White Mountains Insurance (WTM) 10-K 26 Feb 21 2020 FY Annual report Financial data

Cover Page

Cover Page - USD ($)	12 Months Ended
	Dec. 31, 2020	Feb. 24, 2021	Jun. 30, 2020
Cover [Abstract]
Document Type	10-K
Document Annual Report	true
Document Period End Date	Dec. 31, 2020
Current Fiscal Year End Date	--12-31
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 Well-known Seasoned Issuer	Yes
Entity Voluntary Filers	No
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
ICFR Auditor Attestation Flag	true
Entity Shell Company	false
Entity Public Float			$ 2,685,847,299
Entity Common Stock, Shares Outstanding (in shares)		3,095,829
Documents Incorporated by Reference	Portions of the Registrant’s Definitive Proxy Statement to be filed with the Securities and Exchange Commission (“SEC”) pursuant to Regulation 14A under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), relating to the Registrant’s Annual General Meeting of Members scheduled to be held May 27, 2021 are incorporated by reference into Part III of this Form 10-K. With the exception of the portions of the Proxy Statement specifically incorporated herein by reference, the Proxy Statement is not deemed to be filed as part of this Form 10-K.
Entity Central Index Key	0000776867
Amendment Flag	false
Document Fiscal Year Focus	2020
Document Fiscal Period Focus	FY

CONSOLIDATED BALANCE SHEETS

CONSOLIDATED BALANCE SHEETS - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Investments [Abstract]
Other long-term investments	$ 786.8
Total investments	2,939.1	$ 2,947.2
Goodwill and other intangible assets	782.4	656.7
Total assets	4,831.4	3,983.2
Liabilities
Debt	376.4	283.5
Total liabilities	1,013.5	838.5
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 3,102,011 and 3,185,353 shares	3.1	3.2
Paid-in surplus	592.1	593.1
Retained earnings	3,311.2	2,672.4
Accumulated other comprehensive loss, after-tax:
Net unrealized losses from foreign currency translation and interest rate swap	(0.4)	(7.2)
Total White Mountains’s common shareholders’ equity	3,906	3,261.5
Non-controlling interests	(88.1)	(116.8)
Total equity	3,817.9	3,144.7
Total liabilities and equity	4,831.4	3,983.2
HG Global-BAM
Investments [Abstract]
Fixed maturity investments, at fair value	859.5	799.3
Short-term investments, at fair value	60.4	46.3
Total investments	919.9	845.6
Cash	42.8	24.2
Insurance premiums receivable	6.9	6.7
Deferred acquisition costs	27.8	22.1
Accrued investment income	5	5.4
Accounts receivable on unsettled investment sales	0	3.9
Other assets	15.4	16.1
Total assets	1,017.8	924
Liabilities
Unearned insurance premiums	237.5	198.4
Accrued incentive compensation	25.7	21.7
Other liabilities	28.3	26.7
Total liabilities	291.5	246.8
NSM
Investments [Abstract]
Cash	126.5	89.7
Premium and commission receivable	76.7	70.8
Goodwill and other intangible assets	736.8	623
Other assets	59.6	41.7
Total assets	999.6	825.2
Liabilities
Debt	272.6	219.2
Premiums payable	113.4	102.3
Contingent consideration earnout liabilities	14.6	20.6
Other liabilities	91.2	59
Total liabilities	491.8	401.1
Kudu
Investments [Abstract]
Short-term investments, at fair value	0.1	0.1
Other long-term investments	400.6	266.5
Total investments	400.7	266.6
Cash	7.8	5.8
Accrued investment income	9.8	5.8
Goodwill and other intangible assets	9.2	9.6
Other assets	2.7	2.7
Total assets	430.2	290.5
Liabilities
Debt	86.3	53.6
Other liabilities	10	3.4
Total liabilities	96.3	57
Other Operations
Investments [Abstract]
Fixed maturity investments, at fair value	347.7	406.5
Short-term investments, at fair value	82.4	154.8
Investment in MediaAlpha, at fair value	802.2	180
Common equity securities, at fair value	0	683.9
Other long-term investments	386.2	409.8
Total investments	1,618.5	1,835
Cash	34.1	41.3
Cash pre-funded/placed in escrow for Ark Transaction	646.3	0
Accrued investment income	2.4	5.7
Accounts receivable on unsettled investment sales	3.4	5.1
Goodwill and other intangible assets	36.4	22.1
Other assets	40.4	31.3
Assets held for sale	2.3	3
Total assets	2,383.8	1,943.5
Liabilities
Debt	17.5	10.7
Accrued incentive compensation	70.1	55.1
Other liabilities	46.3	67.8
Total liabilities	$ 133.9	$ 133.6

CONSOLIDATED BALANCE SHEETS (Pa

CONSOLIDATED BALANCE SHEETS (Parenthetical) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Cash restricted	$ 78.4	$ 56.3
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)	3,102,011	3,185,353
Common shares, outstanding shares (in shares)	3,102,011	3,185,353
NSM
Cash restricted	$ 78.4	$ 56.3

CONSOLIDATED STATEMENTS OF OPER

CONSOLIDATED STATEMENTS OF OPERATIONS - USD ($) $ in Millions	3 Months Ended								10 Months Ended	12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Revenues:
Earned insurance premiums										$ 22.8	$ 16.3	$ 13.9
Net investment income										131	79.7	59
Net realized and unrealized investment gains (losses)										30.8	253.2	(108.3)
Net realized and unrealized investment gains from MediaAlpha										716.8	433.2	(108.3)
Realized gain from the 2019 MediaAlpha Transaction											67.5
Commission revenues										240.8	249.1	389.2
Other revenues										69.3	47.6	15.3
Total revenues	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6		1,180.7	893.4	369.1
Expenses:
Insurance acquisition expenses										7	5.7	5.3
Other underwriting expenses										0.4	0.4	0.4
Cost of sales										11.3	48.1	248.7
General and administrative expenses										387	327.8	233.5
Broker commission expense										75.3	64.8	28.4
Change in fair value of contingent consideration earnout liabilities										(3.3)	2.1	2.7
Amortization of other intangible assets										28.3	21.8	18.8
Interest expense										29.5	17.6	9.5
Total expenses	163.5	138.3	126.9	106.8	118.8	104.4	113.2	151.9		535.5	488.3	547.3
Pre-tax income (loss) from continuing operations	357.3	321.2	132.7	(166)	56.5	51.1	15.8	281.7		645.2	405.1	(178.2)
Income tax benefit (expense)	117.6	(98.5)	(24.1)	25.5	(10.4)	(8.8)	0.1	(10.2)		20.5	(29.3)	4
Net income (loss) from continuing operations	474.9	222.7	108.6	(140.5)	46.1	42.3	15.9	271.5		665.7	375.8	(174.2)
(Loss) gain from sale of Sirius Group, net of tax										(2.3)	0.8	(17.2)
Net income (loss)										663.4	376.6	(191.4)
Net loss attributable to non-controlling interests	15.8	10.9	7.8	10.8	15.6	5.5	4.6	12.2		45.3	37.9	50.2
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4		708.7	414.5	(141.2)
MediaAlpha
Revenues:
Net investment income										95	14.8	3.7
Net realized and unrealized investment gains from MediaAlpha										686	180	0
Total revenues									$ 359.2
Kudu
Revenues:
Earned insurance premiums										0	0
Net investment income										29.5	14.7	0
Net realized and unrealized investment gains (losses)										15.9	6.3	0
Realized gain from the 2019 MediaAlpha Transaction
Commission revenues										0	0
Other revenues										0.3	0.2	0
Total revenues										45.7	21.2	0
Expenses:
Insurance acquisition expenses										0	0
Other underwriting expenses										0	0
Cost of sales										0	0
General and administrative expenses										11.8	10.1	0
Broker commission expense										0	0
Change in fair value of contingent consideration earnout liabilities										0	0
Amortization of other intangible assets										0.3	0.2	0
Interest expense										6	0.1	0
Total expenses										18.1	10.4	0
Pre-tax income (loss) from continuing operations										27.6	10.8
Kudu | MediaAlpha
Revenues:
Net realized and unrealized investment gains from MediaAlpha										0	0
HG Global-BAM
Revenues:
Earned insurance premiums										22.8	16.3	13.9
Net investment income										19.5	21.6	16.7
Net realized and unrealized investment gains (losses)										23.7	27.1	(7.5)
Realized gain from the 2019 MediaAlpha Transaction											0
Commission revenues										0	0	0
Other revenues										2.5	1.6	1.2
Total revenues										68.5	66.6	24.3
Expenses:
Insurance acquisition expenses										7	5.7	5.3
Other underwriting expenses										0.4	0.4	0.4
Cost of sales										0	0	0
General and administrative expenses										56.4	50.5	48
Broker commission expense										0	0	0
Change in fair value of contingent consideration earnout liabilities										0	0	0
Amortization of other intangible assets										0	0	0
Interest expense										0	0	0
Total expenses										63.8	56.6	53.7
Pre-tax income (loss) from continuing operations										4.7	10	(29.4)
HG Global-BAM | MediaAlpha
Revenues:
Net realized and unrealized investment gains from MediaAlpha										0	0
NSM
Revenues:
Earned insurance premiums										0	0	0
Net investment income										0	0	0
Net realized and unrealized investment gains (losses)										0	0	0
Realized gain from the 2019 MediaAlpha Transaction											0
Commission revenues										232.5	193.4	89.6
Other revenues										52.6	39.7	12
Total revenues										285.1	233.1	101.6
Expenses:
Insurance acquisition expenses										0	0	0
Other underwriting expenses										0	0	0
Cost of sales										0	0	0
General and administrative expenses										176.9	132.2	59.4
Broker commission expense										75.3	64.8	28.4
Change in fair value of contingent consideration earnout liabilities										(3.3)	2.1	2.7
Amortization of other intangible assets										26.7	19.4	8.3
Interest expense										22.1	16.7	8
Total expenses										297.7	235.2	106.8
Pre-tax income (loss) from continuing operations										(12.6)	(2.1)	(5.2)
NSM | MediaAlpha
Revenues:
Net realized and unrealized investment gains from MediaAlpha										0	0
Other Operations
Revenues:
Earned insurance premiums										0	0	0
Net investment income										82	43.4	42.3
Net realized and unrealized investment gains (losses)										(8.8)	219.8	(100.8)
Net realized and unrealized investment gains from MediaAlpha												0
Realized gain from the 2019 MediaAlpha Transaction										0	67.5	0
Commission revenues										8.3	6.9	4.1
Other revenues										13.9	6.1	0.5
Total revenues										781.4	523.7	(53.9)
Expenses:
Insurance acquisition expenses										0	0	0
Other underwriting expenses										0	0	0
Cost of sales										11.3	7.5	3.7
General and administrative expenses										141.9	122.5	94.4
Broker commission expense										0	0	0
Change in fair value of contingent consideration earnout liabilities										0	0	0
Amortization of other intangible assets										1.3	0.6	0.2
Interest expense										1.4	0.6	0.3
Total expenses										155.9	131.2	98.6
Pre-tax income (loss) from continuing operations										625.5	392.5	(152.5)
Other Operations | MediaAlpha
Revenues:
Net realized and unrealized investment gains from MediaAlpha										686	180
MediaAlpha
Revenues:
Earned insurance premiums											0	0
Net investment income											0	0
Net realized and unrealized investment gains (losses)											0	0
Realized gain from the 2019 MediaAlpha Transaction											0
Commission revenues										0	48.8	295.5
Other revenues										0	0	1.6
Total revenues										0	48.8	297.1
Expenses:
Insurance acquisition expenses											0	0
Other underwriting expenses											0	0
Cost of sales										0	40.6	245
General and administrative expenses										0	12.5	31.7
Broker commission expense											0	0
Change in fair value of contingent consideration earnout liabilities											0	0
Amortization of other intangible assets										0	1.6	10.3
Interest expense										0	0.2	1.2
Total expenses										$ 0	54.9	288.2
Pre-tax income (loss) from continuing operations											(6.1)	$ 8.9
MediaAlpha | MediaAlpha
Revenues:
Net realized and unrealized investment gains from MediaAlpha											$ 0

CONSOLIDATED STATEMENTS OF COMP

CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Statement of Comprehensive Income [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders	$ 708.7	$ 414.5	$ (141.2)
Other comprehensive income (loss), net of tax	7.3	(1.4)	(4.8)
Comprehensive income (loss)	716	413.1	(146)
Comprehensive (income) loss attributable to non-controlling interests	(0.5)	0	0.3
Comprehensive income (loss) attributable to White Mountains’s common shareholders	$ 715.5	$ 413.1	$ (145.7)
Basic earnings (loss) per share
Continuing operations (usd per share)	$ 227.72	$ 130.02	$ (36.67)
Discontinued operations (usd per share)	(0.75)	0.25	(5.09)
Total consolidated operations (usd per share)	226.97	130.27	(41.76)
Diluted earnings (loss) per share
Continuing operations (usd per share)	227.72	130.02	(36.67)
Discontinued operations (usd per share)	(0.75)	0.25	(5.09)
Total consolidated operations (usd per share)	226.97	130.27	(41.76)
Dividends declared and paid per White Mountains’s common share (usd per share)	$ 1	$ 1	$ 1

CONSOLIDATED STATEMENTS OF CHAN

CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY - USD ($) $ in Millions	Total	Common Shares and Paid-in Surplus	Retained Earnings	AOCL, After-tax	Total	Non-controlling Interests	Total Equity
Beginning balance at Dec. 31, 2017		$ 670.6	$ 2,823.2	$ (1.3)	$ 3,492.5	$ (131.7)	$ 3,360.8
Increase (Decrease) in Shareholders' Equity
Net income (loss)	$ (191.4)		(141.2)		(141.2)	(50.2)	(191.4)
Net change in foreign currency translation and interest rate swap				(4.5)	(4.5)	(0.3)	(4.8)
Comprehensive income (loss)			(141.2)	(4.5)	(145.7)	(50.5)	(196.2)
Dividends declared on common shares			(3.8)		(3.8)		(3.8)
Dividends to non-controlling interests						(8)	(8)
Issuances of common shares		2			2		2
Repurchases and retirements of common shares	(519.1)	(105.8)	(413.3)		(519.1)	0	(519.1)
Capital contributions from BAM members, net of tax						45	45
Amortization of restricted share awards		13			13	0	13
Recognition of compensation costs for equity-based units of subsidiary		7.4			7.4	4.3	11.7
Dilution from equity units of subsidiary		(1.5)			(1.5)	1.5	0
Acquisition of non-controlling interests						14.5	14.5
Acquisition of subsidiary		(1.7)			(1.7)		(1.7)
Ending balance at Dec. 31, 2018		584	2,264.9	(5.8)	2,843.1	(124.9)	2,718.2
Increase (Decrease) in Shareholders' Equity
Net income (loss)	376.6		414.5		414.5	(37.9)	376.6
Net change in foreign currency translation and interest rate swap				(1.4)	(1.4)	0	(1.4)
Comprehensive income (loss)			414.5	(1.4)	413.1	(37.9)	375.2
Dividends declared on common shares			(3.2)		(3.2)		(3.2)
Dividends to non-controlling interests						(2)	(2)
Issuances of common shares		2.2			2.2		2.2
Repurchases and retirements of common shares	(4.9)	(1.1)	(3.8)		(4.9)		(4.9)
Capital contributions from BAM members, net of tax						57.6	57.6
Amortization of restricted share awards		10.6			10.6		10.6
Recognition of compensation costs for equity-based units of subsidiary		1.5			1.5		1.5
Net contributions from other non-controlling interests		(0.9)			(0.9)	2.4	1.5
Acquisition of non-controlling interests						1.8	1.8
Deconsolidation of non-controlling interests associated with the MediaAlpha Transaction						(13.8)	(13.8)
Ending balance at Dec. 31, 2019	3,144.7	596.3	2,672.4	(7.2)	3,261.5	(116.8)	3,144.7
Increase (Decrease) in Shareholders' Equity
Net income (loss)	663.4		708.7		708.7	(45.3)	663.4
Net change in foreign currency translation and interest rate swap				6.8	6.8	0.5	7.3
Comprehensive income (loss)			708.7	6.8	715.5	(44.8)	670.7
Dividends declared on common shares			(3.2)		(3.2)		(3.2)
Dividends to non-controlling interests						(2.1)	(2.1)
Issuances of common shares		1.5			1.5		1.5
Repurchases and retirements of common shares	(85.1)	(18.5)	(66.7)		(85.2)		(85.2)
Capital contributions from BAM members, net of tax						68.9	68.9
Amortization of restricted share awards		16.6			16.6		16.6
Recognition of compensation costs for equity-based units of subsidiary		2.3			2.3	0.1	2.4
Net contributions from other non-controlling interests		(3)			(3)	5.3	2.3
Acquisition of non-controlling interests						1.3	1.3
Ending balance at Dec. 31, 2020	$ 3,817.9	$ 595.2	$ 3,311.2	$ (0.4)	$ 3,906	$ (88.1)	$ 3,817.9

CONSOLIDATED STATEMENTS OF CASH

CONSOLIDATED STATEMENTS OF CASH FLOWS - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cash flows from operations:
Net income (loss)	$ 663.4	$ 376.6	$ (191.4)
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment (gains) losses	(716.8)	(433.2)	108.3
Realized gain from the 2019 MediaAlpha Transaction	0	(67.5)	0
Amortization of restricted share awards	16.6	10.5	13
Amortization and depreciation	43.4	29.8	25.7
Deferred income tax (benefit) expense	(36.2)	24.8	(8.4)
Net loss (gain) from sale of discontinued operations, net of tax	2.3	(0.8)	17.2
Other operating items:
Net change in premiums and commissions receivable	(3.1)	(26.8)	(9.6)
Net change in premiums payable	1.8	25.1	21.3
Net change in unearned insurance premiums	39.1	35.8	39.2
Net change in deferred acquisition costs	(5.8)	(3.1)	(4.2)
Net change in restricted cash	22.1	6.3	(3.4)
Investments in asset management firms - Kudu	(118.3)	(118.4)	0
Net change in other assets and liabilities, net	30.9	20.4	(38.8)
Net cash used for operations	(60.6)	(120.5)	(31.1)
Cash flows from investing activities:
Net change in short-term investments	58.7	21.9	(39)
Sales of fixed maturity investments	390	334.3	1,848.5
Maturities, calls and paydowns of fixed maturity investments	180.4	119.3	141
Sales of common equity securities	787.9	467.2	169.9
Distributions and redemptions of other long-term investments and settlements of forward contracts	69.9	29.4	5
Purchases of other long-term investments	(76.8)	(177.7)	(95.9)
Purchases of common equity securities	(33.8)	(29.8)	(328.3)
Purchases of fixed maturity and convertible investments	(537.7)	(539.2)	(970.2)
Purchases of consolidated subsidiaries, net of cash acquired of $13.4, $12.8, and $90.9 and including restricted cash of $8.4, $0.0, $53.4	(127.3)	(258)	(295.2)
Cash pre-funded/placed in escrow for Ark Transaction	(646.3)	0	0
Other investing activities, net	(0.4)	(27.3)	23.4
Net cash provided from (used for) investing activities	64.6	(59.9)	459.2
Cash flows from financing activities:
Draw down of debt and revolving lines of credit	84.6	206.4	84.1
Repayment of debt and revolving lines of credit	(4.5)	(22.9)	(15.4)
Cash dividends paid to the Company’s common shareholders	(3.2)	(3.2)	(3.8)
Acquisitions of additional shares from non-controlling interest	0	0	(1.7)
Common shares repurchased	(78.5)	0	(511.9)
Repurchase of shares from non-controlling interest shareholders	(0.5)	(21.1)	0
Proceeds from issuance of shares to non-controlling interest shareholders	0	62.7	0
Capital contributions from non-controlling interest shareholders	2.4	1.9	1.3
Distributions to non-controlling interest shareholders	(0.7)	(28.1)	(6)
Payments to contingent considerations related to purchases of consolidated subsidiaries	(7)	(7.6)	(2.6)
Capital contributions from BAM members	68.9	54.6	53.8
Fidus Re premium payments	(3)	(3)	(3.7)
Other financing activities, net	(9.5)	(9.2)	(8.4)
Net cash provided from (used for) financing activities	49	230.5	(414.3)
Effect of exchange rate changes on cash	(2.8)	0.6	(0.6)
Net change in cash during the period - continuing operations, including the effect of exchange rate changes	50.2	50.7	13.2
Cash balance at beginning of year	161	110.3	97.1
Cash balance at end of year	211.2	161	110.3
MediaAlpha
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment (gains) losses	(686)	(180)	0
White Mountains
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment (gains) losses	$ (30.8)	$ (253.2)	$ 108.3

CONSOLIDATED STATEMENTS OF CA_2

CONSOLIDATED STATEMENTS OF CASH FLOWS (Parenthetical) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cash acquired	$ 13.4	$ 12.8	$ 90.9
Restricted cash acquired	8.4	0	53.4
Cash restricted	$ 78.4	$ 56.3	$ 50

Basis of Presentation and Signi

Basis of Presentation and Significant Accounting Policies	12 Months Ended
	Dec. 31, 2020
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 insurance 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 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. See Note 16 — “Variable Interest Entities” . Intercompany transactions have been eliminated in consolidation. Certain amounts in the prior period financial statements have been reclassified to conform to the current presentation. 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. 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 December 31, 2020, White Mountains’s reportable segments were HG Global/BAM, NSM, Kudu and Other Operations. On February 26, 2019, MediaAlpha completed the sale of a significant minority stake to Insignia Capital Group in connection with a recapitalization and cash distribution to existing equityholders (the “2019 MediaAlpha Transaction”). MediaAlpha also repurchased a portion of the holdings of existing equityholders. White Mountains deconsolidated MediaAlpha as a result of the 2019 MediaAlpha Transaction, and consequently it was no longer a reportable segment. White Mountains’s consolidated statement of comprehensive income and its segment disclosures include MediaAlpha’s results of operations through the date of the 2019 MediaAlpha Transaction. See Note 2 — “ Significant Transactions ” and Note 14 — “ Segment Information ”. The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. 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, (the “BAM Surplus Notes”). As of December 31, 2020 and 2019, 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 attributed to non-controlling interests. 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 profitability of the insurance that it places. NSM does not take insurance risk. As of December 31, 2020 and 2019, White Mountains owned 96.6% and 96.4% of the basic units outstanding of NSM (89.6% and 88.4% on a fully diluted, fully converted basis). NSM was acquired by White Mountains in 2018. See Note 2 — “Significant Transactions ". The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”), a capital solutions provider for asset management firms. 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, typically tied to gross revenues and designed to generate immediate strong, stable cash yields. On April 4, 2019, White Mountains acquired the ownership interests in Kudu held by certain funds managed by Oaktree Capital Management, L.P. (“Oaktree”) for cash consideration of $81.4 million. In addition, White Mountains assumed all of Oaktree’s unfunded capital commitments to Kudu, increasing White Mountains’s total capital commitment to $250.0 million (the “Kudu Transaction”). As a result of the Kudu Transaction, White Mountains’s basic unit ownership of Kudu increased from 49.5% to 99.1% (42.7% to 85.4% on a fully diluted, fully converted basis), and White Mountains began consolidating Kudu in its financial statements during the second quarter of 2019. See Note 2 — “Significant Transactions ". 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 (for periods after the 2019 MediaAlpha Transaction), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/ DavidShield”), Elementum Holdings LP (“Elementum”), Kudu (for periods prior to the Kudu Transaction), certain other consolidated and unconsolidated entities and certain other assets. The MediaAlpha segment consisted of QL Holdings LLC and its wholly-owned subsidiary QuoteLab, LLC (collectively “MediaAlpha”). MediaAlpha is a marketing technology company. It operates a transparent and efficient customer acquisition technology platform that facilitates real-time transactions between buyers and sellers of consumer referrals (i.e., clicks, calls and leads), primarily in the property & casualty, health and life insurance verticals. MediaAlpha generates revenue by earning a fee for each consumer referral sold on its platform. A transaction becomes payable only on a qualifying consumer action, and is not contingent on the sale of a product to the consumer. MediaAlpha’s core verticals are property & casualty insurance, health insurance and life insurance. White Mountains deconsolidated MediaAlpha as a result of the 2019 MediaAlpha Transaction and stopped reporting it as a segment. Subsequent to the 2019 MediaAlpha Transaction, White Mountains’s non-c ontrolling equity interest in MediaAlpha was accounted for at fair value within other long-term investments. On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3,609,894 shares and received total proceeds of $63.8 million. Following the completion of the MediaAlpha IPO, White Mountains owns 20,532,202 MediaAlpha shares, representing a 35.0% ownership interest (32.3% on a fully-diluted, fully converted basis). Subsequent to the MediaAlpha IPO, White Mountains’s non-controlling equity interest in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock. As of December 31, 2020, White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet within the Other Operations segment. For comparability purposes, the amounts related to MediaAlpha in 2019 subsequent to the 2019 MediaAlpha Transaction have been reclassified from other long-term investments to investment in MediaAlpha. Discontinued Operations and Assets and Liabilities Held for Sale White Mountains has classified its Guilford, Connecticut property, which consists of an office building that was sold in August of 2020, and adjacent land as held for sale as of December 31, 2020 and 2019. The property has been measured at its estimated fair value, net of disposal costs. As of December 31, 2020, assets held for sale also includes a corporate aircraft. The aircraft has been measured at its carrying value of $1.7 million, which is lower than its estimated fair value. See Note 19 — “Held for Sale and Discontinued Operations” . Significant Accounting Policies 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. Cash balances that are not immediately available for general corporate purposes, including fiduciary accounts held by NSM on behalf of insurance carriers, are classified as restricted. Short-Term Investments Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year. Short-term investments are carried at amortized or accreted cost, which approximated fair value as of December 31, 2020 and 2019. Investment Securities As of December 31, 2020 and 2019, White Mountains’s invested assets consisted of securities and other investments held for general investment purposes. White Mountains’s portfolio of fixed maturity investments, investment in MediaAlpha, common equity securities and other long-term investments held for general investment purposes are generally classified as trading securities and are reported at fair value as of the balance sheet date. Changes in net unrealized investment gains (losses) are reported pre-tax in revenues. Realized investment gains (losses) are accounted for using the specific identification method and are reported pre-tax in revenues. Premiums and discounts on all fixed maturity investments are amortized and accreted to income over the anticipated life of the investment. White Mountains’s invested assets that are measured at fair value include fixed maturity investments, its investment in MediaAlpha, common equity securities and other long-term investments, that consists primarily of unconsolidated entities, including non-controlling equity interests in the form of revenue and earnings participation contracts (“Kudu’s Participation Contracts”), private equity funds, hedge funds, insurance-linked securities (“ILS”) funds and private debt instruments. Whenever possible, White Mountains estimates fair value using valuation methods that maximize the use of quoted prices and other observable inputs. Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants (an exit price) at a particular measurement date. 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 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”). Assets and liabilities carried at fair value include substantially all of White Mountains’s investment portfolio, and derivative instruments, both exchange-traded and over the counter instruments. Valuation of assets and liabilities measured at fair value require management to make estimates and apply judgment to matters that may carry a significant degree of uncertainty. In determining fair value estimates, White Mountains uses a variety of valuation approaches and inputs. Whenever possible, White Mountains estimates fair value using valuation methods that maximize the use of quoted market prices or other observable inputs. Where appropriate, assets and liabilities measured at fair value have been adjusted for the effect of counterparty credit risk. White Mountains uses outside pricing services and brokers to assist in determining fair values. The outside pricing services White Mountains uses have indicated that they will only provide prices where observable inputs are available. As of December 31, 2020, approximately 73% of the investment portfolio recorded at fair value was priced based upon quoted market prices or other observable inputs. Level 1 Measurements Investments valued using Level 1 inputs include White Mountains’s investment in MediaAlpha subsequent to the MediaAlpha IPO, common equity securities and fixed maturity investments, primarily investments in U.S. Treasuries and short-term investments, which include U.S. Treasury Bills. For investments in active markets, White Mountains uses the quoted market prices provided by outside pricing services to determine fair value. Level 2 Measurements Investments valued using Level 2 inputs include fixed maturity investments which have been disaggregated into classes, including debt securities issued by corporations, municipal obligations and mortgage and asset-backed securities. Investments valued using Level 2 inputs also include certain passive exchange traded funds (“ETFs”) that track U.S. stock indices such as the S&P 500 Index, but are traded on foreign exchanges, which White Mountains values using the fund manager’s published net asset value per share (“NAV”) to account for the difference in market close times. In circumstances where quoted market prices are unavailable or are not considered reasonable, White Mountains estimates the fair value using industry standard pricing methodologies and observable inputs such as benchmark yields, reported trades, broker-dealer quotes, issuer spreads, benchmark securities, bids, offers, credit ratings, prepayment speeds, reference data including research publications and other relevant inputs. Given that many fixed maturity investments do not trade on a daily basis, the outside pricing services evaluate a wide range of fixed maturity investments by regularly drawing parallels from recent trades and quotes of comparable securities with similar features. The characteristics used to identify comparable fixed maturity investments vary by asset type and take into account market convention. White Mountains’s process to assess the reasonableness of the market prices obtained from the outside pricing sources covers substantially all of its fixed maturity investments and includes, but is not limited to, the evaluation of pricing methodologies and a review of the pricing services’ quality control procedures on at least an annual basis, a comparison of its invested asset prices obtained from alternate independent pricing vendors on at least a semi-annual basis, monthly analytical reviews of certain prices and a review of the underlying assumptions utilized by the pricing services for select measurements on an ad hoc basis throughout the year. White Mountains also performs back-testing of selected investment sales activity to determine whether there are any significant differences between the market price used to value the security prior to sale and the actual sale price of the security on an ad-hoc basis throughout the year. Prices provided by the pricing services that vary by more than $0.5 million and 5% from the expected price based on these assessment procedures are considered outliers, as are prices that have not changed from period to period and prices that have trended unusually compared to market conditions. In circumstances where the results of White Mountains’s review process does not appear to support the market price provided by the pricing services, White Mountains challenges the vendor provided price. If White Mountains cannot gain satisfactory evidence to support the challenged price, White Mountains will rely upon its own internal pricing methodologies to estimate the fair value of the security in question. The valuation process described above is generally applicable to all of White Mountains’s fixed maturity investments. The techniques and inputs specific to asset classes within White Mountains’s fixed maturity investments for Level 2 securities that use observable inputs are as follows: Debt Securities Issued by Corporations: The fair value of debt securities issued by corporations is determined from a pricing evaluation technique that uses information from market sources and integrates relative credit information, observed market movements, and sector news. Key inputs include benchmark yields, reported trades, broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including sector, coupon, credit quality ratings, duration, credit enhancements, early redemption features and market research publications. Municipal Obligations: The fair value of municipal obligations is determined from a pricing evaluation technique that uses information from market makers, brokers-dealers, buy-side firms, and analysts along with general market information. Key inputs include benchmark yields, reported trades, issuer financial statements, material event notices and new issue data, as well as broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including type, coupon, credit quality ratings, duration, credit enhancements, geographic location and market research publications. Mortgage and Asset-Backed Securities: The fair value of mortgage and asset-backed securities is determined from a pricing evaluation technique that uses information from market sources and leveraging similar securities. Key inputs include benchmark yields, reported trades, underlying tranche cash flow data, collateral performance, plus new issue data, as well as broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including issuer, vintage, loan type, collateral attributes, prepayment speeds, default rates, recovery rates, cash flow stress testing, credit quality ratings and market research publications. Level 3 Measurements Fair value estimates for investments that trade infrequently and have few or no quoted market prices or other observable inputs are classified as Level 3 measurements. Investments valued using Level 3 fair value estimates are based upon unobservable inputs and include investments in certain fixed maturity investments, common equity securities and other long-term investments where quoted market prices or other observable inputs are unavailable or are not considered reliable or reasonable. Level 3 valuations are generated from techniques that use assumptions not observable in the market. These unobservable inputs reflect White Mountains’s assumptions of what market participants would use in valuing the investment. In certain circumstances, investment securities may start out as Level 3 when they are originally issued, but as observable inputs become available in the market, they may be reclassified to Level 2. Transfers of securities between levels are based on investments held as of the beginning of the period. Other Long-Term Investments As of December 31, 2020, White Mountains owned a portfolio of other long-term investments valued at $786.8 million, that consisted primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, the Elementum managed ILS funds (the “ILS Funds”) and private debt instruments. As of December 31, 2020, $614.2 million of White Mountains’s other long-term investments, that consisted primarily of unconsolidated entities, including Kudu’s Participation Contracts and private debt instruments were classified as Level 3 investments in the GAAP fair value hierarchy, were not actively traded in public markets and did not have readily observable market prices. The determination of the fair value of these securities involves significant management judgment, and the use of valuation models and assumptions that are inherently subjective and uncertain. As of December 31, 2020, $172.6 million of White Mountains’s other long-term investments, consisting of private equity funds and the ILS Funds, were valued at fair value using NAV as a practical expedient. Investments for which fair value is measured at NAV using the practical expedient are not classified within the fair value hierarchy. White Mountains may use a variety of valuation techniques to determine fair value depending on the nature of the investment, including a discounted cash flow analysis, market multiple approach, cost approach and/or liquidation analysis. On an ongoing basis, White Mountains also considers qualitative changes in facts and circumstances, which may impact the valuation of unconsolidated entities, including economic and market changes in relevant industries, changes to the entity’s capital structure, business strategy and key personnel, and any recent transactions relating to the unconsolidated entity. On a quarterly basis, White Mountains evaluates the most recent qualitative and quantitative information of the business and completes a fair valuation analysis for all Level 3 other long-term investments. Periodically, and at least on an annual basis, White Mountains uses a third-party valuation firm to complete an independent valuation analysis of significant unconsolidated entities. Other Long-term Investments - NAV White Mountains’s portfolio of other long-term investments includes investments in private equity funds, hedge funds and the ILS Funds. White Mountains employs a number of procedures to assess the reasonableness of the fair value measurements for its private equity funds, hedge funds and the ILS Funds, including obtaining and reviewing periodic and audited annual financial statements as well as discussing each fund’s pricing with the fund manager throughout the year. However, since the fund managers do not provide sufficient information to evaluate the pricing methods and inputs for each underlying investment, White Mountains considers the inputs to be unobservable. The fair value of White Mountains’s private equity fund, hedge fund and ILS fund investments are generally determined using the fund manager’s NAV. In the event that White Mountains believes the fair value of a private equity fund, hedge fund or ILS fund differs from the NAV reported by the fund manager due to illiquidity or other factors, White Mountains will adjust the reported NAV to more appropriately represent the fair value of its investment in the private equity fund, hedge fund or ILS fund. 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 its 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 December 31, 2020, White Mountains holds interest rate cap derivative instruments that do not meet the criteria for hedge accounting. As of December 31, 2020 and 2019, White Mountains holds an interest rate swap derivative instrument that meets the criteria for hedge accounting. See Note 7 — “Derivatives” . Receivables BAM’s receivables consist primarily of premiums receivable from customers for municipal bond insurance policies. NSM’s receivables consist of insurance premiums receivable from customers and commissions receivable from insurance carriers, net of a provision for amounts estimated to be uncollectible. Incentive Compensation 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. Non-share-based awards are recognized over the related service periods based on management’s best estimate of the amounts at which the awards are expected to be paid. Share-based compensation which is typically settled in cash, such as performance shares, is classified as a liability-type award. The compensation cost for liability-classified awards is measured initially at the grant date fair value and remeasured each reporting period until settlement. The compensation cost for equity-classified awards expected to be settled in shares, such as options and restricted shares, is measured at the original grant date fair value of the award. The compensation cost for all awards is recognized for the vested portion of the awards over the related service periods. See Note 10 — “Employee Share-Based Incentive Compensation Plans”. 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 trade names, URL and online names, customer relationships and contracts, information technology platforms and insurance licenses. Goodwill and other intangible assets with indefinite lives are not amortized, but rather are evaluated for impairment on an annual basis, or whenever indications of potential impairment exist. In the absence of any indications of potential impairment, the evaluation of goodwill and indefinite-lived intangible assets is performed no later than the interim period in which the anniversary of the acquisition date falls. White Mountains initially evaluates goodwill using a qualitative approach (step zero) to determine whether it is more likely than not that the implied fair value of goodwill is greater than its carrying value. If the results of the qualitative evaluation indicate that it is more likely than not that the carrying value of goodwill exceeds its implied fair value, White Mountains performs the two-step quantitative test for impairment. Other intangible assets with finite lives are measured at their acquisition date fair values, are amortized over their economic lives and presented net of accumulated amortization on the balance sheet. Other intangible assets with finite lives are reviewed for impairment when events occur or there are changes in circumstances indicating that their carrying value may exceed fair value. Impairment exists when the carrying value of other intangible assets exceeds fair value. Municipal Bond Guarantee Insurance All of the contracts issued by BAM are accounted for as insurance contracts under ASC 944-605, Financial Guarantee Insurance Contracts. Premiums are generally received upfront and an unearned premium revenue liability, equal to the amount of the premium received, is established at contract inception. Installment premiums are measured at the present value of contractual premiums, discounted at the risk-free rate, which is set at the inception of the insurance contract. Premium revenues are recognized in revenue over the period of the contracts in proportion to the amount of insurance protection provided using a constant rate. The constant rate is calculated based on the relationship between the par outstanding in a given reporting period compared with the sum of each of the par amounts outstanding for all periods. Deferred acquisition costs represent commissions, premium taxes, excise taxes and other costs which are directly attributable to and vary with the production of business. These costs are deferred and amortized to the extent they relate to successful contract acquisitions over the applicable premium recognition period as acquisition expenses. Deferred acquisition costs are limited to the amount expected to be recovered from future earned premiums and anticipated investment income. BAM’s obligation for outstanding contracts consists of the unearned premium reserve and any loss reserves. Loss reserves are recorded only to the extent that the present value of the expected amount of any losses to be paid, net of any expected recoveries, exceeds the associated unearned premium reserve. As of December 31, 2020 and 2019, BAM did not have any loss or loss adjustment expense reserves. Revenue Recognition NSM’s revenues consist primarily of commissions and broker revenues for placement of insurance policies and administrative fees for claims and other services provided to insurance carriers. Commission and broker revenues and service fees are measured based on the contractual rates with insurance carriers, net of any amounts expected to be uncollectible and any amounts associated with expected policy cancellations, adjustments, and are recognized when contractual performance obligations have been fulfilled. NSM’s primary contractual performance obligations are generally satisfied upon the issuance of an insurance policy by the carrier. Where NSM has significant performance obligations beyond the policy issuance date, NSM estimates the relative standalone selling price for the post-issuance services in order to allocate the transaction price using the price charged for the service when sold separately in similar circumstances to similar customers. Deferred revenues associated with unsatisfied performance obligations are recognized within other liabilities. Contingent commissions are based upon the overall profit and/or volume of the business placed with the insurance carrier during a calendar year and are determined after the contractual period has ended. NSM recognizes revenue on contingent commissions when management has determined that it is probable that the contingent commission requirements have been

Significant Transactions

Significant Transactions	12 Months Ended
	Dec. 31, 2020
Significant Transactions [Abstract]
Significant Transactions	Significant Transactions MediaAlpha On February 26, 2019, MediaAlpha completed the 2019 MediaAlpha Transaction. White Mountains received net cash proceeds of $89.3 million from the transaction. White Mountains recognized a realized gain of $67.5 million and reduced its ownership interest to 48.3% of the basic units outstanding of MediaAlpha (42.0% on a fully diluted, fully converted basis) as a result of the 2019 MediaAlpha Transaction. White Mountains’s remaining ownership interest in MediaAlpha no longer met the criteria for a controlling ownership interest and, accordingly, White Mountains deconsolidated MediaAlpha on February 26, 2019. White Mountains’s consolidated statement of operations and comprehensive income and its segment disclosures include MediaAlpha’s results of operations for the period from January 1, 2019 through February 26, 2019. Upon deconsolidation, White Mountains’s investment in MediaAlpha met the criteria to be accounted for under the equity method or under the fair value option. See Note 15 — “Equity-Method Eligible Investments” . White Mountains elected the fair value option and the investment in MediaAlpha was initially measured at its estimated fair value of $114.7 million as of the transaction date, with the change in fair value of $114.7 million recognized as an unrealized investment gain. White Mountains recognized a total of $182.2 million of realized gain and unrealized investment gain on the 2019 MediaAlpha Transaction. On October 30, 2020, MediaAlpha completed the MediaAlpha IPO. In the offering, White Mountains sold 3,609,894 shares 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. Following the MediaAlpha IPO, White Mountains owns 20,532,202 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 value of White Mountains’s remaining investment in MediaAlpha was $802.2 million. See Note 15 — “Equity-Method Eligible Investments” Ark O n October 1, 2020, White Mountains entered into a subscription and purchase agreement (the “Ark SPA”) with Ark Insurance Holdings Limited (“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 Acquisition Agreement, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and to purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020 White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a credit facility agreement and $366.3 million placed in escrow, which is reflected on the balance sheet within the Other Operations segment as of December 31, 2020. On January 1, 2021, White Mountains closed the transaction in accordance with the terms of the Ark SPA. At closing, 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). If the additional $200.0 million is contributed in full, White Mountains will own 77.1% of Ark on a basic shares outstanding basis (67.5% on a fully-diluted, fully-converted basis). Management’s equity incentives are subject to an 8.0% rate of return threshold with no catch-up. 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. These additional shares are generally eligible to vest in three equal tranches at multiple on invested capital (“MOIC”) thresholds of 2.0x, 2.5x and 3.0x. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. Ark writes a diversified and balanced portfolio of reinsurance and insurance, including property, accident & health, energy, marine and political risks, through Lloyd’s Syndicates 4020 and 3902. Beginning in January 2021, Ark began writing certain classes of its business through Group Ark Insurance Limited, Ark’s wholly-owned Bermuda-based insurance and reinsurance company. See Note 20 — “Subsequent Events” . Elementum On May 31, 2019, White Mountains acquired a 30.0% limited partnership interest in Elementum, a third-party registered investment adviser specializing in natural catastrophe ILS, for $55.1 million (the “Elementum Transaction”). Elementum manages separate accounts and pooled investment vehicles across various ILS sectors, including catastrophe bonds, collateralized reinsurance investments and industry loss warranties, on behalf of third-party clients. As part of the Elementum Transaction, White Mountains also invested $50.0 million in the ILS Funds. White Mountains has elected the fair value option for its investment in Elementum and the ILS Funds. Both the investment in Elementum and the investments in the ILS Funds are included within other long-term investments. NSM On May 11, 2018, White Mountains acquired a 95.0% basic unit ownership interest in NSM (83.6% on a fully diluted, fully converted basis). White Mountains funded the acquisition through a combination of cash on hand and new borrowings by NSM. White Mountains paid $274.2 million of cash consideration for its equity interest in NSM, and NSM borrowed $100.0 million in new debt as part of the transaction. During the third quarter of 2018, White Mountains recorded a purchase price adjustment of an additional $2.1 million of consideration, which was paid in the fourth quarter of 2018. White Mountains recognized total assets acquired related to NSM of $495.2 million, including $383.0 million of goodwill and other intangible assets, total liabilities assumed of $204.6 million, including contingent consideration earnout liabilities related to NSM’s previous acquisitions of its U.K.-based operations, of $10.2 million, and non-controlling interest of $14.4 million reflecting acquisition date fair values. In connection with the acquisition, White Mountains incurred transaction costs of $6.3 million in the Other Operations segment, which were expensed in 2018. On May 18, 2018, NSM acquired 100% of Fresh Insurance Services Group Limited (“Fresh Insurance”). Fresh Insurance 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. During 2020, Fresh Insurance was rebranded as part of Kingfisher UK Holdings Ltd. NSM borrowed $51.0 million to fund the transaction. During the twelve months ended December 31, 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, ending in February 2020 and February 2022. No purchase price adjustment was made related to the earnout period that ended in February 2020. NSM recognized total assets acquired related to Fresh Insurance of $72.6 million, including $54.6 million of goodwill and other intangible assets, and total liabilities assumed of $22.3 million, reflecting acquisition date fair values. In connection with the acquisition, NSM recorded a contingent consideration earnout liability of $7.5 million. 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 and NSM borrowed $30.1 million to fund the transaction. White Mountains recognized $59.4 million of goodwill and other intangible assets, reflecting acquisition date fair values, for which the relative fair values of goodwill and other intangible assets had not yet been finalized as of December 31, 2018. During 2019, NSM determined that the relative values of goodwill and other intangible assets recorded in connection with the KBK transaction were $32.6 million and $32.7 million, reflecting acquisition date fair values. The purchase price is subject to additional adjustments based upon growth in EBITDA during three earn out periods ending in December 2019, December 2020 and December 2021. During 2019, NSM recorded a purchase price adjustment of $5.9 million relating to the fair value of the contingent consideration earnout liability in connection with the acquisition. During 2020, NSM paid $6.4 million related to the first KBK earnout period. On April 1, 2019, NSM acquired 100% of Embrace Pet Insurance (“Embrace”), a nationwide provider of pet health insurance for dogs and cats. NSM paid $71.5 million of cash consideration, net of cash acquired, for Embrace. White Mountains contributed $58.2 million to NSM and NSM borrowed $20.4 million to fund the transaction. White Mountains recognized $52.2 million of goodwill and $15.4 million of other intangible assets, reflecting acquisition date fair values. On June 28, 2019, NSM acquired the renewal rights on its U.S. collector car business (the “Renewal Rights”) from American International Group, Inc. (“AIG”) for $82.5 million. The acquisition satisfied NSM’s obligation to acquire the Renewal Rights from AIG. See Note 18 — “Commitments and Contingencies” . White Mountains contributed $59.1 million to NSM and NSM borrowed $22.5 million to fund the transaction. White Mountains recognized $82.5 million of other intangible assets, reflecting the acquisition date fair value. See Note 4 — “Goodwill and Other Intangible Assets” . 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 (approximately $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 (approximately $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 earnout of $4.1 million. During 2020, NSM recognized pre-tax income of $4.1 million for the change in fair value of the Kingsbridge contingent consideration earnout liability and a foreign currency translation unrealized gain of $0.3 million. As of December 31, 2020, the Kingsbridge contingent consideration earnout liability was $0.3 million. The contingent consideration earnout liabilities related to the Fresh Insurance, KBK and Kingsbridge acquisitions are subject to adjustments based upon EBITDA, EBITDA projections, and present value factors for acquired entities. For the year ended December 31, 2020 and 2019, NSM recognized pre-tax (revenue) expense of $(3.3) million and $2.1 million for the change in the fair value of its contingent consideration earnout liabilities. Any future adjustments to contingent consideration earnout liabilities under the agreements will be recognized through pre-tax income. As of December 31, 2020 and 2019, NSM recognized total contingent consideration earnout liabilities of $14.6 million and $20.6 million. During 2020, NSM paid $7.0 million of contingent consideration earnout liabilities related to KBK and the U.K. vertical. During 2019, NSM paid $7.6 million of contingent consideration earnout liabilities related to the U.K. vertical. PassportCard/DavidShield On January 24, 2018, White Mountains acquired a 50% 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% 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% 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 loss in PassportCard and DavidShield is limited to the amount invested Kudu On February 5, 2018, White Mountains entered into an agreement to fund up to $125.0 million in Kudu in exchange for a 49.5% basic unit ownership interest in Kudu (42.7% on a fully diluted, fully converted basis). On April 4, 2019, White Mountains acquired the ownership interests in Kudu held by certain funds managed by Oaktree for cash consideration of $81.4 million. In addition, White Mountains assumed all of Oaktree’s unfunded capital commitments to Kudu, increasing White Mountains’s total capital commitment to $250.0 million. White Mountains recognized total assets acquired of $155.5 million, including $7.6 million of goodwill and $2.2 million of other intangible assets, total liabilities assumed of $0.8 million and non-controlling interest of $1.5 million. As a result of the Kudu Transaction, White Mountains’s basic unit ownership of Kudu increased from 49.5% to 99.1% (42.7% to 85.4% on a fully diluted, fully converted basis), and White Mountains began consolidating Kudu as a reportable segment in its financial statements during the second quarter of 2019. White Mountains’s consolidated financial statements and its segment disclosures include Kudu’s results for the period from April 4, 2019 to December 31, 2019. For periods prior to the Kudu Transaction, White Mountains determined that Kudu was a VIE, but White Mountains was not the primary beneficiary. In those periods, White Mountains elected to use the fair value option. During the fourth quarter of 2019, White Mountains increased its total capital commitment to Kudu by $100.0 million to $350.0 million of which $47.5 million and $129.0 million is undrawn as of December 31, 2020 and 2019. Also during the fourth quarter of 2019, Kudu obtained a committed $124.0 million credit facility, of which $34.8 million and $68.0 million was undrawn as of December 31, 2020 and 2019. See Note 5 — “Debt” .

Investment Securities

Investment Securities	12 Months Ended
	Dec. 31, 2020
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, its investment in MediaAlpha, common equity securities and other long-term investments, which are classified as trading securities. Trading securities are reported at fair value as of the balance sheet date. Net realized and unrealized investment gains (losses) on trading securities are reported in pre-tax revenues. White Mountains’s fixed maturity investments are generally valued using industry standard pricing methodologies. Key inputs include benchmark yields, benchmark securities, reported trades, issuer spreads, bids, offers, credit ratings and prepayment speeds. Income on mortgage and asset-backed securities is recognized using an effective yield based on anticipated prepayments and the estimated economic life of the securities. When actual prepayments differ significantly from anticipated prepayments, the estimated economic life is recalculated and the remaining unamortized premium or discount is amortized prospectively over the remaining economic life. Realized investment gains (losses) resulting from sales of investment securities are accounted for using the specific identification method. Premiums and discounts on all fixed maturity investments are amortized or accreted to income over the anticipated life of the investment. Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year. Short-term investments are carried at amortized or accreted cost, which approximated fair value as of December 31, 2020 and 2019. Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, hedge funds, the ILS Funds and private debt instruments. Net Investment Income White Mountains’s net investment income is comprised primarily of interest income associated with White Mountains’s fixed maturity investments and short-term investments, distributions from its investment in MediaAlpha, dividend income from common equity securities and distributions from other long-term investments. The following table presents pre-tax net investment income for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Fixed maturity investments $ 29.0 $ 32.4 $ 35.1 Short-term investments 1.1 5.0 8.0 Investment in MediaAlpha (1) 59.9 8.0 — Common equity securities 6.6 13.5 15.1 Other long-term investments 35.6 22.1 3.8 Total investment income 132.2 81.0 62.0 Third-party investment expenses (1.2) (1.3) (3.0) Net investment income $ 131.0 $ 79.7 $ 59.0 (1) For 2018, MediaAlpha was a majority-owned consolidated subsidiary of White Mountains. See Note 2 — “Significant Transactions” Net Realized and Unrealized Investment Gains (Losses) The following table presents net realized and unrealized investment gains (losses) for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Fixed maturity investments $ 38.5 $ 43.5 $ (34.7) Short-term investments .4 .2 (.8) Investment in MediaAlpha (1) 686.0 180.0 — Common equity securities 6.5 195.7 (98.9) Other long-term investments (2) (14.6) 13.8 26.1 Net realized and unrealized investment gains (losses) 716.8 433.2 (108.3) Less: net gains (losses) on investment securities sold 20.2 24.6 (33.0) Net realized and unrealized investment gains (losses) on investment securities held at the end of the period $ 696.6 $ 408.6 $ (75.3) (1) For 2018, MediaAlpha was a majority-owned consolidated subsidiary of White Mountains. See Note 2 — “Significant Transactions” (2) For 2020, 2019 and 2018, includes $4.0, $(0.3) and $(0.8) of realized and unrealized investment gains (losses) related to foreign currency exchange. For the years ended December 31, 2020, 2019 and 2018, all of White Mountains’s net realized and unrealized investment gains (losses) were recorded in the consolidated statements of operations. There were no investment gains (losses) recorded in other comprehensive income. White Mountains recognized gross realized investment gains of $214.4 million, $104.0 million and $49.4 million and gross realized investment losses of $27.3 million, $7.4 million and $62.3 million on sales of investment securities for the years ending December 31, 2020, 2019 and 2018. The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the years ended December 31, 2020, 2019 and 2018 for investments still held at the end of the period: Year Ended December 31, Millions 2020 2019 2018 Other long-term investments (1) $ 276.0 $ 181.9 $ 22.6 Total net unrealized investment gains, pre-tax - Level 3 investments $ 276.0 $ 181.9 $ 22.6 (1) For 2020 and 2019, includes $278.7 and $180.0 of unrealized investment gains from White Mountains’s investment in MediaAlpha. Proceeds from the sales and maturities of investments, excluding short-term investments, totaled $1.4 billion, $1.0 billion and $2.2 billion for the years ended December 31, 2020, 2019 and 2018. 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 December 31, 2020 and 2019. 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 December 31, 2019 Millions Cost or Gross Gross Carrying U.S. Government and agency obligations $ 231.7 $ 1.0 $ (.2) $ 232.5 Debt securities issued by corporations 454.9 12.5 (.2) 467.2 Municipal obligations 284.7 12.5 (.1) 297.1 Mortgage and asset-backed securities 206.6 2.7 (.3) 209.0 Total fixed maturity investments $ 1,177.9 $ 28.7 $ (.8) $ 1,205.8 The weighted average duration of White Mountains’s fixed income portfolio was approximately 3.2 years, including short-term investments, and approximately 3.6 years, excluding short-term investments, as of December 31, 2020. The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of December 31, 2020. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties. December 31, 2020 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 126.0 $ 127.0 Due after one year through five years 417.5 433.6 Due after five years through ten years 283.2 303.2 Due after ten years 113.3 124.9 Mortgage and asset-backed securities 211.7 218.5 Total $ 1,151.7 $ 1,207.2 The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency losses, and carrying values of White Mountains’s investment in MediaAlpha, common equity securities and other long-term investments as of December 31, 2020 and 2019: December 31, 2020 Millions Cost or Gross Unrealized Gross Unrealized Net Foreign Carrying Investment in MediaAlpha $ — $ 802.2 $ — $ — $ 802.2 Common equity securities $ — $ — $ — $ — $ — Other long-term investments $ 767.4 $ 95.8 $ (78.1) $ 1.7 $ 786.8 December 31, 2019 Millions Cost or Gross Unrealized Gross Unrealized Net Foreign Carrying Investment in MediaAlpha $ — $ 180.0 $ — $ — $ 180.0 Common equity securities $ 553.3 $ 130.6 $ — $ — $ 683.9 Other long-term investments $ 667.4 $ 75.2 $ (64.1) $ (2.2) $ 676.3 Fair Value Measurements as of December 31, 2020 Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (“observable inputs”) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (“unobservable inputs”). Quoted prices in active markets for identical assets or liabilities have the highest priority (“Level 1”), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (“Level 2”) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (“Level 3”). As of December 31, 2020 and 2019, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 73% and 71% of the investment portfolio. See Note 1 — “Basis of Presentation and Significant Accounting Policies”. Fair Value Measurements by Level The following tables present White Mountains’s fair value measurements for investments as of December 31, 2020 and 2019 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations and common equity securities by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated these asset classes into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate and S&P 500 indices. 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 (1) 142.9 142.9 — — Investment in MediaAlpha 802.2 802.2 — — Other long-term investments 614.2 — — 614.2 Other long-term investments — NAV (2) 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) Short-term investments are measured at amortized cost, which approximates fair value. (2) Consists of private equity funds and the ILS Funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2019 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 232.5 $ 232.5 $ — $ — Debt securities issued by corporations: Financials 144.8 — 144.8 — Industrial 59.0 — 59.0 — Healthcare 52.6 — 52.6 — Consumer 50.9 — 50.9 — Energy 44.9 — 44.9 — Technology 41.2 — 41.2 — Communications 31.3 — 31.3 — Utilities 25.0 — 25.0 — Materials 17.5 — 17.5 — Total debt securities issued by corporations 467.2 — 467.2 — Municipal obligations 297.1 — 297.1 — Mortgage and asset-backed securities 209.0 — 209.0 — Total fixed maturity investments 1,205.8 232.5 973.3 — Short-term investments (1) 201.2 189.4 11.8 — Investment in MediaAlpha 180.0 — — 180.0 Common equity securities: Exchange traded funds (2) 536.4 521.6 14.8 — Other (3) 147.5 25.9 121.5 .1 Total common equity securities 683.9 547.5 136.3 .1 Other long-term investments 474.0 — — 474.0 Other long-term investments — NAV (4) 202.3 — — — Total other long-term investments 676.3 — — 474.0 Total investments $ 2,947.2 $ 969.4 $ 1,121.4 $ 654.1 (1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement. (3) Primarily consists of two investments in unit trusts that predominantly invest in international equities and an open-end mutual fund that invests in domestic large-cap companies. (4) Consists of private equity funds, one hedge fund and the ILS Funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. Investments Held on Deposit or as Collateral As of December 31, 2020 and 2019, investments of $432.4 million and $319.9 million, were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM. White Mountains’s insurance subsidiaries are required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent state deposits and are included within the investment portfolio, totaled $11.9 million and $9.9 million as of December 31, 2020 and 2019. Debt Securities Issued by Corporations The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2020 and 2019: Fair Value at December 31, Millions 2020 2019 AAA $ 10.6 $ 9.5 AA 57.9 73.9 A 318.3 288.5 BBB 159.6 95.3 BB 1.0 — Debt securities issued by corporations (1) $ 547.4 $ 467.2 (1) Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc. Mortgage and Asset-backed Securities The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 88.7 $ 88.7 $ — $ 88.6 $ 88.6 $ — FHLMC 70.1 70.1 — 60.5 60.5 — GNMA 40.6 40.6 — 30.8 30.8 — Total agency (1) 199.4 199.4 — 179.9 179.9 — Total mortgage-backed securities 199.4 199.4 — 179.9 179.9 — Other asset-backed securities: Credit card receivables 11.3 11.3 — 14.0 14.0 — Vehicle receivables 7.8 7.8 — 15.1 15.1 — Total other asset-backed securities 19.1 19.1 — 29.1 29.1 — Total mortgage and asset-backed securities $ 218.5 $ 218.5 $ — $ 209.0 $ 209.0 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC). Investment in MediaAlpha On February 26, 2019, in connection with the 2019 MediaAlpha Transaction, MediaAlpha was deconsolidated and was subsequently accounted for at fair value within other long-term investments. On October 30, 2020, MediaAlpha completed the MediaAlpha IPO. In the offering, White Mountains sold 3,609,894 shares and received total proceeds of $63.8 million. Following the MediaAlpha IPO, White Mountains owns 20,532,202 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 value of White Mountains’s remaining investment in MediaAlpha was $802.2 million. 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. For comparability purposes, the amounts related to MediaAlpha in 2019 subsequent to the 2019 MediaAlpha Transaction have been reclassified from other long-term investments to the investment in MediaAlpha. Other Long-Term Investments The following table presents the carrying values of White Mountains’s other long-term investments as of December 31, 2020 and 2019: Carrying Value at Millions December 31, 2020 December 31, 2019 Kudu’s Participation Contracts $ 400.6 $ 266.5 PassportCard/DavidShield 95.0 90.0 Elementum Holdings L.P. 55.1 55.1 Other unconsolidated entities (1) 42.4 33.7 Total unconsolidated entities (2) 593.1 445.3 Private equity funds and hedge funds 121.2 161.1 Insurance-linked securities funds 51.4 41.2 Private debt investments (2) (3) 21.1 28.7 Total other long-term investments $ 786.8 $ 676.3 (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. (2) See Fair Value Measurements by Level table. (3) Includes $5.8 and $5.0 in private debt investments carried at fair value as of December 31. 2020 and amortized cost as of December 31, 2019. Private Equity Funds and Hedge Funds White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the net asset value (“NAV”) of the funds. As of December 31, 2020, White Mountains held investments in fourteen private equity funds. The largest investment in a single private equity fund or hedge fund was $29.1 million as of December 31, 2020 and $54.6 million as of December 31, 2019. In the first quarter of 2020, White Mountains redeemed its sole hedge fund having a fair value of $45.6 million. The bulk of the redemption proceeds, subject to customary audit holdbacks, were received in April 2020 and the remaining balance is expected to be received in April 2021. The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 69.1 $ 15.3 $ 33.8 $ 23.3 Manufacturing/Industrial 28.6 — 57.7 4.1 Financial services 23.5 30.4 15.0 22.8 Total private equity funds 121.2 45.7 106.5 50.2 Hedge funds Long/short banks and financial — — 54.6 — Total hedge funds — — 54.6 — Total private equity funds and hedge funds included in other long-term investments $ 121.2 $ 45.7 $ 161.1 $ 50.2 Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period. The following table presents investments in private equity funds that were subject to lock-up periods as of December 31, 2020: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $ 8.0 $ 40.7 $ 64.7 $ 7.8 $ 121.2 Investors in private equity funds are generally subject to indemnification obligations outside of the capital commitment period and prior to the winding up of the fund. As of December 31, 2020 and 2019, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds. Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. Insurance-Linked Securities Funds White Mountains’s other long-term investments include the ILS Funds. The fair value of these investments is generally estimated using the NAV of the funds. As of December 31, 2020, White Mountains held investments in four ILS Funds with a fair value of $51.4 million. Investments in the 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. The 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 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 December 31, 2020 and 2019 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities. The following tables present the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2020 and 2019: Level 3 Investments Other Long-term Investments Measured at NAV (1) Millions Level 1 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 436.4 15.9 — 275.6 (11.5) 716.4 (3) Amortization/accretion (.1) (4.4) — — — (4.5) Purchases 133.9 437.6 — 151.5 43.6 766.6 Sales (830.4) (527.8) (.1) (8.2) (61.8) (1,428.3) Effect of MediaAlpha IPO (4) 458.7 — — (458.7) — — Transfers in — — — — — — Transfers out — — — — — — Balance at December 31, 2020 $ 978.5 $ 1,030.9 $ — $ 614.2 $ 172.6 $ 2,796.2 (2) (1) Includes private equity funds, hedge funds and the 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 $142.9 and $201.2 as of December 31, 2020 and 2019 classified as short-term investments. (3) Excludes realized and unrealized losses associated with short-term investments of $0.4 for the year ended December 31, 2020. (4) Represents the reclassification of White Mountains’s investment in MediaAlpha from a level 3 measurement to a level 1 measurement in connection with the MediaAlpha IPO. See Note 2 - “Significant Transactions” . Level 3 Investments Other Long-term Investments Measured at NAV (1) Millions Level 1 Level 2 Common Other Long- term Total Balance at December 31, 2018 $ 842.6 $ 1,160.5 $ — $ 138.7 $ 186.9 $ 2,328.7 (2) Net realized and unrealized gains 163.0 76.1 — 181.2 12.7 433.0 (3) Amortization/accretion .2 (1.8) — — — (1.6) Purchases 165.3 404.5 .1 185.4 110.8 866.1 Sales (391.1) (529.7) — — (29.5) (950.3) Effect of Kudu Transaction — — — 141.8 (71.7) 70.1 Transfers in — — — 10.9 4.0 14.9 Transfers out — — — (4.0) (10.9) (14.9) Balance at December 31, 2019 $ 780.0 $ 1,109.6 $ .1 $ 654.0 $ 202.3 $ 2,746.0 (2) (1) Includes private equity funds, hedge funds and the 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 $201.2 and $214.2 as of December 31, 2019 and 2018 classified as short-term investments. (3) Includes $114.7 unrealized investment gain associated with the 2019 MediaAlpha Transaction. See Note 2 — “Significant Transactions”. (4) Excludes realized and unrealized losses associated with short-term investments of $0.2 for the year ended December 31, 2019. Fair Value Measurements — Transfers Between Levels - For Years Ended December 31, 2020 and 2019 Transfers between levels are generally 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 2020 and 2019, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements. During 2020 and 2019, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 measurements. During 2020, in connection with the MediaAlpha IPO, White Mountains’s investment in MediaAlpha was reclassified from a Level 3 measurement to a Level 1 measurement. Significant Unobservable Inputs The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s investment in MediaAlpha and other long-term investments, other than private equity funds, hedge funds and the ILS Funds, classified within Level 3 as of December 31, 2020 and 2019. The fair value of investments in private equity funds, hedge funds and the ILS Funds are generally estimated using the NAV of the funds. $ 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 instruments Discounted cash flow $17.1 4% - 8% N/A All other Discounted cash flow $18.8 20% - 24% 4% New Market Solutions, LLC Recent transaction $9.9 Transaction price: $9.9 Noblr, Inc. Recent transaction $8.7 Transaction price: $8.7 Zillion Insurance Services, Inc. (7) Recent transaction $5.0 Transaction price: $5.0 (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” . (7) In 2020, White Mountains made an additional $2.5 investment in Zillion Insurance Services, Inc. $ in Millions December 31, 2019 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (3) Kudu’s Participation Contracts (4) Discounted cash flow $266.5 15% - 22% 6x - 12x Investment in MediaAlpha Discounted cash flow $180.0 15% 4% PassportCard/DavidShield Discounted cash flow $90.0 22% 4% Elementum Holdings, L.P. (5) Discounted cash flow $55.1 20% 4% Private debt instruments Discounted cash flow $23.7 4% - 9% N/A All other Discounted cash flow $23.7 25% - 32% 4% Noblr, Inc. Recent transaction $5.0 Transaction price: $5.0 Zillion Insurance Services, Inc. (6) Recent transaction $2.5 Transaction price: $2.5 Compare.com Estimated net realizable value $2.5 Net realizable value: $2.5 (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) 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. (4) In 2019, Kudu deployed a total of $198.0 in new Kudu Participation Contracts, including Fair Oaks Capital, Versus Capital Advisors, First Long Island Investors, EJF Capital, Warwick Capital Partners and Pennybacker Capital Management. (5) In 2019, White Mountains made a $55.1 investment in Elementum Holdings, L.P. See Note 2 - “Significant Transactions” .

Goodwill and Other Intangible A

Goodwill and Other Intangible Assets	12 Months Ended
	Dec. 31, 2020
Goodwill and Intangible Assets Disclosure [Abstract]
Goodwill and Other Intangible Assets	Goodwill and Other Intangible Assets White Mountains accounts for business combinations using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. The estimated acquisition date fair values, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date. The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by company as of December 31, 2020 and 2019: $ in Millions Weighted Average Economic December 31, 2020 December 31, 2019 Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Goodwill: NSM (1)(2) N/A $ 506.4 $ — $ — $ 506.4 $ 381.6 $ — $ — $ 381.6 Kudu N/A 7.6 — — 7.6 7.6 — — 7.6 Other Operations N/A 11.5 — — 11.5 13.1 — 7.6 5.5 Total goodwill 525.5 — — 525.5 402.3 — 7.6 394.7 Other intangible NSM (1)(2) Customer 8.9 136.2 36.7 3.5 96.0 121.7 19.8 1.4 100.5 Trade names 16 65.4 8.3 1.0 56.1 61.9 5.3 .4 56.2 Information 0 3.1 1.4 1.7 — 3.9 1.4 .6 1.9 Renewal rights 12 82.5 4.9 — 77.6 82.5 .7 — 81.8 Other 3.4 1.7 1.0 — .7 1.7 .7 — 1.0 Subtotal 288.9 52.3 6.2 230.4 271.7 27.9 2.4 241.4 Kudu Trade names 7 2.2 .6 — 1.6 2.2 .2 — 2.0 Other Operations Trade names 9.6 3.6 .3 — 3.3 1.7 .5 .2 1.0 Customer 10.7 14.2 1.4 — 12.8 7.2 .4 — 6.8 Information 5 — — — — .5 .3 .2 — Insurance N/A 8.6 — — 8.6 8.6 — — 8.6 Other 5.4 .3 .1 — .2 .2 — — .2 Subtotal 26.7 1.8 24.9 18.2 1.2 .4 16.6 Total other intangible assets 317.8 54.7 6.2 256.9 292.1 29.3 2.8 260.0 Total goodwill and other intangible assets $ 843.3 $ 54.7 $ 6.2 782.4 $ 694.4 $ 29.3 $ 10.4 656.7 Goodwill and other intangible assets attributed to non-controlling interests (28.1) (23.4) Goodwill and other intangible assets included in White Mountains’s common $ 754.3 $ 631.3 (1) During 2020, NSM’s goodwill and intangible assets includes $13.4 and $1.6 of the effect of foreign currency translation. During 2019, NSM’s goodwill and intangible assets includes $1.8 and $0.7 of the effect of foreign currency translation. (2) The attribution of acquisition date fair value estimates between goodwill and other intangible assets for Kingsbridge was completed during 2020.The attribution of acquisition date fair value estimates between goodwill and other intangible assets for KBK was completed during 2019. 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 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 during 2020 and 2019: $ in Millions Acquisition of Subsidiary/ Asset Goodwill and Other Intangible Assets (1) Acquisition Date Embrace (2) $ 67.6 April 1, 2019 Renewal Rights (3) 82.5 June 28, 2019 Kingsbridge 131.7 April 7, 2020 Total NSM segment $ 281.8 Kudu Transaction $ 9.8 April 4, 2019 Other Operations $ 38.1 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. (2) Excludes $3.4 of software classified within other assets. (3) NSM’s purchase of the Renewal Rights from AIG was an asset acquisition. 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 for potential impairment. During 2020, White Mountains recognized impairments of other intangible assets of $6.2 million related to Fresh Insurance. The impairments related to lower premium volumes, including due to the impact of the COVID-19 pandemic, and certain reorganization initiatives at Fresh Insurance. During 2020, White Mountains performed its periodic reviews for potential impairment, including a quantitative review of the goodwill associated with NSM. During 2019, White Mountains recognized an impairment of other intangible assets of $2.4 million related to Fresh Insurance and impairments of goodwill and other intangible assets of $7.6 million and $0.4 million, respectively, related to Other Operations. During 2020 and 2019, White Mountains concluded that there was no impairment of the goodwill associated with NSM. During 2018, there were no impairments of goodwill and other intangible assets. Impairment charges are presented within general and administrative expenses for the segments affected on the statement of operations. The following table presents the change in goodwill and other intangible assets: December 31, 2020 2019 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 394.7 $ 260.0 $ 654.7 $ 379.9 $ 157.6 $ 537.5 Acquisitions of businesses (1) 140.0 — 140.0 64.8 34.6 99.4 Acquisition of collector car renewal rights — — — — 82.5 82.5 Dispositions of businesses (2) — — — (18.3) (23.5) (41.8) Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3) (23.2) 23.2 — (26.8) 26.8 — Impairments (4) — (6.2) (6.2) (7.6) (2.8) (10.4) Measurement period adjustments (5) .6 6.6 7.2 .9 5.9 6.8 Foreign currency translation 13.4 1.6 15.0 1.8 .7 2.5 Amortization — (28.3) (28.3) — (21.8) (21.8) Ending balance $ 525.5 $ 256.9 $ 782.4 $ 394.7 $ 260.0 $ 654.7 (1) During 2020, amounts include acquisitions of Kingsbridge and Other Operations. During 2019, amounts include acquisitions related to Kudu, Other Operations and Embrace. (2) Dispositions relate to the 2019 MediaAlpha Transaction. See Note 2 — “Significant Transactions” . (3) The determination of the relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge and Other Operations were completed in 2020. The determination of the relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of KBK was completed in 2019. (4) In 2020, impairments relate to NSM’s UK vertical. In 2019, impairments of $7.6 and $0.4 of goodwill and other intangible assets relate to Other Operations and $2.4 of impairments to other intangible assets relate to NSM’s UK vertical. (5) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During 2020, adjustments primarily relate to contingent considerations of $4.1 in connection with the acquisition of Kingsbridge. During 2019, $5.9 in connection with the acquisition of KBK. Amortization expense was $28.3 million, $21.8 million and $18.8 million for the years ended December 31, 2020, 2019 and 2018. White Mountains expects to recognize amortization expense in each of the next five years as the following table presents: Millions Amortization Expense 2021 $ 36.3 2022 35.2 2023 34.1 2024 28.6 2025 and years after 114.1 Total (1) $ 248.3 (1) Excludes indefinite-lived intangible assets of $8.6.

Debt

Debt	12 Months Ended
	Dec. 31, 2020
Debt Disclosure [Abstract]
Debt	Debt The following table presents White Mountains’s debt outstanding as of December 31, 2020 and 2019: December 31, Effective December 31, Effective $ in Millions 2020 Rate 2019 Rate (1) NSM Bank Facility $ 277.4 7.5% (1) $ 221.3 7.5% (1) Unamortized issuance cost (6.1) (3.9) NSM Bank Facility, carrying value 271.3 217.4 Other NSM debt 1.3 2.5% 1.8 3.0% Kudu Bank Facility 89.2 8.3% 57.0 8.3% Unamortized issuance cost (2.9) (3.4) Kudu Bank Facility, carrying value 86.3 53.6 Other Operations debt 18.0 7.4% 11.1 8.3 % Unamortized issuance cost (.5) (.4) Other Operations debt, carrying value 17.5 10.7 Total debt $ 376.4 $ 283.5 (1) Effective rate includes the effect of the amortization of debt issuance costs and excludes the effect of the interest rate swap on the hedged portion of the debt. The weighted average interest rate for the years ended December 31, 2020 and 2019, excluding the effect of the amortization of debt issuance costs, was 7.0% and 7.0%. The weighted average interest rate for the years ended December 31, 2020 and 2019 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 8.4% and 8.1%. The following table presents a schedule of contractual repayments of White Mountains’s debt as of December 31, 2020: Millions December 31, 2020 Due in one year or less $ 4.5 Due in two to three years 12.2 Due in four to five years 106.0 Due after five years 263.3 Total $ 386.0 NSM Bank Facility On April 7, 2020, NSM amended its secured credit facility (the “NSM Bank Facility”) with Ares Capital Corporation in connection with the acquisition of Kingsbridge. Under the amendment, the total commitment increased from $234.0 million, comprised of term loans of $224.0 million and a revolving credit loan of $10.0 million, to $291.4 million, comprised of term loans of $276.4 million, including £42.5 million (approximately $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. The term loans under the NSM Bank Facility mature on May 11, 2026, and the revolving loan matures on November 11, 2025. 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 changes to the terms of the NSM Bank Facility on the expected discounted future cash flows was less than 10%. Interest on the NSM Bank Facility accrues at a floating interest rate equal to the three-month LIBOR plus an applicable margin. In connection with the 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%. For GBP denominated borrowings, the GBP-LIBOR rate floor is 1.25% and the margin over GBP-LIBOR ranges from 6.00% to 6.50%. The margins over the reference interest rates vary within the range depending on the consolidated total leverage ratio of NSM. The following table presents the change in debt under the NSM Bank Facility for the years ended December 31, 2020 and 2019: Millions Year Ended December 31, NSM Bank Facility 2020 2019 Beginning balance $ 221.3 $ 180.4 Term loans Borrowings (1) 52.4 42.9 Repayments (2.0) (2.0) Foreign currency translation 5.7 — Revolving credit loan Borrowings — 6.5 Repayments — (6.5) Ending balance $ 277.4 $ 221.3 (1) Borrowings for the year ended December 31, 2020 included $52.4 for the funding of the acquisition of Kingsbridge. Borrowings for the year ended December 31, 2019 included $20.4 and $22.5 for the funding of the acquisitions of Embrace and the Renewal Rights. As of December 31, 2020, the term loans had an outstanding balance of $277.4 million, including £42.5 million (approximately $58.1 million based upon the foreign exchange spot rate as of December 31, 2020) in a GBP term loan, and the revolving credit loan was undrawn. 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. As of December 31, 2020, $147.6 million of the outstanding term loans were hedged by the swap and $129.8 million of the outstanding term loans were unhedged. For the twelve months ended December 31, 2020, 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 9.0%, and the weighted average effective interest rate on the outstanding term loans that were unhedged, including the effect of the amortization of debt issuance costs, was 7.6%. For the twelve months ended December 31, 2020, the weighted average interest rate on the total NSM Bank Facility, including the effect of the amortization of debt issuance costs and the effect of the interest rate swap, was 8.4%. 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 December 31, 2020, the secured term loan had an outstanding balance of $1.3 million and a maturity date of December 31, 2022. Kudu Bank Facility On December 23, 2019, Kudu entered into a secured credit facility (the “Kudu Bank Facility”) with Monroe Capital Management Advisors, LLC to provide funding for distributions to unitholders and fund new investments and related transaction expenses. As of December 31, 2020, the Kudu Bank Facility has a maximum borrowing capacity of $124.0 million, which is comprised of a revolving credit loan commitment of $5.0 million, an initial term loan of $57.0 million and a delayed-draw term loan of $62.0 million. The term loans and revolving credit loans, under the Kudu Bank Facility, mature in 2025. During 2020, Kudu borrowed $32.2 million in term loans under the Kudu Bank Facility and made no repayments. During 2019, Kudu borrowed $57.0 million in term loans under the Kudu Bank Facility and made no repayments. As of December 31, 2020, the term loans had an outstanding balance of $89.2 million and the revolving credit loan was undrawn. Interest on the Kudu Bank Facility accrues at a floating interest rate equal to the greater of the one-month USD-LIBOR and 1.0% or the Prime Rate plus 1.0%, plus in each case, an applicable margin. The margin over USD-LIBOR may vary between 5.50% and 6.25% and the margin over the base rate may vary between 4.50% and 5.25%, depending on the consolidated total leverage ratio of the borrower. The Kudu 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 Operations Debt As of December 31, 2020, debt in White Mountains’s Other Operations segment consisted of two secured credit facilities. 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. During 2020, White Mountains’s Other Operations segment made no borrowings and made repayments of $2.0 million on the term loans under the first credit facility. During 2019, the first credit facility had no borrowings and made repayments of $0.2 million on the term loans. As of December 31, 2020, the term loans had an outstanding balance of $9.1 million and the revolving credit loan was undrawn. 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. During 2020, White Mountains’s Other Operations segment had no borrowings and made repayments of $0.1 million on the term loans under the second credit facility. As of December 31, 2020, the term loans had an outstanding balance of $8.9 million and the revolving credit loan was undrawn. Compliance As of December 31, 2020, White Mountains was in compliance in all material respects with all of the covenants under all of its debt facilities. Interest Total interest expense incurred by White Mountains for its indebtedness was $29.5 million, $17.6 million and $9.5 million for the periods ended December 31, 2020, 2019 and 2018. Total interest paid by White Mountains for its indebtedness was $27.0 million, $16.3 million, and $8.8 million for the twelve months ended December 31, 2020, 2019 and 2018.

Income Taxes

Income Taxes	12 Months Ended
	Dec. 31, 2020
Income Tax Disclosure [Abstract]
Income Taxes	Income Taxes The Company and its Bermuda-domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law such that taxes are imposed, the 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 and are subject to tax in the jurisdictions in which they operate. As of December 31, 2020, the jurisdictions in which the Company’s subsidiaries and branches were subject to tax were Barbados, Ireland, Israel, Luxembourg, the United Kingdom and the United States. The following table presents the total income tax (expense) benefit for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Current income tax (expense): U.S. federal $ (10.4) $ .9 $ (.1) State (4.2) (3.7) (1.4) Non-U.S. (1.1) (1.7) (2.9) Total current income tax (expense) (15.7) (4.5) (4.4) Deferred income tax benefit (expense): U.S. federal 23.2 (14.9) 8.3 State 10.3 (10.4) — Non-U.S. 2.7 .5 .1 Total deferred income tax benefit (expense) 36.2 (24.8) 8.4 Total income tax benefit (expense) $ 20.5 $ (29.3) $ 4.0 Effective Rate Reconciliation The following table presents a reconciliation of taxes calculated for 2020, 2019 and 2018 using the 21% U.S. federal statutory rate U.S. federal statutory rate (the tax rate at which the majority of White Mountains’s worldwide operations are taxed) to the income tax (expense) benefit on pre-tax income (loss): Year Ended December 31, Millions 2020 2019 2018 Tax (expense) benefit at the U.S. statutory rate $ (135.5) $ (85.1) $ 37.4 Differences in taxes resulting from: Reorganization 130.5 — — Non-U.S. earnings, net of foreign taxes 78.4 27.1 (2.9) Change in valuation allowance (29.2) 63.6 (31.0) State taxes (8.5) (17.5) 4.0 Withholding tax (5.0) (1.6) (2.7) Member’s surplus contributions (4.8) (3.6) (2.6) Tax rate changes 2.7 (5.7) 1.7 Tax reserve adjustments 1.9 (.7) (.8) Officer compensation (1.1) — — Tax exempt interest and dividends .8 1.1 .6 Other, net (9.7) (6.9) .3 Total income tax benefit (expense) on pre-tax income (loss) $ 20.5 $ (29.3) $ 4.0 The non-U.S. component of pre-tax income (loss) was $327.8 million, $100.4 million and $(30.1) million for the years ended December 31, 2020, 2019 and 2018. The reorganization benefit resulted from the release of a deferred tax liability following an internal reorganization completed in connection with the MediaAlpha IPO. Tax Payments and Receipts Net income tax payments (primarily to the United States) totaled $16.2 million, $3.7 million, and $3.5 million for the years ended December 31, 2020, 2019 and 2018. Deferred Tax Assets and Liabilities Deferred taxes reflect the net tax effects of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and the amounts for tax purposes. The following table presents an outline of the significant components of White Mountains’s U.S. federal, state and non-U.S. deferred tax assets and liabilities: December 31, Millions 2020 2019 Deferred tax assets related to: U.S. federal and state net operating and capital $ 79.6 $ 92.3 Non-U.S. net operating loss carryforwards 50.5 41.7 Incentive compensation 17.5 15.0 Accrued interest 7.9 5.1 Deferred acquisition costs 5.5 4.3 Tax credit carryforwards 5.5 4.2 Other items 1.3 3.4 Total gross deferred tax assets 167.8 166.0 Less: valuation allowances 97.4 77.9 Total net deferred tax assets 70.4 88.1 Deferred tax liabilities related to: Member’s surplus contributions 52.9 43.2 Investment basis difference 11.8 6.6 Purchase accounting 5.1 3.1 Net unrealized investment gains .3 66.3 Other items 2.8 1.5 Total deferred tax liabilities 72.9 120.7 Net deferred tax (liability) $ (2.5) $ (32.6) White Mountains’s deferred tax (liabilities) assets are net of U.S. federal, state and non-U.S. valuation allowances and, to the extent they relate to non-U.S. jurisdictions, they are shown at year-end exchange rates. Valuation Allowance 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. It is possible that certain planning strategies or projected earnings in certain subsidiaries may not be sufficient to utilize the entire deferred tax asset, which could result in material changes to White Mountains’s deferred tax assets and tax expense. Of the $97.4 million valuation allowance as of December 31, 2020, $46.5 million related to deferred tax assets on net operating losses in U.S. subsidiaries and other federal and state deferred tax benefits, $26.8 million related to deferred tax assets on net operating losses and net investment unrealized gains and losses in Luxembourg subsidiaries, $20.0 million related to net operating losses and other deferred tax benefits in Israeli subsidiaries and $4.1 million related to net operating losses and other deferred tax benefits in U.K. subsidiaries. Of the $77.9 million valuation allowance as of December 31, 2019, $34.9 million related to deferred tax assets on net operating losses in U.S. subsidiaries and other federal and state deferred tax benefits, $22.6 million related to deferred tax assets on net operating losses and net investment unrealized gains and losses in Luxembourg subsidiaries, $17.3 million related to net operating losses in Israeli subsidiaries and $3.1 million related to net operating losses and other deferred tax benefits in U.K. subsidiaries. United States In 2020, White Mountains recorded income tax expense of $14.9 million to establish a full valuation allowance on the deferred tax assets of WM Lincoln, Inc. and subsidiaries (“WM Lincoln”) as White Mountains management is unsure they will generate sufficient taxable income to utilize the deferred tax assets. WM Lincoln includes WM Lafayette Holdings, Inc., WM Capital, WM Advisors and certain other entities and investments that are included in the Other Operations segment. During 2019, White Mountains recorded income tax benefit of $63.2 million to release a valuation allowance against deferred tax assets of Guilford Holdings, Inc. and subsidiaries (“Guilford”), which included Kudu, White Mountains’s investment in MediaAlpha, WM Capital, WM Advisors and certain other entities and investments that are included in the Other Operations segment. Guilford recorded the tax benefit in 2019 due to a release of the full valuation allowance from 2018. During 2020 and 2019, White Mountains recorded income tax expense (benefit) of $4.5 million and $(4.5) million to reflect the increase and decrease of the valuation allowance on net deferred tax assets of BAM. In the first quarter of 2020, White Mountains adopted ASU 2019-12, simplifying the Accounting for Income Taxes (ASC 740) (“ASU 2019-12”). For periods subsequent to the adoption of ASU 2019-12, White Mountains records both the tax expense related to BAM’s MSC and the related changes in valuation allowance on such taxes directly through non-controlling interest equity. Prior to the adoption of ASU 2019-12, White Mountains recorded the tax expense related to BAM’s MSC to non-controlling interest equity, while the change in valuation allowance on such taxes was recorded through the income statement. During 2020 and 2019, BAM had income included in equity due to MSC that was available to offset its loss from continuing operations. In 2019, BAM recorded an income tax benefit related to MSC of $10.5 million in continuing operations, with an offsetting tax expense in paid-in surplus. In 2020, based on the adoption of ASU 2019-12, BAM recorded both the income tax benefit on MSC of $9.7 million and the offsetting expense in paid-in surplus. During 2020 and 2019, BAM continued to have a full valuation allowance recorded against its net deferred tax assets, as White Mountains management is unsure it will generate sufficient taxable income to utilize the deferred tax assets. During 2020 and 2019, White Mountains recorded income tax expense of $1.9 million and $0.1 million to establish a valuation allowance against a deferred tax asset related to foreign tax credits at White Mountains Catskill Holdings, Inc., as White Mountains management is unsure it will generate sufficient taxable income to utilize the deferred tax asset. Non-U.S. Jurisdictions During 2020 and 2019, White Mountains recorded income tax expense of $4.2 million and $1.1 million to establish a valuation allowance against most of the deferred tax assets which primarily relate to losses on the write-down of foreign subsidiaries and the unrealized losses on investments held in Luxembourg-domiciled subsidiaries. During 2020 and 2019, White Mountains recorded income tax expense of $2.7 million and $1.6 million to establish a full valuation allowance against deferred tax assets at certain Israel-domiciled subsidiaries, as White Mountains management does not currently anticipate sufficient taxable income to utilize the deferred tax assets. During 2020 and 2019, White Mountains recorded income tax expense of $1.0 million and $1.3 million to establish a full valuation allowance against deferred tax assets at certain U.K. subsidiaries, as White Mountains management does not currently anticipate sufficient taxable income to utilize the deferred tax assets. Net Operating Loss and Capital Loss Carryforwards The following table presents net operating loss and capital loss carryforwards as of December 31, 2020, the expiration dates and the deferred tax assets thereon: December 31, 2020 Millions United States Luxembourg United Kingdom Israel Total 2020-2024 $ — $ — $ — $ — $ — 2025-2029 — — — — — 2030-2039 250.7 73.2 — — 323.9 No expiration date 118.4 31.0 25.9 85.2 260.5 Total $ 369.1 $ 104.2 $ 25.9 $ 85.2 $ 584.4 Gross deferred tax asset $ 77.5 $ 26.0 $ 4.9 $ 19.6 $ 128.0 Valuation allowance (66.8) (25.9) (3.3) (19.6) (115.6) Net deferred tax asset $ 10.7 $ .1 $ 1.6 $ — $ 12.4 As of December 31, 2020, there are U.S. foreign tax credit carryforwards available of $5.5 million, which begin to expire in 2028. Uncertain Tax Positions Recognition of the benefit of a given tax position is based upon whether a company determines that it is more likely than not that a tax position will be sustained upon examination based upon the technical merits of the position. In evaluating the more-likely-than-not recognition threshold, White Mountains must presume that the tax position will be subject to examination by a taxing authority with full knowledge of all relevant information. If the recognition threshold is met, then the tax position is measured at the largest amount of benefit that is more than 50% likely of being realized upon ultimate settlement. The following table presents a reconciliation of the beginning and ending amount of unrecognized tax benefits from 2018 to 2020: Millions Permanent Differences (1) Temporary Differences (2) Interest and Penalties (3) Total Balance at December 31, 2017 $ .3 $ — $ — $ .3 Changes in prior year tax positions .8 — — .8 Balance at December 31, 2018 1.1 — — 1.1 Changes in prior year tax positions 1.3 — — 1.3 Balance at December 31, 2019 2.4 — — 2.4 Changes in prior year tax positions .1 — — .1 Tax positions taken during the current year .1 — — .1 Reorganization (2.6) — — (2.6) Balance at December 31, 2020 $ — $ — $ — $ — (1) Represents the amount of unrecognized tax benefits that, if recognized, would impact the effective tax rate. (2) Represents the amount of unrecognized tax benefits that, if recognized, would create a temporary difference between the reported amount of an item in White Mountains’s Consolidated Balance Sheet and its tax basis. (3) Net of tax benefit. White Mountains classifies all interest and penalties on unrecognized tax benefits as part of income tax expense. During the years ended December 31, 2020, 2019 and 2018, White Mountains did not recognize any net interest (income) expense. There was no accrued interest as of December 31, 2020 and 2019. Tax Examinations 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	12 Months Ended
	Dec. 31, 2020
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 December 31, 2020, 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. As of December 31, 2020, $147.6 million of the outstanding term loans were hedged by the swap. For the twelve months ended December 31, 2020, 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 9.0%. 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 twelve months ended December 31, 2020 and 2019, White Mountains recognized net interest expense of $2.5 million and $1.1 million for the periodic net settlement payments on the swap. As of December 31, 2020 and December 31, 2019, the estimated fair value of the swap and the accrual of the periodic net settlement payments recorded in other liabilities was $8.2 million and $6.6 million. There was no ineffectiveness in the hedge for the years ended December 31, 2020 and December 31, 2019. For the twelve months ended December 31, 2020 and 2019, the $(1.6) million and $(3.9) 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 (approximately $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 approximately $0.1 million for the interest rate caps. Under the terms of the interest rate cap agreements, if the current GBP-LIBOR at the measurement date exceeds 1.25%, NSM will receive payments from the counterparty equal to the then-current GBP-LIBOR rate, less the 1.25% cap rate. As of December 31, 2020, the GBP-LIBOR rate was 0.03%.

Municipal Bond Guarantee Insura

Municipal Bond Guarantee Insurance	12 Months Ended
	Dec. 31, 2020
Insurance [Abstract]
Municipal Bond Guarantee Insurance	Municipal Bond Guarantee Insurance HG Global was established to fund the startup of BAM, a newly formed mutual municipal bond insurer, and, through HG Re, to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. At inception in 2012, HG Global was capitalized with $594.5 million from White Mountains and $14.5 million from non-controlling interests. HG Global, together with its subsidiaries, provided the initial capitalization of BAM through the purchase of $503.0 million of BAM Surplus Notes. As of December 31, 2020, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. 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 In addition to the FLRT, BAM is party to a collateralized financial guarantee excess of loss reinsurance agreement that serves to increase BAM’s claims paying resources and is provided by Fidus Re, Ltd. (“Fidus Re”), a Bermuda based special purpose insurer created in 2018 solely to provide reinsurance protection to BAM. Fidus Re was capitalized by the issuance of $100.0 million of insurance linked securities. 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. Fidus Re reinsures 90% of aggregate losses exceeding $165.0 million on a portion of BAM’s financial guarantee portfolio (the “Covered Portfolio”) up to a total reimbursement of $100.0 million. The Fidus Re agreement does not provide coverage for losses in excess of $276.1 million. The Covered Portfolio consists of approximately 42% of BAM’s portfolio of financial guaranty policies issued through December 31, 2020. 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. 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. At inception, the Supplemental Trust contained the original $300.0 million of Series B Notes and $100.0 million of cash and fixed income securities. During 2017, in order to further support BAM’s long-term capital position and business prospects, HG Global agreed to contribute the original $203.0 million of Series A Notes into the Supplemental Trust. In connection with the contribution, the Series A Notes were merged into the Series B Notes. 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 December 31, 2020 and 2019 was $222.8 million and $190.3 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 December 31, 2020 and 2019 was $604.3 million and $596.4 million. As of December 31, 2020 and 2019, the Collateral Trusts held assets of $827.1 million and $786.7 million, which included $434.5 million and $321.6 million of cash and investments, $388.2 million and $457.6 million of BAM Surplus Notes and $4.4 million and $7.5 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 will be 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. Under GAAP, if the terms of a debt instrument are amended, unless there is greater than a 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 changes to the terms of the BAM Surplus Notes on the expected discounted future cash flows was less than 10%. 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 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. In December 2019, BAM made a $32.0 million cash payment (which included a one-time $10.0 million cash payment) of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $23.7 million was a repayment of principal held in the Supplemental Trust, $0.3 million was a payment of accrued interest held in the Supplemental Trust and $8.0 million was a payment of accrued interest held outside the Supplemental Trust. As of December 31, 2020 and 2019, total interest receivable on the BAM Surplus Notes was $155.7 million and $162.7 million. Insured Obligations and Premiums The following table presents a schedule of BAM’s insured obligations as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Contracts outstanding 10,997 8,987 Remaining weighted average contract period (in years) 10.7 10.7 Contractual debt service outstanding (in millions): Principal $ 75,287.7 $ 62,250.5 Interest and capital appreciation 36,448.8 31,799.7 Total debt service outstanding $ 111,736.5 $ 94,050.2 Gross unearned insurance premiums $ 237.5 $ 198.4 The following table presents a schedule of BAM’s future premium revenues as of December 31, 2020: Millions December 31, 2020 January 1, 2021 - March 31, 2021 $ 5.6 April 1, 2021 - June 30, 2021 5.5 July 1, 2021 - September 30, 2021 5.5 October 1, 2021 - December 31, 2021 5.4 22.0 2022 20.9 2023 19.8 2024 18.3 2025 17.0 2026 and thereafter 139.5 Total gross unearned insurance premiums $ 237.5 The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the years ended December 31, 2020, 2019 and 2018: Millions December 31, 2020 December 31, 2019 December 31, 2018 Written premiums: Direct $ 61.5 $ 28.1 $ 44.8 Assumed .2 10.6 8.1 Gross written premiums $ 61.7 $ 38.7 $ 52.9 Earned premiums: Direct $ 19.4 $ 13.6 $ 13.6 Assumed 3.4 2.7 .3 Gross earned premiums $ 22.8 $ 16.3 $ 13.9 In September 2019, BAM entered into facultative quota share reinsurance agreements under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $1.1 billion. In the second quarter of 2020, BAM assumed an additional municipal bond guarantee contract with a par value of $36.9 million through an endorsement to the facultative quota share reinsurance agreement. In November 2018, BAM entered into a 100% quota share facultative reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $2.2 billion. None of the contracts assumed under these reinsurance agreements were non-performing and no loss reserves have been established for any of the contracts, either as of the transaction dates or as of December 31, 2020. The agreements, which cover future claims exposure only, meets the risk transfer criteria under ASC 944-20, Insurance Activities

Earnings Per Share

Earnings Per Share	12 Months Ended
	Dec. 31, 2020
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 years ended December 31, 2020, 2019 and 2018. See Note 19 — “Held for Sale and Discontinued Operations” . Year Ended December 31, 2020 2019 2018 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 708.7 $ 414.5 $ (141.2) Less: total (loss) income from discontinued operations, net of tax (2.3) .8 (17.2) Net income (loss) from continuing operations attributable to 711.0 413.7 (124.0) Allocation of (earnings) losses to participating restricted common shares (1) (9.3) (5.3) 1.4 Basic and diluted earnings (losses) per share numerators $ 701.7 $ 408.4 $ (122.6) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (2) (40.8) (40.5) (40.1) Basic earnings (losses) per share denominator 3,081.4 3,141.1 3,342.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (2) (40.8) (40.5) (40.1) Diluted earnings (losses) per share denominator 3,081.4 3,141.1 3,342.4 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ 1.00 $ 1.00 $ 1.00 Undistributed earnings (losses) 226.72 129.02 (37.67) Basic and diluted earnings (losses) per share $ 227.72 $ 130.02 $ (36.67) (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (2) Restricted shares outstanding vest either in equal annual installments or upon a stated date. See Note 10 — “Employee Share-Based Incentive Compensation Plans”. The following table presents the undistributed net earnings (losses) from continuing operations for the years ended December 31, 2020, 2019 and 2018. See Note 19 — “Held for Sale and Discontinued Operations” . Year Ended December 31, Millions 2020 2019 2018 Undistributed net earnings - continuing operations: Net income (loss) attributable to White Mountains’s common shareholders, $ 701.7 $ 408.4 $ (122.6) Dividends declared, net of restricted common share amounts (1) (3.1) (3.2) (3.7) Total undistributed net earnings (losses), net of restricted common share amounts $ 698.6 $ 405.2 $ (126.3) (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	12 Months Ended
	Dec. 31, 2020
Share-based Payment Arrangement [Abstract]
Employee Share-Based Incentive Compensation Plans	Employee Share-Based Incentive Compensation Plans White Mountains’s share-based incentive compensation plans are designed to incentivize key employees to maximize shareholder value over long periods of time. White Mountains believes that this is best pursued by utilizing a pay-for-performance program that closely aligns the financial interests of management with those of its shareholders. White Mountains accomplishes this by emphasizing highly variable long-term compensation that is contingent on performance over a number of years rather than entitlements. White Mountains expenses all its share-based compensation. As a result, White Mountains’s calculation of its owners’ returns includes the expense of all outstanding share-based compensation awards. 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 and directors of White Mountains. The WTM Incentive Plan was adopted by the Board, was approved by the Company’s sole shareholder in 1985 and was subsequently amended by its shareholders in 1995, 2001, 2003, 2005, 2010, 2013 and 2019. Share-based incentive awards that may be granted under the plan include performance shares, restricted shares, incentive stock options and non-qualified stock options (“Non-Qualified Options”). Performance Shares Performance shares are designed to reward employees for meeting company-wide performance targets. Performance shares are conditional grants of a specified maximum number of common shares or an equivalent amount of cash. Awards generally vest at the end of a three-year service period, are subject to the attainment of pre-specified performance goals, and are valued based on the market value of common shares at the time awards are paid. Performance shares earned under the WTM Incentive Plan are typically paid in cash but may be paid in common shares. Compensation expense is recognized for the vested portion of the awards over the related service periods. The level of payout ranges from zero to two times the number of shares initially granted, depending on White Mountains’s financial performance. Performance shares become payable at the conclusion of a performance cycle (typically three years) if pre-defined financial targets are met. The performance measures used for determining performance share payouts are growth in White Mountains’s adjusted book value per share and intrinsic value per share. Intrinsic value per share is generally calculated by adjusting adjusted book value per share for differences between the adjusted book value of certain assets and liabilities and White Mountains’s estimate of their underlying intrinsic values. The following table presents performance share activity for the years ended December 31, 2020, 2019 and 2018 for performance shares granted under the WTM Incentive Plan: Year Ended December 31, 2020 2019 2018 $ in Millions Target Accrued Target Accrued Target Accrued Beginning of period 42,473 $ 43.7 40,616 $ 31.7 50,515 $ 45.8 Shares paid or expired (1) (14,070) (27.7) (13,715) (18.1) (23,186) (28.4) New grants 14,055 — 15,600 — 14,105 — Forfeitures (2) — (.4) (28) (.1) (818) .1 Expense recognized — 40.7 — 30.2 — 14.2 End of period 42,458 $ 56.3 42,473 $ 43.7 40,616 $ 31.7 (1) WTM performance share payments in 2020 for the 2017-2019 performance cycle, which were paid in March 2020, ranged from 174% to 180% of target. WTM performance share payments in 2019 for the 2016-2018 performance cycle, which were paid in March 2019, ranged from 139% to 166% of target. WTM performance share payments in 2018 for the 2015-2017 performance cycle, which were paid in March 2018, ranged from 145% to 147% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP. During 2020, White Mountains granted 14,055 performance shares for the 2020-2022 performance cycle. During 2019, White Mountains granted 15,600 performance shares for the 2019-2021 performance cycle. During 2018, White Mountains granted 13,450 performance shares for the 2018-2020 performance cycle, 290 performance shares for the 2017-2019 performance cycle and 365 performance shares for the 2016-2018 performance cycle. For the 2017-2019, 2016-2018 and 2015-2017 performance cycles, all performance shares earned were settled in cash. If the outstanding performance shares had vested on December 31, 2020, the total additional compensation cost to be recognized would have been $28.8 million, based on accrual factors as of December 31, 2020 (common share price and payout assumptions). The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of December 31, 2020 for each performance cycle: $ in Millions Target Accrued Expense Performance cycle: 2020 – 2022 14,055 $ 9.5 2019 – 2021 15,600 20.7 2018 – 2020 13,450 27.1 Sub-total 43,105 57.3 Assumed forfeitures (647) (1.0) Total 42,458 $ 56.3 For the 2020-2022 performance cycle, the targeted performance goal for full payment of outstanding performance shares granted under the WTM Incentive Plan to non-investment personnel is 7% average growth in adjusted book value per share and intrinsic value per share. Average growth of 2% or less would result in no payout and average growth of 12% or more would result in a payout of 200%. For the 2019-2021 performance cycle, the targeted performance goal for full payment of outstanding performance shares granted under the WTM Incentive Plan is 7% average growth in adjusted book value per share and intrinsic value per share. Average growth of 2% or less would result in no payout and average growth of 12% or more would result in a payout of 200%. For the 2018-2020 performance cycle, the targeted performance goal for full payment of outstanding performance shares granted under the WTM Incentive Plan is 6% average growth in adjusted book value per share and intrinsic value per share. Average growth of 2% or less would result in no payout and average growth of 10% or more would result in a payout of 200%. Restricted Shares Restricted shares are grants of a specified number of common shares that generally vest at the end of a three-year service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards under the WTM Incentive Plan for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, 2020 2019 2018 $ in Millions Restricted Unamortized Restricted Unamortized Restricted Unamortized Non-vested, Beginning of period 43,395 $ 16.7 41,510 $ 12.5 53,755 $ 14.3 Issued 14,055 15.1 15,600 14.5 14,105 11.4 Vested (14,345) — (13,715) — (25,381) — Forfeited — — — — (969) (.2) Expense recognized — (16.6) — (10.3) — (13.0) End of period 43,105 $ 15.2 43,395 $ 16.7 41,510 $ 12.5

Leases

Leases	12 Months Ended
	Dec. 31, 2020
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. On January 1, 2019, White Mountains adopted ASU 2016-02, Leases (ASC 842). See Note 1 — “Basis of Presentation and Significant Accounting Policies” — Basis of Presentation and Significant Accounting Policies . Prior to adoption of ASU 2016-02, White Mountains recognized lease expense for operating leases on a straight-line basis, but did not recognize lease assets or liabilities on its consolidated balance sheet. Upon adoption on January 1, 2019, White Mountains recognized lease ROU assets of $23.2 million and lease liabilities of $23.2 million. As of December 31, 2020, the ROU asset was $37.6 million and lease liabilities were $38.3 million. The following table summarizes net lease expense recognized in White Mountains’s consolidated statement of operations for the years ended December 31, 2020 and 2019: Millions December 31, 2020 December 31, 2019 Lease cost $ 7.7 $ 7.2 Less: sublease income .4 .4 Net lease cost $ 7.3 $ 6.8 The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of December 31, 2020: Millions December 31, 2020 2021 $ 7.7 2022 7.3 2023 7.1 2024 5.8 2025 5.1 Thereafter 12.2 Total undiscounted lease payments 45.2 Less: present value adjustment (6.9) Operating lease liability $ 38.3 The following table presents lease related assets and liabilities by reportable segment as of December 31, 2020 and 2019: As of December 31, 2020 $ in 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. December 31, 2019 $ in Millions HG/BAM NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 10.4 $ 4.8 $ 2.3 $ 5.1 $ 22.6 4.6% Lease liability $ 10.4 $ 4.8 $ 2.3 $ 5.3 $ 22.8 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

Common Shareholders_ Equity and

Common Shareholders’ Equity and Non-controlling Interests	12 Months Ended
	Dec. 31, 2020
Stockholders' Equity Note [Abstract]
Common Shareholders’ Equity and Non-controlling Interests	Common Shareholders’ Equity and Non-controlling Interests Common Shares Repurchased and Retired During the past several years, White Mountains’s board of directors authorized the Company to repurchase its common shares, from time to time, subject to market conditions. Shares may be repurchased on the open market or through privately negotiated transactions. The repurchase authorizations do not have a stated expiration date. As of December 31, 2020, White Mountains may repurchase an additional 542,517 shares under these board authorizations. In addition, from time to time White Mountains has also repurchased its common shares through tender offers that were separately authorized by its board of directors. During 2020, the Company repurchased 99,087 common shares for $85.1 million at an average share price of $859, which were comprised of 93,188 common shares repurchased under the board authorizations for $78.5 million at an average share price of $843 and 5,899 common shares repurchased pursuant to employee benefit plans. During 2019, the Company repurchased 5,679 common shares for $4.9 million at an average share price of $858 pursuant to employee benefit plans. During 2018, the Company repurchased 592,458 common shares for $519.1 million at an average share price of $877, which were comprised of 582,493 common shares repurchased under the board authorizations for $511.0 million at an average share price of $877 and 9,965 common shares repurchased pursuant to employee benefit plans. Common Shares Issued During 2020, the Company issued a total of 15,745 common shares, which consisted of 14,055 restricted shares issued to key personnel, 1,440 shares issued to directors of the Company and 250 shares issued to MediaAlpha’s management. During 2019, the Company issued a total of 17,917 common shares, which consisted of 15,600 restricted shares issued to key personnel and 2,317 shares issued to directors of the Company. During 2018, the Company issued a total of 16,377 common shares, which consisted of 14,105 restricted shares issued to key personnel, 2,272 shares issued to directors of the Company. Dividends on Common Shares For the years ended December 31, 2020, 2019 and 2018, the Company declared and paid cash dividends totaling $3.2 million, $3.2 million and $3.8 million (or $1.00 per common share). 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 December 31, 2020 and 2019: December 31, 2020 December 31, 2019 $ in Millions Non-controlling Percentage Non-controlling Equity Non-controlling Percentage Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ 13.5 3.1 % $ 14.4 NSM 3.4 % 17.0 3.6 % 14.9 Kudu .7 % 2.3 .9 % 2.2 Other various 2.4 various (1.6) Total, excluding BAM 35.2 29.9 BAM 100.0 % (123.3) 100.0 % (146.7) Total non-controlling interests $ (88.1) $ (116.8)

Statutory Capital and Surplus

Statutory Capital and Surplus	12 Months Ended
	Dec. 31, 2020
Insurance [Abstract]
Statutory Capital and Surplus	Statutory Capital and Surplus White Mountains’s insurance operations are subject to regulation and supervision in each of the jurisdictions where they are domiciled and licensed to conduct business. Generally, regulatory authorities have broad supervisory and administrative powers over such matters as licenses, standards of solvency, premium rates, policy forms, investments, security deposits, methods of accounting, form and content of financial statements, minimum capital and surplus requirements, dividends and other distributions to shareholders, periodic examinations and annual and other report filings. In general, such regulation is for the protection of policyholders rather than shareholders. The Insurance Act 1978 of Bermuda and related regulations, as amended (“Insurance Act”), regulates the insurance business of Bermuda-domiciled insurers. Under the Insurance Act, insurers are required to maintain available statutory capital and surplus at a level equal to or in excess of its enhanced capital requirement which is established by reference to either a Bermuda Solvency Capital Requirement (“BSCR”) model or an approved internal capital model. Generally, the Bermuda Monetary Authority (“BMA”) has broad supervisory and administrative powers over such matters as licenses, standards of solvency, investments, methods of accounting, form and content of financial statements, minimum capital and surplus requirements, and annual and other report filings. HG Global/BAM HG Re is a Special Purpose Insurer under Bermuda insurance regulations and is subject to regulation and supervision by the BMA. As of December 31, 2020, HG Re had statutory capital and surplus of $768.1 million. As a Special Purpose Insurer, HG Re has a nominal minimum regulatory capital requirement of $1. BAM is domiciled in New York and is subject to regulation by the NYDFS. New York financial guarantee insurance law establishes single risk and aggregate limits with respect to insured obligations insured by financial guarantee insurers. BAM’s statutory net loss for the years ended December 31, 2020, 2019 and 2018 was $59.3 million, $38.3 million and $34.6 million. BAM’s members’ surplus, as reported to regulatory authorities as of December 31, 2020, was $324.7 million, which exceeds the minimum members’ surplus necessary for BAM to maintain its New York State financial guarantee insurance license of $66.0 million. Dividend Capacity There are no restrictions under Bermuda law or the law of any other jurisdiction on the payment of dividends from retained earnings by White Mountains, provided that after the payment of any dividend, the Company would continue to be able to pay its liabilities as they become due and the realizable value of the Company’s assets would remain greater that its liabilities. Following is a description of the dividend capacity of White Mountains’s reinsurance and other operating subsidiaries: HG Global/BAM As of December 31, 2020, HG Global had $619.0 million face value of preferred shares outstanding, of which White Mountains owned 96.9%. Holders of the HG Global preferred shares receive cumulative dividends at a fixed annual rate of 6.0% on a quarterly basis, when and if declared by HG Global. During 2020, HG Global declared and paid a $23.0 million preferred dividend, of which $22.3 million was paid to White Mountains. As of December 31, 2020, HG Global had accrued $376.6 million of dividends payable to holders of its preferred shares, of which $363.9 million was payable to White Mountains and eliminated in consolidation. As of December 31, 2020, HG Global and its subsidiaries had $2.8 million of cash outside of HG Re. HG Re is a Special Purpose Insurer subject to regulation and supervision by the BMA, but does not require regulatory approval to pay dividends. However, HG Re’s dividend capacity is limited to amounts held outside of the Collateral Trusts pursuant to the FLRT with BAM. As of December 31, 2020, HG Re had $768.1 million of statutory capital and surplus and $827.1 million of assets held in the Collateral Trusts pursuant to the FLRT with BAM. 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 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. 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. As of December 31, 2020, the Collateral Trusts held assets of $827.1 million, which included $434.5 million of cash and investments, $388.2 million of BAM Surplus Notes and $4.4 million of interest receivable on the BAM Surplus Notes. As of December 31, 2020, HG Re had $20.1 million of cash and investments and $114.0 million of accrued interest on the BAM Surplus Notes held outside the Collateral Trusts. 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 will be 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, 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 in 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 accrued interest held in the Supplemental Trust and $16.2 million was a payment of accrued interest held outside the Supplemental Trust. In December 2019, BAM made a $32.0 million cash payment (which included a one-time $10.0 million cash payment) of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $23.7 million was a repayment of principal held in the Supplemental Trust, $0.3 million was a payment of accrued interest held in the Supplemental Trust and $8.0 million was a payment of accrued interest held outside the Supplemental Trust. NSM During 2020, NSM did not make any distributions to unitholders. As of December 31, 2020, NSM had $48.1 million of net unrestricted cash. Kudu In December 2019, Kudu entered into a secured credit facility to provide funding for distributions to unitholders and fund new investments and related transaction expenses. At closing, Kudu drew an initial term loan of $57.0 million to pay transaction expenses and to distribute $53.7 million to unitholders, of which $53.3 million was paid to White Mountains. During 2020, Kudu distributed $4.0 million to unitholders, substantially all of which was paid to White Mountains. As of December 31, 2020, Kudu had $7.8 million of net unrestricted cash and short-term investments. Other Operations

Segment Information

Segment Information	12 Months Ended
	Dec. 31, 2020
Segment Reporting [Abstract]
Segment Information	Segment Information As of December 31, 2020, White Mountains conducted its operations through four segments: (1) HG Global/BAM, (2) NSM, (3) Kudu and (4) Other Operations. In addition, MediaAlpha was consolidated as a reportable segment until the date of the 2019 MediaAlpha Transaction. A discussion of White Mountains’s consolidated investment operations is included after the discussion of operations by segment. As a result of the Kudu Transaction, White Mountains began consolidating Kudu in its financial statements in the second quarter of 2019. White Mountains’s segment disclosures for the year ended December 31, 2019 include Kudu’s results of operations for the period from April 4, 2019, the date of the Kudu Transaction, to December 31, 2019. See Note 2 — “Significant Transactions” . As a result of the 2019 MediaAlpha Transaction, White Mountains no longer consolidated MediaAlpha, and consequently it was no longer a reportable segment. White Mountains’s segment disclosures for the year ended December 31, 2019 include MediaAlpha’s results of operations for the period from January 1, 2019 to February 26, 2019, the date of the 2019 MediaAlpha Transaction. See Note 2 — “Significant Transactions” . 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 (1) NSM Kudu Other Total Year Ended December 31, 2020 Earned insurance premiums $ 22.8 $ — $ — $ — $ 22.8 Net investment income 19.5 — 29.5 82.0 131.0 Net realized and unrealized investment gains (losses) 23.7 — 15.9 (8.8) 30.8 Net realized and unrealized investment gains from — — — 686.0 686.0 Advertising and commission revenues (2) — 232.5 — 8.3 240.8 Other revenues 2.5 52.6 .3 13.9 69.3 Total revenues 68.5 285.1 45.7 781.4 1,180.7 Insurance acquisition expenses 7.0 — — — 7.0 Other underwriting expenses .4 — — — .4 Cost of sales — — — 11.3 11.3 General and administrative expenses 56.4 176.9 11.8 141.9 387.0 Broker commission expense — 75.3 — — 75.3 Change in fair value of contingent consideration — (3.3) — — (3.3) Amortization of other intangible assets — 26.7 .3 1.3 28.3 Interest expense — 22.1 6.0 1.4 29.5 Total expenses 63.8 297.7 18.1 155.9 535.5 Pre-tax income (loss) $ 4.7 $ (12.6) $ 27.6 $ 625.5 $ 645.2 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Approximately 19% of NSM’s commission revenue was associated with one single carrier. Millions HG Global/BAM (1) NSM Kudu (2) MediaAlpha (3) Other Total Year Ended December 31, 2019 Earned insurance premiums $ 16.3 $ — $ — $ — $ — $ 16.3 Net investment income 21.6 — 14.7 — 43.4 79.7 Net realized and unrealized investment gains 27.1 — 6.3 — 219.8 253.2 Net realized and unrealized investment gains — — — — 180.0 180.0 Gain from deconsolidation of MediaAlpha — — — 67.5 67.5 Advertising and commission revenues (4) — 193.4 — 48.8 6.9 249.1 Other revenues 1.6 39.7 .2 — 6.1 47.6 Total revenues 66.6 233.1 21.2 48.8 523.7 893.4 Insurance acquisition expenses 5.7 — — — — 5.7 Other underwriting expenses .4 — — — — .4 Cost of sales — — — 40.6 7.5 48.1 General and administrative expenses 50.5 132.2 10.1 12.5 122.5 327.8 Broker commission expense — 64.8 — — — 64.8 Change in fair value of contingent — 2.1 — — — 2.1 Amortization of other intangible assets — 19.4 .2 1.6 .6 21.8 Interest expense — 16.7 .1 .2 .6 17.6 Total expenses 56.6 235.2 10.4 54.9 131.2 488.3 Pre-tax income (loss) $ 10.0 $ (2.1) $ 10.8 $ (6.1) $ 392.5 $ 405.1 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Kudu’s results are from April 4, 2019, the date of the Kudu Transaction, to December 31, 2019. (3) MediaAlpha’s results are from January 1, 2019 to February 26, 2019, the date of the 2019 MediaAlpha Transaction. (4) Approximately 17% of NSM’s commission revenue was associated with one single carrier. Millions HG Global/BAM (1) NSM MediaAlpha Other Total Year Ended December 31, 2018 Earned insurance premiums $ 13.9 $ — $ — $ — $ 13.9 Net investment income 16.7 — — 42.3 59.0 Net realized and unrealized investment losses (7.5) — — (100.8) (108.3) Advertising and commission revenues (2) — 89.6 295.5 4.1 389.2 Other revenues 1.2 12.0 1.6 .5 15.3 Total revenues 24.3 101.6 297.1 (53.9) 369.1 Insurance acquisition expenses 5.3 — — — 5.3 Other underwriting expenses .4 — — — .4 Cost of sales — — 245.0 3.7 248.7 General and administrative expenses 48.0 59.4 31.7 94.4 233.5 Broker commission expense — 28.4 — — 28.4 Change in fair value of contingent — 2.7 — — 2.7 Amortization of other intangible assets — 8.3 10.3 .2 18.8 Interest expense — 8.0 1.2 .3 9.5 Total expenses 53.7 106.8 288.2 98.6 547.3 Pre-tax (loss) income $ (29.4) $ (5.2) $ 8.9 $ (152.5) $ (178.2) (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Approximately 29% of MediaAlpha’s advertising revenue was associated with one customer and approximately 33% of NSM’s commission revenue was associated with one single carrier. Millions HG Global/BAM NSM Kudu Other Held for Sale Total December 31, 2020: Total investments $ 919.9 $ — $ 400.7 $ 1,618.5 $ — $ 2,939.1 Total assets $ 1,017.8 (1) $ 999.6 $ 430.2 $ 2,381.5 (2) $ 2.3 $ 4,831.4 Total liabilities $ 291.5 (2) $ 491.8 $ 96.3 $ 133.9 $ — $ 1,013.5 Total White Mountains’s common $ 836.1 (2) $ 490.7 $ 331.6 $ 2,245.3 (2) $ 2.3 $ 3,906.0 Non-controlling interest $ (109.8) $ 17.1 $ 2.3 $ 2.3 $ — $ (88.1) December 31, 2019: Total investments $ 845.6 $ — $ 266.6 $ 1,835.0 $ — $ 2,947.2 Total assets $ 924.0 (1) $ 825.2 $ 290.5 $ 1,940.5 (2) $ 3.0 $ 3,983.2 Total liabilities $ 246.8 (2) $ 401.1 $ 57.0 $ 133.6 $ — $ 838.5 Total White Mountains’s common $ 809.5 (2) $ 409.3 $ 231.3 $ 1,808.4 (2) $ 3.0 $ 3,261.5 Non-controlling interest $ (132.3) $ 14.8 $ 2.2 $ (1.5) $ — $ (116.8) (1) As of December 2020 and 2019, total assets in the HG Global/BAM segment reflected the elimination of $388.2 and $457.6 of BAM Surplus Notes issued to HG Global and its subsidiaries, and $155.7 and $162.7 in accrued interest related to the BAM Surplus Notes. (2) HG Global preferred dividends payable to White Mountains’s subsidiaries is eliminated in White Mountains’s consolidated financial statements. For segment reporting, the HG Global preferred dividends payable to White Mountains’s subsidiaries included within the HG Global/BAM segment are eliminated against the offsetting receivable included within the Other Operations segment and therefore added back to White Mountains’s common shareholders’ equity within the HG Global/BAM segment. As of December 31, 2020 and 2019, the HG Global preferred dividends payable to White Mountains’s subsidiaries was $363.9 and $330.3. In compliance with ASC 606, Revenues from Contracts with Customers, the following tables present White Mountains’s total revenues by revenue source: Millions HG Global/BAM NSM Kudu Other Total Year Ended December 31, 2020 Commission and Other Revenue Specialty Transportation $ — $ 85.5 $ — $ — $ 85.5 Real Estate — 44.9 — — 44.9 Social Services — 28.9 — — 28.9 Pet — 55.0 — — 55.0 United Kingdom — 49.4 — — 49.4 Other — 21.4 — 8.3 29.7 Total Commission and Other Revenue — 285.1 — 8.3 293.4 Products — — — 14.5 14.5 Total revenues from contracts with customers — 285.1 — 22.8 307.9 Other revenues (1) 68.5 — 45.7 758.6 872.8 Total revenues $ 68.5 $ 285.1 $ 45.7 $ 781.4 $ 1,180.7 (1) Other revenues consist 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 (2) MediaAlpha (3) Other Total Year Ended December 31, 2019 Commission and Other Revenue Specialty Transportation $ — $ 77.6 $ — $ — $ — $ 77.6 Real Estate — 34.7 — — — 34.7 Social Services — 25.9 — — — 25.9 Pet — 30.0 — — — 30.0 United Kingdom — 45.9 — — — 45.9 Other — 19.0 — — 6.9 25.9 Total Commission and Other Revenue — 233.1 — — 6.9 240.0 Advertising revenues — — — 48.8 — 48.8 Products — — — — 5.5 5.5 Total revenues from contracts with customers — 233.1 — 48.8 12.4 294.3 Other revenues (1) 66.6 — 21.2 — 511.3 599.1 Total revenues $ 66.6 $ 233.1 $ 21.2 $ 48.8 $ 523.7 $ 893.4 (1) Other revenues consist of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. (2) Kudu’s results are from April 4, 2019, the date of the Kudu Transaction, to December 31, 2019. (3) MediaAlpha’s results are from January 1, 2019 to February 26, 2019, the date of the 2019 MediaAlpha Transaction. Millions HG Global/BAM NSM MediaAlpha Other Total Year Ended December 31, 2018 Commission and Other Revenue Specialty Transportation $ — $ 28.3 $ — $ — $ 28.3 Real Estate — 17.8 — — 17.8 Social Services — 14.7 — — 14.7 United Kingdom — 28.0 — — 28.0 Other — 12.8 — 4.1 16.9 Total Commission and Other Revenue — 101.6 — 4.1 105.7 Advertising revenues — — 295.5 — 295.5 Total revenues from contracts with customers — 101.6 295.5 4.1 401.2 Other revenues (1) 24.3 — 1.6 (58.0) (32.1) Total revenues $ 24.3 $ 101.6 $ 297.1 $ (53.9) $ 369.1 (1) Other revenues consist of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.

Equity-Method Eligible Investme

Equity-Method Eligible Investments	12 Months Ended
	Dec. 31, 2020
Equity Method Investments and Joint Ventures [Abstract]
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 carrying values of White Mountains’s equity method eligible investments as of December 31, 2020 and 2019: December 31, Millions 2020 2019 Investment in MediaAlpha $ 802.2 $ 180.0 Other equity method eligible investments, at fair value $ 698.1 $ 581.7 For the years ended December 31, 2020, 2019 and 2018, White Mountains’s received dividend and income distributions from equity method eligible investments, including White Mountains’s investment in MediaAlpha, of $95.0 million, $14.8 million and $3.7 million, which were recorded within net investment income in the consolidated statement of operations. The following table presents White Mountains’s significant equity method eligible investments as of December 31, 2020 and 2019: Basic Ownership Interest Investee December 31, 2020 December 31, 2019 Instrument Held PassportCard/DavidShield 53.8% 50.0% Common shares New Market Solutions, LLC. 46.7% n/a Units durchblicker 45.0% 45.0% Common shares MediaAlpha (1) 35.0% 48.3% Common Shares/Units (1) Elementum Holdings, L.P. 28.9% 30.0% Limited partnership interest Compare.com 18.4% 18.4% Common shares Tuckerman Capital Funds 14.9 - 62.0% 17.5 - 62.4% Limited and general partnership interests JAM Partners L.P. n/a 11.1% Limited partnership interest Enlightenment Capital Funds 9.7- 66.7% 10.0 - 38.4% Limited and general partnership interests Kudu’s Participation Contracts 3.2 - 35.0% 3.2 - 30.0% Revenue and earnings participation contracts (1) On October 30, 2020, MediaAlpha completed the MediaAlpha IPO. See Note 2 — “Significant Transactions” The following tables present aggregated summarized financial information for White Mountains’s investments in equity method eligible unconsolidated entities, excluding MediaAlpha: December 31, Millions 2020 2019 Balance sheet data (1) : Total assets $ 1,328.5 $ 1,959.2 Total liabilities $ 228.7 $ 653.2 (1) Financial data for White Mountains’s equity method eligible investees is generally reported on a one-quarter lag. Year Ended December 31, Millions 2020 2019 2018 Income statement data (1) : Total revenues $ 526.5 $ 344.6 $ 226.0 Total expenses $ 325.9 $ 88.3 $ 141.4 Net income (loss) $ 201.7 $ 255.1 $ 83.6 (1) Financial data for White Mountains’s equity method eligible investees is generally reported on a one-quarter lag. As a result of the 2019 MediaAlpha Transaction, White Mountains reduced its ownership interest of the basic units outstanding of MediaAlpha from 61.0% to 48.3% (58.9% to 42.0% on a fully diluted, fully converted basis). White Mountains’s remaining ownership interest in MediaAlpha no longer meets the criteria for a controlling ownership interest and, accordingly, White Mountains deconsolidated MediaAlpha as of February 26, 2019. Upon deconsolidation, White Mountains’s investment in MediaAlpha met the criteria to be accounted for under the equity method or under the fair value option. White Mountains elected the fair value option and the investment in MediaAlpha was initially measured at its estimated fair value of $114.7 million as of March 31, 2019, with the change in fair value of $114.7 million recognized as an unrealized investment gain. For the twelve months ended December 31, 2019, White Mountains recognized $180.0 million in unrealized investment gains associated with its investment in MediaAlpha including changes in the fair value of White Mountains’s investment in MediaAlpha subsequent to the 2019 MediaAlpha Transaction. On October 30, 2020, MediaAlpha completed the MediaAlpha IPO. Following the completion of the MediaAlpha IPO, White Mountains owns 20,532,202 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 value of White Mountains’s remaining investment in MediaAlpha was $802.2 million. For the twelve months ended December 31, 2020, White Mountains recognized $686.0 million in realized and unrealized investment gains associated with its investment in MediaAlpha. White Mountains’s consolidated statement of comprehensive income and its segment disclosures include MediaAlpha’s results of operations for the period from January 1, 2019 through February 26, 2019. See Note 2 — “ Significant Transactions ”. For the period from February 26, 2019 to December 31, 2019, MediaAlpha was considered a significant subsidiary. For the period from February 26, 2019 to December 31, 2019, MediaAlpha’s total revenues, total expenses, and net income were $359.2 million, $336.3 million, and $22.9 million. For the twelve months ended December 31, 2020, MediaAlpha was considered a significant subsidiary. The following tables present summarized financial information for MediaAlpha as of December 31, 2020 and 2019 for the twelve months ended December 31, 2020, 2019, and 2018: December 31, Millions 2020 2019 (1) Balance sheet data: Total assets $ 212.7 $ 105.4 Total liabilities $ 315.8 $ 144.9 (1) As of December 31, 2019, MediaAlpha recorded out of period adjustments that (decreased) increased total assets and total liabilities by $(1.5) and $0.3. The adjustments primarily related to MediaAlpha’s accounting for its other intangible assets and debt. White Mountains has evaluated the impact of the adjustments and concluded that they are not material, individually and in the aggregate, to current or prior period financial statements. Year Ended December 31, Millions 2020 2019 (1) 2018 (1) Income statement data: Total revenues $ 584.8 $ 408.0 $ 296.9 Total expenses $ 575.4 $ 390.2 $ 278.8 Net income (loss) $ 9.4 $ 17.8 $ 18.1 (1) For the twelve months ended December 31, 2019 and 2018, MediaAlpha recorded out of period adjustments that increased (decreased) total revenues by $0.1 and $(0.2), total expenses by $1.2 and $(9.4) and net income by $(1.1) and $9.2. The adjustments primarily related to MediaAlpha’s accounting for its equity-based compensation and amortization of other intangible assets. White Mountains has evaluated the impact of the adjustments and concluded that they are not material, individually and in the aggregate, to current or prior period financial statements.

Variable Interest Entities

Variable Interest Entities	12 Months Ended
	Dec. 31, 2020
Variable Interest Entity, Not Primary Beneficiary, Disclosures [Abstract]
Variable Interest Entities	Variable Interest Entities BAM As a mutual insurance company, BAM is owned by its members. BAM charges an insurance premium on each municipal bond insurance policy it writes. A portion of the premium is a member surplus contribution (“MSC”) and the remainder is a risk premium. In the event of a municipal bond refunding, a portion of the MSC from the original issuance can be reutilized, in effect serving as a credit against the total insurance premium on the refunding of the municipal bond. Issuers of debt insured by BAM are members of BAM so long as any of their BAM-insured debt is outstanding. As members, they have certain interests in BAM, including the right to vote for BAM’s directors and to receive dividends in the future, if declared. The equity at risk funded by BAM’s members is not sufficient to fund its operations without the additional financial support provided by the BAM Surplus Notes and accordingly, BAM is considered to be a VIE. At inception, BAM and HG Re also entered into the FLRT. 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, net of a ceding commission. HG Re’s obligations under the FLRT are limited to the assets in the Regulation 114 Trust and the Supplemental Trust. 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. In addition, under the FLRT, HG Holdings Ltd, a subsidiary of HG Global, has the right to designate two directors for election to BAM’s board of directors. Since BAM is owned by its members, its equity and results of operations are included in non-controlling interests. 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. Elementum On May 31, 2019, White Mountains acquired a 30.0% limited partnership interest in Elementum for $55.1 million. White Mountains has determined that Elementum is a VIE but that White Mountains is not the primary beneficiary. White Mountains’s ownership interest gives White Mountains the opportunity to exert significant influence over the significant financial and operating activities of Elementum. Accordingly, Elementum meets the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in Elementum. Changes in the fair value of Elementum are recorded in realized and unrealized investment gains. As of December 31, 2020, White Mountains’s maximum exposure to loss on its investment in Elementum is limited to the carrying value of $55.1 million. PassportCard/DavidShield On January 24, 2018, White Mountains acquired a 50% ownership interest in DavidShield, its joint venture partner in 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% 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/DavidShield. The gross purchase price for the 50% 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 operations. As a result of the transaction, White Mountains’s re-evaluated its accounting treatment for its investment in PassportCard/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 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/DavidShield. Accordingly, White Mountains’s investment in PassportCard/DavidShield meets the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard/DavidShield. Changes in the fair value of PassportCard/DavidShield are recorded in realized and unrealized investment gains. As of December 31, 2020, 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 $104.4 million. Kudu On April 4, 2019, White Mountains completed the Kudu Transaction for cash consideration of $81.4 million. White Mountains recognized total assets acquired of $155.5 million, including $7.6 million of goodwill and $2.2 million other intangible assets, total liabilities assumed of $0.8 million and non-controlling interest of $1.5 million. As a result of the Kudu Transaction, White Mountains’s basic unit ownership of Kudu increased from 49.5% to 99.1% (42.7% to 85.4% on a fully diluted, fully converted basis), and White Mountains began consolidating Kudu as a reportable segment in its financial statements during the second quarter of 2019. White Mountains’s consolidated financial statements and its segment disclosures include Kudu’s results for the period from April 4, 2019 to December 31, 2019. For periods prior to the Kudu Transaction, White Mountains determined that Kudu was a VIE but that White Mountains was not the primary beneficiary. White Mountains’s ownership interest gave White Mountains the opportunity to exert significant influence over the significant financial and operating activities of Kudu. Accordingly, for the year ended December 31, 2018, Kudu met the criteria to be accounted for under the equity method. White Mountains took the fair value option for its investment in Kudu, measuring its investment in Kudu at fair value using NAV as a practical expedient with changes therein recorded in realized and unrealized investment gains for the year ended December 31, 2018.

Fair Value of Financial Instrum

Fair Value of Financial Instruments	12 Months Ended
	Dec. 31, 2020
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. The following tables presents the fair value and carrying value of these financial instruments as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Carrying Value Fair Value Carrying Value NSM Bank Facility $ 279.3 $ 271.3 $ 221.2 $ 217.4 Other NSM debt $ 1.3 $ 1.3 $ 1.7 $ 1.8 Kudu Bank Facility (1) $ 89.3 $ 86.3 $ 53.6 $ 53.6 Other Operations debt $ 18.8 $ 17.5 $ 11.3 $ 10.7 (1) As of December 31, 2019, White Mountains measured the fair value of the Kudu Bank Facility debt at the carrying value as a result of the debt being acquired on December 23, 2019. See Note 5 — “Debt” .

Commitments and Contingencies

Commitments and Contingencies	12 Months Ended
	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	Commitments and Contingencies White Mountains leases certain office spaces under non-cancellable operating leases that expire on various dates through 2022. Rental expense for all of White Mountains’s locations was $7.7 million, $7.2 million and $5.5 million for the years ended December 31, 2020, 2019 and 2018. White Mountains also has various other lease obligations that are immaterial in the aggregate. White Mountains’s future annual minimum rental payments required under non-cancellable leases, which are primarily for office space, are $7.7 million, $7.3 million, $7.1 million, and $23.1 million for the years ending December 31, 2021, 2022, 2023 and 2024 and thereafter. White Mountains also has future binding commitments to fund certain other long-term investments. These commitments, which totaled $297.8 million as of December 31, 2020, do not have fixed funding dates. 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 December 31, 2020: Sirius Group Tax Contingency On April 18, 2016, White Mountains completed the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) to CM International Pte. Ltd. and CM Bermuda Limited (collectively “CMI”). In connection with the sale, White Mountains indemnified Sirius Group against the loss of certain interest deductions. In late October 2018, the Swedish Administrative Court ruled against Sirius Group on its appeal of the Swedish Tax Agency’s denial of these interest deductions, which related to periods prior to the sale of Sirius Group to CMI. As a result, in 2018 White Mountains recorded a loss of $17.3 million within net (loss) gain on sale of discontinued operations reflecting the value of these interest deductions. As of December 31, 2020 and December 31, 2019, White Mountains reported a liability of $18.7 million and $16.5 million, reflecting the value of these interest deductions. During 2020, the increase in the liability of $2.2 million is related to foreign currency translation and included within net loss on sale of discontinued operations. Sirius Group has appealed the decision to the Swedish Administrative Court of Appeal.

Held for Sale and Discontinued

Held for Sale and Discontinued Operations	12 Months Ended
	Dec. 31, 2020
Discontinued Operations and Disposal Groups [Abstract]
Held for Sale and Discontinued Operations	Held for Sale and Discontinued Operations Sirius Group On April 18, 2016, White Mountains completed the sale of Sirius Group to CMI. In connection with the sale, White Mountains indemnified Sirius Group against the loss of certain interest deductions. In late October 2018, the Swedish Administrative Court ruled against Sirius Group on its appeal of the Swedish Tax Agency’s denial of these interest deductions, which related to periods prior to the sale of Sirius Group to CMI. As a result, in 2018 White Mountains recorded a loss of $17.3 million within net (loss) gain on sale of discontinued operations reflecting the value of these interest deductions. As of December 31, 2020 and 2019, White Mountains reported a liability of $18.7 million and $16.5 million. During 2020, the increase in the liability of $2.2 million is related to foreign currency translation and included within net loss on sale of discontinued operations. Sirius Group has appealed the decision to the Swedish Administrative Court of Appeal. See Note 18 — “Commitments and Contingencies” . Other As of December 31, 2017, White Mountains has classified its Guilford, Connecticut property, which consists of an office building and adjacent land, as held for sale. On August 20, 2020, the office building was sold for $2.3 million. For the twelve months ended December 31, 2020, White Mountains recognized $0.1 million of realized loss on the sale of the office building. As of December 31, 2020, the adjacent land has been measured at its estimated fair value, net of costs of disposal, of $0.7 million. As of December 31, 2019, the property was measured at its estimated fair value, net of costs of disposal, of $3.0 million. As of December 31, 2020, assets held for sale also includes a corporate aircraft. The aircraft has been measured at its carrying value of $1.7 million, which is lower than its estimated fair value. 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 years ended December 31, 2020, 2019 and 2018: Year Ended December 31, 2020 2019 2018 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 708.7 $ 414.5 $ (141.2) Less: total income (loss) from continuing operations, net of tax 711.0 413.7 (124.0) Net (loss) income from discontinued operations attributable to (2.3) .8 (17.2) Allocation of (earnings) losses to participating restricted common shares (1) — — .2 Basic and diluted (loss) earnings per share numerators $ (2.3) $ .8 $ (17.0) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (3) (40.8) (40.5) (40.1) Basic earnings (loss) per share denominator 3,081.4 3,141.1 3,342.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (3) (40.8) (40.5) (40.1) Diluted earnings (loss) per share denominator 3,081.4 3,141.1 3,342.4 Basic (loss) earnings per share (in dollars) - discontinued operations: $ (.75) $ .25 $ (5.09) Diluted (loss) earnings per share (in dollars) - discontinued operations: $ (.75) $ .25 $ (5.09) (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 years ended December 31, 2020, 2019 and 2018. (3) Restricted common shares outstanding vest either in equal annual installments or upon a stated date. See Note 10 — “Employee Share-Based Compensation Plans” .

Subsequent Event

Subsequent Event	12 Months Ended
	Dec. 31, 2020
Subsequent Events [Abstract]
Subsequent Event	Subsequent Event Ark On October 1, 2020, White Mountains entered into the Ark SPA with the Ark Sellers. Certain Ark Sellers also entered into the Ark Acquisition Agreement pursuant to which they made certain warranties about the Ark business. Under the terms of the Ark Acquisition Agreement, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and to purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020 White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a credit facility agreement and $366.3 million placed in escrow, which is reflected on the balance sheet within the Other Operations segment as of December 31, 2020. On January 1, 2021, White Mountains closed the transaction in accordance with the terms of the Ark SPA. At closing, 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). If the additional $200.0 million is contributed in full, White Mountains will own 77.1% of Ark on a basic shares outstanding basis (67.5% on a fully-diluted, fully-converted basis). Management’s equity incentives are subject to an 8.0% rate of return threshold with no catch-up. 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. These additional shares are generally eligible to vest in three equal tranches at MOIC thresholds of 2.0x, 2.5x and 3.0x. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. Ark writes a diversified and balanced portfolio of reinsurance and insurance, including property, accident & health, energy, marine and political risks, through Lloyd’s Syndicates 4020 and 3902. Beginning in January 2021, Ark began writing certain classes of its business through Group Ark Insurance Limited, Ark’s wholly-owned Bermuda-based insurance and reinsurance company.

Selected Quarterly Financial Da

Selected Quarterly Financial Data (Unaudited)	12 Months Ended
	Dec. 31, 2020
Quarterly Financial Information Disclosure [Abstract]
Selected Quarterly Financial Data (Unaudited)	SELECTED QUARTERLY FINANCIAL DATA (Unaudited) The following table presents selected quarterly financial data for 2020 and 2019. The quarterly financial data includes, in the opinion of management, all recurring adjustments necessary for a fair presentation of the results of operations for the interim periods. Prior year amounts have been reclassified to conform to the current period’s presentation. Prior year amounts have also been adjusted for the impact of White Mountains’s financial statement revisions. 2020 Three Months Ended 2019 Three Months Ended Millions, Except Per Share Amounts Dec. 31 Sept. 30 June 30 Mar. 31 Dec. 31 Sept. 30 June 30 Mar. 31 Revenues $ 520.8 $ 459.5 $ 259.6 $ (59.2) $ 175.3 $ 155.5 $ 129.0 $ 433.6 Expenses 163.5 138.3 126.9 106.8 118.8 104.4 113.2 151.9 Pre-tax income (loss) 357.3 321.2 132.7 (166.0) 56.5 51.1 15.8 281.7 Tax (expense) benefit 117.6 (98.5) (24.1) 25.5 (10.4) (8.8) .1 (10.2) Income (loss) from continuing operations 474.9 222.7 108.6 (140.5) 46.1 42.3 15.9 271.5 Net (loss) gain from discontinued operations, net of tax (1) (1.5) (.7) (1.0) .9 (.8) .9 — .7 Non-controlling interest in consolidated subsidiaries 15.8 10.9 7.8 10.8 15.6 5.5 4.6 12.2 Income (loss) attributable to White Mountains’s common shareholders $ 489.2 $ 232.9 $ 115.4 $ (128.8) $ 60.9 $ 48.7 $ 20.5 $ 284.4 Income (loss) attributable to White Mountains’s common shareholders per share: Basic Continuing operations $ 158.19 $ 75.32 $ 37.46 $ (40.82) $ 19.37 $ 15.01 $ 6.44 $ 89.42 Discontinued operations (.49) (.23) (.32) .28 (.25) .28 — .22 Total consolidated operations $ 157.70 $ 75.09 $ 37.14 $ (40.54) $ 19.12 $ 15.29 $ 6.44 $ 89.64 Diluted Continuing operations $ 158.19 $ 75.32 $ 37.46 $ (40.82) $ 19.37 $ 15.01 $ 6.44 $ 89.42 Discontinued operations (.49) (.23) (.32) .28 (.25) .28 — .22 Total consolidated operations $ 157.70 $ 75.09 $ 37.14 $ (40.54) $ 19.12 $ 15.29 $ 6.44 $ 89.64 (1) During 2020 and 2019, net (loss) gain from discontinued operations arose from the tax contingency on the sale of Sirius Group. See Note 18 — “Commitments and Contingencies

SCHEDULE I SUMMARY OF INVESTMEN

SCHEDULE I SUMMARY OF INVESTMENTS-OTHER THAN INVESTMENTS IN RELATED PARTIES	12 Months Ended
	Dec. 31, 2020
SEC Schedule, 12-15, Insurance Companies, Summary of Investments, Other than Investments in Related Parties [Abstract]
Schedule I - Summary of Investments-Other Than Investments in Related Parties	WHITE MOUNTAINS INSURANCE GROUP, LTD. SUMMARY OF INVESTMENTS—OTHER THAN INVESTMENTS IN RELATED PARTIES At December 31, 2020 Millions Cost Carrying Fair Fixed maturity investments: U.S. Government and agency obligations $ 173.2 $ 176.3 $ 176.3 Debt securities issued by corporations 522.8 547.4 547.4 Municipal obligations 244.0 265.0 265.0 Mortgage and asset-backed securities 211.7 218.5 218.5 Total fixed maturity investments 1,151.7 1,207.2 1,207.2 Short-term investments 142.9 142.9 142.9 Investment in MediaAlpha — 802.2 802.2 Other long-term investments 767.4 786.8 786.8 Total investments $ 2,062.0 $ 2,939.1 $ 2,939.1

SCHEDULE II CONDENSED FINANCIAL

SCHEDULE II CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT	12 Months Ended
	Dec. 31, 2020
Condensed Financial Information Disclosure [Abstract]
Schedule II - Condensed Financial Information of the Registrant	CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT CONDENSED BALANCE SHEETS (1) December 31, Millions 2020 2019 Assets: Cash $ .7 $ .7 Fixed maturity investments, at fair value 10.1 10.0 Common equity securities, at fair value — 193.5 Short-term investments, at amortized cost 24.3 66.2 Other assets 2.5 1.9 Investments in consolidated subsidiaries 3,726.0 2,969.0 Total assets $ 3,763.6 $ 3,241.3 Liabilities: Payable to subsidiary $ (195.6) $ (69.3) Other liabilities 39.7 34.7 Total liabilities (2) (155.9) (34.6) White Mountains’s common shareholders’ equity 3,906.0 3,261.5 Non-controlling interests 13.5 14.4 Total liabilities and equity $ 3,763.6 $ 3,241.3 (1) These condensed unconsolidated financial statements reflect the results of operations, financial condition and cash flows for the Company. Investments in which White Mountains holds a controlling financial interest are accounted for using the equity method. Under the equity method, investments in subsidiaries are recorded on the condensed balance sheets at the amount of the Company’s ownership percentage of the subsidiary’s GAAP book value. The income from subsidiaries is reported on a net of tax basis as equity in earnings from consolidated and unconsolidated subsidiaries on the condensed statements of operations and comprehensive income. Capital contributions to and distributions from consolidated subsidiaries are presented within investing activities on the condensed statements of cash flows. (2) As of December 31, 2020 and 2019, White Mountains’s other liabilities includes $18.7 and $16.5 related to the Sirius Group tax contingency. See Note 18 — “Commitments and Contingencies ”. Schedules of the Registrant should be read in conjunction with the Consolidated Financial Statements and Notes. SCHEDULE II (continued) CONDENSED STATEMENTS OF OPERATIONS AND COMPREHENSIVE INCOME (1) Year Ended December 31, Millions 2020 2019 2018 Revenues (loss) (including realized and unrealized gains and losses) $ (8.7) $ 65.0 $ (47.7) Expenses 61.0 47.1 45.9 Pre-tax income (loss) (69.7) 17.9 (93.6) Income tax expense (.3) (.9) (2.5) Net income (loss) (70.0) 17.0 (96.1) Net gain (loss) from discontinued operations, net of tax (2) (2.3) .8 (17.2) Equity in earnings from consolidated and unconsolidated subsidiaries, 782.0 398.5 (27.4) Net income attributable to non-controlling interests (1.0) (1.8) (0.5) Net income (loss) attributable to White Mountains’s 708.7 414.5 (141.2) Other comprehensive (loss) income items, net of tax 6.8 (1.4) (4.5) Comprehensive income (loss) attributable to White Mountains’s $ 715.5 $ 413.1 $ (145.7) (1) These condensed unconsolidated financial statements reflect the results of operations, financial condition and cash flows for the Company. Investments in which White Mountains holds a controlling financial interest are accounted for using the equity method. Under the equity method, investments in subsidiaries are recorded on the condensed balance sheets at the amount of the Company’s ownership percentage of the subsidiary’s GAAP book value. The income from subsidiaries is reported on a net of tax basis as equity in earnings of subsidiaries on the condensed statements of operations and comprehensive income. Capital contributions to and distributions from subsidiaries are presented within investing activities on the condensed statements of cash flows. (2) During 2020, 2019 and 2018, net gain (loss) from discontinued operations includes $(2.3), $0.8 and $(17.3) arising from the tax contingency on the sale of Sirius Group. See Note 18 — “Commitments and Contingencies” . Schedules of the Registrant should be read in conjunction with the Consolidated Financial Statements and Notes. SCHEDULE II (continued) CONDENSED STATEMENTS OF CASH FLOWS (1) Year Ended December 31, Millions 2020 2019 2018 Net income (loss) attributable to White Mountains’s common shareholders $ 708.7 $ 414.5 $ (141.2) Charges (credits) to reconcile net income to net cash from operations: Net realized and unrealized investment (gains) losses on sales of investments 10.1 (61.0) 57.8 Undistributed earnings from subsidiaries (782.0) (398.5) 27.4 Net (gain) loss from sale of discontinued operations, net of tax (2) 2.3 (.8) 17.2 Other non-cash reconciling items, primarily amortization of restricted share and option awards (3) 19.0 20.0 34.6 Net change in other assets and liabilities (4) (2.6) 3.0 16.7 Net cash (used for) provided from operations (44.5) (22.8) 12.5 Cash flows from investing activities: Net change in short-term investments (5) (127.4) (37.6) 134.0 Purchases of investment securities (6) (6.7) (14.8) (321.2) Sales and maturities of investment securities (7) 189.7 207.9 967.6 Issuance of debt (to) from subsidiaries (8) (44.5) (83.5) (55.2) Repayment of debt to (from) subsidiaries (9) 92.6 5.0 31.0 Net distributions from (contributions to) subsidiaries (10)(11) 29.1 (46.1) (258.2) Net cash provided from (used for) investing activities 132.8 30.9 498.0 Cash flows from financing activities: Repurchases and retirement of common shares (8) (78.5) — (510.9) Dividends paid on common shares (3.2) (3.2) (3.8) Payments of restricted shares withholding taxes (6.6) (4.9) (10.0) Net cash used for financing activities (88.3) (8.1) (524.7) Net decrease in cash during the year — — (14.2) Cash balance at beginning of year .7 .7 14.9 Cash balance at end of year $ .7 $ .7 $ .7 (1) These condensed unconsolidated financial statements reflect the results of operations, financial condition and cash flows for the Company. Investments in which White Mountains holds a controlling financial interest are accounted for using the equity method. Under the equity method, investments in consolidated subsidiaries are recorded on the condensed balance sheets at the amount of the Company’s ownership percentage of the subsidiary’s GAAP book value. The income from consolidated subsidiaries is reported on a net of tax basis as equity in earnings of subsidiaries on the condensed statements of operations and comprehensive income. Capital contributions to and distributions from consolidated subsidiaries are presented within investing activities on the condensed statements of cash flows. (2) During 2020, 2019 and 2018, net gain (loss) from sale of discontinued operations includes $(2.3), $0.8 and $(17.3) arising from the tax contingency on the sale of Sirius Group. See Note 18 — “Commitments and Contingencies” . (3) For the years ended December 31, 2020, 2019 and 2018, amortization of restricted share awards was $16.6, $10.5 and $13.0. (4) For 2020, 2019 and 2018, net change in other assets and liabilities also included a $(4.8), $(6.6), and $4.0 net change in (receivables) payables to the Company’s subsidiaries. (5) During 2020, the Company had non-cash purchases of short-term investments of $169.6. During 2018, the Company had non-cash purchases of short-term investments of $284.6 and non-cash sales of short-term investments of $179.2. (6) During 2018, the Company had non-cash purchases of investment securities of $603.9, which included $170.5 of fixed maturity securities, $148.8 of common equity securities and $22.7 of other long term investments. (7) During 2018, the Company had non-cash sales of investment securities of $1,065.4, which included $373.4 of fixed maturity securities, $490.1 of common equity securities and $22.7 of other long-term investments. (8) During 2020, the Company had non-cash issuance of debt of $169.6 to its wholly-owned subsidiary, Bridge Holdings (“Bridge”). Proceeds of the debt, which were short-term investments, were transferred to Bridge. During 2018, the Company had non-cash issuance of debt of $349.5 to its wholly-owned subsidiary, Guilford Holding, Inc. (“Guilford”). Proceeds of the debt, which included $170.4 of fixed maturity securities and $179.2 of short-term investments, were transferred to Guilford. (9) During 2018, the Company received non-cash repayments of $22.7 from its wholly-owned subsidiary, Bridge in the form of other long term investments. (10) During 2019, the Company made cash contributions of $70.5 and $2.0 to Bridge and its wholly-owned subsidiary, White Mountains Investment Bermuda, Ltd (“WMIB”). During 2018, the Company made non-cash contributions of $350.0 by transferring intercompany debt receivable from Guilford to Bridge. Also during 2018, the Company made a non-cash contribution of $1.0 by transferring intercompany debt receivable from White Mountains Investments (Luxembourg) S.a’r.l. (“White Mountains Investments”), a wholly-owned subsidiary of Bridge, to Bridge. During 2018, the Company made cash contributions of $255.3 and $2.9 to Bridge and WMIB. (11) During 2020, the Company received cash distributions of $6.8 and $22.3 from its wholly-owned subsidiary, PSC Holdings, Ltd. and the Company’s subsidiary, HG Global Ltd. During 2019, the Company received cash distributions of $24.4 and $1.9 from WMIB and the Company’s subsidiary, HG Global Ltd. Schedules of the Registrant should be read in conjunction with the Consolidated Financial Statements and Notes.

SCHEDULE III SUPPLEMENTARY INSU

SCHEDULE III SUPPLEMENTARY INSURANCE INFORMATION	12 Months Ended
	Dec. 31, 2020
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Abstract]
Schedule III - Supplementary Insurance Information	WHITE MOUNTAINS INSURANCE GROUP, LTD. SUPPLEMENTARY INSURANCE INFORMATION Column Column Column C Column Column E Column Column Column Column Column Column Millions Deferred Future Unearned Other Policy Premiums Net Benefits, Amortization Other Operating Premiums Years ended: December 31, 2020 HG Global/ BAM $ 27.8 $ — $ 237.5 $ — $ 22.8 $ 19.5 $ — $ 7.0 $ .4 $ 61.7 December 31, 2019 HG Global/ BAM 22.1 — 198.4 — 16.3 21.6 — 5.7 .4 38.7 December 31, 2018 HG Global/ BAM 19.0 — 176.0 — 13.9 16.7 — 5.3 .4 52.9 Schedules of the Registrant should be read in conjunction with the Consolidated Financial Statements and Notes.

SCHEDULE IV REINSURANCE

SCHEDULE IV REINSURANCE	12 Months Ended
	Dec. 31, 2020
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Abstract]
Schedule IV - Reinsurance	WHITE MOUNTAINS INSURANCE GROUP, LTD. REINSURANCE Column A Column B Column C Column D Column E Column F $ in Millions Gross Amount Ceded to Other Assumed from Net Amount Percentage of Year ended: December 31, 2020 HG Global/BAM $ 19.4 $ — $ 3.4 $ 22.8 14.9 % December 31, 2019 HG Global/BAM 13.6 — 2.7 16.3 16.6 December 31, 2018 HG Global/BAM 13.6 — .3 13.9 2.2 Schedules of the Registrant should be read in conjunction with the Consolidated Financial Statements and Notes.

Basis of Presentation and Sig_2

Basis of Presentation and Significant Accounting Policies (Policies)	12 Months Ended
	Dec. 31, 2020
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 insurance 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 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. See Note 16 — “Variable Interest Entities” .
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.
Reporting 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 December 31, 2020, White Mountains’s reportable segments were HG Global/BAM, NSM, Kudu and Other Operations. On February 26, 2019, MediaAlpha completed the sale of a significant minority stake to Insignia Capital Group in connection with a recapitalization and cash distribution to existing equityholders (the “2019 MediaAlpha Transaction”). MediaAlpha also repurchased a portion of the holdings of existing equityholders. White Mountains deconsolidated MediaAlpha as a result of the 2019 MediaAlpha Transaction, and consequently it was no longer a reportable segment. White Mountains’s consolidated statement of comprehensive income and its segment disclosures include MediaAlpha’s results of operations through the date of the 2019 MediaAlpha Transaction. See Note 2 — “ Significant Transactions ” and Note 14 — “ Segment Information ”. The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purpose projects, such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its reinsurance subsidiary HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. 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, (the “BAM Surplus Notes”). As of December 31, 2020 and 2019, 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 attributed to non-controlling interests. 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 profitability of the insurance that it places. NSM does not take insurance risk. As of December 31, 2020 and 2019, White Mountains owned 96.6% and 96.4% of the basic units outstanding of NSM (89.6% and 88.4% on a fully diluted, fully converted basis). NSM was acquired by White Mountains in 2018. See Note 2 — “Significant Transactions ". The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”), a capital solutions provider for asset management firms. 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, typically tied to gross revenues and designed to generate immediate strong, stable cash yields. On April 4, 2019, White Mountains acquired the ownership interests in Kudu held by certain funds managed by Oaktree Capital Management, L.P. (“Oaktree”) for cash consideration of $81.4 million. In addition, White Mountains assumed all of Oaktree’s unfunded capital commitments to Kudu, increasing White Mountains’s total capital commitment to $250.0 million (the “Kudu Transaction”). As a result of the Kudu Transaction, White Mountains’s basic unit ownership of Kudu increased from 49.5% to 99.1% (42.7% to 85.4% on a fully diluted, fully converted basis), and White Mountains began consolidating Kudu in its financial statements during the second quarter of 2019. See Note 2 — “Significant Transactions ". 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 (for periods after the 2019 MediaAlpha Transaction), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/ DavidShield”), Elementum Holdings LP (“Elementum”), Kudu (for periods prior to the Kudu Transaction), certain other consolidated and unconsolidated entities and certain other assets. The MediaAlpha segment consisted of QL Holdings LLC and its wholly-owned subsidiary QuoteLab, LLC (collectively “MediaAlpha”). MediaAlpha is a marketing technology company. It operates a transparent and efficient customer acquisition technology platform that facilitates real-time transactions between buyers and sellers of consumer referrals (i.e., clicks, calls and leads), primarily in the property & casualty, health and life insurance verticals. MediaAlpha generates revenue by earning a fee for each consumer referral sold on its platform. A transaction becomes payable only on a qualifying consumer action, and is not contingent on the sale of a product to the consumer. MediaAlpha’s core verticals are property & casualty insurance, health insurance and life insurance. White Mountains deconsolidated MediaAlpha as a result of the 2019 MediaAlpha Transaction and stopped reporting it as a segment. Subsequent to the 2019 MediaAlpha Transaction, White Mountains’s non-c ontrolling equity interest in MediaAlpha was accounted for at fair value within other long-term investments. On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3,609,894 shares and received total proceeds of $63.8 million. Following the completion of the MediaAlpha IPO, White Mountains owns 20,532,202 MediaAlpha shares, representing a 35.0% ownership interest (32.3% on a fully-diluted, fully converted basis). Subsequent to the MediaAlpha IPO, White Mountains’s non-controlling equity interest in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock. As of December 31, 2020, White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet within the Other Operations segment. For comparability purposes, the amounts related to MediaAlpha in 2019 subsequent to the 2019 MediaAlpha Transaction have been reclassified from other long-term investments to investment in MediaAlpha.
Discontinued Operations and Assets and Liabilities Held for Sale	Discontinued Operations and Assets and Liabilities Held for Sale White Mountains has classified its Guilford, Connecticut property, which consists of an office building that was sold in August of 2020, and adjacent land as held for sale as of December 31, 2020 and 2019. The property has been measured at its estimated fair value, net of disposal costs. As of December 31, 2020, assets held for sale also includes a corporate aircraft. The aircraft has been measured at its carrying value of $1.7 million, which is lower than its estimated fair value. See Note 19 — “Held for Sale and Discontinued Operations” .
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. Cash balances that are not immediately available for general corporate purposes, including fiduciary accounts held by NSM on behalf of insurance carriers, are classified as restricted.
Short-Term Investments	Short-Term Investments Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year. Short-term investments are carried at amortized or accreted cost, which approximated fair value as of December 31, 2020 and 2019.
Investment Securities	Investment Securities As of December 31, 2020 and 2019, White Mountains’s invested assets consisted of securities and other investments held for general investment purposes. White Mountains’s portfolio of fixed maturity investments, investment in MediaAlpha, common equity securities and other long-term investments held for general investment purposes are generally classified as trading securities and are reported at fair value as of the balance sheet date. Changes in net unrealized investment gains (losses) are reported pre-tax in revenues. Realized investment gains (losses) are accounted for using the specific identification method and are reported pre-tax in revenues. Premiums and discounts on all fixed maturity investments are amortized and accreted to income over the anticipated life of the investment. White Mountains’s invested assets that are measured at fair value include fixed maturity investments, its investment in MediaAlpha, common equity securities and other long-term investments, that consists primarily of unconsolidated entities, including non-controlling equity interests in the form of revenue and earnings participation contracts (“Kudu’s Participation Contracts”), private equity funds, hedge funds, insurance-linked securities (“ILS”) funds and private debt instruments. Whenever possible, White Mountains estimates fair value using valuation methods that maximize the use of quoted prices and other observable inputs. Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants (an exit price) at a particular measurement date. 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 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”). Assets and liabilities carried at fair value include substantially all of White Mountains’s investment portfolio, and derivative instruments, both exchange-traded and over the counter instruments. Valuation of assets and liabilities measured at fair value require management to make estimates and apply judgment to matters that may carry a significant degree of uncertainty. In determining fair value estimates, White Mountains uses a variety of valuation approaches and inputs. Whenever possible, White Mountains estimates fair value using valuation methods that maximize the use of quoted market prices or other observable inputs. Where appropriate, assets and liabilities measured at fair value have been adjusted for the effect of counterparty credit risk. White Mountains uses outside pricing services and brokers to assist in determining fair values. The outside pricing services White Mountains uses have indicated that they will only provide prices where observable inputs are available. As of December 31, 2020, approximately 73% of the investment portfolio recorded at fair value was priced based upon quoted market prices or other observable inputs. Level 1 Measurements Investments valued using Level 1 inputs include White Mountains’s investment in MediaAlpha subsequent to the MediaAlpha IPO, common equity securities and fixed maturity investments, primarily investments in U.S. Treasuries and short-term investments, which include U.S. Treasury Bills. For investments in active markets, White Mountains uses the quoted market prices provided by outside pricing services to determine fair value. Level 2 Measurements Investments valued using Level 2 inputs include fixed maturity investments which have been disaggregated into classes, including debt securities issued by corporations, municipal obligations and mortgage and asset-backed securities. Investments valued using Level 2 inputs also include certain passive exchange traded funds (“ETFs”) that track U.S. stock indices such as the S&P 500 Index, but are traded on foreign exchanges, which White Mountains values using the fund manager’s published net asset value per share (“NAV”) to account for the difference in market close times. In circumstances where quoted market prices are unavailable or are not considered reasonable, White Mountains estimates the fair value using industry standard pricing methodologies and observable inputs such as benchmark yields, reported trades, broker-dealer quotes, issuer spreads, benchmark securities, bids, offers, credit ratings, prepayment speeds, reference data including research publications and other relevant inputs. Given that many fixed maturity investments do not trade on a daily basis, the outside pricing services evaluate a wide range of fixed maturity investments by regularly drawing parallels from recent trades and quotes of comparable securities with similar features. The characteristics used to identify comparable fixed maturity investments vary by asset type and take into account market convention. White Mountains’s process to assess the reasonableness of the market prices obtained from the outside pricing sources covers substantially all of its fixed maturity investments and includes, but is not limited to, the evaluation of pricing methodologies and a review of the pricing services’ quality control procedures on at least an annual basis, a comparison of its invested asset prices obtained from alternate independent pricing vendors on at least a semi-annual basis, monthly analytical reviews of certain prices and a review of the underlying assumptions utilized by the pricing services for select measurements on an ad hoc basis throughout the year. White Mountains also performs back-testing of selected investment sales activity to determine whether there are any significant differences between the market price used to value the security prior to sale and the actual sale price of the security on an ad-hoc basis throughout the year. Prices provided by the pricing services that vary by more than $0.5 million and 5% from the expected price based on these assessment procedures are considered outliers, as are prices that have not changed from period to period and prices that have trended unusually compared to market conditions. In circumstances where the results of White Mountains’s review process does not appear to support the market price provided by the pricing services, White Mountains challenges the vendor provided price. If White Mountains cannot gain satisfactory evidence to support the challenged price, White Mountains will rely upon its own internal pricing methodologies to estimate the fair value of the security in question. The valuation process described above is generally applicable to all of White Mountains’s fixed maturity investments. The techniques and inputs specific to asset classes within White Mountains’s fixed maturity investments for Level 2 securities that use observable inputs are as follows: Debt Securities Issued by Corporations: The fair value of debt securities issued by corporations is determined from a pricing evaluation technique that uses information from market sources and integrates relative credit information, observed market movements, and sector news. Key inputs include benchmark yields, reported trades, broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including sector, coupon, credit quality ratings, duration, credit enhancements, early redemption features and market research publications. Municipal Obligations: The fair value of municipal obligations is determined from a pricing evaluation technique that uses information from market makers, brokers-dealers, buy-side firms, and analysts along with general market information. Key inputs include benchmark yields, reported trades, issuer financial statements, material event notices and new issue data, as well as broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including type, coupon, credit quality ratings, duration, credit enhancements, geographic location and market research publications. Mortgage and Asset-Backed Securities: The fair value of mortgage and asset-backed securities is determined from a pricing evaluation technique that uses information from market sources and leveraging similar securities. Key inputs include benchmark yields, reported trades, underlying tranche cash flow data, collateral performance, plus new issue data, as well as broker-dealer quotes, issuer spreads, two-sided markets, benchmark securities, bids, offers, and reference data including issuer, vintage, loan type, collateral attributes, prepayment speeds, default rates, recovery rates, cash flow stress testing, credit quality ratings and market research publications. Level 3 Measurements Fair value estimates for investments that trade infrequently and have few or no quoted market prices or other observable inputs are classified as Level 3 measurements. Investments valued using Level 3 fair value estimates are based upon unobservable inputs and include investments in certain fixed maturity investments, common equity securities and other long-term investments where quoted market prices or other observable inputs are unavailable or are not considered reliable or reasonable. Level 3 valuations are generated from techniques that use assumptions not observable in the market. These unobservable inputs reflect White Mountains’s assumptions of what market participants would use in valuing the investment. In certain circumstances, investment securities may start out as Level 3 when they are originally issued, but as observable inputs become available in the market, they may be reclassified to Level 2. Transfers of securities between levels are based on investments held as of the beginning of the period.
Other Long-Term Investments	Other Long-Term Investments As of December 31, 2020, White Mountains owned a portfolio of other long-term investments valued at $786.8 million, that consisted primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, the Elementum managed ILS funds (the “ILS Funds”) and private debt instruments. As of December 31, 2020, $614.2 million of White Mountains’s other long-term investments, that consisted primarily of unconsolidated entities, including Kudu’s Participation Contracts and private debt instruments were classified as Level 3 investments in the GAAP fair value hierarchy, were not actively traded in public markets and did not have readily observable market prices. The determination of the fair value of these securities involves significant management judgment, and the use of valuation models and assumptions that are inherently subjective and uncertain. As of December 31, 2020, $172.6 million of White Mountains’s other long-term investments, consisting of private equity funds and the ILS Funds, were valued at fair value using NAV as a practical expedient. Investments for which fair value is measured at NAV using the practical expedient are not classified within the fair value hierarchy. White Mountains may use a variety of valuation techniques to determine fair value depending on the nature of the investment, including a discounted cash flow analysis, market multiple approach, cost approach and/or liquidation analysis. On an ongoing basis, White Mountains also considers qualitative changes in facts and circumstances, which may impact the valuation of unconsolidated entities, including economic and market changes in relevant industries, changes to the entity’s capital structure, business strategy and key personnel, and any recent transactions relating to the unconsolidated entity. On a quarterly basis, White Mountains evaluates the most recent qualitative and quantitative information of the business and completes a fair valuation analysis for all Level 3 other long-term investments. Periodically, and at least on an annual basis, White Mountains uses a third-party valuation firm to complete an independent valuation analysis of significant unconsolidated entities.
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 its 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 December 31, 2020, White Mountains holds interest rate cap derivative instruments that do not meet the criteria for hedge accounting. As of December 31, 2020 and 2019, White Mountains holds an interest rate swap derivative instrument that meets the criteria for hedge accounting. See Note 7 — “Derivatives” .
Receivables	ReceivablesBAM’s receivables consist primarily of premiums receivable from customers for municipal bond insurance policies. NSM’s receivables consist of insurance premiums receivable from customers and commissions receivable from insurance carriers, net of a provision for amounts estimated to be uncollectible.
Incentive Compensation	Incentive Compensation 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. Non-share-based awards are recognized over the related service periods based on management’s best estimate of the amounts at which the awards are expected to be paid. Share-based compensation which is typically settled in cash, such as performance shares, is classified as a liability-type award. The compensation cost for liability-classified awards is measured initially at the grant date fair value and remeasured each reporting period until settlement. The compensation cost for equity-classified awards expected to be settled in shares, such as options and restricted shares, is measured at the original grant date fair value of the award. The compensation cost for all awards is recognized for the vested portion of the awards over the related service periods. See Note 10 — “Employee Share-Based Incentive Compensation Plans”.
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 trade names, URL and online names, customer relationships and contracts, information technology platforms and insurance licenses. Goodwill and other intangible assets with indefinite lives are not amortized, but rather are evaluated for impairment on an annual basis, or whenever indications of potential impairment exist. In the absence of any indications of potential impairment, the evaluation of goodwill and indefinite-lived intangible assets is performed no later than the interim period in which the anniversary of the acquisition date falls. White Mountains initially evaluates goodwill using a qualitative approach (step zero) to determine whether it is more likely than not that the implied fair value of goodwill is greater than its carrying value. If the results of the qualitative evaluation indicate that it is more likely than not that the carrying value of goodwill exceeds its implied fair value, White Mountains performs the two-step quantitative test for impairment. Other intangible assets with finite lives are measured at their acquisition date fair values, are amortized over their economic lives and presented net of accumulated amortization on the balance sheet. Other intangible assets with finite lives are reviewed for impairment when events occur or there are changes in circumstances indicating that their carrying value may exceed fair value. Impairment exists when the carrying value of other intangible assets exceeds fair value.
Municipal Bond Guarantee Insurance	Municipal Bond Guarantee Insurance All of the contracts issued by BAM are accounted for as insurance contracts under ASC 944-605, Financial Guarantee Insurance Contracts. Premiums are generally received upfront and an unearned premium revenue liability, equal to the amount of the premium received, is established at contract inception. Installment premiums are measured at the present value of contractual premiums, discounted at the risk-free rate, which is set at the inception of the insurance contract. Premium revenues are recognized in revenue over the period of the contracts in proportion to the amount of insurance protection provided using a constant rate. The constant rate is calculated based on the relationship between the par outstanding in a given reporting period compared with the sum of each of the par amounts outstanding for all periods. Deferred acquisition costs represent commissions, premium taxes, excise taxes and other costs which are directly attributable to and vary with the production of business. These costs are deferred and amortized to the extent they relate to successful contract acquisitions over the applicable premium recognition period as acquisition expenses. Deferred acquisition costs are limited to the amount expected to be recovered from future earned premiums and anticipated investment income. BAM’s obligation for outstanding contracts consists of the unearned premium reserve and any loss reserves. Loss reserves are recorded only to the extent that the present value of the expected amount of any losses to be paid, net of any expected recoveries, exceeds the associated unearned premium reserve. As of December 31, 2020 and 2019, BAM did not have any loss or loss adjustment expense reserves.
Revenue Recognition	Revenue Recognition NSM’s revenues consist primarily of commissions and broker revenues for placement of insurance policies and administrative fees for claims and other services provided to insurance carriers. Commission and broker revenues and service fees are measured based on the contractual rates with insurance carriers, net of any amounts expected to be uncollectible and any amounts associated with expected policy cancellations, adjustments, and are recognized when contractual performance obligations have been fulfilled. NSM’s primary contractual performance obligations are generally satisfied upon the issuance of an insurance policy by the carrier. Where NSM has significant performance obligations beyond the policy issuance date, NSM estimates the relative standalone selling price for the post-issuance services in order to allocate the transaction price using the price charged for the service when sold separately in similar circumstances to similar customers. Deferred revenues associated with unsatisfied performance obligations are recognized within other liabilities. Contingent commissions are based upon the overall profit and/or volume of the business placed with the insurance carrier during a calendar year and are determined after the contractual period has ended. NSM recognizes revenue on contingent commissions when management has determined that it is probable that the contingent commission requirements have been met. Kudu’s revenues are primarily generated from non-controlling equity interests in revenue and earnings participation contracts with asset management firms. The participation contracts are measured at fair value with the change therein recognized within unrealized investment gains and losses. Distributions from Kudu’s clients are recognized through investment income when Kudu’s right to receive payment has been established and can be reliably measured, which generally occurs on a quarterly basis in accordance with the terms of the underlying participation contracts. During the period in which MediaAlpha was consolidated by White Mountains, MediaAlpha recognized advertising and publishing fee revenues based on the contractual amount of the fees, adjusted for any amounts expected to be refunded or uncollectible, when it had satisfied its contractual performance obligations, which was generally at the time each transaction was executed. For transactions where MediaAlpha acted as the principal, such as the Open exchange, revenue amounts were reported gross. For transactions where MediaAlpha acted as an agent facilitating transactions between third parties, revenue amounts were reported at the net fee billed.
Cost of Sales and Broker Commission Expense	Cost of Sales and Broker Commission Expense NSM’s broker commission expense consists of commissions paid to sub-agents and brokers. Broker commission expense is measured in accordance with contractual terms and recognized when incurred, which is generally at the policy issuance date. MediaAlpha’s cost of sales consisted primarily of revenue sharing payments to publisher partners and traffic acquisition costs to top tier search engines. Cost of sales were measured based on contract terms and recognized when the related revenue transactions are executed. Other Operations’s cost of sales consists of salaries and related expenses, professional services and marketing and advertising expenses directly related to sales generation. These expenses are recognized as incurred.
Income Taxes	Income Taxes White Mountains has subsidiaries and branches that operate in various jurisdictions around the world and are subject to tax in the jurisdictions in which they operate. As of December 31, 2020, the jurisdictions in which White Mountains’s subsidiaries and branches were subject to tax were Barbados, Ireland, Israel, Luxembourg, the United Kingdom and the United States. Income earned or losses generated by companies outside the United States are generally subject to an overall effective tax rate lower than that imposed by the United States.
Foreign Currency Exchange	Foreign Currency Exchange The functional currency for White Mountains’s non-U.S. based subsidiaries are measured, in most instances, using functional currencies other than the U.S. dollar. Net foreign exchange gains and losses arising from the translation of functional currencies are generally reported in shareholders’ equity, in accumulated other comprehensive income or loss. White Mountains also invests in securities denominated in foreign currencies. Assets and liabilities recorded in these foreign currencies are translated into U.S. dollars at exchange rates in effect at the balance sheet date, and revenues and expenses are converted using the weighted average exchange rates for the period. As of December 31, 2020 and 2019, White Mountains had unrealized foreign currency translation gains (losses) of $5.6 million and $(2.4) million recorded in accumulated other comprehensive income (loss) on its consolidated balance sheet.
Leases	LeasesLeases consist primarily of operating leases for office space and equipment. Lease assets and liabilities are recognized at the lease commencement date based on the present value of future minimum lease payments over the lease term. Lease assets and liabilities are not recorded for leases with a term at inception of one year or less. Lease expense is included in operating expenses.
Non-controlling Interests	Non-controlling Interests Non-controlling interests consist of the ownership interests of non-controlling shareholders in consolidated subsidiaries, and are presented separately on the balance sheet. The portion of comprehensive income attributable to non-controlling interests is presented net of related income taxes in the statement of operations and comprehensive income. See Note 12 — “Common Shareholders’ Equity and Non-controlling Interests”
Recent Accounting Pronouncements	Recently Adopted Changes in Accounting Principles Income Taxes On January 1, 2020, White Mountains adopted ASU 2019-12, Simplifying the Accounting for Income Taxes (ASC 740), which removes exceptions to standard guidance. Under the new guidance non-income-based taxes, such as franchise taxes, are reported within pre-tax income rather than being included in income taxes. In addition, the new guidance eliminated the exception to the incremental approach for inter-period tax allocation, which previously allowed consideration of the tax effect of items such as discontinued operations and items recognized through other comprehensive income. For periods subsequent to the adoption of ASU 2019-12, White Mountains has recorded both the tax expense related to BAM’s member surplus contributions (“MSC”) and the related valuation allowance on such taxes through the non-controlling interest equity. Prior to the adoption of ASU 2019-12, White Mountains recorded the tax expense related to BAM’s MSC directly to non-controlling interest equity, while the valuation allowance on such taxes was recorded through the income statement. Goodwill On January 1, 2020, White Mountains adopted ASU 2017-04, Simplifying the Test for Goodwill Impairment (ASC 350), which changed the guidance on goodwill impairment testing. Under the new guidance, the qualitative assessment of the recoverability of goodwill remains the same, but the second step of the two-step qualitative test, which required calculation of the implied fair value of goodwill, has been eliminated. Instead, an impairment charge is recognized when the carrying value of a reporting unit exceeds its fair value. Any excess of carrying value over fair value is written down as an impairment. White Mountains did not identify any impairment indicators associated with its reporting units and therefore did not recognize an impairment of goodwill during the year ended December 31, 2020, and accordingly, adoption of ASU 2017-04 did not have any impact on White Mountains’s financial statements. Credit Losses On January 1, 2020, White Mountains adopted ASU 2016-13, Measurement of Credit Losses on Financial Instruments (ASC 326), which establishes new guidance for the recognition of credit losses for financial assets measured at amortized cost. The new ASU requires reporting entities to estimate the credit losses expected over the life of a credit exposure using historical information, current information and reasonable and supportable forecasts that affect the collectability of the financial asset. White Mountains measures its portfolio of investment securities at fair value with changes therein recognized through current period earnings and, accordingly, adoption of ASU 2016-13 did not have any impact on White Mountains’s financial statements. Premium Amortization on Callable Debt Securities On January 1, 2019, White Mountains adopted ASU 2017-08, Premium Amortization on Purchased Callable Debt Securities

Investment Securities (Tables)

Investment Securities (Tables)	12 Months Ended
	Dec. 31, 2020
Investments, Debt and Equity Securities [Abstract]
Schedule of pre-tax net investment income	The following table presents pre-tax net investment income for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Fixed maturity investments $ 29.0 $ 32.4 $ 35.1 Short-term investments 1.1 5.0 8.0 Investment in MediaAlpha (1) 59.9 8.0 — Common equity securities 6.6 13.5 15.1 Other long-term investments 35.6 22.1 3.8 Total investment income 132.2 81.0 62.0 Third-party investment expenses (1.2) (1.3) (3.0) Net investment income $ 131.0 $ 79.7 $ 59.0 (1) For 2018, MediaAlpha was a majority-owned consolidated subsidiary of White Mountains. See Note 2 — “Significant Transactions”
Schedule of net realized and unrealized investment gains and losses	The following table presents net realized and unrealized investment gains (losses) for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Fixed maturity investments $ 38.5 $ 43.5 $ (34.7) Short-term investments .4 .2 (.8) Investment in MediaAlpha (1) 686.0 180.0 — Common equity securities 6.5 195.7 (98.9) Other long-term investments (2) (14.6) 13.8 26.1 Net realized and unrealized investment gains (losses) 716.8 433.2 (108.3) Less: net gains (losses) on investment securities sold 20.2 24.6 (33.0) Net realized and unrealized investment gains (losses) on investment securities held at the end of the period $ 696.6 $ 408.6 $ (75.3) (1) For 2018, MediaAlpha was a majority-owned consolidated subsidiary of White Mountains. See Note 2 — “Significant Transactions” (2) For 2020, 2019 and 2018, includes $4.0, $(0.3) and $(0.8) of realized and unrealized investment gains (losses) related to foreign currency exchange.
Schedule of 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 years ended December 31, 2020, 2019 and 2018 for investments still held at the end of the period: Year Ended December 31, Millions 2020 2019 2018 Other long-term investments (1) $ 276.0 $ 181.9 $ 22.6 Total net unrealized investment gains, pre-tax - Level 3 investments $ 276.0 $ 181.9 $ 22.6 (1) For 2020 and 2019, includes $278.7 and $180.0 of unrealized investment gains from White Mountains’s investment in MediaAlpha.
Schedule of fixed maturity 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 December 31, 2020 and 2019. 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 December 31, 2019 Millions Cost or Gross Gross Carrying U.S. Government and agency obligations $ 231.7 $ 1.0 $ (.2) $ 232.5 Debt securities issued by corporations 454.9 12.5 (.2) 467.2 Municipal obligations 284.7 12.5 (.1) 297.1 Mortgage and asset-backed securities 206.6 2.7 (.3) 209.0 Total fixed maturity investments $ 1,177.9 $ 28.7 $ (.8) $ 1,205.8 The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of December 31, 2020. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties. December 31, 2020 Millions Cost or Amortized Cost Carrying Value Due in one year or less $ 126.0 $ 127.0 Due after one year through five years 417.5 433.6 Due after five years through ten years 283.2 303.2 Due after ten years 113.3 124.9 Mortgage and asset-backed securities 211.7 218.5 Total $ 1,151.7 $ 1,207.2
Schedule of equity securities and other long-term investments	The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency losses, and carrying values of White Mountains’s investment in MediaAlpha, common equity securities and other long-term investments as of December 31, 2020 and 2019: December 31, 2020 Millions Cost or Gross Unrealized Gross Unrealized Net Foreign Carrying Investment in MediaAlpha $ — $ 802.2 $ — $ — $ 802.2 Common equity securities $ — $ — $ — $ — $ — Other long-term investments $ 767.4 $ 95.8 $ (78.1) $ 1.7 $ 786.8 December 31, 2019 Millions Cost or Gross Unrealized Gross Unrealized Net Foreign Carrying Investment in MediaAlpha $ — $ 180.0 $ — $ — $ 180.0 Common equity securities $ 553.3 $ 130.6 $ — $ — $ 683.9 Other long-term investments $ 667.4 $ 75.2 $ (64.1) $ (2.2) $ 676.3
Schedule of fair value measurements for investment securities by level	The following tables present White Mountains’s fair value measurements for investments as of December 31, 2020 and 2019 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations and common equity securities by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated these asset classes into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate and S&P 500 indices. 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 (1) 142.9 142.9 — — Investment in MediaAlpha 802.2 802.2 — — Other long-term investments 614.2 — — 614.2 Other long-term investments — NAV (2) 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) Short-term investments are measured at amortized cost, which approximates fair value. (2) Consists of private equity funds and the ILS Funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. December 31, 2019 Millions Fair Value Level 1 Level 2 Level 3 Fixed maturity investments: U.S. Government and agency obligations $ 232.5 $ 232.5 $ — $ — Debt securities issued by corporations: Financials 144.8 — 144.8 — Industrial 59.0 — 59.0 — Healthcare 52.6 — 52.6 — Consumer 50.9 — 50.9 — Energy 44.9 — 44.9 — Technology 41.2 — 41.2 — Communications 31.3 — 31.3 — Utilities 25.0 — 25.0 — Materials 17.5 — 17.5 — Total debt securities issued by corporations 467.2 — 467.2 — Municipal obligations 297.1 — 297.1 — Mortgage and asset-backed securities 209.0 — 209.0 — Total fixed maturity investments 1,205.8 232.5 973.3 — Short-term investments (1) 201.2 189.4 11.8 — Investment in MediaAlpha 180.0 — — 180.0 Common equity securities: Exchange traded funds (2) 536.4 521.6 14.8 — Other (3) 147.5 25.9 121.5 .1 Total common equity securities 683.9 547.5 136.3 .1 Other long-term investments 474.0 — — 474.0 Other long-term investments — NAV (4) 202.3 — — — Total other long-term investments 676.3 — — 474.0 Total investments $ 2,947.2 $ 969.4 $ 1,121.4 $ 654.1 (1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement. (3) Primarily consists of two investments in unit trusts that predominantly invest in international equities and an open-end mutual fund that invests in domestic large-cap companies. (4) Consists of private equity funds, one hedge fund and the 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.
Schedule of credit ratings of debt securities issued	The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2020 and 2019: Fair Value at December 31, Millions 2020 2019 AAA $ 10.6 $ 9.5 AA 57.9 73.9 A 318.3 288.5 BBB 159.6 95.3 BB 1.0 — Debt securities issued by corporations (1) $ 547.4 $ 467.2 (1) Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.
Schedule of mortgage and asset-backed securities	The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Level 2 Level 3 Fair Value Level 2 Level 3 Mortgage-backed securities: Agency: FNMA $ 88.7 $ 88.7 $ — $ 88.6 $ 88.6 $ — FHLMC 70.1 70.1 — 60.5 60.5 — GNMA 40.6 40.6 — 30.8 30.8 — Total agency (1) 199.4 199.4 — 179.9 179.9 — Total mortgage-backed securities 199.4 199.4 — 179.9 179.9 — Other asset-backed securities: Credit card receivables 11.3 11.3 — 14.0 14.0 — Vehicle receivables 7.8 7.8 — 15.1 15.1 — Total other asset-backed securities 19.1 19.1 — 29.1 29.1 — Total mortgage and asset-backed securities $ 218.5 $ 218.5 $ — $ 209.0 $ 209.0 $ — (1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).
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 December 31, 2020 and 2019: Carrying Value at Millions December 31, 2020 December 31, 2019 Kudu’s Participation Contracts $ 400.6 $ 266.5 PassportCard/DavidShield 95.0 90.0 Elementum Holdings L.P. 55.1 55.1 Other unconsolidated entities (1) 42.4 33.7 Total unconsolidated entities (2) 593.1 445.3 Private equity funds and hedge funds 121.2 161.1 Insurance-linked securities funds 51.4 41.2 Private debt investments (2) (3) 21.1 28.7 Total other long-term investments $ 786.8 $ 676.3 (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. (2) See Fair Value Measurements by Level table. (3) Includes $5.8 and $5.0 in private debt investments carried at fair value as of December 31. 2020 and amortized cost as of December 31, 2019.
Schedule of investments and unfunded commitments by investment objective and sector	The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Unfunded Fair Value Unfunded Private equity funds Aerospace/Defense/Government $ 69.1 $ 15.3 $ 33.8 $ 23.3 Manufacturing/Industrial 28.6 — 57.7 4.1 Financial services 23.5 30.4 15.0 22.8 Total private equity funds 121.2 45.7 106.5 50.2 Hedge funds Long/short banks and financial — — 54.6 — Total hedge funds — — 54.6 — Total private equity funds and hedge funds included in other long-term investments $ 121.2 $ 45.7 $ 161.1 $ 50.2
Schedule investments in 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 December 31, 2020: Millions 1 – 3 years 3 – 5 years 5 – 10 years >10 years Total Private equity funds — expected lock-up period remaining $ 8.0 $ 40.7 $ 64.7 $ 7.8 $ 121.2
Schedule of fair value investments by level	The following tables present the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2020 and 2019: Level 3 Investments Other Long-term Investments Measured at NAV (1) Millions Level 1 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 436.4 15.9 — 275.6 (11.5) 716.4 (3) Amortization/accretion (.1) (4.4) — — — (4.5) Purchases 133.9 437.6 — 151.5 43.6 766.6 Sales (830.4) (527.8) (.1) (8.2) (61.8) (1,428.3) Effect of MediaAlpha IPO (4) 458.7 — — (458.7) — — Transfers in — — — — — — Transfers out — — — — — — Balance at December 31, 2020 $ 978.5 $ 1,030.9 $ — $ 614.2 $ 172.6 $ 2,796.2 (2) (1) Includes private equity funds, hedge funds and the 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 $142.9 and $201.2 as of December 31, 2020 and 2019 classified as short-term investments. (3) Excludes realized and unrealized losses associated with short-term investments of $0.4 for the year ended December 31, 2020. (4) Represents the reclassification of White Mountains’s investment in MediaAlpha from a level 3 measurement to a level 1 measurement in connection with the MediaAlpha IPO. See Note 2 - “Significant Transactions” . Level 3 Investments Other Long-term Investments Measured at NAV (1) Millions Level 1 Level 2 Common Other Long- term Total Balance at December 31, 2018 $ 842.6 $ 1,160.5 $ — $ 138.7 $ 186.9 $ 2,328.7 (2) Net realized and unrealized gains 163.0 76.1 — 181.2 12.7 433.0 (3) Amortization/accretion .2 (1.8) — — — (1.6) Purchases 165.3 404.5 .1 185.4 110.8 866.1 Sales (391.1) (529.7) — — (29.5) (950.3) Effect of Kudu Transaction — — — 141.8 (71.7) 70.1 Transfers in — — — 10.9 4.0 14.9 Transfers out — — — (4.0) (10.9) (14.9) Balance at December 31, 2019 $ 780.0 $ 1,109.6 $ .1 $ 654.0 $ 202.3 $ 2,746.0 (2) (1) Includes private equity funds, hedge funds and the 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 $201.2 and $214.2 as of December 31, 2019 and 2018 classified as short-term investments. (3) Includes $114.7 unrealized investment gain associated with the 2019 MediaAlpha Transaction. See Note 2 — “Significant Transactions”. (4) Excludes realized and unrealized losses associated with short-term investments of $0.2 for the year ended December 31, 2019.
Schedule of significant unobservable inputs used in estimating the fair value of other long-term investments	The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s investment in MediaAlpha and other long-term investments, other than private equity funds, hedge funds and the ILS Funds, classified within Level 3 as of December 31, 2020 and 2019. The fair value of investments in private equity funds, hedge funds and the ILS Funds are generally estimated using the NAV of the funds. $ 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 instruments Discounted cash flow $17.1 4% - 8% N/A All other Discounted cash flow $18.8 20% - 24% 4% New Market Solutions, LLC Recent transaction $9.9 Transaction price: $9.9 Noblr, Inc. Recent transaction $8.7 Transaction price: $8.7 Zillion Insurance Services, Inc. (7) Recent transaction $5.0 Transaction price: $5.0 (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” . (7) In 2020, White Mountains made an additional $2.5 investment in Zillion Insurance Services, Inc. $ in Millions December 31, 2019 Description Valuation Technique(s) (1) Fair Value (2) Unobservable Inputs Discount Rate (3) Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (3) Kudu’s Participation Contracts (4) Discounted cash flow $266.5 15% - 22% 6x - 12x Investment in MediaAlpha Discounted cash flow $180.0 15% 4% PassportCard/DavidShield Discounted cash flow $90.0 22% 4% Elementum Holdings, L.P. (5) Discounted cash flow $55.1 20% 4% Private debt instruments Discounted cash flow $23.7 4% - 9% N/A All other Discounted cash flow $23.7 25% - 32% 4% Noblr, Inc. Recent transaction $5.0 Transaction price: $5.0 Zillion Insurance Services, Inc. (6) Recent transaction $2.5 Transaction price: $2.5 Compare.com Estimated net realizable value $2.5 Net realizable value: $2.5 (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) 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. (4) In 2019, Kudu deployed a total of $198.0 in new Kudu Participation Contracts, including Fair Oaks Capital, Versus Capital Advisors, First Long Island Investors, EJF Capital, Warwick Capital Partners and Pennybacker Capital Management. (5) In 2019, White Mountains made a $55.1 investment in Elementum Holdings, L.P. See Note 2 - “Significant Transactions” .

Goodwill and Other Intangible_2

Goodwill and Other Intangible Assets (Tables)	12 Months Ended
	Dec. 31, 2020
Goodwill and Intangible Assets Disclosure [Abstract]
Schedule of Recognized Identified Assets Acquired	The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by company as of December 31, 2020 and 2019: $ in Millions Weighted Average Economic December 31, 2020 December 31, 2019 Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Acquisition Date Fair Value Accumulated Amortization Impairments Net Carrying Value Goodwill: NSM (1)(2) N/A $ 506.4 $ — $ — $ 506.4 $ 381.6 $ — $ — $ 381.6 Kudu N/A 7.6 — — 7.6 7.6 — — 7.6 Other Operations N/A 11.5 — — 11.5 13.1 — 7.6 5.5 Total goodwill 525.5 — — 525.5 402.3 — 7.6 394.7 Other intangible NSM (1)(2) Customer 8.9 136.2 36.7 3.5 96.0 121.7 19.8 1.4 100.5 Trade names 16 65.4 8.3 1.0 56.1 61.9 5.3 .4 56.2 Information 0 3.1 1.4 1.7 — 3.9 1.4 .6 1.9 Renewal rights 12 82.5 4.9 — 77.6 82.5 .7 — 81.8 Other 3.4 1.7 1.0 — .7 1.7 .7 — 1.0 Subtotal 288.9 52.3 6.2 230.4 271.7 27.9 2.4 241.4 Kudu Trade names 7 2.2 .6 — 1.6 2.2 .2 — 2.0 Other Operations Trade names 9.6 3.6 .3 — 3.3 1.7 .5 .2 1.0 Customer 10.7 14.2 1.4 — 12.8 7.2 .4 — 6.8 Information 5 — — — — .5 .3 .2 — Insurance N/A 8.6 — — 8.6 8.6 — — 8.6 Other 5.4 .3 .1 — .2 .2 — — .2 Subtotal 26.7 1.8 24.9 18.2 1.2 .4 16.6 Total other intangible assets 317.8 54.7 6.2 256.9 292.1 29.3 2.8 260.0 Total goodwill and other intangible assets $ 843.3 $ 54.7 $ 6.2 782.4 $ 694.4 $ 29.3 $ 10.4 656.7 Goodwill and other intangible assets attributed to non-controlling interests (28.1) (23.4) Goodwill and other intangible assets included in White Mountains’s common $ 754.3 $ 631.3 (1) During 2020, NSM’s goodwill and intangible assets includes $13.4 and $1.6 of the effect of foreign currency translation. During 2019, NSM’s goodwill and intangible assets includes $1.8 and $0.7 of the effect of foreign currency translation. (2) The attribution of acquisition date fair value estimates between goodwill and other intangible assets for Kingsbridge was completed during 2020.The attribution of acquisition date fair value estimates between goodwill and other intangible assets for KBK was completed during 2019. The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed during 2020 and 2019: $ in Millions Acquisition of Subsidiary/ Asset Goodwill and Other Intangible Assets (1) Acquisition Date Embrace (2) $ 67.6 April 1, 2019 Renewal Rights (3) 82.5 June 28, 2019 Kingsbridge 131.7 April 7, 2020 Total NSM segment $ 281.8 Kudu Transaction $ 9.8 April 4, 2019 Other Operations $ 38.1 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. (2) Excludes $3.4 of software classified within other assets.
Schedule of Goodwill and Intangible Assets Rollforward	The following table presents the change in goodwill and other intangible assets: December 31, 2020 2019 Millions Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Goodwill Other Intangible Assets Total Goodwill and Other Intangible Assets Beginning balance $ 394.7 $ 260.0 $ 654.7 $ 379.9 $ 157.6 $ 537.5 Acquisitions of businesses (1) 140.0 — 140.0 64.8 34.6 99.4 Acquisition of collector car renewal rights — — — — 82.5 82.5 Dispositions of businesses (2) — — — (18.3) (23.5) (41.8) Attribution of acquisition date fair value estimates between goodwill and other intangible assets (3) (23.2) 23.2 — (26.8) 26.8 — Impairments (4) — (6.2) (6.2) (7.6) (2.8) (10.4) Measurement period adjustments (5) .6 6.6 7.2 .9 5.9 6.8 Foreign currency translation 13.4 1.6 15.0 1.8 .7 2.5 Amortization — (28.3) (28.3) — (21.8) (21.8) Ending balance $ 525.5 $ 256.9 $ 782.4 $ 394.7 $ 260.0 $ 654.7 (1) During 2020, amounts include acquisitions of Kingsbridge and Other Operations. During 2019, amounts include acquisitions related to Kudu, Other Operations and Embrace. (2) Dispositions relate to the 2019 MediaAlpha Transaction. See Note 2 — “Significant Transactions” . (3) The determination of the relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge and Other Operations were completed in 2020. The determination of the relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of KBK was completed in 2019. (4) In 2020, impairments relate to NSM’s UK vertical. In 2019, impairments of $7.6 and $0.4 of goodwill and other intangible assets relate to Other Operations and $2.4 of impairments to other intangible assets relate to NSM’s UK vertical.
Schedule of Finite-Lived Intangible Assets, Future Amortization Expense	White Mountains expects to recognize amortization expense in each of the next five years as the following table presents: Millions Amortization Expense 2021 $ 36.3 2022 35.2 2023 34.1 2024 28.6 2025 and years after 114.1 Total (1) $ 248.3 (1) Excludes indefinite-lived intangible assets of $8.6.

Debt (Tables)

Debt (Tables)	12 Months Ended
	Dec. 31, 2020
Debt Disclosure [Abstract]
Schedule of debt outstanding	The following table presents White Mountains’s debt outstanding as of December 31, 2020 and 2019: December 31, Effective December 31, Effective $ in Millions 2020 Rate 2019 Rate (1) NSM Bank Facility $ 277.4 7.5% (1) $ 221.3 7.5% (1) Unamortized issuance cost (6.1) (3.9) NSM Bank Facility, carrying value 271.3 217.4 Other NSM debt 1.3 2.5% 1.8 3.0% Kudu Bank Facility 89.2 8.3% 57.0 8.3% Unamortized issuance cost (2.9) (3.4) Kudu Bank Facility, carrying value 86.3 53.6 Other Operations debt 18.0 7.4% 11.1 8.3 % Unamortized issuance cost (.5) (.4) Other Operations debt, carrying value 17.5 10.7 Total debt $ 376.4 $ 283.5 (1) Effective rate includes the effect of the amortization of debt issuance costs and excludes the effect of the interest rate swap on the hedged portion of the debt. The weighted average interest rate for the years ended December 31, 2020 and 2019, excluding the effect of the amortization of debt issuance costs, was 7.0% and 7.0%. The weighted average interest rate for the years ended December 31, 2020 and 2019 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 8.4% and 8.1%. The following table presents the change in debt under the NSM Bank Facility for the years ended December 31, 2020 and 2019: Millions Year Ended December 31, NSM Bank Facility 2020 2019 Beginning balance $ 221.3 $ 180.4 Term loans Borrowings (1) 52.4 42.9 Repayments (2.0) (2.0) Foreign currency translation 5.7 — Revolving credit loan Borrowings — 6.5 Repayments — (6.5) Ending balance $ 277.4 $ 221.3 (1) Borrowings for the year ended December 31, 2020 included $52.4 for the funding of the acquisition of Kingsbridge. Borrowings for the year ended December 31, 2019 included $20.4 and $22.5 for the funding of the acquisitions of Embrace and the Renewal Rights.
Schedule of contractual repayments of debt	The following table presents a schedule of contractual repayments of White Mountains’s debt as of December 31, 2020: Millions December 31, 2020 Due in one year or less $ 4.5 Due in two to three years 12.2 Due in four to five years 106.0 Due after five years 263.3 Total $ 386.0

Income Taxes (Tables)

Income Taxes (Tables)	12 Months Ended
	Dec. 31, 2020
Income Tax Disclosure [Abstract]
Schedule of total income tax benefit (expense)	The following table presents the total income tax (expense) benefit for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, Millions 2020 2019 2018 Current income tax (expense): U.S. federal $ (10.4) $ .9 $ (.1) State (4.2) (3.7) (1.4) Non-U.S. (1.1) (1.7) (2.9) Total current income tax (expense) (15.7) (4.5) (4.4) Deferred income tax benefit (expense): U.S. federal 23.2 (14.9) 8.3 State 10.3 (10.4) — Non-U.S. 2.7 .5 .1 Total deferred income tax benefit (expense) 36.2 (24.8) 8.4 Total income tax benefit (expense) $ 20.5 $ (29.3) $ 4.0
Schedule of U.S. federal statutory income tax rate and actual effective tax rate on pre-tax income	The following table presents a reconciliation of taxes calculated for 2020, 2019 and 2018 using the 21% U.S. federal statutory rate U.S. federal statutory rate (the tax rate at which the majority of White Mountains’s worldwide operations are taxed) to the income tax (expense) benefit on pre-tax income (loss): Year Ended December 31, Millions 2020 2019 2018 Tax (expense) benefit at the U.S. statutory rate $ (135.5) $ (85.1) $ 37.4 Differences in taxes resulting from: Reorganization 130.5 — — Non-U.S. earnings, net of foreign taxes 78.4 27.1 (2.9) Change in valuation allowance (29.2) 63.6 (31.0) State taxes (8.5) (17.5) 4.0 Withholding tax (5.0) (1.6) (2.7) Member’s surplus contributions (4.8) (3.6) (2.6) Tax rate changes 2.7 (5.7) 1.7 Tax reserve adjustments 1.9 (.7) (.8) Officer compensation (1.1) — — Tax exempt interest and dividends .8 1.1 .6 Other, net (9.7) (6.9) .3 Total income tax benefit (expense) on pre-tax income (loss) $ 20.5 $ (29.3) $ 4.0
Schedule of components of deferred income tax assets and liabilities	The following table presents an outline of the significant components of White Mountains’s U.S. federal, state and non-U.S. deferred tax assets and liabilities: December 31, Millions 2020 2019 Deferred tax assets related to: U.S. federal and state net operating and capital $ 79.6 $ 92.3 Non-U.S. net operating loss carryforwards 50.5 41.7 Incentive compensation 17.5 15.0 Accrued interest 7.9 5.1 Deferred acquisition costs 5.5 4.3 Tax credit carryforwards 5.5 4.2 Other items 1.3 3.4 Total gross deferred tax assets 167.8 166.0 Less: valuation allowances 97.4 77.9 Total net deferred tax assets 70.4 88.1 Deferred tax liabilities related to: Member’s surplus contributions 52.9 43.2 Investment basis difference 11.8 6.6 Purchase accounting 5.1 3.1 Net unrealized investment gains .3 66.3 Other items 2.8 1.5 Total deferred tax liabilities 72.9 120.7 Net deferred tax (liability) $ (2.5) $ (32.6)
Schedule of net operating and capital loss carryforwards	The following table presents net operating loss and capital loss carryforwards as of December 31, 2020, the expiration dates and the deferred tax assets thereon: December 31, 2020 Millions United States Luxembourg United Kingdom Israel Total 2020-2024 $ — $ — $ — $ — $ — 2025-2029 — — — — — 2030-2039 250.7 73.2 — — 323.9 No expiration date 118.4 31.0 25.9 85.2 260.5 Total $ 369.1 $ 104.2 $ 25.9 $ 85.2 $ 584.4 Gross deferred tax asset $ 77.5 $ 26.0 $ 4.9 $ 19.6 $ 128.0 Valuation allowance (66.8) (25.9) (3.3) (19.6) (115.6) Net deferred tax asset $ 10.7 $ .1 $ 1.6 $ — $ 12.4
Schedule of changes in amount of unrecognized tax benefits	The following table presents a reconciliation of the beginning and ending amount of unrecognized tax benefits from 2018 to 2020: Millions Permanent Differences (1) Temporary Differences (2) Interest and Penalties (3) Total Balance at December 31, 2017 $ .3 $ — $ — $ .3 Changes in prior year tax positions .8 — — .8 Balance at December 31, 2018 1.1 — — 1.1 Changes in prior year tax positions 1.3 — — 1.3 Balance at December 31, 2019 2.4 — — 2.4 Changes in prior year tax positions .1 — — .1 Tax positions taken during the current year .1 — — .1 Reorganization (2.6) — — (2.6) Balance at December 31, 2020 $ — $ — $ — $ — (1) Represents the amount of unrecognized tax benefits that, if recognized, would impact the effective tax rate. (2) Represents the amount of unrecognized tax benefits that, if recognized, would create a temporary difference between the reported amount of an item in White Mountains’s Consolidated Balance Sheet and its tax basis. (3) Net of tax benefit.

Municipal Bond Guarantee Insu_2

Municipal Bond Guarantee Insurance (Tables)	12 Months Ended
	Dec. 31, 2020
Insurance [Abstract]
Schedule of Insured Obligations	The following table presents a schedule of BAM’s insured obligations as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Contracts outstanding 10,997 8,987 Remaining weighted average contract period (in years) 10.7 10.7 Contractual debt service outstanding (in millions): Principal $ 75,287.7 $ 62,250.5 Interest and capital appreciation 36,448.8 31,799.7 Total debt service outstanding $ 111,736.5 $ 94,050.2 Gross unearned insurance premiums $ 237.5 $ 198.4
Schedule of BAM’s future premium revenues	The following table presents a schedule of BAM’s future premium revenues as of December 31, 2020: Millions December 31, 2020 January 1, 2021 - March 31, 2021 $ 5.6 April 1, 2021 - June 30, 2021 5.5 July 1, 2021 - September 30, 2021 5.5 October 1, 2021 - December 31, 2021 5.4 22.0 2022 20.9 2023 19.8 2024 18.3 2025 17.0 2026 and thereafter 139.5 Total gross unearned insurance premiums $ 237.5
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 years ended December 31, 2020, 2019 and 2018: Millions December 31, 2020 December 31, 2019 December 31, 2018 Written premiums: Direct $ 61.5 $ 28.1 $ 44.8 Assumed .2 10.6 8.1 Gross written premiums $ 61.7 $ 38.7 $ 52.9 Earned premiums: Direct $ 19.4 $ 13.6 $ 13.6 Assumed 3.4 2.7 .3 Gross earned premiums $ 22.8 $ 16.3 $ 13.9

Earnings Per Share (Tables)

Earnings Per Share (Tables)	12 Months Ended
	Dec. 31, 2020
Earnings Per Share [Abstract]
Schedule of earnings per share from continuing operations	The following table presents the Company’s computation of earnings per share from continuing operations for the years ended December 31, 2020, 2019 and 2018. See Note 19 — “Held for Sale and Discontinued Operations” . Year Ended December 31, 2020 2019 2018 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s $ 708.7 $ 414.5 $ (141.2) Less: total (loss) income from discontinued operations, net of tax (2.3) .8 (17.2) Net income (loss) from continuing operations attributable to 711.0 413.7 (124.0) Allocation of (earnings) losses to participating restricted common shares (1) (9.3) (5.3) 1.4 Basic and diluted earnings (losses) per share numerators $ 701.7 $ 408.4 $ (122.6) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (2) (40.8) (40.5) (40.1) Basic earnings (losses) per share denominator 3,081.4 3,141.1 3,342.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (2) (40.8) (40.5) (40.1) Diluted earnings (losses) per share denominator 3,081.4 3,141.1 3,342.4 Basic and diluted earnings per share (in dollars) - continuing operations: Distributed earnings - dividends declared and paid $ 1.00 $ 1.00 $ 1.00 Undistributed earnings (losses) 226.72 129.02 (37.67) Basic and diluted earnings (losses) per share $ 227.72 $ 130.02 $ (36.67) (1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities. (2) Restricted shares outstanding vest either in equal annual installments or upon a stated date. See Note 10 — “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 years ended December 31, 2020, 2019 and 2018. See Note 19 — “Held for Sale and Discontinued Operations” . Year Ended December 31, Millions 2020 2019 2018 Undistributed net earnings - continuing operations: Net income (loss) attributable to White Mountains’s common shareholders, $ 701.7 $ 408.4 $ (122.6) Dividends declared, net of restricted common share amounts (1) (3.1) (3.2) (3.7) Total undistributed net earnings (losses), net of restricted common share amounts $ 698.6 $ 405.2 $ (126.3) (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)	12 Months Ended
	Dec. 31, 2020
Share-based Payment Arrangement [Abstract]
Schedule of performance share activity	The following table presents performance share activity for the years ended December 31, 2020, 2019 and 2018 for performance shares granted under the WTM Incentive Plan: Year Ended December 31, 2020 2019 2018 $ in Millions Target Accrued Target Accrued Target Accrued Beginning of period 42,473 $ 43.7 40,616 $ 31.7 50,515 $ 45.8 Shares paid or expired (1) (14,070) (27.7) (13,715) (18.1) (23,186) (28.4) New grants 14,055 — 15,600 — 14,105 — Forfeitures (2) — (.4) (28) (.1) (818) .1 Expense recognized — 40.7 — 30.2 — 14.2 End of period 42,458 $ 56.3 42,473 $ 43.7 40,616 $ 31.7 (1) WTM performance share payments in 2020 for the 2017-2019 performance cycle, which were paid in March 2020, ranged from 174% to 180% of target. WTM performance share payments in 2019 for the 2016-2018 performance cycle, which were paid in March 2019, ranged from 139% to 166% of target. WTM performance share payments in 2018 for the 2015-2017 performance cycle, which were paid in March 2018, ranged from 145% to 147% of target. (2) Amounts include changes in assumed forfeitures, as required under GAAP.
Schedule of performance shares outstanding and accrued expense for performance shares awarded	The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of December 31, 2020 for each performance cycle: $ in Millions Target Accrued Expense Performance cycle: 2020 – 2022 14,055 $ 9.5 2019 – 2021 15,600 20.7 2018 – 2020 13,450 27.1 Sub-total 43,105 57.3 Assumed forfeitures (647) (1.0) Total 42,458 $ 56.3
Schedule of unrecognized compensation costs associated with outstanding restricted share awards	The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards under the WTM Incentive Plan for the years ended December 31, 2020, 2019 and 2018: Year Ended December 31, 2020 2019 2018 $ in Millions Restricted Unamortized Restricted Unamortized Restricted Unamortized Non-vested, Beginning of period 43,395 $ 16.7 41,510 $ 12.5 53,755 $ 14.3 Issued 14,055 15.1 15,600 14.5 14,105 11.4 Vested (14,345) — (13,715) — (25,381) — Forfeited — — — — (969) (.2) Expense recognized — (16.6) — (10.3) — (13.0) End of period 43,105 $ 15.2 43,395 $ 16.7 41,510 $ 12.5

Leases (Tables)

Leases (Tables)	12 Months Ended
	Dec. 31, 2020
Leases [Abstract]
Schedule of net lease expense	The following table summarizes net lease expense recognized in White Mountains’s consolidated statement of operations for the years ended December 31, 2020 and 2019: Millions December 31, 2020 December 31, 2019 Lease cost $ 7.7 $ 7.2 Less: sublease income .4 .4 Net lease cost $ 7.3 $ 6.8
Schedule of contractual maturities of lease liabilities	The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of December 31, 2020: Millions December 31, 2020 2021 $ 7.7 2022 7.3 2023 7.1 2024 5.8 2025 5.1 Thereafter 12.2 Total undiscounted lease payments 45.2 Less: present value adjustment (6.9) Operating lease liability $ 38.3
Schedule of lease related assets and liabilities	The following table presents lease related assets and liabilities by reportable segment as of December 31, 2020 and 2019: As of December 31, 2020 $ in 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. December 31, 2019 $ in Millions HG/BAM NSM Kudu Other Operations Total Weighted Average Incremental Borrowing Rate (1) ROU lease asset $ 10.4 $ 4.8 $ 2.3 $ 5.1 $ 22.6 4.6% Lease liability $ 10.4 $ 4.8 $ 2.3 $ 5.3 $ 22.8 (1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

Common Shareholders_ Equity a_2

Common Shareholders’ Equity and Non-controlling Interests (Tables)	12 Months Ended
	Dec. 31, 2020
Stockholders' Equity Note [Abstract]
Schedule of noncontrolling interest	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 December 31, 2020 and 2019: December 31, 2020 December 31, 2019 $ in Millions Non-controlling Percentage Non-controlling Equity Non-controlling Percentage Non-controlling Equity Non-controlling interests, excluding BAM HG Global 3.1 % $ 13.5 3.1 % $ 14.4 NSM 3.4 % 17.0 3.6 % 14.9 Kudu .7 % 2.3 .9 % 2.2 Other various 2.4 various (1.6) Total, excluding BAM 35.2 29.9 BAM 100.0 % (123.3) 100.0 % (146.7) Total non-controlling interests $ (88.1) $ (116.8)

Segment Information (Tables)

Segment Information (Tables)	12 Months Ended
	Dec. 31, 2020
Segment Reporting [Abstract]
Schedule of financial information for segments	The following tables present the financial information for White Mountains’s segments: Millions HG Global/BAM (1) NSM Kudu Other Total Year Ended December 31, 2020 Earned insurance premiums $ 22.8 $ — $ — $ — $ 22.8 Net investment income 19.5 — 29.5 82.0 131.0 Net realized and unrealized investment gains (losses) 23.7 — 15.9 (8.8) 30.8 Net realized and unrealized investment gains from — — — 686.0 686.0 Advertising and commission revenues (2) — 232.5 — 8.3 240.8 Other revenues 2.5 52.6 .3 13.9 69.3 Total revenues 68.5 285.1 45.7 781.4 1,180.7 Insurance acquisition expenses 7.0 — — — 7.0 Other underwriting expenses .4 — — — .4 Cost of sales — — — 11.3 11.3 General and administrative expenses 56.4 176.9 11.8 141.9 387.0 Broker commission expense — 75.3 — — 75.3 Change in fair value of contingent consideration — (3.3) — — (3.3) Amortization of other intangible assets — 26.7 .3 1.3 28.3 Interest expense — 22.1 6.0 1.4 29.5 Total expenses 63.8 297.7 18.1 155.9 535.5 Pre-tax income (loss) $ 4.7 $ (12.6) $ 27.6 $ 625.5 $ 645.2 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Approximately 19% of NSM’s commission revenue was associated with one single carrier. Millions HG Global/BAM (1) NSM Kudu (2) MediaAlpha (3) Other Total Year Ended December 31, 2019 Earned insurance premiums $ 16.3 $ — $ — $ — $ — $ 16.3 Net investment income 21.6 — 14.7 — 43.4 79.7 Net realized and unrealized investment gains 27.1 — 6.3 — 219.8 253.2 Net realized and unrealized investment gains — — — — 180.0 180.0 Gain from deconsolidation of MediaAlpha — — — 67.5 67.5 Advertising and commission revenues (4) — 193.4 — 48.8 6.9 249.1 Other revenues 1.6 39.7 .2 — 6.1 47.6 Total revenues 66.6 233.1 21.2 48.8 523.7 893.4 Insurance acquisition expenses 5.7 — — — — 5.7 Other underwriting expenses .4 — — — — .4 Cost of sales — — — 40.6 7.5 48.1 General and administrative expenses 50.5 132.2 10.1 12.5 122.5 327.8 Broker commission expense — 64.8 — — — 64.8 Change in fair value of contingent — 2.1 — — — 2.1 Amortization of other intangible assets — 19.4 .2 1.6 .6 21.8 Interest expense — 16.7 .1 .2 .6 17.6 Total expenses 56.6 235.2 10.4 54.9 131.2 488.3 Pre-tax income (loss) $ 10.0 $ (2.1) $ 10.8 $ (6.1) $ 392.5 $ 405.1 (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Kudu’s results are from April 4, 2019, the date of the Kudu Transaction, to December 31, 2019. (3) MediaAlpha’s results are from January 1, 2019 to February 26, 2019, the date of the 2019 MediaAlpha Transaction. (4) Approximately 17% of NSM’s commission revenue was associated with one single carrier. Millions HG Global/BAM (1) NSM MediaAlpha Other Total Year Ended December 31, 2018 Earned insurance premiums $ 13.9 $ — $ — $ — $ 13.9 Net investment income 16.7 — — 42.3 59.0 Net realized and unrealized investment losses (7.5) — — (100.8) (108.3) Advertising and commission revenues (2) — 89.6 295.5 4.1 389.2 Other revenues 1.2 12.0 1.6 .5 15.3 Total revenues 24.3 101.6 297.1 (53.9) 369.1 Insurance acquisition expenses 5.3 — — — 5.3 Other underwriting expenses .4 — — — .4 Cost of sales — — 245.0 3.7 248.7 General and administrative expenses 48.0 59.4 31.7 94.4 233.5 Broker commission expense — 28.4 — — 28.4 Change in fair value of contingent — 2.7 — — 2.7 Amortization of other intangible assets — 8.3 10.3 .2 18.8 Interest expense — 8.0 1.2 .3 9.5 Total expenses 53.7 106.8 288.2 98.6 547.3 Pre-tax (loss) income $ (29.4) $ (5.2) $ 8.9 $ (152.5) $ (178.2) (1) BAM manages its affairs on a statutory accounting basis. BAM’s statutory surplus includes the BAM Surplus Notes and is not reduced by accruals of interest expense on the BAM Surplus Notes. BAM’s statutory surplus is reduced only after a payment of principal or interest has been approved by the NYDFS. (2) Approximately 29% of MediaAlpha’s advertising revenue was associated with one customer and approximately 33% of NSM’s commission revenue was associated with one single carrier.
Schedule of selected balance sheet data by segment	Millions HG Global/BAM NSM Kudu Other Held for Sale Total December 31, 2020: Total investments $ 919.9 $ — $ 400.7 $ 1,618.5 $ — $ 2,939.1 Total assets $ 1,017.8 (1) $ 999.6 $ 430.2 $ 2,381.5 (2) $ 2.3 $ 4,831.4 Total liabilities $ 291.5 (2) $ 491.8 $ 96.3 $ 133.9 $ — $ 1,013.5 Total White Mountains’s common $ 836.1 (2) $ 490.7 $ 331.6 $ 2,245.3 (2) $ 2.3 $ 3,906.0 Non-controlling interest $ (109.8) $ 17.1 $ 2.3 $ 2.3 $ — $ (88.1) December 31, 2019: Total investments $ 845.6 $ — $ 266.6 $ 1,835.0 $ — $ 2,947.2 Total assets $ 924.0 (1) $ 825.2 $ 290.5 $ 1,940.5 (2) $ 3.0 $ 3,983.2 Total liabilities $ 246.8 (2) $ 401.1 $ 57.0 $ 133.6 $ — $ 838.5 Total White Mountains’s common $ 809.5 (2) $ 409.3 $ 231.3 $ 1,808.4 (2) $ 3.0 $ 3,261.5 Non-controlling interest $ (132.3) $ 14.8 $ 2.2 $ (1.5) $ — $ (116.8) (1) As of December 2020 and 2019, total assets in the HG Global/BAM segment reflected the elimination of $388.2 and $457.6 of BAM Surplus Notes issued to HG Global and its subsidiaries, and $155.7 and $162.7 in accrued interest related to the BAM Surplus Notes.
Schedule of revenue by revenue source	In compliance with ASC 606, Revenues from Contracts with Customers, the following tables present White Mountains’s total revenues by revenue source: Millions HG Global/BAM NSM Kudu Other Total Year Ended December 31, 2020 Commission and Other Revenue Specialty Transportation $ — $ 85.5 $ — $ — $ 85.5 Real Estate — 44.9 — — 44.9 Social Services — 28.9 — — 28.9 Pet — 55.0 — — 55.0 United Kingdom — 49.4 — — 49.4 Other — 21.4 — 8.3 29.7 Total Commission and Other Revenue — 285.1 — 8.3 293.4 Products — — — 14.5 14.5 Total revenues from contracts with customers — 285.1 — 22.8 307.9 Other revenues (1) 68.5 — 45.7 758.6 872.8 Total revenues $ 68.5 $ 285.1 $ 45.7 $ 781.4 $ 1,180.7 (1) Other revenues consist 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 (2) MediaAlpha (3) Other Total Year Ended December 31, 2019 Commission and Other Revenue Specialty Transportation $ — $ 77.6 $ — $ — $ — $ 77.6 Real Estate — 34.7 — — — 34.7 Social Services — 25.9 — — — 25.9 Pet — 30.0 — — — 30.0 United Kingdom — 45.9 — — — 45.9 Other — 19.0 — — 6.9 25.9 Total Commission and Other Revenue — 233.1 — — 6.9 240.0 Advertising revenues — — — 48.8 — 48.8 Products — — — — 5.5 5.5 Total revenues from contracts with customers — 233.1 — 48.8 12.4 294.3 Other revenues (1) 66.6 — 21.2 — 511.3 599.1 Total revenues $ 66.6 $ 233.1 $ 21.2 $ 48.8 $ 523.7 $ 893.4 (1) Other revenues consist of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers. (2) Kudu’s results are from April 4, 2019, the date of the Kudu Transaction, to December 31, 2019. (3) MediaAlpha’s results are from January 1, 2019 to February 26, 2019, the date of the 2019 MediaAlpha Transaction. Millions HG Global/BAM NSM MediaAlpha Other Total Year Ended December 31, 2018 Commission and Other Revenue Specialty Transportation $ — $ 28.3 $ — $ — $ 28.3 Real Estate — 17.8 — — 17.8 Social Services — 14.7 — — 14.7 United Kingdom — 28.0 — — 28.0 Other — 12.8 — 4.1 16.9 Total Commission and Other Revenue — 101.6 — 4.1 105.7 Advertising revenues — — 295.5 — 295.5 Total revenues from contracts with customers — 101.6 295.5 4.1 401.2 Other revenues (1) 24.3 — 1.6 (58.0) (32.1) Total revenues $ 24.3 $ 101.6 $ 297.1 $ (53.9) $ 369.1 (1) Other revenues consist of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.

Equity-Method Eligible Invest_2

Equity-Method Eligible Investments (Tables)	12 Months Ended
	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Schedule of equity method eligible investments	The following table presents the carrying values of White Mountains’s equity method eligible investments as of December 31, 2020 and 2019: December 31, Millions 2020 2019 Investment in MediaAlpha $ 802.2 $ 180.0 Other equity method eligible investments, at fair value $ 698.1 $ 581.7
Schedule of significant equity method eligible investments	The following table presents White Mountains’s significant equity method eligible investments as of December 31, 2020 and 2019: Basic Ownership Interest Investee December 31, 2020 December 31, 2019 Instrument Held PassportCard/DavidShield 53.8% 50.0% Common shares New Market Solutions, LLC. 46.7% n/a Units durchblicker 45.0% 45.0% Common shares MediaAlpha (1) 35.0% 48.3% Common Shares/Units (1) Elementum Holdings, L.P. 28.9% 30.0% Limited partnership interest Compare.com 18.4% 18.4% Common shares Tuckerman Capital Funds 14.9 - 62.0% 17.5 - 62.4% Limited and general partnership interests JAM Partners L.P. n/a 11.1% Limited partnership interest Enlightenment Capital Funds 9.7- 66.7% 10.0 - 38.4% Limited and general partnership interests Kudu’s Participation Contracts 3.2 - 35.0% 3.2 - 30.0% Revenue and earnings participation contracts (1) On October 30, 2020, MediaAlpha completed the MediaAlpha IPO. See Note 2 — “Significant Transactions” The following tables present aggregated summarized financial information for White Mountains’s investments in equity method eligible unconsolidated entities, excluding MediaAlpha: December 31, Millions 2020 2019 Balance sheet data (1) : Total assets $ 1,328.5 $ 1,959.2 Total liabilities $ 228.7 $ 653.2 (1) Financial data for White Mountains’s equity method eligible investees is generally reported on a one-quarter lag. Year Ended December 31, Millions 2020 2019 2018 Income statement data (1) : Total revenues $ 526.5 $ 344.6 $ 226.0 Total expenses $ 325.9 $ 88.3 $ 141.4 Net income (loss) $ 201.7 $ 255.1 $ 83.6 (1) Financial data for White Mountains’s equity method eligible investees is generally reported on a one-quarter lag.
Financials
Schedule of Equity Method Investments [Line Items]
Schedule of significant equity method eligible investments	The following tables present summarized financial information for MediaAlpha as of December 31, 2020 and 2019 for the twelve months ended December 31, 2020, 2019, and 2018: December 31, Millions 2020 2019 (1) Balance sheet data: Total assets $ 212.7 $ 105.4 Total liabilities $ 315.8 $ 144.9 (1) As of December 31, 2019, MediaAlpha recorded out of period adjustments that (decreased) increased total assets and total liabilities by $(1.5) and $0.3. The adjustments primarily related to MediaAlpha’s accounting for its other intangible assets and debt. White Mountains has evaluated the impact of the adjustments and concluded that they are not material, individually and in the aggregate, to current or prior period financial statements. Year Ended December 31, Millions 2020 2019 (1) 2018 (1) Income statement data: Total revenues $ 584.8 $ 408.0 $ 296.9 Total expenses $ 575.4 $ 390.2 $ 278.8 Net income (loss) $ 9.4 $ 17.8 $ 18.1 (1) For the twelve months ended December 31, 2019 and 2018, MediaAlpha recorded out of period adjustments that increased (decreased) total revenues by $0.1 and $(0.2), total expenses by $1.2 and $(9.4) and net income by $(1.1) and $9.2. The adjustments primarily related to MediaAlpha’s accounting for its equity-based compensation and amortization of other intangible assets. White Mountains has evaluated the impact of the adjustments and concluded that they are not material, individually and in the aggregate, to current or prior period financial statements.

Fair Value of Financial Instr_2

Fair Value of Financial Instruments (Tables)	12 Months Ended
	Dec. 31, 2020
Fair Value Disclosures [Abstract]
Schedule of the fair value and carrying value of financial instruments	The following tables presents the fair value and carrying value of these financial instruments as of December 31, 2020 and 2019: December 31, 2020 December 31, 2019 Millions Fair Value Carrying Value Fair Value Carrying Value NSM Bank Facility $ 279.3 $ 271.3 $ 221.2 $ 217.4 Other NSM debt $ 1.3 $ 1.3 $ 1.7 $ 1.8 Kudu Bank Facility (1) $ 89.3 $ 86.3 $ 53.6 $ 53.6 Other Operations debt $ 18.8 $ 17.5 $ 11.3 $ 10.7 (1) As of December 31, 2019, White Mountains measured the fair value of the Kudu Bank Facility debt at the carrying value as a result of the debt being acquired on December 23, 2019. See Note 5 — “Debt” .

Held for Sale and Discontinue_2

Held for Sale and Discontinued Operations (Tables)	12 Months Ended
	Dec. 31, 2020
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 years ended December 31, 2020, 2019 and 2018: Year Ended December 31, 2020 2019 2018 Basic and diluted earnings per share numerators (in millions): Net income (loss) attributable to White Mountains’s common shareholders $ 708.7 $ 414.5 $ (141.2) Less: total income (loss) from continuing operations, net of tax 711.0 413.7 (124.0) Net (loss) income from discontinued operations attributable to (2.3) .8 (17.2) Allocation of (earnings) losses to participating restricted common shares (1) — — .2 Basic and diluted (loss) earnings per share numerators $ (2.3) $ .8 $ (17.0) Basic earnings per share denominators (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (3) (40.8) (40.5) (40.1) Basic earnings (loss) per share denominator 3,081.4 3,141.1 3,342.4 Diluted earnings per share denominator (in thousands): Total average common shares outstanding during the period 3,122.2 3,181.6 3,382.5 Average unvested restricted common shares (3) (40.8) (40.5) (40.1) Diluted earnings (loss) per share denominator 3,081.4 3,141.1 3,342.4 Basic (loss) earnings per share (in dollars) - discontinued operations: $ (.75) $ .25 $ (5.09) Diluted (loss) earnings per share (in dollars) - discontinued operations: $ (.75) $ .25 $ (5.09) (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 years ended December 31, 2020, 2019 and 2018. (3) Restricted common shares outstanding vest either in equal annual installments or upon a stated date. See Note 10 — “Employee Share-Based Compensation Plans” .

Selected Quarterly Financial _2

Selected Quarterly Financial Data (Unaudited) (Tables)	12 Months Ended
	Dec. 31, 2020
Quarterly Financial Information Disclosure [Abstract]
Schedule of Quarterly Financial Information	The following table presents selected quarterly financial data for 2020 and 2019. The quarterly financial data includes, in the opinion of management, all recurring adjustments necessary for a fair presentation of the results of operations for the interim periods. Prior year amounts have been reclassified to conform to the current period’s presentation. Prior year amounts have also been adjusted for the impact of White Mountains’s financial statement revisions. 2020 Three Months Ended 2019 Three Months Ended Millions, Except Per Share Amounts Dec. 31 Sept. 30 June 30 Mar. 31 Dec. 31 Sept. 30 June 30 Mar. 31 Revenues $ 520.8 $ 459.5 $ 259.6 $ (59.2) $ 175.3 $ 155.5 $ 129.0 $ 433.6 Expenses 163.5 138.3 126.9 106.8 118.8 104.4 113.2 151.9 Pre-tax income (loss) 357.3 321.2 132.7 (166.0) 56.5 51.1 15.8 281.7 Tax (expense) benefit 117.6 (98.5) (24.1) 25.5 (10.4) (8.8) .1 (10.2) Income (loss) from continuing operations 474.9 222.7 108.6 (140.5) 46.1 42.3 15.9 271.5 Net (loss) gain from discontinued operations, net of tax (1) (1.5) (.7) (1.0) .9 (.8) .9 — .7 Non-controlling interest in consolidated subsidiaries 15.8 10.9 7.8 10.8 15.6 5.5 4.6 12.2 Income (loss) attributable to White Mountains’s common shareholders $ 489.2 $ 232.9 $ 115.4 $ (128.8) $ 60.9 $ 48.7 $ 20.5 $ 284.4 Income (loss) attributable to White Mountains’s common shareholders per share: Basic Continuing operations $ 158.19 $ 75.32 $ 37.46 $ (40.82) $ 19.37 $ 15.01 $ 6.44 $ 89.42 Discontinued operations (.49) (.23) (.32) .28 (.25) .28 — .22 Total consolidated operations $ 157.70 $ 75.09 $ 37.14 $ (40.54) $ 19.12 $ 15.29 $ 6.44 $ 89.64 Diluted Continuing operations $ 158.19 $ 75.32 $ 37.46 $ (40.82) $ 19.37 $ 15.01 $ 6.44 $ 89.42 Discontinued operations (.49) (.23) (.32) .28 (.25) .28 — .22 Total consolidated operations $ 157.70 $ 75.09 $ 37.14 $ (40.54) $ 19.12 $ 15.29 $ 6.44 $ 89.64 (1) During 2020 and 2019, net (loss) gain from discontinued operations arose from the tax contingency on the sale of Sirius Group. See Note 18 — “Commitments and Contingencies

Basis of Presentation and Sig_3

Basis of Presentation and Significant Accounting Policies - Reportable Segments (Details) - USD ($) $ in Millions	Oct. 30, 2020	Apr. 04, 2019	Dec. 31, 2020	Dec. 31, 2019	Apr. 03, 2019	May 11, 2018	Feb. 05, 2018	Dec. 31, 2012
Basis of Presentation
Percentage of par value of policy reinsured			15.00%
Payments to acquire business, net		$ 81.4
MediaAlpha
Basis of Presentation
Ownership interest (as a percent)	35.00%
Fully diluted ownership interest (as a percent)	32.30%
Investment owned (in shares)	20,532,202
IPO | MediaAlpha
Basis of Presentation
Sale of stock, number of shares issued in transaction (in shares)	3,609,894
Sale of stock, consideration received in transaction	$ 63.8
HG Global
Basis of Presentation
Percentage of par value of policy reinsured			15.00%
Surplus notes								$ 503
Preferred stocks | HG Global
Basis of Presentation
Ownership interest (as a percent)			96.90%	96.90%
Common equity securities | HG Global
Basis of Presentation
Ownership interest (as a percent)			88.40%	88.40%
NSM
Basis of Presentation
Ownership interest (as a percent)			96.60%	96.40%		95.00%
Fully diluted ownership interest (as a percent)			89.60%	88.40%		83.60%
Kudu
Basis of Presentation
Ownership interest (as a percent)		99.10%			49.50%		49.50%
Fully diluted ownership interest (as a percent)		85.40%			42.70%		42.70%
Payments to acquire business, net		$ 81.4
Funded capital commitment		$ 250		$ 350

Basis of Presentation and Sig_4

Basis of Presentation and Significant Accounting Policies - Discontinued Operating and Assets and Liabilities Held for Sale (Details) $ in Millions	Dec. 31, 2020USD ($)
Carrying Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Aircraft held for sale, carrying value	$ 1.7

Basis of Presentation and Sig_5

Basis of Presentation and Significant Accounting Policies - Investment Securities (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Accounting Policies [Abstract]
Percentage of investments recorded at fair value	73.00%	71.00%
Variance threshold for outliers	$ 0.5
Variance threshold for outliers (as a percent)	5.00%

Basis of Presentation and Sig_6

Basis of Presentation and Significant Accounting Policies - Fair Value Measurements and Other Long-Term Investments (Details) $ in Millions	Dec. 31, 2020USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other long-term investments	$ 786.8
Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other long-term investments	614.2
Fair Value Measured at Net Asset Value Per Share
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other long-term investments	$ 172.6

Basis of Presentation and Sig_7

Basis of Presentation and Significant Accounting Policies - Foreign Currency Exchange (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Accounting Policies [Abstract]
Net unrealized foreign currency translation gain (losses)	$ 5.6	$ (2.4)

Significant Transactions - Medi

Significant Transactions - MediaAlpha (Details) - USD ($) $ / shares in Units, $ in Millions	Oct. 30, 2020	Feb. 26, 2019	Dec. 31, 2019	Dec. 31, 2020
Other Significant Noncash Transactions [Line Items]
Realized gain from transaction			$ 67.5
Unrealized investment gain			$ 180
MediaAlpha
Other Significant Noncash Transactions [Line Items]
Proceeds from dividends received	$ 55
Ownership interest (as a percent)	35.00%
Fully diluted ownership interest (as a percent)	32.30%
Investment owned (in shares)	20,532,202
Share price (in USD per share)				$ 39.07
Investment owned, balance				$ 802.2
MediaAlpha | IPO
Other Significant Noncash Transactions [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	3,609,894
Sale of stock, consideration received in transaction	$ 63.8
MediaAlpha
Other Significant Noncash Transactions [Line Items]
Proceeds from dividends received		$ 89.3
Realized gain from transaction		$ 67.5
Ownership interest (as a percent)		48.30%
Fully diluted ownership interest (as a percent)		42.00%
Assets, fair value		$ 114.7
Unrealized investment gain		114.7
Total realized and unrealized gain on sale of minority stake		$ 182.2

Significant Transactions - Ark

Significant Transactions - Ark (Details) - USD ($) $ in Millions	Oct. 01, 2020	Dec. 31, 2020	Dec. 31, 2019
Other Operations
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction		$ 646.3	$ 0
Ark Insurance Holdings Limited
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction		366.3
Ark Insurance Holdings Limited | Lloyd
Other Significant Noncash Transactions [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction		$ 280
Ark Insurance Holdings Limited
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

Significant Transactions - Elem

Significant Transactions - Elementum (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	May 31, 2019
Other Significant Noncash Transactions [Line Items]
Other investments	$ 786.8	$ 676.3
Elementum Holdings, L.P.
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	28.90%	30.00%	30.00%
Other investments	$ 55.1		$ 55.1
Insurance-Linked Securities Funds
Other Significant Noncash Transactions [Line Items]
Commitment			$ 50

Significant Transactions - NSM

Significant Transactions - NSM (Details) £ in Millions	Apr. 07, 2020USD ($)	Apr. 07, 2020GBP (£)	Jun. 28, 2019USD ($)	Apr. 01, 2019USD ($)	Dec. 03, 2018USD ($)	May 11, 2018USD ($)	Mar. 31, 2019USD ($)	Sep. 30, 2018USD ($)	Dec. 31, 2020USD ($)	Dec. 31, 2020GBP (£)	Dec. 31, 2019USD ($)earnout_period	Dec. 31, 2018USD ($)	Apr. 07, 2020GBP (£)	May 18, 2018USD ($)	Feb. 05, 2018USD ($)
Other Significant Noncash Transactions [Line Items]
Purchases of consolidated subsidiaries, net of cash acquired									$ 127,300,000		$ 258,000,000	$ 295,200,000
Equity method investment, aggregate cost															$ 125,000,000
Change in fair value of contingent consideration earnout liabilities									(3,300,000)		2,100,000	$ 2,700,000
Business Combination, Earnout Period Payments									6,400,000
Goodwill									525,500,000		394,700,000
Embrace Pet Insurance
Other Significant Noncash Transactions [Line Items]
Goodwill and intangible assets acquired				$ 67,600,000
Intangible assets acquired				15,400,000
Goodwill				52,200,000
Kingsbridge Group Limited
Other Significant Noncash Transactions [Line Items]
Goodwill and intangible assets acquired	$ 131,700,000
NSM
Other Significant Noncash Transactions [Line Items]
Long-term line of credit						$ 100,000,000
Contingent consideration earnout liabilities									14,600,000		20,600,000
Change in fair value of contingent consideration earnout liabilities									(3,300,000)		2,100,000
NSM | KBK Insurance Group, Inc. & KBK Premium Services, Inc.
Other Significant Noncash Transactions [Line Items]
Contingent consideration earnout liabilities									7,000,000		7,600,000
NSM | Embrace Pet Insurance
Other Significant Noncash Transactions [Line Items]
Additional investment in acquisition				58,200,000
Proceeds from borrowings				$ 20,400,000
Percentage of voting interests acquired				100.00%
Payments to acquire businesses, gross				$ 71,500,000
NSM | Kingsbridge Group Limited
Other Significant Noncash Transactions [Line Items]
Contingent consideration earnout liabilities	4,100,000								300,000
Equity method investment, aggregate cost	132,200,000												£ 107.2
Additional investment in acquisition	80,300,000
Proceeds from borrowings	$ 52,400,000	£ 42.5
Percentage of voting interests acquired	100.00%												100.00%
Acquisitions of businesses	$ 111,500,000
Finite-lived Intangible Assets Acquired	20,200,000
Pretax income	4,100,000
Foreign currency translation gain	300,000
NSM | NSM Bank Facility
Other Significant Noncash Transactions [Line Items]
Long-term line of credit									277,400,000
NSM | NSM Bank Facility | Term Loan
Other Significant Noncash Transactions [Line Items]
Long-term line of credit	276,400,000								277,400,000		221,300,000			$ 51,000,000
Proceeds from borrowings	$ 52,400,000	£ 42.5							$ 52,400,000	£ 42.5	42,900,000
NSM | NSM Bank Facility | Term Loan | Embrace Pet Insurance
Other Significant Noncash Transactions [Line Items]
Proceeds from borrowings											$ 20,400,000
NSM
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)						95.00%			96.60%		96.40%
Fully diluted ownership interest (as a percent)						83.60%			89.60%		88.40%
Purchases of consolidated subsidiaries, net of cash acquired						$ 274,200,000
Purchase price adjustment								$ 2,100,000
Assets acquired						495,200,000
Goodwill and intangible assets acquired						383,000,000
Liabilities acquired						204,600,000
Contingent consideration earnout liabilities						10,200,000
Noncontrolling interest acquired						14,400,000
Transaction costs						$ 6,300,000
Number of earnout periods | earnout_period											2
Fresh Insurance Services Group Limited
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)														100.00%
Purchase price adjustment											$ 700,000
Assets acquired														$ 72,600,000
Goodwill and intangible assets acquired														54,600,000
Liabilities acquired														22,300,000
Contingent consideration earnout liabilities														7,500,000
Equity method investment, aggregate cost														$ 49,600,000
KBK Insurance Group, Inc. & KBK Premium Services, Inc.
Other Significant Noncash Transactions [Line Items]
Purchases of consolidated subsidiaries, net of cash acquired					$ 60,000,000
Goodwill and intangible assets acquired					59,400,000						32,600,000
Additional investment in acquisition					29,000,000
Proceeds from borrowings					$ 30,100,000
Intangible assets acquired											$ 32,700,000
Change in fair value of contingent consideration earnout liabilities							$ 5,900,000
AIG Collector Car Business
Other Significant Noncash Transactions [Line Items]
Purchases of consolidated subsidiaries, net of cash acquired			$ 82,500,000
Additional investment in acquisition			59,100,000
Intangible assets acquired			82,500,000
AIG Collector Car Business | NSM
Other Significant Noncash Transactions [Line Items]
Proceeds from borrowings			$ 22,500,000

Significant Transactions - Pass

Significant Transactions - PassportCard/DavidShield (Details) - USD ($) $ in Millions	May 07, 2020	Apr. 04, 2019	Jan. 24, 2018	Dec. 31, 2020	May 06, 2020	Dec. 31, 2019
Other Significant Noncash Transactions [Line Items]
Payments to acquire business, net		$ 81.4
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%
DavidShield & PassportCard
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	53.80%			53.80%	50.00%	50.00%
Payments to acquire businesses, gross			$ 41.8
Payments to acquire business, net			$ 28.3
Additional investment in acquisition	$ 15

Significant Transactions - Kudu

Significant Transactions - Kudu (Details) - USD ($) $ in Millions	Apr. 04, 2019	Dec. 31, 2019	Dec. 31, 2020	Apr. 07, 2020	Apr. 03, 2019	Feb. 05, 2018
Other Significant Noncash Transactions [Line Items]
Equity method investment, aggregate cost						$ 125
Payments to acquire business, net	$ 81.4
Goodwill		$ 394.7	$ 525.5
Total commitment under revolving credit facility				$ 291.4
Kudu Debt | Delayed Draw Term Loans | Kudu
Other Significant Noncash Transactions [Line Items]
Total commitment under revolving credit facility		124
Undrawn amount on facility		68	34.8
Kudu
Other Significant Noncash Transactions [Line Items]
Ownership interest (as a percent)	99.10%				49.50%	49.50%
Fully diluted ownership interest (as a percent)	85.40%				42.70%	42.70%
Payments to acquire business, net	$ 81.4
Funded capital commitment	250	350
Assets acquired	155.5
Goodwill	7.6
Intangible assets acquired	2.2
Liabilities acquired	0.8
Noncontrolling interest acquired	$ 1.5
Increase in capital commitment		100
Unfunded Capital Commitment		$ 129	$ 47.5

Investment Securities - Net Inv

Investment Securities - Net Investment Income (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Investment income:
Total investment income	$ 132.2	$ 81	$ 62
Third-party investment expenses	(1.2)	(1.3)	(3)
Net investment income	131	79.7	59
Fixed maturity investments
Investment income:
Total investment income	29	32.4	35.1
Short-term investments
Investment income:
Total investment income	1.1	5	8
Common equity securities
Investment income:
Total investment income	6.6	13.5	15.1
Other long-term investments
Investment income:
Total investment income	35.6	22.1	3.8
MediaAlpha
Investment income:
Total investment income	$ 59.9	$ 8	$ 0

Investment Securities - Net Rea

Investment Securities - Net Realized and Unrealized Investment Gains and Losses - (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	$ 716.8	$ 433.2	$ (108.3)
Less: net gains (losses) on investment securities sold during the period	20.2	24.6	(33)
Realized gains	214.4	104	49.4
Realized losses	27.3	7.4	62.3
MediaAlpha
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	686	180	0
Investments Held
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	696.6	408.6	(75.3)
Fixed maturity investments
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	38.5	43.5	(34.7)
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	0.4	0.2	(0.8)
Common equity securities
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	6.5	195.7	(98.9)
Other long-term investments
Debt Securities, Available-for-sale [Line Items]
Net realized and unrealized investment gains (losses)	(14.6)	13.8	26.1
Gain (loss) on investments related to foreign currency exchange	$ 4	$ (0.3)	$ (0.8)

Investment Securities - Investm

Investment Securities - Investment Gains and Losses For Level 3 (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Investment securities
Proceeds from sale and maturity of investments	$ 1,400	$ 1,000	$ 2,200
Level 3
Investment securities
Unrealized investment gains	276	181.9	22.6
Other long-term investments | Level 3
Investment securities
Unrealized investment gains	276	181.9	$ 22.6
MediaAlpha
Investment securities
Unrealized gain associated with unconsolidated affiliates	$ 278.7	$ 180

Investment Securities - Inves_2

Investment Securities - Investment Holdings (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
U.S. Government and agency obligations
Investment securities
Cost or Amortized Cost	$ 173.2	$ 231.7
Gross Unrealized Gains	3.1	1
Gross Unrealized Losses	0	(0.2)
Carrying Value	176.3	232.5
Debt securities issued by corporations
Investment securities
Cost or Amortized Cost	522.8	454.9
Gross Unrealized Gains	24.7	12.5
Gross Unrealized Losses	(0.1)	(0.2)
Carrying Value	547.4	467.2
Municipal obligations
Investment securities
Cost or Amortized Cost	244	284.7
Gross Unrealized Gains	21	12.5
Gross Unrealized Losses	0	(0.1)
Carrying Value	265	297.1
Mortgage and asset-backed securities
Investment securities
Cost or Amortized Cost	211.7	206.6
Gross Unrealized Gains	6.8	2.7
Gross Unrealized Losses	0	(0.3)
Carrying Value	218.5	209
Total fixed maturity investments
Investment securities
Cost or Amortized Cost	1,151.7	1,177.9
Gross Unrealized Gains	55.6	28.7
Gross Unrealized Losses	(0.1)	(0.8)
Carrying Value	$ 1,207.2	$ 1,205.8
Including short term fixed
Investment securities
Duration of fixed maturities (years)	3 years 2 months 12 days
Excluding short term investments
Investment securities
Duration of fixed maturities (years)	3 years 7 months 6 days

Investment Securities - Cost an

Investment Securities - Cost and Amortized Cost Maturity Schedule (Details) $ in Millions	Dec. 31, 2020USD ($)
Cost or Amortized Cost
Total	$ 1,151.7
Carrying Value
Total	1,207.2
Fixed Maturities and Convertible Fixed Maturities Excluding Mortgage Backed Securities
Cost or Amortized Cost
Due in one year or less	126
Due after one year through five years	417.5
Due after five years through ten years	283.2
Due after ten years	113.3
Carrying Value
Due in one year or less	127
Due after one year through five years	433.6
Due after five years through ten years	303.2
Due after ten years	124.9
Mortgage and asset-backed securities
Cost or Amortized Cost
Mortgage and asset-backed securities	211.7
Carrying Value
Mortgage and asset-backed securities	$ 218.5

Investment Securities - Cost or

Investment Securities - Cost or Amortized Cost, Gross Unrealized Investment Gains and Losses (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
MediaAlpha
Investment securities
Cost or Amortized Cost	$ 0	$ 0
Gross Unrealized Gains	802.2	180
Gross Unrealized Losses	0	0
Net Foreign Currency Gains	0	0
Common equity securities, at fair value	802.2	180
Common equity securities
Investment securities
Cost or Amortized Cost	0	553.3
Gross Unrealized Gains	0	130.6
Gross Unrealized Losses	0	0
Net Foreign Currency Gains	0	0
Common equity securities, at fair value	0	683.9
Other long-term investments
Investment securities
Cost or Amortized Cost	767.4	667.4
Gross Unrealized Gains	95.8	75.2
Gross Unrealized Losses	(78.1)	(64.1)
Net Foreign Currency Gains	1.7	(2.2)
Common equity securities, at fair value	$ 786.8	$ 676.3

Investment Securities - Inves_3

Investment Securities - Investments Held on Deposit or as Collateral (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Investments, Debt and Equity Securities [Abstract]
Percentage of investments recorded at fair value	73.00%	71.00%
Investments held in trusts	$ 432.4	$ 319.9
Assets held by insurance regulators	$ 11.9	$ 9.9

Investment Securities - Fair Va

Investment Securities - Fair Value Measurement by Level (Details) $ in Millions	Dec. 31, 2020USD ($)fund	Dec. 31, 2019USD ($)Investment	Dec. 31, 2018USD ($)
Investment securities
Fair value investments	$ 2,796.2	$ 2,746	$ 2,328.7
Other long-term investments	$ 786.8
Number of investments | fund	14
Debt securities issued by corporations
Investment securities
Fair value investments	$ 547.4	467.2
Mortgage and asset-backed securities
Investment securities
Fair value investments	218.5	209
Equity Securities
Investment securities
Fair value investments		$ 0.1	0
Common equity securities
Investment securities
Number of investments | Investment		2
Level 1
Investment securities
Fair value investments	978.5	$ 780	842.6
Level 2
Investment securities
Fair value investments	1,030.9	1,109.6	1,160.5
Level 2 | Mortgage and asset-backed securities
Investment securities
Fair value investments	218.5	209
Level 3
Investment securities
Other long-term investments	614.2
Level 3 | Mortgage and asset-backed securities
Investment securities
Fair value investments	0	0
Level 3 | Equity Securities
Investment securities
Fair value investments	0	0.1
Level 3 | Other long-term investments
Investment securities
Fair value investments	614.2	654	138.7
Fair value measured on a recurring basis
Investment securities
Fair value investments	2,939.1	2,947.2
Other long-term investments	786.8	676.3
Fair value measured on a recurring basis | MediaAlpha
Investment securities
Other long-term investments	802.2	180
Fair value measured on a recurring basis | U.S. Government and agency obligations
Investment securities
Fair value investments	176.3	232.5
Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	547.4	467.2
Fair value measured on a recurring basis | Municipal obligations
Investment securities
Fair value investments	265	297.1
Fair value measured on a recurring basis | Mortgage and asset-backed securities
Investment securities
Fair value investments	218.5	209
Fair value measured on a recurring basis | Fixed maturity investments
Investment securities
Fair value investments	1,207.2	1,205.8
Fair value measured on a recurring basis | Short-term investments
Investment securities
Short-term investments, at fair value	142.9	201.2	$ 214.2
Fair value measured on a recurring basis | Other long-term investments
Investment securities
Fair value investments	614.2	474
Fair value measured on a recurring basis | Other long-term investments — NAV
Investment securities
Fair value investments	172.6	202.3
Fair value measured on a recurring basis | Level 1
Investment securities
Fair value investments	1,121.4	969.4
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 1 | MediaAlpha
Investment securities
Other long-term investments	802.2	0
Fair value measured on a recurring basis | Level 1 | U.S. Government and agency obligations
Investment securities
Fair value investments	176.3	232.5
Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Municipal obligations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Mortgage and asset-backed securities
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Fixed maturity investments
Investment securities
Fair value investments	176.3	232.5
Fair value measured on a recurring basis | Level 1 | Short-term investments
Investment securities
Short-term investments, at fair value	142.9	189.4
Fair value measured on a recurring basis | Level 1 | Other long-term investments
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 1 | Other long-term investments — NAV
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 2
Investment securities
Fair value investments	1,030.9	1,121.4
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 2 | MediaAlpha
Investment securities
Other long-term investments	0	0
Fair value measured on a recurring basis | Level 2 | U.S. Government and agency obligations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	547.4	467.2
Fair value measured on a recurring basis | Level 2 | Municipal obligations
Investment securities
Fair value investments	265	297.1
Fair value measured on a recurring basis | Level 2 | Mortgage and asset-backed securities
Investment securities
Fair value investments	218.5	209
Fair value measured on a recurring basis | Level 2 | Fixed maturity investments
Investment securities
Fair value investments	1,030.9	973.3
Fair value measured on a recurring basis | Level 2 | Short-term investments
Investment securities
Short-term investments, at fair value	0	11.8
Fair value measured on a recurring basis | Level 2 | Other long-term investments
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 2 | Other long-term investments — NAV
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3
Investment securities
Fair value investments	614.2	654.1
Other long-term investments	614.2	474
Fair value measured on a recurring basis | Level 3 | MediaAlpha
Investment securities
Other long-term investments	0	180
Fair value measured on a recurring basis | Level 3 | U.S. Government and agency obligations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Municipal obligations
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Mortgage and asset-backed securities
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Fixed maturity investments
Investment securities
Fair value investments	0	0
Fair value measured on a recurring basis | Level 3 | Short-term investments
Investment securities
Short-term investments, at fair value	0	0
Fair value measured on a recurring basis | Level 3 | Other long-term investments
Investment securities
Fair value investments	614.2	474
Fair value measured on a recurring basis | Level 3 | Other long-term investments — NAV
Investment securities
Fair value investments	0	0
Financials | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	133.9	144.8
Financials | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Financials | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	133.9	144.8
Financials | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Industrial | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	66.9	59
Industrial | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Industrial | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	66.9	59
Industrial | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Healthcare | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	51.5	52.6
Healthcare | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Healthcare | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	51.5	52.6
Healthcare | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Consumer | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	81.9	50.9
Consumer | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Consumer | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	81.9	50.9
Consumer | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Energy | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	35.8	44.9
Energy | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Energy | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	35.8	44.9
Energy | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Technology | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	66.7	41.2
Technology | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Technology | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	66.7	41.2
Technology | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Communications | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	44.5	31.3
Communications | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Communications | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	44.5	31.3
Communications | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Utilities | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	32.3	25
Utilities | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Utilities | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	32.3	25
Utilities | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Materials | Fair value measured on a recurring basis | Debt securities issued by corporations
Investment securities
Fair value investments	33.9	17.5
Materials | Fair value measured on a recurring basis | Level 1 | Debt securities issued by corporations
Investment securities
Fair value investments	0	0
Materials | Fair value measured on a recurring basis | Level 2 | Debt securities issued by corporations
Investment securities
Fair value investments	33.9	17.5
Materials | Fair value measured on a recurring basis | Level 3 | Debt securities issued by corporations
Investment securities
Fair value investments	$ 0	0
Exchange traded funds | Fair value measured on a recurring basis | Equity Securities
Investment securities
Fair value investments		536.4
Exchange traded funds | Fair value measured on a recurring basis | Level 1 | Equity Securities
Investment securities
Fair value investments		521.6
Exchange traded funds | Fair value measured on a recurring basis | Level 2 | Equity Securities
Investment securities
Fair value investments		14.8
Exchange traded funds | Fair value measured on a recurring basis | Level 3 | Equity Securities
Investment securities
Fair value investments		0
Other | Fair value measured on a recurring basis | Equity Securities
Investment securities
Fair value investments		147.5
Other | Fair value measured on a recurring basis | Level 1 | Equity Securities
Investment securities
Fair value investments		25.9
Other | Fair value measured on a recurring basis | Level 2 | Equity Securities
Investment securities
Fair value investments		121.5
Other | Fair value measured on a recurring basis | Level 3 | Equity Securities
Investment securities
Fair value investments		0.1
Equity Securities | Fair value measured on a recurring basis | Equity Securities
Investment securities
Fair value investments		683.9
Equity Securities | Fair value measured on a recurring basis | Level 1 | Equity Securities
Investment securities
Fair value investments		547.5
Equity Securities | Fair value measured on a recurring basis | Level 2 | Equity Securities
Investment securities
Fair value investments		136.3
Equity Securities | Fair value measured on a recurring basis | Level 3 | Equity Securities
Investment securities
Fair value investments		$ 0.1

Investment Securities - Debt Se

Investment Securities - Debt Securities Issued By Corporation (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Investment securities
Fair value investments	$ 2,796.2	$ 2,746	$ 2,328.7
Debt securities issued by corporations
Investment securities
Fair value investments	547.4	467.2
AAA | Debt securities issued by corporations
Investment securities
Fair value investments	10.6	9.5
AA | Debt securities issued by corporations
Investment securities
Fair value investments	57.9	73.9
A | Debt securities issued by corporations
Investment securities
Fair value investments	318.3	288.5
BBB | Debt securities issued by corporations
Investment securities
Fair value investments	159.6	95.3
BB | Debt securities issued by corporations
Investment securities
Fair value investments	$ 1	$ 0

Investment Securities - Mortgag

Investment Securities - Mortgage-backed Asset Securities (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Investment securities
Fair value investments	$ 2,796.2	$ 2,746	$ 2,328.7
FNMA
Investment securities
Fair value investments	88.7	88.6
FHLMC
Investment securities
Fair value investments	70.1	60.5
GNMA
Investment securities
Fair value investments	40.6	30.8
Total Agency
Investment securities
Fair value investments	199.4	179.9
Total mortgage-backed securities
Investment securities
Fair value investments	199.4	179.9
Credit card receivables
Investment securities
Fair value investments	11.3	14
Vehicle receivables
Investment securities
Fair value investments	7.8	15.1
Total other asset-backed securities
Investment securities
Fair value investments	19.1	29.1
Total mortgage and asset- backed securities
Investment securities
Fair value investments	218.5	209
Level 2
Investment securities
Fair value investments	1,030.9	1,109.6	$ 1,160.5
Level 2 | FNMA
Investment securities
Fair value investments	88.7	88.6
Level 2 | FHLMC
Investment securities
Fair value investments	70.1	60.5
Level 2 | GNMA
Investment securities
Fair value investments	40.6	30.8
Level 2 | Total Agency
Investment securities
Fair value investments	199.4	179.9
Level 2 | Total mortgage-backed securities
Investment securities
Fair value investments	199.4	179.9
Level 2 | Credit card receivables
Investment securities
Fair value investments	11.3	14
Level 2 | Vehicle receivables
Investment securities
Fair value investments	7.8	15.1
Level 2 | Total other asset-backed securities
Investment securities
Fair value investments	19.1	29.1
Level 2 | Total mortgage and asset- backed securities
Investment securities
Fair value investments	218.5	209
Level 3 | FNMA
Investment securities
Fair value investments	0	0
Level 3 | FHLMC
Investment securities
Fair value investments	0	0
Level 3 | GNMA
Investment securities
Fair value investments	0	0
Level 3 | Total Agency
Investment securities
Fair value investments	0	0
Level 3 | Total mortgage-backed securities
Investment securities
Fair value investments	0	0
Level 3 | Credit card receivables
Investment securities
Fair value investments	0	0
Level 3 | Vehicle receivables
Investment securities
Fair value investments	0	0
Level 3 | Total other asset-backed securities
Investment securities
Fair value investments	0	0
Level 3 | Total mortgage and asset- backed securities
Investment securities
Fair value investments	$ 0	$ 0

Investment Securities - Inves_4

Investment Securities - Investment in MediaAlpha (Details) - MediaAlpha - USD ($) $ / shares in Units, $ in Millions	Oct. 30, 2020	Dec. 31, 2020
Investment securities
Investment owned (in shares)	20,532,202
Ownership interest (as a percent)	35.00%
Fully diluted ownership interest (as a percent)	32.30%
Share price (in USD per share)		$ 39.07
Value of investment		$ 802.2
IPO
Investment securities
Sale of stock, number of shares issued in transaction (in shares)	3,609,894
Sale of stock, consideration received in transaction	$ 63.8

Investment Securities - Other L

Investment Securities - Other Long-Term Investments (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Investment securities
Other investments	$ 786.8	$ 676.3
Kudu
Investment securities
Other investments	400.6	266.5
PassportCard/DavidShield
Investment securities
Other investments	95	90
Elementum
Investment securities
Other investments	55.1	55.1
Other unconsolidated entities
Investment securities
Other investments	42.4	33.7
Unconsolidated entities
Investment securities
Other investments	593.1	445.3
Private equity funds and hedge funds
Investment securities
Other investments	121.2	161.1
Insurance-linked securities funds
Investment securities
Other investments	51.4	41.2
Private debt investments
Investment securities
Other investments	21.1	28.7
Private debt instruments
Investment securities
Alternative investment	$ 5.8	$ 5

Investment Securities - Fair _2

Investment Securities - Fair Value of Hedge Funds Subject to Restrictions on Redemption Frequency (Details) $ in Millions	3 Months Ended
	Mar. 31, 2020USD ($)	Dec. 31, 2020USD ($)fund	Dec. 31, 2019USD ($)
Investment securities
Number of investments | fund		14
Private equity funds
Investment securities
Trading security, fair value		$ 121.2
Total private equity funds and hedge funds included in other long-term investments
Investment securities
Other long-term investments largest single investment		29.1	$ 54.6
Trading security, fair value		121.2	161.1
Fair value unfunded commitments		45.7	50.2
Private equity funds | Private equity funds
Investment securities
Trading security, fair value		121.2	106.5
Fair value unfunded commitments		45.7	50.2
Private equity funds | Aerospace/Defense/Government
Investment securities
Trading security, fair value		69.1	33.8
Fair value unfunded commitments		15.3	23.3
Private equity funds | Manufacturing/Industrial
Investment securities
Trading security, fair value		28.6	57.7
Fair value unfunded commitments		0	4.1
Private equity funds | Financial services
Investment securities
Trading security, fair value		23.5	15
Fair value unfunded commitments		30.4	22.8
Hedge funds | Hedge funds
Investment securities
Transfer from investments	$ 45.6
Trading security, fair value		0	54.6
Fair value unfunded commitments		0	0
Hedge funds | Long/short banks and financial
Investment securities
Trading security, fair value		0	54.6
Fair value unfunded commitments		$ 0	$ 0

Investment Securities - Inves_5

Investment Securities - Investments In Private Equity Funds Subject to Lock-Up Periods (Details) $ in Millions	12 Months Ended
	Dec. 31, 2020USD ($)fund	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)
Investment securities
Number of investments | fund	14
Fair value investments	$ 2,796.2	$ 2,746	$ 2,328.7
Private equity funds
Investment securities
Trading security, fair value	$ 121.2
Insurance-linked securities funds
Investment securities
Number of investments | fund	4
Fair value investments	$ 51.4
1 – 3 years | Private equity funds
Investment securities
Trading security, fair value	8
3 – 5 years | Private equity funds
Investment securities
Trading security, fair value	40.7
5 – 10 years | Private equity funds
Investment securities
Trading security, fair value	64.7
>10 years | Private equity funds
Investment securities
Trading security, fair value	$ 7.8
Minimum
Investment securities
Redemptions and advanced redemption notice period	30 days
Maximum
Investment securities
Redemptions and advanced redemption notice period	90 days

Investment Securities - Rollfor

Investment Securities - Rollforward of Fair Value Measurements by Level (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	$ 2,746	$ 2,328.7
Net realized and unrealized gains	716.4	433
Amortization/accretion	(4.5)	(1.6)
Purchases	766.6	866.1
Sales	(1,428.3)	(950.3)
Effect of Kudu Transaction		70.1
Transfers in	0	14.9
Transfers out	0	(14.9)
Ending balance	2,796.2	2,746
Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	2,947.2
Ending balance	2,939.1	2,947.2
Equity Securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	0.1	0
Net realized and unrealized gains		0
Amortization/accretion		0
Purchases		0.1
Sales		0
Effect of Kudu Transaction		0
Transfers in		0
Transfers out		0
Ending balance		0.1
Other long-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	474
Ending balance	614.2	474
Short-term investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Securities, realized and unrealized gain losses	0.4	0.2
Short-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Short-term investments at carrying value	142.9	201.2	$ 214.2
Level 1 Inputs
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	780	842.6
Net realized and unrealized gains	436.4	163
Amortization/accretion	(0.1)	0.2
Purchases	133.9	165.3
Sales	(830.4)	(391.1)
Effect of Kudu Transaction		0
Transfers in	0	0
Transfers out	0	0
Ending balance	978.5	780
Level 1 Inputs | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	969.4
Ending balance	1,121.4	969.4
Level 1 Inputs | Other long-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	0
Ending balance	0	0
Level 1 Inputs | Short-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Short-term investments at carrying value	142.9	189.4
Level 2
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	1,109.6	1,160.5
Net realized and unrealized gains	15.9	76.1
Amortization/accretion	(4.4)	(1.8)
Purchases	437.6	404.5
Sales	(527.8)	(529.7)
Effect of Kudu Transaction		0
Transfers in	0	0
Transfers out	0	0
Ending balance	1,030.9	1,109.6
Level 2 | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	1,121.4
Ending balance	1,030.9	1,121.4
Level 2 | Other long-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	0
Ending balance	0	0
Level 2 | Short-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Short-term investments at carrying value	0	11.8
Level 3 | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	654.1
Ending balance	614.2	654.1
Level 3 | Equity Securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	0.1
Net realized and unrealized gains	0
Amortization/accretion	0
Purchases	0
Sales	(0.1)
Transfers in	0
Transfers out	0
Ending balance	0	0.1
Level 3 | Other long-term investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	654	138.7
Net realized and unrealized gains	275.6	181.2
Amortization/accretion	0	0
Purchases	151.5	185.4
Sales	(8.2)	0
Effect of Kudu Transaction		141.8
Transfers in	0	10.9
Transfers out	0	(4)
Ending balance	614.2	654
Level 3 | Other long-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	474
Ending balance	614.2	474
Level 3 | Hedge funds and private equity funds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Amortization/accretion		0
Level 3 | Short-term investments | Fair value measured on a recurring basis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Short-term investments at carrying value	0	0
Other Long-term Investments Measured at NAV | Hedge funds and private equity funds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	202.3	186.9
Net realized and unrealized gains	(11.5)	12.7
Amortization/accretion	0
Purchases	43.6	110.8
Sales	(61.8)	(29.5)
Effect of Kudu Transaction		(71.7)
Transfers in	0	4
Transfers out	0	(10.9)
Ending balance	172.6	202.3
MediaAlpha
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	0
Unrealized gain associated with unconsolidated affiliates		$ 114.7
MediaAlpha | Level 1 Inputs
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	458.7
MediaAlpha | Level 2
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	0
MediaAlpha | Level 3 | Equity Securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	0
MediaAlpha | Level 3 | Other long-term investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	(458.7)
MediaAlpha | Other Long-term Investments Measured at NAV | Hedge funds and private equity funds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Effect of MediaAlpha IPO	$ 0

Investment Securities - Signifi

Investment Securities - Significant Unobservable Inputs (Details) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2020USD ($)Contract$ / shares	Dec. 31, 2019USD ($)$ / sharesContract	Dec. 31, 2018USD ($)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Trading securities	$ 118.3	$ 118.4	$ 0
Kudu’s Participation Contracts (5) | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Cash flow exit multiple | Contract	7	6
Kudu’s Participation Contracts (5) | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Cash flow exit multiple | Contract	12	12
MediaAlpha | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)		4.00%
DavidShield & PassportCard
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Trading securities	$ 15
DavidShield & PassportCard | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)		4.00%
Elementum Holdings, L.P.
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Trading securities		$ 55.1
Elementum Holdings, L.P. | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)		4.00%
All other | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)		4.00%
Zillion Insurance Services, Inc. (7)
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Trading securities	2.5	$ 2.5
Kudu
Quantitative information for Level 3 Fair Value Measurements Assets
Investments in Trading securities	$ 118.2	$ 198
Measurement Input, Discount Rate | Kudu’s Participation Contracts (5) | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	18.00%	15.00%
Measurement Input, Discount Rate | Kudu’s Participation Contracts (5) | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	23.00%	22.00%
Measurement Input, Discount Rate | MediaAlpha | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)		15.00%
Measurement Input, Discount Rate | DavidShield & PassportCard | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	23.00%	22.00%
Measurement Input, Discount Rate | Elementum Holdings, L.P. | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	17.00%	20.00%
Terminal revenue growth rate (as a percent)	4.00%
Measurement Input, Discount Rate | Private debt instruments | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	4.00%	4.00%
Measurement Input, Discount Rate | Private debt instruments | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	8.00%	9.00%
Measurement Input, Discount Rate | All other | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)	4.00%
Measurement Input, Discount Rate | All other | Standard Poors NR Rating | Minimum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	20.00%	25.00%
Measurement Input, Discount Rate | All other | Standard Poors NR Rating | Maximum
Quantitative information for Level 3 Fair Value Measurements Assets
Fair value, discount rate (as a percent)	24.00%	32.00%
Measurement Input, Long-term Revenue Growth Rate | DavidShield & PassportCard | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Terminal revenue growth rate (as a percent)	4.00%
Measurement Input, Long-term Revenue Growth Rate | Noblr, Inc. | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Share price (in USD per share) | $ / shares	$ 8.7
Measurement Input, Long-term Revenue Growth Rate | Zillion Insurance Services, Inc. (7) | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 5
Measurement Input, Long-term Revenue Growth Rate | New Market Solutions, LLC | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Share price (in USD per share) | $ / shares	$ 9.9
Discounted Cash Flow Valuation Technique | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value		$ 23.7
Discounted Cash Flow Valuation Technique | Kudu’s Participation Contracts (5) | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 400.6	266.5
Discounted Cash Flow Valuation Technique | MediaAlpha | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value		180
Discounted Cash Flow Valuation Technique | DavidShield & PassportCard | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	95	90
Discounted Cash Flow Valuation Technique | Elementum Holdings, L.P. | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	55.1	55.1
Discounted Cash Flow Valuation Technique | Private debt instruments | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	17.1
Discounted Cash Flow Valuation Technique | All other | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	18.8
Recent Transaction | Noblr, Inc. | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	8.7	$ 5
Share price (in USD per share) | $ / shares		$ 5
Recent Transaction | Zillion Insurance Services, Inc. (7) | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	5	$ 2.5
Investment, measurement input | $ / shares		2.5
Recent Transaction | New Market Solutions, LLC | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value	$ 9.9
Estimated Net Realizable Value | Compare.com | Standard Poors NR Rating
Quantitative information for Level 3 Fair Value Measurements Assets
Assets, fair value		$ 2.5
Investment, measurement input | $ / shares		2.5

Goodwill and Other Intangible_3

Goodwill and Other Intangible Assets - Summary of Goodwill and Intangible Assets (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Goodwill [Line Items]
Goodwill, fair value	$ 525.5	$ 402.3
Goodwill, impairment loss	0	7.6
Goodwill	525.5	394.7
Other intangible assets, fair value	843.3	694.4
Other intangible assets, accumulated amortization	54.7	29.3
Other intangible assets, net	248.3
Goodwill and intangible asset impairment	6.2	10.4
Goodwill and other intangible assets	782.4	656.7
NSM
Goodwill [Line Items]
Goodwill, fair value	506.4	381.6
Goodwill, impairment loss	0	0
Goodwill	506.4	381.6
Other intangible assets, fair value	288.9	271.7
Other intangible assets, accumulated amortization	52.3	27.9
Other intangible assets, net	230.4	241.4
NSM | Fresh Insurance Services Group Limited
Goodwill [Line Items]
Impairments	6.2	2.4
Kudu
Goodwill [Line Items]
Goodwill, fair value	7.6	7.6
Goodwill, impairment loss	0	0
Goodwill	7.6	7.6
Other
Goodwill [Line Items]
Goodwill, fair value	11.5	13.1
Goodwill, impairment loss	0	7.6
Goodwill	11.5	5.5
Other intangible assets, fair value	26.7	18.2
Other intangible assets, accumulated amortization	1.8	1.2
Impairments		0.4
Other intangible assets, net	$ 24.9	16.6
Customer relationships | NSM
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	8 years 10 months 24 days
Other intangible assets, fair value	$ 136.2	121.7
Other intangible assets, accumulated amortization	36.7	19.8
Other intangible assets, net	96	100.5
Customer relationships | NSM | Fresh Insurance Services Group Limited
Goodwill [Line Items]
Impairments	$ 3.5	1.4
Customer relationships | Other
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	10 years 8 months 12 days
Other intangible assets, fair value	$ 14.2	7.2
Other intangible assets, accumulated amortization	1.4	0.4
Impairments	0	0
Other intangible assets, net	$ 12.8	6.8
Trade names | NSM
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	16 years
Other intangible assets, fair value	$ 65.4	61.9
Other intangible assets, accumulated amortization	8.3	5.3
Other intangible assets, net	56.1	56.2
Trade names | NSM | Fresh Insurance Services Group Limited
Goodwill [Line Items]
Impairments	$ 1	0.4
Trade names | Kudu
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	7 years
Other intangible assets, fair value	$ 2.2	2.2
Other intangible assets, accumulated amortization	0.6	0.2
Impairments	0	0
Other intangible assets, net	$ 1.6	2
Trade names | Other
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	9 years 7 months 6 days
Other intangible assets, fair value	$ 3.6	1.7
Other intangible assets, accumulated amortization	0.3	0.5
Impairments	0	0.2
Other intangible assets, net	$ 3.3	1
Information technology platform | NSM
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	0 years
Other intangible assets, fair value	$ 3.1	3.9
Other intangible assets, accumulated amortization	1.4	1.4
Other intangible assets, net	0	1.9
Information technology platform | NSM | Fresh Insurance Services Group Limited
Goodwill [Line Items]
Impairments	$ 1.7	0.6
Information technology platform | Other
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	5 years
Other intangible assets, fair value	$ 0	0.5
Other intangible assets, accumulated amortization	0	0.3
Impairments	0	0.2
Other intangible assets, net	0	0
Insurance licenses | Other
Goodwill [Line Items]
Other intangible assets, fair value	8.6	8.6
Other intangible assets, accumulated amortization	0	0
Impairments	0	0
Other intangible assets, net	$ 8.6	8.6
Renewal rights | NSM
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	12 years
Other intangible assets, fair value	$ 82.5	82.5
Other intangible assets, accumulated amortization	4.9	0.7
Impairments	0	0
Other intangible assets, net	$ 77.6	81.8
Other | NSM
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	3 years 4 months 24 days
Other intangible assets, fair value	$ 1.7	1.7
Other intangible assets, accumulated amortization	1	0.7
Impairments	0	0
Other intangible assets, net	$ 0.7	1
Other | Other
Goodwill [Line Items]
Acquired other intangible assets, weighted average useful life (in years)	5 years 4 months 24 days
Other intangible assets, fair value	$ 0.3	0.2
Other intangible assets, accumulated amortization	0.1	0
Impairments	0	0
Other intangible assets, net	0.2	0.2
Total other intangible assets
Goodwill [Line Items]
Other intangible assets, fair value	317.8	292.1
Other intangible assets, accumulated amortization	54.7	29.3
Impairments	6.2	2.8
Other intangible assets, net	256.9	260
Non-controlling Interests
Goodwill [Line Items]
Goodwill and other intangible assets	(28.1)	(23.4)
Total
Goodwill [Line Items]
Goodwill and other intangible assets	754.3	631.3
Goodwill
Goodwill [Line Items]
Goodwill	525.5	394.7	$ 379.9
Goodwill, foreign currency translation gain	13.4	1.8
Goodwill | NSM
Goodwill [Line Items]
Goodwill, foreign currency translation gain	13.4	1.8
Total other intangible assets | NSM
Goodwill [Line Items]
Goodwill, foreign currency translation gain	$ 1.6	$ 0.7

Goodwill and Other Intangible_4

Goodwill and Other Intangible Assets - Fair Value of Goodwill and Intangible Assets (Details) - USD ($) $ in Millions	Dec. 31, 2020	Apr. 07, 2020	Jun. 28, 2019	Apr. 04, 2019	Apr. 01, 2019
NSM
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 281.8
Renewal rights
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired			$ 82.5
Embrace
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired					$ 67.6
Kingsbridge
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired		$ 131.7
Kudu Transaction
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired				$ 9.8
Other Operations
Finite-Lived Intangible Assets [Line Items]
Goodwill and intangible assets acquired	$ 38.1
Other Assets | Embrace
Finite-Lived Intangible Assets [Line Items]
Software					$ 3.4

Goodwill and Other Intangible_5

Goodwill and Other Intangible Assets - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Finite-Lived Intangible Assets [Line Items]
Goodwill, impairment loss	$ 0	$ 7.6
Other Operations
Finite-Lived Intangible Assets [Line Items]
Impairments	0.4	0.4
Goodwill, impairment loss	7.6	7.6
Fresh Insurance Services Group Limited
Finite-Lived Intangible Assets [Line Items]
Impairments	6.2	2.4
NSM
Finite-Lived Intangible Assets [Line Items]
Goodwill, impairment loss	0	0
Total other intangible assets
Finite-Lived Intangible Assets [Line Items]
Impairments	$ 6.2	$ 2.8

Goodwill and Other Intangible_6

Goodwill and Other Intangible Assets - Goodwill and Intangible Assets Rollforward (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Goodwill [Roll Forward]
Beginning balance	$ 394.7
Ending balance	525.5	$ 394.7
Finite-lived Intangible Assets [Roll Forward]
Amortization	(28.3)	(21.8)	$ (18.8)
Goodwill and Intangible Assets [Roll Forward]
Goodwill, impairment loss	0	7.6
Total other intangible assets
Goodwill [Roll Forward]
Contingent considerations	23.2	26.8
Measurement period adjustments	6.6	5.9
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	260	157.6
Acquisitions of businesses	0	34.6
Impairments	(6.2)	(2.8)
Foreign currency translation	1.6	0.7
Amortization	(28.3)	(21.8)
Ending balance	256.9	260	157.6
Renewal rights
Finite-lived Intangible Assets [Roll Forward]
Acquisitions of businesses	0	82.5
Goodwill
Goodwill [Roll Forward]
Beginning balance	394.7	379.9
Acquisitions of businesses	140	64.8
Acquisition of collector car renewal rights	0	0
Dispositions of businesses	0
Contingent considerations	(23.2)	(26.8)
Impairment	0	(7.6)
Measurement period adjustments	0.6	0.9
Foreign currency translation	13.4	1.8
Ending balance	525.5	394.7	379.9
Intangible Asset and Goodwill
Goodwill [Roll Forward]
Dispositions of businesses	0	(41.8)
Contingent considerations	0	0
Measurement period adjustments	7.2	6.8
Finite-lived Intangible Assets [Roll Forward]
Acquisitions of businesses	140	99.4
Foreign currency translation	15	2.5
Amortization	(28.3)	(21.8)
Goodwill and Intangible Assets [Roll Forward]
Beginning balance	654.7	537.5
Write-off	(6.2)	(10.4)
Ending balance	782.4	654.7	$ 537.5
Intangible Asset and Goodwill | Renewal rights
Finite-lived Intangible Assets [Roll Forward]
Acquisitions of businesses	0	82.5
MediaAlpha
Goodwill [Roll Forward]
Dispositions of businesses		(18.3)
MediaAlpha | Total other intangible assets
Goodwill [Roll Forward]
Dispositions of businesses	0	(23.5)
Other Operations
Finite-lived Intangible Assets [Roll Forward]
Impairments	(0.4)	(0.4)
Goodwill and Intangible Assets [Roll Forward]
Goodwill, impairment loss	7.6	7.6
Fresh Insurance Services Group Limited
Finite-lived Intangible Assets [Roll Forward]
Impairments	(6.2)	(2.4)
KBK Insurance Group, Inc. & KBK Premium Services, Inc. | Goodwill
Goodwill [Roll Forward]
Contingent considerations	$ 4.1	$ 5.9

Goodwill and Other Intangible_7

Goodwill and Other Intangible Assets - Amortization Expense (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of other intangible assets	$ 28.3	$ 21.8	$ 18.8
2021	36.3
2022	35.2
2023	34.1
2024	28.6
2025 and years after	114.1
Total	248.3
Indefinite-lived intangible assets	$ 8.6

Debt - Debt Outstanding (Detail

Debt - Debt Outstanding (Details) - USD ($)	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Apr. 07, 2020	Dec. 31, 2018	May 18, 2018	May 11, 2018
Debt Instrument
Debt	$ 376,400,000	$ 283,500,000
Weighted average interest rate	7.00%	7.00%
NSM Bank Facility
Debt Instrument
Effective yield (as a percent)	8.40%	8.10%
NSM
Debt Instrument
Debt instrument at face value						$ 100,000,000
Debt	$ 272,600,000	$ 219,200,000
NSM | NSM Bank Facility
Debt Instrument
Debt instrument at face value	277,400,000
Debt	277,400,000	221,300,000		$ 180,400,000
Kudu | Kudu Debt
Debt Instrument
Debt	86,300,000	53,600,000
Other Operations | Other
Debt Instrument
Debt	17,500,000	10,700,000
Term Loan | NSM | NSM Bank Facility
Debt Instrument
Debt instrument at face value	277,400,000	221,300,000	$ 276,400,000		$ 51,000,000
Unamortized Debt Issuance Expense	(6,100,000)	(3,900,000)
Debt	$ 271,300,000	$ 217,400,000
Effective yield (as a percent)	7.50%	7.50%
Term Loan | NSM | Other NSM
Debt Instrument
Debt instrument at face value	$ 1,300,000
Debt	$ 1,300,000	$ 1,800,000
Effective yield (as a percent)	2.50%	3.00%
Term Loan | Kudu | Kudu Debt
Debt Instrument
Unamortized Debt Issuance Expense	$ (2,900,000)	$ (3,400,000)
Effective yield (as a percent)	8.30%	8.30%
Term Loan | Kudu | Kudu Debt
Debt Instrument
Debt instrument at face value	$ 89,200,000	$ 57,000,000
Term Loan | Other Operations | Other Debt
Debt Instrument
Effective yield (as a percent)	7.40%	8.30%
Term Loan | Other Operations | Other
Debt Instrument
Debt instrument at face value	$ 18,000,000	$ 11,100,000
Unamortized Debt Issuance Expense	$ (500,000)	(400,000)
Debt		$ 10,700,000

Debt - Schedule of Contractual

Debt - Schedule of Contractual Repayments (Details) $ in Millions	Dec. 31, 2020USD ($)
Debt Disclosure [Abstract]
Due in one year or less	$ 4.5
Due in two to three years	12.2
Due in four to five years	106
Due after five years	263.3
Total	$ 386

Debt - Narrative (Details)

Debt - Narrative (Details) £ in Millions	Apr. 07, 2020USD ($)	Apr. 07, 2020GBP (£)	Apr. 01, 2019USD ($)	May 11, 2018USD ($)	Dec. 31, 2020USD ($)credit_facility	Dec. 31, 2020GBP (£)	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)	Jun. 15, 2018USD ($)	May 18, 2018USD ($)
Debt Instrument
Total commitment under revolving credit facility	$ 291,400,000
Debt					$ 376,400,000		$ 283,500,000
Secured credit facilities | credit_facility					2
Interest expense					$ 29,500,000		17,600,000	$ 9,500,000
Interest paid					27,000,000		16,300,000	8,800,000
First Credit Facility
Debt Instrument
Total commitment under revolving credit facility					16,300,000
Second Credit Facility
Debt Instrument
Total commitment under revolving credit facility					15,000,000
NSM
Debt Instrument
Debt instrument at face value				$ 100,000,000
Debt					272,600,000		219,200,000
NSM | NSM Bank Facility
Debt Instrument
Total commitment under revolving credit facility				234,000,000
Debt instrument at face value					$ 277,400,000
Percentage of discounted future cash flows					10.00%	10.00%
Debt					$ 277,400,000		221,300,000	180,400,000
Kudu | Kudu Debt
Debt Instrument
Total commitment under revolving credit facility					124,000,000
Term Loan | First Credit Facility
Debt Instrument
Total commitment under revolving credit facility					11,300,000
Long-term debt, gross					9,100,000
Term Loan | Second Credit Facility
Debt Instrument
Total commitment under revolving credit facility					9,000,000
Long-term debt, gross					8,900,000
Term Loan | NSM | NSM Bank Facility
Debt Instrument
Total commitment under revolving credit facility				224,000,000
Debt instrument at face value	276,400,000				277,400,000		221,300,000			$ 51,000,000
Proceeds from borrowings	52,400,000	£ 42.5			52,400,000	£ 42.5	42,900,000
Debt					271,300,000		217,400,000
Term Loan | NSM | Other NSM
Debt Instrument
Debt instrument at face value					1,300,000
Debt					1,300,000		1,800,000
Term Loan | Kudu | Kudu Debt
Debt Instrument
Total commitment under revolving credit facility					57,000,000
Debt instrument at face value					89,200,000		57,000,000
Delayed Draw Term Loans | First Credit Facility
Debt Instrument
Total commitment under revolving credit facility					3,000,000
Delayed Draw Term Loans | Second Credit Facility
Debt Instrument
Total commitment under revolving credit facility					4,000,000
Delayed Draw Term Loans | Kudu | Kudu Debt
Debt Instrument
Total commitment under revolving credit facility					62,000,000
Revolving Credit Facility | First Credit Facility
Debt Instrument
Total commitment under revolving credit facility					2,000,000
Repayments of Lines of Credit					2,000,000		200,000
Revolving Credit Facility | Second Credit Facility
Debt Instrument
Total commitment under revolving credit facility					2,000,000
Repayments of Lines of Credit					100,000
Revolving Credit Facility | NSM | NSM Bank Facility
Debt Instrument
Total commitment under revolving credit facility	$ 15,000,000			$ 10,000,000
Proceeds from borrowings					0		6,500,000
Revolving Credit Facility | Kudu | Kudu Debt
Debt Instrument
Total commitment under revolving credit facility					5,000,000
Current borrowing capacity					$ 32,200,000		57,000,000
London Interbank Offered Rate (LIBOR) | Line of Credit | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					1.00%	1.00%
London Interbank Offered Rate (LIBOR) | Line of Credit | Minimum | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					5.50%	5.50%
London Interbank Offered Rate (LIBOR) | Line of Credit | Maximum | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					6.25%	6.25%
British Sterling Pound London Interbank Offered Rate LIBOR | Term Loan | Minimum | NSM | NSM Bank Facility
Debt Instrument
Basis spread on variable rate					6.00%	6.00%
British Sterling Pound London Interbank Offered Rate LIBOR | Term Loan | Maximum | NSM | NSM Bank Facility
Debt Instrument
Basis spread on variable rate					6.50%	6.50%
Derivative, cap interest rate					1.25%
Prime Rate | Line of Credit | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					1.00%	1.00%
Prime Rate | Line of Credit | Minimum | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					4.50%	4.50%
Prime Rate | Line of Credit | Maximum | Kudu | Kudu Debt
Debt Instrument
Basis spread on variable rate					5.25%	5.25%
United States Dollar London Interbank Offered Rate LIBOR | Term Loan | Minimum | NSM | NSM Bank Facility
Debt Instrument
Basis spread on variable rate				4.25%	5.50%	5.50%
United States Dollar London Interbank Offered Rate LIBOR | Term Loan | Maximum | NSM | NSM Bank Facility
Debt Instrument
Debt instrument, interest rate					1.25%	1.25%
Basis spread on variable rate				4.75%	6.00%	6.00%
Foreign Exchange Spot Rate | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Proceeds from borrowings					$ 58,100,000
Interest Rate Swap | NSM | NSM Bank Facility
Debt Instrument
Debt, weighted average interest rate					8.40%
Interest Rate Swap | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Total commitment under revolving credit facility					$ 151,000,000
Hedged liability, fair value hedge									$ 151,000,000
Debt					$ 147,600,000
Interest Rate Cap | London Interbank Offered Rate (LIBOR) | NSM
Debt Instrument
Derivative, cap interest rate					1.25%
Embrace Pet Insurance | NSM
Debt Instrument
Proceeds from borrowings			$ 20,400,000
Embrace Pet Insurance | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Proceeds from borrowings							20,400,000
NSM
Debt Instrument
Interest expense					$ 22,100,000		$ 16,700,000	$ 8,000,000
Designated as Hedging Instrument | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Debt, weighted average interest rate					7.60%
Designated as Hedging Instrument | Interest Rate Swap | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Debt					$ 147,600,000
Debt, weighted average interest rate					9.00%
Not Designated as Hedging Instrument | Interest Rate Swap | Term Loan | NSM | NSM Bank Facility
Debt Instrument
Debt					$ 129,800,000

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 ($)	Apr. 07, 2020GBP (£)	Apr. 01, 2019USD ($)	Dec. 31, 2020USD ($)	Dec. 31, 2020GBP (£)	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)
Debt Instrument
Beginning balance				$ 283.5
Repayment of debt and revolving lines of credit				(4.5)		$ (22.9)	$ (15.4)
Ending balance				376.4		283.5
NSM
Debt Instrument
Beginning balance				219.2
Ending balance				272.6		219.2
NSM | Embrace Pet Insurance
Debt Instrument
Borrowings			$ 20.4
NSM | NSM Bank Facility
Debt Instrument
Beginning balance				221.3		180.4
Ending balance				277.4		221.3	$ 180.4
NSM | NSM Bank Facility | Term Loan
Debt Instrument
Beginning balance				217.4
Borrowings	$ 52.4	£ 42.5		52.4	£ 42.5	42.9
Repayment of debt and revolving lines of credit				(2)		(2)
Foreign currency translation				5.7		0
Ending balance				271.3		217.4
NSM | NSM Bank Facility | Term Loan | Kingsbridge
Debt Instrument
Borrowings				52.4
NSM | NSM Bank Facility | Term Loan | Embrace Pet Insurance
Debt Instrument
Borrowings						20.4
NSM | NSM Bank Facility | Term Loan | Renewal rights
Debt Instrument
Borrowings						22.5
NSM | NSM Bank Facility | Revolving Credit Facility
Debt Instrument
Borrowings				0		6.5
Repayment of debt and revolving lines of credit				$ 0		$ (6.5)

Income Taxes - Income Tax (Bene

Income Taxes - Income Tax (Benefit) Expense (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Current income tax (expense):
U.S. federal									$ (10.4)	$ 0.9	$ (0.1)
State									(4.2)	(3.7)	(1.4)
Non-U.S.									(1.1)	(1.7)	(2.9)
Total current income tax (expense)									(15.7)	(4.5)	(4.4)
Deferred income tax benefit (expense):
U.S. federal									23.2	(14.9)	8.3
State									10.3	(10.4)	0
Non-U.S.									2.7	0.5	0.1
Total deferred income tax benefit (expense)									36.2	(24.8)	8.4
Total income tax benefit (expense)	$ 117.6	$ (98.5)	$ (24.1)	$ 25.5	$ (10.4)	$ (8.8)	$ 0.1	$ (10.2)	$ 20.5	$ (29.3)	$ 4
U.S. statutory rate (as a percent)									21.00%	21.00%	21.00%

Income Taxes - Effective Rate R

Income Taxes - Effective Rate Reconciliation (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Contingency [Line Items]
U.S. statutory rate (as a percent)									21.00%	21.00%	21.00%
Tax (expense) benefit at the U.S. statutory rate									$ (135.5)	$ (85.1)	$ 37.4
Differences in taxes resulting from:
Reorganization									130.5	0	0
Non-U.S. earnings, net of foreign taxes									78.4	27.1	(2.9)
Change in valuation allowance									(29.2)	63.6	(31)
State taxes									(8.5)	(17.5)	4
Withholding tax									(5)	(1.6)	(2.7)
Member’s surplus contributions									(4.8)	(3.6)	(2.6)
Tax rate changes									2.7	(5.7)	1.7
Tax reserve adjustments									1.9	(0.7)	(0.8)
Officer compensation									(1.1)	0	0
Tax exempt interest and dividends									0.8	1.1	0.6
Other, net									(9.7)	(6.9)	0.3
Total income tax benefit (expense)	$ 117.6	$ (98.5)	$ (24.1)	$ 25.5	$ (10.4)	$ (8.8)	$ 0.1	$ (10.2)	20.5	(29.3)	4
Pre-tax income (loss)	$ 357.3	$ 321.2	$ 132.7	$ (166)	$ 56.5	$ 51.1	$ 15.8	$ 281.7	645.2	405.1	(178.2)
Tax Payments and Receipts
Net income tax payments to US									16.2	3.7	3.5
Non-US
Differences in taxes resulting from:
Pre-tax income (loss)									$ 327.8	$ 100.4	$ (30.1)

Income Taxes - Deferred Tax Ass

Income Taxes - Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Deferred tax assets related to:
U.S. federal and state net operating and capital loss carryforwards	$ 79.6	$ 92.3
Non-U.S. net operating loss carryforwards	50.5	41.7
Incentive compensation	17.5	15
Accrued interest	7.9	5.1
Deferred acquisition costs	5.5	4.3
Tax credit carryforwards	5.5	4.2
Other items	1.3	3.4
Total gross deferred tax assets	167.8	166
Less: valuation allowances	97.4	77.9
Total net deferred tax assets	70.4	88.1
Deferred tax liabilities related to:
Member’s surplus contributions	52.9	43.2
Investment basis difference	11.8	6.6
Purchase accounting	5.1	3.1
Net unrealized investment gains	0.3	66.3
Other items	2.8	1.5
Total deferred tax liabilities	72.9	120.7
Net deferred tax (liability)	$ (2.5)	$ (32.6)

Income Taxes - Valuation Allowa

Income Taxes - Valuation Allowance (Detail) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Valuation Allowance [Line Items]
Valuation allowance	$ 97.4				$ 77.9				$ 97.4	$ 77.9
Change in valuation allowance									29.2	(63.6)	$ 31
Income tax benefit (expense)	117.6	$ (98.5)	$ (24.1)	$ 25.5	(10.4)	$ (8.8)	$ 0.1	$ (10.2)	20.5	(29.3)	$ 4
U.S. losses and other federal deferred tax benefits
Valuation Allowance [Line Items]
Valuation allowance	46.5				34.9				46.5	34.9
Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	26.8								26.8
Net Operating Losses in Israel Subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	20				17.3				20	17.3
Net Operating Losses in United Kingdom Subsidiaries
Valuation Allowance [Line Items]
Valuation allowance	$ 4.1								4.1
Luxembourg | U.S. losses and other federal deferred tax benefits
Valuation Allowance [Line Items]
Change in valuation allowance									4.2	1.1
Israel | Net Operating Losses in Israel Subsidiaries
Valuation Allowance [Line Items]
Change in valuation allowance									2.7	1.6
United Kingdom | Net Operating Losses in United Kingdom Subsidiaries
Valuation Allowance [Line Items]
Change in valuation allowance									1	1.3
Subsidiaries | Luxembourg | Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance					22.6					22.6
Subsidiaries | United Kingdom | Net operating losses in Luxembourg subsidiaries
Valuation Allowance [Line Items]
Valuation allowance					$ 3.1					3.1
Guilford Holdings, Inc. | United States
Valuation Allowance [Line Items]
Change in valuation allowance									14.9
Income tax benefit (expense)										63.2
BAM | United States
Valuation Allowance [Line Items]
Income tax benefit (expense)									(4.5)	4.5
BAM | United States | MSC [Member]
Valuation Allowance [Line Items]
Income tax benefit (expense)									9.7	10.5
BAM | United States | Foreign Tax Credits
Valuation Allowance [Line Items]
Income tax benefit (expense)									$ (1.9)	$ (0.1)

Income Taxes - Net Operating an

Income Taxes - Net Operating and Capital Loss Carryforwards (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Net deferred tax assets
Total net deferred tax assets	$ 70.4	$ 88.1
Tax credit carryforwards, foreign	5.5
Operating and Capital Loss Carryforward
Net deferred tax assets
Operating loss carryforwards	584.4
Gross deferred tax asset	128
Valuation allowance	(115.6)
Total net deferred tax assets	12.4
Operating and Capital Loss Carryforward | United States
Net deferred tax assets
Operating loss carryforwards	369.1
Gross deferred tax asset	77.5
Valuation allowance	(66.8)
Total net deferred tax assets	10.7
Operating and Capital Loss Carryforward | Luxembourg
Net deferred tax assets
Operating loss carryforwards	104.2
Gross deferred tax asset	26
Valuation allowance	(25.9)
Total net deferred tax assets	0.1
Operating and Capital Loss Carryforward | United Kingdom
Net deferred tax assets
Operating loss carryforwards	25.9
Gross deferred tax asset	4.9
Valuation allowance	(3.3)
Total net deferred tax assets	1.6
Operating and Capital Loss Carryforward | Israel
Net deferred tax assets
Operating loss carryforwards	85.2
Gross deferred tax asset	19.6
Valuation allowance	(19.6)
Total net deferred tax assets	0
2020-2024 | Operating and Capital Loss Carryforward
Net deferred tax assets
Operating loss carryforwards	0
2020-2024 | Operating and Capital Loss Carryforward | United States
Net deferred tax assets
Operating loss carryforwards	0
2020-2024 | Operating and Capital Loss Carryforward | Luxembourg
Net deferred tax assets
Operating loss carryforwards	0
2020-2024 | Operating and Capital Loss Carryforward | United Kingdom
Net deferred tax assets
Operating loss carryforwards	0
2020-2024 | Operating and Capital Loss Carryforward | Israel
Net deferred tax assets
Operating loss carryforwards	0
2025-2029 | Operating and Capital Loss Carryforward
Net deferred tax assets
Operating loss carryforwards	0
2025-2029 | Operating and Capital Loss Carryforward | United States
Net deferred tax assets
Operating loss carryforwards	0
2025-2029 | Operating and Capital Loss Carryforward | Luxembourg
Net deferred tax assets
Operating loss carryforwards	0
2025-2029 | Operating and Capital Loss Carryforward | United Kingdom
Net deferred tax assets
Operating loss carryforwards	0
2025-2029 | Operating and Capital Loss Carryforward | Israel
Net deferred tax assets
Operating loss carryforwards	0
2030-2039 | Operating and Capital Loss Carryforward
Net deferred tax assets
Operating loss carryforwards	323.9
2030-2039 | Operating and Capital Loss Carryforward | United States
Net deferred tax assets
Operating loss carryforwards	250.7
2030-2039 | Operating and Capital Loss Carryforward | Luxembourg
Net deferred tax assets
Operating loss carryforwards	73.2
2030-2039 | Operating and Capital Loss Carryforward | United Kingdom
Net deferred tax assets
Operating loss carryforwards	0
2030-2039 | Operating and Capital Loss Carryforward | Israel
Net deferred tax assets
Operating loss carryforwards	0
No expiration date | Operating and Capital Loss Carryforward
Net deferred tax assets
Operating loss carryforwards	260.5
No expiration date | Operating and Capital Loss Carryforward | United States
Net deferred tax assets
Operating loss carryforwards	118.4
No expiration date | Operating and Capital Loss Carryforward | Luxembourg
Net deferred tax assets
Operating loss carryforwards	31
No expiration date | Operating and Capital Loss Carryforward | United Kingdom
Net deferred tax assets
Operating loss carryforwards	25.9
No expiration date | Operating and Capital Loss Carryforward | Israel
Net deferred tax assets
Operating loss carryforwards	$ 85.2

Income Taxes - ASC 740-10 (Deta

Income Taxes - ASC 740-10 (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Contingency [Line Items]
Percentage of likelihood for realization of benefit upon ultimate settlement	50.00%
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns
Balance at beginning	$ 2.4	$ 1.1	$ 0.3
Changes in prior year tax positions	0.1	1.3	0.8
Tax positions taken during the current year	0.1
Reorganization	(2.6)
Balance at year end	0	2.4	1.1
Permanent Differences
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns
Balance at beginning	2.4	1.1	0.3
Changes in prior year tax positions	0.1	1.3	0.8
Tax positions taken during the current year	0.1
Reorganization	(2.6)
Balance at year end	0	2.4	1.1
Temporary Differences
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns
Balance at beginning	0	0	0
Changes in prior year tax positions	0	0	0
Tax positions taken during the current year	0
Reorganization	0
Balance at year end	0	0	0
Interest and Penalties Net of Tax Benefit
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns
Balance at beginning	0	0	0
Changes in prior year tax positions	0	0	0
Tax positions taken during the current year	0
Reorganization	0
Balance at year end	$ 0	$ 0	$ 0

Derivatives - Forward Contracts

Derivatives - Forward Contracts (Details) $ in Millions	12 Months Ended
	Dec. 31, 2018USD ($)
Forward Contracts
Derivative [Line Items]
Realized and unrealized gains (losses)	$ (3.5)

Derivatives - Narrative (Detail

Derivatives - Narrative (Details) £ in Millions	12 Months Ended
	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Dec. 31, 2020GBP (£)	Apr. 07, 2020USD ($)	Dec. 31, 2018USD ($)	May 18, 2018USD ($)	May 11, 2018USD ($)
Derivative [Line Items]
Total commitment under revolving credit facility				$ 291,400,000
Debt	$ 376,400,000	$ 283,500,000
NSM
Derivative [Line Items]
Debt	272,600,000	219,200,000
Long-term line of credit							$ 100,000,000
NSM Bank Facility | NSM
Derivative [Line Items]
Total commitment under revolving credit facility							234,000,000
Debt	277,400,000	221,300,000			$ 180,400,000
Long-term line of credit	277,400,000
NSM Bank Facility | NSM | Term Loan
Derivative [Line Items]
Total commitment under revolving credit facility							$ 224,000,000
Debt	271,300,000	217,400,000
Long-term line of credit	$ 277,400,000	221,300,000		$ 276,400,000		$ 51,000,000
Interest Rate Swap | NSM
Derivative [Line Items]
Fixed interest rate	2.97%		2.97%
Variable interest rate	1.00%		1.00%
Net interest expense	$ 2,500,000	1,100,000
Derivative, fair value, net	8,200,000	6,600,000
Change in fair value of derivative instruments	$ (1,600,000)	$ (3,900,000)
Interest Rate Swap | NSM Bank Facility | NSM
Derivative [Line Items]
Debt, weighted average interest rate	8.40%		8.40%
Interest Rate Swap | NSM Bank Facility | NSM | Term Loan
Derivative [Line Items]
Total commitment under revolving credit facility	$ 151,000,000
Debt	147,600,000
Interest Rate Cap | NSM
Derivative [Line Items]
Derivative, fair value, net	100,000
Change in fair value of derivative instruments	(100,000)
Premiums paid	$ 100,000
GBP-LIBOR rate	0.03%
Interest Rate Cap | NSM | London Interbank Offered Rate (LIBOR)
Derivative [Line Items]
Derivative, cap interest rate	1.25%		1.25%
Interest Rate Cap | NSM Bank Facility | NSM
Derivative [Line Items]
Debt instrument extension term (in years)	1 year
Interest Rate Cap | NSM Bank Facility | Term Loan
Derivative [Line Items]
Long-term line of credit	$ 52,400,000		£ 42.5
Designated as Hedging Instrument | NSM Bank Facility | NSM | Term Loan
Derivative [Line Items]
Debt, weighted average interest rate	7.60%		7.60%
Designated as Hedging Instrument | Interest Rate Swap | NSM Bank Facility | NSM | Term Loan
Derivative [Line Items]
Debt	$ 147,600,000
Debt, weighted average interest rate	9.00%		9.00%

Municipal Bond Guarantee Insu_3

Municipal Bond Guarantee Insurance (Details) - USD ($) $ in Millions	Nov. 30, 2018	Dec. 31, 2020	Jan. 31, 2020	Dec. 31, 2019	Apr. 30, 2018	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2012	Dec. 31, 2021	Jun. 30, 2020	Sep. 30, 2019	Dec. 31, 2017	Jul. 31, 2012
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Percentage of par value of policy reinsured		15.00%				15.00%
Percentage of risk premium ceded		60.00%				60.00%
Cash and investments included in collateral trust		$ 434.5				$ 434.5
Percent change in discounted future cash flows						10.00%
HG Re
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Percentage of par value of policy reinsured		15.00%				15.00%
Trust balance		$ 222.8		$ 190.3		$ 222.8	$ 190.3
White Mountains
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Capital contributions								$ 594.5
HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Percentage of par value of policy reinsured		15.00%				15.00%
Surplus notes								503
Cash and fixed income securities													$ 100
Percent over a target trust balance						102.00%
Supplement trust target		$ 603				$ 603
BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Principal		$ 75,287.7		$ 62,250.5		$ 75,287.7	$ 62,250.5			$ 36.9	$ 1,100
BAM Management
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Capital contributions								$ 14.5
Preferred stocks | HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Ownership interest (as a percent)		96.90%		96.90%		96.90%	96.90%
Common equity securities | HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Ownership interest (as a percent)		88.40%		88.40%		88.40%	88.40%
HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Collateral held in supplement trust		$ 827.1		$ 786.7		$ 827.1	$ 786.7
Cash and investments included in collateral trust		434.5		321.6		434.5	321.6
Interest receivable		155.7		162.7		155.7	162.7
BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Surplus notes		388.2		457.6		388.2	457.6
Interest receivable		4.4		7.5		4.4	7.5
Accrued interest on surplus notes		155.7		162.7		155.7	162.7
Supplemental Trust | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Cash repayments on notes		21.5	$ 47.9	23.7
Accrued interest on surplus notes		0.2	0.9	0.3		0.2	0.3
Surplus Note | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Cash repayments on notes		30.1	65	32			10
Accrued interest on surplus notes		8.4	16.2	8		$ 8.4	8
One-time cash payment				10
BAM | Fidus Re Ltd.
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Losses above retention, percentage of liability					90.00%
Fidus Re Ltd. | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Insurance linked securities					$ 100
Collateralized financial guarantee term (in years)					12 years
Collateral financial guarantee, callable term (in years)						5 years
Aggregate loss limit on contracts					$ 165
Reimbursement guarantee under contracts					$ 100
Covered Portfolio rate						42.00%
Percentage of quota share reinsurance agreement	100.00%
Direct written premiums	$ 2,200
Maximum | BAM | HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Aggregate loss limit on contracts			$ 75
Maximum | Fidus Re Ltd. | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Aggregate loss limit on contracts		276.1				$ 276.1
Series B BAM Surplus Note | HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Surplus notes													$ 300
Series A BAM Surplus Note | HG Global
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Surplus notes												$ 203
Trust balance		604.3		596.4		604.3	596.4
Surplus Note | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Cash repayments on notes						30.1	32
Accrued interest on surplus notes		$ 8.4		$ 8		$ 8.4	$ 8
Fixed interest rate | Surplus Note | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Interest rate		8.00%				8.00%
U.S. treasury rate plus | Surplus Note | BAM
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Basis spread on variable rate						3.00%
U.S. treasury rate plus | Surplus Note | BAM | Forecast
Schedule of Insured Financial Obligations with Credit Deterioration [Line Items]
Effective yield (as a percent)									3.10%

Municipal Bond Guarantee Insu_4

Municipal Bond Guarantee Insurance - Schedule of Municipal Bond Guarantee Insured Obligations (Details) - BAM $ in Millions	12 Months Ended
	Dec. 31, 2020USD ($)Contract	Dec. 31, 2019USD ($)Contract	Jun. 30, 2020USD ($)	Sep. 30, 2019USD ($)
Guarantor Obligations [Line Items]
Contracts outstanding | Contract	10,997	8,987
Remaining weighted average contract period (in years)	10 years 8 months 12 days	10 years 8 months 12 days
Principal	$ 75,287.7	$ 62,250.5	$ 36.9	$ 1,100
Interest and capital appreciation	36,448.8	31,799.7
Total debt service outstanding	111,736.5	94,050.2
Gross unearned insurance premiums	$ 237.5	$ 198.4

Municipal Bond Guarantee - Sche

Municipal Bond Guarantee - Schedule of Municipal Guarantee Insurance Contracts, Premium Received Over Contract Period (Details) - BAM - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Guarantor Obligations [Line Items]
January 1, 2021 - March 31, 2021	$ 5.6
April 1, 2021 - June 30, 2021	5.5
July 1, 2021 - September 30, 2021	5.5
October 1, 2021 - December 31, 2021	5.4
Total 2021	22
2022	20.9
2023	19.8
2024	18.3
2025	17
2026 and thereafter	139.5
Total gross unearned insurance premiums	$ 237.5	$ 198.4

Municipal Bond Guarantee Insu_5

Municipal Bond Guarantee Insurance - Schedule of Net Written Premiums (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Earned premiums:
Gross earned premiums	$ 22.8	$ 16.3	$ 13.9
HG/BAM
Written premiums:
Direct	61.5	28.1	44.8
Assumed	0.2	10.6	8.1
Gross written premiums	61.7	38.7	52.9
Earned premiums:
Direct	19.4	13.6	13.6
Assumed	3.4	2.7	0.3
Gross earned premiums	$ 22.8	$ 16.3	$ 13.9

Earnings Per Share - Schedule o

Earnings Per Share - Schedule of Earnings Per Share from Continuing Operations (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4	$ 708.7	$ 414.5	$ (141.2)
Less: total (loss) income from discontinued operations, net of tax									(2.3)	0.8	(17.2)
Net income (loss) from continuing operations attributable to White Mountains’s common shareholders									711	413.7	(124)
Allocation of (earnings) losses to participating restricted common shares									(9.3)	(5.3)	1.4
Basic and diluted earnings (losses) per share numerators									$ 701.7	$ 408.4	$ (122.6)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Basic earnings (losses) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Diluted earnings per share denominator (in thousands):
Average outstanding dilutive options to acquire common shares (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Diluted earnings (loss) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Diluted earnings per share (in dollars) - continuing operations:
Dividends declared and paid (usd per share)									$ 1	$ 1	$ 1
Undistributed earnings (losses) (usd per share)									226.72	129.02	(37.67)
Basic and diluted earnings (losses) per share (usd per share)									$ 227.72	$ 130.02	$ (36.67)

Earnings Per Share - Schedule_2

Earnings Per Share - Schedule of Undistributed Net Earnings (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Earnings Per Share [Abstract]
Net income (loss) attributable to White Mountains’s common shareholders, net of restricted common share amounts	$ 701.7	$ 408.4	$ (122.6)
Dividends declared, net of restricted common share amounts	(3.1)	(3.2)	(3.7)
Total undistributed net earnings (losses), net of restricted common share amounts	$ 698.6	$ 405.2	$ (126.3)

Employee Share-Based Incentiv_3

Employee Share-Based Incentive Compensation Plans - Performance Shares (Details) $ in Millions	12 Months Ended
	Dec. 31, 2020USD ($)multipliershares	Dec. 31, 2019USD ($)shares	Dec. 31, 2018USD ($)shares
Performance Shares
Share-based compensation arrangement by share-based payment award
Multiplier for determining payout, low end of range | multiplier	0
Multiplier for determining payout, high end of range | multiplier	2
Performance cycle period	3 years
Unamortized grant date fair value | $	$ 28.8
Performance Share Roll forward
Beginning of period (in shares)	42,473	40,616	50,515
Shares paid or expired (in shares)	(14,070)	(13,715)	(23,186)
New grants (in shares)	14,055	15,600	14,105
Forfeitures (in shares)	0	(28)	(818)
Expense recognized (in shares)	0	0	0
End of period (in shares)	42,458	42,473	40,616
Unamortized Issue Date Fair Value
Beginning of period | $	$ 43.7	$ 31.7	$ 45.8
Shares paid or expired | $	(27.7)	(18.1)	(28.4)
New grants | $	0	0	0
Forfeitures | $	(0.4)	(0.1)	0.1
Expense recognized | $	40.7	30.2	14.2
End of period | $	$ 56.3	$ 43.7	$ 31.7
Performance Shares | Performance Cycle 2020 to 2022
Unamortized Issue Date Fair Value
Targeted performance goal (as a percent)	7.00%
Payout for maximum growth target percentage	200.00%
Performance Shares | W T M Incentive and Phantom Plan | Range Of Performance Cycle From 2017 to 2019
Unamortized Issue Date Fair Value
Payout for minimum growth target percentage	174.00%
Payout for maximum growth target percentage	180.00%
Performance Shares | W T M Incentive and Phantom Plan | Range Of Performance Cycle From 2016-2018
Unamortized Issue Date Fair Value
Payout for minimum growth target percentage		139.00%
Payout for maximum growth target percentage		166.00%
Performance Shares | W T M Incentive and Phantom Plan | Range Of Performance Cycle From 2015 to 2017
Unamortized Issue Date Fair Value
Payout for minimum growth target percentage			145.00%
Payout for maximum growth target percentage			147.00%
Restricted Share Cliff Vesting in January 2022 | W T M Incentive and Phantom Plan
Share-based compensation arrangement by share-based payment award
Performance shares (in shares)	14,055	15,600
Restricted Share Cliff Vesting in January 2021 | W T M Incentive and Phantom Plan
Share-based compensation arrangement by share-based payment award
Performance shares (in shares)		15,600
Restricted Share Cliff Vesting in January 2020 | W T M Incentive and Phantom Plan
Share-based compensation arrangement by share-based payment award
Performance shares (in shares)			13,450
Restricted Share Cliff Vesting in January 2019 | W T M Incentive and Phantom Plan
Share-based compensation arrangement by share-based payment award
Performance shares (in shares)			290
Restricted Share Cliff Vesting in January 2018 | W T M Incentive and Phantom Plan
Share-based compensation arrangement by share-based payment award
Performance shares (in shares)			365

Employee Share-Based Incentiv_4

Employee Share-Based Incentive Compensation Plans - Performance Shares Granted (Details) - Performance Shares - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based compensation arrangement by share-based payment award
Number of nonvested options before forfeitures (in shares)	43,105
Incentive compensation payable before forfeitures	$ 57.3
Assumed forfeitures (in shares)	(647)
Assumed forfeitures	$ (1)
Shares outstanding (in shares)	42,458	42,473	40,616	50,515
Accrued incentive compensation	$ 56.3	$ 43.7	$ 31.7	$ 45.8
Performance Cycle 2020 to 2022
Share-based compensation arrangement by share-based payment award
Number of nonvested options before forfeitures (in shares)	14,055
Incentive compensation payable before forfeitures	$ 9.5
Targeted performance goal (as a percent)	7.00%
Payout for maximum growth target percentage	200.00%
Performance Cycle 2019 to 2021
Share-based compensation arrangement by share-based payment award
Number of nonvested options before forfeitures (in shares)	15,600
Incentive compensation payable before forfeitures	$ 20.7
Targeted performance goal (as a percent)	7.00%
Payout for maximum growth target percentage	200.00%
Performance Cycle 2018 to 2020
Share-based compensation arrangement by share-based payment award
Number of nonvested options before forfeitures (in shares)	13,450
Incentive compensation payable before forfeitures	$ 27.1
Targeted performance goal (as a percent)	6.00%
Payout for maximum growth target percentage	200.00%
Minimum | Performance Cycle 2020 to 2022
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	2.00%
Minimum | Performance Cycle 2019 to 2021
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	2.00%
Minimum | Performance Cycle 2018 to 2020
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	2.00%
Maximum | Performance Cycle 2020 to 2022
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	12.00%
Maximum | Performance Cycle 2019 to 2021
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	12.00%
Maximum | Performance Cycle 2018 to 2020
Share-based compensation arrangement by share-based payment award
Payout for minimum growth target percentage	10.00%

Employee Share-Based Incentiv_5

Employee Share-Based Incentive Compensation Plans - Restricted Shares (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Restricted Stock
Restricted Share Roll forward
Beginning of period (in shares)	43,395	41,510	53,755
Issued (in shares)	14,055	15,600	14,105
Vested (in shares)	(14,345)	(13,715)	(25,381)
Assumed forfeitures and cancellations (in shares)	0	0	(969)
Expense recognized (in shares)	0	0	0
End of period (in shares)	43,105	43,395	41,510
Unamortized Issue Date Fair Value
Beginning of period	$ 16.7	$ 12.5	$ 14.3
Issued	15.1	14.5	11.4
Vested	0	0	0
Forfeited	0	0	(0.2)
Expense recognized	(16.6)	(10.3)	(13)
End of period	$ 15.2	$ 16.7	$ 12.5
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2023
Restricted Share Roll forward
Issued (in shares)	14,055
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2022
Restricted Share Roll forward
Issued (in shares)	14,055	15,600
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2021
Restricted Share Roll forward
Issued (in shares)		15,600
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2019
Restricted Share Roll forward
Issued (in shares)			290
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2018
Restricted Share Roll forward
Issued (in shares)			365
W T M Incentive and Phantom Plan | Restricted Share Cliff Vesting in January 2020
Restricted Share Roll forward
Issued (in shares)			13,450

Leases - Narrative (Details)

Leases - Narrative (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Jan. 01, 2019
Lessee, Lease, Description [Line Items]
ROU lease asset	$ 37.6	$ 22.6
Operating lease liability	$ 38.3	$ 22.8
Accounting Standards Update 2016-02
Lessee, Lease, Description [Line Items]
ROU lease asset			$ 23.2
Operating lease liability			$ 23.2

Leases - Schedule of Lease Cost

Leases - Schedule of Lease Cost (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019
Leases [Abstract]
Lease cost	$ 7.7	$ 7.2
Less: sublease income	0.4	0.4
Net lease cost	$ 7.3	$ 6.8

Leases - Schedule of Future Min

Leases - Schedule of Future Minimum Payments on Operating Leases (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Leases [Abstract]
2021	$ 7.7
2022	7.3
2023	7.1
2024	5.8
2025	5.1
Thereafter	12.2
Total undiscounted lease payments	45.2
Less: present value adjustment	(6.9)
Operating lease liability	$ 38.3	$ 22.8

Leases - Schedule of Right-of-U

Leases - Schedule of Right-of-Use Assets and Lease Liabilities (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Lessee, Lease, Description [Line Items]
ROU lease asset	$ 37.6	$ 22.6
Lease liability	$ 38.3	$ 22.8
Weighted Average Incremental Borrowing Rate	4.60%	4.60%
Operating Lease, Liability, Statement of Financial Position [Extensible List]	us-gaap:OtherLiabilities	us-gaap:OtherLiabilities
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List]	us-gaap:OtherAssets	us-gaap:OtherAssets
HG/BAM
Lessee, Lease, Description [Line Items]
ROU lease asset	$ 10.1	$ 10.4
Lease liability	10.1	10.4
NSM
Lessee, Lease, Description [Line Items]
ROU lease asset	17.1	4.8
Lease liability	17.1	4.8
Kudu
Lessee, Lease, Description [Line Items]
ROU lease asset	2	2.3
Lease liability	2	2.3
Other
Lessee, Lease, Description [Line Items]
ROU lease asset	8.4	5.1
Lease liability	$ 9.1	$ 5.3

Common Shareholders_ Equity a_3

Common Shareholders’ Equity and Non-controlling Interests (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Common Shares Repurchased and Retired
Value of common shares repurchased and retired	$ 85.1	$ 4.9	$ 519.1
Value of each common share repurchased and retired (in usd per share)	$ 859	$ 858	$ 877
Common Shares Issued
Stock issued (in shares)	15,745	17,917	16,377
Dividends on Common Shares
Cash dividends declared and paid	$ 3.2	$ 3.2	$ 3.8
Dividends declared and paid (in usd per share)	$ 1
Non-controlling interests	$ (88.1)	$ (116.8)
HG Global
Dividends on Common Shares
Non-controlling Percentage	3.10%	3.10%
NSM
Dividends on Common Shares
Non-controlling Percentage	3.40%	3.60%
Kudu
Dividends on Common Shares
Non-controlling Percentage	0.70%	0.90%
BAM
Dividends on Common Shares
Non-controlling Percentage	100.00%	100.00%
Common equity securities
Common Shares Repurchased and Retired
Common shares repurchased and retired (in shares)	99,087	5,679	592,458
Restricted Stock
Common Shares Issued
Stock issued (in shares)	14,055	15,600	14,105
General Board Authorization
Common Shares Repurchased and Retired
Additional authorized repurchase of common shares (in shares)	542,517
Common shares repurchased and retired (in shares)	93,188		582,493
Value of common shares repurchased and retired	$ 78.5		$ 511
Value of each common share repurchased and retired (in usd per share)	$ 843		$ 877
Directors | Restricted Stock
Common Shares Issued
Shares issued to directors (in shares)	1,440	2,317	2,272
Repurchased for Employee Benefit Plans
Common Shares Repurchased and Retired
Common shares repurchased and retired (in shares)	5,899		9,965
MediaAlpha | Restricted Stock
Common Shares Issued
Stock issued (in shares)	250
HG Global
Dividends on Common Shares
Non-controlling interests	$ 13.5	$ 14.4
NSM
Dividends on Common Shares
Non-controlling interests	17	14.9
Kudu
Dividends on Common Shares
Non-controlling interests	2.3	2.2
Other
Dividends on Common Shares
Non-controlling interests	2.4	(1.6)
BAM
Dividends on Common Shares
Non-controlling interests	(123.3)	(146.7)
Total Non-Controlling Excluding Reciprocals
Dividends on Common Shares
Non-controlling interests	$ 35.2	$ 29.9

Statutory Capital and Surplus (

Statutory Capital and Surplus (Details) - USD ($)	1 Months Ended			12 Months Ended
	Dec. 31, 2020	Jan. 31, 2020	Dec. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2021	Dec. 31, 2012
Statutory Accounting Practices [Line Items]
Cash and investments included in collateral trust	$ 434,500,000			$ 434,500,000
Repayments of principal debt				4,500,000	$ 22,900,000	$ 15,400,000
Other long-term investments	786,800,000			786,800,000
BAM
Statutory Accounting Practices [Line Items]
Surplus notes	388,200,000		$ 457,600,000	388,200,000	457,600,000
Interest receivable	4,400,000		7,500,000	4,400,000	7,500,000
Accrued interest on surplus notes	155,700,000		162,700,000	155,700,000	162,700,000
Kudu
Statutory Accounting Practices [Line Items]
Proceeds from borrowings			57,000,000
Distributions made			53,700,000	4,000,000
Other Operations
Statutory Accounting Practices [Line Items]
Unrestricted cash	464,200,000			464,200,000
Other long-term investments	172,700,000			172,700,000
HG Global
Statutory Accounting Practices [Line Items]
Collateral held in supplement trust	827,100,000		786,700,000	827,100,000	786,700,000
Cash and investments included in collateral trust	434,500,000		321,600,000	434,500,000	321,600,000
Interest receivable	155,700,000		162,700,000	155,700,000	162,700,000
HG Re | HG Global-BAM
Statutory Accounting Practices [Line Items]
Statutory capital and surplus	768,100,000			768,100,000
Surplus required	1			1
Cash outside of collateral trusts	2,800,000			2,800,000
Collateral held in supplement trust	827,100,000			827,100,000
Cash and investments outside of collateral trusts	20,100,000			20,100,000
Accrued interest held in supplemental trust	114,000,000			114,000,000
BAM | HG Global-BAM
Statutory Accounting Practices [Line Items]
Statutory capital and surplus	324,700,000			324,700,000
Surplus required	66,000,000			66,000,000
Statutory net loss				$ (59,300,000)	(38,300,000)	$ (34,600,000)
HG Global
Statutory Accounting Practices [Line Items]
Percent over a target trust balance				102.00%
Supplement trust target	603,000,000			$ 603,000,000
Surplus notes								$ 503,000,000
HG Global | HG Global-BAM
Statutory Accounting Practices [Line Items]
Preferred stock value	$ 619,000,000			$ 619,000,000
Ownership interest (as a percent)	96.90%			96.90%
Preferred stock dividend rate (as a percent)				6.00%
White Mountains | Kudu
Statutory Accounting Practices [Line Items]
Distributions made			53,300,000
NSM | NSM
Statutory Accounting Practices [Line Items]
Cash	$ 48,100,000			$ 48,100,000
Kudu
Statutory Accounting Practices [Line Items]
Cash and short-term investments	7,800,000			7,800,000
Surplus Note | BAM
Statutory Accounting Practices [Line Items]
Cash repayments on notes	30,100,000	$ 65,000,000	32,000,000		10,000,000
Accrued interest on surplus notes	$ 8,400,000	16,200,000	8,000,000	$ 8,400,000	8,000,000
Surplus Note | BAM | U.S. treasury rate plus
Statutory Accounting Practices [Line Items]
Basis spread on variable rate				3.00%
Surplus Note | BAM | Fixed interest rate
Statutory Accounting Practices [Line Items]
Interest rate	8.00%			8.00%
Surplus Note | BAM | Forecast | U.S. treasury rate plus
Statutory Accounting Practices [Line Items]
Effective yield (as a percent)							3.10%
Supplemental Trust | BAM
Statutory Accounting Practices [Line Items]
Cash repayments on notes	$ 21,500,000	47,900,000	23,700,000
Accrued interest on surplus notes	200,000	$ 900,000	300,000	$ 200,000	300,000
Preferred stocks | HG Global
Statutory Accounting Practices [Line Items]
Dividends				23,000,000
Preferred stocks | HG Global | HG Global-BAM
Statutory Accounting Practices [Line Items]
Dividends payable	376,600,000			376,600,000
Preferred stocks | White Mountains | HG Global | HG Global-BAM
Statutory Accounting Practices [Line Items]
Dividends				22,300,000
Dividends payable	363,900,000			363,900,000
Common Equities | Other Operations
Statutory Accounting Practices [Line Items]
Distributions made				3,200,000
Common Equities | MediaAlpha
Statutory Accounting Practices [Line Items]
Common equity securities, at fair value	802,200,000			802,200,000
Surplus Note | BAM
Statutory Accounting Practices [Line Items]
Accrued interest held in supplemental trust	200,000		300,000	200,000	300,000
Cash repayments on notes				30,100,000	32,000,000
Repayments of principal debt				21,500,000	23,700,000
Accrued interest on surplus notes	$ 8,400,000		$ 8,000,000	$ 8,400,000	$ 8,000,000

Segment Information (Details)

Segment Information (Details) $ in Millions	Feb. 26, 2019USD ($)	Dec. 31, 2020USD ($)	Sep. 30, 2020USD ($)	Jun. 30, 2020USD ($)	Mar. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Sep. 30, 2019USD ($)	Jun. 30, 2019USD ($)	Mar. 31, 2019USD ($)	Dec. 31, 2019USD ($)	Dec. 31, 2020USD ($)numberOfSegments	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)
Segment reporting information
Number of operating segments | numberOfSegments											4
Earned insurance premiums											$ 22.8	$ 16.3	$ 13.9
Net investment income											131	79.7	59
Net realized and unrealized investment gains (losses)											30.8	253.2	(108.3)
Net realized and unrealized investment gains from MediaAlpha											716.8	433.2	(108.3)
Realized gain from the 2019 MediaAlpha Transaction												67.5
Commission revenues											240.8	249.1	389.2
Other revenues											69.3	47.6	15.3
Total revenues		$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6		1,180.7	893.4	369.1
Insurance acquisition expenses											7	5.7	5.3
Other underwriting expenses											0.4	0.4	0.4
Cost of sales											11.3	48.1	248.7
General and administrative expenses											387	327.8	233.5
Broker commission expense											75.3	64.8	28.4
Change in fair value of contingent consideration earnout liabilities											(3.3)	2.1	2.7
Amortization of other intangible assets											28.3	21.8	18.8
Interest expense											29.5	17.6	9.5
Total expenses		163.5	138.3	126.9	106.8	118.8	104.4	113.2	151.9		535.5	488.3	547.3
Pre-tax income (loss) from continuing operations		$ 357.3	$ 321.2	$ 132.7	$ (166)	$ 56.5	$ 51.1	$ 15.8	$ 281.7		645.2	405.1	(178.2)
MediaAlpha
Segment reporting information
Net investment income											95	14.8	3.7
Net realized and unrealized investment gains from MediaAlpha											686	180	0
Total revenues										$ 359.2
HG Global-BAM
Segment reporting information
Earned insurance premiums											22.8	16.3	13.9
Net investment income											19.5	21.6	16.7
Net realized and unrealized investment gains (losses)											23.7	27.1	(7.5)
Realized gain from the 2019 MediaAlpha Transaction												0
Commission revenues											0	0	0
Other revenues											2.5	1.6	1.2
Total revenues											68.5	66.6	24.3
Insurance acquisition expenses											7	5.7	5.3
Other underwriting expenses											0.4	0.4	0.4
Cost of sales											0	0	0
General and administrative expenses											56.4	50.5	48
Broker commission expense											0	0	0
Change in fair value of contingent consideration earnout liabilities											0	0	0
Amortization of other intangible assets											0	0	0
Interest expense											0	0	0
Total expenses											63.8	56.6	53.7
Pre-tax income (loss) from continuing operations											4.7	10	(29.4)
HG Global-BAM | MediaAlpha
Segment reporting information
Net realized and unrealized investment gains from MediaAlpha											0	0
NSM
Segment reporting information
Earned insurance premiums											0	0	0
Net investment income											0	0	0
Net realized and unrealized investment gains (losses)											0	0	0
Realized gain from the 2019 MediaAlpha Transaction												0
Commission revenues											232.5	193.4	89.6
Other revenues											52.6	39.7	12
Total revenues											285.1	233.1	101.6
Insurance acquisition expenses											0	0	0
Other underwriting expenses											0	0	0
Cost of sales											0	0	0
General and administrative expenses											176.9	132.2	59.4
Broker commission expense											75.3	64.8	28.4
Change in fair value of contingent consideration earnout liabilities											(3.3)	2.1	2.7
Amortization of other intangible assets											26.7	19.4	8.3
Interest expense											22.1	16.7	8
Total expenses											297.7	235.2	106.8
Pre-tax income (loss) from continuing operations											$ (12.6)	$ (2.1)	$ (5.2)
Percentage of commission revenue											19.00%	17.00%	33.00%
Percentage of advertising revenue													29.00%
NSM | MediaAlpha
Segment reporting information
Net realized and unrealized investment gains from MediaAlpha											$ 0	$ 0
Kudu
Segment reporting information
Earned insurance premiums											0	0
Net investment income											29.5	14.7	$ 0
Net realized and unrealized investment gains (losses)											15.9	6.3	0
Realized gain from the 2019 MediaAlpha Transaction
Commission revenues											0	0
Other revenues											0.3	0.2	0
Total revenues											45.7	21.2	0
Insurance acquisition expenses											0	0
Other underwriting expenses											0	0
Cost of sales											0	0
General and administrative expenses											11.8	10.1	0
Broker commission expense											0	0
Change in fair value of contingent consideration earnout liabilities											0	0
Amortization of other intangible assets											0.3	0.2	0
Interest expense											6	0.1	0
Total expenses											18.1	10.4	0
Pre-tax income (loss) from continuing operations											27.6	10.8
Kudu | MediaAlpha
Segment reporting information
Net realized and unrealized investment gains from MediaAlpha											0	0
MediaAlpha
Segment reporting information
Earned insurance premiums												0	0
Net investment income												0	0
Net realized and unrealized investment gains (losses)												0	0
Realized gain from the 2019 MediaAlpha Transaction												0
Commission revenues											0	48.8	295.5
Other revenues											0	0	1.6
Total revenues											0	48.8	297.1
Insurance acquisition expenses												0	0
Other underwriting expenses												0	0
Cost of sales											0	40.6	245
General and administrative expenses											0	12.5	31.7
Broker commission expense												0	0
Change in fair value of contingent consideration earnout liabilities												0	0
Amortization of other intangible assets											0	1.6	10.3
Interest expense											0	0.2	1.2
Total expenses											0	54.9	288.2
Pre-tax income (loss) from continuing operations												(6.1)	8.9
MediaAlpha | MediaAlpha
Segment reporting information
Net realized and unrealized investment gains from MediaAlpha												0
Other Operations
Segment reporting information
Earned insurance premiums											0	0	0
Net investment income											82	43.4	42.3
Net realized and unrealized investment gains (losses)											(8.8)	219.8	(100.8)
Net realized and unrealized investment gains from MediaAlpha													0
Realized gain from the 2019 MediaAlpha Transaction											0	67.5	0
Commission revenues											8.3	6.9	4.1
Other revenues											13.9	6.1	0.5
Total revenues											781.4	523.7	(53.9)
Insurance acquisition expenses											0	0	0
Other underwriting expenses											0	0	0
Cost of sales											11.3	7.5	3.7
General and administrative expenses											141.9	122.5	94.4
Broker commission expense											0	0	0
Change in fair value of contingent consideration earnout liabilities											0	0	0
Amortization of other intangible assets											1.3	0.6	0.2
Interest expense											1.4	0.6	0.3
Total expenses											155.9	131.2	98.6
Pre-tax income (loss) from continuing operations											625.5	392.5	$ (152.5)
Other Operations | MediaAlpha
Segment reporting information
Net realized and unrealized investment gains from MediaAlpha											$ 686	$ 180
MediaAlpha
Segment reporting information
Realized gain from the 2019 MediaAlpha Transaction	$ 67.5

Segment Information - Assets (D

Segment Information - Assets (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2012
Segment reporting information
Total investments	$ 2,939.1	$ 2,947.2
Total assets	4,831.4	3,983.2
Total liabilities	1,013.5	838.5
Total White Mountains’s common shareholders’ equity	3,906	3,261.5
Non-controlling interests	(88.1)	(116.8)
Held for Sale
Segment reporting information
Total investments	0	0
Total assets	2.3	3
Total liabilities	0	0
Total White Mountains’s common shareholders’ equity	2.3	3
Non-controlling interests	0	0
HG Global-BAM
Segment reporting information
Total investments	919.9	845.6
Total assets	1,017.8	924
Total liabilities	291.5	246.8
Total White Mountains’s common shareholders’ equity	836.1	809.5
Non-controlling interests	(109.8)	(132.3)
NSM
Segment reporting information
Total investments	0	0
Total assets	999.6	825.2
Total liabilities	491.8	401.1
Total White Mountains’s common shareholders’ equity	490.7	409.3
Non-controlling interests	17.1	14.8
Kudu
Segment reporting information
Total investments	400.7	266.6
Total assets	430.2	290.5
Total liabilities	96.3	57
Total White Mountains’s common shareholders’ equity	331.6	231.3
Non-controlling interests	2.3	2.2
Other Operations
Segment reporting information
Total investments	1,618.5	1,835
Total assets	2,381.5	1,940.5
Total liabilities	133.9	133.6
Total White Mountains’s common shareholders’ equity	2,245.3	1,808.4
Non-controlling interests	2.3	(1.5)
BAM
Segment reporting information
Surplus notes	388.2	457.6
Accrued interest on surplus notes	155.7	162.7
HG Global
Segment reporting information
Non-controlling interests	13.5	14.4
Surplus notes			$ 503
Preferred Dividends Payable | HG Global
Segment reporting information
Total liabilities	$ 363.9	$ 330.3

Segment Information - Revenue (

Segment Information - Revenue (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Segment reporting information
Total revenues from contracts with customers									$ 307.9	$ 294.3	$ 401.2
Other revenues									872.8	599.1	(32.1)
Total revenues	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6	1,180.7	893.4	369.1
HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Other revenues									68.5	66.6	24.3
Total revenues									68.5	66.6	24.3
NSM
Segment reporting information
Total revenues from contracts with customers									285.1	233.1	101.6
Other revenues									0	0	0
Total revenues									285.1	233.1	101.6
Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Other revenues									45.7	21.2
Total revenues									45.7	21.2
MediaAlpha
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Other revenues										0	1.6
Total revenues									0	48.8	297.1
Other Operations
Segment reporting information
Total revenues from contracts with customers									22.8	12.4	4.1
Other revenues									758.6	511.3	(58)
Total revenues									781.4	523.7	(53.9)
Specialty Transportation
Segment reporting information
Total revenues from contracts with customers									85.5	77.6	28.3
Specialty Transportation | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Specialty Transportation | NSM
Segment reporting information
Total revenues from contracts with customers									85.5	77.6	28.3
Specialty Transportation | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Specialty Transportation | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
Specialty Transportation | Other Operations
Segment reporting information
Total revenues from contracts with customers									0	0	0
Real Estate
Segment reporting information
Total revenues from contracts with customers									44.9	34.7	17.8
Real Estate | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Real Estate | NSM
Segment reporting information
Total revenues from contracts with customers									44.9	34.7	17.8
Real Estate | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Real Estate | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
Real Estate | Other Operations
Segment reporting information
Total revenues from contracts with customers									0	0	0
Social Services
Segment reporting information
Total revenues from contracts with customers									28.9	25.9	14.7
Social Services | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Social Services | NSM
Segment reporting information
Total revenues from contracts with customers									28.9	25.9	14.7
Social Services | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Social Services | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
Social Services | Other Operations
Segment reporting information
Total revenues from contracts with customers									0	0	0
Pet
Segment reporting information
Total revenues from contracts with customers									55	30
Pet | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0
Pet | NSM
Segment reporting information
Total revenues from contracts with customers									55	30
Pet | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Pet | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0
Pet | Other Operations
Segment reporting information
Total revenues from contracts with customers									0	0
Other
Segment reporting information
Total revenues from contracts with customers									29.7	25.9	16.9
Other | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Other | NSM
Segment reporting information
Total revenues from contracts with customers									21.4	19	12.8
Other | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Other | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
Other | Other Operations
Segment reporting information
Total revenues from contracts with customers									8.3	6.9	4.1
Total Commission and Other Revenue
Segment reporting information
Total revenues from contracts with customers									293.4	240	105.7
Total Commission and Other Revenue | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
Total Commission and Other Revenue | NSM
Segment reporting information
Total revenues from contracts with customers									285.1	233.1	101.6
Total Commission and Other Revenue | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Total Commission and Other Revenue | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
Total Commission and Other Revenue | Other Operations
Segment reporting information
Total revenues from contracts with customers									8.3	6.9	4.1
Advertising revenues
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Advertising revenues | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers										0	0
Advertising revenues | NSM
Segment reporting information
Total revenues from contracts with customers										0	0
Advertising revenues | Kudu
Segment reporting information
Total revenues from contracts with customers										0
Advertising revenues | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										48.8	295.5
Advertising revenues | Other Operations
Segment reporting information
Total revenues from contracts with customers										0	0
Products
Segment reporting information
Total revenues from contracts with customers									14.5	5.5
Products | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0
Products | NSM
Segment reporting information
Total revenues from contracts with customers									0	0
Products | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
Products | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0
Products | Other Operations
Segment reporting information
Total revenues from contracts with customers									14.5	5.5
United Kingdom
Segment reporting information
Total revenues from contracts with customers									49.4	45.9	28
United Kingdom | HG Global-BAM
Segment reporting information
Total revenues from contracts with customers									0	0	0
United Kingdom | NSM
Segment reporting information
Total revenues from contracts with customers									49.4	45.9	28
United Kingdom | Kudu
Segment reporting information
Total revenues from contracts with customers									0	0
United Kingdom | MediaAlpha
Segment reporting information
Total revenues from contracts with customers										0	0
United Kingdom | Other Operations
Segment reporting information
Total revenues from contracts with customers									$ 0	$ 0	$ 0

Equity-Method Eligible Invest_3

Equity-Method Eligible Investments - Carrying Values of Investments (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
MediaAlpha
Schedule of Equity Method Investments [Line Items]
Investment in MediaAlpha, at fair value	$ 802.2	$ 180
Other unconsolidated investments
Schedule of Equity Method Investments [Line Items]
Investment in MediaAlpha, at fair value	$ 698.1	$ 581.7

Equity-Method Eligible Invest_4

Equity-Method Eligible Investments - Ownership Percentages (Details)	Dec. 31, 2020	May 07, 2020	May 06, 2020	Dec. 31, 2019	May 31, 2019	Feb. 26, 2019	Feb. 25, 2019
DavidShield & PassportCard
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	53.80%	53.80%	50.00%	50.00%
MediaAlpha
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	35.00%			48.30%
MediaAlpha | Minimum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)						48.30%
MediaAlpha | Maximum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)							61.00%
durchblicker
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	45.00%			45.00%
Elementum Holdings, L.P.
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	28.90%			30.00%	30.00%
Compare.com
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	18.40%			18.40%
JAM Partners L.P.
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)				11.10%
Enlightenment Capital Funds | Minimum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	9.70%			10.00%
Enlightenment Capital Funds | Maximum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	66.70%			38.40%
Tuckerman Capital Funds | Minimum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	14.90%			17.50%
Tuckerman Capital Funds | Maximum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	62.00%			62.40%
Kudu Investments | Minimum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	3.20%			3.20%
Kudu Investments | Maximum
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	35.00%			30.00%
New Market Solutions, LLC
Investments in and Advances to Affiliates [Line Items]
Ownership interest (as a percent)	46.70%

Equity-Method Eligible Invest_5

Equity-Method Eligible Investments - Balance Sheet and Income Statement Tables (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Investments in unconsolidated affiliates
Total assets	$ 4,831.4				$ 3,983.2				$ 4,831.4	$ 3,983.2
Total liabilities	1,013.5				838.5				1,013.5	838.5
Total revenues	520.8	$ 459.5	$ 259.6	$ (59.2)	175.3	$ 155.5	$ 129	$ 433.6	1,180.7	893.4	$ 369.1
MediaAlpha
Investments in unconsolidated affiliates
Total assets	212.7				105.4				212.7	105.4
Total liabilities	315.8				144.9				315.8	144.9
Total revenues									584.8	408	296.9
Total expenses									575.4	390.2	278.8
Net income (loss)									9.4	17.8	18.1
White Mountains
Investments in unconsolidated affiliates
Total assets	1,328.5				1,959.2				1,328.5	1,959.2
Total liabilities	$ 228.7				$ 653.2				228.7	653.2
Total revenues									526.5	344.6	226
Total expenses									325.9	88.3	141.4
Net income (loss)									$ 201.7	$ 255.1	$ 83.6

Equity-Method Eligible Invest_6

Equity-Method Eligible Investments - MediaAlpha Investment (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Subsidiary, Sale of Stock [Line Items]
Total assets	$ 4,831.4				$ 3,983.2				$ 4,831.4	$ 3,983.2
Total liabilities	1,013.5				838.5				1,013.5	838.5
Total revenues	520.8	$ 459.5	$ 259.6	$ (59.2)	175.3	$ 155.5	$ 129	$ 433.6	1,180.7	893.4	$ 369.1
MediaAlpha
Subsidiary, Sale of Stock [Line Items]
Total assets	212.7				105.4				212.7	105.4
Total liabilities	$ 315.8				$ 144.9				315.8	144.9
Total revenues									584.8	408	296.9
Total expenses									575.4	390.2	278.8
Net income (loss) attributable to White Mountains’s common shareholders									$ 9.4	17.8	18.1
MediaAlpha | Total Assets
Subsidiary, Sale of Stock [Line Items]
Out of period adjustments										(1.5)
MediaAlpha | Total Liabilities
Subsidiary, Sale of Stock [Line Items]
Out of period adjustments										0.3
MediaAlpha | Total Revenues
Subsidiary, Sale of Stock [Line Items]
Out of period adjustments										0.1	(0.2)
MediaAlpha | Total Operating Expenses
Subsidiary, Sale of Stock [Line Items]
Out of period adjustments										1.2	(9.4)
MediaAlpha | Total Net Income (Loss)
Subsidiary, Sale of Stock [Line Items]
Out of period adjustments										$ (1.1)	$ 9.2

Equity-Method Eligible Invest_7

Equity-Method Eligible Investments - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								10 Months Ended	12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Oct. 30, 2020	Feb. 26, 2019	Feb. 25, 2019
Schedule of Equity Method Investments [Line Items]
Net investment income										$ 131	$ 79.7	$ 59
Unrealized investment gain											180
Net realized and unrealized investment gains from MediaAlpha										716.8	433.2	(108.3)
Total revenues	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6		1,180.7	893.4	369.1
Other Operations
Schedule of Equity Method Investments [Line Items]
Net investment income										82	43.4	42.3
Net realized and unrealized investment gains from MediaAlpha												0
Total revenues										$ 781.4	523.7	(53.9)
MediaAlpha
Schedule of Equity Method Investments [Line Items]
Ownership interest (as a percent)													35.00%
Fully diluted ownership interest (as a percent)													32.30%
Investment owned (in shares)													20,532,202
Share price (in USD per share)	$ 39.07									$ 39.07
Investment owned, balance	$ 802.2									$ 802.2
MediaAlpha
Schedule of Equity Method Investments [Line Items]
Net investment income										$ 95	$ 14.8	3.7
Ownership interest (as a percent)	35.00%				48.30%				48.30%	35.00%	48.30%
Assets, fair value								114.7
Unrealized investment gain								$ 114.7
Net realized and unrealized investment gains from MediaAlpha										$ 686	$ 180	$ 0
Total revenues									$ 359.2
Total expenses									336.3
Net income									$ 22.9
MediaAlpha | Other Operations
Schedule of Equity Method Investments [Line Items]
Net realized and unrealized investment gains from MediaAlpha										$ 686	$ 180
MediaAlpha | Minimum
Schedule of Equity Method Investments [Line Items]
Ownership interest (as a percent)														48.30%
Fully diluted ownership interest (as a percent)														42.00%
MediaAlpha | Maximum
Schedule of Equity Method Investments [Line Items]
Ownership interest (as a percent)															61.00%
Fully diluted ownership interest (as a percent)															58.90%

Variable Interest Entities (Det

Variable Interest Entities (Details) $ in Millions	May 07, 2020USD ($)	Apr. 04, 2019USD ($)	Jan. 24, 2018USD ($)	Dec. 31, 2020USD ($)director	May 06, 2020	Dec. 31, 2019USD ($)	May 31, 2019USD ($)	Apr. 03, 2019	Feb. 05, 2018
Variable Interest Entity [Line Items]
Percentage of par value of policy reinsured				15.00%
Other investments				$ 786.8		$ 676.3
Payments to acquire business		$ 81.4
Goodwill				$ 525.5		$ 394.7
HG Global
Variable Interest Entity [Line Items]
Percentage of par value of policy reinsured				15.00%
BAM
Variable Interest Entity [Line Items]
Number directors to designate for election | director				2
First Loss Reinsurance Treaty | HG Global
Variable Interest Entity [Line Items]
Percentage of par value of policy reinsured				15.00%
First Loss Reinsurance Treaty | BAM
Variable Interest Entity [Line Items]
Percentage of premiums				60.00%
Elementum Holdings, L.P.
Variable Interest Entity [Line Items]
Ownership interest (as a percent)				28.90%		30.00%	30.00%
Other investments				$ 55.1			$ 55.1
Kudu
Variable Interest Entity [Line Items]
Ownership interest (as a percent)		99.10%						49.50%	49.50%
Payments to acquire business		$ 81.4
Assets acquired		155.5
Goodwill		7.6
Intangible assets acquired		2.2
Liabilities acquired		0.8
Noncontrolling interest acquired		$ 1.5
Fully diluted ownership interest (as a percent)		85.40%						42.70%	42.70%
DavidShield & PassportCard
Variable Interest Entity [Line Items]
Ownership interest (as a percent)	53.80%			53.80%	50.00%	50.00%
Other investments				$ 104.4
Payments to acquire businesses, gross			$ 41.8
Payments to acquire business			$ 28.3
Additional investment in acquisition	$ 15
Elementum Holdings, L.P.
Variable Interest Entity [Line Items]
Other investments				$ 55.1		$ 55.1

Fair Value of Financial Instr_3

Fair Value of Financial Instruments (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	$ 376.4	$ 283.5
NSM
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	272.6	219.2
NSM | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	277.4	221.3	$ 180.4
NSM | Fair value | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt, fair value	279.3	221.2
NSM | Fair value | Other NSM
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt, fair value	1.3	1.7
Kudu | Kudu Debt
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt, fair value	89.3	53.6
Debt	86.3	53.6
Other Operations | Other
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	17.5	10.7
Other Operations | Fair value
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt, fair value	18.8	11.3
Term Loan | NSM | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	271.3	217.4
Term Loan | NSM | Other NSM
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	1.3	1.8
Term Loan | NSM | Carrying Value | NSM Bank Facility
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	$ 271.3	217.4
Term Loan | Other Operations | Other
Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt		$ 10.7

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Loss Contingencies [Line Items]
Operating lease expense	$ 7.7	$ 7.2	$ 5.5
Finance Lease, Liability, Payment, Due [Abstract]
Due year one	7.7
Due year two	7.3
Due year three	7.1
Due after year three	23.1
Commitments to fund other-long term investments	297.8
Net loss (gain) from sale of discontinued operations, net of tax	2.3	(0.8)	17.2
Sirius Group
Finance Lease, Liability, Payment, Due [Abstract]
Net loss (gain) from sale of discontinued operations, net of tax			17.3
Sirius Group | Swedish Tax Authority
Finance Lease, Liability, Payment, Due [Abstract]
Loss contingency due to foreign currency translations	(2.3)	0.8	$ (17.3)
Sirius Group | Sirius Group | Swedish Tax Authority
Finance Lease, Liability, Payment, Due [Abstract]
Loss contingency accrual	18.7	$ 16.5
Loss contingency due to foreign currency translations	$ 2.2

Held for Sale and Discontinue_3

Held for Sale and Discontinued Operations (Details) - USD ($) $ in Millions	Aug. 20, 2020	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Discontinued Operations
Loss on sale of discontinued operations		$ (2.3)	$ 0.8	$ (17.2)
Corporate Aircraft
Discontinued Operations
Assets held for sale		1.7
Sirius Group
Discontinued Operations
Loss on sale of discontinued operations				(17.3)
Discontinued operations, liability			16.5
Connecticut | Held for Sale
Discontinued Operations
Proceeds from sale of property held-for-sale	$ 2.3
Realized gain losses on sales of other real estate		(0.1)
Assets held for sale		0.7	3
Swedish Tax Authority | Sirius Group
Discontinued Operations
Loss contingency due to foreign currency translations		(2.3)	0.8	$ (17.3)
Swedish Tax Authority | Sirius Group | Sirius Group
Discontinued Operations
Loss contingency accrual		18.7	$ 16.5
Loss contingency due to foreign currency translations		$ 2.2

Held for Sale and Discontinue_4

Held for Sale and Discontinued Operations - Earnings Per Share (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4	$ 708.7	$ 414.5	$ (141.2)
Net income (loss) from continuing operations attributable to White Mountains’s common shareholders									711	413.7	(124)
Total income (loss) from discontinued operations									2.3	(0.8)	17.2
Allocation of (earnings) losses to participating restricted common shares									(9.3)	(5.3)	1.4
Basic and diluted earnings (losses) per share numerators									$ 701.7	$ 408.4	$ (122.6)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Basic earnings (losses) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Diluted earnings (loss) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Basic (losses) earnings per share (in usd per share)	$ 157.70	$ 75.09	$ 37.14	$ (40.54)	$ 19.12	$ 15.29	$ 6.44	$ 89.64	$ 226.97	$ 130.27	$ (41.76)
Diluted (losses) earnings per share (in usd per share)	$ 157.70	$ 75.09	$ 37.14	$ (40.54)	$ 19.12	$ 15.29	$ 6.44	$ 89.64	$ 226.97	$ 130.27	$ (41.76)
Discontinued Operations
Basic and diluted earnings per share numerators (in millions):
Net income (loss) attributable to White Mountains’s common shareholders									$ 708.7	$ 414.5	$ (141.2)
Net income (loss) from continuing operations attributable to White Mountains’s common shareholders									711	413.7	(124)
Total income (loss) from discontinued operations									(2.3)	0.8	(17.2)
Allocation of (earnings) losses to participating restricted common shares									0	0	0.2
Basic and diluted earnings (losses) per share numerators									$ (2.3)	$ 0.8	$ (17)
Basic earnings per share denominators (in thousands):
Total average common shares outstanding during the period (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Basic earnings (losses) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Diluted earnings per share denominator (in thousands):
Total average common shares outstanding during the period (in shares)									3,122,200	3,181,600	3,382,500
Average unvested restricted common shares (in shares)									(40,800)	(40,500)	(40,100)
Diluted earnings (loss) per share denominator (in shares)									3,081,400	3,141,100	3,342,400
Basic (losses) earnings per share (in usd per share)									$ (0.75)	$ 0.25	$ (5.09)
Diluted (losses) earnings per share (in usd per share)									$ (0.75)	$ 0.25	$ (5.09)

Subsequent Event - Narrative (D

Subsequent Event - Narrative (Details) $ in Millions	Jan. 01, 2021USD ($)	Oct. 01, 2020USD ($)	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)
Other Operations
Subsequent Event [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction			$ 646.3	$ 0
Ark Insurance Holdings Limited
Subsequent Event [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction			366.3
Ark Insurance Holdings Limited | Lloyd
Subsequent Event [Line Items]
Cash pre-funded/placed in escrow for Ark Transaction			$ 280
Ark Insurance Holdings Limited
Subsequent Event [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
Ark Insurance Holdings Limited | Subsequent Event
Subsequent Event [Line Items]
Investment, potential additional contribution of equity capital	$ 200
Ownership interest after all transactions (as a percent)	72.00%
Ownership interest on fully-diluted basis (as a percent)	63.00%
Equity incentives, rate of return threshold	8.00%
Percent of shares outstanding	12.50%
Ark Insurance Holdings Limited | Subsequent Event | Tranche One
Subsequent Event [Line Items]
Invested capital return threshold, multiples	2
Ark Insurance Holdings Limited | Subsequent Event | Tranche Two
Subsequent Event [Line Items]
Invested capital return threshold, multiples	2.5
Ark Insurance Holdings Limited | Subsequent Event | Tranche Three
Subsequent Event [Line Items]
Invested capital return threshold, multiples	3
Ark Insurance Holdings Limited | Subsequent Event | Forecast
Subsequent Event [Line Items]
Ownership interest on fully-diluted basis (as a percent)	67.50%
Ownership interest after additional funding	77.10%

Selected Quarterly Financial _3

Selected Quarterly Financial Data (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Quarterly Financial Information Disclosure [Abstract]
Total revenues	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6	$ 1,180.7	$ 893.4	$ 369.1
Expenses	163.5	138.3	126.9	106.8	118.8	104.4	113.2	151.9	535.5	488.3	547.3
Pre-tax income (loss)	357.3	321.2	132.7	(166)	56.5	51.1	15.8	281.7	645.2	405.1	(178.2)
Tax (expense) benefit	117.6	(98.5)	(24.1)	25.5	(10.4)	(8.8)	0.1	(10.2)	20.5	(29.3)	4
Net income (loss) from continuing operations	474.9	222.7	108.6	(140.5)	46.1	42.3	15.9	271.5	665.7	375.8	(174.2)
Net income from discontinued operations, net of tax	(1.5)	(0.7)	(1)	0.9	(0.8)	0.9	0	0.7
Non-controlling interest in consolidated subsidiaries	15.8	10.9	7.8	10.8	15.6	5.5	4.6	12.2	45.3	37.9	50.2
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4	$ 708.7	$ 414.5	$ (141.2)
Basic earnings (loss) per share
Continuing operations (usd per share)	$ 158.19	$ 75.32	$ 37.46	$ (40.82)	$ 19.37	$ 15.01	$ 6.44	$ 89.42	$ 227.72	$ 130.02	$ (36.67)
Discontinued operations (usd per share)	(0.49)	(0.23)	(0.32)	0.28	(0.25)	0.28	0	0.22	(0.75)	0.25	(5.09)
Total consolidated operations (usd per share)	157.70	75.09	37.14	(40.54)	19.12	15.29	6.44	89.64	226.97	130.27	(41.76)
Diluted earnings (loss) per share
Continuing operations (usd per share)	158.19	75.32	37.46	(40.82)	19.37	15.01	6.44	89.42	227.72	130.02	(36.67)
Discontinued operations (usd per share)	(0.49)	(0.23)	(0.32)	0.28	(0.25)	0.28	0	0.22	(0.75)	0.25	(5.09)
Total consolidated operations (usd per share)	$ 157.70	$ 75.09	$ 37.14	$ (40.54)	$ 19.12	$ 15.29	$ 6.44	$ 89.64	$ 226.97	$ 130.27	$ (41.76)

SCHEDULE I SUMMARY OF INVESTM_2

SCHEDULE I SUMMARY OF INVESTMENTS-OTHER THAN INVESTMENTS IN RELATED PARTIES (Details) $ in Millions	Dec. 31, 2020USD ($)
Summary of investments other than investments in related parties
Cost	$ 2,062
Carrying Value	2,939.1
Fair Value	2,939.1
Fixed maturity investments
Summary of investments other than investments in related parties
Cost	1,151.7
Carrying Value	1,207.2
Fair Value	1,207.2
U.S. Government and agency obligations
Summary of investments other than investments in related parties
Cost	173.2
Carrying Value	176.3
Fair Value	176.3
Debt securities issued by corporations
Summary of investments other than investments in related parties
Cost	522.8
Carrying Value	547.4
Fair Value	547.4
Municipal obligations
Summary of investments other than investments in related parties
Cost	244
Carrying Value	265
Fair Value	265
Mortgage and asset-backed securities
Summary of investments other than investments in related parties
Cost	211.7
Carrying Value	218.5
Fair Value	218.5
Short-term investments
Summary of investments other than investments in related parties
Cost	142.9
Carrying Value	142.9
Fair Value	142.9
Other long-term investments
Summary of investments other than investments in related parties
Cost	767.4
Carrying Value	786.8
Fair Value	786.8
MediaAlpha
Summary of investments other than investments in related parties
Cost	0
Carrying Value	802.2
Fair Value	$ 802.2

SCHEDULE II CONDENSED FINANCI_2

SCHEDULE II CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT - Balance Sheet (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Assets
Total assets	$ 4,831.4	$ 3,983.2
Liabilities
Payable to subsidiary	4.8	6.6	$ 4
Total liabilities	1,013.5	838.5
Total White Mountains’s common shareholders’ equity	3,906	3,261.5
Non-controlling interests	(88.1)	(116.8)
Total liabilities and equity	4,831.4	3,983.2
White Mountains Insurance Group Ltd.
Assets
Cash	0.7	0.7
Fixed maturity investments, at fair value	10.1	10
Common equity securities, at fair value	0	193.5
Short-term investments, at amortized cost	24.3	66.2
Other assets	2.5	1.9
Investments in consolidated subsidiaries	3,726	2,969
Total assets	3,763.6	3,241.3
Liabilities
Payable to subsidiary	(195.6)	(69.3)
Other liabilities	39.7	34.7
Total liabilities	(155.9)	(34.6)
Total White Mountains’s common shareholders’ equity	3,906	3,261.5
Non-controlling interests	13.5	14.4
Total liabilities and equity	3,763.6	3,241.3
Sirius Group | Swedish Tax Authority | Sirius Group
Liabilities
Loss contingency accrual	$ 18.7	$ 16.5

SCHEDULE II CONDENSED FINANCI_3

SCHEDULE II CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT - Statement of Operations and Comprehensive Income (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Revenues (loss) (including realized and unrealized gains and losses)	$ 520.8	$ 459.5	$ 259.6	$ (59.2)	$ 175.3	$ 155.5	$ 129	$ 433.6	$ 1,180.7	$ 893.4	$ 369.1
Expenses	163.5	138.3	126.9	106.8	118.8	104.4	113.2	151.9	535.5	488.3	547.3
Pre-tax income (loss)	357.3	321.2	132.7	(166)	56.5	51.1	15.8	281.7	645.2	405.1	(178.2)
Income tax benefit (expense)	117.6	(98.5)	(24.1)	25.5	(10.4)	(8.8)	0.1	(10.2)	20.5	(29.3)	4
Net income (loss) from continuing operations	474.9	222.7	108.6	(140.5)	46.1	42.3	15.9	271.5	665.7	375.8	(174.2)
Net income from discontinued operations, net of tax	(1.5)	(0.7)	(1)	0.9	(0.8)	0.9	0	0.7
Net loss attributable to non-controlling interests	15.8	10.9	7.8	10.8	15.6	5.5	4.6	12.2	45.3	37.9	50.2
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4	708.7	414.5	(141.2)
Other comprehensive income (loss), net of tax									7.3	(1.4)	(4.8)
Comprehensive income (loss) attributable to White Mountains’s common shareholders									715.5	413.1	(145.7)
White Mountains Insurance Group Ltd.
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Revenues (loss) (including realized and unrealized gains and losses)									(8.7)	65	(47.7)
Expenses									61	47.1	45.9
Pre-tax income (loss)									(69.7)	17.9	(93.6)
Income tax benefit (expense)									0.3	0.9	2.5
Net income (loss) from continuing operations									(70)	17	(96.1)
Net income from discontinued operations, net of tax									(2.3)	0.8	(17.2)
Equity in earnings from consolidated and unconsolidated subsidiaries, net of tax									782	398.5	(27.4)
Net loss attributable to non-controlling interests									(1)	(1.8)	(0.5)
Net income (loss) attributable to White Mountains’s common shareholders									708.7	414.5	(141.2)
Other comprehensive income (loss), net of tax									6.8	(1.4)	(4.5)
Comprehensive income (loss) attributable to White Mountains’s common shareholders									715.5	413.1	(145.7)
Swedish Tax Authority | Sirius Group
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Loss contingency accrual, period increase (decrease)									(2.3)	$ 0.8	$ (17.3)
Swedish Tax Authority | Sirius Group | Sirius Group
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Loss contingency accrual, period increase (decrease)									$ 2.2

SCHEDULE II CONDENSED FINANCI_4

SCHEDULE II CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT - Statement of Cash Flows (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Net income (loss) attributable to White Mountains’s common shareholders	$ 489.2	$ 232.9	$ 115.4	$ (128.8)	$ 60.9	$ 48.7	$ 20.5	$ 284.4	$ 708.7	$ 414.5	$ (141.2)
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment (gains) losses									(716.8)	(433.2)	108.3
Net income from discontinued operations, net of tax	1.5	$ 0.7	$ 1	(0.9)	0.8	$ (0.9)	$ 0	(0.7)
Net change in other assets and liabilities, net									30.9	20.4	(38.8)
Net cash used for operations									(60.6)	(120.5)	(31.1)
Cash flows from investing activities:
Net decrease in short-term investments									58.7	21.9	(39)
Net cash provided from (used for) investing activities									64.6	(59.9)	459.2
Cash flows from financing activities:
Repurchases and retirement of common shares									(78.5)	0	(511.9)
Dividends paid on common shares									(3.2)	(3.2)	(3.8)
Net cash provided from (used for) financing activities									49	230.5	(414.3)
Net (decrease) increase in cash during the year									50.2	50.7	13.2
Cash balance at beginning of year				161				110.3	161	110.3	97.1
Cash balance at end of year	211.2				161				211.2	161	110.3
Amortization of restricted share awards									16.6	10.5	13
Payable to subsidiary	(4.8)				(6.6)				(4.8)	(6.6)	(4)
White Mountains Insurance Group Ltd.
CONDENSED FINANCIAL INFORMATION OF THE REGISTRANT
Net income (loss) attributable to White Mountains’s common shareholders									708.7	414.5	(141.2)
Adjustments to reconcile net income to net cash used for operations:
Net realized and unrealized investment (gains) losses									10.1	(61)	57.8
Undistributed earnings from subsidiaries									(782)	(398.5)	27.4
Net income from discontinued operations, net of tax									2.3	(0.8)	17.2
Other non-cash reconciling items, primarily amortization of restricted shares and option awards									19	20	34.6
Net change in other assets and liabilities, net									(2.6)	3	16.7
Net cash used for operations									(44.5)	(22.8)	12.5
Cash flows from investing activities:
Net decrease in short-term investments									(127.4)	(37.6)	134
Purchases of investment securities									(6.7)	(14.8)	(321.2)
Sales and maturities of investment securities									189.7	207.9	967.6
Issuance of debt (to) from subsidiaries									(44.5)	(83.5)	(55.2)
Repayment of debt to (from) subsidiaries									92.6	5	31
Net (contributions to) distributions from subsidiaries									29.1	(46.1)	(258.2)
Net cash provided from (used for) investing activities									132.8	30.9	498
Cash flows from financing activities:
Repurchases and retirement of common shares									(78.5)	0	(510.9)
Dividends paid on common shares									(3.2)	(3.2)	(3.8)
Payments of restricted shares withholding taxes									(6.6)	(4.9)	(10)
Net cash provided from (used for) financing activities									(88.3)	(8.1)	(524.7)
Net (decrease) increase in cash during the year									0	0	(14.2)
Cash balance at beginning of year				$ 0.7				$ 0.7	0.7	0.7	14.9
Cash balance at end of year	0.7				0.7				0.7	0.7	0.7
Payable to subsidiary	$ 195.6				$ 69.3				195.6	69.3
Bridge Holdings, Ltd. | White Mountains Insurance Group Ltd.
Cash flows from investing activities:
Net (contributions to) distributions from subsidiaries											255.3
Cash flows from financing activities:
Transfer to investments										70.5	(22.7)
White Mountains Investment, Ltd. | White Mountains Insurance Group Ltd.
Cash flows from investing activities:
Net (contributions to) distributions from subsidiaries											2.9
Cash flows from financing activities:
Transfer to investments										2
Transfer from investments									6.8	24.4
HG Global | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer from investments									22.3	1.9
Non-cash reconciling item | Guilford Holdings, Inc.
Cash flows from financing activities:
Transfer to investments									(169.6)		(349.5)
Noncash Total | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer to investments											603.9
Transfer from investments											1,065.4
Fixed maturity investments | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer to investments											170.5
Transfer from investments											373.4
Fixed maturity investments | Guilford Holdings, Inc.
Cash flows from financing activities:
Transfer from investments											170.4
Equity Securities | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer to investments											148.8
Transfer from investments											490.1
Other long-term investments | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer to investments											22.7
Transfer from investments											22.7
Short-term investments | White Mountains Insurance Group Ltd.
Cash flows from financing activities:
Transfer to investments									169.6		284.6
Transfer from investments											179.2
Short-term investments | Guilford Holdings, Inc.
Cash flows from financing activities:
Transfer from investments											179.2
Bridge Holdings, Ltd. | Guilford Holdings, Inc.
Cash flows from financing activities:
Transfer to investments											(350)
Bridge Holdings, Ltd. | White Mountains Investment, Ltd.
Cash flows from financing activities:
Transfer to investments											(1)
Swedish Tax Authority | Sirius Group
Cash flows from financing activities:
Loss contingency accrual, period increase (decrease)									(2.3)	$ 0.8	$ (17.3)
Swedish Tax Authority | Sirius Group | Sirius Group
Cash flows from financing activities:
Loss contingency accrual, period increase (decrease)									$ 2.2

SCHEDULE III SUPPLEMENTARY IN_2

SCHEDULE III SUPPLEMENTARY INSURANCE INFORMATION (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
SUPPLEMENTARY INSURANCE INFORMATION
Net investment income	$ 131	$ 79.7	$ 59
HG Global-BAM
SUPPLEMENTARY INSURANCE INFORMATION
Deferred Acqui- sition Costs	27.8	22.1	19
Future Policy Benefits, Losses, Claims and Loss Expenses	0	0	0
Unearned Premiums	237.5	198.4	176
Other Policy Claims and Benefits Payable	0	0	0
Premiums Earned	22.8	16.3	13.9
Net Investment Income	19.5	21.6	16.7
Benefits, Claims, Losses and Settlement Expenses	0	0	0
Amortization of Deferred Policy Acquisition Costs	7	5.7	5.3
Other Operating Expenses	0.4	0.4	0.4
Premiums Written	61.7	38.7	52.9
Net investment income	$ 19.5	$ 21.6	$ 16.7

SCHEDULE IV REINSURANCE (Detail

SCHEDULE IV REINSURANCE (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Premiums earned
Gross earned premiums	$ 22.8	$ 16.3	$ 13.9
HG Global/BAM
Premiums earned
Gross Amount	19.4	13.6	13.6
Ceded to Other Companies	0	0	0
Assumed from Other Companies	3.4	2.7	0.3
Gross earned premiums	$ 22.8	$ 16.3	$ 13.9
Percentage of Amount Assumed to Net	14.90%	16.60%	2.20%