White Mountains Insurance (WTM) 10-Q 8 Nov 21 2021 Q3 Quarterly report Financial data

Cover Page

Cover Page - shares	9 Months Ended
	Sep. 30, 2021	Nov. 05, 2021
Cover [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Sep. 30, 2021
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)		3,017,772
Entity Central Index Key	0000776867
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2021
Document Fiscal Period Focus	Q3
Amendment Flag	false

CONSOLIDATED BALANCE SHEETS

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Investments
Other long-term investments	$ 1,285.5	$ 786.8
Total assets	7,113.6	4,831.4
Liabilities
Loss and loss adjustment expense reserves	890.9	696
Debt	710.4	376.4
Total liabilities	3,459.3	1,013.5
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 3,029,620 and 3,102,011 shares and paid-in surplus	3	3.1
Paid-in surplus	583.2	592.1
Retained earnings	2,935.3	3,311.2
Accumulated other comprehensive gain (loss), after-tax:
Net unrealized foreign currency translation and interest rate swap gains (losses)	0.2	(0.4)
Total White Mountains’s common shareholders’ equity	3,521.7	3,906
Non-controlling interests	132.6	(88.1)
Total equity	3,654.3	3,817.9
Total liabilities and equity	7,113.6	4,831.4
Financial Guarantee (HG Global/BAM)
Investments
Fixed maturity investments, at fair value	898.4	859.5
Short-term investments, at fair value	50.3	60.4
Total investments	948.7	919.9
Cash	21.8	42.8
Insurance premiums receivable	6.9	6.9
Deferred acquisition costs	31.7	27.8
Other assets	18.7	20.4
Total assets	1,027.8	1,017.8
Liabilities
Unearned insurance premiums	257	237.5
Accrued incentive compensation	21	25.7
Other liabilities	32.5	28.3
Total liabilities	310.5	291.5
P&C Insurance and Reinsurance (Ark)
Investments
Fixed maturity investments, at fair value	618.1	0
Common equity securities, at fair value	159.6	0
Short-term investments, at fair value	396.5	0
Other long-term investments	320.6	0
Total investments	1,494.8	0
Cash	116.5	0
Reinsurance recoverables	465.6	0
Insurance premiums receivable	482.3	0
Ceded unearned premiums	92.1	0
Deferred acquisition costs	127.8	0
Goodwill and other intangible assets	292.5	0
Other assets	61.3	0
Total assets	3,132.9	0
Liabilities
Loss and loss adjustment expense reserves	890.9	0
Unearned insurance premiums	596.6	0
Debt	200.7	0
Reinsurance payable	481.4	0
Contingent consideration	24	0
Other liabilities	87.4	0
Total liabilities	2,281	0
Specialty Insurance Distribution (NSM)
Investments
Cash	126.5	126.5
Premiums and commissions receivable	78.8	76.7
Goodwill and other intangible assets	734.8	736.8
Other assets	56.4	59.6
Total assets	996.5	999.6
Liabilities
Debt	295	272.6
Premiums Payable	132.5	113.4
Contingent consideration	6.7	14.6
Other liabilities	84.2	91.2
Total liabilities	518.4	491.8
Asset Management (Kudu)
Investments
Short-term investments, at fair value	0.1	0.1
Other long-term investments	604.7	400.6
Total investments	604.8	400.7
Cash	14.8	7.8
Accrued investment income	9	9.8
Goodwill and other intangible assets	9	9.2
Other assets	8.4	2.7
Total assets	646	430.2
Liabilities
Debt	195.6	86.3
Other liabilities	40.2	10
Total liabilities	235.8	96.3
Other Operations
Investments
Fixed maturity investments, at fair value	316.4	347.7
Short-term investments, at fair value	162.6	82.4
Investment in MediaAlpha, at fair value	316.4	802.2
Other long-term investments	360.2	386.2
Total investments	1,155.6	1,618.5
Cash	31.1	34.1
Cash pre-funded/placed in escrow for Ark Transaction	0	646.3
Goodwill and other intangible assets	48.7	36.4
Other assets	75	48.5
Total assets	1,310.4	2,383.8
Liabilities
Debt	19.1	17.5
Accrued incentive compensation	44.7	70.1
Other liabilities	49.8	46.3
Total liabilities	$ 113.6	$ 133.9

CONSOLIDATED BALANCE SHEETS (Pa

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
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)	3,029,620	3,102,011
Common shares, outstanding shares (in shares)	3,029,620	3,102,011
Specialty Insurance Distribution (NSM)
Restricted cash	$ 92.2	$ 78.4
Kudu
Restricted cash	$ 4.5	$ 0

CONSOLIDATED STATEMENTS OF OPER

CONSOLIDATED STATEMENTS OF OPERATIONS (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Revenues:
Earned insurance premiums	$ 220.1	$ 6.2	$ 455.4	$ 17.2
Net investment income	19.5	71.2	57.2	113.7
Net realized and unrealized investment (losses) gains	30.5	56.6	91.2	7.8
Commission revenues	69.4	60.3	201.6	180.3
Other revenues	47.2	15.2	114.9	45.9
Total revenues	(10.1)	459.5	594.8	659.9
Expenses:
Loss and loss adjustment expenses	129.2		247.8
Insurance and reinsurance acquisition expenses	56.7	1.6	130.9	5.4
Cost of sales	24	2.3	45.9	6.5
General and administrative expenses	100.8	103.4	357.9	267
Broker commission expenses	20.4	17.1	60.9	56.4
Change in fair value of contingent consideration	0.6	0.7	0.8	(1.6)
Amortization of other intangible assets	10.2	5.4	28.1	17.1
Loss on assets held for sale			28.7
Interest expense	10.3	7.8	32.5	21.2
Total expenses	352.2	138.3	933.5	372
Pre-tax (loss) income from continuing operations	(362.3)	321.2	(338.7)	287.9
Income tax expense	(21.6)	(98.5)	(41.9)	(97.1)
Net (loss) income from continuing operations	(383.9)	222.7	(380.6)	190.8
Net (loss) gain from sale of discontinued operations, net of tax	0	(0.7)	18.7	(0.8)
Net (loss) income	(383.9)	222	(361.9)	190
Net loss attributable to non-controlling interests	12.5	10.9	53.7	29.5
Net (loss) income attributable to White Mountains’s common shareholders	(371.4)	232.9	(308.2)	219.5
Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	(396.8)	250	(325.5)	295
Financial Guarantee (HG Global/BAM)
Revenues:
Earned insurance premiums	6.7	6.2	19.6	17.2
Net investment income	4.4	4.7	13.2	15.1
Net realized and unrealized investment (losses) gains	(4)	3.2	(15.6)	23.7
Commission revenues	0	0	0	0
Other revenues	0.3	0.4	0.9	2.1
Total revenues	7.4	14.5	18.1	58.1
Expenses:
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	3	1.6	6.5	5.4
Cost of sales	0	0	0	0
General and administrative expenses	12.4	14	42.7	41.4
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	0	0	0	0
Loss on assets held for sale			0
Interest expense	0	0	0	0
Total expenses	15.4	15.6	49.2	46.8
Pre-tax (loss) income from continuing operations	(8)	(1.1)	(31.1)	11.3
Financial Guarantee (HG Global/BAM) | Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
P&C Insurance and Reinsurance (Ark)
Revenues:
Earned insurance premiums	213.4	0	435.8	0
Net investment income	0.6	0	1.8	0
Net realized and unrealized investment (losses) gains	0.3	0	10.3	0
Commission revenues	0		0
Other revenues	3.4	0	9.4	0
Total revenues	217.7	0	457.3	0
Expenses:
Loss and loss adjustment expenses	129.2	0	247.8	0
Insurance and reinsurance acquisition expenses	53.7	0	124.4	0
Cost of sales	0		0
General and administrative expenses	21.8	0	84.4	0
Broker commission expenses	0		0
Change in fair value of contingent consideration	0		0
Amortization of other intangible assets	0		0
Loss on assets held for sale			0
Interest expense	2.1	0	4.5	0
Total expenses	206.8	0	461.1	0
Pre-tax (loss) income from continuing operations	10.9		(3.8)
P&C Insurance and Reinsurance (Ark) | Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0		0
Specialty Insurance Distribution (NSM)
Revenues:
Earned insurance premiums	0	0	0	0
Net investment income	0	0	0	0
Net realized and unrealized investment (losses) gains	0	0	0	0
Commission revenues	67	58.2	194.6	174.2
Other revenues	15.3	12.5	46.8	37.6
Total revenues	82.3	70.7	241.4	211.8
Expenses:
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	48.8	42.9	142.1	131
Broker commission expenses	20.4	17.1	60.9	56.4
Change in fair value of contingent consideration	0.6	0.7	0.8	(1.6)
Amortization of other intangible assets	8.2	5.1	25	16.2
Loss on assets held for sale	0	0	28.7	0
Interest expense	5.9	6.1	17.7	16.1
Total expenses	83.9	71.9	275.2	218.1
Pre-tax (loss) income from continuing operations	(1.6)	(1.2)	(33.8)	(6.3)
Specialty Insurance Distribution (NSM) | Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
Asset Management (Kudu)
Revenues:
Earned insurance premiums	0	0	0	0
Net investment income	9.5	6.4	26.1	19.3
Net realized and unrealized investment (losses) gains	18.9	9.8	62.5	1.5
Commission revenues	0	0	0	0
Other revenues	0.1	0.1	0.2	0.2
Total revenues	28.5	16.3	88.8	21
Expenses:
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	3.3	2.2	9	7.5
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	0	0.1	0.2	0.3
Loss on assets held for sale			0
Interest expense	1.9	1.4	9.2	4.3
Total expenses	5.2	3.7	18.4	12.1
Pre-tax (loss) income from continuing operations	23.3	12.6	70.4	8.9
Asset Management (Kudu) | Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
Other Operations
Revenues:
Earned insurance premiums	0	0	0	0
Net investment income	5	60.1	16.1	79.3
Net realized and unrealized investment (losses) gains	15.3	43.6	34	(17.4)
Commission revenues	2.4	2.1	7	6.1
Other revenues	28.1	2.2	57.6	6
Total revenues	(346)	358	(210.8)	369
Expenses:
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	24	2.3	45.9	6.5
General and administrative expenses	14.5	44.3	79.7	87.1
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	2	0.2	2.9	0.6
Loss on assets held for sale			0
Interest expense	0.4	0.3	1.1	0.8
Total expenses	40.9	47.1	129.6	95
Pre-tax (loss) income from continuing operations	(386.9)	310.9	(340.4)	274
Other Operations | Marketing Technology (MediaAlpha)
Revenues:
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	$ (396.8)	$ 250	$ (325.5)	$ 295

CONSOLIDATED STATEMENTS OF COMP

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Statement of Comprehensive Income [Abstract]
Net (loss) income attributable to White Mountains’s common shareholders	$ (371.4)	$ 232.9	$ (308.2)	$ 219.5
Other comprehensive (loss) income, net of tax	(2.2)	3.9	0.6	1
Comprehensive (loss) income	(373.6)	236.8	(307.6)	220.5
Other comprehensive loss (income) attributable to non-controlling interests	0.2	(0.1)	0	(0.3)
Comprehensive (loss) income attributable to White Mountains’s common shareholders	$ (373.4)	$ 236.7	$ (307.6)	$ 220.2
Basic (loss) earnings per share
Continuing operations (in usd per share)	$ (120.18)	$ 75.32	$ (105.48)	$ 70.40
Discontinued operations (in usd per share)	0	(0.23)	6.03	(0.26)
Total consolidated operations (in usd per share)	(120.18)	75.09	(99.45)	70.14
Diluted (loss) earnings per share
Continuing operations (in usd per share)	(120.18)	75.32	(105.48)	70.40
Discontinued operations (in usd per share)	0	(0.23)	6.03	(0.26)
Total consolidated operations (in usd per share)	(120.18)	75.09	(99.45)	70.14
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	BAMNon-controlling interest	BAMTotal Equity
Beginning Balances at Dec. 31, 2019		$ 3,261.5	$ 596.3	$ 2,672.4	$ (7.2)	$ (116.8)	$ 3,144.7
Increase (Decrease) in Shareholders' Equity
Net (loss) income	$ 190	219.5		219.5		(29.5)	190
Net change in foreign currency translation and other		0.7			0.7	0.3	1
Comprehensive (loss) income	220.5	220.2		219.5	0.7	(29.2)	191
Dividends declared on common shares		(3.2)		(3.2)			(3.2)
Dividends to non-controlling interests						(2.3)	(2.3)
Issuances of common shares		1.5	1.5				1.5
Repurchases and retirements of common shares		(85.2)	(18.6)	(66.6)			(85.2)
BAM member surplus contribution, net of tax								$ 46.9	$ 46.9
Amortization of restricted share awards		12.3	12.3				12.3
Recognition of equity-based compensation expense of subsidiaries	1	1	1
Net contributions and dilution from other non-controlling interests		(0.4)	(0.4)			2.1	1.7
Acquisition of non-controlling interests						0.8	0.8
Ending Balances at Sep. 30, 2020		3,407.7	592.1	2,822.1	(6.5)	(98.5)	3,309.2
Beginning Balances at Jun. 30, 2020		3,166	587	2,589.3	(10.3)	(102.7)	3,063.3
Increase (Decrease) in Shareholders' Equity
Net (loss) income	222	232.9		232.9		(10.9)	222
Net change in foreign currency translation and other		3.8			3.8	0.2	4
Comprehensive (loss) income	236.8	236.7		232.9	3.8	(10.7)	226
Dividends to non-controlling interests						(0.9)	(0.9)
Issuances of common shares		0.2	0.2				0.2
Repurchases and retirements of common shares		(0.1)		(0.1)			(0.1)
BAM member surplus contribution, net of tax								15.4	15.4
Amortization of restricted share awards		3.6	3.6				3.6
Recognition of equity-based compensation expense of subsidiaries		1	1				1
Net contributions and dilution from other non-controlling interests		0.3	0.3			(0.4)	(0.1)
Acquisition of non-controlling interests	0.8					0.8
Ending Balances at Sep. 30, 2020		3,407.7	592.1	2,822.1	(6.5)	(98.5)	3,309.2
Beginning Balances at Dec. 31, 2020	3,817.9	3,906	595.2	3,311.2	(0.4)	(88.1)	3,817.9
Increase (Decrease) in Shareholders' Equity
Net (loss) income	(361.9)	(308.2)		(308.2)		(53.7)	(361.9)
Net change in foreign currency translation and other		0.4			0.4		0.4
Comprehensive (loss) income	(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	3,654.3	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 (loss) income	(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)
Comprehensive (loss) income	(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	$ 3,654.3	$ 3,521.7	$ 586.2	$ 2,935.3	$ 0.2	$ 132.6	$ 3,654.3

CONSOLIDATED STATEMENTS OF CASH

CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited) - USD ($) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Cash flows from operations:
Net (loss) income	$ (383.9)	$ 222	$ (361.9)	$ 190
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment gains	(30.5)	(56.6)	(91.2)	(7.8)
Deferred income tax expense			29	87.9
Net (gain) loss from sale of discontinued operations, net of tax	0	0.7	(18.7)	0.8
Amortization of restricted share and option awards			11.1	12.2
Amortization and depreciation			42.9	27.2
Other operating items:
Net change in reinsurance recoverables			(32.3)	0
Net change in insurance premiums receivable			(245.7)	0
Net change in commissions receivable			(1.2)	6
Net change in ceded unearned premiums			78.1	0
Net change in loss and loss adjustment expense reserves			194.9	0
Net change in premiums payable			9.5	5.3
Net change in unearned insurance premiums			290	28.6
Net change in deferred acquisition costs			(60)	(4)
Net change in reinsurance payable			(46.8)	0
Net change in restricted cash			18.3	26.6
Investments in Kudu Participation Contracts			(141.6)	(57.5)
Net change in other assets and liabilities, net			46.1	(8.1)
Net cash provided from operations			46	12.2
Cash flows from investing activities:
Net change in short-term investments			(87.3)	(370.3)
Sales of fixed maturity and convertible investments			215.9	293.2
Maturities, calls and paydowns of fixed maturity and convertible investments			144.6	135.2
Sales of common equity securities			176.8	582.9
Distributions and redemptions of other long-term investments and settlements of forward contracts			98.2	64.5
Release of cash pre-funded/placed in escrow for Ark Transaction			646.3	0
Purchases of consolidated subsidiaries, net of cash acquired of $52.2 and $13.4			(39)	(129.4)
Purchases of other long-term investments			(206.5)	(61)
Purchases of common equity securities			(119.7)	(33.8)
Purchases of fixed maturity and convertible investments			(996)	(411.3)
Other investing activities, net			(2.7)	(42)
Net cash (used to) provided from investing activities			(169.4)	28
Cash flows from financing activities:
Draw down of debt and revolving line of credit			403.9	69.4
Repayment of debt and revolving line of credit			(105.9)	(2.7)
Cash dividends paid to the Company’s common shareholders			(3.2)	(3.2)
Common shares repurchased			(87.1)	(78.5)
Net contributions from non-controlling interest shareholders			2	1
Contingent consideration payments related to acquisitions of subsidiaries			(8.8)	(7)
Acquisition of subsidiary shares from non-controlling interest shareholders			(0.4)	0
Capital contributions from BAM members			44.8	46.9
Acquisition of subsidiary shares by non-controlling interest shareholders			6.1	0
Fidus Re premium payment			(6.9)	(2.3)
Other financing activities, net			(22.2)	(9.8)
Net cash provided from financing activities			222.3	13.8
Effect of exchange rate changes on cash			0.6	(0.2)
Net change in cash during the period - continuing operations, including the effect of exchange rate changes			99.5	53.8
Cash balances at beginning of period (includes restricted cash balances of $78.4 and $56.3)			211.2	161	$ 161
Cash balances at end of period (includes restricted cash balances of $96.7 and $82.9)	310.7	214.8	310.7	214.8	$ 211.2
Supplemental cash flows information:
Interest paid			(21.9)	(11.4)
Net income tax payments			(2.1)	(0.1)
Marketing Technology (MediaAlpha)
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment loss (gains) from investment in MediaAlpha	$ 396.8	$ (250)	$ 325.5	$ (295)

CONSOLIDATED STATEMENTS OF CA_2

CONSOLIDATED STATEMENTS OF CASH FLOWS (Parenthetical) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Statement of Cash Flows [Abstract]
Cash acquired from acquisition	$ 52.2	$ 13.4
Restricted cash balance	$ 96.7	$ 82.9	$ 78.4	$ 56.3

Basis of Presentation and Signi

Basis of Presentation and Significant Accounting Policies	9 Months Ended
	Sep. 30, 2021
Accounting Policies [Abstract]
Basis of Presentation and Significant Accounting Policies	Basis of Presentation and Significant Accounting Policies Basis of Presentation The Company 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 located at 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 White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”), its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP. Consolidation Principles Under GAAP, the Company is required to consolidate any entity in which it holds a controlling financial interest. A controlling financial interest is usually in the form of an investment representing the majority of the subsidiary’s voting interests. However, a controlling financial interest may also arise from a financial interest in a variable interest entity (“VIE”) through arrangements that do not involve ownership of voting interests. The Company consolidates a VIE if it determines that it is the primary beneficiary. The primary beneficiary is defined as the entity who holds a variable interest that gives it both the power to direct the VIE’s activities that most significantly impact its economic performance and the obligation to absorb losses of, or the right to receive returns from, the VIE that could potentially be significant to the VIE. Intercompany transactions have been eliminated in consolidation. 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 2020 Annual Report on Form 10-K. Business Combinations White Mountains accounts for purchases of businesses using the acquisition method, which requires the measurement of assets acquired, including goodwill and other intangible assets, and liabilities assumed, including contingent liabilities, at their estimated fair values as of the acquisition date. The acquisition date fair values represent management’s best estimates and are based upon established valuation techniques, reasonable assumptions and, where appropriate, valuations performed by independent third parties. In circumstances where additional information is required in order to determine the acquisition date fair value of balance sheet amounts, provisional amounts may be recorded as of the acquisition date and may be subject to subsequent adjustment throughout the measurement period, which is up to one year from the acquisition date. Measurement period adjustments are recognized in the period in which they are determined. The results of operations and cash flows of businesses acquired are included in the consolidated financial statements from the date of acquisition. White Mountains accounts for purchases of other intangible assets that do not meet the definition of a business as asset acquisitions. Asset acquisitions are recognized at the amount of consideration paid, which is deemed to equal fair value. Use of Estimates 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. Fair Value Measurement s 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”). 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, 2021, White Mountains’s reportable segments were HG Global/BAM, Ark, NSM, Kudu and 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 purposes 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 wholly-owned subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. 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, consisting of $203.0 million of Series A Notes and $300.0 million of Series B Notes (the “BAM Surplus Notes”). As of September 30, 2021 and December 31, 2020, 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 VIE 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 writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through Lloyd’s of London (“Lloyd’s”) Syndicates 4020 and 3902 (the “Syndicates”). Beginning in January 2021, Ark began writing certain classes of its business through Group Ark Insurance Limited (“GAIL”), Ark’s wholly-owned Class 4 Bermuda-based insurance and reinsurance company. As of September 30, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% on a fully-diluted, fully-converted basis, taking account of management’s equity incentives). The remaining shares are owned by employees. In the future, management rollover shareholders could earn additional shares in the company 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. See Note 2 — “Significant Transactions ”. The NSM segment consists of NSM Insurance HoldCo, LLC and its subsidiaries (collectively, “NSM”). NSM is a full-service managing general underwriting agency (“MGU”) and program administrator for specialty property and casualty insurance. The company places insurance in niche sectors such as specialty transportation, real estate, social services and pet. On behalf of its insurance carrier partners, NSM typically manages all aspects of the placement process, including product development, marketing, underwriting, policy issuance and claims. NSM earns commissions based on the volume and, in some cases, profitability of the insurance that it places. NSM does not take insurance risk. As of September 30, 2021 and December 31, 2020, White Mountains owned 96.6% and 96.5% of the basic units outstanding of NSM (87.3% and 89.6% on a fully diluted, fully converted basis). See Note 2 — “Significant Transactions ”. The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset 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 immediate strong, stable cash yields. As of September 30, 2021 and December 31, 2020, White Mountains owned 99.3% and 99.1% of the basic units outstanding (84.7% and 85.4% on a fully diluted, fully converted basis). The Other Operations segment 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 and certain other assets. See Note 2 — “Significant Transactions” . Discontinued Operations and Assets Held for Sale In the first quarter of 2021, White Mountains recorded a gain on sale of discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) in 2016. On April 12, 2021, NSM sold the Fresh Insurance Services Group Limited (“Fresh Insurance”) motor business, which was classified as held for sale at March 31, 2021. The transaction did not meet the criteria to be classified as discontinued operations. See Note 19 — “Held for Sale and Discontinued Operations”. Significant Accounting Policies In addition to the following, refer to the Notes to Consolidated Financial Statements in the Company’s 2020 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies. Ark Insurance Operations Ark writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through the Syndicates. Beginning in January 2021, Ark began writing certain classes of its business through GAIL. For the years of account prior to White Mountains’s transaction with Ark, a significant proportion of the Syndicates’ underwriting capital was provided by other third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts through Ark’s corporate member. The TPC Providers’ economic participation in the Syndicates for the remaining open years of account prior to White Mountains’s transaction with Ark is approximately 51% of the total net result of 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. Ark’s premiums written comprise premiums on insurance contracts incepted during the year as well as premium adjustments related to prior years of account. Insurance premiums are recognized as revenues over the loss exposure or coverage period in proportion to the level of insurance protection provided. In most cases, premiums are earned ratably over the term of the contract with unearned premiums calculated on a monthly pro-rata basis. Catastrophe premiums are earned in proportion to the level of insurance protection provided. Premiums earned are presented net of amounts ceded to reinsurers. Premiums receivable, representing amounts due from insureds, are presented net of an allowance for uncollectible premiums, including expected credit losses, both dispute and credit related. The allowance is based upon Ark’s ongoing review of amounts outstanding, historical loss data, including delinquencies and write-offs, current and forecasted economic conditions and other relevant factors. Credit risk is partially mitigated by Ark’s ability to cancel the policy if the policyholder does not pay the premium. Deferred acquisition costs comprise brokerage and taxes which are directly attributable to and vary with the production of business. These costs are deferred and amortized to the extent they related to successful contract acquisitions over the applicable premium recognition period. Losses and loss adjustment expenses (“LAE”) are charged against income as incurred. Unpaid losses and LAE, including estimates for amounts incurred but not reported (“IBNR”) are based on estimates of the ultimate costs of settling claims, including the effects of inflation and other societal and economic factors. Unpaid loss and LAE reserves represent management’s best estimate of ultimate losses and LAE, net of estimated salvage and subrogation recoveries, if applicable. Such estimates are regularly reviewed and updated and any resulting adjustments are reflected in current results of operations. The process of estimating loss and LAE involves a considerable degree of judgment by management and the ultimate amount of expense to be incurred could be considerably greater than or less than the amounts currently reflected in the financial statements. Reinsurance recoverables represent amounts of paid losses and loss adjustment expenses, case reserves and IBNR amounts ceded to reinsurers under reinsurance treaties. Amounts recoverable from reinsurers are estimated in a manner consistent with the associated claim liability. Ark reports its reinsurance recoverables net of an allowance for estimated uncollectible reinsurance, including expected credit losses. The allowance is based upon its ongoing review of amounts outstanding, length of collection periods, changes in reinsurer credit standing, disputes, applicable coverage defenses and other relevant factors. Goodwill and Other Intangible Assets Goodwill represents the excess of the amount paid to acquire subsidiaries over the fair value of identifiable net assets at the date of acquisition. Other intangible assets consist primarily of underwriting capacity, customer relationships, renewal rights and trade names. Derivatives From time to time, White Mountains holds derivative financial instruments for risk management purposes. White Mountains recognizes all derivatives as either assets or liabilities, measured at fair value, on the consolidated balance sheet. Changes in the fair value of derivative instruments that meet the criteria for hedge accounting are recognized in other comprehensive income and reclassified into current period pre-tax income when the hedged items are recognized therein. Changes in the fair value of derivative instruments that do not meet the criteria for hedge accounting are recognized in current period pre-tax income. As of September 30, 2021 and December 31, 2020, NSM holds an interest rate swap derivative instrument that meets the criteria for hedge accounting. See Note 9 — “Derivatives” . Reinsurance Contracts Accounted for as Deposits Reinsurance contracts that do not meet the risk transfer requirements necessary to be accounted for as reinsurance are accounted for using the deposit method. Under the deposit method, ceded premiums paid are not recognized through income but rather treated as a deposit. BAM entered into ceded reinsurance agreements with Fidus Re Ltd. (“Fidus Re”) during the second quarter of 2018 and the first quarter of 2021, which are both accounted for using the deposit method. See Note 10 — “Municipal Bond Guarantee Insurance” . The nonrefundable consideration paid by BAM to Fidus Re is charged to financing expense within general and administrative expenses. Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), formerly Third Point Reinsurance Ltd., 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 three months ended June 30, 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, 2021, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.3 million. Cash and Restricted Cash Cash includes amounts on hand and demand deposits with banks and other financial institutions. Amounts presented in the statement of cash flows are shown net of balances acquired and sold in the purchase or sale of the Company’s consolidated subsidiaries.

Significant Transactions

Significant Transactions	9 Months Ended
	Sep. 30, 2021
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Significant Transactions	Significant Transactions 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. As of December 31, 2020, White Mountains owned 20.5 million MediaAlpha shares, representing a 35.0% ownership interest (32.3% on a fully-diluted, fully converted basis). At the December 31, 2020 closing price of $39.07 per share, the fair value of White Mountains’s remaining investment in MediaAlpha was $802.2 million. 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, 2021, White Mountains owned 16.9 million shares, representing a 28.4% basic ownership interest (26.3% fully-diluted/fully-converted basis). At the September 30, 2021 closing price of $18.68 per share, the fair value of White Mountains’s investment in MediaAlpha was $316.4 million. At this level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $5.60 per share increase or decrease in White Mountains’s book value per share. At the October 2021 month-end closing price of $17.53 per share, the fair value of White Mountains’s investment in MediaAlpha was $297.0 million. See Note 16 — “Equity-Method Eligible Investments” . 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”). Certain Ark Sellers also entered into a related management warranty deed (together with the Ark SPA, the “Ark Acquisition Agreement”) pursuant to which they made certain warranties about the Ark business (collectively the “Ark Transaction”). 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 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 Deposit Trust Deed and $366.3 million placed in escrow, which is reflected on the balance sheet within the Other Operations segment as of December 31, 2020. On January 1, 2021, White Mountains completed the Ark Transaction in accordance with the terms of the Ark SPA. As of September 30, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% on a fully-diluted, fully-converted basis, taking account of management’s equity incentives). The remaining shares are owned by employees. In the future, management rollover shareholders could earn additional shares in the company 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 acquisition date fair values of assets and liabilities, including insurance reserves and intangible assets, are provisional and are subject to revision within one year of the acquisition date. 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. 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, 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. Ark’s segment income and expenses for the three and nine months ended September 30, 2021 are presented in Note 15 - “Segment Information.” Pro forma financial information for Ark for the three and nine months ended September 30, 2020 has not been presented because as a private U.K. domiciled company Ark does not have quarterly financial reporting requirements and therefore quarterly financial information is not available for periods prior to the January 1, 2021 acquisition date. NSM On May 18, 2018, NSM acquired 100% of Fresh Insurance, which is an insurance broker that offers non-standard personal lines products in the United Kingdom. NSM paid $49.6 million of upfront cash consideration for Fresh Insurance. NSM borrowed $51.0 million to fund the transaction. During the nine months ended September 30, 2019, NSM paid a purchase price adjustment of an additional $0.7 million of consideration. The purchase price is subject to additional adjustments based upon growth in EBITDA during two earnout periods, one which ended in February 2020 and one ending in February 2022. NSM did not make any payments related to the first Fresh Insurance earnout period. On April 12, 2021, NSM sold Fresh Insurance’s motor business for net proceeds of £1.1 million ($1.5 million based upon the foreign exchange spot rate as of the transaction date). As of March 31, 2021, the Fresh Insurance motor business was classified as held for sale and NSM recognized a loss of $28.7 million in the first quarter of 2021. See Note 19 — “Held for Sale and Discontinued Operations”. On December 3, 2018, NSM acquired all the net assets of KBK Insurance Group, Inc. (“KBK”), a specialized MGU focused on the towing and transportation space. NSM paid $60.0 million of upfront cash consideration for KBK. White Mountains contributed $29.0 million to NSM and NSM borrowed $30.1 million to fund the transaction. As of March 31, 2019, White Mountains determined that the relative values of goodwill and other intangible assets from the KBK transaction were $32.6 million and $32.7 million, reflecting acquisition date fair values, and recorded a liability of $5.9 million relating to the fair value of contingent consideration made in connection with the acquisition. The purchase price is subject to adjustments based upon growth in EBITDA during three earnout periods, one which ended in December 2019, one which ended in December 2020 and one ending in December 2021. In the first quarter of 2021 and 2020, NSM paid $6.7 million and $6.4 million related to the first and second KBK earnout periods. As of September 30, 2021, the KBK contingent consideration liability was $6.6 million. On April 7, 2020, NSM acquired 100% of Kingsbridge Group Limited (“Kingsbridge”), a leading provider of commercial lines insurance and consulting services for the professional contractor and freelancer markets in the United Kingdom. NSM paid £107.2 million ($132.2 million based upon the foreign exchange spot rate at the date of acquisition) of upfront cash consideration for Kingsbridge. White Mountains contributed $80.3 million to NSM and NSM borrowed £42.5 million ($52.4 million based upon the foreign exchange spot rate at the date of acquisition) to fund the transaction. During 2020, NSM determined that the relative values of goodwill and other intangible assets recorded in connection with the Kingsbridge transaction were $111.5 million and $20.2 million, reflecting acquisition date fair values. The purchase price is subject to adjustment based upon growth in EBITDA during an earnout period ending in January 2022. During 2020, NSM initially recorded a liability relating to the fair value of the Kingsbridge contingent consideration of $4.1 million. During the fourth quarter of 2020, NSM recognized pre-tax income of $4.1 million for the change in fair value of the Kingsbridge contingent consideration liability and a foreign currency translation unrealized gain of $0.3 million. As of September 30, 2021, the Kingsbridge contingent consideration liability was $0.1 million. On August 6, 2021, NSM acquired 100% of J.C. Taylor Insurance (“J.C. Taylor”), a managing general agent (“MGA”) offering classic and antique collector car insurance. NSM paid $49.6 million of upfront cash consideration for J.C. Taylor. NSM borrowed $35.0 million under its credit facility to fund the acquisition. NSM recognized total assets acquired related to the J.C. transaction of $60.3 million, including goodwill and other intangible assets of $55.7 million, and total liabilities of $10.7 million. The relative fair values of goodwill and of other intangible assets recognized in connection with the acquisition of J.C. Taylor had not yet been finalized as of September 30, 2021. The contingent consideration liabilities related to NSM’s acquisitions are subject to adjustments based upon EBITDA, EBITDA projections, and present value factors for acquired entities. For the three and nine months ended September 30, 2021, NSM recognized pre-tax loss of $0.6 million and $0.8 million for the change in the fair value of its contingent consideration liabilities. For the three and nine months ended September 30, 2020, NSM recognized pre-tax loss (income) of $0.7 million and $(1.6) million for the change in the fair value of its contingent consideration liabilities. Any future adjustments to contingent consideration liabilities under the agreements will be recognized through pre-tax income. As of September 30, 2021 and December 31, 2020, NSM recorded total contingent consideration liabilities of $6.7 million and $14.6 million. PassportCard/DavidShield On January 24, 2018, White Mountains acquired a 50.0% ownership interest in DavidShield, its joint venture partner in PassportCard. DavidShield is a managing general agency 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. As a result of the transaction, White Mountains’s re-evaluated its accounting treatment for 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 $114.4 million.

Investment Securities

Investment Securities	9 Months Ended
	Sep. 30, 2021
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, 2021 and December 31, 2020. Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, insurance-linked securities funds (“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, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Fixed maturity investments $ 8.2 $ 7.0 $ 21.9 $ 22.4 Short-term investments — .1 .5 1.0 Common equity securities .1 .5 .1 6.5 Investment in MediaAlpha — 55.0 — 60.0 Other long-term investments 12.0 8.9 37.1 24.7 Amount attributable to TPC Providers (.2) — (.8) — Total investment income 20.1 71.5 58.8 114.6 Third-party investment expenses (.6) (.3) (1.6) (.9) Net investment income, pre-tax $ 19.5 $ 71.2 $ 57.2 $ 113.7 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, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Fixed maturity investments $ (6.8) $ 3.6 $ (23.2) $ 35.8 Short-term investments (.3) — — .4 Common equity securities 1.6 48.4 7.7 5.9 Investment in MediaAlpha (396.8) 250.0 (325.5) 295.0 Other long-term investments 37.7 4.6 113.2 (34.3) Amount attributable to TPC Providers (1.7) — (6.5) — Net realized and unrealized investment (losses) gains (1) (366.3) 306.6 (234.3) 302.8 Less: net (losses) gains on investment securities sold during the period (4.8) 36.1 (5.1) 29.6 Net realized and unrealized investment (losses) gains on investment securities held at the end of the period $ (361.5) $ 270.5 $ (229.2) $ 273.2 (1) For the three months ended September 30, 2021 and 2020, includes $(7.0) and $0.8 of realized and unrealized investment gains (losses) related to foreign currency exchange. For the nine months ended September 30, 2021 and 2020, includes $(7.4) and $(0.8) 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, 2021 and 2020 for investments still held at the end of the period: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Other long-term investments $ 26.5 $ 260.1 $ 75.5 $ 276.0 Total net unrealized investment gains, pre-tax - Level 3 investments $ 26.5 $ 260.1 $ 75.5 $ 276.0 Investment Holdings The following tables present the cost or amortized cost, gross unrealized investment gains (losses) and carrying values of White Mountains’s fixed maturity investments as of September 30, 2021 and December 31, 2020: September 30, 2021 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 207.4 $ .8 $ (.6) $ — $ 207.6 Debt securities issued by corporations 945.2 13.1 (3.4) (.7) 954.2 Municipal obligations 276.1 18.0 (.7) — 293.4 Mortgage and asset-backed securities 247.3 4.2 (1.4) — 250.1 Collateralized loan obligations 128.5 — (.4) (.5) 127.6 Total fixed maturity investments $ 1,804.5 $ 36.1 $ (6.5) $ (1.2) $ 1,832.9 December 31, 2020 Millions Cost or Gross Gross Carrying U.S. Government and agency obligations $ 173.2 $ 3.1 $ — $ 176.3 Debt securities issued by corporations 522.8 24.7 (.1) 547.4 Municipal obligations 244.0 21.0 — 265.0 Mortgage and asset-backed securities 211.7 6.8 — 218.5 Total fixed maturity investments $ 1,151.7 $ 55.6 $ (.1) $ 1,207.2 The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2021. 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, 2021 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 111.9 $ 112.7 Due after one year through five years 836.1 843.4 Due after five years through ten years 368.5 377.3 Due after ten years 112.2 121.8 Mortgage and asset-backed securities and collateralized loan obligations 375.8 377.7 Total fixed maturity investments $ 1,804.5 $ 1,832.9 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, 2021 and December 31, 2020: September 30, 2021 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 152.5 $ 8.8 $ (.5) $ (1.2) $ 159.6 Investment in MediaAlpha $ — $ 316.4 $ — $ — $ 316.4 Other long-term investments $ 1,154.7 $ 197.6 $ (62.9) $ (3.9) $ 1,285.5 December 31, 2020 Millions Cost or Gross Gross Net Foreign Carrying Investment in MediaAlpha $ — $ 802.2 $ — $ — $ 802.2 Other long-term investments $ 767.4 $ 95.8 $ (78.1) $ 1.7 $ 786.8 Fair Value Measurements As of September 30, 2021 and December 31, 2020, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 69% and 73% 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, 2021 and December 31, 2020 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, 2021 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 207.6 $ 207.6 $ — $ — Debt securities issued by corporations: Financials 246.5 — 246.5 — Consumer 180.5 — 180.5 — Industrial 114.8 — 114.8 — Technology 110.8 — 110.8 — Healthcare 98.2 — 98.2 — Utilities 69.9 — 69.9 — Communications 53.2 — 53.2 — Energy 47.0 — 47.0 — Materials 33.3 — 33.3 — Total debt securities issued by corporations 954.2 — 954.2 — Municipal obligations 293.4 — 293.4 — Mortgage and asset-backed securities 250.1 — 250.1 — Collateralized loan obligations 127.6 — 127.6 — Total fixed maturity investments 1,832.9 207.6 1,625.3 — Short-term investments 609.5 601.6 7.9 — Common equity securities (1) 159.6 — 159.6 — Investment in MediaAlpha 316.4 316.4 — — Other long-term investments 814.5 — — 814.5 Other long-term investments — NAV (2) 471.0 — — — Total other long-term investments 1,285.5 — — 814.5 Total investments $ 4,203.9 $ 1,125.6 $ 1,792.8 $ 814.5 (1) Consist of investments in listed funds that predominantly invest in international equities. (2) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2020 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 176.3 $ 176.3 $ — $ — Debt securities issued by corporations: Financials 133.9 — 133.9 — Consumer 81.9 — 81.9 — Industrial 66.9 — 66.9 — Technology 66.7 — 66.7 — Healthcare 51.5 — 51.5 — Communications 44.5 — 44.5 — Energy 35.8 — 35.8 — Materials 33.9 — 33.9 — Utilities 32.3 — 32.3 — Total debt securities issued by corporations 547.4 — 547.4 — Municipal obligations 265.0 — 265.0 — Mortgage and asset-backed securities 218.5 — 218.5 — Total fixed maturity investments 1,207.2 176.3 1,030.9 — Short-term investments 142.9 142.9 — — Investment in MediaAlpha 802.2 802.2 — — Other long-term investments 614.2 — — 614.2 Other long-term investments — NAV (1) 172.6 — — — Total other long-term investments 786.8 — — 614.2 Total investments $ 2,939.1 $ 1,121.4 $ 1,030.9 $ 614.2 (1) Consists of private equity funds and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. 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, 2021 and December 31, 2020: Fair Value at Millions September 30, 2021 December 31, 2020 AAA $ 12.7 $ 10.6 AA 85.7 57.9 A 473.3 318.3 BBB 373.7 159.6 BB — 1.0 Other 8.8 — Debt securities issued by corporations (1) $ 954.2 $ 547.4 (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, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 125.3 $ 125.3 $ — $ 88.7 $ 88.7 $ — FHLMC 76.5 76.5 — 70.1 70.1 — GNMA 29.4 29.4 — 40.6 40.6 — Total agency (1) 231.2 231.2 — 199.4 199.4 — Non-agency: Residential .6 .6 — — — — Total non-agency .6 .6 — — — — Total mortgage-backed securities 231.8 231.8 — 199.4 199.4 — Other asset-backed securities: Credit card receivables 11.2 11.2 — 11.3 11.3 — Vehicle receivables 7.1 7.1 — 7.8 7.8 — Total other asset-backed securities 18.3 18.3 — 19.1 19.1 — Total mortgage and asset-backed securities 250.1 250.1 — 218.5 218.5 — Collateralized loan obligations 127.6 127.6 — — — — Total mortgage and asset-backed securities and collateralized loan obligations $ 377.7 $ 377.7 $ — $ 218.5 $ 218.5 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC). As of September 30, 2021, White Mountains’s investment portfolio included $127.6 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, 2021. Investment in 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 is presented as a separate line item on the balance sheet. At the September 30, 2021 closing price of $18.68 per share, the fair value of White Mountains’s investment in MediaAlpha was $316.4 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, 2021 and December 31, 2020: Fair Value at Millions September 30, 2021 December 31, 2020 Kudu’s Participation Contracts $ 604.7 $ 400.6 PassportCard/DavidShield 105.0 95.0 Elementum Holdings L.P. 56.7 55.1 Other unconsolidated entities (1) 27.0 42.4 Total unconsolidated entities 793.4 593.1 Private equity funds and hedge funds 144.2 121.2 Bank loan fund 161.7 — Lloyd’s trust deposits 111.2 — ILS funds 53.9 51.4 Private debt investments 13.3 21.1 Other 7.8 — Total other long-term investments $ 1,285.5 $ 786.8 (1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities and Simple Agreement for Future Equity (“SAFE”) investments. Private Equity Funds and Hedge Funds White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the net asset value (“NAV”) of the funds. As of September 30, 2021, White Mountains held investments in fourteen private equity funds and one hedge fund. The largest investment in a single private equity fund or hedge fund was $27.4 million as of September 30, 2021 and $29.1 million as of December 31, 2020. 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, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 63.9 $ 14.0 $ 69.1 $ 15.3 Financial services 63.2 29.6 23.5 30.4 Real estate 4.8 2.9 — — Manufacturing/Industrial .1 — 28.6 — Total private equity funds 132.0 46.5 121.2 45.7 Hedge funds European small/mid cap 12.2 — — — Total hedge funds 12.2 — — — Total private equity funds and hedge funds included in other long-term investments $ 144.2 $ 46.5 $ 121.2 $ 45.7 Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period. The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2021: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $.3 $14.0 $109.0 $8.7 $132.0 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, 2021 and December 31, 2020, 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. White Mountains’s hedge fund investment is subject to a perpetual two-year restriction on redemption frequency from the initial investment in the fund and a 90-days advanced notice period requirement. Lloyd’s Trust Deposits White Mountains’s other long-term investments include Lloyd’s trust deposits, which consists of overseas 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 required of Lloyd's syndicates to protect policyholders in overseas 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, 2021, White Mountains held Lloyd’s trust deposits with a fair value of $111.2 million. Bank Loan Fund White Mountains’s other long-term investments include a bank loan fund with a fair value of $161.7 million as of September 30, 2021. 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 and 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. 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, 2021, White Mountains held investments in ILS funds with a fair value of $53.9 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 Fair Value Measurements by Level White Mountains uses quoted market prices where available as the inputs to estimate fair value for its investments in active markets. Such measurements are considered to be either Level 1 or Level 2 measurements, depending on whether the quoted market price inputs are for identical securities (Level 1) or similar securities (Level 2). Level 3 measurements for fixed maturity investments, common equity securities and other long-term investments as of September 30, 2021 and 2020 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities. The following tables present the changes in White Mountains’s fair value measurements by level for the nine months ended September 30, 2021 and 2020: Level 3 Other Long-term Investments Measured at NAV (1) Millions Level 1 Investments Level 2 Other Long-term Total Balance at December 31, 2020 $ 978.5 $ 1,030.9 $ 614.2 $ 172.6 $ 2,796.2 (2) Net realized and unrealized gains (losses) (327.6) (13.1) 79.0 33.9 (227.8) (3) Amortization/Accretion (.1) (5.9) — — (6.0) Purchases 130.9 989.7 143.6 199.6 1,463.8 Sales (257.7) (284.9) (31.9) (70.9) (645.4) Effect of Ark Transaction — 68.2 9.6 135.8 213.6 Transfers in — — — — — Transfers out — — — — — Balance at September 30, 2021 $ 524.0 $ 1,784.9 $ 814.5 $ 471.0 $ 3,594.4 (2) (1) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies” . (2) Excludes carrying value of $609.5 and $142.9 as of September 30, 2021 and December 31, 2020 classified as short-term investments. (3) Includes amounts attributable to TPC Providers of $6.5 for the nine months ended September 30, 2021. Level 3 Other Long-term Investments Measured at NAV (1) Millions Level 1 Investments Level 2 Common Other Long-term Total Balance at December 31, 2019 $ 780.0 $ 1,109.6 $ .1 $ 654.0 $ 202.3 $ 2,746.0 (2) Net realized and unrealized gains (losses) 29.2 12.5 — 275.6 (14.9) 302.4 (3) Amortization/Accretion — (3.0) — — — (3.0) Purchases 128.8 316.2 — 78.8 39.8 563.6 Sales (642.7) (368.5) — (8.1) (56.3) (1,075.6) Transfers in — — — — — — Transfers out — — — — — — Balance at September 30, 2020 $ 295.3 $ 1,066.8 $ .1 $ 1,000.3 $ 170.9 $ 2,533.4 (2) (1) Includes private equity funds, a hedge fund and ILS funds for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies ”. (2) Excludes carrying value of $571.8 and $201.2 as of September 30, 2020 and December 31, 2019 classified as short-term investments. (3) Excludes realized and unrealized gains associated with short-term investments of $0.4 for the nine months ended September 30, 2020. Fair Value Measurements — Transfers Between Levels - Nine-months ended September 30, 2021 and 2020 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, 2021 and 2020, 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, 2021 and 2020, 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, 2021 and December 31, 2020. The tables below exclude $14.9 million and $27.6 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, hedge funds, Lloyd’s trust deposits, bank loans funds and ILS funds are generally estimated using the NAV of the funds. $ in Millions September 30, 2021 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3)(4) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4) Kudu’s Participation Contracts (5)(6) Discounted cash flow $604.7 18% - 23% 7x - 13x PassportCard/DavidShield Discounted cash flow $105.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $56.7 17% 4% Private debt investments Discounted cash flow $11.2 4% - 8% N/A Other Discounted cash flow $22.0 20% - 24% 4% (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. (4) 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. (5) For the nine months ended September 30, 2021, Kudu deployed a total of $141.6 in new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management and Douglass Winthrop Advisors. (6) As of September 30, 2021, certain Kudu Participation Contracts with a total fair value of $121.0 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. $ in Millions December 31, 2020 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3)(4) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4) Kudu’s Participation Contracts (5) Discounted cash flow $400.6 18% - 23% 7x - 12x PassportCard/DavidShield (6) Discounted cash flow $95.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $55.1 17% 4% Private debt investments Discounted cash flow $17.1 4% - 8% N/A Other Discounted cash flow $18.8 20% - 24% 4% (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. (4) 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. (5) In 2020, Kudu deployed a total of $118.2 in new Kudu Participation Contracts, including Creation Investments Capital, Sequoia Financial Group, Channel Capital and Ranger Investment Management. (6) In 2020, White Mountains made an additional $15.0 investment in PassportCard/DavidShield. See Note 2 — “Significant Transactions” .

Goodwill and Other Intangible A

Goodwill and Other Intangible Assets	9 Months Ended
	Sep. 30, 2021
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 acquisition date fair values of certain assets and liabilities, 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 acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by segment as of September 30, 2021 and December 31, 2020: $ in Millions Weighted Average Economic September 30, 2021 December 31, 2020 Acquisition Date Fair Value Accumulated Amortization Impairments and Amounts Allocated to Held for Sale Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Goodwill: Ark N/A $ 116.8 $ — $ — $ 116.8 $ — $ — $ — $ — NSM (1) N/A 559.8 — 30.2 529.6 506.4 — — 506.4 Kudu N/A 7.6 — — 7.6 7.6 — — 7.6 Other Operations N/A 17.4 — — 17.4 11.5 — — 11.5 Total goodwill 701.6 — 30.2 671.4 525.5 — — 525.5 Other intangible assets: Ark Underwriting Capacity N/A 175.7 — — 175.7 — — — — NSM (1) Customer 8.9 136.0 50.6 3.5 81.9 136.2 36.7 3.5 96.0 Trade names 16 65.3 10.9 1.0 53.4 65.4 8.3 1.0 56.1 Information 0 3.1 1.4 1.7 — 3.1 1.4 1.7 — Renewal rights 12 82.5 13.1 — 69.4 82.5 4.9 — 77.6 Other 3.4 1.1 .6 — .5 1.7 1.0 — .7 Subtotal 288.0 76.6 6.2 205.2 288.9 52.3 6.2 230.4 Kudu Trade names 7 2.2 .8 — 1.4 2.2 .6 — 1.6 Other Operations Trade names 18.1 8.2 1.0 — 7.2 3.6 .3 — 3.3 Customer 13.3 18.9 3.5 — 15.4 14.2 1.4 — 12.8 Insurance N/A 8.6 — — 8.6 8.6 — — 8.6 Other 5.4 .3 .2 — .1 .3 .1 — .2 Subtotal 36.0 4.7 — 31.3 26.7 1.8 — 24.9 Total other intangible assets 501.9 82.1 6.2 413.6 317.8 54.7 6.2 256.9 Total goodwill and other intangible assets $ 1,203.5 $ 82.1 $ 36.4 1,085.0 $ 843.3 $ 54.7 6.2 782.4 Goodwill and other intangible assets attributed to non-controlling interests (118.0) (28.1) Goodwill and other intangible assets included in White Mountains’s $ 967.0 $ 754.3 (1) As of September 30, 2021, NSM’s goodwill and intangible assets included $(2.3) and $(0.2) of the effect of foreign currency translation. As of December 31, 2020, NSM’s goodwill and intangible assets included $13.4 and $1.6 of the effect of foreign currency translation. 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 an other intangible asset that provides 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. The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2020 through September 30, 2021: $ in Millions Acquisition of subsidiary/ asset Goodwill and Other intangible asset (1) Acquisition Date Kingsbridge $ 131.7 April 7, 2020 J.C. Taylor 55.7 August 6, 2021 Total NSM segment $ 187.4 Ark $ 292.5 January 1, 2021 Other Operations $ 30.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and excludes the effect of foreign currency translation subsequent to the acquisition date. 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. On April 12, 2021, NSM sold Fresh Insurance’s motor business. In connection with the sale, White Mountains recognized a loss of $28.7 million during the three months ended March 31, 2021. See Note 19 — “Held for Sale and Discontinued Operations” . During the three months ended June 30, 2020, White Mountains recognized impairments of other intangible assets of $6.2 million. The impairments related to NSM’s write-off of intangible assets in its U.K. vertical. The impairments related to lower premium volumes, including due to the impact of the COVID-19 pandemic, and certain reorganization initiatives in the U.K. vertical. There were no other impairments of other intangible assets and no impairments of goodwill for the three and nine months ended September 30, 2021 and 2020. The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2021 and 2020: Three Months Ended September 30, 2021 2020 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 629.4 $ 414.8 $ 1,044.2 $ 518.2 $ 241.7 $ 759.9 Acquisition of businesses 55.7 (1) — 55.7 14.9 (2) — 14.9 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3) (9.3) 9.3 — — — — Foreign currency translation (4.0) (.3) (4.3) 7.0 (.1) 6.9 Measurement period adjustments (4) (.4) — (.4) — — — Amortization — (10.2) (10.2) — (5.4) (5.4) Ending balance $ 671.4 $ 413.6 $ 1,085.0 $ 540.1 $ 236.2 $ 776.3 (1) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of J.C. Taylor had not yet been finalized at September 30, 2021. (2) The relative fair values of goodwill and other intangible assets recognized in connection with an acquisition within Other Operations had not yet been finalized at September 30, 2020. (3) Relates to an acquisition within the Other Operations segment. (4) 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, 2021, adjustments relate to an acquisition within the Other Operations segment. Nine Months Ended September 30, 2021 2020 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 525.5 $ 256.9 $ 782.4 $ 394.7 $ 260.0 $ 654.7 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (9.3) 9.3 — — — — Ark Transaction 116.8 175.7 292.5 — — — Acquisition of businesses 71.5 (2) — 71.5 140.0 (3) — 140.0 Foreign currency translation (2.3) (.2) (2.5) 5.2 (.5) 4.7 Impairments — — — — (6.2) (6.2) Loss on assets held for sale (4) (30.2) — (30.2) — — — Measurement period adjustments (5) (.6) — (.6) .2 — .2 Amortization — (28.1) (28.1) — (17.1) (17.1) Ending balance $ 671.4 $ 413.6 $ 1,085.0 $ 540.1 $ 236.2 $ 776.3 (1) Relates to an acquisition within the Other Operations segment. (2) The relative fair values of goodwill and other intangible assets of $55.7 recognized in connection with the acquisition of J.C. Taylor had not yet been finalized at September 30, 2021. The remaining $15.8 relates to the relative fair values of goodwill and other intangible assets recognized in connection with an acquisition within the Other Operations segment. (3) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge and an acquisition within Other Operations had not yet been finalized at September 30, 2020. (4) Relates to the sale of NSM’s Fresh Insurance’s motor business recorded in the first quarter of 2021. This amount excludes $1.5 of net proceeds related to the sale. (5) 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, 2021, adjustments relate to acquisitions within the Other Operations segment.

Loss and Loss Adjustment Expens

Loss and Loss Adjustment Expense Reserves	9 Months Ended
	Sep. 30, 2021
Insurance Loss Reserves [Abstract]
Loss and Loss Adjustment Expense Reserves	Loss and Loss Adjustment Expense Reserves Ark establishes loss and LAE reserves that are estimates of amounts needed to pay claims and related expenses in the future for insured events that have already occurred. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. Loss and LAE reserves typically comprise case reserves for claims reported and reserves for losses that have occurred but for which claims have not yet been reported, referred to as IBNR reserves. IBNR reserves include a provision for expected future development on case reserves. Case reserves are estimated based on the experience and knowledge of claims staff regarding the nature and potential cost of each claim and are adjusted as additional information becomes known or payments are made. IBNR reserves are typically derived by subtracting paid loss and LAE and case reserves from estimates of ultimate losses and LAE. Actuaries estimate ultimate loss and LAE using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. Ultimate loss and LAE are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate loss and LAE with respect to any line of business, past experience with respect to that line of business is the primary resource, but cannot be relied upon in isolation. Ark’s own experience, particularly claims development experience, such as trends in case reserves, payments on and closings of claims, as well as changes in business mix and coverage limits, is the most important information for estimating its reserves. Ultimate loss and LAE for major losses and catastrophes are estimated based on the known and expected exposures to the loss event, rather than simply relying on the extrapolation of reported and settled claims. Uncertainties in estimating ultimate loss and LAE are magnified by the time lag between when a claim actually occurs and when it is reported and eventually settled. This time lag is sometimes referred to as the “claim-tail”. The claim-tail for most property coverages is typically short (usually a few days up to a few months). The claim-tail for liability/casualty coverages can be quite long as claims are often reported and ultimately paid or settled years after the related loss events occur. During the long claims reporting and settlement period, additional facts regarding coverages written in prior accident years, as well as about actual claims and trends may become known and, as a result, Ark may adjust its reserves. If management determines that an adjustment is appropriate, the adjustment is booked in the accounting period in which such determination is made. Accordingly, should reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted. In determining ultimate loss and LAE, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. Because of the factors previously discussed, the process requires the use of informed judgment and is inherently uncertain. Ark performs an actuarial review of its recorded reserves each quarter, using several generally accepted actuarial methods to evaluate its loss reserves, each of which has its own strengths and weaknesses. Management places more or less reliance on a particular method based on the facts and circumstances at the time the reserve estimates are made. 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, 2021: Millions Three Months Ended September 30, 2021 Nine Months Ended September 30, 2021 Gross beginning balance $ 760.0 $ 696.0 Less: beginning reinsurance recoverable on unpaid losses (425.3) (433.4) Net loss and LAE reserves 334.7 262.6 Loss and LAE incurred relating to: Current year losses 141.9 269.0 Prior year losses (12.7) (21.2) Total incurred losses and LAE 129.2 247.8 Foreign currency translation adjustment to loss and LAE reserves (1.2) (3.4) Loss and LAE paid relating to: Current year losses (9.0) (11.5) Prior year losses (20.3) (62.1) Total loss and LAE payments (29.3) (73.6) Net ending balance 433.4 433.4 Plus: ending reinsurance recoverable on unpaid losses 457.5 457.5 Gross ending balance $ 890.9 $ 890.9 Ark’s GAAP combined ratio in the third quarter of 2021 included $12.7 million (6 points) of favorable prior year development, primarily related to the Property line of business. Ark’s GAAP combined ratio in the first nine months of 2021 included $21.2 million (5 points) of favorable prior year development, primarily related to the Property, Marine & Energy and Accident & Health lines of business. See Note 10 — “Municipal Bond Guarantee Insurance” for loss and LAE reserve balances related to White Mountains financial guarantee business.

Third Party Reinsurance

Third Party Reinsurance	9 Months Ended
	Sep. 30, 2021
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. Three Months Ended September 30, 2021 Nine Months Ended September 30, 2021 Millions Written premiums: Gross $ 162.4 $ 895.0 Ceded (41.5) (169.5) Net written premiums $ 120.9 $ 725.5 Earned premiums: Gross $ 284.5 $ 622.0 Ceded (71.1) (186.2) Net earned premiums $ 213.4 $ 435.8 Losses and LAE: Gross $ 193.5 $ 372.7 Ceded (64.3) (124.9) Net Losses and LAE $ 129.2 $ 247.8 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, 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 related 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, 2021 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 122.8 $ 23.9 $ 98.9 84.2 % A- to A 32.7 15.6 17.1 14.6 B++ or lower and not rated 10.2 8.8 1.4 1.2 Total $ 165.7 $ 48.3 $ 117.4 100.0 % (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 financial guarantee business.

Debt

Debt	9 Months Ended
	Sep. 30, 2021
Debt Disclosure [Abstract]
Debt	Debt The following table presents White Mountains’s debt outstanding as of September 30, 2021 and December 31, 2020: Millions September 30, Effective (1) December 31, Effective (1) Ark 2007 Notes Tranche 1 $ 30.0 $ — Ark 2007 Notes Tranche 2 13.9 — Ark 2007 Subordinated Notes, carrying value 43.9 — Ark 2021 Notes Tranche 1 45.3 — Ark 2021 Notes Tranche 2 47.0 — Ark 2021 Notes Tranche 3 70.0 — Unamortized issuance cost (5.5) Ark 2021 Subordinated Notes, carrying value 156.8 Total Ark Subordinated Notes, carrying value 200.7 5.1% — NSM Bank Facility 300.4 7.4% (2) 277.4 7.5% (2) Unamortized issuance cost (6.7) (6.1) NSM Bank Facility, carrying value 293.7 271.3 Other NSM debt, carrying value 1.3 3.3% 1.3 2.5% Kudu Credit Facility 203.0 4.1% — Unamortized issuance cost (7.4) — Kudu Credit Facility, carrying value 195.6 — Kudu Bank Facility — 89.2 8.3% Unamortized issuance cost — (2.9) Kudu Bank Facility, carrying value — 86.3 Other Operations debt 19.5 7.4% 18.0 7.4% Unamortized issuance cost (.4) (.5) Other Operations, carrying value 19.1 17.5 Total debt $ 710.4 $ 376.4 (1) Effective rate includes the effect of the amortization of debt issuance costs. (2) NSM’s effective rate excludes the effect of the interest rate swap on the hedged portion of the debt. The weighted average interest rate for the quarter ended September 30, 2021 and December 31, 2020, excluding the effect of amortization of debt issuance costs, was 6.7% and 7.0%. The weighted average interest rate for the quarter ended September 30, 2021 and December 31, 2020 on the total NSM Bank Facility including both the effect of the amortization of debt issuance costs and the effect of the interest rate swap was 8.3% and 8.4%. Ark Subordinated Notes In March 2007, GAIL, a wholly-owned subsidiary of Ark, 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 Notes Tranche 1”) and a €12.0 million floating rate subordinated note to Dekania Europe CDO II plc (the “Ark 2007 Notes Tranche 2”) (together, the “Ark 2007 Subordinated Notes”). The Ark 2007 Notes Tranche 1, which mature in June 2037, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 4.6%. The Ark 2007 Notes Tranche 2, which matures in June 2027, accrues interest at a floating rate equal to the three-month EURIBOR plus 4.6%. As of September 30, 2021, the Ark 2007 Notes Tranche 1 had an outstanding balance of $30.0 million and the Ark 2007 Notes Tranche 2 had an outstanding balance of €12.0 million ($13.9 million based upon the foreign exchange spot rate as of September 30, 2021). 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 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%. 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%. 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%. 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, 2021, the Ark 2021 Notes Tranche 1 had an outstanding balance of €39.1 million ($45.3 million based upon the foreign exchange spot rate as of September 30, 2021), the Ark 2021 Notes Tranche 2 had an outstanding balance of $47.0 million, and the Ark 2021 Notes Tranche 3 had an outstanding balance of $70.0 million. Ark Stand By Letter of Credit Facility Ark has a secured stand by letter of credit facility (the “Ark LOC Facility”) with three lenders, Lloyds Bank plc, National Westminster Bank plc and ING Bank N.V, London Branch to provide capital support for the Syndicates. As of September 30, 2021, the utilized level of the facility was $45.0 million, with the ability to increase up to $150.0 million, subject to formal approval by Lloyd’s. The Ark LOC Facility has a termination date of December 31, 2025. During the three and nine months ended September 30, 2021, Ark did not borrow or make any repayments under the Ark LOC Facility. The Ark LOC Facility, which provides funds at Lloyd’s, is secured by all property of the loan parties and contains various affirmative, negative and financial covenants that White Mountains considers to be customary for such borrowings, including a minimum tangible net worth covenant. NSM Bank Facility NSM maintains a secured credit facility (the “NSM Bank Facility”) with Ares Capital Corporation. In both 2021 and 2020, NSM amended the terms of the facility. On April 7, 2020, NSM amended the NSM Bank Facility to increase the total commitment from $234.0 million, comprised of term loans of $224.0 million and a revolving credit loan commitment of $10.0 million, to $291.4 million, comprised of term loans of $276.4 million, including £42.5 million ($52.4 million based upon the foreign exchange spot rate as of the date of the transaction) in a GBP term loan, and a revolving credit loan commitment of $15.0 million . In connection with the April 7, 2020 amendment, the reference rates for USD denominated borrowings increased. The USD-LIBOR rate floor increased to 1.25% and the margin over USD-LIBOR increased from a range of 4.25% to 4.75% to a range of 5.50% to 6.00%. On June 2, 2021, NSM amended the NSM Bank Facility to reduce the margin over the reference interest rate for USD LIBOR loans from a range of 5.5% to 6.00% to a range of 4.50% to 5.00%, and reduce the margin over the reference rate for GBP loans from a range of 6.0% to 6.50% to a range of 5.00% to 5.50%. The amendment also increased the revolving credit loan commitment to $40.0 million and added a $50.0 million delayed-draw term loan commitment. The amendment also changed the reference interest rate for the GBP loan from GBP-LIBOR to SONIA. The maturity dates of the term loans and the revolving credit loans were not changed as part of the amendment. The term loans under the NSM Bank Facility mature on May 11, 2026, and the revolving loan matures on November 11, 2025. The reference interest rates under the NSM Bank Facility are generally subject to a 1.25% rate floor. Under GAAP, if the terms of a debt instrument are amended, unless there is greater than 10% change in the expected discounted future cash flows of such instrument, the instrument’s carrying value does not change. White Mountains has determined that the impact of the 2021 and 2020 amendments to the NSM Bank Facility was less than 10% on the expected discounted future cash flows. The following table presents the change in debt under the NSM Bank Facility for the three and nine months ended September 30, 2021 and 2020: NSM Bank Facility Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Beginning balance $ 276.6 $ 273.4 $ 277.4 $ 221.3 Term loans Borrowings (1) — — — 52.4 Repayments (.7) (.7) (2.1) (1.3) Foreign currency translation (1.5) 2.3 (.9) 2.6 Revolving credit loan Borrowings (2) 35.0 — 35.0 — Repayments (9.0) — (9.0) — Ending balance 300.4 275.0 $ 300.4 $ 275.0 (1) Borrowings for the nine months ended September 30, 2020 included $52.4 for the funding of the acquisition of Kingsbridge. (2) Borrowings for both the three and nine months ended September 30, 2021 included $35.0 for the funding of the acquisition of J.C. Taylor. As of September 30, 2021, the term loans had an outstanding balance of $274.4 million, including £41.9 million ($56.6 million based upon the foreign exchange spot rate as of September 30, 2021) in a GBP term loan, and the revolving credit loan had an outstanding balance of $26.0 million. On June 15, 2018, NSM entered into an interest rate swap agreement to hedge its exposure to interest rate risk on $151.0 million of its USD denominated variable rate term loans. See Note 9 — “Derivatives” . As of September 30, 2021, $146.5 million of the outstanding term loans were hedged by the swap and $128.0 million of the outstanding term loans were unhedged. The following table presents the NSM weighted average interest rate for the nine months ended September 30, 2021 and 2020: NSM Weighted Average Interest Rate Nine Months Ended September 30, 2021 2020 Millions Weighted Average Interest Expense (1) Weighted Average Interest rate Weighted Average Interest Expense (1) Weighted Average Interest rate Term loan - hedged $ 147.1 $ 10.0 9.1 % $ 148.5 $ 10.0 9.0 % Term loan - unhedged 129.5 7.3 7.5 % 125.1 6.1 6.5 % Total NSM Facility $ 276.6 $ 17.3 8.3 % $ 273.6 $ 16.1 7.8 % ( 1) Interest expense includes the amortization of debt issuance costs and the effect of the interest rate swap and excludes interest expense related to the Other NSM Debt. The NSM Bank Facility is secured by all property of the loan parties and contains various affirmative, negative and financial covenants that White Mountains considers to be customary for such borrowings, including a maximum consolidated total leverage ratio covenant. Other NSM Debt NSM also has a secured term loan related to its U.K. vertical. As of September 30, 2021, the secured term loan had an outstanding balance of $1.4 million and a maturity date of December 31, 2022. 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 Massachusetts Mutual Life Insurance Company 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. Interest on the Kudu Credit Facility accrues at a floating interest rate equal to the greater of the three-month USD-LIBOR and 0.25%, plus in each case, the applicable spread of 4.30%. The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of September 30, 2021, the interest reserve account is $4.5 million. The Kudu Credit Facility requires Kudu to maintain a ratio of outstanding balance to the sum of fair market value of 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, 2021, Kudu has a 34% LTV Percentage. Kudu may borrow undrawn balances within the initial three-year availability period, subject to customary terms and conditions, to the extent the amount borrowed under the Kudu Credit Facility does not exceed the borrowing base, which is equal to 35% of the fair value of Kudu’s qualifying participation contracts. When considering White Mountains’s remaining equity commitment to Kudu and the fair value of Kudu’s qualifying participation contracts as of September 30, 2021, the available undrawn balance was $11.7 million. During the nine months ended September 30, 2021, Kudu borrowed $3.0 million and repaid the outstanding Kudu Bank Facility balance of $92.2 million. During the three and nine months ended September 30, 2021, Kudu borrowed $101.0 million and $203.0 million and made no repayments on the Kudu Credit Facility. As of September 30, 2021, the Kudu Credit Facility had an undrawn balance of $97.0 million. 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, 2021, debt in White Mountains’s Other Operations segment consisted of three secured credit facilities (collectively, “Other Operations debt”). The first credit facility has a maximum borrowing capacity of $16.3 million, which is comprised of a term loan of $11.3 million, a delayed-draw term loan of $3.0 million and a revolving credit loan commitment of $2.0 million, all with a maturity date of March 12, 2024. The second credit facility has a maximum borrowing capacity of $15.0 million, which is comprised of a term loan of $9.0 million, a delayed-draw term loan of $4.0 million and a revolving credit loan commitment of $2.0 million, all with a maturity date of July 2, 2025. The third credit facility has a maximum borrowing capacity of $4.0 million, which is comprised of a revolving credit loan commitment, with a maturity date of October 26, 2021. During the three and nine months ended September 30, 2021, White Mountains’s Other Operations segment borrowed $0.4 million and $0.7 million. During the three and nine months ended September 30, 2021, White Mountains’s Other Operations segment made repayments of $1.2 million and $2.6 million. As of September 30, 2021, the Other Operations debt had an outstanding balance of $19.5 million. Compliance At September 30, 2021, 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, 2021
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 and taxes are imposed, the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035, pursuant to the Bermuda Exempted Undertakings Tax Protection Act of 1966. The Company has subsidiaries and branches that operate in various other jurisdictions around the world that are subject to tax in the jurisdictions in which they operate. The jurisdictions in which the Company’s subsidiaries and branches are subject to tax are Ireland, Israel, Luxembourg, the United Kingdom and the United States. 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 (6.0)% and (12.4)%. The effective tax rate was different from the U.S. statutory rate of 21.0%, due to 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 the Other Operations segment 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. White Mountains’s income tax expense related to pre-tax income from continuing operations for the three and nine months ended September 30, 2020 represented an effective tax rate of 30.7% and 33.7%. The effective tax rate was different from the U.S. statutory rate of 21.0% due to tax expense associated with the reorganization of the Guilford Holdings, Inc. consolidated U.S. tax group in preparation for the MediaAlpha IPO and state income taxes, partially offset by income generated in jurisdictions with lower tax rates than the United States. The additional tax expense associated with the reorganization of the Guilford Holdings, Inc. consolidated U.S. tax group within the Other Operations segment consisted of withholding taxes and the establishment of a partial valuation allowance on deferred tax assets of various service companies, other entities and investments. In arriving at the effective tax rate for the three and nine months ended September 30, 2021 and 2020, 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, 2021 and 2020. 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 2015.

Derivatives

Derivatives	9 Months Ended
	Sep. 30, 2021
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivatives	Derivatives NSM Interest Rate Swap On June 15, 2018, NSM entered into an interest rate swap agreement to hedge its exposure to interest rate risk on $151.0 million of its USD denominated variable rate term loans under the NSM Bank Facility. Under the terms of the swap agreement, NSM pays a fixed-rate of 2.97% and receives a variable rate, which is reset monthly, based on the then-current USD-LIBOR. As of September 30, 2021, the variable rate received by NSM under the swap agreement was 1.00%. Over the term of the swap, the notional amount decreases in accordance with the principal repayments NSM expects to make on its term loans. The interest rate swap is scheduled to mature on June 30, 2024. As of September 30, 2021, $146.5 million of the outstanding term loans were hedged by the swap. For the three and nine months ended September 30, 2021, the weighted average effective interest rate on the outstanding term loans that were hedged, including the effect of the amortization of debt issuance costs and the effect of the interest rate swap, was 9.1%. NSM’s obligations under the swap are secured by the same collateral securing the NSM Bank Facility on a pari passu basis. NSM does not currently hold any collateral deposits from or provide any collateral deposits to the swap counterparty. NSM evaluated the effectiveness of the swap to hedge its interest rate risk associated with its variable rate debt and concluded at the swap inception date that the swap was highly effective in hedging that risk. NSM evaluates the effectiveness of the hedging relationship on an ongoing basis. For the three and nine months ended September 30, 2021, White Mountains recognized net interest expense of $0.6 million and $1.9 million for the periodic net settlement payments on the swap. For the three and nine months ended September 30, 2020, White Mountains recognized net interest expense of $0.6 million and $1.9 million for the periodic net settlement payments on the swap. As of September 30, 2021 and December 31, 2020, the estimated fair value of the swap and the accrual of the periodic net settlement payments recorded in other liabilities was $6.0 million and $8.2 million. There was no ineffectiveness in the hedge for the three and nine months ended September 30, 2021 and 2020. For the three and nine months ended September 30, 2021, the $(0.6) million and $(2.2) million change in the fair value of the swap is included within White Mountains’s accumulated other comprehensive income (loss). For the three and nine months ended September 30, 2020, the $0.5 million and $(2.3) million change in the fair value of the swap is included within White Mountains’s accumulated other comprehensive income (loss). NSM Interest Rate Cap On June 4, 2020, NSM entered into an interest rate cap agreement to limit its exposure to the risk of interest rate increases on the GBP denominated term loan under the NSM Bank Facility. The notional amount of the interest rate cap is £42.5 million ($52.4 million based upon the foreign exchange spot rate as of the date of the transaction) and the termination date is June 4, 2022. On August 18, 2020, NSM entered into a separate interest rate cap agreement to extend the term of the original interest rate cap agreement by one year. The second interest rate cap agreement has an effective date of June 15, 2022 and a termination date of June 15, 2023. NSM paid total initial premiums of $0.1 million for the interest rate caps. Under the terms of the interest rate cap agreements, if the GBP-LIBOR rate at the measurement date exceeds 1.25%, NSM will receive payments from the counterparty equal to the GBP-LIBOR rate, less the 1.25% cap rate. As of September 30, 2021, the GBP-LIBOR rate was 0.08%. NSM accounts for the interest rate caps as derivatives 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, 2021, White Mountains recognized a negligible amount related to the change in fair value on the interest rate caps within interest expense. For the three and nine months ended September 30, 2020, White Mountains recognized a change in fair value of $(0.1) million on the interest rate caps within interest expense. As of September 30, 2021 and December 31, 2020, the estimated fair value of the caps recorded in other assets was less than $0.1 million.

Municipal Bond Guarantee Insura

Municipal Bond Guarantee Insurance	9 Months Ended
	Sep. 30, 2021
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 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 an initial term through the end of 2022. Fidus Re BAM is party to two collateralized financial guarantee excess of loss reinsurance agreements that serve to increase BAM’s claims paying resources and are provided by Fidus Re, a Bermuda based special purpose insurer created in 2018 solely to provide reinsurance protection to BAM. In the second quarter of 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 36% of BAM’s portfolio of financial guaranty policies issued through September 30, 2021. 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. 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 40% of BAM’s portfolio of financial guaranty policies issued through September 30, 2021. 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 NYDFS single issuer limits. The XOLT is subject to an aggregate limit equal to the lesser of $75.0 million or the assets held in 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: a Regulation 114 Trust and a supplemental collateral trust (the “Supplemental Trust” and together with the Regulation 114 Trust, 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 expenses, 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, 2021 and December 31, 2020 was $241.0 million and $222.8 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, 2021 and December 31, 2020 was $603.8 million and $604.3 million. As of September 30, 2021 and December 31, 2020, the Collateral Trusts held assets of $844.8 million and $827.1 million, which included $449.7 million and $434.5 million of cash and investments, $388.2 million and $388.2 million of BAM Surplus Notes and $6.9 million and $4.4 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 2021, the interest rate on the BAM Surplus Notes is 3.1%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. 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 2020, BAM made a $30.1 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $21.5 million was a repayment of principal held in the Supplemental Trust, $0.2 million was a payment of accrued interest held inside the Supplemental Trust and $8.4 million was a payment of accrued interest held outside the Supplemental Trust. In January 2020, BAM made a one-time $65.0 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $47.9 million was a repayment of principal held in the Supplemental Trust, $0.9 million was a payment of accrued interest held inside the Supplemental Trust and $16.2 million was a payment of accrued interest held outside the Supplemental Trust. During the three and nine months ended September 30, 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest. As of September 30, 2021 and December 31, 2020, the principal balance on the BAM Surplus Notes was $388.2 million and $388.2 million and total interest receivable on the BAM Surplus Notes was $164.8 million and $155.7 million. Insured Obligations and Premiums The following table presents a schedule of BAM’s insured obligations as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Contracts outstanding 11,877 10,997 Remaining weighted average contract period outstanding (in years) 10.7 10.7 Contractual debt service outstanding (in millions): Principal $ 83,829.0 $ 75,287.7 Interest 39,528.4 36,448.8 Total debt service outstanding $ 123,357.4 $ 111,736.5 Gross unearned insurance premiums (in millions) $ 257.0 $ 237.5 The following table presents a schedule of BAM’s future premium revenues as of September 30, 2021: Millions September 30, 2021 October 1, 2021 - December 31, 2021 $ 6.2 January 1, 2022 - March 31, 2022 6.1 April 1, 2022 - June 30, 2022 6.1 July 1, 2022 - September 30, 2022 6.0 October 1, 2022 - December 31, 2022 5.9 Total 2022 24.1 2023 22.8 2024 21.1 2025 19.6 2026 18.1 2027 and thereafter 145.1 Total gross unearned insurance premiums $ 257.0 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, 2021 and 2020: Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Written premiums: Direct $ 12.8 $ 14.4 $ 34.5 $ 45.5 Assumed — — 4.5 .1 Gross written premiums (1) $ 12.8 $ 14.4 $ 39.0 $ 45.6 Earned premiums: Direct $ 5.9 $ 5.3 $ 16.8 $ 14.5 Assumed .8 .9 2.8 2.7 Gross earned premiums (1) $ 6.7 $ 6.2 $ 19.6 $ 17.2 (1) There are no ceded premium amounts in the periods presented. Gross written premiums and Gross earned premium are equivalent to net written premiums and net earned premiums. In the second quarter of 2020, BAM assumed a municipal bond guarantee contract with a par value of $36.9 million through an endorsement to the facultative quota share reinsurance agreement. 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 $0.8 billion. None of the contracts assumed were non-performing and no loss reserves have been established for any of the contracts, either as of the transaction dates or as of September 30, 2021. The agreements, which cover future claims exposure only, meet the risk transfer criteria under ASC 944-20, Insurance Activities

Earnings Per Share

Earnings Per Share	9 Months Ended
	Sep. 30, 2021
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, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations” . Three Months Ended Nine Months Ended September 30, September 30, 2021 2020 2021 2020 Basic and diluted earnings per share numerators (in millions): Net (loss) income attributable to White Mountains’s $ (371.4) $ 232.9 $ (308.2) $ 219.5 Less: total income (loss) from discontinued operations, net of tax — (.7) 18.7 (.8) Net (loss) income from continuing operations attributable to $ (371.4) $ 233.6 $ (326.9) $ 220.3 Allocation of losses (earnings) to participating restricted common shares (1) 4.5 (3.2) 3.8 (2.9) Basic and diluted (losses) earnings per share numerators $ (366.9) $ 230.4 $ (323.1) $ 217.4 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (2) (37.8) (43.1) (36.0) (40.0) Basic earnings (losses) per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (2) (37.8) (43.1) (36.0) (40.0) Diluted earnings (losses) per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ — $ — $ 1.00 $ 1.00 Undistributed (losses) earnings (120.18) 75.32 (106.48) 69.40 Basic and diluted (losses) earnings per share $ (120.18) $ 75.32 $ (105.48) $ 70.40 (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (2) 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, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations” . Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Undistributed net earnings (losses) - continuing operations: Net (losses) earnings attributable to White Mountains’s common shareholders, net of restricted common share amounts $ (366.9) $ 230.4 $ (323.1) $ 217.4 Dividends declared, net of restricted common share amounts (1) — — (3.1) (3.1) Total undistributed net (losses) earnings, net of restricted common share amounts $ (366.9) $ 230.4 $ (326.2) $ 214.3 (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, 2021
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, 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, 2021 and 2020 for performance shares granted under the WTM Incentive Plan: Three Months Ended September 30, Nine Months Ended September 30, 2021 2020 2021 2020 Millions, except share amounts Target Performance Accrued Target Performance Accrued Target Performance Accrued Target Performance Accrued Beginning of period 41,252 $ 45.7 42,458 $ 15.8 42,458 $ 56.3 42,473 $ 43.7 Shares paid (1) (219) (.6) — — (14,336) (35.2) (14,070) (27.7) New grants — — — — 13,475 — 14,055 — Forfeitures and cancellations (2) (205) .2 — (.3) (769) .4 — .1 Expense recognized — (6.5) — 13.6 — 17.3 — 13.0 End of period 40,828 $ 38.8 42,458 $ 29.1 40,828 $ 38.8 42,458 $ 29.1 (1) WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in cash in March 2021 at 200% of target. WTM performance share payments in 2020 for the 2017-2019 performance cycle, which were paid in cash in March 2020, ranged from 174% to 180% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP. During the nine months ended September 30, 2021, White Mountains granted 13,475 performance shares for the 2021-2023 performance cycle. During the nine months ended September 30, 2020, White Mountains granted 14,055 performance shares for the 2020-2022 performance cycle. All performance shares earned were settled in cash. If all the outstanding WTM performance shares had vested on September 30, 2021, the total additional compensation cost to be recognized would have been $17.2 million, based on accrual factors (common share price and payout assumptions) as of September 30, 2021. The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of September 30, 2021 for each performance cycle: Nine Months Ended September 30, 2021 Millions, except share amounts Target Performance Accrued Performance cycle: 2019 – 2021 14,625 $ 24.4 2020 – 2022 13,350 13.4 2021 – 2023 13,475 1.6 Sub-total 41,450 39.4 Assumed forfeitures (622) (.6) September 30, 2021 40,828 $ 38.8 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, 2021 and 2020: Three Months Ended September 30, Nine Months Ended September 30, 2021 2020 2021 2020 Millions, except share amounts Restricted Unamortized Restricted Unamortized Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,280 $ 23.2 43,105 $ 23.0 43,105 $ 15.2 43,395 $ 16.7 Issued — — — — 13,475 16.1 14,055 15.1 Vested (219) — — — (17,936) — (14,345) — Forfeited (211) (.2) — — (794) (.8) — — Expense recognized — (3.6) — (3.6) — (11.1) — (12.4) End of period 37,850 $ 19.4 43,105 $ 19.4 37,850 $ 19.4 43,105 $ 19.4

Leases

Leases	9 Months Ended
	Sep. 30, 2021
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, 2021 and December 31, 2020, the right of use (“ROU”) asset was $42.9 million and $37.6 million and lease liabilities were $45.9 million and $38.3 million. The following table summarizes net lease expense recognized in White Mountains’s consolidated statement of operations for the three and nine months ended September 30, 2021 and 2020: Millions Three Months Ended September 30, Nine Months Ended September 30, Lease Cost 2021 2020 2021 2020 Lease cost $ 2.7 $ 1.6 $ 7.2 $ 5.7 Less: sublease income .1 .1 .3 .3 Net lease cost $ 2.6 $ 1.5 $ 6.9 $ 5.4 The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of September 30, 2021: Millions As of September 30, 2021 Remainder of 2021 $ 2.0 2022 10.8 2023 9.8 2024 8.5 2025 6.7 Thereafter 16.4 Total undiscounted lease payments 54.2 Less: present value adjustment 8.3 Operating lease liability $ 45.9 The following tables present lease related assets and liabilities by reportable segment as of September 30, 2021 and December 31, 2020: As of September 30, 2021 Millions HG/BAM Ark NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 8.0 $ 7.0 $ 13.8 $ 6.7 $ 7.4 $ 42.9 5.0% Lease liability $ 8.6 $ 7.0 $ 15.0 $ 7.1 $ 8.2 $ 45.9 (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, 2020 Millions HG/BAM NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 10.1 $ 17.1 $ 2.0 $ 8.4 $ 37.6 4.6% Lease liability $ 10.1 $ 17.1 $ 2.0 $ 9.1 $ 38.3 (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, 2021
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 related percentage of each consolidated entity’s total equity owned by non-controlling shareholders as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 $ in Millions Non-controlling Percentage Non-controlling Equity Non-controlling Percentage Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ 10.1 3.1 % $ 13.5 Ark 28.0 % 216.1 — % — NSM 3.5 % 16.5 3.4 % 17.0 Kudu .7 % 3.1 .7 % 2.3 Other various 12.1 various 2.4 Total, excluding BAM 257.9 35.2 BAM 100.0 % (125.3) 100.0 % (123.3) Total non-controlling interests $ 132.6 $ (88.1)

Segment Information

Segment Information	9 Months Ended
	Sep. 30, 2021
Segment Reporting [Abstract]
Segment Information	Segment Information As of September 30, 2021, White Mountains conducted its operations through five segments: (1) HG Global/BAM, (2) Ark, (3) NSM, (4) Kudu and (5) Other Operations. A discussion of White Mountains’s consolidated investment operations is included after the discussion of operations by segment. As a result of the Ark Transaction, White Mountains began consolidating Ark in its financial statements as of January 1, 2021. 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 NSM 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 (4.0) .3 — 18.9 15.3 30.5 Net realized and unrealized investment — — — — (396.8) (396.8) Commission revenues — — 67.0 — 2.4 69.4 Other revenue .3 3.4 15.3 .1 28.1 47.2 Total revenues 7.4 217.7 82.3 28.5 (346.0) (10.1) Loss and loss adjustment expenses — 129.2 — — — 129.2 Insurance acquisition expenses 3.0 53.7 — — — 56.7 Cost of sales — — — — 24.0 24.0 General and administrative expenses 12.4 21.8 48.8 3.3 14.5 100.8 Broker commission expense — — 20.4 — — 20.4 Change in fair value of contingent — — .6 — — .6 Amortization of other intangible assets — — 8.2 — 2.0 10.2 Interest expense — 2.1 5.9 1.9 .4 10.3 Total expenses 15.4 206.8 83.9 5.2 40.9 352.2 Pre-tax (loss) income $ (8.0) $ 10.9 $ (1.6) $ 23.3 $ (386.9) $ (362.3) Millions HG Global/ BAM NSM Kudu Other Operations Total Three Months Ended September 30, 2020 Earned insurance premiums $ 6.2 $ — $ — $ — $ 6.2 Net investment income 4.7 — 6.4 60.1 71.2 Net realized and unrealized investment gains 3.2 — 9.8 43.6 56.6 Net unrealized investment gains from investment in MediaAlpha — — — 250.0 250.0 Commission revenues — 58.2 — 2.1 60.3 Other revenue .4 12.5 .1 2.2 15.2 Total revenues 14.5 70.7 16.3 358.0 459.5 Insurance acquisition expenses 1.6 — — — 1.6 Cost of sales — — — 2.3 2.3 General and administrative expenses 14.0 42.9 2.2 44.3 103.4 Broker commission expense — 17.1 — — 17.1 Change in fair value of contingent — .7 — — .7 Amortization of other intangible assets — 5.1 .1 .2 5.4 Interest expense — 6.1 1.4 .3 7.8 Total expenses 15.6 71.9 3.7 47.1 138.3 Pre-tax (loss) income $ (1.1) $ (1.2) $ 12.6 $ 310.9 $ 321.2 Millions HG Global/ BAM Ark NSM 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 — — — — (325.5) (325.5) Commission revenues — — 194.6 — 7.0 201.6 Other revenue .9 9.4 46.8 .2 57.6 114.9 Total revenues 18.1 457.3 241.4 88.8 (210.8) 594.8 Loss and loss adjustment expenses — 247.8 — — — 247.8 Insurance acquisition expenses 6.5 124.4 — — — 130.9 Cost of sales — — — — 45.9 45.9 General and administrative expenses 42.7 84.4 142.1 9.0 79.7 357.9 Broker commission expense — — 60.9 — — 60.9 Change in fair value of contingent — — .8 — — .8 Amortization of other intangible assets — — 25.0 .2 2.9 28.1 Loss on assets held for sale — — 28.7 — — 28.7 Interest expense — 4.5 17.7 9.2 1.1 32.5 Total expenses 49.2 461.1 275.2 18.4 129.6 933.5 Pre-tax (loss) income $ (31.1) $ (3.8) $ (33.8) $ 70.4 $ (340.4) $ (338.7) Millions HG Global/ BAM NSM Kudu Other Operations Total Nine Months Ended September 30, 2020 Earned insurance premiums $ 17.2 $ — $ — $ — $ 17.2 Net investment income 15.1 — 19.3 79.3 113.7 Net realized and unrealized investment gains 23.7 — 1.5 (17.4) 7.8 Net unrealized investment gains from investment in MediaAlpha — — — 295.0 295.0 Commission revenues — 174.2 — 6.1 180.3 Other revenue 2.1 37.6 .2 6.0 45.9 Total revenues 58.1 211.8 21.0 369.0 659.9 Insurance acquisition expenses 5.4 — — — 5.4 Cost of sales — — — 6.5 6.5 General and administrative expenses 41.4 131.0 7.5 87.1 267.0 Broker commission expense — 56.4 — — 56.4 Change in fair value of contingent — (1.6) — — (1.6) Amortization of other intangible assets — 16.2 .3 .6 17.1 Interest expense — 16.1 4.3 .8 21.2 Total expenses 46.8 218.1 12.1 95.0 372.0 Pre-tax income (loss) $ 11.3 $ (6.3) $ 8.9 $ 274.0 $ 287.9 In compliance with ASC 606, Revenues from Contracts with Customers, the following tables present White Mountains’s total revenues by revenue source for the three and nine months ended September 30, 2021 and 2020: Millions HG Global/BAM Ark NSM Kudu Other Total Three Months Ended September 30, 2021 Commission and other revenue Specialty Transportation (1) $ — $ — $ 25.7 $ — $ — $ 25.7 Real Estate — — 6.2 — — 6.2 Social Services — — 10.2 — — 10.2 Pet — — 19.9 — — 19.9 United Kingdom — — 13.0 — — 13.0 Other — — 7.3 — 2.4 9.7 Total commission and other revenue — — 82.3 — 2.4 84.7 Product and service revenues — — — — 28.2 28.2 Revenues from contracts with customers — — 82.3 — 30.6 112.9 Other (2) 7.4 217.7 — 28.5 (376.6) (123.0) Total revenues $ 7.4 $ 217.7 $ 82.3 $ 28.5 $ (346.0) $ (10.1) (1) Includes the results of J.C. Taylor from August 6, 2021, the date of the J.C. Taylor transaction. (2) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM NSM Kudu Other Total Three Months Ended September 30, 2020 Commission and other revenue Specialty Transportation $ — $ 21.9 $ — $ — $ 21.9 Real Estate — 6.0 — — 6.0 Social Services — 8.6 — — 8.6 Pet — 14.7 — — 14.7 United Kingdom — 13.9 — — 13.9 Other — 5.6 — 2.1 7.7 Total commission and other revenue — 70.7 — 2.1 72.8 Product revenues — — — 2.0 2.0 Revenues from contracts with customers — 70.7 — 4.1 74.8 Other (1) 14.5 — 16.3 353.9 384.7 Total revenues $ 14.5 $ 70.7 $ 16.3 $ 358.0 $ 459.5 (1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM Ark NSM Kudu Other Total Nine Months Ended September 30, 2021 Commission and other revenue Specialty Transportation (1) $ — $ — $ 73.0 $ — $ — $ 73.0 Real Estate — — 25.2 — — 25.2 Social Services — — 26.2 — — 26.2 Pet — — 55.6 — — 55.6 United Kingdom — — 39.9 — — 39.9 Other — — 21.5 — 7.0 28.5 Total commission and other revenue — — 241.4 — 7.0 248.4 Product and service revenues — — — — 57.5 57.5 Revenues from contracts with customers — — 241.4 — 64.5 305.9 Other (2) 18.1 457.3 — 88.8 (275.3) 288.9 Total revenues $ 18.1 $ 457.3 $ 241.4 $ 88.8 $ (210.8) $ 594.8 (1) Includes the results of J.C. Taylor from August 6, 2021, the date of the J.C. Taylor transaction. (2) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM NSM Kudu Other Total Nine Months Ended September 30, 2020 Commission and other revenue Specialty Transportation $ — $ 66.1 $ — $ — $ 66.1 Real Estate — 32.7 — — 32.7 Social Services — 22.2 — — 22.2 Pet — 39.8 — — 39.8 United Kingdom (2) — 36.3 — — 36.3 Other — 14.7 — 6.1 20.8 Total commission and other revenue — 211.8 — 6.1 217.9 Product revenues — — — 6.4 6.4 Revenues from contracts with customers — 211.8 — 12.5 224.3 Other (1) 58.1 — 21.0 356.5 435.6 Total revenues $ 58.1 $ 211.8 $ 21.0 $ 369.0 $ 659.9 (1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. (2) Includes the results of Kingsbridge from April 7, 2020, the date of the Kingsbridge transaction.

Equity-Method Eligible Investme

Equity-Method Eligible Investments	9 Months Ended
	Sep. 30, 2021
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 basic ownership interests and carrying values of White Mountains’s equity method eligible investments as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Basic Ownership Interest Carrying Value Basic Ownership Interest Carrying Value Kudu Participation Contracts 3.2 - 32.7% 604.7 3.2 - 35.0% 400.6 Investment in MediaAlpha 28.4 % $ 316.4 35.0 % $ 802.2 PassportCard/DavidShield 53.8 % 105.0 53.8 % 95.0 Elementum Holdings, L.P. 29.7 % 56.7 28.9 % 55.1 Other equity method eligible investments, at fair value Under 50.0% 95.6 Under 50.0% 132.2 Other equity method eligible investments, at fair value 50.0% and over 17.2 50.0% and over 15.2 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 statement of operations. For the three and nine months ended September 30, 2020, White Mountains received dividend and income distributions from equity method eligible investments of $63.9 million and $85.3 million, which were recorded within net investment income in the consolidated statement 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 and 2020, MediaAlpha was considered a significant subsidiary. The following tables present summarized financial information for MediaAlpha as of September 30, 2021 and December 31, 2020 and for the three and nine months ended September 30, 2021 and 2020: Millions September 30, 2021 December 31, 2020 Balance sheet data: Total assets $ 245.5 $ 210.3 Total liabilities $ 318.4 $ 315.5 Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Income statement data: Total revenues $ 152.7 $ 151.5 $ 483.7 $ 394.6 Total expenses $ 157.0 $ 146.7 $ 488.2 $ 370.8 Net (loss) income $ (4.3) $ 4.8 $ (4.5) $ 23.8

Fair Value of Financial Instrum

Fair Value of Financial Instruments	9 Months Ended
	Sep. 30, 2021
Fair Value Disclosures [Abstract]
Fair Value of Financial Instruments	Fair Value of Financial Instruments White Mountains records its financial instruments at fair value with the exception of debt obligations, which are recorded as debt at face value less unamortized original issue discount. See Note 7 — “Debt”. The following table presents the fair value and carrying value of these financial instruments as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Carrying Fair Carrying Ark 2007 Subordinated Notes $ 42.0 $ 43.9 $ — $ — Ark 2021 Subordinated Notes $ 163.1 $ 156.8 $ — $ — NSM Bank Facility $ 300.6 $ 293.7 $ 279.3 $ 271.3 Other NSM debt $ 1.3 $ 1.3 $ 1.3 $ 1.3 Kudu Credit Facility $ 218.2 $ 195.6 $ — $ — Kudu Bank Facility $ — $ — $ 89.3 $ 86.3 Other Operations debt $ 20.5 $ 19.1 $ 18.8 $ 17.5

Commitments and Contingencies

Commitments and Contingencies	9 Months Ended
	Sep. 30, 2021
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	Commitments and Contingencies Legal Contingencies White Mountains is subject to litigation and arbitration in the normal course of business. White Mountains considers the requirements of ASC 450 when evaluating its exposure to litigation and arbitration. ASC 450 requires that accruals be established for litigation and arbitration if it is probable that a loss has been incurred and it can be reasonably estimated. ASC 450 also requires that litigation and arbitration be disclosed if it is probable that a loss has been incurred or if there is a reasonable possibility that a loss may have been incurred. White Mountains does not have any current litigation that may have a material adverse effect on White Mountains’s financial condition, results of operations or cash flows. The following description presents significant legal contingencies, ongoing non-claims related litigation or arbitration as of September 30, 2021: Esurance On October 7, 2011, the Company completed the sale of its Esurance Holdings, Inc. and its subsidiaries and Answer Financial Inc. and its subsidiaries (collectively, “Esurance”) to The Allstate Corporation (“Allstate”) pursuant to a Stock Purchase Agreement dated as of May 17, 2011. Subject to specified thresholds and limits, the Company remains contingently liable to Allstate for specified matters related to the pre-closing period, including (a) losses of Esurance arising from extra-contractual claims and claims in excess of policy limits, (b) certain corporate reorganizations effected to remove entities from Esurance that were not being sold in the transaction, and (c) certain tax matters, including certain net operating losses being less than stated levels. No claims relating to these matters were outstanding as of September 30, 2021. Sirius Group Tax Contingency In the first quarter of 2021, White Mountains recorded a $17.6 million gain within discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius Group in 2016. The liability related to certain interest deductions claimed by Sirius Group that had been disputed by the Swedish Tax Agency (STA). In April 2021, the STA 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.

Held for Sale and Discontinued

Held for Sale and Discontinued Operations	9 Months Ended
	Sep. 30, 2021
Discontinued Operations and Disposal Groups [Abstract]
Held for Sale and Discontinued Operations	Held for Sale and Discontinued Operations Sirius Group As of December 31, 2020, White Mountains recorded a liability of $18.7 million, related to the tax indemnification provided in connection with the sale of Sirius Group in 2016. 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. See Note 18 — “Commitments and Contingencies” . NSM On April 12, 2021, NSM completed the sale of the Fresh Insurance motor business for net proceeds of £1.1 million ($1.5 million based upon the foreign exchange spot rate as of the transaction date). The assets and liabilities included in the transaction, were measured at their estimated fair values, net of disposal and classified as held for sale at March 31, 2021. However, the transaction did not meet the criteria to be classified as discontinued operations. In the first quarter of 2021, NSM recorded a loss of $28.7 million related to the sale. 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, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, 2021 2020 2021 2020 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ (371.4) $ 232.9 $ (308.2) $ 219.5 Less: total income (loss) from continuing operations, net of tax (371.4) 233.6 (326.9) 220.3 Net (loss) gain from discontinued operations attributable to White Mountains’s common shareholders $ — $ (.7) $ 18.7 $ (.8) Allocation of earnings to participating restricted common shares (1) — — (.2) — Basic and diluted earnings(losses) per share numerators (2) $ — $ (.7) $ 18.5 $ (.8) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (3) (37.8) (43.1) (36.0) (40.0) Basic earnings per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (3) (37.8) (43.1) (36.0) (40.0) Diluted earnings per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Basic and diluted earnings (losses) per share (in dollars) - discontinued operations: $ — $ (.23) $ 6.03 $ (.26) (1) Restricted shares issued by White Mountains contain dividend participation features, and therefore, are considered participating securities. (2) 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, 2021 and 2020. (3) Restricted common 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, 2021
Accounting Policies [Abstract]
Basis of Presentation	Basis of Presentation The Company 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 located at 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.
Consolidation Principles	Consolidation Principles Under GAAP, the Company is required to consolidate any entity in which it holds a controlling financial interest. A controlling financial interest is usually in the form of an investment representing the majority of the subsidiary’s voting interests. However, a controlling financial interest may also arise from a financial interest in a variable interest entity (“VIE”) through arrangements that do not involve ownership of voting interests. The Company consolidates a VIE if it determines that it is the primary beneficiary. The primary beneficiary is defined as the entity who holds a variable interest that gives it both the power to direct the VIE’s activities that most significantly impact its economic performance and the obligation to absorb losses of, or the right to receive returns from, the VIE that could potentially be significant to the VIE. Intercompany transactions have been eliminated in consolidation. 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 2020 Annual Report on Form 10-K.
Business Combinations	Business Combinations White Mountains accounts for purchases of businesses using the acquisition method, which requires the measurement of assets acquired, including goodwill and other intangible assets, and liabilities assumed, including contingent liabilities, at their estimated fair values as of the acquisition date. The acquisition date fair values represent management’s best estimates and are based upon established valuation techniques, reasonable assumptions and, where appropriate, valuations performed by independent third parties. In circumstances where additional information is required in order to determine the acquisition date fair value of balance sheet amounts, provisional amounts may be recorded as of the acquisition date and may be subject to subsequent adjustment throughout the measurement period, which is up to one year from the acquisition date. Measurement period adjustments are recognized in the period in which they are determined. The results of operations and cash flows of businesses acquired are included in the consolidated financial statements from the date of acquisition. White Mountains accounts for purchases of other intangible assets that do not meet the definition of a business as asset acquisitions. Asset acquisitions are recognized at the amount of consideration paid, which is deemed to equal fair value.
Use of Estimates	Use of Estimates 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.
Fair Value Measurements	Fair Value Measurement s 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”).
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, 2021, White Mountains’s reportable segments were HG Global/BAM, Ark, NSM, Kudu and 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 purposes 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 wholly-owned subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. 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, consisting of $203.0 million of Series A Notes and $300.0 million of Series B Notes (the “BAM Surplus Notes”). As of September 30, 2021 and December 31, 2020, 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 VIE 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 writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through Lloyd’s of London (“Lloyd’s”) Syndicates 4020 and 3902 (the “Syndicates”). Beginning in January 2021, Ark began writing certain classes of its business through Group Ark Insurance Limited (“GAIL”), Ark’s wholly-owned Class 4 Bermuda-based insurance and reinsurance company. As of September 30, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% on a fully-diluted, fully-converted basis, taking account of management’s equity incentives). The remaining shares are owned by employees. In the future, management rollover shareholders could earn additional shares in the company 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. See Note 2 — “Significant Transactions ”. The NSM segment consists of NSM Insurance HoldCo, LLC and its subsidiaries (collectively, “NSM”). NSM is a full-service managing general underwriting agency (“MGU”) and program administrator for specialty property and casualty insurance. The company places insurance in niche sectors such as specialty transportation, real estate, social services and pet. On behalf of its insurance carrier partners, NSM typically manages all aspects of the placement process, including product development, marketing, underwriting, policy issuance and claims. NSM earns commissions based on the volume and, in some cases, profitability of the insurance that it places. NSM does not take insurance risk. As of September 30, 2021 and December 31, 2020, White Mountains owned 96.6% and 96.5% of the basic units outstanding of NSM (87.3% and 89.6% on a fully diluted, fully converted basis). See Note 2 — “Significant Transactions ”. The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset 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 immediate strong, stable cash yields. As of September 30, 2021 and December 31, 2020, White Mountains owned 99.3% and 99.1% of the basic units outstanding (84.7% and 85.4% on a fully diluted, fully converted basis). The Other Operations segment 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 and certain other assets. See Note 2 — “Significant Transactions” .
Discontinued Operations and Assets Held for Sale	Discontinued Operations and Assets Held for Sale In the first quarter of 2021, White Mountains recorded a gain on sale of discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) in 2016.
Ark Insurance Operations	Ark Insurance Operations Ark writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through the Syndicates. Beginning in January 2021, Ark began writing certain classes of its business through GAIL. For the years of account prior to White Mountains’s transaction with Ark, a significant proportion of the Syndicates’ underwriting capital was provided by other third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts through Ark’s corporate member. The TPC Providers’ economic participation in the Syndicates for the remaining open years of account prior to White Mountains’s transaction with Ark is approximately 51% of the total net result of 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. Ark’s premiums written comprise premiums on insurance contracts incepted during the year as well as premium adjustments related to prior years of account. Insurance premiums are recognized as revenues over the loss exposure or coverage period in proportion to the level of insurance protection provided. In most cases, premiums are earned ratably over the term of the contract with unearned premiums calculated on a monthly pro-rata basis. Catastrophe premiums are earned in proportion to the level of insurance protection provided. Premiums earned are presented net of amounts ceded to reinsurers. Premiums receivable, representing amounts due from insureds, are presented net of an allowance for uncollectible premiums, including expected credit losses, both dispute and credit related. The allowance is based upon Ark’s ongoing review of amounts outstanding, historical loss data, including delinquencies and write-offs, current and forecasted economic conditions and other relevant factors. Credit risk is partially mitigated by Ark’s ability to cancel the policy if the policyholder does not pay the premium. Deferred acquisition costs comprise brokerage and taxes which are directly attributable to and vary with the production of business. These costs are deferred and amortized to the extent they related to successful contract acquisitions over the applicable premium recognition period. Losses and loss adjustment expenses (“LAE”) are charged against income as incurred. Unpaid losses and LAE, including estimates for amounts incurred but not reported (“IBNR”) are based on estimates of the ultimate costs of settling claims, including the effects of inflation and other societal and economic factors. Unpaid loss and LAE reserves represent management’s best estimate of ultimate losses and LAE, net of estimated salvage and subrogation recoveries, if applicable. Such estimates are regularly reviewed and updated and any resulting adjustments are reflected in current results of operations. The process of estimating loss and LAE involves a considerable degree of judgment by management and the ultimate amount of expense to be incurred could be considerably greater than or less than the amounts currently reflected in the financial statements. Reinsurance recoverables represent amounts of paid losses and loss adjustment expenses, case reserves and IBNR amounts ceded to reinsurers under reinsurance treaties. Amounts recoverable from reinsurers are estimated in a manner consistent with the associated claim liability. Ark reports its reinsurance recoverables net of an allowance for estimated uncollectible reinsurance, including expected credit losses. The allowance is based upon its ongoing review of amounts outstanding, length of collection periods, changes in reinsurer credit standing, disputes, applicable coverage defenses and other relevant factors.
Goodwill and Other Intangible Assets	Goodwill and Other Intangible Assets Goodwill represents the excess of the amount paid to acquire subsidiaries over the fair value of identifiable net assets at the date of acquisition. Other intangible assets consist primarily of underwriting capacity, customer relationships, renewal rights and trade names.
Derivatives	Derivatives From time to time, White Mountains holds derivative financial instruments for risk management purposes. White Mountains recognizes all derivatives as either assets or liabilities, measured at fair value, on the consolidated balance sheet. Changes in the fair value of derivative instruments that meet the criteria for hedge accounting are recognized in other comprehensive income and reclassified into current period pre-tax income when the hedged items are recognized therein. Changes in the fair value of derivative instruments that do not meet the criteria for hedge accounting are recognized in current period pre-tax income. As of September 30, 2021 and December 31, 2020, NSM holds an interest rate swap derivative instrument that meets the criteria for hedge accounting. See Note 9 — “Derivatives”
Reinsurance Contracts Accounted For As Deposits	Reinsurance Contracts Accounted for as Deposits Reinsurance contracts that do not meet the risk transfer requirements necessary to be accounted for as reinsurance are accounted for using the deposit method. Under the deposit method, ceded premiums paid are not recognized through income but rather treated as a deposit. BAM entered into ceded reinsurance agreements with Fidus Re Ltd. (“Fidus Re”) during the second quarter of 2018 and the first quarter of 2021, which are both accounted for using the deposit method. See Note 10 — “Municipal Bond Guarantee Insurance” . The nonrefundable consideration paid by BAM to Fidus Re is charged to financing expense within general and administrative expenses. Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), formerly Third Point Reinsurance Ltd., 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 three months ended June 30, 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, 2021, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.3 million.
Cash and Restricted Cash	Cash and Restricted Cash Cash includes amounts on hand and demand deposits with banks and other financial institutions. Amounts presented in the statement of cash flows are shown net of balances acquired and sold in the purchase or sale of the Company’s consolidated subsidiaries.

Significant Transactions (Table

Significant Transactions (Tables)	9 Months Ended
	Sep. 30, 2021
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, 2020 through September 30, 2021: $ in Millions Acquisition of subsidiary/ asset Goodwill and Other intangible asset (1) Acquisition Date Kingsbridge $ 131.7 April 7, 2020 J.C. Taylor 55.7 August 6, 2021 Total NSM segment $ 187.4 Ark $ 292.5 January 1, 2021 Other Operations $ 30.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and excludes the effect of foreign currency translation subsequent to the acquisition date.

Investment Securities (Tables)

Investment Securities (Tables)	9 Months Ended
	Sep. 30, 2021
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, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Fixed maturity investments $ 8.2 $ 7.0 $ 21.9 $ 22.4 Short-term investments — .1 .5 1.0 Common equity securities .1 .5 .1 6.5 Investment in MediaAlpha — 55.0 — 60.0 Other long-term investments 12.0 8.9 37.1 24.7 Amount attributable to TPC Providers (.2) — (.8) — Total investment income 20.1 71.5 58.8 114.6 Third-party investment expenses (.6) (.3) (1.6) (.9) Net investment income, pre-tax $ 19.5 $ 71.2 $ 57.2 $ 113.7
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, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Fixed maturity investments $ (6.8) $ 3.6 $ (23.2) $ 35.8 Short-term investments (.3) — — .4 Common equity securities 1.6 48.4 7.7 5.9 Investment in MediaAlpha (396.8) 250.0 (325.5) 295.0 Other long-term investments 37.7 4.6 113.2 (34.3) Amount attributable to TPC Providers (1.7) — (6.5) — Net realized and unrealized investment (losses) gains (1) (366.3) 306.6 (234.3) 302.8 Less: net (losses) gains on investment securities sold during the period (4.8) 36.1 (5.1) 29.6 Net realized and unrealized investment (losses) gains on investment securities held at the end of the period $ (361.5) $ 270.5 $ (229.2) $ 273.2
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, 2021 and 2020 for investments still held at the end of the period: Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Other long-term investments $ 26.5 $ 260.1 $ 75.5 $ 276.0 Total net unrealized investment gains, pre-tax - Level 3 investments $ 26.5 $ 260.1 $ 75.5 $ 276.0
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) and carrying values of White Mountains’s fixed maturity investments as of September 30, 2021 and December 31, 2020: September 30, 2021 Millions Cost or Gross Gross Net Foreign Carrying U.S. Government and agency obligations $ 207.4 $ .8 $ (.6) $ — $ 207.6 Debt securities issued by corporations 945.2 13.1 (3.4) (.7) 954.2 Municipal obligations 276.1 18.0 (.7) — 293.4 Mortgage and asset-backed securities 247.3 4.2 (1.4) — 250.1 Collateralized loan obligations 128.5 — (.4) (.5) 127.6 Total fixed maturity investments $ 1,804.5 $ 36.1 $ (6.5) $ (1.2) $ 1,832.9 December 31, 2020 Millions Cost or Gross Gross Carrying U.S. Government and agency obligations $ 173.2 $ 3.1 $ — $ 176.3 Debt securities issued by corporations 522.8 24.7 (.1) 547.4 Municipal obligations 244.0 21.0 — 265.0 Mortgage and asset-backed securities 211.7 6.8 — 218.5 Total fixed maturity investments $ 1,151.7 $ 55.6 $ (.1) $ 1,207.2 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, 2021 and December 31, 2020: September 30, 2021 Millions Cost or Gross Gross Net Foreign Carrying Common equity securities $ 152.5 $ 8.8 $ (.5) $ (1.2) $ 159.6 Investment in MediaAlpha $ — $ 316.4 $ — $ — $ 316.4 Other long-term investments $ 1,154.7 $ 197.6 $ (62.9) $ (3.9) $ 1,285.5 December 31, 2020 Millions Cost or Gross Gross Net Foreign Carrying Investment in MediaAlpha $ — $ 802.2 $ — $ — $ 802.2 Other long-term investments $ 767.4 $ 95.8 $ (78.1) $ 1.7 $ 786.8
Schedule of fixed maturity investment holdings	The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of September 30, 2021. 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, 2021 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 111.9 $ 112.7 Due after one year through five years 836.1 843.4 Due after five years through ten years 368.5 377.3 Due after ten years 112.2 121.8 Mortgage and asset-backed securities and collateralized loan obligations 375.8 377.7 Total fixed maturity investments $ 1,804.5 $ 1,832.9
Fair value measurements by level, investment securities	The following tables present White Mountains’s fair value measurements for investments as of September 30, 2021 and December 31, 2020 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, 2021 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 207.6 $ 207.6 $ — $ — Debt securities issued by corporations: Financials 246.5 — 246.5 — Consumer 180.5 — 180.5 — Industrial 114.8 — 114.8 — Technology 110.8 — 110.8 — Healthcare 98.2 — 98.2 — Utilities 69.9 — 69.9 — Communications 53.2 — 53.2 — Energy 47.0 — 47.0 — Materials 33.3 — 33.3 — Total debt securities issued by corporations 954.2 — 954.2 — Municipal obligations 293.4 — 293.4 — Mortgage and asset-backed securities 250.1 — 250.1 — Collateralized loan obligations 127.6 — 127.6 — Total fixed maturity investments 1,832.9 207.6 1,625.3 — Short-term investments 609.5 601.6 7.9 — Common equity securities (1) 159.6 — 159.6 — Investment in MediaAlpha 316.4 316.4 — — Other long-term investments 814.5 — — 814.5 Other long-term investments — NAV (2) 471.0 — — — Total other long-term investments 1,285.5 — — 814.5 Total investments $ 4,203.9 $ 1,125.6 $ 1,792.8 $ 814.5 (1) Consist of investments in listed funds that predominantly invest in international equities. (2) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2020 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 176.3 $ 176.3 $ — $ — Debt securities issued by corporations: Financials 133.9 — 133.9 — Consumer 81.9 — 81.9 — Industrial 66.9 — 66.9 — Technology 66.7 — 66.7 — Healthcare 51.5 — 51.5 — Communications 44.5 — 44.5 — Energy 35.8 — 35.8 — Materials 33.9 — 33.9 — Utilities 32.3 — 32.3 — Total debt securities issued by corporations 547.4 — 547.4 — Municipal obligations 265.0 — 265.0 — Mortgage and asset-backed securities 218.5 — 218.5 — Total fixed maturity investments 1,207.2 176.3 1,030.9 — Short-term investments 142.9 142.9 — — Investment in MediaAlpha 802.2 802.2 — — Other long-term investments 614.2 — — 614.2 Other long-term investments — NAV (1) 172.6 — — — Total other long-term investments 786.8 — — 614.2 Total investments $ 2,939.1 $ 1,121.4 $ 1,030.9 $ 614.2 (1) Consists of private equity funds and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
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, 2021 and December 31, 2020: Fair Value at Millions September 30, 2021 December 31, 2020 AAA $ 12.7 $ 10.6 AA 85.7 57.9 A 473.3 318.3 BBB 373.7 159.6 BB — 1.0 Other 8.8 — Debt securities issued by corporations (1) $ 954.2 $ 547.4 (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, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 125.3 $ 125.3 $ — $ 88.7 $ 88.7 $ — FHLMC 76.5 76.5 — 70.1 70.1 — GNMA 29.4 29.4 — 40.6 40.6 — Total agency (1) 231.2 231.2 — 199.4 199.4 — Non-agency: Residential .6 .6 — — — — Total non-agency .6 .6 — — — — Total mortgage-backed securities 231.8 231.8 — 199.4 199.4 — Other asset-backed securities: Credit card receivables 11.2 11.2 — 11.3 11.3 — Vehicle receivables 7.1 7.1 — 7.8 7.8 — Total other asset-backed securities 18.3 18.3 — 19.1 19.1 — Total mortgage and asset-backed securities 250.1 250.1 — 218.5 218.5 — Collateralized loan obligations 127.6 127.6 — — — — Total mortgage and asset-backed securities and collateralized loan obligations $ 377.7 $ 377.7 $ — $ 218.5 $ 218.5 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).
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, 2021 and December 31, 2020: Fair Value at Millions September 30, 2021 December 31, 2020 Kudu’s Participation Contracts $ 604.7 $ 400.6 PassportCard/DavidShield 105.0 95.0 Elementum Holdings L.P. 56.7 55.1 Other unconsolidated entities (1) 27.0 42.4 Total unconsolidated entities 793.4 593.1 Private equity funds and hedge funds 144.2 121.2 Bank loan fund 161.7 — Lloyd’s trust deposits 111.2 — ILS funds 53.9 51.4 Private debt investments 13.3 21.1 Other 7.8 — Total other long-term investments $ 1,285.5 $ 786.8 (1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities and Simple Agreement for Future Equity (“SAFE”) investments.
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, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 63.9 $ 14.0 $ 69.1 $ 15.3 Financial services 63.2 29.6 23.5 30.4 Real estate 4.8 2.9 — — Manufacturing/Industrial .1 — 28.6 — Total private equity funds 132.0 46.5 121.2 45.7 Hedge funds European small/mid cap 12.2 — — — Total hedge funds 12.2 — — — Total private equity funds and hedge funds included in other long-term investments $ 144.2 $ 46.5 $ 121.2 $ 45.7
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, 2021: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $.3 $14.0 $109.0 $8.7 $132.0
Rollforward of fair value investments by level	The following tables present the changes in White Mountains’s fair value measurements by level for the nine months ended September 30, 2021 and 2020: Level 3 Other Long-term Investments Measured at NAV (1) Millions Level 1 Investments Level 2 Other Long-term Total Balance at December 31, 2020 $ 978.5 $ 1,030.9 $ 614.2 $ 172.6 $ 2,796.2 (2) Net realized and unrealized gains (losses) (327.6) (13.1) 79.0 33.9 (227.8) (3) Amortization/Accretion (.1) (5.9) — — (6.0) Purchases 130.9 989.7 143.6 199.6 1,463.8 Sales (257.7) (284.9) (31.9) (70.9) (645.4) Effect of Ark Transaction — 68.2 9.6 135.8 213.6 Transfers in — — — — — Transfers out — — — — — Balance at September 30, 2021 $ 524.0 $ 1,784.9 $ 814.5 $ 471.0 $ 3,594.4 (2) (1) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies” . (2) Excludes carrying value of $609.5 and $142.9 as of September 30, 2021 and December 31, 2020 classified as short-term investments. (3) Includes amounts attributable to TPC Providers of $6.5 for the nine months ended September 30, 2021. Level 3 Other Long-term Investments Measured at NAV (1) Millions Level 1 Investments Level 2 Common Other Long-term Total Balance at December 31, 2019 $ 780.0 $ 1,109.6 $ .1 $ 654.0 $ 202.3 $ 2,746.0 (2) Net realized and unrealized gains (losses) 29.2 12.5 — 275.6 (14.9) 302.4 (3) Amortization/Accretion — (3.0) — — — (3.0) Purchases 128.8 316.2 — 78.8 39.8 563.6 Sales (642.7) (368.5) — (8.1) (56.3) (1,075.6) Transfers in — — — — — — Transfers out — — — — — — Balance at September 30, 2020 $ 295.3 $ 1,066.8 $ .1 $ 1,000.3 $ 170.9 $ 2,533.4 (2) (1) Includes private equity funds, a hedge fund and ILS funds for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies ”. (2) Excludes carrying value of $571.8 and $201.2 as of September 30, 2020 and December 31, 2019 classified as short-term investments. (3) Excludes realized and unrealized gains associated with short-term investments of $0.4 for the nine months ended September 30, 2020.
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, 2021 and December 31, 2020. The tables below exclude $14.9 million and $27.6 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, hedge funds, Lloyd’s trust deposits, bank loans funds and ILS funds are generally estimated using the NAV of the funds. $ in Millions September 30, 2021 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3)(4) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4) Kudu’s Participation Contracts (5)(6) Discounted cash flow $604.7 18% - 23% 7x - 13x PassportCard/DavidShield Discounted cash flow $105.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $56.7 17% 4% Private debt investments Discounted cash flow $11.2 4% - 8% N/A Other Discounted cash flow $22.0 20% - 24% 4% (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. (4) 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. (5) For the nine months ended September 30, 2021, Kudu deployed a total of $141.6 in new and existing Kudu Participation Contracts, including TIG Advisors, TK Partners, Third Eye Capital Management and Douglass Winthrop Advisors. (6) As of September 30, 2021, certain Kudu Participation Contracts with a total fair value of $121.0 were valued using a probability weighted expected return method, which was based on a discounted cash flow analysis and an expected sale transaction. $ in Millions December 31, 2020 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3)(4) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4) Kudu’s Participation Contracts (5) Discounted cash flow $400.6 18% - 23% 7x - 12x PassportCard/DavidShield (6) Discounted cash flow $95.0 23% 4% Elementum Holdings, L.P. Discounted cash flow $55.1 17% 4% Private debt investments Discounted cash flow $17.1 4% - 8% N/A Other Discounted cash flow $18.8 20% - 24% 4% (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. (4) 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. (5) In 2020, Kudu deployed a total of $118.2 in new Kudu Participation Contracts, including Creation Investments Capital, Sequoia Financial Group, Channel Capital and Ranger Investment Management. (6) In 2020, White Mountains made an additional $15.0 investment in PassportCard/DavidShield. See Note 2 — “Significant Transactions” .

Goodwill and Other Intangible_2

Goodwill and Other Intangible Assets (Tables)	9 Months Ended
	Sep. 30, 2021
Goodwill and Intangible Assets Disclosure [Abstract]
Schedule of Intangible Assets and Goodwill	The following table presents the acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by segment as of September 30, 2021 and December 31, 2020: $ in Millions Weighted Average Economic September 30, 2021 December 31, 2020 Acquisition Date Fair Value Accumulated Amortization Impairments and Amounts Allocated to Held for Sale Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Goodwill: Ark N/A $ 116.8 $ — $ — $ 116.8 $ — $ — $ — $ — NSM (1) N/A 559.8 — 30.2 529.6 506.4 — — 506.4 Kudu N/A 7.6 — — 7.6 7.6 — — 7.6 Other Operations N/A 17.4 — — 17.4 11.5 — — 11.5 Total goodwill 701.6 — 30.2 671.4 525.5 — — 525.5 Other intangible assets: Ark Underwriting Capacity N/A 175.7 — — 175.7 — — — — NSM (1) Customer 8.9 136.0 50.6 3.5 81.9 136.2 36.7 3.5 96.0 Trade names 16 65.3 10.9 1.0 53.4 65.4 8.3 1.0 56.1 Information 0 3.1 1.4 1.7 — 3.1 1.4 1.7 — Renewal rights 12 82.5 13.1 — 69.4 82.5 4.9 — 77.6 Other 3.4 1.1 .6 — .5 1.7 1.0 — .7 Subtotal 288.0 76.6 6.2 205.2 288.9 52.3 6.2 230.4 Kudu Trade names 7 2.2 .8 — 1.4 2.2 .6 — 1.6 Other Operations Trade names 18.1 8.2 1.0 — 7.2 3.6 .3 — 3.3 Customer 13.3 18.9 3.5 — 15.4 14.2 1.4 — 12.8 Insurance N/A 8.6 — — 8.6 8.6 — — 8.6 Other 5.4 .3 .2 — .1 .3 .1 — .2 Subtotal 36.0 4.7 — 31.3 26.7 1.8 — 24.9 Total other intangible assets 501.9 82.1 6.2 413.6 317.8 54.7 6.2 256.9 Total goodwill and other intangible assets $ 1,203.5 $ 82.1 $ 36.4 1,085.0 $ 843.3 $ 54.7 6.2 782.4 Goodwill and other intangible assets attributed to non-controlling interests (118.0) (28.1) Goodwill and other intangible assets included in White Mountains’s $ 967.0 $ 754.3 (1) As of September 30, 2021, NSM’s goodwill and intangible assets included $(2.3) and $(0.2) of the effect of foreign currency translation. As of December 31, 2020, NSM’s goodwill and intangible assets included $13.4 and $1.6 of the effect of foreign currency translation. The following tables present the change in goodwill and other intangible assets for the three and nine months ended September 30, 2021 and 2020: Three Months Ended September 30, 2021 2020 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 629.4 $ 414.8 $ 1,044.2 $ 518.2 $ 241.7 $ 759.9 Acquisition of businesses 55.7 (1) — 55.7 14.9 (2) — 14.9 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3) (9.3) 9.3 — — — — Foreign currency translation (4.0) (.3) (4.3) 7.0 (.1) 6.9 Measurement period adjustments (4) (.4) — (.4) — — — Amortization — (10.2) (10.2) — (5.4) (5.4) Ending balance $ 671.4 $ 413.6 $ 1,085.0 $ 540.1 $ 236.2 $ 776.3 (1) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of J.C. Taylor had not yet been finalized at September 30, 2021. (2) The relative fair values of goodwill and other intangible assets recognized in connection with an acquisition within Other Operations had not yet been finalized at September 30, 2020. (3) Relates to an acquisition within the Other Operations segment. (4) 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, 2021, adjustments relate to an acquisition within the Other Operations segment. Nine Months Ended September 30, 2021 2020 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 525.5 $ 256.9 $ 782.4 $ 394.7 $ 260.0 $ 654.7 Attribution of acquisition date fair value estimates between goodwill and other intangible assets (1) (9.3) 9.3 — — — — Ark Transaction 116.8 175.7 292.5 — — — Acquisition of businesses 71.5 (2) — 71.5 140.0 (3) — 140.0 Foreign currency translation (2.3) (.2) (2.5) 5.2 (.5) 4.7 Impairments — — — — (6.2) (6.2) Loss on assets held for sale (4) (30.2) — (30.2) — — — Measurement period adjustments (5) (.6) — (.6) .2 — .2 Amortization — (28.1) (28.1) — (17.1) (17.1) Ending balance $ 671.4 $ 413.6 $ 1,085.0 $ 540.1 $ 236.2 $ 776.3 (1) Relates to an acquisition within the Other Operations segment. (2) The relative fair values of goodwill and other intangible assets of $55.7 recognized in connection with the acquisition of J.C. Taylor had not yet been finalized at September 30, 2021. The remaining $15.8 relates to the relative fair values of goodwill and other intangible assets recognized in connection with an acquisition within the Other Operations segment. (3) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge and an acquisition within Other Operations had not yet been finalized at September 30, 2020. (4) Relates to the sale of NSM’s Fresh Insurance’s motor business recorded in the first quarter of 2021. This amount excludes $1.5 of net proceeds related to the sale. (5) 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, 2021, adjustments relate to acquisitions within the Other Operations segment.
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, 2020 through September 30, 2021: $ in Millions Acquisition of subsidiary/ asset Goodwill and Other intangible asset (1) Acquisition Date Kingsbridge $ 131.7 April 7, 2020 J.C. Taylor 55.7 August 6, 2021 Total NSM segment $ 187.4 Ark $ 292.5 January 1, 2021 Other Operations $ 30.6 Various (1) Acquisition date fair values include the effect of adjustments during the measurement period and excludes 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, 2021
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, 2021: Millions Three Months Ended September 30, 2021 Nine Months Ended September 30, 2021 Gross beginning balance $ 760.0 $ 696.0 Less: beginning reinsurance recoverable on unpaid losses (425.3) (433.4) Net loss and LAE reserves 334.7 262.6 Loss and LAE incurred relating to: Current year losses 141.9 269.0 Prior year losses (12.7) (21.2) Total incurred losses and LAE 129.2 247.8 Foreign currency translation adjustment to loss and LAE reserves (1.2) (3.4) Loss and LAE paid relating to: Current year losses (9.0) (11.5) Prior year losses (20.3) (62.1) Total loss and LAE payments (29.3) (73.6) Net ending balance 433.4 433.4 Plus: ending reinsurance recoverable on unpaid losses 457.5 457.5 Gross ending balance $ 890.9 $ 890.9

Related Party Disclosures (Tabl

Related Party Disclosures (Tables)	9 Months Ended
	Sep. 30, 2021
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. Three Months Ended September 30, 2021 Nine Months Ended September 30, 2021 Millions Written premiums: Gross $ 162.4 $ 895.0 Ceded (41.5) (169.5) Net written premiums $ 120.9 $ 725.5 Earned premiums: Gross $ 284.5 $ 622.0 Ceded (71.1) (186.2) Net earned premiums $ 213.4 $ 435.8 Losses and LAE: Gross $ 193.5 $ 372.7 Ceded (64.3) (124.9) Net Losses and LAE $ 129.2 $ 247.8 As of September 30, 2021 A.M. Best Rating (1) Gross Collateral Net % of Total A+ or better $ 122.8 $ 23.9 $ 98.9 84.2 % A- to A 32.7 15.6 17.1 14.6 B++ or lower and not rated 10.2 8.8 1.4 1.2 Total $ 165.7 $ 48.3 $ 117.4 100.0 % (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, 2021
Debt Disclosure [Abstract]
Schedule of debt outstanding	The following table presents White Mountains’s debt outstanding as of September 30, 2021 and December 31, 2020: Millions September 30, Effective (1) December 31, Effective (1) Ark 2007 Notes Tranche 1 $ 30.0 $ — Ark 2007 Notes Tranche 2 13.9 — Ark 2007 Subordinated Notes, carrying value 43.9 — Ark 2021 Notes Tranche 1 45.3 — Ark 2021 Notes Tranche 2 47.0 — Ark 2021 Notes Tranche 3 70.0 — Unamortized issuance cost (5.5) Ark 2021 Subordinated Notes, carrying value 156.8 Total Ark Subordinated Notes, carrying value 200.7 5.1% — NSM Bank Facility 300.4 7.4% (2) 277.4 7.5% (2) Unamortized issuance cost (6.7) (6.1) NSM Bank Facility, carrying value 293.7 271.3 Other NSM debt, carrying value 1.3 3.3% 1.3 2.5% Kudu Credit Facility 203.0 4.1% — Unamortized issuance cost (7.4) — Kudu Credit Facility, carrying value 195.6 — Kudu Bank Facility — 89.2 8.3% Unamortized issuance cost — (2.9) Kudu Bank Facility, carrying value — 86.3 Other Operations debt 19.5 7.4% 18.0 7.4% Unamortized issuance cost (.4) (.5) Other Operations, carrying value 19.1 17.5 Total debt $ 710.4 $ 376.4 (1) Effective rate includes the effect of the amortization of debt issuance costs. (2) NSM’s effective rate excludes the effect of the interest rate swap on the hedged portion of the debt. The weighted average interest rate for the quarter ended September 30, 2021 and December 31, 2020, excluding the effect of amortization of debt issuance costs, was 6.7% and 7.0%. The weighted average interest rate for the quarter ended September 30, 2021 and December 31, 2020 on the total NSM Bank Facility including both the effect of the amortization of debt issuance costs and the effect of the interest rate swap was 8.3% and 8.4%. The following table presents the change in debt under the NSM Bank Facility for the three and nine months ended September 30, 2021 and 2020: NSM Bank Facility Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Beginning balance $ 276.6 $ 273.4 $ 277.4 $ 221.3 Term loans Borrowings (1) — — — 52.4 Repayments (.7) (.7) (2.1) (1.3) Foreign currency translation (1.5) 2.3 (.9) 2.6 Revolving credit loan Borrowings (2) 35.0 — 35.0 — Repayments (9.0) — (9.0) — Ending balance 300.4 275.0 $ 300.4 $ 275.0 (1) Borrowings for the nine months ended September 30, 2020 included $52.4 for the funding of the acquisition of Kingsbridge.
Schedule of Debt	The following table presents the NSM weighted average interest rate for the nine months ended September 30, 2021 and 2020: NSM Weighted Average Interest Rate Nine Months Ended September 30, 2021 2020 Millions Weighted Average Interest Expense (1) Weighted Average Interest rate Weighted Average Interest Expense (1) Weighted Average Interest rate Term loan - hedged $ 147.1 $ 10.0 9.1 % $ 148.5 $ 10.0 9.0 % Term loan - unhedged 129.5 7.3 7.5 % 125.1 6.1 6.5 % Total NSM Facility $ 276.6 $ 17.3 8.3 % $ 273.6 $ 16.1 7.8 % ( 1) Interest expense includes the amortization of debt issuance costs and the effect of the interest rate swap and excludes interest expense related to the Other NSM Debt.

Municipal Bond Guarantee Insu_2

Municipal Bond Guarantee Insurance (Tables)	9 Months Ended
	Sep. 30, 2021
Guarantees [Abstract]
Schedule of Municipal Bond Guarantee Insured Obligations	The following table presents a schedule of BAM’s insured obligations as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Contracts outstanding 11,877 10,997 Remaining weighted average contract period outstanding (in years) 10.7 10.7 Contractual debt service outstanding (in millions): Principal $ 83,829.0 $ 75,287.7 Interest 39,528.4 36,448.8 Total debt service outstanding $ 123,357.4 $ 111,736.5 Gross unearned insurance premiums (in millions) $ 257.0 $ 237.5
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, 2021: Millions September 30, 2021 October 1, 2021 - December 31, 2021 $ 6.2 January 1, 2022 - March 31, 2022 6.1 April 1, 2022 - June 30, 2022 6.1 July 1, 2022 - September 30, 2022 6.0 October 1, 2022 - December 31, 2022 5.9 Total 2022 24.1 2023 22.8 2024 21.1 2025 19.6 2026 18.1 2027 and thereafter 145.1 Total gross unearned insurance premiums $ 257.0
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, 2021 and 2020: Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Written premiums: Direct $ 12.8 $ 14.4 $ 34.5 $ 45.5 Assumed — — 4.5 .1 Gross written premiums (1) $ 12.8 $ 14.4 $ 39.0 $ 45.6 Earned premiums: Direct $ 5.9 $ 5.3 $ 16.8 $ 14.5 Assumed .8 .9 2.8 2.7 Gross earned premiums (1) $ 6.7 $ 6.2 $ 19.6 $ 17.2 (1) There are no ceded premium amounts in the periods presented. Gross written premiums and Gross earned premium are equivalent to net written premiums and net earned premiums.

Earnings Per Share (Tables)

Earnings Per Share (Tables)	9 Months Ended
	Sep. 30, 2021
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, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations” . Three Months Ended Nine Months Ended September 30, September 30, 2021 2020 2021 2020 Basic and diluted earnings per share numerators (in millions): Net (loss) income attributable to White Mountains’s $ (371.4) $ 232.9 $ (308.2) $ 219.5 Less: total income (loss) from discontinued operations, net of tax — (.7) 18.7 (.8) Net (loss) income from continuing operations attributable to $ (371.4) $ 233.6 $ (326.9) $ 220.3 Allocation of losses (earnings) to participating restricted common shares (1) 4.5 (3.2) 3.8 (2.9) Basic and diluted (losses) earnings per share numerators $ (366.9) $ 230.4 $ (323.1) $ 217.4 Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (2) (37.8) (43.1) (36.0) (40.0) Basic earnings (losses) per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (2) (37.8) (43.1) (36.0) (40.0) Diluted earnings (losses) per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ — $ — $ 1.00 $ 1.00 Undistributed (losses) earnings (120.18) 75.32 (106.48) 69.40 Basic and diluted (losses) earnings per share $ (120.18) $ 75.32 $ (105.48) $ 70.40 (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (2) 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, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations” . Three Months Ended Nine Months Ended September 30, September 30, Millions 2021 2020 2021 2020 Undistributed net earnings (losses) - continuing operations: Net (losses) earnings attributable to White Mountains’s common shareholders, net of restricted common share amounts $ (366.9) $ 230.4 $ (323.1) $ 217.4 Dividends declared, net of restricted common share amounts (1) — — (3.1) (3.1) Total undistributed net (losses) earnings, net of restricted common share amounts $ (366.9) $ 230.4 $ (326.2) $ 214.3 (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, 2021
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, 2021 and 2020 for performance shares granted under the WTM Incentive Plan: Three Months Ended September 30, Nine Months Ended September 30, 2021 2020 2021 2020 Millions, except share amounts Target Performance Accrued Target Performance Accrued Target Performance Accrued Target Performance Accrued Beginning of period 41,252 $ 45.7 42,458 $ 15.8 42,458 $ 56.3 42,473 $ 43.7 Shares paid (1) (219) (.6) — — (14,336) (35.2) (14,070) (27.7) New grants — — — — 13,475 — 14,055 — Forfeitures and cancellations (2) (205) .2 — (.3) (769) .4 — .1 Expense recognized — (6.5) — 13.6 — 17.3 — 13.0 End of period 40,828 $ 38.8 42,458 $ 29.1 40,828 $ 38.8 42,458 $ 29.1 (1) WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in cash in March 2021 at 200% of target. WTM performance share payments in 2020 for the 2017-2019 performance cycle, which were paid in cash in March 2020, ranged from 174% to 180% 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, 2021 for each performance cycle: Nine Months Ended September 30, 2021 Millions, except share amounts Target Performance Accrued Performance cycle: 2019 – 2021 14,625 $ 24.4 2020 – 2022 13,350 13.4 2021 – 2023 13,475 1.6 Sub-total 41,450 39.4 Assumed forfeitures (622) (.6) September 30, 2021 40,828 $ 38.8
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, 2021 and 2020: Three Months Ended September 30, Nine Months Ended September 30, 2021 2020 2021 2020 Millions, except share amounts Restricted Unamortized Restricted Unamortized Restricted Unamortized Issue Date Restricted Unamortized Issue Date Non-vested, Beginning of period 38,280 $ 23.2 43,105 $ 23.0 43,105 $ 15.2 43,395 $ 16.7 Issued — — — — 13,475 16.1 14,055 15.1 Vested (219) — — — (17,936) — (14,345) — Forfeited (211) (.2) — — (794) (.8) — — Expense recognized — (3.6) — (3.6) — (11.1) — (12.4) End of period 37,850 $ 19.4 43,105 $ 19.4 37,850 $ 19.4 43,105 $ 19.4

Leases (Tables)

Leases (Tables)	9 Months Ended
	Sep. 30, 2021
Leases [Abstract]
Summary of Lease Expense	The following table summarizes net lease expense recognized in White Mountains’s consolidated statement of operations for the three and nine months ended September 30, 2021 and 2020: Millions Three Months Ended September 30, Nine Months Ended September 30, Lease Cost 2021 2020 2021 2020 Lease cost $ 2.7 $ 1.6 $ 7.2 $ 5.7 Less: sublease income .1 .1 .3 .3 Net lease cost $ 2.6 $ 1.5 $ 6.9 $ 5.4
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, 2021: Millions As of September 30, 2021 Remainder of 2021 $ 2.0 2022 10.8 2023 9.8 2024 8.5 2025 6.7 Thereafter 16.4 Total undiscounted lease payments 54.2 Less: present value adjustment 8.3 Operating lease liability $ 45.9
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, 2021 and December 31, 2020: As of September 30, 2021 Millions HG/BAM Ark NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 8.0 $ 7.0 $ 13.8 $ 6.7 $ 7.4 $ 42.9 5.0% Lease liability $ 8.6 $ 7.0 $ 15.0 $ 7.1 $ 8.2 $ 45.9 (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, 2020 Millions HG/BAM NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 10.1 $ 17.1 $ 2.0 $ 8.4 $ 37.6 4.6% Lease liability $ 10.1 $ 17.1 $ 2.0 $ 9.1 $ 38.3 (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, 2021
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 related percentage of each consolidated entity’s total equity owned by non-controlling shareholders as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 $ in Millions Non-controlling Percentage Non-controlling Equity Non-controlling Percentage Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ 10.1 3.1 % $ 13.5 Ark 28.0 % 216.1 — % — NSM 3.5 % 16.5 3.4 % 17.0 Kudu .7 % 3.1 .7 % 2.3 Other various 12.1 various 2.4 Total, excluding BAM 257.9 35.2 BAM 100.0 % (125.3) 100.0 % (123.3) Total non-controlling interests $ 132.6 $ (88.1)

Segment Information (Tables)

Segment Information (Tables)	9 Months Ended
	Sep. 30, 2021
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 NSM 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 (4.0) .3 — 18.9 15.3 30.5 Net realized and unrealized investment — — — — (396.8) (396.8) Commission revenues — — 67.0 — 2.4 69.4 Other revenue .3 3.4 15.3 .1 28.1 47.2 Total revenues 7.4 217.7 82.3 28.5 (346.0) (10.1) Loss and loss adjustment expenses — 129.2 — — — 129.2 Insurance acquisition expenses 3.0 53.7 — — — 56.7 Cost of sales — — — — 24.0 24.0 General and administrative expenses 12.4 21.8 48.8 3.3 14.5 100.8 Broker commission expense — — 20.4 — — 20.4 Change in fair value of contingent — — .6 — — .6 Amortization of other intangible assets — — 8.2 — 2.0 10.2 Interest expense — 2.1 5.9 1.9 .4 10.3 Total expenses 15.4 206.8 83.9 5.2 40.9 352.2 Pre-tax (loss) income $ (8.0) $ 10.9 $ (1.6) $ 23.3 $ (386.9) $ (362.3) Millions HG Global/ BAM NSM Kudu Other Operations Total Three Months Ended September 30, 2020 Earned insurance premiums $ 6.2 $ — $ — $ — $ 6.2 Net investment income 4.7 — 6.4 60.1 71.2 Net realized and unrealized investment gains 3.2 — 9.8 43.6 56.6 Net unrealized investment gains from investment in MediaAlpha — — — 250.0 250.0 Commission revenues — 58.2 — 2.1 60.3 Other revenue .4 12.5 .1 2.2 15.2 Total revenues 14.5 70.7 16.3 358.0 459.5 Insurance acquisition expenses 1.6 — — — 1.6 Cost of sales — — — 2.3 2.3 General and administrative expenses 14.0 42.9 2.2 44.3 103.4 Broker commission expense — 17.1 — — 17.1 Change in fair value of contingent — .7 — — .7 Amortization of other intangible assets — 5.1 .1 .2 5.4 Interest expense — 6.1 1.4 .3 7.8 Total expenses 15.6 71.9 3.7 47.1 138.3 Pre-tax (loss) income $ (1.1) $ (1.2) $ 12.6 $ 310.9 $ 321.2 Millions HG Global/ BAM Ark NSM 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 — — — — (325.5) (325.5) Commission revenues — — 194.6 — 7.0 201.6 Other revenue .9 9.4 46.8 .2 57.6 114.9 Total revenues 18.1 457.3 241.4 88.8 (210.8) 594.8 Loss and loss adjustment expenses — 247.8 — — — 247.8 Insurance acquisition expenses 6.5 124.4 — — — 130.9 Cost of sales — — — — 45.9 45.9 General and administrative expenses 42.7 84.4 142.1 9.0 79.7 357.9 Broker commission expense — — 60.9 — — 60.9 Change in fair value of contingent — — .8 — — .8 Amortization of other intangible assets — — 25.0 .2 2.9 28.1 Loss on assets held for sale — — 28.7 — — 28.7 Interest expense — 4.5 17.7 9.2 1.1 32.5 Total expenses 49.2 461.1 275.2 18.4 129.6 933.5 Pre-tax (loss) income $ (31.1) $ (3.8) $ (33.8) $ 70.4 $ (340.4) $ (338.7) Millions HG Global/ BAM NSM Kudu Other Operations Total Nine Months Ended September 30, 2020 Earned insurance premiums $ 17.2 $ — $ — $ — $ 17.2 Net investment income 15.1 — 19.3 79.3 113.7 Net realized and unrealized investment gains 23.7 — 1.5 (17.4) 7.8 Net unrealized investment gains from investment in MediaAlpha — — — 295.0 295.0 Commission revenues — 174.2 — 6.1 180.3 Other revenue 2.1 37.6 .2 6.0 45.9 Total revenues 58.1 211.8 21.0 369.0 659.9 Insurance acquisition expenses 5.4 — — — 5.4 Cost of sales — — — 6.5 6.5 General and administrative expenses 41.4 131.0 7.5 87.1 267.0 Broker commission expense — 56.4 — — 56.4 Change in fair value of contingent — (1.6) — — (1.6) Amortization of other intangible assets — 16.2 .3 .6 17.1 Interest expense — 16.1 4.3 .8 21.2 Total expenses 46.8 218.1 12.1 95.0 372.0 Pre-tax income (loss) $ 11.3 $ (6.3) $ 8.9 $ 274.0 $ 287.9
Schedule of Reconciliation of Revenue from Segments to Consolidated	In compliance with ASC 606, Revenues from Contracts with Customers, the following tables present White Mountains’s total revenues by revenue source for the three and nine months ended September 30, 2021 and 2020: Millions HG Global/BAM Ark NSM Kudu Other Total Three Months Ended September 30, 2021 Commission and other revenue Specialty Transportation (1) $ — $ — $ 25.7 $ — $ — $ 25.7 Real Estate — — 6.2 — — 6.2 Social Services — — 10.2 — — 10.2 Pet — — 19.9 — — 19.9 United Kingdom — — 13.0 — — 13.0 Other — — 7.3 — 2.4 9.7 Total commission and other revenue — — 82.3 — 2.4 84.7 Product and service revenues — — — — 28.2 28.2 Revenues from contracts with customers — — 82.3 — 30.6 112.9 Other (2) 7.4 217.7 — 28.5 (376.6) (123.0) Total revenues $ 7.4 $ 217.7 $ 82.3 $ 28.5 $ (346.0) $ (10.1) (1) Includes the results of J.C. Taylor from August 6, 2021, the date of the J.C. Taylor transaction. (2) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM NSM Kudu Other Total Three Months Ended September 30, 2020 Commission and other revenue Specialty Transportation $ — $ 21.9 $ — $ — $ 21.9 Real Estate — 6.0 — — 6.0 Social Services — 8.6 — — 8.6 Pet — 14.7 — — 14.7 United Kingdom — 13.9 — — 13.9 Other — 5.6 — 2.1 7.7 Total commission and other revenue — 70.7 — 2.1 72.8 Product revenues — — — 2.0 2.0 Revenues from contracts with customers — 70.7 — 4.1 74.8 Other (1) 14.5 — 16.3 353.9 384.7 Total revenues $ 14.5 $ 70.7 $ 16.3 $ 358.0 $ 459.5 (1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM Ark NSM Kudu Other Total Nine Months Ended September 30, 2021 Commission and other revenue Specialty Transportation (1) $ — $ — $ 73.0 $ — $ — $ 73.0 Real Estate — — 25.2 — — 25.2 Social Services — — 26.2 — — 26.2 Pet — — 55.6 — — 55.6 United Kingdom — — 39.9 — — 39.9 Other — — 21.5 — 7.0 28.5 Total commission and other revenue — — 241.4 — 7.0 248.4 Product and service revenues — — — — 57.5 57.5 Revenues from contracts with customers — — 241.4 — 64.5 305.9 Other (2) 18.1 457.3 — 88.8 (275.3) 288.9 Total revenues $ 18.1 $ 457.3 $ 241.4 $ 88.8 $ (210.8) $ 594.8 (1) Includes the results of J.C. Taylor from August 6, 2021, the date of the J.C. Taylor transaction. (2) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. Millions HG Global/BAM NSM Kudu Other Total Nine Months Ended September 30, 2020 Commission and other revenue Specialty Transportation $ — $ 66.1 $ — $ — $ 66.1 Real Estate — 32.7 — — 32.7 Social Services — 22.2 — — 22.2 Pet — 39.8 — — 39.8 United Kingdom (2) — 36.3 — — 36.3 Other — 14.7 — 6.1 20.8 Total commission and other revenue — 211.8 — 6.1 217.9 Product revenues — — — 6.4 6.4 Revenues from contracts with customers — 211.8 — 12.5 224.3 Other (1) 58.1 — 21.0 356.5 435.6 Total revenues $ 58.1 $ 211.8 $ 21.0 $ 369.0 $ 659.9 (1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. (2) Includes the results of Kingsbridge from April 7, 2020, the date of the Kingsbridge transaction.

Equity-Method Eligible Invest_2

Equity-Method Eligible Investments (Tables)	9 Months Ended
	Sep. 30, 2021
Equity Method Investments and Joint Ventures [Abstract]
Equity Method Investments	The following table presents the basic ownership interests and carrying values of White Mountains’s equity method eligible investments as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Basic Ownership Interest Carrying Value Basic Ownership Interest Carrying Value Kudu Participation Contracts 3.2 - 32.7% 604.7 3.2 - 35.0% 400.6 Investment in MediaAlpha 28.4 % $ 316.4 35.0 % $ 802.2 PassportCard/DavidShield 53.8 % 105.0 53.8 % 95.0 Elementum Holdings, L.P. 29.7 % 56.7 28.9 % 55.1 Other equity method eligible investments, at fair value Under 50.0% 95.6 Under 50.0% 132.2 Other equity method eligible investments, at fair value 50.0% and over 17.2 50.0% and over 15.2 The following tables present summarized financial information for MediaAlpha as of September 30, 2021 and December 31, 2020 and for the three and nine months ended September 30, 2021 and 2020: Millions September 30, 2021 December 31, 2020 Balance sheet data: Total assets $ 245.5 $ 210.3 Total liabilities $ 318.4 $ 315.5 Three Months Ended September 30, Nine Months Ended September 30, Millions 2021 2020 2021 2020 Income statement data: Total revenues $ 152.7 $ 151.5 $ 483.7 $ 394.6 Total expenses $ 157.0 $ 146.7 $ 488.2 $ 370.8 Net (loss) income $ (4.3) $ 4.8 $ (4.5) $ 23.8

Fair Value of Financial Instr_2

Fair Value of Financial Instruments (Tables)	9 Months Ended
	Sep. 30, 2021
Fair Value Disclosures [Abstract]
Summary of the fair value and carrying value of financial instruments	The following table presents the fair value and carrying value of these financial instruments as of September 30, 2021 and December 31, 2020: September 30, 2021 December 31, 2020 Millions Fair Carrying Fair Carrying Ark 2007 Subordinated Notes $ 42.0 $ 43.9 $ — $ — Ark 2021 Subordinated Notes $ 163.1 $ 156.8 $ — $ — NSM Bank Facility $ 300.6 $ 293.7 $ 279.3 $ 271.3 Other NSM debt $ 1.3 $ 1.3 $ 1.3 $ 1.3 Kudu Credit Facility $ 218.2 $ 195.6 $ — $ — Kudu Bank Facility $ — $ — $ 89.3 $ 86.3 Other Operations debt $ 20.5 $ 19.1 $ 18.8 $ 17.5

Held for Sale and Discontinue_2

Held for Sale and Discontinued Operations (Tables)	9 Months Ended
	Sep. 30, 2021
Discontinued Operations and Disposal Groups [Abstract]
Schedule of Earnings Per Share for Discontinued Operations	The following table presents the Company’s computation of earnings per share for discontinued operations for the three and nine months ended September 30, 2021 and 2020: Three Months Ended Nine Months Ended September 30, September 30, 2021 2020 2021 2020 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ (371.4) $ 232.9 $ (308.2) $ 219.5 Less: total income (loss) from continuing operations, net of tax (371.4) 233.6 (326.9) 220.3 Net (loss) gain from discontinued operations attributable to White Mountains’s common shareholders $ — $ (.7) $ 18.7 $ (.8) Allocation of earnings to participating restricted common shares (1) — — (.2) — Basic and diluted earnings(losses) per share numerators (2) $ — $ (.7) $ 18.5 $ (.8) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (3) (37.8) (43.1) (36.0) (40.0) Basic earnings per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,090.3 3,101.8 3,099.4 3,129.0 Average unvested restricted common shares (3) (37.8) (43.1) (36.0) (40.0) Diluted earnings per share denominator 3,052.5 3,058.7 3,063.4 3,089.0 Basic and diluted earnings (losses) per share (in dollars) - discontinued operations: $ — $ (.23) $ 6.03 $ (.26) (1) Restricted shares issued by White Mountains contain dividend participation features, and therefore, are considered participating securities. (2) 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, 2021 and 2020. (3) Restricted common 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	3 Months Ended	9 Months Ended
	Jun. 30, 2021	Sep. 30, 2021	Dec. 31, 2020	Dec. 31, 2012	Jul. 31, 2012
Ark
Basis of Presentation
Percent of shares outstanding		12.50%
Ark
Basis of Presentation
Percent of underwriting capital provided by third parties		51.00%
NSM Insurance HoldCo, LLC
Basis of Presentation
Ownership interest (as a percent)		96.60%	96.50%
Fully diluted ownership interest (as a percent)		87.30%	89.60%
Asset Management (Kudu)
Basis of Presentation
Ownership interest (as a percent)		99.30%	99.10%
Fully diluted ownership interest (as a percent)		84.70%	85.40%
HG Global
Basis of Presentation
Percentage of par value of policy reinsured		15.00%
Surplus notes				$ 503	$ 503
HG Global | Preferred Stock
Basis of Presentation
Ownership interest (as a percent)		96.90%	96.90%
HG Global | Common equity securities
Basis of Presentation
Ownership interest (as a percent)		88.40%	88.40%
HG Global | Series A BAM Surplus Note
Basis of Presentation
Surplus notes					203
HG Global | Series B BAM Surplus Note
Basis of Presentation
Surplus notes					$ 300
Ark
Basis of Presentation
Ownership interest (as a percent)		72.00%
Ark | Ark
Basis of Presentation
Ownership interest (as a percent)		72.00%
Fully diluted ownership interest (as a percent)		63.00%
Ark | Ark
Basis of Presentation
Fully diluted ownership interest (as a percent)		63.00%
Ark | Third Point Re
Basis of Presentation
Annual crediting rate		3.00%
Decrease in investment	$ (31.7)
Carrying value of investment		$ 20.3

Significant Transactions - Medi

Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions	Mar. 23, 2021	Oct. 30, 2020	Sep. 30, 2021	Oct. 31, 2021	Dec. 31, 2020
White Mountains
Other Significant Noncash Transactions [Line Items]
Increase in value per share of investment (in dollars per share)			$ 5.60
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	$ 19
Sale of stock, price per share, net of underwriting fees (in USD per share)	$ 44.62	$ 17.67
Marketing Technology (MediaAlpha)
Other Significant Noncash Transactions [Line Items]
Proceeds from dividends received		$ 55
Investment owned (in shares)			16,900,000		20,500,000
Ownership interest (as a percent)			28.40%		35.00%
Fully diluted ownership interest (as a percent)			26.30%		32.30%
Share price (in usd per share)			$ 18.68		$ 39.07
Investment owned, balance			$ 316.4		$ 802.2
Increase in value per share of investment (in dollars per share)			$ 1
Marketing Technology (MediaAlpha) | Subsequent Event
Other Significant Noncash Transactions [Line Items]
Share price (in usd per share)				$ 17.53
Investment owned, balance				$ 297
Marketing Technology (MediaAlpha) | IPO
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)		3,600,000
Sale of stock, consideration received in transaction		$ 63.8
Marketing Technology (MediaAlpha) | Secondary Offering
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	3,600,000
Sale of stock, consideration received in transaction	$ 160.3

Significant Transactions - Ark

Significant Transactions - Ark (Details) - USD ($) $ in Millions	Jan. 01, 2021	Oct. 01, 2020	Mar. 31, 2021	Sep. 30, 2021	Dec. 31, 2020
Ark
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction					$ 366.3
Ark
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)				72.00%
Goodwill and other intangible assets				$ 292.5	0
Contingent consideration				$ 24	0
Ark | Ark
Other Significant Noncash Transactions [Line Items]
Fully diluted ownership interest (as a percent)				63.00%
Ark | Lloyd
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction					280
Other Operations
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction				$ 0	646.3
Goodwill and other intangible assets				48.7	$ 36.4
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)				72.00%
Fully diluted ownership interest (as a percent)				63.00%
Percent of outstanding shares after performance obligations are satisfied				12.50%
Ark | Group Ark Insurance Limited | Unsecured Subordinated Debt
Other Significant Noncash Transactions [Line Items]
Notes issued				$ 163.3

Significant Transactions - Sche

Significant Transactions - Schedule of Assets Acquired and Liabilities Assumed, Ark (Details) - USD ($) $ in Millions	Jan. 01, 2021	Sep. 30, 2021	Dec. 31, 2020
Other Significant Transactions [Line Items]
Goodwill		$ 671.4	$ 525.5
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 - NSM

Significant Transactions - NSM (Details) £ in Millions, $ in Millions	Aug. 06, 2021USD ($)	Apr. 12, 2021USD ($)	Apr. 12, 2021GBP (£)	Apr. 07, 2020USD ($)	Apr. 07, 2020GBP (£)	Mar. 31, 2019USD ($)	Dec. 03, 2018USD ($)	May 18, 2018USD ($)earnout_period	Sep. 30, 2021USD ($)	Mar. 31, 2021USD ($)	Dec. 31, 2020USD ($)	Sep. 30, 2020USD ($)	Mar. 31, 2020USD ($)	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Sep. 30, 2019USD ($)	Apr. 07, 2020GBP (£)
Other Significant Noncash Transactions [Line Items]
Loss on sale										$ 28.7
Goodwill									$ 671.4		$ 525.5			$ 671.4
Change in fair value of contingent consideration earnout liabilities									0.6			$ 0.7		0.8	$ (1.6)
Contingent consideration payments related to acquisitions of subsidiaries														8.8	7
Recognized pre-tax expense (revenue)									0.6			$ (0.7)		0.8	$ 1.6
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Fresh Insurance Services Group Limited
Other Significant Noncash Transactions [Line Items]
Proceeds from sale of business		$ 1.5	£ 1.1
Disposal Group, Held-for-sale, Not Discontinued Operations | Fresh Insurance Services Group Limited
Other Significant Noncash Transactions [Line Items]
Loss on sale										28.7
Fresh Insurance Services Group Limited
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)								100.00%
Equity method investment, aggregate cost								$ 49.6
Borrowings								$ 51
Purchase price adjustment																$ 0.7
Number of earnout periods | earnout_period								2
KBK Insurance Group, Inc. & KBK Premium Services, Inc.
Other Significant Noncash Transactions [Line Items]
Borrowings							$ 30.1
Cash consideration to acquire businesses and interest in affiliates							60
Goodwill						$ 32.6
Intangible assets acquired						32.7
NSM Insurance HoldCo, LLC
Other Significant Noncash Transactions [Line Items]
Cash consideration to acquire businesses and interest in affiliates							$ 29
J.C. Taylor Insurance
Other Significant Noncash Transactions [Line Items]
Borrowings	$ 35
Cash consideration to acquire businesses and interest in affiliates	49.6
Assets acquired	60.3
Goodwill and other intangible assets	55.7
Liabilities acquired	$ 10.7
Specialty Insurance Distribution (NSM)
Other Significant Noncash Transactions [Line Items]
Contingent consideration									6.7		14.6			6.7
Goodwill and other intangible assets									734.8		736.8			734.8
Specialty Insurance Distribution (NSM) | Kingsbridge Group Limited
Other Significant Noncash Transactions [Line Items]
Equity method investment, aggregate cost				$ 132.2													£ 107.2
Borrowings				$ 52.4	£ 42.5
Percentage of voting interests acquired				100.00%													100.00%
Stock issued during period, value, acquisitions				$ 80.3
Acquisitions of businesses				111.5
Attribution of acquisition date fair value estimates between goodwill and other intangible assets				20.2
Contingent consideration				$ 4.1					0.1					0.1
Pretax income											4.1
Foreign currency translation gain											$ 0.3
Specialty Insurance Distribution (NSM) | J.C. Taylor Insurance
Other Significant Noncash Transactions [Line Items]
Percentage of voting interests acquired	100.00%
KBK Insurance Group, Inc. & KBK Premium Services, Inc.
Other Significant Noncash Transactions [Line Items]
Change in fair value of contingent consideration earnout liabilities						$ 5.9
Contingent consideration payments related to acquisitions of subsidiaries										$ 6.7			$ 6.4
KBK Insurance Group, Inc. & KBK Premium Services, Inc. | Specialty Insurance Distribution (NSM)
Other Significant Noncash Transactions [Line Items]
Contingent consideration									$ 6.6					$ 6.6

Significant Transactions - Pass

Significant Transactions - PassportCard/DavidShield (Details) - USD ($) $ in Millions	May 07, 2020	Jan. 24, 2018	Sep. 30, 2021	Dec. 31, 2020	May 06, 2020
DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50.00%
PassportCard
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)		50.00%
PassportCard/DavidShield
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	53.80%		53.80%	53.80%	50.00%
Payments to acquire businesses, gross		$ 41.8
Payments to acquire business, net		$ 28.3
Stock issued during period, value, acquisitions	$ 15
Maximum loss exposure			$ 114.4

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Schedule of Investments [Line Items]
Total investment income	$ (20.1)	$ (71.5)	$ (58.8)	$ (114.6)
Third-party investment expenses	(0.6)	(0.3)	(1.6)	(0.9)
Net investment income	19.5	71.2	57.2	113.7
Fixed maturity investments
Schedule of Investments [Line Items]
Total investment income	(8.2)	(7)	(21.9)	(22.4)
Short-term investments
Schedule of Investments [Line Items]
Total investment income	0	(0.1)	(0.5)	(1)
Common equity securities
Schedule of Investments [Line Items]
Total investment income	(0.1)	(0.5)	(0.1)	(6.5)
Marketing Technology (MediaAlpha)
Schedule of Investments [Line Items]
Total investment income	0	(55)	0	(60)
Other long-term investments
Schedule of Investments [Line Items]
Total investment income	(12)	(8.9)	(37.1)	(24.7)
Amount attributable to TPC Providers
Schedule of Investments [Line Items]
Total investment income	$ (0.2)	$ 0	$ (0.8)	$ 0

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Debt and Equity Securities, FV-NI [Line Items]
Less: net (losses) gains on investment securities sold during the period	$ (4.8)	$ 36.1	$ (5.1)	$ 29.6
Investments Held
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	(361.5)	270.5	(229.2)	273.2
Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	(6.8)	3.6	(23.2)	35.8
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	(0.3)	0	0	0.4
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	1.6	48.4	7.7	5.9
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	(396.8)	250	(325.5)	295
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	37.7	4.6	113.2	(34.3)
Gain (loss) on investments, exchange rate effect	(7)	0.8	(7.4)	(0.8)
Amount attributable to TPC Providers
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	(1.7)	0	(6.5)	0
Net realized and unrealized investment (losses) gains
Debt and Equity Securities, FV-NI [Line Items]
Net realized and unrealized investment (losses) gains	$ (366.3)	$ 306.6	$ (234.3)	$ 302.8

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 26.5	$ 260.1	$ 75.5	$ 276
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Total net unrealized investment gains, pre-tax - Level 3 investments	$ 26.5	$ 260.1	$ 75.5	$ 276

Investment Securities - Inves_2

Investment Securities - Investment Holdings Fixed Maturity Table (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 207.4	$ 173.2
Gross Unrealized Gains	0.8	3.1
Gross Unrealized Losses	(0.6)	0
Net Foreign Currency Gains (Losses)	0
Carrying Value	207.6	176.3
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	945.2	522.8
Gross Unrealized Gains	13.1	24.7
Gross Unrealized Losses	(3.4)	(0.1)
Net Foreign Currency Gains (Losses)	(0.7)
Carrying Value	954.2	547.4
Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	276.1	244
Gross Unrealized Gains	18	21
Gross Unrealized Losses	(0.7)	0
Net Foreign Currency Gains (Losses)	0
Carrying Value	293.4	265
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	247.3	211.7
Gross Unrealized Gains	4.2	6.8
Gross Unrealized Losses	(1.4)	0
Net Foreign Currency Gains (Losses)	0
Carrying Value	250.1	218.5
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	128.5
Gross Unrealized Gains	0
Gross Unrealized Losses	(0.4)
Net Foreign Currency Gains (Losses)	(0.5)
Carrying Value	127.6
Total fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,804.5	1,151.7
Gross Unrealized Gains	36.1	55.6
Gross Unrealized Losses	(6.5)	(0.1)
Net Foreign Currency Gains (Losses)	(1.2)
Carrying Value	$ 1,832.9	$ 1,207.2

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, 2021	Dec. 31, 2020
Common equity securities
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	$ 152.5
Gross Unrealized Gains	8.8
Gross Unrealized Losses	(0.5)
Net Foreign Currency Gains (Losses)	(1.2)
Common equity securities, at fair value	159.6
Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	0	$ 0
Gross Unrealized Gains	316.4	802.2
Gross Unrealized Losses	0	0
Net Foreign Currency Gains (Losses)	0	0
Common equity securities, at fair value	316.4	802.2
Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Cost or Amortized Cost	1,154.7	767.4
Gross Unrealized Gains	197.6	95.8
Gross Unrealized Losses	(62.9)	(78.1)
Net Foreign Currency Gains (Losses)	(3.9)	1.7
Common equity securities, at fair value	$ 1,285.5	$ 786.8

Investment Securities - Cost an

Investment Securities - Cost and Amortized Cost Maturity Schedule (Details) $ in Millions	Sep. 30, 2021USD ($)
Cost or Amortized Cost
Total fixed maturity investments	$ 1,804.5
Carrying Value
Total fixed maturity investments	1,832.9
Fixed Maturities and Convertible Fixed Maturities Excluding Mortgage Backed Securities
Cost or Amortized Cost
Due in one year or less	111.9
Due after one year through five years	836.1
Due after five years through ten years	368.5
Due after ten years	112.2
Carrying Value
Due in one year or less	112.7
Due after one year through five years	843.4
Due after five years through ten years	377.3
Due after ten years	121.8
Mortgage and asset-backed securities
Cost or Amortized Cost
Mortgage and asset-backed securities and collateralized loan obligations	375.8
Carrying Value
Mortgage and asset-backed securities and collateralized loan obligations	$ 377.7

Investment Securities - Fair Va

Investment Securities - Fair Value Measurements (Details)	9 Months Ended	12 Months Ended
	Sep. 30, 2021	Dec. 31, 2020
Investments, Debt and Equity Securities [Abstract]
Percentage of investments recorded at fair value	69.00%	73.00%

Investment Securities - Fair _2

Investment Securities - Fair Value Measurement by Level (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020	Sep. 30, 2020	Dec. 31, 2019
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 3,594.4	$ 2,796.2	$ 2,533.4	$ 2,746
Other long-term investments	1,285.5	786.8
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	954.2	547.4
Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	250.1	218.5
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6	0
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	609.5	142.9	571.8	201.2
Level 1
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	524	978.5	295.3	780
Level 2
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,784.9	1,030.9	1,066.8	1,109.6
Level 2 | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	250.1	218.5
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6	0
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	814.5	614.2	$ 1,000.3	$ 654
Fair value measured on a recurring basis
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	4,203.9	2,939.1
Other long-term investments	1,285.5
Fair value measured on a recurring basis | Marketing Technology (MediaAlpha)
Debt and Equity Securities, FV-NI [Line Items]
Other long-term investments	316.4	802.2
Fair value measured on a recurring basis | U.S. Government and agency obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	207.6	176.3
Fair value measured on a recurring basis | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	954.2	547.4
Fair value measured on a recurring basis | Debt securities issued by corporations | Financials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	246.5	133.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Consumer
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	180.5	81.9
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	66.7
Fair value measured on a recurring basis | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.8	66.9
Fair value measured on a recurring basis | Debt securities issued by corporations | Healthcare
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	98.2	51.5
Fair value measured on a recurring basis | Debt securities issued by corporations | Utilities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	69.9	32.3
Fair value measured on a recurring basis | Debt securities issued by corporations | Communications
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	53.2	44.5
Fair value measured on a recurring basis | Debt securities issued by corporations | Energy
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	47	35.8
Fair value measured on a recurring basis | Debt securities issued by corporations | Materials
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	33.3	33.9
Fair value measured on a recurring basis | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	293.4	265
Fair value measured on a recurring basis | Mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	250.1	218.5
Fair value measured on a recurring basis | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6
Fair value measured on a recurring basis | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,832.9	1,207.2
Fair value measured on a recurring basis | Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	609.5	142.9
Fair value measured on a recurring basis | Common Equity Securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	159.6
Fair value measured on a recurring basis | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		786.8
Other long-term investments	814.5
Fair value measured on a recurring basis | Other Long-term Investments, Excluding NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		614.2
Fair value measured on a recurring basis | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		172.6
Other long-term investments	471
Fair value measured on a recurring basis | Level 1
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,125.6	1,121.4
Other long-term investments	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	316.4	802.2
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	207.6	176.3
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 | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations | 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 | 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
Fair value measured on a recurring basis | Level 1 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	207.6	176.3
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	601.6	142.9
Fair value measured on a recurring basis | Level 1 | Common Equity Securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0
Fair value measured on a recurring basis | Level 1 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Other long-term investments	0
Fair value measured on a recurring basis | Level 1 | Other Long-term Investments, Excluding NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Fair value measured on a recurring basis | Level 1 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Other long-term investments	0
Fair value measured on a recurring basis | Level 2
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,792.8	1,030.9
Other long-term investments	0
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	954.2	547.4
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	246.5	133.9
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	180.5	81.9
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	66.7
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	114.8	66.9
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	98.2	51.5
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	69.9	32.3
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	53.2	44.5
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	47	35.8
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	33.3	33.9
Fair value measured on a recurring basis | Level 2 | Municipal obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	293.4	265
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	250.1	218.5
Fair value measured on a recurring basis | Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6
Fair value measured on a recurring basis | Level 2 | Fixed maturity investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,625.3	1,030.9
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	7.9	0
Fair value measured on a recurring basis | Level 2 | Common Equity Securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	159.6
Fair value measured on a recurring basis | Level 2 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Other long-term investments	0
Fair value measured on a recurring basis | Level 2 | Other Long-term Investments, Excluding NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Fair value measured on a recurring basis | Level 2 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		0
Other long-term investments	0
Fair value measured on a recurring basis | Level 3
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	814.5	614.2
Other long-term investments	814.5
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 | Technology
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations | 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 | 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
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
Fair value measured on a recurring basis | Level 3 | Other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		614.2
Other long-term investments	814.5
Fair value measured on a recurring basis | Level 3 | Other Long-term Investments, Excluding NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		614.2
Fair value measured on a recurring basis | Level 3 | Other long-term investments — NAV
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments		$ 0
Other long-term investments	$ 0

Investment Securities - Debt se

Investment Securities - Debt securities issued by corporation (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020	Sep. 30, 2020	Dec. 31, 2019
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 3,594.4	$ 2,796.2	$ 2,533.4	$ 2,746
Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	954.2	547.4
AAA | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	12.7	10.6
AA | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	85.7	57.9
A | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	473.3	318.3
BBB | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	373.7	159.6
BB | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0	1
Other | Debt securities issued by corporations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 8.8	$ 0

Investment Securities - Mortgag

Investment Securities - Mortgage-backed Asset Securities Table (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020	Sep. 30, 2020	Dec. 31, 2019
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 3,594.4	$ 2,796.2	$ 2,533.4	$ 2,746
Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	231.8	199.4
Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	18.3	19.1
Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	250.1	218.5
Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6	0
Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	377.7	218.5
Level 2
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	1,784.9	1,030.9	$ 1,066.8	$ 1,109.6
Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	231.8	199.4
Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	18.3	19.1
Level 2 | Total mortgage and asset-backed securities
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	250.1	218.5
Level 2 | Collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	127.6	0
Level 2 | Total mortgage and asset-backed securities and collateralized loan obligations
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	377.7	218.5
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	125.3	88.7
FNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	125.3	88.7
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	76.5	70.1
FHLMC | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	76.5	70.1
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	29.4	40.6
GNMA | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	29.4	40.6
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	231.2	199.4
Total agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	231.2	199.4
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	0.6	0
Non-agency: Residential | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.6	0
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	0.6	0
Total non-agency | Level 2 | Mortgage-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	0.6	0
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	11.2	11.3
Credit card receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	11.2	11.3
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	7.1	7.8
Vehicle receivables | Level 2 | Other asset-backed securities:
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	7.1	7.8
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	$ 127.6

Investment Securities - Inves_4

Investment Securities - Investment in MediaAlpha textual (Details) - Marketing Technology (MediaAlpha) - USD ($) $ / shares in Units, $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Subsidiary, Sale of Stock [Line Items]
Share price (in usd per share)	$ 18.68	$ 39.07
Investment owned, balance	$ 316.4	$ 802.2

Investment Securities - Other l

Investment Securities - Other long-term investments (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 1,285.5	$ 786.8
Asset Management (Kudu)
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	604.7	400.6
PassportCard/DavidShield
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	105	95
Elementum Holdings L.P.
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	56.7	55.1
Other unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	27	42.4
Total unconsolidated entities
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	793.4	593.1
Private equity funds and hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	144.2	121.2
Lloyd’s trust deposits
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	111.2	0
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	161.7	0
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	53.9	51.4
Private debt investments
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	13.3	21.1
Other
Debt and Equity Securities, FV-NI [Line Items]
Total other long-term investments	$ 7.8	$ 0

Investment Securities - Hedge F

Investment Securities - Hedge Funds and Private Equity Funds (Details) $ in Millions	Sep. 30, 2021USD ($)fund	Dec. 31, 2020USD ($)
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments	14
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Number of investments	1
Hedge and private equity funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Largest single fund investment | $	$ 27.4	$ 29.1

Investment Securities - Fair _3

Investment Securities - Fair Value of Hedge Funds and Private Equity Funds (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Hedge and private equity funds included in other long-term investments
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 144.2	$ 121.2
Unfunded Commitments	46.5	45.7
Private equity funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	132	121.2
Unfunded Commitments	46.5	45.7
Private equity funds | Aerospace/Defense/Government
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	63.9	69.1
Unfunded Commitments	14	15.3
Private equity funds | Financial services
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	63.2	23.5
Unfunded Commitments	29.6	30.4
Private equity funds | Real Estate
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	4.8	0
Unfunded Commitments	2.9	0
Private equity funds | Manufacturing/Industrial
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	0.1	28.6
Unfunded Commitments	0	0
Hedge funds
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	12.2	0
Unfunded Commitments	0	0
Hedge funds | European small/mid cap
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	12.2	0
Unfunded Commitments	$ 0	$ 0

Investment Securities - Inves_5

Investment Securities - Investments In Private Equity Funds Subject to Lock-Up Periods (Details) - Private equity funds $ in Millions	Sep. 30, 2021USD ($)
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 132
1 – 3 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	0.3
3 – 5 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	14
5 – 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	109
Greater than 10 years
Debt and Equity Securities, FV-NI [Line Items]
Fair Value	$ 8.7

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, 2021	Dec. 31, 2020	Sep. 30, 2020	Dec. 31, 2019
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 3,594.4	$ 2,796.2	$ 2,533.4	$ 2,746
Minimum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	30 days
Maximum
Debt and Equity Securities, FV-NI [Line Items]
Redemptions and advanced redemption notice period	90 days
Lloyds Bank
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 111.2
Bank loan fund
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	161.7
ILS funds
Debt and Equity Securities, FV-NI [Line Items]
Fair value investments	$ 53.9

Investment Securities - Rollfor

Investment Securities - Rollforward of Fair Value Measurements by Level (Details) - USD ($) $ in Millions	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020	Dec. 31, 2019
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	$ 2,796.2	$ 2,746
Net realized and unrealized gains (losses)	(227.8)	302.4
Amortization/Accretion	(6)	(3)
Purchases	1,463.8	563.6
Sales	(645.4)	(1,075.6)
Transfers in	0	0
Transfers out	0	0
Ending balance	3,594.4	2,533.4
Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	213.6
Short-term investments, at fair value	396.5		$ 0
Third Party Capital Providers
Debt and Equity Securities, FV-NI [Line Items]
Realized and unrealized gains (losses)	6.5
Level 1 Investments
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	978.5	780
Net realized and unrealized gains (losses)	(327.6)	29.2
Amortization/Accretion	(0.1)	0
Purchases	130.9	128.8
Sales	(257.7)	(642.7)
Transfers in	0	0
Transfers out	0	0
Ending balance	524	295.3
Level 1 Investments | Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	0
Level 2  Investments
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	1,030.9	1,109.6
Net realized and unrealized gains (losses)	(13.1)	12.5
Amortization/Accretion	(5.9)	(3)
Purchases	989.7	316.2
Sales	(284.9)	(368.5)
Transfers in	0	0
Transfers out	0	0
Ending balance	1,784.9	1,066.8
Level 2  Investments | Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	68.2
Common equity securities | Level 3  Investments
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance		0.1
Net realized and unrealized gains (losses)		0
Amortization/Accretion		0
Purchases		0
Transfers in		0
Transfers out		0
Ending balance		0.1
Other long-term investments | Level 3  Investments
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	614.2	654
Net realized and unrealized gains (losses)	79	275.6
Amortization/Accretion	0	0
Purchases	143.6	78.8
Sales	(31.9)	(8.1)
Transfers in	0	0
Transfers out	0	0
Ending balance	814.5	1,000.3
Other long-term investments | Level 3  Investments | Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	9.6
Hedge and private equity funds included in other long-term investments | NAV
Debt and Equity Securities, FV-NI [Line Items]
Beginning balance	172.6	202.3
Net realized and unrealized gains (losses)	33.9	(14.9)
Amortization/Accretion	0	0
Purchases	199.6	39.8
Sales	(70.9)	(56.3)
Transfers in	0	0
Transfers out	0	0
Ending balance	471	170.9
Hedge and private equity funds included in other long-term investments | NAV | Ark
Debt and Equity Securities, FV-NI [Line Items]
Purchases	135.8
Short-term investments
Debt and Equity Securities, FV-NI [Line Items]
Short-term investments, at fair value	$ 609.5	571.8	$ 142.9	$ 201.2
Realized and unrealized gains (losses)		$ 0.4

Investment Securities - Signifi

Investment Securities - Significant Unobservable Inputs (Details) $ in Millions	9 Months Ended		12 Months Ended
	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Dec. 31, 2020USD ($)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Other Long-Term Investments	$ 141.6	$ 57.5
Kudu
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Other Long-Term Investments			$ 118.2
Kudu investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	18.00%		18.00%
Kudu investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	23.00%		23.00%
Kudu investments | Terminal Multiple | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal Cash Flow Exit Multiple	7		7
Kudu investments | Terminal Multiple | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal Cash Flow Exit Multiple	13		12
PassportCard/DavidShield
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Other Long-Term Investments			$ 15
Private debt investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	4.00%		4.00%
Private debt investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	8.00%		8.00%
Other long-term investments | Discount rate | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	20.00%		20.00%
Other long-term investments | Discount rate | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	24.00%		24.00%
TIG Advisors LLC, TK Partners LLC, Third Eye Capital Management And Douglass Winthrop Advisors | Kudu
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Other Long-Term Investments	$ 141.6
Level 3 | Kudu investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	604.7		$ 400.6
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	121
Level 3 | PassportCard/DavidShield | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 105		$ 95
Level 3 | PassportCard/DavidShield | Discount rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate	23.00%		23.00%
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	4.00%		4.00%
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	$ 56.7		$ 55.1
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	17.00%		17.00%
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	4.00%		4.00%
Level 3 | Private debt investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 11.2		$ 17.1
Level 3 | Other long-term investments | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	14.9		27.6
Level 3 | Other long-term investments | Standard Poors NR Rating | Discounted cash flow
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 22		$ 18.8
Level 3 | Other long-term investments | Measurement Input, Long-term Revenue Growth Rate | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal Revenue Growth Rate	4.00%		4.00%

Goodwill and Other Intangible_3

Goodwill and Other Intangible Assets - Schedule of Acquisition Date Fair Values, Accumulated Amortization and Net Carrying Values for Other Intangibles Assets and Goodwill, By Company (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020	Jun. 30, 2021	Jun. 30, 2020	Dec. 31, 2019
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	$ 701.6		$ 701.6		$ 525.5
Goodwill, impairments			30.2		0
Goodwill, net carrying value	671.4		671.4		525.5
Other intangible assets, acquisition date fair value	501.9		501.9		317.8
Intangible assets and goodwill, acquisition date fair value	1,203.5		1,203.5		843.3
Other intangible assets, accumulated amortization	82.1		82.1		54.7
Other intangible assets, impairments			6.2		6.2
Impairment of intangible assets, including goodwill			36.4		6.2
Other intangible assets, net carrying value	413.6		413.6		256.9
Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, impairments			30.2	$ 0
Goodwill, net carrying value	671.4	$ 540.1	671.4	540.1	525.5	$ 629.4	$ 518.2	$ 394.7
Goodwill, foreign currency translation gain (loss)	(4)	7	(2.3)	5.2
Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, impairments			0	0
Other intangible assets, foreign currency translation gain (loss)	(0.3)	$ (0.1)	(0.2)	$ (0.5)
Total Equity Including Noncontrolling Interest
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets	1,085		1,085		782.4
Non-controlling interest
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets	118		118		28.1
Total
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets	967		967		754.3
Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	116.8		116.8		0
Goodwill, impairments			0		0
Goodwill, net carrying value	116.8		116.8		0
Ark | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	175.7		175.7		0
Other intangible assets, accumulated amortization	0		0		0
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	175.7		175.7		0
Specialty Insurance Distribution (NSM)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	559.8		559.8		506.4
Goodwill, impairments			30.2		0
Goodwill, net carrying value	529.6		529.6		506.4
Other intangible assets, acquisition date fair value	288		288		288.9
Other intangible assets, accumulated amortization	76.6		76.6		52.3
Other intangible assets, impairments			6.2		6.2
Other intangible assets, net carrying value	205.2		205.2		230.4
Specialty Insurance Distribution (NSM) | Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, foreign currency translation gain (loss)			(2.3)		13.4
Specialty Insurance Distribution (NSM) | Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, foreign currency translation gain (loss)			$ (0.2)		1.6
Specialty Insurance Distribution (NSM) | Customer relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			8 years 10 months 24 days
Other intangible assets, acquisition date fair value	136		$ 136		136.2
Other intangible assets, accumulated amortization	50.6		50.6		36.7
Other intangible assets, impairments			3.5		3.5
Other intangible assets, net carrying value	81.9		$ 81.9		96
Specialty Insurance Distribution (NSM) | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			16 years
Other intangible assets, acquisition date fair value	65.3		$ 65.3		65.4
Other intangible assets, accumulated amortization	10.9		10.9		8.3
Other intangible assets, impairments			1		1
Other intangible assets, net carrying value	53.4		53.4		56.1
Specialty Insurance Distribution (NSM) | Information technology platform
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	3.1		3.1		3.1
Other intangible assets, accumulated amortization	1.4		1.4		1.4
Other intangible assets, impairments			1.7		1.7
Other intangible assets, net carrying value	0		$ 0		0
Specialty Insurance Distribution (NSM) | Renewal rights
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			12 years
Other intangible assets, acquisition date fair value	82.5		$ 82.5		82.5
Other intangible assets, accumulated amortization	13.1		13.1		4.9
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	69.4		$ 69.4		77.6
Specialty Insurance Distribution (NSM) | Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			3 years 4 months 24 days
Other intangible assets, acquisition date fair value	1.1		$ 1.1		1.7
Other intangible assets, accumulated amortization	0.6		0.6		1
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	0.5		0.5		0.7
Kudu
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	7.6		7.6		7.6
Goodwill, impairments			0		0
Goodwill, net carrying value	7.6		$ 7.6		7.6
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		2.2
Other intangible assets, accumulated amortization	0.8		0.8		0.6
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	1.4		1.4		1.6
Other Operations
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, acquisition date fair value	17.4		17.4		11.5
Goodwill, impairments			0		0
Goodwill, net carrying value	17.4		17.4		11.5
Other intangible assets, acquisition date fair value	36		36		26.7
Other intangible assets, accumulated amortization	4.7		4.7		1.8
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	31.3		$ 31.3		24.9
Other Operations | Customer relationships
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			13 years 3 months 18 days
Other intangible assets, acquisition date fair value	18.9		$ 18.9		14.2
Other intangible assets, accumulated amortization	3.5		3.5		1.4
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	15.4		$ 15.4		12.8
Other Operations | Trade names
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			18 years 1 month 6 days
Other intangible assets, acquisition date fair value	8.2		$ 8.2		3.6
Other intangible assets, accumulated amortization	1		1		0.3
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	7.2		$ 7.2		3.3
Other Operations | Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, weighted average useful life (in years)			5 years 4 months 24 days
Other intangible assets, acquisition date fair value	0.3		$ 0.3		0.3
Other intangible assets, accumulated amortization	0.2		0.2		0.1
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	0.1		0.1		0.2
Other Operations | Insurance Licenses
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, acquisition date fair value	8.6		8.6		8.6
Other intangible assets, accumulated amortization	0		0		0
Other intangible assets, impairments			0		0
Other intangible assets, net carrying value	$ 8.6		$ 8.6		$ 8.6

Goodwill and Other Intangible_4

Goodwill and Other Intangible Assets - Summary of the Acquisition Date Fair Values of Goodwill and Other Intangible Assets (Details) - USD ($) $ in Millions	Aug. 06, 2021	May 01, 2021	Jan. 01, 2021	Jul. 02, 2020	Apr. 07, 2020
Specialty Insurance Distribution (NSM)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 187.4				$ 187.4
Kingsbridge | Specialty Insurance Distribution (NSM)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired					$ 131.7
J.C. Taylor | Specialty Insurance Distribution (NSM)
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 55.7
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		$ 30.6		$ 30.6

Goodwill and Other Intangible_5

Goodwill and Other Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended
	Mar. 31, 2021	Jun. 30, 2020
Goodwill and Intangible Assets Disclosure [Abstract]
Loss on sale	$ 28.7
Impairment of intangible assets		$ 6.2

Goodwill and Other Intangible_6

Goodwill and Other Intangible Assets - Schedule of Goodwill and Other Intangible Assets Rollforward (Details) - USD ($) $ in Millions	3 Months Ended			9 Months Ended		12 Months Ended
	Sep. 30, 2021	Mar. 31, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance		$ 525.5		$ 525.5
Loss on assets held for sale				(30.2)		$ 0
Amortization of other intangible assets	$ (10.2)		$ (5.4)	(28.1)	$ (17.1)
Goodwill, ending balance	671.4			671.4		525.5
Fresh Insurance Services Group Limited
Acquired Finite-Lived Intangible Assets [Line Items]
Proceeds from sale of other assets		1.5
Goodwill
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill, beginning balance	629.4	525.5	518.2	525.5	394.7	394.7
Acquisitions of businesses	55.7		14.9	71.5	140
Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3)	(9.3)		0	(9.3)	0
Foreign currency translation	(4)		7	(2.3)	5.2
Impairments				0	0
Loss on assets held for sale				(30.2)	0
Measurement period adjustments	(0.4)		0	(0.6)	0.2
Amortization of other intangible assets	0		0	0	0
Goodwill, ending balance	671.4		540.1	671.4	540.1	525.5
Goodwill | Other
Acquired Finite-Lived Intangible Assets [Line Items]
Acquisitions of businesses				15.8
Goodwill | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill acquired				116.8	0
Goodwill | J.C. Taylor
Acquired Finite-Lived Intangible Assets [Line Items]
Acquisitions of businesses				55.7
Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets (excluding goodwill), beginning balance	414.8	256.9	241.7	256.9	260	260
Acquisitions of businesses	0		0	0	0
Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3)	9.3		0	9.3	0
Foreign currency translation	(0.3)		(0.1)	(0.2)	(0.5)
Impairments				0	(6.2)
Loss on assets held for sale				0	0
Measurement period adjustments	0		0	0	0
Amortization of other intangible assets	(10.2)		(5.4)	(28.1)	(17.1)
Other intangible assets (excluding goodwill), ending balance	413.6		236.2	413.6	236.2	256.9
Other Intangible Assets | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Intangible assets acquired				175.7	0
Total Goodwill and Other Intangible Assets
Acquired Finite-Lived Intangible Assets [Line Items]
Other intangible assets, gross (including goodwill), beginning balance	1,044.2	$ 782.4	759.9	782.4	654.7	654.7
Acquisitions of businesses	55.7		14.9	71.5	140
Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3)	0		0	0	0
Foreign currency translation	(4.3)		6.9	(2.5)	4.7
Impairments				0	(6.2)
Loss on assets held for sale				(30.2)	0
Measurement period adjustments	(0.4)		0	(0.6)	0.2
Amortization of other intangible assets	(10.2)		(5.4)	(28.1)	(17.1)
Other intangible assets, gross (including goodwill), ending balance	$ 1,085		$ 776.3	1,085	776.3	$ 782.4
Total Goodwill and Other Intangible Assets | Ark
Acquired Finite-Lived Intangible Assets [Line Items]
Goodwill and other intangible assets acquired				$ 292.5	$ 0

Loss and Loss Adjustment Expe_3

Loss and Loss Adjustment Expense Reserves (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2021
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]
Gross beginning balance	$ 760	$ 696
Less: beginning reinsurance recoverable on unpaid losses	(425.3)	(433.4)
Net loss and LAE reserves	334.7	262.6
Loss and LAE incurred relating to:
Current year losses	141.9	269
Prior year losses	(12.7)	(21.2)
Total incurred losses and LAE	129.2	247.8
Foreign currency translation adjustment to loss and LAE reserves	(1.2)	(3.4)
Loss and LAE paid relating to:
Current year losses	(9)	(11.5)
Prior year losses	(20.3)	(62.1)
Total loss and LAE payments	(29.3)	(73.6)
Net ending balance	433.4	433.4
Plus: ending reinsurance recoverable on unpaid losses	457.5	457.5
Gross ending balance	$ 890.9	$ 890.9
Prior year claims and claims adjustment expense, points	6.00%	5.00%

Third Party Reinsurance - Effec

Third Party Reinsurance - Effects of Reinsurance (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Earned premiums:
Gross earned premiums (1)	$ 220.1	$ 6.2	$ 455.4	$ 17.2
Ark
Written premiums:
Gross	162.4		895
Ceded	(41.5)		(169.5)
Gross written premiums (1)	120.9		725.5
Earned premiums:
Gross	284.5		622
Ceded	(71.1)		(186.2)
Gross earned premiums (1)	213.4		435.8
Losses and Loss Adjustment Expense [Abstract]
Gross	193.5		372.7
Ceded	(64.3)		(124.9)
Net Losses and LAE	$ 129.2		$ 247.8

Third Party Reinsurance - Narra

Third Party Reinsurance - Narrative (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses	$ 457.5
Reinsurance recoverables on paid losses	8.1
Ark
Reinsurance [Line Items]
Reinsurance recoverables	465.6	$ 0
Amount attributable to TPC Providers
Reinsurance [Line Items]
Reinsurance recoverables on unpaid losses	$ 299.9

Third Party Reinsurance - Remai

Third Party Reinsurance - Remaining Gross and Net Reinsurance Recoverables (Details) - All Entities Except TCP Providers $ in Millions	Sep. 30, 2021USD ($)
Reinsurance [Line Items]
Reinsurance recoverables	$ 165.7
Reinsurance Recoverables, Collateral	48.3
Reinsurance Recoverables, Including Reinsurance Premium Paid	$ 117.4
Percent of reinsurance recoverables from insurers that are collateralized	100.00%
A+ or better
Reinsurance [Line Items]
Reinsurance recoverables	$ 122.8
Reinsurance Recoverables, Collateral	23.9
Reinsurance Recoverables, Including Reinsurance Premium Paid	$ 98.9
Percent of reinsurance recoverables from insurers that are collateralized	84.20%
A- to A
Reinsurance [Line Items]
Reinsurance recoverables	$ 32.7
Reinsurance Recoverables, Collateral	15.6
Reinsurance Recoverables, Including Reinsurance Premium Paid	$ 17.1
Percent of reinsurance recoverables from insurers that are collateralized	14.60%
B++ or lower and not rated
Reinsurance [Line Items]
Reinsurance recoverables	$ 10.2
Reinsurance Recoverables, Collateral	8.8
Reinsurance Recoverables, Including Reinsurance Premium Paid	$ 1.4
Percent of reinsurance recoverables from insurers that are collateralized	1.20%

Debt - Summary of Debt Outstand

Debt - Summary of Debt Outstanding (Details) € in Millions, $ in Millions	3 Months Ended	12 Months Ended
	Sep. 30, 2021USD ($)	Dec. 31, 2020USD ($)	Sep. 30, 2021EUR (€)
Debt Instrument
Total debt	$ 710.4	$ 376.4
Weighted average interest rate	6.70%	7.00%
Ark Subordinated Debt
Debt Instrument
Unamortized issuance cost	$ (5.5)
Ark 2007 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	30
Ark 2007 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	13.9
Ark 2007 Notes | Ark Subordinated Debt
Debt Instrument
Total debt	43.9
Ark 2021 Notes Tranche 1
Debt Instrument
Amount borrowed | €			€ 39.1
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	45.3
Ark 2021 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	47
Ark 2021 Notes Tranche 3 | Ark Subordinated Debt
Debt Instrument
Amount borrowed	70
Ark 2021 Notes | Ark Subordinated Debt
Debt Instrument
Total debt	$ 156.8
Ark
Debt Instrument
Effective percentage	5.10%		5.10%
Ark | Ark Subordinated Debt
Debt Instrument
Total debt	$ 200.7
NSM Bank Facility
Debt Instrument
Effective percentage	8.30%	8.40%	8.30%
Other NSM debt
Debt Instrument
Total debt	$ 1.3	$ 1.3
Kudu Credit Facility
Debt Instrument
Total debt	195.6
Other
Debt Instrument
Total debt	19.1
Term Loan | NSM Bank Facility
Debt Instrument
Amount borrowed	300.4	277.4
Unamortized issuance cost	(6.7)	(6.1)
Total debt	$ 293.7	$ 271.3
Effective percentage	7.40%	7.50%	7.40%
Term Loan | Other NSM debt
Debt Instrument
Effective percentage	3.30%	2.50%	3.30%
Term Loan | Kudu Credit Facility
Debt Instrument
Amount borrowed	$ 203
Unamortized issuance cost	$ (7.4)
Effective percentage	4.10%		4.10%
Term Loan | Kudu Bank Facility
Debt Instrument
Amount borrowed		$ 89.2
Unamortized issuance cost		(2.9)
Total debt		$ 86.3
Effective percentage		8.30%
Term Loan | Other Operations
Debt Instrument
Amount borrowed	$ 19.5	$ 18
Unamortized issuance cost	$ (0.4)	$ (0.5)
Effective percentage	7.40%	7.40%	7.40%
Term Loan | Other
Debt Instrument
Total debt		$ 17.5

Debt - Narrative (Details)

Debt - Narrative (Details) £ in Millions	Sep. 08, 2021USD ($)	Jun. 02, 2021USD ($)	Jun. 01, 2021	Apr. 07, 2020USD ($)	Apr. 07, 2020GBP (£)	Apr. 06, 2020USD ($)	Sep. 30, 2021USD ($)credit_facility	Aug. 31, 2021	Jul. 31, 2021	Mar. 31, 2007USD ($)	Sep. 30, 2021USD ($)credit_facility	Sep. 30, 2020USD ($)	Sep. 30, 2021USD ($)credit_facility	Sep. 30, 2021GBP (£)	Sep. 30, 2020USD ($)	Sep. 30, 2021EUR (€)credit_facility	Aug. 11, 2021USD ($)	Jul. 13, 2021USD ($)	Jul. 13, 2021EUR (€)	Jun. 30, 2021USD ($)	Dec. 31, 2020USD ($)	Jun. 30, 2020USD ($)	Dec. 31, 2019USD ($)	Jun. 15, 2018USD ($)	Mar. 31, 2007EUR (€)
Debt Instrument
Debt							$ 710,400,000				$ 710,400,000		$ 710,400,000								$ 376,400,000
Debt covenant, maximum loan to value percent, period one							50.00%				50.00%		50.00%			50.00%
Debt covenant, maximum loan to value percent, period two							40.00%				40.00%		40.00%			40.00%
Debt covenant, maximum loan to value percent, period three							25.00%				25.00%		25.00%			25.00%
Debt covenant, maximum loan to value percent, period four							15.00%				15.00%		15.00%			15.00%
Debt covenant, maximum loan to value percent, period five							0.00%				0.00%		0.00%			0.00%
Debt covenant, maximum loan to value percent							34.00%				34.00%		34.00%			34.00%
Draw down of debt and revolving line of credit													$ 403,900,000		$ 69,400,000
Other
Debt Instrument
Secured credit facilities | credit_facility							3				3		3			3
Specialty Insurance Distribution (NSM)
Debt Instrument
Debt							$ 295,000,000				$ 295,000,000		$ 295,000,000								272,600,000
Specialty Insurance Distribution (NSM) | Kingsbridge Group Limited
Debt Instrument
Borrowings				$ 52,400,000	£ 42.5
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
Ark 2007 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							30,000,000				30,000,000		30,000,000
Ark 2007 Notes Tranche 1 | Junior Notes | Ark
Debt Instrument
Amount borrowed										$ 30,000,000
Debt							30,000,000				30,000,000		30,000,000
Ark 2007 Notes Tranche 1 | Junior Notes | USD-LIBOR | Ark
Debt Instrument
Basis spread on variable rate										4.60%
Ark 2007 Notes Tranche 2 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							13,900,000				13,900,000		13,900,000
Ark 2007 Notes Tranche 2 | Junior Notes | Ark
Debt Instrument
Amount borrowed | €																									€ 12,000,000
Debt							13,900,000				13,900,000		13,900,000			€ 12,000,000
Ark 2007 Notes Tranche 2 | Junior Notes | EURIBOR | Ark
Debt Instrument
Basis spread on variable rate										4.60%
Ark 2021 Notes Tranche 1
Debt Instrument
Outstanding balance | €																€ 39,100,000
Ark 2021 Notes Tranche 1 | Ark Subordinated Debt
Debt Instrument
Outstanding balance							45,300,000				45,300,000		45,300,000
Ark 2021 Notes Tranche 1 | Unsecured Subordinated Debt | Group Ark Insurance Limited
Debt Instrument
Notes issued																		$ 46,300,000	€ 39,100,000
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
Notes issued	$ 70,000,000
Additional interest rate	1.00%
Solvency capital requirement							120.00%
Debt to capital requirement							40.00%
Ark 2021 Notes Tranche 3 | Unsecured Subordinated Debt | Group Ark Insurance Limited | USD-LIBOR
Debt Instrument
Basis spread on variable rate	6.10%
Ark | Ark Subordinated Debt
Debt Instrument
Debt							$ 200,700,000				200,700,000		200,700,000
Ark | Term Loan
Debt Instrument
Line of credit							45,000,000				45,000,000		45,000,000
Total commitment under revolving credit facility							150,000,000				150,000,000		150,000,000
NSM Bank Facility | Specialty Insurance Distribution (NSM)
Debt Instrument
Debt							300,400,000				300,400,000	$ 275,000,000	$ 300,400,000		275,000,000					$ 276,600,000	277,400,000	$ 273,400,000	$ 221,300,000
Total commitment under revolving credit facility				291,400,000		$ 234,000,000
Percentage of discounted future cash flows													10.00%	10.00%
NSM Bank Facility | Term Loan
Debt Instrument
Debt							293,700,000				293,700,000		$ 293,700,000								271,300,000
Outstanding balance							300,400,000				300,400,000		300,400,000								277,400,000
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM)
Debt Instrument
Amount borrowed		$ 50,000,000		276,400,000		$ 224,000,000	274,400,000				274,400,000		274,400,000
Borrowings				$ 52,400,000	£ 42.5						0	0	0		52,400,000
Floor rate				1.25%	1.25%
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | Kingsbridge Group Limited
Debt Instrument
Borrowings												52,400,000			52,400,000
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | Interest Rate Swap
Debt Instrument
Total commitment under revolving credit facility																								$ 151,000,000
Hedged liability, fair value																								$ 151,000,000
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | Interest Rate Swap | Term loan - hedged
Debt Instrument
Debt							146,500,000				146,500,000		146,500,000
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | Interest Rate Swap | Term loan - unhedged
Debt Instrument
Debt							128,000,000				128,000,000		128,000,000
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | USD-LIBOR
Debt Instrument
Floor rate				1.25%	1.25%
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | USD-LIBOR | Minimum
Debt Instrument
Basis spread on variable rate		4.50%	5.50%	5.50%	5.50%	4.25%
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | USD-LIBOR | Maximum
Debt Instrument
Basis spread on variable rate		5.00%	6.00%	6.00%	6.00%	4.75%
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | GBP-LIBOR | Minimum
Debt Instrument
Basis spread on variable rate		5.00%	6.00%
NSM Bank Facility | Term Loan | Specialty Insurance Distribution (NSM) | GBP-LIBOR | Maximum
Debt Instrument
Basis spread on variable rate		5.50%	6.50%
NSM Bank Facility | GBP Term Loan | Specialty Insurance Distribution (NSM)
Debt Instrument
Borrowings													56,600,000	£ 41.9
NSM Bank Facility | Revolving credit loan | Specialty Insurance Distribution (NSM)
Debt Instrument
Amount borrowed							26,000,000				26,000,000		26,000,000
Borrowings											35,000,000	$ 0	35,000,000		$ 0
Total commitment under revolving credit facility		$ 40,000,000		$ 15,000,000		$ 10,000,000
Other NSM
Debt Instrument
Debt							1,300,000				1,300,000		1,300,000								1,300,000
Other NSM | Term Loan | Specialty Insurance Distribution (NSM)
Debt Instrument
Debt							1,400,000				1,400,000		1,400,000
Kudu Bank Facility | Kudu
Debt Instrument
Total commitment under revolving credit facility							300,000,000				300,000,000		300,000,000
Draw down of debt and revolving line of credit											101,000,000		203,000,000
Kudu Bank Facility | Term Loan
Debt Instrument
Debt																					86,300,000
Outstanding balance																					$ 89,200,000
Kudu Bank Facility | Term Loan | Kudu
Debt Instrument
Amount borrowed							$ 97,000,000				$ 97,000,000		$ 97,000,000
Percentage of borrowing base							35.00%				35.00%		35.00%			35.00%
Remaining borrowing capacity under revolving credit facility							$ 11,700,000				$ 11,700,000		$ 11,700,000
Kudu Bank Facility | Revolving credit loan | Kudu
Debt Instrument
Loss on debt extinguishment													4,100,000
Draw down of debt and revolving line of credit													3,000,000
Repayments on credit facility													92,200,000
Kudu Bank Facility | Line of Credit | Kudu
Debt Instrument
Interest reserve							4,500,000				4,500,000		$ 4,500,000
Kudu Bank Facility | Line of Credit | Kudu | USD-LIBOR
Debt Instrument
Basis spread on variable rate													4.30%	4.30%
Kudu Bank Facility | Line of Credit | Kudu | Base Rate
Debt Instrument
Basis spread on variable rate													0.25%	0.25%
First Credit Facility | Other
Debt Instrument
Total commitment under revolving credit facility							16,300,000				16,300,000		$ 16,300,000
First Credit Facility | Term Loan | Other
Debt Instrument
Total commitment under revolving credit facility							11,300,000				11,300,000		11,300,000
First Credit Facility | Revolving credit loan | Other
Debt Instrument
Total commitment under revolving credit facility							2,000,000				2,000,000		2,000,000
First Credit Facility | Delayed Draw Term Loans | Other
Debt Instrument
Total commitment under revolving credit facility							3,000,000				3,000,000		3,000,000
Second Credit Facility | Other
Debt Instrument
Total commitment under revolving credit facility							15,000,000				15,000,000		15,000,000
Second Credit Facility | Term Loan | Other
Debt Instrument
Total commitment under revolving credit facility							9,000,000				9,000,000		9,000,000
Second Credit Facility | Revolving credit loan | Other
Debt Instrument
Total commitment under revolving credit facility							2,000,000				2,000,000		2,000,000
Second Credit Facility | Delayed Draw Term Loans | Other
Debt Instrument
Total commitment under revolving credit facility							4,000,000				4,000,000		4,000,000
Third Credit Facility | Other
Debt Instrument
Total commitment under revolving credit facility							4,000,000				4,000,000		4,000,000
Third Credit Facility | Term Loan | Other
Debt Instrument
Outstanding balance							$ 19,500,000				19,500,000		19,500,000
Repayments of lines of credit											1,200,000		2,600,000
Third Credit Facility | Revolving credit loan | Other
Debt Instrument
Draw down of debt and revolving line of credit											$ 400,000		$ 700,000

Debt - Schedule of the Change i

Debt - Schedule of the Change in Debt under the NSM Bank Facility (Details) £ in Millions, $ in Millions	Apr. 07, 2020USD ($)	Apr. 07, 2020GBP (£)	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)
Debt Instrument
Beginning balance					$ 376.4
Repayments					(105.9)	$ (2.7)
Ending balance			$ 710.4		710.4
Term Loan | NSM Bank Facility
Debt Instrument
Beginning balance					271.3
Ending balance			293.7		293.7
Specialty Insurance Distribution (NSM)
Debt Instrument
Beginning balance					272.6
Ending balance			295		295
Specialty Insurance Distribution (NSM) | NSM Bank Facility
Debt Instrument
Beginning balance			276.6	$ 273.4	277.4	221.3
Ending balance			300.4	275	300.4	275
Specialty Insurance Distribution (NSM) | Term Loan | NSM Bank Facility
Debt Instrument
Borrowings	$ 52.4	£ 42.5	0	0	0	52.4
Repayments			(0.7)	(0.7)	(2.1)	(1.3)
Foreign currency translation			(1.5)	2.3	(0.9)	2.6
Specialty Insurance Distribution (NSM) | Revolving credit loan | NSM Bank Facility
Debt Instrument
Borrowings			35	0	35	0
Repayments			$ (9)	$ 0	$ (9)	$ 0

Debt - Schedule of Weighted Ave

Debt - Schedule of Weighted Average Interest Rates (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Debt Instrument
Interest expense	$ 10.3	$ 7.8	$ 32.5	$ 21.2
Specialty Insurance Distribution (NSM)
Debt Instrument
Weighted Average			276.6	273.6
Interest expense			$ 17.3	$ 16.1
Weighted Average Interest rate	8.30%	7.80%	8.30%	7.80%
Specialty Insurance Distribution (NSM) | Term loan - hedged
Debt Instrument
Weighted Average			$ 147.1	$ 148.5
Interest expense			$ 10	$ 10
Weighted Average Interest rate	9.10%	9.00%	9.10%	9.00%
Specialty Insurance Distribution (NSM) | Term loan - unhedged
Debt Instrument
Weighted Average			$ 129.5	$ 125.1
Interest expense			$ 7.3	$ 6.1
Weighted Average Interest rate	7.50%	6.50%	7.50%	6.50%

Income Taxes (Details)

Income Taxes (Details)	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Income Tax Disclosure [Abstract]
Effective income tax rate reconciliation, percent	(6.00%)	30.70%	(12.40%)	33.70%

Derivatives - NSM Interest Rate

Derivatives - NSM Interest Rate Swap and Cap (Details)	Aug. 18, 2020	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Jun. 30, 2021USD ($)	Dec. 31, 2020USD ($)	Jun. 30, 2020USD ($)	Jun. 04, 2020USD ($)	Jun. 04, 2020GBP (£)	Apr. 07, 2020USD ($)	Apr. 06, 2020USD ($)	Dec. 31, 2019USD ($)	Jun. 15, 2018USD ($)
Derivative [Line Items]
Debt		$ 710,400,000		$ 710,400,000			$ 376,400,000
NSM Bank Facility | Term Loan
Derivative [Line Items]
Debt		293,700,000		293,700,000			271,300,000
Specialty Insurance Distribution (NSM)
Derivative [Line Items]
Debt		$ 295,000,000		$ 295,000,000			272,600,000
Weighted Average Interest rate		8.30%	7.80%	8.30%	7.80%
Specialty Insurance Distribution (NSM) | Term loan - hedged
Derivative [Line Items]
Weighted Average Interest rate		9.10%	9.00%	9.10%	9.00%
Specialty Insurance Distribution (NSM) | Interest Rate Swap
Derivative [Line Items]
Derivative, fixed interest rate														2.97%
Derivative, variable interest rate		1.00%		1.00%
Interest expense, net		$ 600,000	$ 600,000	$ 1,900,000	$ 1,900,000
Derivative, fair value, net		6,000,000		6,000,000			8,200,000
Change in fair value of derivative instruments		(600,000)	500,000	(2,200,000)	(2,300,000)
Specialty Insurance Distribution (NSM) | Interest Rate Cap
Derivative [Line Items]
Derivative, fair value, net		$ 100,000		100,000			100,000
Premiums paid				$ 100,000
GBP-LIBOR rate		0.08%		0.08%
Decrease in fair value of derivative		$ (100,000)		$ (100,000)
Specialty Insurance Distribution (NSM) | Interest Rate Cap | GBP-LIBOR
Derivative [Line Items]
Derivative, cap interest rate		1.25%		1.25%
Specialty Insurance Distribution (NSM) | NSM Bank Facility
Derivative [Line Items]
Total commitment under revolving credit facility											$ 291,400,000	$ 234,000,000
Debt		$ 300,400,000	$ 275,000,000	$ 300,400,000	$ 275,000,000	$ 276,600,000	$ 277,400,000	$ 273,400,000					$ 221,300,000
Specialty Insurance Distribution (NSM) | NSM Bank Facility | Interest Rate Swap | Term Loan
Derivative [Line Items]
Total commitment under revolving credit facility														$ 151,000,000
Specialty Insurance Distribution (NSM) | NSM Bank Facility | Interest Rate Swap | Term Loan | Term loan - hedged
Derivative [Line Items]
Debt		$ 146,500,000		$ 146,500,000
Specialty Insurance Distribution (NSM) | NSM Bank Facility | Interest Rate Cap
Derivative [Line Items]
Debt instrument, term extension	1 year
Specialty Insurance Distribution (NSM) | NSM Bank Facility | Interest Rate Cap | United Kingdom, Pounds
Derivative [Line Items]
Notional amount | £										£ 42,500,000
Specialty Insurance Distribution (NSM) | NSM Bank Facility | Interest Rate Cap | United States of America, Dollars
Derivative [Line Items]
Notional amount									$ 52,400,000

Municipal Bond Guarantee Insu_3

Municipal Bond Guarantee Insurance - Narrative (Details) - USD ($) $ in Millions	1 Months Ended			3 Months Ended		9 Months Ended
	Jan. 31, 2021	Dec. 31, 2020	Jan. 31, 2020	Mar. 31, 2021	Jun. 30, 2018	Sep. 30, 2021	Dec. 31, 2021	Jun. 30, 2020	Dec. 31, 2012	Jul. 31, 2012
Guarantor Obligations [Line Items]
Percentage of risk premium ceded						60.00%
Insurance-linked securities, term				12 years	12 years
Insurance-linked securities, callable term				5 years	5 years
Debt		$ 376.4				$ 710.4
HG Global
Guarantor Obligations [Line Items]
Collateral held in supplement trust		827.1				844.8
Collateral trusts, investments and cash		434.5				449.7
BAM
Guarantor Obligations [Line Items]
Surplus notes		388.2				388.2
Interest receivable		4.4				$ 6.9
HG Global
Guarantor Obligations [Line Items]
Surplus notes									$ 503	$ 503
Percentage of par value of policy reinsured						15.00%
Percent over a target trust balance						102.00%
Supplement trust target						$ 603
HG Global | Series A BAM Surplus Note
Guarantor Obligations [Line Items]
Surplus notes										$ 203
Assets Held-in-trust		604.3				$ 603.8
HG Global | BAM | Maximum
Guarantor Obligations [Line Items]
Aggregate losses on ceded business			$ 75
HG Re
Guarantor Obligations [Line Items]
Percentage of par value of policy reinsured						15.00%
Assets Held-in-trust		222.8				$ 241
BAM
Guarantor Obligations [Line Items]
Additional municipal bond guarantee								$ 36.9
Principal	$ 800	75,287.7				83,829
BAM | HG Global
Guarantor Obligations [Line Items]
Interest receivable		155.7				164.8
BAM | Surplus Note
Guarantor Obligations [Line Items]
Repayments of unsecured debt		30.1	65
Accrued interest payment on surplus notes		8.4	16.2
BAM | Surplus Note | HG Global
Guarantor Obligations [Line Items]
Debt		388.2				$ 388.2
BAM | Supplemental Trust
Guarantor Obligations [Line Items]
Repayments of unsecured debt		21.5	47.9
Accrued interest payment on surplus notes		$ 0.2	$ 0.9
BAM | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Basis spread on variable rate						3.00%
BAM | Fixed interest rate | Surplus Note
Guarantor Obligations [Line Items]
Derivative, fixed interest rate (as a percent)						8.00%
BAM | Forecast | US Treasury (UST) Interest Rate | Surplus Note
Guarantor Obligations [Line Items]
Effective percentage							3.10%
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	100.00%
BAM | Fidus Re Ltd. | 2018 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						36.00%
BAM | Fidus Re Ltd. | 2021 Covered Portfolio
Guarantor Obligations [Line Items]
Percentage of financial guaranty policies covered						40.00%
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				90.00%	90.00%

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, 2021USD ($)Contract	Dec. 31, 2020USD ($)Contract	Jan. 31, 2021USD ($)
Guarantor Obligations [Line Items]
Contracts outstanding | Contract	11,877	10,997
Remaining weighted average contract period outstanding (in years)	10 years 8 months 12 days	10 years 8 months 12 days
Principal	$ 83,829	$ 75,287.7	$ 800
Interest	39,528.4	36,448.8
Total debt service outstanding	123,357.4	111,736.5
Total gross unearned insurance premiums	$ 257	$ 237.5

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, 2021	Dec. 31, 2020
Guarantor Obligations [Line Items]
October 1, 2021 - December 31, 2021	$ 6.2
January 1, 2022 - March 31, 2022	6.1
April 1, 2022 - June 30, 2022	6.1
July 1, 2022 - September 30, 2022	6
October 1, 2022 - December 31, 2022	5.9
Total 2022	24.1
2023	22.8
2024	21.1
2025	19.6
2026	18.1
2027 and thereafter	145.1
Total gross unearned insurance premiums	$ 257	$ 237.5

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Earned premiums:
Gross earned premiums (1)	$ 220.1	$ 6.2	$ 455.4	$ 17.2
HG/BAM
Written premiums:
Direct	12.8	14.4	34.5	45.5
Assumed	0	0	4.5	0.1
Gross written premiums (1)	12.8	14.4	39	45.6
Earned premiums:
Direct	5.9	5.3	16.8	14.5
Assumed	0.8	0.9	2.8	2.7
Gross earned premiums (1)	$ 6.7	$ 6.2	$ 19.6	$ 17.2

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Basic and diluted earnings per share numerators (in millions):
Net (loss) income attributable to White Mountains’s common shareholders	$ (371.4)	$ 232.9	$ (308.2)	$ 219.5
Less: total income (loss) from discontinued operations, net of tax	0	0.7	(18.7)	0.8
Less: total income (loss) from continuing operations, net of tax	(371.4)	233.6	(326.9)	220.3
Allocation of losses (earnings) to participating restricted common shares	4.5	(3.2)	3.8	(2.9)
Basic and diluted (losses) earnings per share numerators	$ (366.9)	$ 230.4	$ (323.1)	$ 217.4
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Basic earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Diluted earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
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)	(120.18)	75.32	(106.48)	69.40
Basic and diluted (losses) earnings per share (in usd per share)	$ (120.18)	$ 75.32	$ (105.48)	$ 70.40

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Earnings Per Share [Abstract]
Net (losses) earnings attributable to White Mountains’s common shareholders, net of restricted common share amounts	$ (366.9)	$ 230.4	$ (323.1)	$ 217.4
Dividends declared net of restricted common share amounts	0	0	(3.1)	(3.1)
Total undistributed net (losses) earnings, net of restricted common share amounts	$ (366.9)	$ 230.4	$ (326.2)	$ 214.3

Employee Share-Based Incentiv_3

Employee Share-Based Incentive Compensation Plans - Narrative (Details) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021USD ($)shares	Sep. 30, 2020USD ($)shares	Sep. 30, 2021USD ($)shares	Sep. 30, 2020USD ($)shares	Jun. 30, 2021USD ($)	Dec. 31, 2020USD ($)	Jun. 30, 2020USD ($)	Dec. 31, 2019USD ($)
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	13,475	14,055
Additional compensation cost that would be recognized if all outstanding performance shares vested | $	$ 17.2		$ 17.2
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 | $	$ 19.4	$ 19.4	$ 19.4	$ 19.4	$ 23.2	$ 15.2	$ 23	$ 16.7
Issued (in shares) | shares	0	0	13,475	14,055

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
	Mar. 31, 2021	Mar. 31, 2020	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Target Performance Shares Outstanding
Beginning of period (in shares)			41,252	42,458	42,458	42,473
Shares paid (in shares)			(219)	0	(14,336)	(14,070)
New grants (in shares)			0	0	13,475	14,055
Forfeitures and cancellations (in shares)			(205)	0	(769)	0
Expense recognized (in shares)			0	0	0	0
End of period (in shares)			40,828	42,458	40,828	42,458
Accrued Expense
Beginning of period			$ 45.7	$ 15.8	$ 56.3	$ 43.7
Shares paid			(0.6)	0	(35.2)	(27.7)
New grants			0	0	0	0
Forfeitures and cancellations			0.2	(0.3)	0.4	0.1
Expense recognized			(6.5)	13.6	17.3	13
End of period			$ 38.8	$ 29.1	$ 38.8	$ 29.1
Performance Cycle 2018 to 2020
Accrued Expense
Percentage of target payout - minimum actual	200.00%
Performance Cycle 2017 to 2019
Accrued Expense
Percentage of target payout - minimum actual		174.00%
Percentage of target payout - maximum actual		180.00%

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, 2021	Jun. 30, 2021	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Dec. 31, 2019
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	41,450
Assumed forfeitures (in shares)	(622)
Total target performance shares outstanding (in shares)	40,828	41,252	42,458	42,458	42,458	42,473
Accrued Expense	$ 39.4
Assumed forfeitures	(0.6)
Total Accrued Expense	$ 38.8	$ 45.7	$ 56.3	$ 29.1	$ 15.8	$ 43.7
2019 – 2021
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	14,625
Accrued Expense	$ 24.4
2020 – 2022
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,350
Accrued Expense	$ 13.4
2021 – 2023
Share-based compensation arrangement by share-based payment award
Target performance shares outstanding (in shares)	13,475
Accrued Expense	$ 1.6

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Restricted Shares
Beginning of period (in shares)	38,280	43,105	43,105	43,395
Issued (in shares)	0	0	13,475	14,055
Vested (in shares)	(219)	0	(17,936)	(14,345)
Forfeited (in shares)	(211)	0	(794)	0
Expense recognized (in shares)	0	0	0	0
End of period (in shares)	37,850	43,105	37,850	43,105
Unamortized Issue Date Fair Value
Beginning of period	$ 23.2	$ 23	$ 15.2	$ 16.7
Issued	0	0	16.1	15.1
Vested	0	0	0	0
Forfeited	(0.2)	0	(0.8)	0
Expense recognized	(3.6)	(3.6)	(11.1)	(12.4)
End of period	$ 19.4	$ 19.4	$ 19.4	$ 19.4

Leases - Narrative (Details)

Leases - Narrative (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Leases [Abstract]
ROU lease asset	$ 42.9	$ 37.6
Operating lease liability	$ 45.9	$ 38.3

Leases - Schedule of Lease Cost

Leases - Schedule of Lease Cost (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Leases [Abstract]
Lease cost	$ 2.7	$ 1.6	$ 7.2	$ 5.7
Less: sublease income	0.1	0.1	0.3	0.3
Net lease cost	$ 2.6	$ 1.5	$ 6.9	$ 5.4

Leases - Schedule of Future Min

Leases - Schedule of Future Minimum Payments on Operating Leases (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Leases [Abstract]
Remainder of 2021	$ 2
2022	10.8
2023	9.8
2024	8.5
2025	6.7
Thereafter	16.4
Total undiscounted lease payments	54.2
Less: present value adjustment	8.3
Operating lease liability	$ 45.9	$ 38.3

Leases - Schedule of Right-of-U

Leases - Schedule of Right-of-Use Assets and Lease Liabilities (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Lessee, Lease, Description [Line Items]
ROU lease asset	$ 42.9	$ 37.6
Lease liability	$ 45.9	$ 38.3
Operating lease, weighted average incremental borrowing rate, percent	5.00%	4.60%
HG/BAM
Lessee, Lease, Description [Line Items]
ROU lease asset	$ 8	$ 10.1
Lease liability	8.6	10.1
Ark
Lessee, Lease, Description [Line Items]
ROU lease asset	7
Lease liability	7
NSM
Lessee, Lease, Description [Line Items]
ROU lease asset	13.8	17.1
Lease liability	15	17.1
Kudu
Lessee, Lease, Description [Line Items]
ROU lease asset	6.7	2
Lease liability	7.1	2
Other Operations
Lessee, Lease, Description [Line Items]
ROU lease asset	7.4	8.4
Lease liability	$ 8.2	$ 9.1

Non-controlling Interests (Deta

Non-controlling Interests (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 132.6	$ (88.1)
Total Non-Controlling Excluding Reciprocals
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 257.9	$ 35.2
HG Global
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	3.10%	3.10%
Total non-controlling interests	$ 10.1	$ 13.5
Ark
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	28.00%	0.00%
Total non-controlling interests	$ 216.1	$ 0
NSM
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	3.50%	3.40%
Total non-controlling interests	$ 16.5	$ 17
Kudu
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	0.70%	0.70%
Total non-controlling interests	$ 3.1	$ 2.3
Other
Noncontrolling Interest [Line Items]
Total non-controlling interests	$ 12.1	$ 2.4
BAM
Noncontrolling Interest [Line Items]
Noncontrolling equity percentage	100.00%	100.00%
Total non-controlling interests	$ (125.3)	$ (123.3)

Segment Information - Narrative

Segment Information - Narrative (Details)	9 Months Ended
	Sep. 30, 2021segment
Segment Reporting [Abstract]
Number of operating segments	5

Segment Information - Financial

Segment Information - Financial Information for White Mountain's Segments (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Segment Reporting Information [Line Items]
Earned insurance premiums	$ 220.1	$ 6.2	$ 455.4	$ 17.2
Net investment income	19.5	71.2	57.2	113.7
Net realized and unrealized investment (losses) gains	30.5	56.6	91.2	7.8
Commission revenues	69.4	60.3	201.6	180.3
Other revenues	47.2	15.2	114.9	45.9
Total revenues	(10.1)	459.5	594.8	659.9
Loss and loss adjustment expenses	129.2		247.8
Insurance and reinsurance acquisition expenses	56.7	1.6	130.9	5.4
Cost of sales	24	2.3	45.9	6.5
General and administrative expenses	100.8	103.4	357.9	267
Broker commission expenses	20.4	17.1	60.9	56.4
Change in fair value of contingent consideration	0.6	0.7	0.8	(1.6)
Amortization of other intangible assets	10.2	5.4	28.1	17.1
Loss on assets held for sale			28.7
Interest expense	10.3	7.8	32.5	21.2
Total expenses	352.2	138.3	933.5	372
Pre-tax (loss) income from continuing operations	(362.3)	321.2	(338.7)	287.9
Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	(396.8)	250	(325.5)	295
HG Global/ BAM
Segment Reporting Information [Line Items]
Earned insurance premiums	6.7	6.2	19.6	17.2
Net investment income	4.4	4.7	13.2	15.1
Net realized and unrealized investment (losses) gains	(4)	3.2	(15.6)	23.7
Commission revenues	0	0	0	0
Other revenues	0.3	0.4	0.9	2.1
Total revenues	7.4	14.5	18.1	58.1
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	3	1.6	6.5	5.4
Cost of sales	0	0	0	0
General and administrative expenses	12.4	14	42.7	41.4
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	0	0	0	0
Loss on assets held for sale			0
Interest expense	0	0	0	0
Total expenses	15.4	15.6	49.2	46.8
Pre-tax (loss) income from continuing operations	(8)	(1.1)	(31.1)	11.3
HG Global/ BAM | Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
Ark
Segment Reporting Information [Line Items]
Earned insurance premiums	213.4	0	435.8	0
Net investment income	0.6	0	1.8	0
Net realized and unrealized investment (losses) gains	0.3	0	10.3	0
Commission revenues	0		0
Other revenues	3.4	0	9.4	0
Total revenues	217.7	0	457.3	0
Loss and loss adjustment expenses	129.2	0	247.8	0
Insurance and reinsurance acquisition expenses	53.7	0	124.4	0
Cost of sales	0		0
General and administrative expenses	21.8	0	84.4	0
Broker commission expenses	0		0
Change in fair value of contingent consideration	0		0
Amortization of other intangible assets	0		0
Loss on assets held for sale			0
Interest expense	2.1	0	4.5	0
Total expenses	206.8	0	461.1	0
Pre-tax (loss) income from continuing operations	10.9		(3.8)
Ark | Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0		0
NSM
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0	0	0
Net investment income	0	0	0	0
Net realized and unrealized investment (losses) gains	0	0	0	0
Commission revenues	67	58.2	194.6	174.2
Other revenues	15.3	12.5	46.8	37.6
Total revenues	82.3	70.7	241.4	211.8
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	48.8	42.9	142.1	131
Broker commission expenses	20.4	17.1	60.9	56.4
Change in fair value of contingent consideration	0.6	0.7	0.8	(1.6)
Amortization of other intangible assets	8.2	5.1	25	16.2
Loss on assets held for sale	0	0	28.7	0
Interest expense	5.9	6.1	17.7	16.1
Total expenses	83.9	71.9	275.2	218.1
Pre-tax (loss) income from continuing operations	(1.6)	(1.2)	(33.8)	(6.3)
NSM | Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
Kudu
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0	0	0
Net investment income	9.5	6.4	26.1	19.3
Net realized and unrealized investment (losses) gains	18.9	9.8	62.5	1.5
Commission revenues	0	0	0	0
Other revenues	0.1	0.1	0.2	0.2
Total revenues	28.5	16.3	88.8	21
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	0	0	0	0
General and administrative expenses	3.3	2.2	9	7.5
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	0	0.1	0.2	0.3
Loss on assets held for sale			0
Interest expense	1.9	1.4	9.2	4.3
Total expenses	5.2	3.7	18.4	12.1
Pre-tax (loss) income from continuing operations	23.3	12.6	70.4	8.9
Kudu | Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	0	0	0	0
Other Operations
Segment Reporting Information [Line Items]
Earned insurance premiums	0	0	0	0
Net investment income	5	60.1	16.1	79.3
Net realized and unrealized investment (losses) gains	15.3	43.6	34	(17.4)
Commission revenues	2.4	2.1	7	6.1
Other revenues	28.1	2.2	57.6	6
Total revenues	(346)	358	(210.8)	369
Loss and loss adjustment expenses	0		0
Insurance and reinsurance acquisition expenses	0	0	0	0
Cost of sales	24	2.3	45.9	6.5
General and administrative expenses	14.5	44.3	79.7	87.1
Broker commission expenses	0	0	0	0
Change in fair value of contingent consideration	0	0	0	0
Amortization of other intangible assets	2	0.2	2.9	0.6
Loss on assets held for sale			0
Interest expense	0.4	0.3	1.1	0.8
Total expenses	40.9	47.1	129.6	95
Pre-tax (loss) income from continuing operations	(386.9)	310.9	(340.4)	274
Other Operations | Marketing Technology (MediaAlpha)
Segment Reporting Information [Line Items]
Net realized and unrealized investment (losses) gains from investment in MediaAlpha	$ (396.8)	$ 250	$ (325.5)	$ 295

Segment Information - Reconcili

Segment Information - Reconciliation of Revenue from Segments to Consolidated (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Segment Reporting Information [Line Items]
Revenues from contracts with customers	$ 112.9	$ 74.8	$ 305.9	$ 224.3
Other Revenue	(123)	384.7	288.9	435.6
Total revenues	(10.1)	459.5	594.8	659.9
HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Other Revenue	7.4	14.5	18.1	58.1
Total revenues	7.4	14.5	18.1	58.1
Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Other Revenue	217.7		457.3
Total revenues	217.7	0	457.3	0
NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	82.3	70.7	241.4	211.8
Other Revenue	0	0	0	0
Total revenues	82.3	70.7	241.4	211.8
Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Other Revenue	28.5	16.3	88.8	21
Total revenues	28.5	16.3	88.8	21
Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	30.6	4.1	64.5	12.5
Other Revenue	(376.6)	353.9	(275.3)	356.5
Total revenues	(346)	358	(210.8)	369
United Kingdom
Segment Reporting Information [Line Items]
Revenues from contracts with customers	13	13.9	39.9	36.3
United Kingdom | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
United Kingdom | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
United Kingdom | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	13	13.9	39.9	36.3
United Kingdom | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
United Kingdom | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Specialty Transportation (1)
Segment Reporting Information [Line Items]
Revenues from contracts with customers	25.7	21.9	73	66.1
Specialty Transportation (1) | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Specialty Transportation (1) | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Specialty Transportation (1) | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	25.7	21.9	73	66.1
Specialty Transportation (1) | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Specialty Transportation (1) | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Real Estate
Segment Reporting Information [Line Items]
Revenues from contracts with customers	6.2	6	25.2	32.7
Real Estate | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Real Estate | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Real Estate | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	6.2	6	25.2	32.7
Real Estate | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Real Estate | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Social Services
Segment Reporting Information [Line Items]
Revenues from contracts with customers	10.2	8.6	26.2	22.2
Social Services | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Social Services | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Social Services | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	10.2	8.6	26.2	22.2
Social Services | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Social Services | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Pet
Segment Reporting Information [Line Items]
Revenues from contracts with customers	19.9	14.7	55.6	39.8
Pet | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Pet | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Pet | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	19.9	14.7	55.6	39.8
Pet | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Pet | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Other
Segment Reporting Information [Line Items]
Revenues from contracts with customers	9.7	7.7	28.5	20.8
Other | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Other | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Other | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	7.3	5.6	21.5	14.7
Other | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Other | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	2.4	2.1	7	6.1
Total commission and other revenue
Segment Reporting Information [Line Items]
Revenues from contracts with customers	84.7	72.8	248.4	217.9
Total commission and other revenue | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Total commission and other revenue | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Total commission and other revenue | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	82.3	70.7	241.4	211.8
Total commission and other revenue | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Total commission and other revenue | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	2.4	2.1	7	6.1
Product and service revenues
Segment Reporting Information [Line Items]
Revenues from contracts with customers	28.2	2	57.5	6.4
Product and service revenues | HG Global/ BAM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Product and service revenues | Ark
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0		0
Product and service revenues | NSM
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Product and service revenues | Kudu
Segment Reporting Information [Line Items]
Revenues from contracts with customers	0	0	0	0
Product and service revenues | Other Operations
Segment Reporting Information [Line Items]
Revenues from contracts with customers	$ 28.2	$ 2	$ 57.5	$ 6.4

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, 2021	Dec. 31, 2020	May 07, 2020	May 06, 2020
Investments in unconsolidated affiliates
Other long-term investments	$ 1,285.5	$ 786.8
Kudu investments
Investments in unconsolidated affiliates
Other long-term investments	$ 604.7	$ 400.6
Kudu investments | Minimum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	3.20%	3.20%
Kudu investments | Maximum
Investments in unconsolidated affiliates
Ownership interest (as a percent)	32.70%	35.00%
Marketing Technology (MediaAlpha)
Investments in unconsolidated affiliates
Ownership interest (as a percent)	28.40%	35.00%
Other long-term investments	$ 316.4	$ 802.2
PassportCard/DavidShield
Investments in unconsolidated affiliates
Ownership interest (as a percent)	53.80%	53.80%	53.80%	50.00%
Other long-term investments	$ 105	$ 95
Elementum Holdings L.P.
Investments in unconsolidated affiliates
Ownership interest (as a percent)	29.70%	28.90%
Other long-term investments	$ 56.7	$ 55.1
Other
Investments in unconsolidated affiliates
Other long-term investments	95.6	132.2
Equity Method Investments
Investments in unconsolidated affiliates
Other long-term investments	$ 17.2	$ 15.2

Equity-Method Eligible Invest_4

Equity-Method Eligible Investments - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Equity Method Investee
Schedule of Equity Method Investments [Line Items]
Proceeds from dividends received	$ 13	$ 63.9	$ 37.7	$ 85.3

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, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Total assets	$ 7,113.6		$ 7,113.6		$ 4,831.4
Total liabilities	3,459.3		3,459.3		1,013.5
Total revenues	(10.1)	$ 459.5	594.8	$ 659.9
Net (loss) income	(371.4)	232.9	(308.2)	219.5
Marketing Technology (MediaAlpha)
Schedule of Equity Method Investments [Line Items]
Total assets	245.5		245.5		210.3
Total liabilities	318.4		318.4		$ 315.5
Total revenues	152.7	151.5	483.7	394.6
Total expenses	157	146.7	488.2	370.8
Net (loss) income	$ (4.3)	$ 4.8	$ (4.5)	$ 23.8

Fair Value of Financial Instr_3

Fair Value of Financial Instruments (Details) - USD ($) $ in Millions	Sep. 30, 2021	Dec. 31, 2020
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 710.4	$ 376.4
Other NSM debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	1.3	1.3
Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	195.6
Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	19.1
Fair Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	42	0
Fair Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Fair Value	163.1	0
Fair Value | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	300.6	279.3
Fair Value | Other NSM debt
Balance Sheet Grouping, Financial Statement Captions
Fair Value	1.3	1.3
Fair Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	218.2	0
Fair Value | Kudu Bank Facility
Balance Sheet Grouping, Financial Statement Captions
Fair Value	0	89.3
Fair Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Fair Value	20.5	18.8
Carrying Value | Ark 2007 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	43.9	0
Carrying Value | Ark 2021 Notes
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	156.8	0
Carrying Value | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	293.7	271.3
Carrying Value | Other NSM debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	1.3	1.3
Carrying Value | Kudu Credit Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	195.6	0
Carrying Value | Kudu Bank Facility
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	0	86.3
Carrying Value | Other Operations debt
Balance Sheet Grouping, Financial Statement Captions
Carrying Value	$ 19.1	$ 17.5

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions	3 Months Ended			9 Months Ended
	Sep. 30, 2021	Mar. 31, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Loss Contingencies [Line Items]
Net gain from sale of discontinued operations, net of tax	$ 0		$ (0.7)	$ 18.7	$ (0.8)
Sirius Group | Discontinued Operations
Loss Contingencies [Line Items]
Net gain from sale of discontinued operations, net of tax		$ 17.6

Held for Sale and Discontinue_3

Held for Sale and Discontinued Operations - Narrative (Details) £ in Millions, $ in Millions	Apr. 12, 2021USD ($)	Apr. 12, 2021GBP (£)	Sep. 30, 2021USD ($)	Mar. 31, 2021USD ($)	Sep. 30, 2020USD ($)	Sep. 30, 2021USD ($)	Sep. 30, 2020USD ($)	Dec. 31, 2020USD ($)
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Net gain from sale of discontinued operations, net of tax			$ 0		$ (0.7)	$ 18.7	$ (0.8)
Loss on sale				$ 28.7
Discontinued Operations, Disposed of by Sale | Sirius Group
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Liability related to sale								$ 18.7
Net gain from sale of discontinued operations, net of tax						17.6
Disposal Group, Disposed of by Sale, Not Discontinued Operations | Fresh Insurance Services Group Limited
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Proceeds from sale of business	$ 1.5	£ 1.1
Disposal Group, Held-for-sale, Not Discontinued Operations | Fresh Insurance Services Group Limited
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Loss on sale				$ 28.7
Foreign Currency Gain (Loss) | 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 from sale of discontinued operations, net of tax						$ 1.1

Held for Sale and Discontinue_4

Held for Sale and Discontinued Operations - Earnings Per Share for Discontinued Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020
Basic and diluted earnings per share numerators (in millions):
Net (loss) income	$ (371.4)	$ 232.9	$ (308.2)	$ 219.5
Less: total income (loss) from continuing operations, net of tax	(371.4)	233.6	(326.9)	220.3
Net (loss) gain from discontinued operations attributable to White Mountains’s common shareholders	0	(0.7)	18.7	(0.8)
Allocation of earnings to participating restricted common shares	4.5	(3.2)	3.8	(2.9)
Basic and diluted (losses) earnings per share numerators	$ (366.9)	$ 230.4	$ (323.1)	$ 217.4
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Basic earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Diluted earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
Basic and diluted (losses) earnings per share (in usd per share)	$ (120.18)	$ 75.32	$ (105.48)	$ 70.40
Discontinued Operations
Basic and diluted earnings per share numerators (in millions):
Net (loss) income	$ (371.4)	$ 232.9	$ (308.2)	$ 219.5
Less: total income (loss) from continuing operations, net of tax	(371.4)	233.6	(326.9)	220.3
Net (loss) gain from discontinued operations attributable to White Mountains’s common shareholders	0	(0.7)	18.7	(0.8)
Allocation of earnings to participating restricted common shares	0	0	(0.2)	0
Basic and diluted (losses) earnings per share numerators	$ 0	$ (0.7)	$ 18.5	$ (0.8)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Basic earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)	3,090,300	3,101,800	3,099,400	3,129,000
Average unvested restricted common shares (in shares)	(37,800)	(43,100)	(36,000)	(40,000)
Diluted earnings (losses) per share denominator (in shares)	3,052,500	3,058,700	3,063,400	3,089,000
Basic and diluted (losses) earnings per share (in usd per share)	$ 0	$ (0.23)	$ 6.03	$ (0.26)