 Transfers between levels are recorded using the fair value measurement as of the end of the quarterly period in which the event or change in circumstance giving rise to the transfer occurred. During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements. During the nine months ended September 30, 2022 and 2021, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 measurements. Significant Unobservable Inputs The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s other long-term investments, classified within Level 3 as of September 30, 2022 and December 31, 2021. The tables below exclude $42.9 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds. $ in Millions September 30, 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 $813.2 17% - 24% 7x - 16x PassportCard/DavidShield Discounted cash flow $132.0 24% 4% Elementum Holdings, L.P. Discounted cash flow $45.0 18% 4% Private debt investments Discounted cash flow $11.0 10% 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 20% and 9.7x. (4) As of September 30, 2022, three of Kudu’s Participation Contracts with a total fair value of $312.4 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. (5) In 2022, Kudu deployed a total of $97.9 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners. (6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements. $ in Millions December 31, 2021 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (6) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6) Kudu’s Participation Contracts (3)(4)(5) Discounted cash flow $669.5 18% - 23% 7x - 13x PassportCard/DavidShield Discounted cash flow $120.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $45.0 17% 4% Private debt investments Discounted cash flow $9.4 8% 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 20% and 10x. (4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management. (5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. (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	9 Months Ended
	Sep. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Goodwill and Other Intangible Assets	Goodwill and Other Intangible Assets White Mountains accounts for purchases of businesses using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. 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, by reportable segment as of September 30, 2022 and December 31, 2021: $ in Millions Weighted Average Economic September 30, 2022 December 31, 2021 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 51.1 — 51.1 17.9 — 17.9 Total goodwill 175.5 — 175.5 142.3 — 142.3 Other intangible assets: Ark Underwriting capacity N/A 175.7 — 175.7 175.7 — 175.7 Kudu Trade names 7 2.2 1.1 1.1 2.2 .9 1.3 Other Operations Trade names 15.9 17.9 2.4 15.5 8.2 1.5 6.7 Customer relationships 12.4 29.5 6.6 22.9 18.8 4.5 14.3 Other 12.1 2.8 .3 2.5 .3 .1 .2 Subtotal 50.2 9.3 40.9 27.3 6.1 21.2 Total other intangible assets 228.1 10.4 217.7 205.2 7.0 198.2 Total goodwill and other intangible assets $ 403.6 $ 10.4 393.2 $ 347.5 $ 7.0 340.5 Goodwill and other intangible assets attributed to (103.1) (91.8) Goodwill and other intangible assets included in White Mountains’s $ 290.1 $ 248.7 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, trade names, customer relationships and contracts and information technology. 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 domain names, certain trademarks and brand names. 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. The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022: $ in Millions Goodwill and Other intangible asset (1) Acquisition Date Acquisition of subsidiary/ asset Ark $ 292.5 January 1, 2021 Other Operations $ 86.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date. The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, 2022 2021 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 201.8 $ 196.2 $ 398.0 $ 151.5 $ 201.1 $ 352.6 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (22.9) 22.9 — (9.3) 9.3 — Measurement period adjustments (2) (3.4) — (3.4) (.4) — (.4) Amortization — (1.4) (1.4) — (2.0) (2.0) Ending balance $ 175.5 $ 217.7 $ 393.2 $ 141.8 $ 208.4 $ 350.2 (1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations. Nine Months Ended September 30, 2022 2021 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 142.3 $ 198.2 $ 340.5 $ 19.2 $ 26.4 $ 45.6 Ark Transaction — — — 116.8 175.7 292.5 Acquisition of businesses (1) 59.5 — 59.5 15.8 — 15.8 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (22.9) 22.9 — (9.3) 9.3 — Measurement period adjustments (2) (3.4) (3.4) (.7) .1 (.6) Amortization — (3.4) (3.4) — (3.1) (3.1) Ending balance $ 175.5 $ 217.7 $ 393.2 $ 141.8 $ 208.4 $ 350.2 (1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the nine months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.

Loss and Loss Adjustment Expens

Loss and Loss Adjustment Expense Reserves	9 Months Ended
	Sep. 30, 2022
Insurance Loss Reserves [Abstract]
Loss and Loss Adjustment Expense Reserves	Loss and Loss Adjustment Expense Reserves The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Gross beginning balance $ 1,022.1 $ 760.0 $ 894.7 $ 696.0 Less: beginning reinsurance recoverable on unpaid losses (1) (375.5) (425.3) (428.9) (433.4) Net loss and LAE reserves 646.6 334.7 465.8 262.6 Loss and LAE incurred relating to: Current year losses 222.9 141.9 491.8 269.0 Prior year losses (9.2) (12.7) (35.6) (21.2) Net incurred losses and LAE 213.7 129.2 456.2 247.8 Loss and LAE paid relating to: Current year losses (6.1) (9.0) (20.8) (11.5) Prior year losses (37.0) (20.3) (130.8) (62.1) Net paid loss and LAE (43.1) (29.3) (151.6) (73.6) Change in TPC Providers’ participation (2) — — 57.5 (2.2) Foreign currency translation and other adjustments (9.2) (1.2) (19.9) (1.2) Net ending balance 808.0 433.4 808.0 433.4 Plus: ending reinsurance recoverable on unpaid losses (3) 521.4 457.5 521.4 457.5 Gross ending balance $ 1,329.4 $ 890.9 $ 1,329.4 $ 890.9 (1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $182.4 and $314.6 for the three months ended September 30, 2022 and 2021 and $276.8 and $319.2 for the nine months ended September 30, 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 (“RITC”) process. (3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $168.0 and $299.9 as of September 30, 2022 and 2021. For the three and nine months ended September 30, 2022, Ark recognized $9.2 million and $35.6 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2022 was driven primarily by good claims experience across most classes including the property and accident & health and specialty reserving lines of business, predominantly from business underwritten in London. For the three and nine months ended September 30, 2021, Ark recognized $12.7 million and $21.2 million of net favorable prior year loss reserve development. Ark’s net favorable prior year loss reserve development in 2021 was driven primarily by the property and accident & health reserving line of business. TPC Providers’ Participation 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. The TPC Providers’ participation in the Syndicates for the 2020 open year of account is 42.8% of the total net result of the Syndicates. For the years of account subsequent to the Ark Transaction, Ark is no longer using TPC Providers to provide underwriting capital for the Syndicates. An 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 2022, an RITC 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 is 42.8%. During the first quarter of 2021, an RITC was executed such that the outstanding loss and LAE reserves for claims arising out of the 2018 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 57.6%, were reinsured into the 2019 year of account, for which the TPC Providers’ participation in the total net results of the Syndicates was 58.3%. 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	9 Months Ended
	Sep. 30, 2022
Reinsurance Disclosures [Abstract]
Third-Party Reinsurance	Third-Party 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 Ark for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Written premiums: Gross $ 215.5 $ 162.4 $ 1,252.5 $ 895.0 Ceded (22.9) (41.5) (246.0) (169.5) Net written premiums $ 192.6 $ 120.9 $ 1,006.5 $ 725.5 Earned premiums: Gross $ 454.9 $ 284.5 $ 966.6 $ 622.0 Ceded (108.8) (71.1) (208.8) (186.2) Net earned premiums $ 346.1 $ 213.4 $ 757.8 $ 435.8 Losses and loss adjustment expenses: Gross $ 391.4 $ 193.5 $ 712.9 $ 372.7 Ceded (177.7) (64.3) (256.7) (124.9) Net losses and loss adjustment expenses $ 213.7 $ 129.2 $ 456.2 $ 247.8 As of September 30, 2022, Ark had $521.4 million and $29.5 million of reinsurance recoverables on unpaid and paid losses. As of September 30, 2021, Ark had $457.5 million and $8.1 million of reinsurance recoverables on unpaid and paid losses. 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. As of September 30, 2022, Ark’s reinsurance recoverables of $550.9 million included $168.0 million attributable to TPC Providers, which are collateralized. As of September 30, 2021, Ark’s reinsurance recoverables of $465.6 million included $299.9 million related to TPC Providers, which are collateralized. The following table provides a listing of Ark’s remaining gross and net reinsurance recoverables, excluding amounts attributable to TPC Providers, by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) rating and the percentage of total recoverables as of September 30, 2022: $ in Millions As of September 30, 2022 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 178.3 $ — $ 178.3 67.7 % A- to A 78.9 — 78.9 29.9 B++ or lower and not rated 125.7 119.4 6.3 2.4 Total $ 382.9 $ 119.4 $ 263.5 100.0 % (1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good). See Note 10 — “Municipal Bond Guarantee Insurance” for third-party reinsurance balances related to White Mountains’s financial guarantee business. 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. During the fourth quarter of 2021, Ark negotiated a reduction of $31.7 million, including accrued interest, to the aggregate excess of loss contract with SiriusPoint. As of September 30, 2022, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.3 million. See Note 10 — “Municipal Bond Guarantee Insurance” for reinsurance contracts accounted for as deposits related to White Mountains’s financial guarantee business.

Debt

Debt	9 Months Ended
	Sep. 30, 2022
Debt Disclosure [Abstract]
Debt	Debt The following table presents White Mountains’s debt outstanding as of September 30, 2022 and December 31, 2021: $ in Millions September 30, Effective (1) December 31, Effective (1) HG Global Senior Notes $ 150.0 8.6% $ — N/A Unamortized discount and issuance cost (3.6) — HG Global Senior Notes, carrying value 146.4 — Ark 2007 Subordinated Notes, carrying value 30.0 30.0 Ark 2021 Notes Tranche 1 37.6 44.2 Ark 2021 Notes Tranche 2 47.0 47.0 Ark 2021 Notes Tranche 3 70.0 70.0 Unamortized issuance cost (4.6) (5.3) Ark 2021 Subordinated Notes, carrying value 150.0 155.9 Total Ark Subordinated Notes, carrying value 180.0 7.3% 185.9 6.9% Kudu Credit Facility 260.4 5.6% 225.4 4.3% Unamortized issuance cost (6.9) (7.2) Kudu Credit Facility, carrying value 253.5 218.2 Other Operations debt 36.4 7.1% 17.1 7.5% Unamortized issuance cost (.8) (.3) Other Operations debt, carrying value 35.6 16.8 Total debt $ 615.5 $ 420.9 (1) Effective rate includes the effect of the amortization of debt issuance costs. HG Global Senior Notes On April 29, 2022, HG Global received the proceeds 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 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 run off. 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 amounts plus accrued interest. 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, which is included in short-term investments. As of September 30, 2022, the interest reserve account is $26.4 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 the foregoing collateral. The HG Global Senior Notes contain various affirmative and negative covenants that White Mountains considers to be customary for such borrowings. If the payments of principal and interest under the HG Global Senior Notes become 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 September 30, 2022, the HG Global Senior Notes had an outstanding principal 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 September 30, 2022, the Ark 2007 Subordinated Notes had an outstanding principal balance of $30.0 million. In the third quarter of 2021, GAIL issued $163.3 million face value floating rate subordinated notes at par in three separate transactions for proceeds of $157.8 million, net of debt issuance costs. The unsecured 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 Notes Tranche 1”). The Ark 2021 Notes Tranche 1, which mature in July 2041, accrue interest at a floating rate equal to the three-month EURIBOR plus 5.75% per annum. On August 11, 2021, Ark issued $47.0 million face value floating rate unsecured subordinated notes (“Ark 2021 Notes Tranche 2”). The Ark 2021 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 Notes Tranche 3”). The Ark 2021 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 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 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 Notes Tranche 3 when a different premium load event exists or will be caused by the restricted payment. As of September 30, 2022, the Ark 2021 Notes Tranche 1 had an outstanding principal balance of €39.1 million ($37.6 million based upon the foreign exchange spot rate as of September 30, 2022), the Ark 2021 Notes Tranche 2 had an outstanding principal balance of $47.0 million, and the Ark 2021 Notes Tranche 3 had an outstanding principal 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 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 another 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 September 30, 2022, the ING LOC Facility and Lloyds LOC Facility were undrawn. As of September 30, 2022, the Citibank LOC Facility had an outstanding principal balance of $36.2 million. As of September 30, 2022, $49.8 million of short-term investments were pledged as collateral under the Citibank LOC Facility. Ark’s uncommitted 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 and Kudu Bank Facility On December 23, 2019, Kudu entered into a secured credit facility with Monroe Capital Management Advisors, LLC (the “Kudu Bank Facility”). On March 23, 2021, Kudu replaced the Kudu Bank Facility and entered into a secured revolving credit facility (the “Kudu Credit Facility”) with Mass Mutual to repay the Kudu Bank 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. In connection with the replacement of the Kudu Bank Facility, Kudu recognized a total loss of $4.1 million, representing debt issuance costs and prepayment fees, which are included within interest expense for the year to date period ended September 30, 2021. The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of September 30, 2022, the interest reserve account is $8.9 million. The Kudu Credit Facility requires Kudu to maintain a ratio of the outstanding balance to the sum of the fair market value of the 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 September 30, 2022, Kudu has a 35% 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 qualifying Kudu Participation Contracts. As of September 30, 2022, the available undrawn balance was $39.6 million. The following table presents the change in debt under the Kudu Bank Facility and Kudu Credit Facility for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Kudu Bank Facility Beginning balance $ — $ — $ — $ 89.2 Term loans Borrowings — — — 3.0 Repayments — — — (92.2) Ending balance $ — $ — $ — $ — Kudu Credit Facility Beginning balance $ 260.4 $ 203.0 $ 225.4 $ — Term loans Borrowings — — 35.0 203.0 Repayments — — — — Ending balance $ 260.4 $ 203.0 $ 260.4 $ 203.0 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 September 30, 2022, White Mountains’s Other Operations had debt with an outstanding principal balance of $36.4 million, which consisted of five secured credit facilities (collectively, “Other Operations debt”). Compliance At September 30, 2022, White Mountains was in compliance in all material respects with the covenants under all of its debt instruments.

Income Taxes

Income Taxes	9 Months Ended
	Sep. 30, 2022
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 September 30, 2022, the primary jurisdictions in which the Company’s subsidiaries and branches were subject to tax were Ireland, Israel, Luxembourg, the United Kingdom and the United States. White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2022 represented an effective tax rate of 23.9% and 9.4%. 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, partially offset by a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes. White Mountains’s income tax expense related to pre-tax loss from continuing operations for the three and nine months ended September 30, 2021 represented an effective tax rate of (7.9)% and (17.1)%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by losses in jurisdictions with lower tax rates than the United States, a full valuation allowance on net deferred tax assets in certain U.S. operations, consisting of the WM Adams, Inc. consolidated tax group within Other Operations and BAM, and state income taxes. For the nine months ended September 30, 2021, the effective rate was also different from the U.S. statutory rate of 21.0% due to additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities. On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19.0% to 25.0% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective. 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 its results of operations. In arriving at the effective tax rate for the three and nine months ended September 30, 2022 and 2021, 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, 2022 and 2021. 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 2016.

Derivatives

Derivatives	9 Months Ended
	Sep. 30, 2022
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 and a year equal to 360 days. As of September 30, 2022, the three-month SOFR rate was 3.6%. 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 and nine months ended September 30, 2022, White Mountains recognized a gain of $2.1 million and $0.6 million related to the change in fair value on the interest rate cap within interest expense. As of September 30, 2022, the estimated fair value of the interest rate cap recorded in other assets was $3.9 million. White Mountains classifies the interest rate cap as a Level 2 measurement.

Municipal Bond Guarantee Insura

Municipal Bond Guarantee Insurance	9 Months Ended
	Sep. 30, 2022
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 up to 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”). The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. The insurance-linked securities were issued by Fidus Re with an initial term of 12 years and are callable five years after the date of issuance. 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 28% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022. In the first quarter of 2021, Fidus Re issued an additional $150.0 million of insurance-linked securities (the “Fidus Re 2021 Agreement”) with 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 33% of BAM’s portfolio of financial guaranty policies issued through September 30, 2022. 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 New York State Department of Financial Services (“NYDFS”) single issuer limits. As of September 30, 2022, 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 limited to the assets in two collateral trusts: the Supplemental Trust and a Regulation 114 Trust (together, the “Collateral Trusts”). Losses required to be reimbursed under the FLRT are subject to an aggregate limit equal to the assets held in 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 gross ceded unearned premiums and unpaid ceded loss and LAE, 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 September 30, 2022 and December 31, 2021 was $259.4 million and $250.2 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 September 30, 2022 and December 31, 2021 was $574.5 million and $601.8 million. As of September 30, 2022 and December 31, 2021, the Collateral Trusts held assets of $833.9 million and $852.0 million, which included $457.7 million and $481.7 million of cash and investments, $364.6 million and $364.6 million of BAM Surplus Notes and $11.6 million and $5.7 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 2022, the interest rate on the BAM Surplus Notes is 3.2%. 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 interest and principal 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 2021, BAM made a $33.8 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $23.6 million was a repayment of principal held in the Supplemental Trust, $0.4 million was a payment of accrued interest held inside the Supplemental Trust and $9.8 million was a payment of accrued interest held outside the Supplemental Trust. During the three and nine months ended September 30, 2022 and 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest. As of September 30, 2022 and December 31, 2021, the principal balance on the BAM Surplus Notes was $364.6 million and $364.6 million and total interest receivable on the BAM Surplus Notes was $166.4 million and $157.6 million. Insured Obligations and Premiums The following table presents a schedule of BAM’s insured obligations as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Contracts outstanding 13,094 12,350 Remaining weighted average contract period outstanding (in years) 10.8 10.8 Contractual debt service outstanding (in millions): Principal $ 98,619.0 $ 89,196.5 Interest 47,595.0 41,486.5 Total debt service outstanding $ 146,214.0 $ 130,683.0 Gross unearned insurance premiums (in millions) $ 286.7 $ 266.3 The following table presents a schedule of BAM’s future premium revenues as of September 30, 2022: Millions September 30, 2022 October 1, 2022 - December 31, 2022 $ 6.9 January 1, 2023 - March 31, 2023 6.8 April 1, 2023 - June 30, 2023 6.7 July 1, 2023 - September 30, 2023 6.6 October 1, 2023 - December 31, 2023 6.4 Total 2023 26.5 2024 24.9 2025 23.2 2026 21.6 2027 20.1 2028 and thereafter 163.5 Total gross unearned insurance premiums $ 286.7 The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Written premiums: Direct $ 18.4 $ 12.8 $ 44.9 $ 34.5 Assumed 1.3 — 1.3 4.5 Gross written premiums (1) $ 19.7 $ 12.8 $ 46.2 $ 39.0 Earned premiums: Direct $ 6.5 $ 5.9 $ 22.0 $ 16.8 Assumed .6 .8 4.0 2.8 Gross earned premiums (1) $ 7.1 $ 6.7 $ 26.0 $ 19.6 (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. In January 2021, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $805.5 million. In September 2022, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $42.5 million. None of the contracts assumed under these reinsurance agreements were non-performing, and no loss reserves have been established for any of the contracts, either as of the transaction date or as of September 30, 2022. The agreements, which cover future claims exposure only, meet the risk transfer criteria under ASC 944-20, Insurance Activities and accordingly have been accounted for as reinsurance.

Earnings Per Share

Earnings Per Share	9 Months Ended
	Sep. 30, 2022
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 and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 888.2 $ (371.4) $ 752.4 $ (308.2) Less: total income (loss) from discontinued operations, net of tax (1) 893.1 5.3 903.2 (5.1) Less: net (income) loss from discontinued operations attributable $ (.1) $ — $ (.7) $ 1.1 Net income (loss) from continuing operations attributable to $ (4.8) $ (376.7) $ (150.1) $ (304.2) Allocation of (earnings) losses to participating restricted common shares (2) .1 4.6 1.8 3.5 Basic and diluted earnings (losses) per share numerators $ (4.7) $ (372.1) $ (148.3) $ (300.7) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (3) (38.3) (37.8) (35.5) (36.0) Basic earnings (losses) per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (3) (38.3) (37.8) (35.5) (36.0) Diluted earnings (losses) per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Basic and diluted earnings per share (in dollars) - continuing Distributed earnings - dividends declared and paid $ — $ — $ 1.00 $ 1.00 Undistributed earnings (losses) (1.66) (121.90) (51.73) (99.16) Basic and diluted earnings (losses) per share $ (1.66) $ (121.90) $ (50.73) $ (98.16) (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group and net gain (loss) from sale of discontinued operations, net of tax - Sirius Group. See Note 19 — “Held for Sale and Discontinued Operations. ” (2) Restricted shares issued by White Mountains receive dividends and are therefore 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 and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Undistributed net earnings (losses) - continuing operations: Net income (losses) attributable to White Mountains’s common $ (4.7) $ (372.1) $ (148.3) $ (300.7) Dividends declared, net of restricted common share amounts (1) — — (3.0) (3.1) Total undistributed net earnings (losses), net of restricted $ (4.7) $ (372.1) $ (151.3) $ (303.8) (1) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

Employee Share-Based Incentive

Employee Share-Based Incentive Compensation Plans	9 Months Ended
	Sep. 30, 2022
Share-Based Payment Arrangement [Abstract]
Employee Share-Based Incentive Compensation Plans	Employee Share-Based Incentive Compensation Plans 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 of White Mountains. As of September 30, 2022 and 2021, White Mountains’s share-based compensation incentive 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 3 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 and nine months ended September 30, 2022 and 2021 for performance shares granted under the WTM Incentive Plan: Three Months Ended September 30, Nine Months Ended September 30, 2022 2021 2022 2021 Millions, except share amounts Target Performance Accrued Target Performance Accrued Target Performance Accrued Target Performance Accrued Beginning of period 39,449 $ 41.2 41,252 $ 45.7 40,828 $ 42.2 42,458 $ 56.3 Shares paid (1) — — (219) (.6) (14,625) (26.4) (14,336) (35.2) New grants — — — — 13,225 — 13,475 — Forfeitures and cancellations (2) — (.1) (205) .2 21 (.2) (769) .4 Expense recognized — 11.9 — (6.5) — 37.4 — 17.3 End of period 39,449 $ 53.0 40,828 $ 38.8 39,449 $ 53.0 40,828 $ 38.8 (1) Includes WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target and WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in March 2021 at 200% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP. During the nine months ended September 30, 2022, White Mountains granted 13,225 performance shares for the 2022-2024 performance cycle. During the nine months ended September 30, 2021, White Mountains granted 13,475 performance shares for the 2021-2023 performance cycle. 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. For the 2018-2020 performance cycle, all performance shares earned were settled in cash. If all the outstanding WTM performance shares had vested on September 30, 2022, the total additional compensation cost to be recognized would have been $41.2 million, based on accrual factors (common share price and payout assumptions) as of September 30, 2022. The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of September 30, 2022 for each performance cycle: Nine Months Ended September 30, 2022 Millions, except share amounts Target Performance Accrued Performance cycle: 2020 – 2022 13,350 $ 31.9 2021 – 2023 13,475 14.7 2022 – 2024 13,225 7.2 Sub-total 40,050 53.8 Assumed forfeitures (601) (.8) September 30, 2022 39,449 $ 53.0 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 for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, 2022 2021 2022 2021 Millions, except share amounts Restricted Unamortized Restricted Unamortized Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,350 $ 23.0 38,280 $ 23.2 37,850 $ 15.9 43,105 $ 15.2 Issued — — — — 13,225 13.8 13,475 16.1 Vested — — (219) — (12,725) — (17,936) — Forfeited — — (211) (.2) — — (794) (.8) Expense recognized — (3.8) — (3.6) — (10.5) — (11.1) End of period 38,350 $ 19.2 37,850 $ 19.4 38,350 $ 19.2 37,850 $ 19.4

Leases

Leases	9 Months Ended
	Sep. 30, 2022
Leases [Abstract]
Leases	Leases White Mountains has entered into lease agreements, primarily for office space. These leases are classified as operating leases, with lease expense recognized on a straight-line basis over the term of the lease. Lease incentives, such as free rent or landlord reimbursements for leasehold improvements, are recognized at lease inception and amortized on a straight-line basis over the term of the lease. Lease expense and the amortization of leasehold improvements are recognized within general and administrative expenses. Lease payments related to options to extend or renew the lease term are excluded from the calculation of lease liabilities unless White Mountains is reasonably certain of exercising those options. As of September 30, 2022 and December 31, 2021, the right of use (“ROU”) lease assets were $24.5 million and $28.1 million and lease liabilities were $26.5 million and $30.0 million. The following table summarizes net lease expense recognized in White Mountains’s consolidated statements of operations for the three and nine months ended September 30, 2022 and 2021: Millions Three Months Ended September 30, Nine Months Ended September 30, Lease Cost 2022 2021 2022 2021 Lease cost $ 1.9 $ 1.9 $ 5.9 $ 4.8 Less: sublease income .2 .1 .5 .3 Net lease cost $ 1.7 $ 1.8 $ 5.4 $ 4.5 The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2022: Millions As of September 30, 2022 Remainder of 2022 $ 1.7 2023 8.1 2024 7.1 2025 4.9 2026 2.6 Thereafter 5.0 Total undiscounted lease payments 29.4 Less: present value adjustment 2.9 Operating lease liabilities $ 26.5 The following tables present lease related assets and liabilities by reportable segment as of September 30, 2022 and December 31, 2021: As of September 30, 2022 Millions HG/BAM Ark Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease assets $ 6.2 $ 6.6 $ 5.9 $ 5.8 $ 24.5 4.1% Lease liabilities $ 6.7 $ 6.6 $ 6.8 $ 6.4 $ 26.5 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate. As of December 31, 2021 Millions HG/BAM Ark Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease assets $ 7.6 $ 7.0 $ 6.4 $ 7.1 $ 28.1 4.0% Lease liabilities $ 8.1 $ 7.0 $ 7.1 $ 7.8 $ 30.0 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

Non-controlling Interests

Non-controlling Interests	9 Months Ended
	Sep. 30, 2022
Noncontrolling Interest [Abstract]
Non-controlling Interests	Non-controlling Interests Non-controlling interests consist of the ownership interests of non-controlling shareholders in consolidated entities and are presented separately on the balance sheet. The following table presents the balance of non-controlling interests included in White Mountains’s total equity and the ownership interests held by non-controlling shareholders as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 $ in Millions Non-controlling Percentage (1) Non-controlling Equity Non-controlling Percentage (1) Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ (.3) 3.1 % $ 8.9 Ark 28.0 % 217.1 28.0 % 230.7 Kudu 10.7 % 80.8 .7 % 12.4 NSM (2) — % — 3.5 % 16.7 Other various 20.8 various 11.9 Total, excluding BAM 318.4 280.6 BAM 100.0 % (160.1) 100.0 % (124.0) Total non-controlling interests $ 158.3 $ 156.6 (1) The non-controlling percentage represents the basic ownership interests held by non-controlling shareholders with the exception of HG Global, for which the non-controlling percentage represents the preferred share ownership held by non-controlling shareholders. (2) As a result of the NSM Transaction, NSM has been classified as discontinued operations through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations .”

Segment Information

Segment Information	9 Months Ended
	Sep. 30, 2022
Segment Reporting [Abstract]
Segment Information	Segment Information As of September 30, 2022, White Mountains conducted its operations through four segments: (1) HG Global/BAM, (2) Ark, (3) Kudu, and (4) Other Operations. 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. Prior period amounts have been reclassified to conform to the current period’s presentation. See Note 19 — “Held for Sale and Discontinued 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. The following tables present the financial information for White Mountains’s segments: Millions HG Global/ BAM Ark Kudu Other Operations Total Three Months Ended September 30, 2022 Earned insurance premiums $ 7.1 $ 346.1 $ — $ — $ 353.2 Net investment income 5.7 4.9 14.8 8.5 33.9 Net realized and unrealized investment (38.8) (14.4) 41.1 (17.3) (29.4) Net realized and unrealized investment gains — — — (18.6) (18.6) Commission revenues — — — 3.2 3.2 Other revenues 1.3 6.6 — 33.0 40.9 Total revenues (24.7) 343.2 55.9 8.8 383.2 Loss and loss adjustment expenses — 213.7 — — 213.7 Insurance and reinsurance acquisition expenses 1.7 74.8 — — 76.5 Cost of sales — — — 25.0 25.0 General and administrative expenses 15.8 26.9 4.5 39.9 87.1 Amortization of other intangible assets — — — 1.4 1.4 Interest expense 2.0 3.7 4.2 .6 10.5 Total expenses 19.5 319.1 8.7 66.9 414.2 Pre-tax income (loss) from continuing operations $ (44.2) $ 24.1 $ 47.2 $ (58.1) $ (31.0) Millions HG Global/ BAM Ark Kudu Other Operations Total Three Months Ended September 30, 2021 Earned insurance premiums $ 6.7 $ 213.4 $ — $ — $ 220.1 Net investment income 4.4 .6 9.5 5.0 19.5 Net realized and unrealized investment (4.0) .3 18.9 15.3 30.5 Net realized and unrealized investment gains — — — (396.8) (396.8) Commission revenues — — — 2.4 2.4 Other revenues .3 3.4 .1 28.1 31.9 Total revenues 7.4 217.7 28.5 (346.0) (92.4) Losses and loss adjustment expenses — 129.2 — — 129.2 Insurance and reinsurance acquisition expenses 3.0 53.7 — — 56.7 Cost of sales — — — 24.0 24.0 General and administrative expenses 12.4 21.8 3.3 14.4 51.9 Amortization of other intangible assets — — — 2.0 2.0 Interest expense — 2.1 1.9 .4 4.4 Total expenses 15.4 206.8 5.2 40.8 268.2 Pre-tax income (loss) from continuing operations $ (8.0) $ 10.9 $ 23.3 $ (386.8) $ (360.6) Millions HG Global/ BAM Ark Kudu Other Operations Total Nine Months Ended September 30, 2022 Earned insurance premiums $ 26.0 $ 757.8 $ — $ — $ 783.8 Net investment income 15.1 9.7 41.2 13.6 79.6 Net realized and unrealized investment (114.0) (76.5) 45.8 2.8 (141.9) Net realized and unrealized investment gains — — — (113.3) (113.3) Commission revenues — — — 8.7 8.7 Other revenues 3.7 10.1 — 89.6 103.4 Total revenues (69.2) 701.1 87.0 1.4 720.3 Loss and loss adjustment expenses — 456.2 — — 456.2 Insurance and reinsurance acquisition expenses 9.5 174.9 — — 184.4 Cost of sales — — — 68.8 68.8 General and administrative expenses 49.5 79.8 10.2 118.9 258.4 Amortization of other intangible assets — — .2 3.2 3.4 Interest expense 5.4 10.6 10.3 1.2 27.5 Total expenses 64.4 721.5 20.7 192.1 998.7 Pre-tax income (loss) from continuing operations $ (133.6) $ (20.4) $ 66.3 $ (190.7) $ (278.4) Millions HG Global/ BAM Ark Kudu Other Operations Total Nine Months Ended September 30, 2021 Earned insurance premiums $ 19.6 $ 435.8 $ — $ — $ 455.4 Net investment income 13.2 1.8 26.1 16.1 57.2 Net realized and unrealized investment (15.6) 10.3 62.5 34.0 91.2 Net realized and unrealized investment gains — — — (325.5) (325.5) Commission revenues — — — 7.0 7.0 Other revenues .9 9.4 .2 57.6 68.1 Total revenues 18.1 457.3 88.8 (210.8) 353.4 Losses and loss adjustment expenses — 247.8 — — 247.8 Insurance and reinsurance acquisition expenses 6.5 124.4 — — 130.9 Cost of sales — — — 45.9 45.9 General and administrative expenses 42.7 84.4 9.0 79.4 215.5 Amortization of other intangible assets — — .2 2.9 3.1 Interest expense — 4.5 9.2 1.1 14.8 Total expenses 49.2 461.1 18.4 129.3 658.0 Pre-tax income (loss) from continuing operations $ (31.1) $ (3.8) $ 70.4 $ (340.1) $ (304.6)

Equity-Method Eligible Investme

Equity-Method Eligible Investments	9 Months Ended
	Sep. 30, 2022
Equity Method Investments and Joint Ventures [Abstract]
Equity-Method Eligible Investments	Equity-Method Eligible Investments White Mountains’s equity method eligible investments include White Mountains’s investment in MediaAlpha, certain other unconsolidated entities, including Kudu’s Participation Contracts, 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 September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Ownership Interest Carrying Value Ownership Interest Carrying Value Kudu Participation Contracts (1) 4.1 - 33.0% $ 813.2 3.2 - 32.0% $ 669.5 Investment in MediaAlpha 27.4 % 148.2 28.0 % 261.6 PassportCard/DavidShield 53.8 % 132.0 53.8 % 120.0 Elementum Holdings, L.P. 29.7 % 45.0 29.7 % 45.0 Other equity method eligible investments, at fair value Under 50.0% 102.7 Under 50.0% 109.3 Other equity method eligible investments, at fair value 50.0% and over 27.7 50.0% and over 17.8 (1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are non-controlling equity interests in the form of revenue and earnings participation contracts. For the three and nine months ended September 30, 2022, White Mountains received dividend and income distributions from equity method eligible investments of $16.1 million and $42.9 million, which were recorded within net investment income in the consolidated statements of operations. For the three and nine months ended September 30, 2021, White Mountains received dividend and income distributions from equity method eligible investments of $13.0 million, and $37.7 million, which were recorded within net investment income in the consolidated statements of operations. Subsequent to 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 White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet. See Note 2 — “Significant Transactions.” For the nine months ended September 30, 2021, MediaAlpha was considered a significant subsidiary. The following tables present summarized financial information for MediaAlpha as of September 30, 2022 and December 31, 2021 and for the three and nine months ended September 30, 2022 and 2021: Millions September 30, 2022 December 31, 2021 Balance sheet data: Total assets $ 265.2 $ 289.8 Total liabilities $ 333.6 $ 351.4 Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Income statement data: Total revenues $ 89.0 $ 152.7 $ 335.1 $ 483.7 Total expenses $ 110.2 $ 157.0 $ 379.2 $ 488.2 Net income (loss) $ (21.2) $ (4.3) $ (44.1) $ (4.5)

Fair Value of Financial Instrum

Fair Value of Financial Instruments	9 Months Ended
	Sep. 30, 2022
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 tables presents the fair value and carrying value of these financial instruments as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Carrying Fair Carrying HG Global Senior Notes $ 146.1 $ 146.4 $ — $ — Ark 2007 Subordinated Notes $ 26.2 $ 30.0 $ 27.6 $ 30.0 Ark 2021 Subordinated Notes $ 149.4 $ 150.0 $ 162.8 $ 155.9 Kudu Credit Facility $ 265.5 $ 253.5 $ 246.8 $ 218.2 Other Operations debt $ 36.8 $ 35.6 $ 17.7 $ 16.8 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	9 Months Ended
	Sep. 30, 2022
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	9 Months Ended
	Sep. 30, 2022
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. Sirius Group On April 18, 2016, White Mountains completed the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) to CM International Pte. Ltd. and CM Bermuda Limited (collectively “CMI”). In connection with the sale, White Mountains indemnified Sirius Group against the loss of certain interest deductions claimed by Sirius Group related to periods prior to the sale of Sirius Group to CMI that had been disputed by the Swedish Tax Agency. In late October 2018, the Swedish Administrative Court ruled against Sirius Group on its appeal of the Swedish Tax Agency’s denial of these interest deductions. As a result, in 2018 White Mountains recorded a loss of $17.3 million within net gain (loss) on sale of discontinued operations reflecting the value of these interest deductions. As of December 31, 2020, White Mountains’s liability related to the tax indemnification provided in connection with the sale of Sirius Group in 2016 was $18.7 million. In April 2021, the Swedish Tax Agency informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal and that the interest deductions should not be disallowed. In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor. For the nine months ended September 30, 2021, White Mountains recorded a gain of $17.6 million in discontinued operations to reverse the liability accrued as of December 31, 2020 and $1.1 million gain related to foreign currency translation. Summary of Reclassified Balances and Related Items Net Assets Held for Sale The following summarizes the assets and liabilities associated with NSM Group classified as held for sale. As of December 31, 2021, the amounts presented exclude $16.1 million of insurance licenses, investments and cash classified as assets held for sale related to one of the Other Operating Businesses. Millions December 31, 2021 Assets held for sale Short-term investments, at fair value $ 7.8 Cash (restricted $89.2) 111.6 Premiums and commissions receivable 85.0 Goodwill and other intangible assets 725.4 Other assets 59.2 Total assets held for sale $ 989.0 Liabilities held for sale Debt $ 272.1 Premiums payable 135.9 Contingent consideration 6.8 Other liabilities 80.5 Total liabilities held for sale 495.3 Net assets held for sale $ 493.7 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 and nine months ended September 30, 2022 and 2021: Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 888.2 $ (371.4) $ 752.4 $ (308.2) Less: net income (loss) from continuing operations $ (23.6) $ (389.2) $ (252.3) $ (356.8) Less: net (income) loss from continuing operations attributable to $ 18.8 $ 12.5 $ 102.2 $ 52.6 Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders (1) $ 893.0 $ 5.3 $ 902.5 $ (4.0) Allocation of earnings to participating restricted common shares (2) (11.8) (.1) (10.8) — Basic and diluted earnings per share numerators (3) $ 881.2 $ 5.2 $ 891.7 $ (4.0) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (4) (38.3) (37.8) (35.5) (36.0) Basic earnings per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (4) (38.3) (37.8) (35.5) (36.0) Diluted earnings per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Basic and diluted earnings (losses) per share (in dollars) - $ 308.59 $ 1.72 $ 304.97 $ (1.29) (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - Sirius Group and net (income) loss from discontinued operations attributable to non-controlling interests. (2) Restricted shares issued by White Mountains receive dividends and are therefore 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 and nine months ended September 30, 2022 and 2021. (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)	9 Months Ended
	Sep. 30, 2022
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 White Mountains has determined its reportable segments based on the nature of the underlying businesses, the manner in which the Company’s subsidiaries and affiliates are organized and managed and the organization of the financial information provided to the chief operating decision maker to assess performance and make decisions regarding allocation of resources. As of September 30, 2022, White Mountains’s reportable segments were HG Global/BAM, Ark and Kudu, with our remaining operating businesses, holding companies and other assets included in Other Operations. The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “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 September 30, 2022 and December 31, 2021, 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 for which White Mountains is the primary beneficiary. BAM’s results are all attributed to non-controlling interests. The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark is a specialty property and casualty insurance and reinsurance company that offers a wide range of niche insurance and reinsurance products, including property, marine & energy, specialty, accident & health and casualty. 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”). See Note 2 — “Significant Transactions. ” As of September 30, 2022 and December 31, 2021, 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 are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.
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 previously announced 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 of December 31, 2021, White Mountains owned 96.5% of the basic units outstanding of NSM (87.3% on a fully diluted, fully converted basis). 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 Transactions (Table

Significant Transactions (Tables)	9 Months Ended
	Sep. 30, 2022
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Schedule of Recognized Identified Assets Acquired and Liabilities Assumed	The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date: Millions As of January 1, 2021 Investments $ 594.3 Cash 52.0 (1) Reinsurance recoverables 433.4 Insurance premiums receivable 236.7 Ceded unearned premiums 170.2 Value of in-force business acquired 71.7 Other assets 88.9 Loss and loss adjustment expense reserves (696.0) Unearned insurance premiums (326.1) Debt (46.4) Ceded reinsurance payable (528.3) Other liabilities (25.9) Net tangible assets acquired 24.5 Goodwill 116.8 Other intangible assets - syndicate underwriting capacity 175.7 Deferred tax liability on other intangible assets (33.4) Net assets acquired $ 283.6 (1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction. The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022: $ in Millions Goodwill and Other intangible asset (1) Acquisition Date Acquisition of subsidiary/ asset Ark $ 292.5 January 1, 2021 Other Operations $ 86.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

Investment Securities (Tables)

Investment Securities (Tables)	9 Months Ended
	Sep. 30, 2022
Investments, Debt and Equity Securities [Abstract]
Pre-tax net investment income	The following table presents pre-tax net investment income for the three and nine months ended September 30, 2022 and 2021: Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Fixed maturity investments $ 11.1 $ 8.2 $ 28.6 $ 21.9 Short-term investments 6.7 — 7.2 .5 Common equity securities .1 .1 .2 .1 Other long-term investments 17.1 12.0 45.9 37.1 Amount attributable to TPC Providers (.3) (.2) (.8) (.8) Total investment income 34.7 20.1 81.1 58.8 Third-party investment expenses (.8) (.6) (1.5) (1.6) Net investment income, pre-tax $ 33.9 $ 19.5 $ 79.6 $ 57.2
Schedule of net realized and unrealized investment gains and losses	The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Realized investment gains (losses) Fixed maturity investments $ (4.9) $ 1.0 $ (10.8) $ 3.8 Short-term investments (.1) (.3) (.4) — Common equity securities — — — .4 Investment in MediaAlpha — — — 160.3 Other long-term investments 3.4 9.2 24.1 0.9 Net realized investment gains (losses) (1.6) 9.9 12.9 165.4 Unrealized investment gains (losses) Fixed maturity investments (58.8) (7.9) (192.9) (27.0) Short-term investments (2.1) — (2.6) — Common equity securities 4.3 1.6 (6.3) 7.3 Investment in MediaAlpha (18.6) (396.8) (113.3) (485.8) Other long-term investments 27.5 28.4 40.8 112.3 Net unrealized investment gains (losses) (47.7) (374.7) (274.3) (393.2) Net realized and unrealized investment gains (losses), before amount attributable to TPC providers (1) (49.3) (364.8) (261.4) (227.8) Amount attributable to TPC Providers 1.3 (1.7) 6.2 (6.5) Net realized and unrealized investment gains (losses) $ (48.0) $ (366.5) $ (255.2) $ (234.3) Fixed maturity and short-term investments Net realized and unrealized investment gains (losses) $ (65.9) $ (7.2) $ (206.7) $ (23.2) Less: net realized and unrealized gains (losses) on investment .1 (5.7) (3.0) (6.9) Net unrealized investment gains (losses) on investment $ (66.0) $ (1.5) $ (203.7) $ (16.3) Common equity securities and investment in MediaAlpha Net realized and unrealized investment gains (losses) on common $ 4.3 $ 1.6 $ (6.3) $ 7.7 Net realized and unrealized investment gains (losses) from (18.6) (396.8) (113.3) (325.5) Total net realized and unrealized investment gains (losses) (14.3) (395.2) (119.6) (317.8) Less: net realized and unrealized gains (losses) on investment — .4 — 20.3 Net unrealized investment gains (losses) on investment $ (14.3) $ (395.6) $ (119.6) $ (338.1) (1) For the three months ended September 30, 2022 and 2021, includes $(22.6) and $(7.0) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2022 and 2021, includes $(44.4) and $(7.4) of realized and unrealized investment gains (losses) related to foreign currency exchange.
Net unrealized investment gains (losses) for Level 3 investments	The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and nine months ended September 30, 2022 and 2021 for investments still held at the end of the period: Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Other long-term investments $ 40.8 $ 26.5 $ 57.7 $ 75.5 Total net unrealized investment gains, pre-tax - Level 3 investments $ 40.8 $ 26.5 $ 57.7 $ 75.5
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 September 30, 2022 and December 31, 2021: September 30, 2022 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 227.9 $ — $ (11.0) $ — $ 216.9 Debt securities issued by corporations 1,068.8 — (91.2) (3.1) 974.5 Municipal obligations 289.3 — (24.4) — 264.9 Mortgage and asset-backed securities 278.3 — (37.6) — 240.7 Collateralized loan obligations 169.7 — (7.6) (4.8) 157.3 Total fixed maturity investments $ 2,034.0 $ — $ (171.8) $ (7.9) $ 1,854.3 December 31, 2021 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 212.1 $ .5 $ (1.1) $ — $ 211.5 Debt securities issued by corporations 993.3 8.7 (8.7) (.4) 992.9 Municipal obligations 276.4 16.8 (1.3) — 291.9 Mortgage and asset-backed securities 277.2 2.9 (2.5) — 277.6 Collateralized loan obligations 136.5 — (.4) (1.1) 135.0 Total fixed maturity investments $ 1,895.5 $ 28.9 $ (14.0) $ (1.5) $ 1,908.9 The 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 September 30, 2022 and December 31, 2021: September 30, 2022 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 324.2 $ 32.7 $ (8.7) $ (15.4) $ 332.8 Investment in MediaAlpha $ — $ 148.2 $ — $ — $ 148.2 Other long-term investments $ 1,390.7 $ 345.0 $ (90.0) $ (23.0) $ 1,622.7 December 31, 2021 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 236.3 $ 16.1 $ — $ (1.3) $ 251.1 Investment in MediaAlpha $ — $ 261.6 $ — $ — $ 261.6 Other long-term investments $ 1,186.7 $ 239.0 $ (44.1) $ (3.8) $ 1,377.8
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 September 30, 2022. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties. September 30, 2022 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 207.5 $ 203.8 Due after one year through five years 917.9 849.4 Due after five years through ten years 354.8 309.3 Due after ten years 105.8 93.8 Mortgage and asset-backed securities and collateralized loan obligations 448.0 398.0 Total fixed maturity investments $ 2,034.0 $ 1,854.3
Fair value measurements by level, investment securities	The following tables present White Mountains’s fair value measurements for investments as of September 30, 2022 and December 31, 2021 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate. September 30, 2022 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 216.9 $ 216.9 $ — $ — Debt securities issued by corporations: Financials 269.0 — 269.0 — Consumer 181.4 — 181.4 — Industrial 115.8 — 115.8 — Healthcare 114.3 — 114.3 — Technology 110.8 — 110.8 — Utilities 75.9 — 75.9 — Communications 49.1 — 49.1 — Energy 36.1 — 36.1 — Materials 22.1 — 22.1 — Total debt securities issued by corporations 974.5 — 974.5 — Municipal obligations 264.9 — 264.9 — Mortgage and asset-backed securities 240.7 — 240.7 — Collateralized loan obligations 157.3 — 157.3 — Total fixed maturity investments 1,854.3 216.9 1,637.4 — Short-term investments 1,196.4 1,196.4 — — Common equity securities (1) 332.8 46.4 286.4 — Investment in MediaAlpha 148.2 148.2 — — Other long-term investments 1,058.0 — 13.9 1,044.1 Other long-term investments — NAV (2) 564.7 — — — Total other long-term investments 1,622.7 — 13.9 1,044.1 Total investments $ 5,154.4 $ 1,607.9 $ 1,937.7 $ 1,044.1 (1) Consist of investments in exchange traded funds (“ETFs”) and 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 at net asset value (“NAV”) using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2021 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 211.5 $ 211.5 $ — $ — Debt securities issued by corporations: Financials 264.2 — 264.2 — Consumer 178.1 — 178.1 — Technology 117.9 — 117.9 — Industrial 112.9 — 112.9 — Healthcare 112.8 — 112.8 — Utilities 70.9 — 70.9 — Communications 56.0 — 56.0 — Energy 48.0 — 48.0 — Materials 32.1 — 32.1 — Total debt securities issued by corporations 992.9 — 992.9 — Municipal obligations 291.9 — 291.9 — Mortgage and asset-backed securities 277.6 — 277.6 — Collateralized loan obligations 135.0 — 135.0 — Total fixed maturity investments 1,908.9 211.5 1,697.4 — Short-term investments 465.9 465.9 — — Common equity securities (1) 251.1 — 251.1 — Investment in MediaAlpha 261.6 261.6 — — Other long-term investments 895.3 — 4.7 890.6 Other long-term investments — NAV (2) 482.5 — — — Total other long-term investments 1,377.8 — 4.7 890.6 Total investments $ 4,265.3 $ 939.0 $ 1,953.2 $ 890.6 (1) Consist of investments in listed funds that predominantly invest in international equities. (2) Consists of private equity funds and hedge funds, a bank loan fund, Lloyd’s trust deposits and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
Debt securities issued by corporations, credit ratings	The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of September 30, 2022 and December 31, 2021: Fair Value at Millions September 30, 2022 December 31, 2021 AAA $ 11.2 $ 12.0 AA 90.5 85.0 A 524.0 490.4 BBB 343.0 396.8 Other 5.8 8.7 Debt securities issued by corporations (1) $ 974.5 $ 992.9 (1) Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.
Mortgage-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 September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 114.1 $ 114.1 $ — $ 125.4 $ 125.4 $ — FHLMC 74.5 74.5 — 90.5 90.5 — GNMA 28.9 28.9 — 40.1 40.1 — Total agency (1) 217.5 217.5 — 256.0 256.0 — Non-agency: Residential .4 .4 — .5 .5 — Total non-agency .4 .4 — .5 .5 — Total mortgage-backed securities 217.9 217.9 — 256.5 256.5 — Other asset-backed securities: Credit card receivables 11.9 11.9 — 12.3 12.3 — Vehicle receivables 10.9 10.9 — 8.8 8.8 — Total other asset-backed securities 22.8 22.8 — 21.1 21.1 — Total mortgage and asset-backed securities 240.7 240.7 — 277.6 277.6 — Collateralized loan obligations 157.3 157.3 — 135.0 135.0 — Total mortgage and asset-backed securities and collateralized loan obligations $ 398.0 $ 398.0 $ — $ 412.6 $ 412.6 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).
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 September 30, 2022 and December 31, 2021: Fair Value at Millions September 30, 2022 December 31, 2021 Kudu’s Participation Contracts $ 813.2 $ 669.5 PassportCard/DavidShield 132.0 120.0 Elementum Holdings, L.P. 45.0 45.0 Other unconsolidated entities (1) 37.0 34.4 Total unconsolidated entities 1,027.2 868.9 Private equity funds and hedge funds 239.8 153.8 Bank loan fund 155.7 163.0 Lloyd’s trust deposits 117.8 113.8 ILS funds 49.4 51.9 Private debt investments 13.0 14.1 Other 19.8 12.3 Total other long-term investments $ 1,622.7 $ 1,377.8 (1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, convertible preferred securities, limited liability company units and Simple Agreement for Future Equity (“SAFE”) investments.
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 September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 102.9 $ 45.1 $ 69.8 $ 11.8 Financial services 77.9 54.9 67.7 29.3 Real estate 4.3 2.5 4.3 2.9 Total private equity funds 185.1 102.5 141.8 44.0 Hedge funds Long/short equity financials and business services 49.3 — — — European small/mid cap 5.4 — 12.0 — Total hedge funds 54.7 — 12.0 — Total private equity funds and hedge funds included in other long-term investments $ 239.8 $ 102.5 $ 153.8 $ 44.0
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 September 30, 2022: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $27.5 $19.0 $135.4 $3.2 $185.1
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 nine months ended September 30, 2022 and 2021: Level 3 Investments Millions Other Long-term Other Long-term Balance at December 31, 2021 $ 890.6 Balance at December 31, 2020 $ 614.2 Net realized and unrealized gains 57.3 Net realized and unrealized gains 79.0 Amortization/accretion — Amortization/accretion — Purchases 127.9 Purchases 143.6 Sales (31.7) Sales (31.9) Effect of Ark Transaction — Effect of Ark Transaction 9.6 Transfers in — Transfers in — Transfers out — Transfers out — Balance at September 30, 2022 $ 1,044.1 Balance at September 30, 2021 $ 814.5
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 September 30, 2022 and December 31, 2021. The tables below exclude $42.9 million and $46.7 million of Level 3 other long-term investments generally valued based on recent or expected transaction prices. The fair value of investments in private equity funds and hedge funds, bank loan funds, Lloyd’s trust deposits and ILS funds are generally estimated using the NAV of the funds. $ in Millions September 30, 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 $813.2 17% - 24% 7x - 16x PassportCard/DavidShield Discounted cash flow $132.0 24% 4% Elementum Holdings, L.P. Discounted cash flow $45.0 18% 4% Private debt investments Discounted cash flow $11.0 10% 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 20% and 9.7x. (4) As of September 30, 2022, three of Kudu’s Participation Contracts with a total fair value of $312.4 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. (5) In 2022, Kudu deployed a total of $97.9 into new and existing Kudu Participation Contracts, including Gramercy Funds Management, GenTrust, EC Management Services, and TK Partners. (6) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements. $ in Millions December 31, 2021 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (6) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (6) Kudu’s Participation Contracts (3)(4)(5) Discounted cash flow $669.5 18% - 23% 7x - 13x PassportCard/DavidShield Discounted cash flow $120.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $45.0 17% 4% Private debt investments Discounted cash flow $9.4 8% 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 20% and 10x. (4) In 2021, Kudu deployed a total of $223.4 into new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management. (5) As of December 31, 2021, one of Kudu’s Participation Contracts with a total fair value of $78.8 was valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. (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)	9 Months Ended
	Sep. 30, 2022
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, by reportable segment as of September 30, 2022 and December 31, 2021: $ in Millions Weighted Average Economic September 30, 2022 December 31, 2021 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 51.1 — 51.1 17.9 — 17.9 Total goodwill 175.5 — 175.5 142.3 — 142.3 Other intangible assets: Ark Underwriting capacity N/A 175.7 — 175.7 175.7 — 175.7 Kudu Trade names 7 2.2 1.1 1.1 2.2 .9 1.3 Other Operations Trade names 15.9 17.9 2.4 15.5 8.2 1.5 6.7 Customer relationships 12.4 29.5 6.6 22.9 18.8 4.5 14.3 Other 12.1 2.8 .3 2.5 .3 .1 .2 Subtotal 50.2 9.3 40.9 27.3 6.1 21.2 Total other intangible assets 228.1 10.4 217.7 205.2 7.0 198.2 Total goodwill and other intangible assets $ 403.6 $ 10.4 393.2 $ 347.5 $ 7.0 340.5 Goodwill and other intangible assets attributed to (103.1) (91.8) Goodwill and other intangible assets included in White Mountains’s $ 290.1 $ 248.7 The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, 2022 2021 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 201.8 $ 196.2 $ 398.0 $ 151.5 $ 201.1 $ 352.6 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (22.9) 22.9 — (9.3) 9.3 — Measurement period adjustments (2) (3.4) — (3.4) (.4) — (.4) Amortization — (1.4) (1.4) — (2.0) (2.0) Ending balance $ 175.5 $ 217.7 $ 393.2 $ 141.8 $ 208.4 $ 350.2 (1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the three months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations. Nine Months Ended September 30, 2022 2021 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 142.3 $ 198.2 $ 340.5 $ 19.2 $ 26.4 $ 45.6 Ark Transaction — — — 116.8 175.7 292.5 Acquisition of businesses (1) 59.5 — 59.5 15.8 — 15.8 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (22.9) 22.9 — (9.3) 9.3 — Measurement period adjustments (2) (3.4) (3.4) (.7) .1 (.6) Amortization — (3.4) (3.4) — (3.1) (3.1) Ending balance $ 175.5 $ 217.7 $ 393.2 $ 141.8 $ 208.4 $ 350.2 (1) Relates to acquisitions within Other Operations. The relative fair values of goodwill and other intangible assets recognized in connection with acquisitions during 2022 had not yet been finalized as of the end of the period. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the nine months ended September 30, 2022 and 2021, adjustments relate to acquisitions within Other Operations.
Schedule of Recognized Identified Assets Acquired and Liabilities Assumed	The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date: Millions As of January 1, 2021 Investments $ 594.3 Cash 52.0 (1) Reinsurance recoverables 433.4 Insurance premiums receivable 236.7 Ceded unearned premiums 170.2 Value of in-force business acquired 71.7 Other assets 88.9 Loss and loss adjustment expense reserves (696.0) Unearned insurance premiums (326.1) Debt (46.4) Ceded reinsurance payable (528.3) Other liabilities (25.9) Net tangible assets acquired 24.5 Goodwill 116.8 Other intangible assets - syndicate underwriting capacity 175.7 Deferred tax liability on other intangible assets (33.4) Net assets acquired $ 283.6 (1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction. The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through September 30, 2022: $ in Millions Goodwill and Other intangible asset (1) Acquisition Date Acquisition of subsidiary/ asset Ark $ 292.5 January 1, 2021 Other Operations $ 86.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and exclude the effect of foreign currency translation subsequent to the acquisition date.

Loss and Loss Adjustment Expe_2

Loss and Loss Adjustment Expense Reserves (Tables)	9 Months Ended
	Sep. 30, 2022
Insurance Loss Reserves [Abstract]
Schedule of Liability for Unpaid Claims and Claims Adjustment Expense	The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Gross beginning balance $ 1,022.1 $ 760.0 $ 894.7 $ 696.0 Less: beginning reinsurance recoverable on unpaid losses (1) (375.5) (425.3) (428.9) (433.4) Net loss and LAE reserves 646.6 334.7 465.8 262.6 Loss and LAE incurred relating to: Current year losses 222.9 141.9 491.8 269.0 Prior year losses (9.2) (12.7) (35.6) (21.2) Net incurred losses and LAE 213.7 129.2 456.2 247.8 Loss and LAE paid relating to: Current year losses (6.1) (9.0) (20.8) (11.5) Prior year losses (37.0) (20.3) (130.8) (62.1) Net paid loss and LAE (43.1) (29.3) (151.6) (73.6) Change in TPC Providers’ participation (2) — — 57.5 (2.2) Foreign currency translation and other adjustments (9.2) (1.2) (19.9) (1.2) Net ending balance 808.0 433.4 808.0 433.4 Plus: ending reinsurance recoverable on unpaid losses (3) 521.4 457.5 521.4 457.5 Gross ending balance $ 1,329.4 $ 890.9 $ 1,329.4 $ 890.9 (1) The beginning reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $182.4 and $314.6 for the three months ended September 30, 2022 and 2021 and $276.8 and $319.2 for the nine months ended September 30, 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 (“RITC”) process. (3) The ending reinsurance recoverable on unpaid losses includes amounts attributable to TPC Providers of $168.0 and $299.9 as of September 30, 2022 and 2021.

Third-Party Reinsurance (Tables

Third-Party Reinsurance (Tables)	9 Months Ended
	Sep. 30, 2022
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 Ark for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Written premiums: Gross $ 215.5 $ 162.4 $ 1,252.5 $ 895.0 Ceded (22.9) (41.5) (246.0) (169.5) Net written premiums $ 192.6 $ 120.9 $ 1,006.5 $ 725.5 Earned premiums: Gross $ 454.9 $ 284.5 $ 966.6 $ 622.0 Ceded (108.8) (71.1) (208.8) (186.2) Net earned premiums $ 346.1 $ 213.4 $ 757.8 $ 435.8 Losses and loss adjustment expenses: Gross $ 391.4 $ 193.5 $ 712.9 $ 372.7 Ceded (177.7) (64.3) (256.7) (124.9) Net losses and loss adjustment expenses $ 213.7 $ 129.2 $ 456.2 $ 247.8 The following table provides a listing of Ark’s remaining gross and net reinsurance recoverables, excluding amounts attributable to TPC Providers, by the reinsurer’s A.M. Best Company, Inc (“A.M. Best”) rating and the percentage of total recoverables as of September 30, 2022: $ in Millions As of September 30, 2022 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 178.3 $ — $ 178.3 67.7 % A- to A 78.9 — 78.9 29.9 B++ or lower and not rated 125.7 119.4 6.3 2.4 Total $ 382.9 $ 119.4 $ 263.5 100.0 % (1) A.M. Best ratings as detailed above are: “A+ or better” (Superior) “A- to A” (Excellent), “B++” (Good).

Debt (Tables)

Debt (Tables)	9 Months Ended
	Sep. 30, 2022
Debt Disclosure [Abstract]
Schedule of debt outstanding	The following table presents White Mountains’s debt outstanding as of September 30, 2022 and December 31, 2021: $ in Millions September 30, Effective (1) December 31, Effective (1) HG Global Senior Notes $ 150.0 8.6% $ — N/A Unamortized discount and issuance cost (3.6) — HG Global Senior Notes, carrying value 146.4 — Ark 2007 Subordinated Notes, carrying value 30.0 30.0 Ark 2021 Notes Tranche 1 37.6 44.2 Ark 2021 Notes Tranche 2 47.0 47.0 Ark 2021 Notes Tranche 3 70.0 70.0 Unamortized issuance cost (4.6) (5.3) Ark 2021 Subordinated Notes, carrying value 150.0 155.9 Total Ark Subordinated Notes, carrying value 180.0 7.3% 185.9 6.9% Kudu Credit Facility 260.4 5.6% 225.4 4.3% Unamortized issuance cost (6.9) (7.2) Kudu Credit Facility, carrying value 253.5 218.2 Other Operations debt 36.4 7.1% 17.1 7.5% Unamortized issuance cost (.8) (.3) Other Operations debt, carrying value 35.6 16.8 Total debt $ 615.5 $ 420.9 (1) Effective rate includes the effect of the amortization of debt issuance costs. The following table presents the change in debt under the Kudu Bank Facility and Kudu Credit Facility for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Kudu Bank Facility Beginning balance $ — $ — $ — $ 89.2 Term loans Borrowings — — — 3.0 Repayments — — — (92.2) Ending balance $ — $ — $ — $ — Kudu Credit Facility Beginning balance $ 260.4 $ 203.0 $ 225.4 $ — Term loans Borrowings — — 35.0 203.0 Repayments — — — — Ending balance $ 260.4 $ 203.0 $ 260.4 $ 203.0

Municipal Bond Guarantee Insu_2

Municipal Bond Guarantee Insurance (Tables)	9 Months Ended
	Sep. 30, 2022
Guarantees [Abstract]
Schedule of Municipal Bond Guarantee Insured Obligations	The following table presents a schedule of BAM’s insured obligations as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Contracts outstanding 13,094 12,350 Remaining weighted average contract period outstanding (in years) 10.8 10.8 Contractual debt service outstanding (in millions): Principal $ 98,619.0 $ 89,196.5 Interest 47,595.0 41,486.5 Total debt service outstanding $ 146,214.0 $ 130,683.0 Gross unearned insurance premiums (in millions) $ 286.7 $ 266.3
Financial Guarantee Insurance Contracts, Premium Received over Contract Period	The following table presents a schedule of BAM’s future premium revenues as of September 30, 2022: Millions September 30, 2022 October 1, 2022 - December 31, 2022 $ 6.9 January 1, 2023 - March 31, 2023 6.8 April 1, 2023 - June 30, 2023 6.7 July 1, 2023 - September 30, 2023 6.6 October 1, 2023 - December 31, 2023 6.4 Total 2023 26.5 2024 24.9 2025 23.2 2026 21.6 2027 20.1 2028 and thereafter 163.5 Total gross unearned insurance premiums $ 286.7
Schedule of Net Written Premiums	The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Written premiums: Direct $ 18.4 $ 12.8 $ 44.9 $ 34.5 Assumed 1.3 — 1.3 4.5 Gross written premiums (1) $ 19.7 $ 12.8 $ 46.2 $ 39.0 Earned premiums: Direct $ 6.5 $ 5.9 $ 22.0 $ 16.8 Assumed .6 .8 4.0 2.8 Gross earned premiums (1) $ 7.1 $ 6.7 $ 26.0 $ 19.6 (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)	9 Months Ended
	Sep. 30, 2022
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 and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 888.2 $ (371.4) $ 752.4 $ (308.2) Less: total income (loss) from discontinued operations, net of tax (1) 893.1 5.3 903.2 (5.1) Less: net (income) loss from discontinued operations attributable $ (.1) $ — $ (.7) $ 1.1 Net income (loss) from continuing operations attributable to $ (4.8) $ (376.7) $ (150.1) $ (304.2) Allocation of (earnings) losses to participating restricted common shares (2) .1 4.6 1.8 3.5 Basic and diluted earnings (losses) per share numerators $ (4.7) $ (372.1) $ (148.3) $ (300.7) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (3) (38.3) (37.8) (35.5) (36.0) Basic earnings (losses) per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (3) (38.3) (37.8) (35.5) (36.0) Diluted earnings (losses) per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Basic and diluted earnings per share (in dollars) - continuing Distributed earnings - dividends declared and paid $ — $ — $ 1.00 $ 1.00 Undistributed earnings (losses) (1.66) (121.90) (51.73) (99.16) Basic and diluted earnings (losses) per share $ (1.66) $ (121.90) $ (50.73) $ (98.16) (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group and net gain (loss) from sale of discontinued operations, net of tax - Sirius Group. See Note 19 — “Held for Sale and Discontinued Operations. ” (2) Restricted shares issued by White Mountains receive dividends and are therefore 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 and nine months ended September 30, 2022 and 2021. See Note 19 — “Held for Sale and Discontinued Operations.” Three Months Ended Nine Months Ended September 30, September 30, Millions 2022 2021 2022 2021 Undistributed net earnings (losses) - continuing operations: Net income (losses) attributable to White Mountains’s common $ (4.7) $ (372.1) $ (148.3) $ (300.7) Dividends declared, net of restricted common share amounts (1) — — (3.0) (3.1) Total undistributed net earnings (losses), net of restricted $ (4.7) $ (372.1) $ (151.3) $ (303.8) (1) Restricted shares issued by White Mountains receive dividends and are therefore considered participating securities.

Employee Share-Based Incentiv_2

Employee Share-Based Incentive Compensation Plans (Tables)	9 Months Ended
	Sep. 30, 2022
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 and nine months ended September 30, 2022 and 2021 for performance shares granted under the WTM Incentive Plan: Three Months Ended September 30, Nine Months Ended September 30, 2022 2021 2022 2021 Millions, except share amounts Target Performance Accrued Target Performance Accrued Target Performance Accrued Target Performance Accrued Beginning of period 39,449 $ 41.2 41,252 $ 45.7 40,828 $ 42.2 42,458 $ 56.3 Shares paid (1) — — (219) (.6) (14,625) (26.4) (14,336) (35.2) New grants — — — — 13,225 — 13,475 — Forfeitures and cancellations (2) — (.1) (205) .2 21 (.2) (769) .4 Expense recognized — 11.9 — (6.5) — 37.4 — 17.3 End of period 39,449 $ 53.0 40,828 $ 38.8 39,449 $ 53.0 40,828 $ 38.8 (1) Includes WTM performance share payments in 2022 for the 2019-2021 performance cycle, which were paid in March 2022 at 172% of target and WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in March 2021 at 200% 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 September 30, 2022 for each performance cycle: Nine Months Ended September 30, 2022 Millions, except share amounts Target Performance Accrued Performance cycle: 2020 – 2022 13,350 $ 31.9 2021 – 2023 13,475 14.7 2022 – 2024 13,225 7.2 Sub-total 40,050 53.8 Assumed forfeitures (601) (.8) September 30, 2022 39,449 $ 53.0
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 for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, 2022 2021 2022 2021 Millions, except share amounts Restricted Unamortized Restricted Unamortized Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,350 $ 23.0 38,280 $ 23.2 37,850 $ 15.9 43,105 $ 15.2 Issued — — — — 13,225 13.8 13,475 16.1 Vested — — (219) — (12,725) — (17,936) — Forfeited — — (211) (.2) — — (794) (.8) Expense recognized — (3.8) — (3.6) — (10.5) — (11.1) End of period 38,350 $ 19.2 37,850 $ 19.4 38,350 $ 19.2 37,850 $ 19.4

Leases (Tables)

Leases (Tables)	9 Months Ended
	Sep. 30, 2022
Leases [Abstract]
Summary of Lease Expense	The following table summarizes net lease expense recognized in White Mountains’s consolidated statements of operations for the three and nine months ended September 30, 2022 and 2021: Millions Three Months Ended September 30, Nine Months Ended September 30, Lease Cost 2022 2021 2022 2021 Lease cost $ 1.9 $ 1.9 $ 5.9 $ 4.8 Less: sublease income .2 .1 .5 .3 Net lease cost $ 1.7 $ 1.8 $ 5.4 $ 4.5
Schedule of Future Maturities of Operating Lease Liabilities, Lessee	The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2022: Millions As of September 30, 2022 Remainder of 2022 $ 1.7 2023 8.1 2024 7.1 2025 4.9 2026 2.6 Thereafter 5.0 Total undiscounted lease payments 29.4 Less: present value adjustment 2.9 Operating lease liabilities $ 26.5
Schedule of Right-of-Use Assets and Lease Liabilities	The following tables present lease related assets and liabilities by reportable segment as of September 30, 2022 and December 31, 2021: As of September 30, 2022 Millions HG/BAM Ark Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease assets $ 6.2 $ 6.6 $ 5.9 $ 5.8 $ 24.5 4.1% Lease liabilities $ 6.7 $ 6.6 $ 6.8 $ 6.4 $ 26.5 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate. As of December 31, 2021 Millions HG/BAM Ark Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease assets $ 7.6 $ 7.0 $ 6.4 $ 7.1 $ 28.1 4.0% Lease liabilities $ 8.1 $ 7.0 $ 7.1 $ 7.8 $ 30.0 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

Non-controlling Interests (Tabl

Non-controlling Interests (Tables)	9 Months Ended
	Sep. 30, 2022
Noncontrolling Interest [Abstract]
Non-controlling Interests	The following table presents the balance of non-controlling interests included in White Mountains’s total equity and the ownership interests held by non-controlling shareholders as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 $ in Millions Non-controlling Percentage (1) Non-controlling Equity Non-controlling Percentage (1) Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ (.3) 3.1 % $ 8.9 Ark 28.0 % 217.1 28.0 % 230.7 Kudu 10.7 % 80.8 .7 % 12.4 NSM (2) — % — 3.5 % 16.7 Other various 20.8 various 11.9 Total, excluding BAM 318.4 280.6 BAM 100.0 % (160.1) 100.0 % (124.0) Total non-controlling interests $ 158.3 $ 156.6 (1) The non-controlling percentage represents the basic ownership interests held by non-controlling shareholders with the exception of HG Global, for which the non-controlling percentage represents the preferred share ownership held by non-controlling shareholders. (2) As a result of the NSM Transaction, NSM has been classified as discontinued operations through the closing of the transaction. See Note 19 — “Held for Sale and Discontinued Operations .”

Segment Information (Tables)

Segment Information (Tables)	9 Months Ended
	Sep. 30, 2022
Segment Reporting [Abstract]
Schedule of Financial Information for White Mountains' Segments	The following tables present the financial information for White Mountains’s segments: Millions HG Global/ BAM Ark Kudu Other Operations Total Three Months Ended September 30, 2022 Earned insurance premiums $ 7.1 $ 346.1 $ — $ — $ 353.2 Net investment income 5.7 4.9 14.8 8.5 33.9 Net realized and unrealized investment (38.8) (14.4) 41.1 (17.3) (29.4) Net realized and unrealized investment gains — — — (18.6) (18.6) Commission revenues — — — 3.2 3.2 Other revenues 1.3 6.6 — 33.0 40.9 Total revenues (24.7) 343.2 55.9 8.8 383.2 Loss and loss adjustment expenses — 213.7 — — 213.7 Insurance and reinsurance acquisition expenses 1.7 74.8 — — 76.5 Cost of sales — — — 25.0 25.0 General and administrative expenses 15.8 26.9 4.5 39.9 87.1 Amortization of other intangible assets — — — 1.4 1.4 Interest expense 2.0 3.7 4.2 .6 10.5 Total expenses 19.5 319.1 8.7 66.9 414.2 Pre-tax income (loss) from continuing operations $ (44.2) $ 24.1 $ 47.2 $ (58.1) $ (31.0) Millions HG Global/ BAM Ark Kudu Other Operations Total Three Months Ended September 30, 2021 Earned insurance premiums $ 6.7 $ 213.4 $ — $ — $ 220.1 Net investment income 4.4 .6 9.5 5.0 19.5 Net realized and unrealized investment (4.0) .3 18.9 15.3 30.5 Net realized and unrealized investment gains — — — (396.8) (396.8) Commission revenues — — — 2.4 2.4 Other revenues .3 3.4 .1 28.1 31.9 Total revenues 7.4 217.7 28.5 (346.0) (92.4) Losses and loss adjustment expenses — 129.2 — — 129.2 Insurance and reinsurance acquisition expenses 3.0 53.7 — — 56.7 Cost of sales — — — 24.0 24.0 General and administrative expenses 12.4 21.8 3.3 14.4 51.9 Amortization of other intangible assets — — — 2.0 2.0 Interest expense — 2.1 1.9 .4 4.4 Total expenses 15.4 206.8 5.2 40.8 268.2 Pre-tax income (loss) from continuing operations $ (8.0) $ 10.9 $ 23.3 $ (386.8) $ (360.6) Millions HG Global/ BAM Ark Kudu Other Operations Total Nine Months Ended September 30, 2022 Earned insurance premiums $ 26.0 $ 757.8 $ — $ — $ 783.8 Net investment income 15.1 9.7 41.2 13.6 79.6 Net realized and unrealized investment (114.0) (76.5) 45.8 2.8 (141.9) Net realized and unrealized investment gains — — — (113.3) (113.3) Commission revenues — — — 8.7 8.7 Other revenues 3.7 10.1 — 89.6 103.4 Total revenues (69.2) 701.1 87.0 1.4 720.3 Loss and loss adjustment expenses — 456.2 — — 456.2 Insurance and reinsurance acquisition expenses 9.5 174.9 — — 184.4 Cost of sales — — — 68.8 68.8 General and administrative expenses 49.5 79.8 10.2 118.9 258.4 Amortization of other intangible assets — — .2 3.2 3.4 Interest expense 5.4 10.6 10.3 1.2 27.5 Total expenses 64.4 721.5 20.7 192.1 998.7 Pre-tax income (loss) from continuing operations $ (133.6) $ (20.4) $ 66.3 $ (190.7) $ (278.4) Millions HG Global/ BAM Ark Kudu Other Operations Total Nine Months Ended September 30, 2021 Earned insurance premiums $ 19.6 $ 435.8 $ — $ — $ 455.4 Net investment income 13.2 1.8 26.1 16.1 57.2 Net realized and unrealized investment (15.6) 10.3 62.5 34.0 91.2 Net realized and unrealized investment gains — — — (325.5) (325.5) Commission revenues — — — 7.0 7.0 Other revenues .9 9.4 .2 57.6 68.1 Total revenues 18.1 457.3 88.8 (210.8) 353.4 Losses and loss adjustment expenses — 247.8 — — 247.8 Insurance and reinsurance acquisition expenses 6.5 124.4 — — 130.9 Cost of sales — — — 45.9 45.9 General and administrative expenses 42.7 84.4 9.0 79.4 215.5 Amortization of other intangible assets — — .2 2.9 3.1 Interest expense — 4.5 9.2 1.1 14.8 Total expenses 49.2 461.1 18.4 129.3 658.0 Pre-tax income (loss) from continuing operations $ (31.1) $ (3.8) $ 70.4 $ (340.1) $ (304.6)
Schedule of Reconciliation of Revenue from Segments to Consolidated

Equity-Method Eligible Invest_2

Equity-Method Eligible Investments (Tables)	9 Months Ended
	Sep. 30, 2022
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 September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Ownership Interest Carrying Value Ownership Interest Carrying Value Kudu Participation Contracts (1) 4.1 - 33.0% $ 813.2 3.2 - 32.0% $ 669.5 Investment in MediaAlpha 27.4 % 148.2 28.0 % 261.6 PassportCard/DavidShield 53.8 % 132.0 53.8 % 120.0 Elementum Holdings, L.P. 29.7 % 45.0 29.7 % 45.0 Other equity method eligible investments, at fair value Under 50.0% 102.7 Under 50.0% 109.3 Other equity method eligible investments, at fair value 50.0% and over 27.7 50.0% and over 17.8 (1) Ownership interest generally references basic ownership interest with the exception of Kudu’s Participation Contracts, which are non-controlling equity interests in the form of revenue and earnings participation contracts. The following tables present summarized financial information for MediaAlpha as of September 30, 2022 and December 31, 2021 and for the three and nine months ended September 30, 2022 and 2021: Millions September 30, 2022 December 31, 2021 Balance sheet data: Total assets $ 265.2 $ 289.8 Total liabilities $ 333.6 $ 351.4 Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 2021 2022 2021 Income statement data: Total revenues $ 89.0 $ 152.7 $ 335.1 $ 483.7 Total expenses $ 110.2 $ 157.0 $ 379.2 $ 488.2 Net income (loss) $ (21.2) $ (4.3) $ (44.1) $ (4.5)

Fair Value of Financial Instr_2

Fair Value of Financial Instruments (Tables)	9 Months Ended
	Sep. 30, 2022
Fair Value Disclosures [Abstract]
Summary of the fair value and carrying value of financial instruments	The following tables presents the fair value and carrying value of these financial instruments as of September 30, 2022 and December 31, 2021: September 30, 2022 December 31, 2021 Millions Fair Carrying Fair Carrying HG Global Senior Notes $ 146.1 $ 146.4 $ — $ — Ark 2007 Subordinated Notes $ 26.2 $ 30.0 $ 27.6 $ 30.0 Ark 2021 Subordinated Notes $ 149.4 $ 150.0 $ 162.8 $ 155.9 Kudu Credit Facility $ 265.5 $ 253.5 $ 246.8 $ 218.2 Other Operations debt $ 36.8 $ 35.6 $ 17.7 $ 16.8

Held for Sale and Discontinue_2

Held for Sale and Discontinued Operations (Tables)	9 Months Ended
	Sep. 30, 2022
Discontinued Operations and Disposal Groups [Abstract]
Schedule of Discontinued Operations	The following summarizes the assets and liabilities associated with NSM Group classified as held for sale. As of December 31, 2021, the amounts presented exclude $16.1 million of insurance licenses, investments and cash classified as assets held for sale related to one of the Other Operating Businesses. Millions December 31, 2021 Assets held for sale Short-term investments, at fair value $ 7.8 Cash (restricted $89.2) 111.6 Premiums and commissions receivable 85.0 Goodwill and other intangible assets 725.4 Other assets 59.2 Total assets held for sale $ 989.0 Liabilities held for sale Debt $ 272.1 Premiums payable 135.9 Contingent consideration 6.8 Other liabilities 80.5 Total liabilities held for sale 495.3 Net assets held for sale $ 493.7 The following summarizes the results of operations, including related income taxes associated with the businesses classified as discontinued operations for the three and nine months ended September 30, 2022 and 2021: Three Months Ended September 30, Nine Months Ended September 30, Millions 2022 (1) 2021 2022 (1) 2021 Revenues Commission revenues $ 26.6 $ 67.0 $ 176.9 $ 194.6 Other revenues 7.0 15.3 48.1 46.8 Total revenues - NSM Group 33.6 82.3 225.0 241.4 Expenses General and administrative expenses 15.7 48.9 126.8 142.4 Broker commission expenses 8.2 20.4 52.9 60.9 Change in fair value of contingent consideration — .6 .1 .8 Amortization of other intangible assets — 8.2 9.1 25.0 Loss on assets held for sale — — — 28.7 Interest expense 1.6 5.9 12.1 17.7 Total expenses - NSM Group 25.5 84.0 201.0 275.5 Pre-tax income (loss) from discontinued operations - 8.1 (1.7) 24.0 (34.1) Income tax (expense) benefit (1.8) 7.0 (7.6) 10.3 Net income (loss) from discontinued operations, net of 6.3 5.3 16.4 (23.8) Net gain (loss) from sale of discontinued operations, net of 886.8 — 886.8 — Net gain (loss) from sale of discontinued operations, net of — — — 18.7 Total income (loss) from discontinued operations, 893.1 5.3 903.2 (5.1) Net (income) loss from discontinued operations (.2) — (.8) 1.1 Total income (loss) from discontinued operations 892.9 5.3 902.4 (4.0) Other comprehensive income (loss) from discontinued .7 (1.7) (5.2) .9 Net gain (loss) from foreign currency translation from sale 2.9 — 2.9 — Comprehensive income (loss) from discontinued 896.5 3.6 900.1 (3.1) Other comprehensive income (loss) from discontinued (.1) — .2 (.1) Comprehensive income (loss) from discontinued $ 896.4 $ 3.6 $ 900.3 $ (3.2) (1) As a result of the NSM Transaction, the results of operations for NSM Group are presented for the periods from July 1, 2022 to August 1, 2022 and January 1, 2022 to August 1, 2022. Net Change in Cash from Discontinued Operations The following summarizes the net change in cash associated with the businesses classified as discontinued operations for the nine months ended September 30, 2022 and 2021: Nine Months Ended September 30, Millions 2022 2021 Net cash provided from (used for) operations $ 38.7 $ 40.3 Net cash provided from (used for) investing activities 7.1 (54.6) Net cash used from (used for) financing activities (17.5) 13.8 Effect of exchange rate changes on cash 4.0 .6 Net change in cash during the period 32.3 .1 Cash balances at beginning of period (includes restricted cash of $89.2 and $78.4) 111.6 126.6 Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0) (143.9) — Cash balances at end of period (includes restricted cash of $0.0 and $92.2) — 126.7 Supplemental cash flows information: Interest paid $ (12.0) $ (16.6) Net income tax payments $ — $ — Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 888.2 $ (371.4) $ 752.4 $ (308.2) Less: net income (loss) from continuing operations $ (23.6) $ (389.2) $ (252.3) $ (356.8) Less: net (income) loss from continuing operations attributable to $ 18.8 $ 12.5 $ 102.2 $ 52.6 Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders (1) $ 893.0 $ 5.3 $ 902.5 $ (4.0) Allocation of earnings to participating restricted common shares (2) (11.8) (.1) (10.8) — Basic and diluted earnings per share numerators (3) $ 881.2 $ 5.2 $ 891.7 $ (4.0) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (4) (38.3) (37.8) (35.5) (36.0) Basic earnings per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 2,893.8 3,090.3 2,959.3 3,099.4 Average unvested restricted common shares (4) (38.3) (37.8) (35.5) (36.0) Diluted earnings per share denominator 2,855.5 3,052.5 2,923.8 3,063.4 Basic and diluted earnings (losses) per share (in dollars) - $ 308.59 $ 1.72 $ 304.97 $ (1.29) (1) Includes net income (loss) from discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - NSM Group, net gain (loss) from sale of discontinued operations, net of tax - Sirius Group and net (income) loss from discontinued operations attributable to non-controlling interests. (2) Restricted shares issued by White Mountains receive dividends and are therefore 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 and nine months ended September 30, 2022 and 2021. (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) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021	Jul. 31, 2012
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)	89.30%	99.30%
Fully diluted ownership interest (as a percent)	76.10%	84.70%
NSM Insurance Group
Basis of Presentation
Ownership interest (as a percent)		96.50%
Fully diluted ownership interest (as a percent)		87.30%
Preferred Stock | HG Global
Basis of Presentation
Ownership interest (as a percent)	96.90%	96.90%
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%
Ark | Ark
Basis of Presentation
Ownership interest (as a percent)	72%
Fully diluted ownership interest (as a percent)	63%

Significant Transactions - NSM

Significant Transactions - NSM (Details) - USD ($) $ in Millions		3 Months Ended		9 Months Ended
	Aug. 01, 2022	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Other Significant Noncash Transactions [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group				$ 886.8	$ 18.7
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group		$ 2.9	$ 0	2.9	0
NSM Insurance Group
Other Significant Noncash Transactions [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group		$ 886.8	$ 0	$ 886.8	$ 0
Discontinued Operations, Disposed of by Sale | NSM Insurance Group
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 - Kudu

Significant Transactions - Kudu (Details) $ in Millions		9 Months Ended
	May 26, 2022 USD ($)	Sep. 30, 2022 USD ($)	May 25, 2022
Kudu
Other Significant Noncash Transactions [Line Items]
Basic ownership	89.30%		99.10%
Mass Mutual
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 64.1
Kudu Investment Management, LLC
Other Significant Noncash Transactions [Line Items]
Equity capital raised	0.4
White Mountains
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 50
Kudu
Other Significant Noncash Transactions [Line Items]
Pre-money valuation	1.3
Pre-money valuation, amount	$ 114
Enterprise value excluded		$ 41.1
Kudu
Other Significant Noncash Transactions [Line Items]
Equity capital raised	$ 114.5

Significant Transactions - Ark

Significant Transactions - Ark (Details) - USD ($) $ in Millions			3 Months Ended			9 Months Ended
	Jan. 01, 2021	Oct. 01, 2020	Sep. 30, 2022	Sep. 30, 2021	Mar. 31, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021	Dec. 31, 2020
Ark
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									$ 366.3
Other Operations
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									646.3
Goodwill and other intangible assets			$ 92			$ 92		$ 39.1
Ark
Other Significant Noncash Transactions [Line Items]
Goodwill and other intangible assets			292.5			292.5		292.5
Contingent consideration			32.9			32.9		28
Change in fair value of contingent consideration liabilities			2.7	$ 1.5		4.9	$ 1.5
Ark | In-force Business Acquired
Other Significant Noncash Transactions [Line Items]
Amortization			$ 0.7	11		$ 6.8	54.9
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			72%			72%
Fully diluted ownership interest (as a percent)			63%			63%
Ark | Lloyd
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction									$ 280
Ark
Other Significant Noncash Transactions [Line Items]
Merger agreement, equity capital contributed	$ 605.4
Equity capital, pre money valuation amount		$ 300
Additional equity purchase from shareholders		40.9
Investment, potential additional contribution of equity capital		$ 200
Assets acquired	2,500
Goodwill and other intangible assets	292.5
Liabilities acquired	1,700
Contingent consideration	22.5
Noncontrolling interest acquired	$ 220.2
Transaction costs					$ 25.3
Investment, potential additional contribution of equity capital terminated								$ 200
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			72%			72%		72%
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Fully diluted ownership interest (as a percent)			63%			63%		63%
Percent of outstanding shares after performance obligations are satisfied			12.50%			12.50%
Ark | Group Ark Insurance Limited | Unsecured Subordinated Debt
Other Significant Noncash Transactions [Line Items]
Notes issued				$ 163.3			$ 163.3

Significant Transactions - Sche

Significant Transactions - Schedule of Assets Acquired and Liabilities Assumed, Ark (Details) - USD ($) $ in Millions	Jan. 01, 2021	Sep. 30, 2022	Dec. 31, 2021
Other Significant Transactions [Line Items]
Goodwill		$ 175.5	$ 142.3
Ark
Other Significant Transactions [Line Items]
Investments	$ 594.3
Cash	52
Reinsurance recoverables	433.4
Insurance premiums receivable	236.7
Ceded unearned premiums	170.2
Value of in-force business acquired	71.7
Other assets	88.9
Loss and loss adjustment expense reserves	(696)
Unearned insurance premiums	(326.1)
Debt	(46.4)
Ceded reinsurance payable	(528.3)
Other liabilities	(25.9)
Net tangible assets acquired	24.5
Goodwill	116.8
Other intangible assets - syndicate underwriting capacity	175.7
Deferred tax liability on other intangible assets	(33.4)
Net assets acquired	283.6
Merger agreement, equity capital contributed	$ 605.4

Significant Transactions - Medi

Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions			9 Months Ended
	Mar. 23, 2021	Oct. 30, 2020	Sep. 30, 2022	Dec. 31, 2021
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Share price (in usd per share)			$ 8.75
Investment owned, balance			$ 148.2
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			27.40%	28%
IPO | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)		3,600,000
Sale of stock, price per share (in usd per share)		$ 19
Sale of stock, price per share, net of underwriting fees (in USD per share)		$ 17.67
Sale of stock, consideration received in transaction		$ 63.8
Proceeds from dividends received		$ 55
Investment owned (in shares)			16,900,000
Fully diluted ownership interest (as a percent)			25%
Increase in investment owned (in dollars per share)			$ 1
Increase in book value per share (in dollars per share)			6.60
Share price (in usd per share)			$ 8.75
Investment owned, balance			$ 148.2
IPO | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)			27.40%
Secondary Offering | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	3,600,000
Secondary Offering | Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	8,050,000
Sale of stock, price per share (in usd per share)	$ 46
Sale of stock, price per share, net of underwriting fees (in USD per share)	$ 44.62
Sale of stock, consideration received in transaction	$ 160.3

Significant Transactions - Pass

Significant Transactions - PassportCard/DavidShield (Details) - USD ($) $ in Millions	May 07, 2020	Jan. 24, 2018	Sep. 30, 2022	Dec. 31, 2021	May 06, 2020
DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50%
PassportCard
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50%
PassportCard/DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	53.80%		53.80%	53.80%	50%
Payments to acquire businesses, gross		$ 41.8
Payments to acquire business, net		$ 28.3
Stock issued during period, value, acquisitions	$ 15
Maximum loss exposure			$ 143

Investment Securities - Schedul

Investment Securities - Schedule of Interest Income on Fixed Maturity Investments (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Schedule of Investments [Line Items]
Total investment income	$ 34.7	$ 20.1	$ 81.1	$ 58.8
Third-party investment expenses	(0.8)	(0.6)	(1.5)	(1.6)
Net investment income	33.9	19.5	79.6	57.2
Fixed maturity investments
Schedule of Investments [Line Items]
Total investment income	11.1	8.2	28.6	21.9
Short-term investments
Schedule of Investments [Line Items]
Total investment income	6.7	0	7.2	0.5
Common equity securities
Schedule of Investments [Line Items]
Total investment income	0.1	0.1	0.2	0.1
Other long-term investments
Schedule of Investments [Line Items]
Total investment income	17.1	12	45.9	37.1
TPC Providers
Schedule of Investments [Line Items]
Total investment income	$ 0.3	$ 0.2	$ 0.8	$ 0.8

Investment Securities - Net Rea

Investment Securities - Net Realized and Unrealized Investment Gains (Losses) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	$ (1.6)	$ 9.9	$ 12.9	$ 165.4
Net unrealized investment gains (losses)	(47.7)	(374.7)	(274.3)	(393.2)
Net unrealized investment gains (losses) on investment securities held at the end of the period	(18.6)	(396.8)	(113.3)	(325.5)
Gain (loss) on investments, exchange rate effect	(22.6)	(7)	(44.4)	(7.4)
Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment gains (losses)	(48)	(366.5)	(255.2)	(234.3)
Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(4.9)	1	(10.8)	3.8
Net unrealized investment gains (losses)	(58.8)	(7.9)	(192.9)	(27)
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	(0.1)	(0.3)	(0.4)	0
Net unrealized investment gains (losses)	(2.1)	0	(2.6)	0
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	0	0	0	0.4
Net unrealized investment gains (losses)	4.3	1.6	(6.3)	7.3
Net unrealized investment gains (losses) on investment securities held at the end of the period	4.3	1.6	(6.3)	7.7
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	0	0	0	160.3
Net unrealized investment gains (losses)	(18.6)	(396.8)	(113.3)	(485.8)
Net unrealized investment gains (losses) on investment securities held at the end of the period	(18.6)	(396.8)	(113.3)	(325.5)
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized investment gains (losses)	3.4	9.2	24.1	0.9
Net unrealized investment gains (losses)	27.5	28.4	40.8	112.3
Net realized and unrealized investment (losses) gains
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(49.3)	(364.8)	(261.4)	(227.8)
TPC Providers
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	1.3	(1.7)	6.2	(6.5)
Fixed maturity and short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(65.9)	(7.2)	(206.7)	(23.2)
Net realized and unrealized investment gains (losses)	0.1	(5.7)	(3)	(6.9)
Fixed maturity and short-term investments | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(66)	(1.5)	(203.7)	(16.3)
Common equity securities and investment in MediaAlpha
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	(14.3)	(395.2)	(119.6)	(317.8)
Net realized and unrealized investment gains (losses)	0	(0.4)	0	(20.3)
Common equity securities and investment in MediaAlpha | Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net unrealized investment gains (losses) on investment securities held at the end of the period	$ (14.3)	$ (395.6)	$ (119.6)	$ (338.1)

Investment Securities - Investm

Investment Securities - Investment gains (losses) for Level 3 (Details) - Level 3 - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 40.8	$ 26.5	$ 57.7	$ 75.5
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 40.8	$ 26.5	$ 57.7	$ 75.5

Investment Securities - Inves_2

Investment Securities - Investment Holdings Fixed Maturity Table (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 227.9	$ 212.1
Gross Unrealized Gains	0	0.5
Gross Unrealized Losses	(11)	(1.1)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	216.9	211.5
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,068.8	993.3
Gross Unrealized Gains	0	8.7
Gross Unrealized Losses	(91.2)	(8.7)
Net Foreign Currency Gains (Losses)	(3.1)	(0.4)
Carrying Value	974.5	992.9
Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	289.3	276.4
Gross Unrealized Gains	0	16.8
Gross Unrealized Losses	(24.4)	(1.3)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	264.9	291.9
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	278.3	277.2
Gross Unrealized Gains	0	2.9
Gross Unrealized Losses	(37.6)	(2.5)
Net Foreign Currency Gains (Losses)	0	0
Carrying Value	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	169.7	136.5
Gross Unrealized Gains	0	0
Gross Unrealized Losses	(7.6)	(0.4)
Net Foreign Currency Gains (Losses)	(4.8)	(1.1)
Carrying Value	157.3	135
Total fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	2,034	1,895.5
Gross Unrealized Gains	0	28.9
Gross Unrealized Losses	(171.8)	(14)
Net Foreign Currency Gains (Losses)	(7.9)	(1.5)
Carrying Value	$ 1,854.3	$ 1,908.9

Investment Securities - Cost an

Investment Securities - Cost and Amortized Cost Maturity Schedule (Details) $ in Millions	Sep. 30, 2022 USD ($)
Cost or Amortized Cost
Total fixed maturity investments	$ 2,034
Carrying Value
Total fixed maturity investments	1,854.3
Fixed Maturities and Convertible Fixed Maturities Excluding Mortgage Backed Securities
Cost or Amortized Cost
Due in one year or less	207.5
Due after one year through five years	917.9
Due after five years through ten years	354.8
Due after ten years	105.8
Carrying Value
Due in one year or less	203.8
Due after one year through five years	849.4
Due after five years through ten years	309.3
Due after ten years	93.8
Mortgage and asset-backed securities
Cost or Amortized Cost
Mortgage and asset-backed securities and collateralized loan obligations	448
Carrying Value
Mortgage and asset-backed securities and collateralized loan obligations	$ 398

Investment Securities - Inves_3

Investment Securities - Investment Holding Common Equities/ Other Investments/ MediaAlpha (Details) - USD ($) $ in Millions	9 Months Ended	12 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 324.2	$ 236.3
Gross Unrealized Gains	32.7	16.1
Gross Unrealized Losses	(8.7)	0
Net Foreign Currency Gains (Losses)	(15.4)	(1.3)
Common equity securities, at fair value	332.8	251.1
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	0	0
Gross Unrealized Gains	148.2	261.6
Gross Unrealized Losses	0	0
Net Foreign Currency Gains (Losses)	0	0
Common equity securities, at fair value	148.2	261.6
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,390.7	1,186.7
Gross Unrealized Gains	345	239
Gross Unrealized Losses	(90)	(44.1)
Net Foreign Currency Gains (Losses)	(23)	(3.8)
Common equity securities, at fair value	$ 1,622.7	$ 1,377.8

Investment Securities - Fair Va

Investment Securities - Fair Value Measurements (Details)	9 Months Ended	12 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Investments, Debt and Equity Securities [Abstract]
Percentage of investments recorded at fair value	69%	68%

Investment Securities - Fair _2

Investment Securities - Fair Value Measurement by Level (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Dec. 31, 2020
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	$ 1,622.7	$ 1,377.8
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	974.5	992.9
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
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	1,044.1	890.6	$ 814.5	$ 614.2
Fair value measured on a recurring basis
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	5,154.4	4,265.3
Other long-term investments	1,622.7	1,377.8
Fair value measured on a recurring basis | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	148.2	261.6
Fair value measured on a recurring basis | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	216.9	211.5
Fair value measured on a recurring basis | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	974.5	992.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	269	264.2
Fair value measured on a recurring basis | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	181.4	178.1
Fair value measured on a recurring basis | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	115.8	112.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.3	112.8
Fair value measured on a recurring basis | Debt securities issued by corporations | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	110.8	117.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	75.9	70.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	49.1	56
Fair value measured on a recurring basis | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	36.1	48
Fair value measured on a recurring basis | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.1	32.1
Fair value measured on a recurring basis | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	264.9	291.9
Fair value measured on a recurring basis | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Fair value measured on a recurring basis | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
Fair value measured on a recurring basis | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,854.3	1,908.9
Fair value measured on a recurring basis | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	1,196.4	465.9
Fair value measured on a recurring basis | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	332.8	251.1
Fair value measured on a recurring basis | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	1,058	895.3
Fair value measured on a recurring basis | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	564.7	482.5
Fair value measured on a recurring basis | Level 1
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,607.9	939
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	148.2	261.6
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	216.9	211.5
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 | 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 | 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 | 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	216.9	211.5
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	1,196.4	465.9
Fair value measured on a recurring basis | Level 1 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	46.4	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	1,937.7	1,953.2
Other long-term investments	13.9	4.7
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	974.5	992.9
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	269	264.2
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	181.4	178.1
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	115.8	112.9
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	114.3	112.8
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	110.8	117.9
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	75.9	70.9
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	49.1	56
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	36.1	48
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	22.1	32.1
Fair value measured on a recurring basis | Level 2 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	264.9	291.9
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	240.7	277.6
Fair value measured on a recurring basis | Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
Fair value measured on a recurring basis | Level 2 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,637.4	1,697.4
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	0	0
Fair value measured on a recurring basis | Level 2 | Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	286.4	251.1
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	13.9	4.7
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	1,044.1	890.6
Other long-term investments	1,044.1	890.6
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 | 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 | 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 | 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 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	1,044.1	890.6
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	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	$ 455.1	$ 479.5
Assets held by insurance regulators	4.6	4.8
Other long-term investments	1,622.7	1,377.8
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	117.8	113.8
Short-term investments | Asset Pledged as Collateral | Citibank LOC Facility
Debt and Equity Securities, FV-NI [Line Items]
Investments pledged as collateral	49.8	50
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	117.8
Fair value investments	$ 311.4	$ 342.8

Investment Securities - Debt se

Investment Securities - Debt securities issued by corporation (Details) - Debt securities issued by corporations - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 974.5	$ 992.9
AAA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.2	12
AA
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	90.5	85
A
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	524	490.4
BBB
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	343	396.8
Other
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 5.8	$ 8.7

Investment Securities - Mortgag

Investment Securities - Mortgage-backed Asset Securities Table (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 217.9	$ 256.5
Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.8	21.1
Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	398	412.6
Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.9	256.5
Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	22.8	21.1
Level 2 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	240.7	277.6
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	157.3	135
Level 2 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	398	412.6
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	114.1	125.4
FNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.1	125.4
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	74.5	90.5
FHLMC | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	74.5	90.5
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	28.9	40.1
GNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	28.9	40.1
GNMA | Level 3 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Total agency | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.5	256
Total agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	217.5	256
Total agency | 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	0.4	0.5
Non-agency: Residential | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
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	0.4	0.5
Total non-agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.4	0.5
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	11.9	12.3
Credit card receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.9	12.3
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	10.9	8.8
Vehicle receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	10.9	8.8
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	$ 157.3

Investment Securities - Inves_5

Investment Securities - Investment in MediaAlpha textual (Details) - Marketing Technology (MediaAlpha) $ / shares in Units, $ in Millions	Sep. 30, 2022 USD ($) $ / shares
Subsidiary, Sale of Stock [Line Items]
Share price (in usd per share) | $ / shares	$ 8.75
Investment owned, balance | $	$ 148.2

Investment Securities - Other l

Investment Securities - Other long-term investments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 1,622.7	$ 1,377.8
Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	813.2	669.5
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	132	120
Elementum Holdings, L.P.
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	45	45
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	37	34.4
Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	1,027.2	868.9
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	239.8	153.8
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	155.7	163
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	117.8	113.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	49.4	51.9
Private debt investments
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	13	14.1
Other
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 19.8	$ 12.3

Investment Securities - Hedge F

Investment Securities - Hedge Funds and Private Equity Funds (Details) $ in Millions	9 Months Ended		12 Months Ended
	Sep. 30, 2022 USD ($) fund	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Investments in trading securities	$ 97.9	$ 141.6
TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management | Kudu
Debt and Equity Securities, FV-NI [Line Items]
Investments in trading securities			$ 223.4
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments | fund	16
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	$ 49.3		$ 31.3

Investment Securities - Fair _3

Investment Securities - Fair Value of Hedge Funds and Private Equity Funds (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Total private equity funds and hedge funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 239.8	$ 153.8
Unfunded Commitments	102.5	44
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	185.1	141.8
Unfunded Commitments	102.5	44
Private equity funds | Aerospace/Defense/Government
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	102.9	69.8
Unfunded Commitments	45.1	11.8
Private equity funds | Financial services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	77.9	67.7
Unfunded Commitments	54.9	29.3
Private equity funds | Real estate
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	4.3	4.3
Unfunded Commitments	2.5	2.9
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	54.7	12
Unfunded Commitments	0	0
Hedge funds | Long/short equity financials and business services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	49.3	0
Unfunded Commitments	0	0
Hedge funds | European small/mid cap
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	5.4	12
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	Sep. 30, 2022 USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 185.1
1 – 3 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	27.5
3 – 5 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	19
5 – 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	135.4
Greater than 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 3.2

Investment Securities - Lloyd's

Investment Securities - Lloyd's Trust Deposits, Bank Loan Fund, and Insurance-Linked Securities Funds (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Debt and Equity Securities, FV-NI [Line Items]
Investments held in trusts	$ 455.1	$ 479.5
Hedge funds | Minimum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	45 days
Hedge funds | Maximum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 155.7
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	311.4	$ 342.8
Investments held in trusts	117.8
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 49.4
ILS funds | Minimum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	30 days
ILS funds | Maximum
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	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	$ 890.6	$ 614.2
Net realized and unrealized gains	57.3	79
Amortization/accretion	0	0
Purchases	127.9	143.6
Sales	(31.7)	(31.9)
Transfers in	0	0
Transfers out	0	0
Ending balance	1,044.1	814.5
Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	$ 0	$ 9.6

Investment Securities - Signifi

Investment Securities - Significant Unobservable Inputs (Details) $ in Millions	9 Months Ended		12 Months Ended
	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities	$ 97.9	$ 141.6
Kudu investments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, pretax discount rate	0.20		0.20
Cash flow exit multiple, pretax	9.7		10
TIG Advisors, TK Partners, Third Eye Capital Management, Douglass Winthrop Advisors, Granahan Investment Management and Radcliffe Capital Management | Kudu
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in trading securities			$ 223.4
Level 3 | Other long-term investments | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 42.9		46.7
Level 3 | Kudu investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	813.2		669.5
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	$ 312.4		$ 78.8
Level 3 | Kudu investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	17%		18%
Level 3 | Kudu investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	24%		23%
Level 3 | 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
Level 3 | Kudu investments | Terminal Multiple | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal cash flow exit multiple	16		13
Level 3 | PassportCard/DavidShield | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 132		$ 120
Level 3 | PassportCard/DavidShield | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	24%		23%
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	$ 45		$ 45
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	18%		17%
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 investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 11		$ 9.4
Level 3 | Private debt investments | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	10%		8%
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	$ 97.9

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	9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	$ 175.5	$ 142.3
Goodwill, net carrying value	175.5	142.3
Total Equity Including Noncontrolling Interest
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	403.6	347.5
Other intangible assets, accumulated amortization	10.4	7
Total goodwill and other intangible assets	393.2	340.5
Non-controlling interest
Acquired Finite-Lived Intangible Assets [Line Items]
Total goodwill and other intangible assets	103.1	91.8
Total
Acquired Finite-Lived Intangible Assets [Line Items]
Total goodwill and other intangible assets	290.1	248.7
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	228.1	205.2
Other intangible assets, accumulated amortization	10.4	7
Other intangible assets, net carrying value	217.7	198.2
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	116.8	116.8
Goodwill, net carrying value	116.8	116.8
Ark | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
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, net carrying value	$ 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	1.1	0.9
Other intangible assets, net carrying value	1.1	1.3
Other Operations
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	51.1	17.9
Goodwill, net carrying value	51.1	17.9
Other intangible assets, acquisition date fair value	50.2	27.3
Other intangible assets, accumulated amortization	9.3	6.1
Other intangible assets, net carrying value	$ 40.9	21.2
Other Operations | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	15 years 10 months 24 days
Other intangible assets, acquisition date fair value	$ 17.9	8.2
Other intangible assets, accumulated amortization	2.4	1.5
Other intangible assets, net carrying value	$ 15.5	6.7
Other Operations | Customer relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)	12 years 4 months 24 days
Other intangible assets, acquisition date fair value	$ 29.5	18.8
Other intangible assets, accumulated amortization	6.6	4.5
Other intangible assets, net carrying value	$ 22.9	14.3
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	0.3
Other intangible assets, accumulated amortization	0.3	0.1
Other intangible assets, net carrying value	$ 2.5	$ 0.2

Goodwill and Other Intangible_4

Goodwill and Other Intangible Assets - Summary of the Acquisition Date Fair Values of Goodwill and Other Intangible Assets (Details) $ in Millions	Sep. 30, 2022 USD ($)
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 292.5
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 86.6

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		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance			$ 142.3
Amortization of other intangible assets	$ (1.4)	$ (2)	(3.4)	$ (3.1)
Goodwill, ending balance	175.5		175.5
Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance	201.8	151.5	142.3	19.2
Acquisition of businesses			59.5	15.8
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	(22.9)	(9.3)	(22.9)	(9.3)
Measurement period adjustments	(3.4)	(0.4)	(3.4)	(0.7)
Amortization of other intangible assets	0	0	0	0
Goodwill, ending balance	175.5	141.8	175.5	141.8
Goodwill | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill acquired			0	116.8
Other
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets (excluding goodwill), beginning balance	196.2	201.1	198.2	26.4
Acquisition of businesses			0	0
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	22.9	9.3	22.9	9.3
Measurement period adjustments	0	0		0.1
Amortization of other intangible assets	(1.4)	(2)	(3.4)	(3.1)
Other intangible assets (excluding goodwill), ending balance	217.7	208.4	217.7	208.4
Other | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Intangible assets acquired			0	175.7
Total Goodwill and Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, gross (including goodwill), beginning balance	398	352.6	340.5	45.6
Acquisition of businesses			59.5	15.8
Attribution of acquisition date fair value estimates between goodwill and other intangible assets	0	0	0	0
Measurement period adjustments	(3.4)	(0.4)	(3.4)	(0.6)
Amortization of other intangible assets	(1.4)	(2)	(3.4)	(3.1)
Other intangible assets, gross (including goodwill), ending balance	$ 393.2	$ 350.2	393.2	350.2
Total Goodwill and Other Intangible Assets | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets acquired			$ 0	$ 292.5

Loss and Loss Adjustment Expe_3

Loss and Loss Adjustment Expense Reserves (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance	$ 1,022.1	$ 760	$ 894.7	$ 696
Less: beginning reinsurance recoverable on unpaid losses	(375.5)	(425.3)	(428.9)	(433.4)
Net loss and LAE reserves	646.6	334.7	465.8	262.6
Loss and LAE incurred relating to:
Current year losses	222.9	141.9	491.8	269
Prior year losses	(9.2)	(12.7)	(35.6)	(21.2)
Net incurred losses and LAE	213.7	129.2	456.2	247.8
Loss and LAE paid relating to:
Current year losses	(6.1)	(9)	(20.8)	(11.5)
Prior year losses	(37)	(20.3)	(130.8)	(62.1)
Net paid loss and LAE	(43.1)	(29.3)	(151.6)	(73.6)
Change in TPC providers’ participation	0	0	57.5	(2.2)
Foreign currency translation and other adjustments to loss and LAE reserves	(9.2)	(1.2)	(19.9)	(1.2)
Net ending balance	808	433.4	808	433.4
Plus: ending reinsurance recoverable on unpaid losses	521.4	457.5	521.4	457.5
Gross ending balance	1,329.4	890.9	1,329.4	890.9
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	521.4	457.5	521.4	457.5	$ 428.9	$ 433.4
Ark
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance			894.7
Loss and LAE paid relating to:
Gross ending balance	1,329.4		1,329.4
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	550.9	465.6	550.9	465.6	$ 448.4
TPC Providers | Ark
Liability for Claims and Claims Adjustment Expense [Line Items]
Reinsurance recoverables	168	299.9	168	299.9
TPC Providers
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Less: beginning reinsurance recoverable on unpaid losses	(182.4)	(314.6)
Loss and LAE paid relating to:
Plus: ending reinsurance recoverable on unpaid losses	276.8	319.2	276.8	319.2
Liability for Claims and Claims Adjustment Expense [Line Items]
Loss and loss adjustment expense reserves	$ 276.8	319.2	$ 276.8	319.2
Reinsurance recoverables		$ 299.9		$ 299.9
Ark | TPC Providers
Liability for Claims and Claims Adjustment Expense [Line Items]
Percent of underwriting capital provided by third parties						42.80%	58.30%	57.60%

Third-Party Reinsurance - Effec

Third-Party Reinsurance - Effects of Reinsurance (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earned premiums:
Net earned premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Ark
Written premiums:
Gross	215.5	162.4	1,252.5	895
Ceded	(22.9)	(41.5)	(246)	(169.5)
Net written premiums	192.6	120.9	1,006.5	725.5
Earned premiums:
Gross	454.9	284.5	966.6	622
Ceded	(108.8)	(71.1)	(208.8)	(186.2)
Net earned premiums	346.1	213.4	757.8	435.8
Losses and loss adjustment expenses:
Gross	391.4	193.5	712.9	372.7
Ceded	(177.7)	(64.3)	(256.7)	(124.9)
Net losses and loss adjustment expenses	$ 213.7	$ 129.2	$ 456.2	$ 247.8

Third-Party Reinsurance - Narra

Third-Party Reinsurance - Narrative (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2021	Sep. 30, 2022	Sep. 30, 2021
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses		$ 521.4	$ 457.5
Reinsurance recoverables on paid losses		29.5	8.1
TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables			299.9
Ark
Reinsurance [Line Items]
Reinsurance recoverables	$ 448.4	550.9	465.6
Ark | TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables		168	$ 299.9
Ark | Third Point Re
Reinsurance [Line Items]
Annual crediting rate	3%
Decrease in investment	$ 31.7
Carrying value of investment		$ 20.3

Third-Party Reinsurance - Remai

Third-Party Reinsurance - Remaining Gross and Net Reinsurance Recoverables (Details) - All Entities Except TCP Providers $ in Millions	Sep. 30, 2022 USD ($)
Reinsurance [Line Items]
Reinsurance recoverables	$ 382.9
Reinsurance Recoverables, Collateral	119.4
Net Reinsurance Recoverables	$ 263.5
Percent of reinsurance recoverables from insurers that are collateralized	100%
A+ or better
Reinsurance [Line Items]
Reinsurance recoverables	$ 178.3
Reinsurance Recoverables, Collateral	0
Net Reinsurance Recoverables	$ 178.3
Percent of reinsurance recoverables from insurers that are collateralized	67.70%
A- to A
Reinsurance [Line Items]
Reinsurance recoverables	$ 78.9
Reinsurance Recoverables, Collateral	0
Net Reinsurance Recoverables	$ 78.9
Percent of reinsurance recoverables from insurers that are collateralized	29.90%
B++ or lower and not rated
Reinsurance [Line Items]
Reinsurance recoverables	$ 125.7
Reinsurance Recoverables, Collateral	119.4
Net Reinsurance Recoverables	$ 6.3
Percent of reinsurance recoverables from insurers that are collateralized	2.40%

Debt - Summary of Debt Outstand

Debt - Summary of Debt Outstanding (Details) € in Millions, $ in Millions	Sep. 30, 2022 USD ($)	Sep. 30, 2022 EUR (€)	Dec. 31, 2021 USD ($)
Debt Instrument
Total debt	$ 615.5		$ 420.9
Ark Subordinated Debt
Debt Instrument
Unamortized issuance cost	(4.6)		(5.3)
Ark 2007 Subordinated Notes, carrying value | Ark Subordinated Debt
Debt Instrument
Amount borrowed	30		30
Ark 2021 Notes Tranche 1
Debt Instrument
Amount borrowed | €		€ 39.1
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	37.6		44.2
Ark 2021 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	47		47
Ark 2021 Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	70		70
Ark 2021 Notes | Ark Subordinated Debt
Debt Instrument
Total debt	$ 150		$ 155.9
Ark
Debt Instrument
Effective percentage	7.30%	7.30%	6.90%
Ark | Ark Subordinated Debt
Debt Instrument
Total debt	$ 180		$ 185.9
Kudu Credit Facility
Debt Instrument
Total debt	253.5		218.2
Other
Debt Instrument
Total debt	$ 35.6
HG Global
Debt Instrument
Effective percentage	8.60%	8.60%
Secured Debt | HG Global Senior Notes
Debt Instrument
Amount borrowed	$ 150
Unamortized issuance cost	(3.6)
Total debt	146.4
Term Loan | Kudu Credit Facility
Debt Instrument
Amount borrowed	260.4		225.4
Unamortized issuance cost	$ (6.9)		$ (7.2)
Effective percentage	5.60%	5.60%	4.30%
Term Loan | Other Operations
Debt Instrument
Amount borrowed	$ 36.4		$ 17.1
Unamortized issuance cost	$ (0.8)		$ (0.3)
Effective percentage	7.10%	7.10%	7.50%
Term Loan | Other
Debt Instrument
Total debt			$ 16.8

Debt - Narrative (Details)

Debt - Narrative (Details) € in Millions			1 Months Ended				3 Months Ended		9 Months Ended
	Apr. 29, 2022 USD ($)	Sep. 08, 2021 USD ($)	Sep. 30, 2021 USD ($)	Aug. 31, 2021	Jul. 31, 2021	Mar. 31, 2007 USD ($)	Sep. 30, 2022 USD ($) credit_facility	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($) credit_facility	Sep. 30, 2021 USD ($)	Sep. 30, 2022 EUR (€) credit_facility	Jun. 30, 2022 USD ($)	Dec. 31, 2021 USD ($)	Aug. 11, 2021 USD ($)	Jul. 13, 2021 USD ($)	Jul. 13, 2021 EUR (€)	Jun. 30, 2021 USD ($)	Dec. 31, 2020 USD ($)
Debt Instrument
Debt							$ 615,500,000		$ 615,500,000				$ 420,900,000
Debt covenant, maximum loan to value percent, period one							50%		50%		50%
Debt covenant, maximum loan to value percent, period two							40%		40%		40%
Debt covenant, maximum loan to value percent, period three							25%		25%		25%
Debt covenant, maximum loan to value percent, period four							15%		15%		15%
Debt covenant, maximum loan to value percent, period five							0%		0%		0%
Debt covenant, maximum loan to value percent							35%		35%		35%
Other
Debt Instrument
Secured credit facilities | credit_facility							5		5		5
Ark
Debt Instrument
Debt							$ 180,000,000		$ 180,000,000				185,900,000
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		$ 163,300,000
HG Global Senior Notes | Secured Debt
Debt Instrument
Borrowings	$ 150,000,000
Annual payments							15,000,000		15,000,000
Interest reserve account							26,400,000		$ 26,400,000
Additional interest rate									1%
Outstanding balance							150,000,000		$ 150,000,000
Debt							146,400,000		146,400,000
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				30,000,000
Ark 2007 Subordinated Notes, carrying value | Junior Notes | Ark
Debt Instrument
Face value						$ 30,000,000
Debt							30,000,000		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 Notes Tranche 1
Debt Instrument
Outstanding balance | €											€ 39.1
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							37,600,000		37,600,000				44,200,000
Ark 2021 Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Notes issued															$ 46,300,000	€ 39.1
Ark 2021 Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited | EURIBOR
Debt Instrument
Basis spread on variable rate					5.75%
Ark 2021 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							47,000,000		47,000,000				47,000,000
Ark 2021 Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Notes issued														$ 47,000,000
Ark 2021 Notes Tranche 2 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR
Debt Instrument
Basis spread on variable rate				5.75%
Ark 2021 Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							70,000,000		70,000,000				70,000,000
Ark 2021 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 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							49,800,000		49,800,000				50,000,000
Citibank LOC Facility | Secured Debt
Debt Instrument
Line of credit							36,200,000		36,200,000
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 | Secured Debt | Ark | Letter of Credit | Collateral Pledged
Debt Instrument
Total commitment under revolving credit facility							50,000,000		50,000,000
Kudu Bank Facility | Kudu
Debt Instrument
Total commitment under revolving credit facility							300,000,000		300,000,000
Kudu Bank Facility | Revolving Credit Facility | Kudu
Debt Instrument
Loss on debt extinguishment									4,100,000
Kudu Bank Facility | Line of Credit | Kudu
Debt Instrument
Interest reserve							8,900,000		8,900,000
Kudu Bank Facility | Term Loan | Kudu
Debt Instrument
Borrowings							0	0	0	3,000,000
Debt			$ 0				$ 0	$ 0	$ 0	$ 0		$ 0	0				$ 0	$ 89,200,000
Percentage of borrowing base							35%		35%		35%
Remaining borrowing capacity under revolving credit facility							$ 39,600,000		$ 39,600,000
Other Operations | Term Loan
Debt Instrument
Outstanding balance							$ 36,400,000		$ 36,400,000				$ 17,100,000

Debt - Schedule of the Change i

Debt - Schedule of the Change in Debt (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Debt Instrument
Beginning balance			$ 420.9
Repayments			(10.5)	$ (94.8)
Ending balance	$ 615.5		615.5
Kudu Credit Facility
Debt Instrument
Beginning balance			218.2
Ending balance	253.5		253.5
Kudu | Term Loan | Kudu Bank Facility
Debt Instrument
Beginning balance	0	$ 0	0	89.2
Borrowings	0	0	0	3
Repayments	0	0	0	(92.2)
Ending balance	0	0	0	0
Kudu | Term Loan | Kudu Credit Facility
Debt Instrument
Beginning balance	260.4	203	225.4	0
Borrowings	0	0	35	203
Repayments	0	0	0	0
Ending balance	$ 260.4	$ 203	$ 260.4	$ 203

Income Taxes (Details)

Income Taxes (Details)	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation, percent	23.90%	(7.90%)	9.40%	(17.10%)

Derivatives (Details)

Derivatives (Details) - HG Global - Interest Rate Cap - USD ($)		3 Months Ended	9 Months Ended
	Jun. 16, 2022	Sep. 30, 2022	Sep. 30, 2022
Derivative [Line Items]
Notional amount	$ 150,000,000
Premiums paid	$ 3,300,000
Derivative, fair value, net		$ 3,900,000	$ 3,900,000
Interest Expense
Derivative [Line Items]
Change in fair value of derivative instruments		$ 2,100,000	$ 600,000
Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Derivative [Line Items]
Derivative, cap interest rate	3.50%
3-month variable rate		3.60%	3.60%

Municipal Bond Guarantee Insu_3

Municipal Bond Guarantee Insurance - Narrative (Details) - USD ($) $ in Millions	1 Months Ended			3 Months Ended		9 Months Ended
	Sep. 30, 2022	Dec. 31, 2021	Jan. 31, 2021	Mar. 31, 2021	Jun. 30, 2018	Sep. 30, 2022	Dec. 31, 2022	Sep. 01, 2022	Jan. 31, 2020	Jul. 31, 2012
Guarantor Obligations [Line Items]
Percentage of risk premium ceded	60%					60%
Insurance-linked securities, term				12 years	12 years
Insurance-linked securities, callable term				5 years	5 years
Debt	$ 615.5	$ 420.9				$ 615.5
HG Global
Guarantor Obligations [Line Items]
Collateral held in supplement trust	833.9	852				833.9
Collateral trusts, investments and cash	457.7	481.7				457.7
BAM
Guarantor Obligations [Line Items]
Surplus notes	364.6	364.6				364.6
Interest receivable	11.6	5.7				11.6
HG Global
Guarantor Obligations [Line Items]
Surplus notes	$ 503					$ 503				$ 503
Percentage of par value of policy reinsured	15%					15%
Percent over a target trust balance						102%
Supplement trust target	$ 603					$ 603
HG Global | Series A BAM Surplus Note
Guarantor Obligations [Line Items]
Assets Held-in-trust	$ 574.5	601.8				$ 574.5
HG Global | BAM | Maximum
Guarantor Obligations [Line Items]
Aggregate losses on ceded business									$ 125
HG Re
Guarantor Obligations [Line Items]
Percentage of par value of policy reinsured	15%					15%
Assets Held-in-trust	$ 259.4	250.2				$ 259.4
BAM
Guarantor Obligations [Line Items]
Principal	98,619	89,196.5	$ 805.5			98,619		$ 42.5
BAM | HG Global
Guarantor Obligations [Line Items]
Interest receivable	166.4	157.6				166.4
BAM | Surplus Note
Guarantor Obligations [Line Items]
Repayments of unsecured debt		33.8
Accrued interest payment on surplus notes		9.8
BAM | Surplus Note | HG Global
Guarantor Obligations [Line Items]
Debt	$ 364.6	364.6				$ 364.6
BAM | Supplemental Trust
Guarantor Obligations [Line Items]
Repayments of unsecured debt		23.6
Accrued interest payment on surplus notes		$ 0.4
BAM | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Basis spread on variable rate						3%
BAM | Fixed interest rate | Surplus Note
Guarantor Obligations [Line Items]
Derivative, fixed interest rate (as a percent)	8%					8%
BAM | Forecast | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Effective percentage							3.20%
BAM | Fidus Re Ltd.
Guarantor Obligations [Line Items]
Secured debt				$ 150	$ 100
Aggregate losses on ceded business				135	165
Premium receivable, Premium expected to be collected				150	100
Percentage of quota share reinsurance agreement	100%		100%
BAM | Fidus Re Ltd. | 2018 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						28%
BAM | Fidus Re Ltd. | 2021 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						33%
BAM | Fidus Re Ltd. | Maximum
Guarantor Obligations [Line Items]
Aggregate losses on ceded business				$ 301.7	$ 276.1
Fidus Re Ltd. | BAM
Guarantor Obligations [Line Items]
Losses above retention, percentage of liability				90%	90%

Municipal Bond Guarantee Insu_4

Municipal Bond Guarantee Insurance - Schedule of Municipal Bond Guarantee Insured Obligations (Details) - BAM $ in Millions	9 Months Ended	12 Months Ended
	Sep. 30, 2022 USD ($) Contract	Dec. 31, 2021 USD ($) Contract	Sep. 01, 2022 USD ($)	Jan. 31, 2021 USD ($)
Guarantor Obligations [Line Items]
Contracts outstanding | Contract	13,094	12,350
Remaining weighted average contract period outstanding (in years)	10 years 9 months 18 days	10 years 9 months 18 days
Principal	$ 98,619	$ 89,196.5	$ 42.5	$ 805.5
Interest	47,595	41,486.5
Total debt service outstanding	146,214	130,683
Total gross unearned insurance premiums	$ 286.7	$ 266.3

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	Sep. 30, 2022	Dec. 31, 2021
Guarantor Obligations [Line Items]
October 1, 2022 - December 31, 2022	$ 6.9
January 1, 2023 - March 31, 2023	6.8
April 1, 2023 - June 30, 2023	6.7
July 1, 2023 - September 30, 2023	6.6
October 1, 2023 - December 31, 2023	6.4
Total 2023	26.5
2024	24.9
2025	23.2
2026	21.6
2027	20.1
2028 and thereafter	163.5
Total gross unearned insurance premiums	$ 286.7	$ 266.3

Municipal Bond Guarantee Insu_6

Municipal Bond Guarantee Insurance - Schedule of Net Written Premiums (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earned premiums:
Net earned premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
HG/BAM
Written premiums:
Direct	18.4	12.8	44.9	34.5
Assumed	1.3	0	1.3	4.5
Net written premiums	19.7	12.8	46.2	39
Earned premiums:
Direct	6.5	5.9	22	16.8
Assumed	0.6	0.8	4	2.8
Net earned premiums	$ 7.1	$ 6.7	$ 26	$ 19.6

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		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Less: total income (loss) from discontinued operations, net of tax	893.1	5.3	903.2	(5.1)
Net (income) loss from discontinued operations attributable to non-controlling interests	(0.1)	0	(0.7)	1.1
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(4.8)	(376.7)	(150.1)	(304.2)
Allocation of losses (earnings) to participating restricted common shares	0.1	4.6	1.8	3.5
Basic and diluted earnings (losses) per share numerators	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Basic and diluted earnings per share (in dollars) - continuing operations:
Distributed earnings - dividends declared and paid (in usd per share)	$ 0	$ 0	$ 1	$ 1
Undistributed (losses) earnings (in usd per share)	(1.66)	(121.90)	(51.73)	(99.16)
Continuing operations (in usd per share)	(1.66)	(121.90)	(50.73)	(98.16)
Continuing operations (in usd per share)	$ (1.66)	$ (121.90)	$ (50.73)	$ (98.16)

Earnings Per Share - Undistribu

Earnings Per Share - Undistributed Net Earnings From Continuing Operations (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Earnings Per Share [Abstract]
Net income (losses) attributable to White Mountains’s common shareholders, net of restricted common share amounts	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Dividends declared net of restricted common share amounts	0	0	(3)	(3.1)
Total undistributed net earnings (losses), net of restricted common share amounts	$ (4.7)	$ (372.1)	$ (151.3)	$ (303.8)

Employee Share-Based Incentiv_3

Employee Share-Based Incentive Compensation Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended		36 Months Ended
	Sep. 30, 2022 USD ($) shares	Sep. 30, 2021 USD ($) shares	Sep. 30, 2022 USD ($) shares	Sep. 30, 2021 USD ($) shares	Dec. 31, 2021 USD ($) shares	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Dec. 31, 2020 USD ($)
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	0	0	13,225	13,475	750
Additional compensation cost that would be recognized if all outstanding performance shares vested | $	$ 41.2		$ 41.2
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
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 | $	$ 19.2	$ 19.4	$ 19.2	$ 19.4	$ 15.9	$ 23	$ 23.2	$ 15.2
Issued (in shares) | shares	0	0	13,225	13,475

Employee Share-Based Incentiv_4

Employee Share-Based Incentive Compensation Plans - Performance Shares (Details) - Performance Share - W T M Incentive Plan - USD ($) $ in Millions	1 Months Ended		3 Months Ended		9 Months Ended		36 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Target Performance Shares Outstanding
Beginning of period (in shares)			39,449	41,252	40,828	42,458
Shares paid (in shares)			0	(219)	(14,625)	(14,336)
New grants (in shares)			0	0	13,225	13,475	750
Forfeitures and cancellations (in shares)			0	205	21	769
Expense recognized (in shares)			0	0	0	0
End of period (in shares)			39,449	40,828	39,449	40,828	40,828
Accrued Expense
Beginning of period			$ 41.2	$ 45.7	$ 42.2	$ 56.3
Shares paid			0	(0.6)	(26.4)	(35.2)
New grants			0	0	0	0
Forfeitures and cancellations			(0.1)	0.2	(0.2)	0.4
Expense recognized			11.9	(6.5)	37.4	17.3
End of period			$ 53	$ 38.8	$ 53	$ 38.8	$ 42.2
Range Of Performance Cycle Current Year
Accrued Expense
Percentage of target payout - minimum actual	172%
Range Of Performance Cycle Previous Year
Accrued Expense
Percentage of target payout - minimum actual		200%

Employee Share-Based Incentiv_5

Employee Share-Based Incentive Compensation Plans - Performance Shares Granted Under the WTM Incentive Plan (Details) - Performance Share - W T M Incentive Plan - USD ($) $ in Millions	Sep. 30, 2022	Jun. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Dec. 31, 2020
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	40,050
Assumed forfeitures (in shares)	(601)
Total target performance shares outstanding (in shares)	39,449	39,449	40,828	40,828	41,252	42,458
Accrued Expense	$ 53.8
Assumed forfeitures	(0.8)
Total Accrued Expense	$ 53	$ 41.2	$ 42.2	$ 38.8	$ 45.7	$ 56.3
2020 – 2022
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,350
Accrued Expense	$ 31.9
2021 – 2023
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,475
Accrued Expense	$ 14.7
2022 – 2024
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,225
Accrued Expense	$ 7.2

Employee Share-Based Incentiv_6

Employee Share-Based Incentive Compensation Plans - Restricted Shares (Details) - W T M Incentive Plan - Restricted Stock - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Restricted Shares
Beginning of period (in shares)	38,350	38,280	37,850	43,105
Issued (in shares)	0	0	13,225	13,475
Vested (in shares)	0	(219)	(12,725)	(17,936)
Forfeited (in shares)	0	(211)	0	(794)
Expense recognized (in shares)	0	0	0	0
End of period (in shares)	38,350	37,850	38,350	37,850
Unamortized Issue Date Fair Value
Beginning of period	$ 23	$ 23.2	$ 15.9	$ 15.2
Issued	0	0	13.8	16.1
Vested	0	0	0	0
Forfeited	0	(0.2)	0	(0.8)
Expense recognized	(3.8)	(3.6)	(10.5)	(11.1)
End of period	$ 19.2	$ 19.4	$ 19.2	$ 19.4

Leases - Narrative (Details)

Leases - Narrative (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Leases [Abstract]
ROU lease assets	$ 24.5	$ 28.1
Operating lease liabilities	$ 26.5	$ 30

Leases - Schedule of Lease Cost

Leases - Schedule of Lease Cost (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Leases [Abstract]
Lease cost	$ 1.9	$ 1.9	$ 5.9	$ 4.8
Less: sublease income	0.2	0.1	0.5	0.3
Net lease cost	$ 1.7	$ 1.8	$ 5.4	$ 4.5

Leases - Schedule of Future Min

Leases - Schedule of Future Minimum Payments on Operating Leases (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Leases [Abstract]
Remainder of 2022	$ 1.7
2023	8.1
2024	7.1
2025	4.9
2026	2.6
Thereafter	5
Total undiscounted lease payments	29.4
Less: present value adjustment	2.9
Operating lease liabilities	$ 26.5	$ 30

Leases - Schedule of Right-of-U

Leases - Schedule of Right-of-Use Assets and Lease Liabilities (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Lessee, Lease, Description [Line Items]
ROU lease assets	$ 24.5	$ 28.1
Lease liabilities	$ 26.5	$ 30
Operating lease, weighted average incremental borrowing rate, percent	4.10%	4%
HG/BAM
Lessee, Lease, Description [Line Items]
ROU lease assets	$ 6.2	$ 7.6
Lease liabilities	6.7	8.1
Ark
Lessee, Lease, Description [Line Items]
ROU lease assets	6.6	7
Lease liabilities	6.6	7
Asset Management (Kudu)
Lessee, Lease, Description [Line Items]
ROU lease assets	5.9	6.4
Lease liabilities	6.8	7.1
Other Operations
Lessee, Lease, Description [Line Items]
ROU lease assets	5.8	7.1
Lease liabilities	$ 6.4	$ 7.8

Non-controlling Interests (Deta

Non-controlling Interests (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 158.3	$ 156.6
Total Non-Controlling Excluding Reciprocals
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 318.4	$ 280.6
HG Global
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	3.10%	3.10%
Total non-controlling interests	$ (0.3)	$ 8.9
Ark
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	28%	28%
Total non-controlling interests	$ 217.1	$ 230.7
Asset Management (Kudu)
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	10.70%	0.70%
Total non-controlling interests	$ 80.8	$ 12.4
NSM Insurance Group
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	0%	3.50%
Total non-controlling interests	$ 0	$ 16.7
Other
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 20.8	$ 11.9
BAM
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	100%	100%
Total non-controlling interests	$ (160.1)	$ (124)

Segment Information - Narrative

Segment Information - Narrative (Details)	9 Months Ended
	Sep. 30, 2022 segment
Segment Reporting [Abstract]
Number of operating segments	4

Segment Information - Financial

Segment Information - Financial Information for White Mountain's Segments (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Segment Reporting Information [Line Items]
Earned insurance premiums	$ 353.2	$ 220.1	$ 783.8	$ 455.4
Net investment income	33.9	19.5	79.6	57.2
Net realized and unrealized investment gains (losses)	(29.4)	30.5	(141.9)	91.2
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7
Other revenues	40.9	31.9	103.4	68.1
Total revenues	383.2	(92.4)	720.3	353.4
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	76.5	56.7	184.4	130.9
Cost of sales	25	24	68.8	45.9
General and administrative expenses	87.1	51.9	258.4	215.5
Amortization of other intangible assets	1.4	2	3.4	3.1
Interest expense	10.5	4.4	27.5	14.8
Total expenses	414.2	268.2	998.7	658
Pre-tax income (loss) from continuing operations	(31)	(360.6)	(278.4)	(304.6)
Financial Guarantee (HG Global/BAM)
Segment Reporting Information [Line Items]
Earned insurance premiums	7.1	6.7	26	19.6
Net investment income	5.7	4.4	15.1	13.2
Net realized and unrealized investment gains (losses)	(38.8)	(4)	(114)	(15.6)
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	1.3	0.3	3.7	0.9
Total revenues	(24.7)	7.4	(69.2)	18.1
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	1.7	3	9.5	6.5
Cost of sales	0	0	0	0
General and administrative expenses	15.8	12.4	49.5	42.7
Amortization of other intangible assets	0	0	0	0
Interest expense	2	0	5.4	0
Total expenses	19.5	15.4	64.4	49.2
Pre-tax income (loss) from continuing operations	(44.2)	(8)	(133.6)	(31.1)
Ark
Segment Reporting Information [Line Items]
Earned insurance premiums	346.1	213.4	757.8	435.8
Net investment income	4.9	0.6	9.7	1.8
Net realized and unrealized investment gains (losses)	(14.4)	0.3	(76.5)	10.3
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	6.6	3.4	10.1	9.4
Total revenues	343.2	217.7	701.1	457.3
Loss and loss adjustment expenses	213.7	129.2	456.2	247.8
Insurance and reinsurance acquisition expenses	74.8	53.7	174.9	124.4
Cost of sales	0	0	0	0
General and administrative expenses	26.9	21.8	79.8	84.4
Amortization of other intangible assets	0	0	0	0
Interest expense	3.7	2.1	10.6	4.5
Total expenses	319.1	206.8	721.5	461.1
Pre-tax income (loss) from continuing operations	24.1	10.9	(20.4)	(3.8)
Asset Management (Kudu)
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0	0	0
Net investment income	14.8	9.5	41.2	26.1
Net realized and unrealized investment gains (losses)	41.1	18.9	45.8	62.5
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	0	0	0	0
Commission revenues	0	0	0	0
Other revenues	0	0.1	0	0.2
Total revenues	55.9	28.5	87	88.8
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	4.5	3.3	10.2	9
Amortization of other intangible assets	0	0	0.2	0.2
Interest expense	4.2	1.9	10.3	9.2
Total expenses	8.7	5.2	20.7	18.4
Pre-tax income (loss) from continuing operations	47.2	23.3	66.3	70.4
Other Operations
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0	0	0
Net investment income	8.5	5	13.6	16.1
Net realized and unrealized investment gains (losses)	(17.3)	15.3	2.8	34
Net realized and unrealized investment gains (losses) from investment in MediaAlpha	(18.6)	(396.8)	(113.3)	(325.5)
Commission revenues	3.2	2.4	8.7	7
Other revenues	33	28.1	89.6	57.6
Total revenues	8.8	(346)	1.4	(210.8)
Loss and loss adjustment expenses	0	0	0	0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	25	24	68.8	45.9
General and administrative expenses	39.9	14.4	118.9	79.4
Amortization of other intangible assets	1.4	2	3.2	2.9
Interest expense	0.6	0.4	1.2	1.1
Total expenses	66.9	40.8	192.1	129.3
Pre-tax income (loss) from continuing operations	$ (58.1)	$ (386.8)	$ (190.7)	$ (340.1)

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	Sep. 30, 2022	Dec. 31, 2021	May 07, 2020	May 06, 2020
Investments in unconsolidated affiliates
Other long-term investments	$ 1,622.7	$ 1,377.8
Kudu investments
Investments in unconsolidated affiliates
Other long-term investments	$ 813.2	$ 669.5
Kudu investments | Minimum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	4.10%	3.20%
Kudu investments | Maximum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	33%	32%
Marketing Technology (MediaAlpha)
Investments in unconsolidated affiliates
Ownership interest (as a percent)	27.40%	28%
Other long-term investments	$ 148.2	$ 261.6
PassportCard/DavidShield
Investments in unconsolidated affiliates
Ownership interest (as a percent)	53.80%	53.80%	53.80%	50%
Other long-term investments	$ 132	$ 120
Elementum Holdings, L.P.
Investments in unconsolidated affiliates
Ownership interest (as a percent)	29.70%	29.70%
Other long-term investments	$ 45	$ 45
Other
Investments in unconsolidated affiliates
Other long-term investments	102.7	109.3
Equity Method Investments
Investments in unconsolidated affiliates
Other long-term investments	$ 27.7	$ 17.8

Equity-Method Eligible Invest_4

Equity-Method Eligible Investments - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Equity Method Investee
Schedule of Equity Method Investments [Line Items]
Proceeds from dividends received	$ 16.1	$ 13	$ 42.9	$ 37.7

Equity-Method Eligible Invest_5

Equity-Method Eligible Investments - Equity Method Investments Financial Data (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Total assets	$ 7,545		$ 7,545		$ 7,000.7
Total liabilities	3,678.7		3,678.7		3,296
Total revenues	383.2	$ (92.4)	720.3	$ 353.4
Net income (loss)	888.2	(371.4)	752.4	(308.2)
Marketing Technology (MediaAlpha)
Schedule of Equity Method Investments [Line Items]
Total assets	265.2		265.2		289.8
Total liabilities	333.6		333.6		$ 351.4
Total revenues	89	152.7	335.1	483.7
Total expenses	110.2	157	379.2	488.2
Net income (loss)	$ (21.2)	$ (4.3)	$ (44.1)	$ (4.5)

Fair Value of Financial Instr_3

Fair Value of Financial Instruments (Details) - USD ($) $ in Millions	Sep. 30, 2022	Dec. 31, 2021
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 615.5	$ 420.9
Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	253.5	218.2
Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	35.6
Fair Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	146.1	0
Fair Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	26.2	27.6
Fair Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	149.4	162.8
Fair Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	265.5	246.8
Fair Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Fair Value	36.8	17.7
Carrying Value | HG Global Senior Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	146.4	0
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	150	155.9
Carrying Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	260.4	218.2
Carrying Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 35.6	$ 16.8

Held for Sale and Discontinue_3

Held for Sale and Discontinued Operations - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2018	Dec. 31, 2021	Dec. 31, 2020
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group			$ 886.8	$ 18.7
Other Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Liability related to sale	$ 0		0			$ 495.3
Assets held for sale - Other	0		0			$ 16.1
Sirius Group
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group	$ 0	$ 0	$ 0	18.7	$ 17.3
Discontinued Operations, Disposed of by Sale | Sirius Group
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain (loss) from sale of discontinued operations, net of tax - Sirius Group				17.6
Liability related to sale							$ 18.7
Net (income) loss from discontinued operations attributable to non-controlling interests				$ 1.1

Held for Sale and Discontinue_4

Held for Sale and Discontinued Operations - Financial Statement Disclosure (Details) - USD ($) $ in Millions		3 Months Ended		9 Months Ended		12 Months Ended
	Aug. 01, 2022	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2018	Dec. 31, 2021	Dec. 31, 2020
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net income (loss) from discontinued operations, net of tax - NSM Group		$ 6.3	$ 5.3	$ 16.4	$ (23.8)
Net gain (loss) from sale of discontinued operations, net of tax				886.8	18.7
Total income (loss) from discontinued operations, net of tax		(893.1)	(5.3)	(903.2)	5.1
Net (income) loss from discontinued operations attributable to non-controlling interests		(0.1)	0	(0.7)	1.1
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group		0.7	(2.2)	(5.2)	0.9
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group		2.9	0	2.9	0
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations				38.7	40.3
Net cash provided from (used for) investing activities				7.1	(54.6)
Net cash used from (used for) financing activities				(17.5)	13.8
Net change in cash during the period				98	99.4
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)				147.7	84.6
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)		245.7	184	245.7	184
Restricted cash balance		8.9	4	8.9	4		$ 4.5	$ 0
Interest paid				(10.9)	(5.3)
Net income tax payments				3.2	2.1
NSM Insurance Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		886.8	0	886.8	0
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)				143.9	0
Sirius Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		0	0	0	18.7	$ 17.3
Discontinued Operations, Held-for-sale | NSM Insurance Group
Disposal Group, Including Discontinued Operation, Balance Sheet Disclosures [Abstract]
Short-term investments, at fair value							7.8
Cash (restricted $89.2)							111.6
Restricted cash							89.2
Premiums and commissions receivable							85
Goodwill and other intangible assets							725.4
Other assets							59.2
Total assets held for sale							989
Debt							272.1
Premiums payable							135.9
Contingent consideration							6.8
Other liabilities							80.5
Total liabilities held for sale							495.3
Net assets held for sale							493.7
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Commission revenues		26.6	67	176.9	194.6
Other revenues		7	15.3	48.1	46.8
Total revenues - NSM Group		33.6	82.3	225	241.4
General and administrative expenses		15.7	48.9	126.8	142.4
Broker commission expenses		8.2	20.4	52.9	60.9
Change in fair value of contingent consideration		0	0.6	0.1	0.8
Amortization of other intangible assets		0	8.2	9.1	25
Loss on assets held for sale		0	0	0	(28.7)
Interest expense		1.6	5.9	12.1	17.7
Total expenses - NSM Group		25.5	84	201	275.5
Pre-tax income (loss) from discontinued operations - NSM Group		8.1	(1.7)	24	(34.1)
Income tax (expense) benefit		(1.8)	7	(7.6)	10.3
Net income (loss) from discontinued operations, net of tax - NSM Group		6.3	5.3	16.4	(23.8)
Net gain (loss) from sale of discontinued operations, net of tax		886.8	0	886.8	0
Total income (loss) from discontinued operations, net of tax		893.1	5.3	903.2	(5.1)
Net (income) loss from discontinued operations attributable to non-controlling interests		(0.2)	0	(0.8)	1.1
Total income (loss) from discontinued operations attributable to White Mountains’s common shareholders		892.9	5.3	902.4	(4)
Other comprehensive income (loss) from discontinued operations, net of tax - NSM Group		0.7	(1.7)	(5.2)	0.9
Comprehensive income (loss) from discontinued operations		896.5	3.6	900.1	(3.1)
Other comprehensive income (loss) from discontinued operations attributable to non-controlling interests		(0.1)	0	0.2	(0.1)
Comprehensive income (loss) from discontinued operations attributable to White Mountains’s common shareholders		896.4	3.6	900.3	(3.2)
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Net cash provided from (used for) operations				38.7	40.3
Net cash provided from (used for) investing activities				7.1	(54.6)
Net cash used from (used for) financing activities				(17.5)	13.8
Effect of exchange rate changes on cash				4	0.6
Net change in cash during the period				32.3	0.1
Cash balances at beginning of period (includes restricted cash balances of $4.5 and $0.0 and excludes discontinued operations cash balances of $111.6 and $126.6)				111.6	126.6
Cash sold as part of the sale of NSM Group (includes restricted cash of $105.1 and $0.0)				(143.9)	0
Cash balances at end of period (includes restricted cash balances of $8.9 and $4.0 and excludes discontinued operations cash balances of $0.0 and 126.7)		0	126.7	0	126.7
Restricted cash balance		0	92.2	0	92.2		$ 89.2	78.4
Interest paid				(12)	(16.6)
Net income tax payments				0	0
Discontinued Operations, Held-for-sale | Sirius Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax		0	0	0	18.7
Discontinued Operations, Disposed of by Sale | NSM Insurance Group
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Loss on assets held for sale	$ (875.7)
Net gain (loss) from sale of discontinued operations, net of tax	886.8
Net gain (loss) from foreign currency translation from sale of discontinued operations, net of tax - NSM Group	$ 2.9
Net Cash Provided by (Used in) Discontinued Operations [Abstract]
Restricted cash balance		$ 105.1	$ 0	$ 105.1	0
Discontinued Operations, Disposed of by Sale | Sirius Group
Disposal Group, Including Discontinued Operation, Balance Sheet Disclosures [Abstract]
Total liabilities held for sale								$ 18.7
Disposal Group, Including Discontinued Operation, Income Statement Disclosures [Abstract]
Net gain (loss) from sale of discontinued operations, net of tax					$ 17.6

Held for Sale and Discontinue_5

Held for Sale and Discontinued Operations - Earnings Per Share for Discontinued Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Basic and diluted earnings per share numerators (in millions):
Net income (loss)	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(4.8)	(376.7)	(150.1)	(304.2)
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders	(893.1)	(5.3)	(903.2)	5.1
Allocation of earnings to participating restricted common shares	0.1	4.6	1.8	3.5
Basic and diluted earnings (losses) per share numerators	$ (4.7)	$ (372.1)	$ (148.3)	$ (300.7)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)
Discontinued Operations
Basic and diluted earnings per share numerators (in millions):
Net income (loss)	$ 888.2	$ (371.4)	$ 752.4	$ (308.2)
Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent	(23.6)	(389.2)	(252.3)	(356.8)
Less: net (income) loss from continuing operations attributable to non-controlling interests	18.8	12.5	102.2	52.6
Total gain (loss) from discontinued operations attributable to White Mountains’s common shareholders	893	5.3	902.5	(4)
Allocation of earnings to participating restricted common shares	(11.8)	(0.1)	(10.8)	0
Basic and diluted earnings (losses) per share numerators	$ 881.2	$ 5.2	$ 891.7	$ (4)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Basic earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	2,893,800	3,090,300	2,959,300	3,099,400
Average unvested restricted common shares (in shares)	(38,300)	(37,800)	(35,500)	(36,000)
Diluted earnings (losses) per share denominator (in shares)	2,855,500	3,052,500	2,923,800	3,063,400
Discontinued operations (in usd per share)	$ 308.59	$ 1.72	$ 304.97	$ (1.29)