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UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549
FORM 10-Q
☒ QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
For the period ended June 30, 2021
OR
☐ TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934
For the transition period from to
Commission file number 1-8993
WHITE MOUNTAINS INSURANCE GROUP, LTD.
(Exact name of Registrant as specified in its charter)

Bermuda |  |
(State or other jurisdiction of incorporation or organization) |  | 94-2708455
23 South Main Street, Suite 3B |  | (I.R.S. Employer Identification No.)
Hanover, |  | 03755-2053
New Hampshire |  | (Zip Code)
(Address of principal executive offices) |  |

Registrant’s telephone number, including area code: (603) 640-2200
Securities registered pursuant to Section 12(b) of the Act:

Title of each class |  | Trading Symbol(s) |  | Name of each exchange on which registered
Common Shares, par value $1.00 |  | WTM |  | New York Stock Exchange
per share |  |  |  | Bermuda Stock Exchange

Indicate by check mark whether the Registrant (1) has filed all reports required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the Registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days. Yes ý No ☐
Indicate by check mark whether the Registrant has submitted electronically every Interactive Data File required to be submitted pursuant to Rule 405 of Regulation S-T (§232.405 of this chapter) during the preceding 12 months (or for such shorter period that the Registrant was required to submit such files). Yes ý No ☐
Indicate by check mark whether the Registrant is a large accelerated filer, an accelerated filer, a non-accelerated filer, a smaller reporting company, or an emerging growth company. See the definitions of “large accelerated filer,” “accelerated filer”, “smaller reporting company” and “emerging growth company” in Rule 12b-2 of the Exchange Act.

Large accelerated filer | ý | Accelerated filer | ☐ | Non-accelerated filer | ☐
Smaller reporting company | ☐ | Emerging growth company | ☐ |

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. o
Indicate by check mark whether the Registrant is a shell company (as defined in Rule 12b-2 of the Exchange Act). Yes ☐ No ý
As of August 4, 2021, 3,106,130 common shares with a par value of $1.00 per share were outstanding (which includes 37,850 restricted common shares that were not vested at such date).

WHITE MOUNTAINS INSURANCE GROUP, LTD.
Table of Contents

|  | Page No.
PART I. | FINANCIAL INFORMATION |
Item 1. | Financial Statements (Unaudited) |
| Consolidated Balance Sheets, June 30, 2021 and December 31, 2020 | 1
| Consolidated Statements of Operations and Comprehensive Income, |
| Three and Six Months Ended June 30, 2021 and 2020 | 3
| Consolidated Statements of Changes in Equity, | 6
| Three and Six Months Ended June 30, 2021 and 2020 |
| Consolidated Statements of Cash Flows, Three and Six Months Ended June 30, 2021 and 2020 | 8
| Notes to Consolidated Financial Statements | 9
Item 2. | Management’s Discussion and Analysis of Financial Condition and Results of Operations | 53
| Results of Operations for the Three and Six Months Ended June 30, 2021 and 2020 | 53
| Liquidity and Capital Resources | 79
| Non-GAAP Financial Measures | 84
| Critical Accounting Estimates | 86
| Forward-Looking Statements | 90
Item 3. | Quantitative and Qualitative Disclosures About Market Risk | 90
Item 4. | Controls and Procedures | 91
PART II. | OTHER INFORMATION | 91
Items 1 through 6. | 91
SIGNATURES | 92

Part I.FINANCIAL INFORMATION.
Item 1.Financial Statements
WHITE MOUNTAINS INSURANCE GROUP, LTD.
CONSOLIDATED BALANCE SHEETS

|  | June 30, 2021 |  | December 31, 2020
Millions, except share and per share amounts |  |
Assets |  | Unaudited |  |
Financial Guarantee (HG Global/BAM) |  |  |  |
Fixed maturity investments, at fair value |  | $ | 884.6 |  |  | $ | 859.5 |
Short-term investments, at fair value |  | 44.9 |  |  | 60.4 |
Total investments |  | 929.5 |  |  | 919.9 |
Cash |  | 20.6 |  |  | 42.8 |
Insurance premiums receivable |  | 6.9 |  |  | 6.9 |
Deferred acquisition costs |  | 30.5 |  |  | 27.8 |
Accrued investment income |  | 5.0 |  |  | 5.0 |
Other assets |  | 14.0 |  |  | 15.4 |
Total Financial Guarantee assets |  | 1,006.5 |  |  | 1,017.8 |
P&C Insurance and Reinsurance (Ark) |  |  |  |
Fixed maturity investments, at fair value |  | 519.8 |  |  | — |
Common equity securities, at fair value |  | 142.0 |  |  | — |
Short-term investments, at fair value |  | 251.0 |  |  | — |
Other long-term investments |  | 257.5 |  |  | — |
Total investments |  | 1,170.3 |  |  | — |
Cash |  | 110.6 |  |  | — |
Reinsurance recoverables |  | 431.3 |  |  | — |
Insurance premiums receivable |  | 589.0 |  |  | — |
Ceded unearned premiums |  | 116.1 |  |  | — |
Deferred acquisition cost |  | 122.8 |  |  | — |
Value of in-force business acquired |  | 27.8 |  |  | — |
Goodwill and other intangible assets |  | 292.5 |  |  | — |
Other assets |  | 113.9 |  |  | — |
Total P&C Insurance and Reinsurance assets |  | 2,974.3 |  |  | — |
Specialty Insurance Distribution (NSM) |  |  |  |
Cash (restricted $90.3 and $78.4) |  | 154.6 |  |  | 126.5 |
Premiums and commissions receivable |  | 85.1 |  |  | 76.7 |
Goodwill and other intangible assets |  | 691.6 |  |  | 736.8 |
Other assets |  | 55.7 |  |  | 59.6 |
Total Specialty Insurance Distribution assets |  | 987.0 |  |  | 999.6 |
Asset Management (Kudu) |  |  |  |
Short-term investments, at fair value |  | .1 |  |  | .1 |
Other long-term investments |  | 455.5 |  |  | 400.6 |
Total investments |  | 455.6 |  |  | 400.7 |
Cash (restricted $4.0 and $0.0) |  | 13.5 |  |  | 7.8 |
Accrued investment income |  | 7.6 |  |  | 9.8 |
Goodwill and other intangible assets |  | 9.1 |  |  | 9.2 |
Other assets |  | 8.5 |  |  | 2.7 |
Total Asset Management assets |  | 494.3 |  |  | 430.2 |
Other Operations |  |  |  |
Fixed maturity investments, at fair value |  | 352.9 |  |  | 347.7 |
Short-term investments, at fair value |  | 236.5 |  |  | 82.4 |
Investment in MediaAlpha, at fair value |  | 713.2 |  |  | 802.2 |
Other long-term investments |  | 368.4 |  |  | 386.2 |
Total investments |  | 1,671.0 |  |  | 1,618.5 |
Cash |  | 27.4 |  |  | 34.1 |
Cash pre-funded/placed in escrow for Ark Transaction |  | — |  |  | 646.3 |
Accounts receivable on unsettled investment sales |  | 1.7 |  |  | 3.4 |
Goodwill and other intangible assets |  | 51.0 |  |  | 36.4 |
Other assets |  | 66.7 |  |  | 45.1 |
Total Other Operations assets |  | 1,817.8 |  |  | 2,383.8 |
Total assets |  | $ | 7,279.9 |  |  | $ | 4,831.4 |

See Notes to Consolidated Financial Statements
1

CONSOLIDATED BALANCE SHEETS (CONTINUED)

|  | June 30, 2021 |  | December 31, 2020
Millions, except share and per share amounts |  |
Liabilities |  | Unaudited |  |
Financial Guarantee (HG Global/BAM) |  |  |  |
Unearned insurance premiums |  | $ | 250.9 |  |  | $ | 237.5 |
Accrued incentive compensation |  | 16.1 |  |  | 25.7 |
Other liabilities |  | 28.5 |  |  | 28.3 |
Total Financial Guarantee liabilities |  | 295.5 |  |  | 291.5 |
P&C Insurance and Reinsurance (Ark) |  |  |  |
Loss and loss adjustment expense reserves |  | 760.0 |  |  | — |
Unearned insurance premiums |  | 718.7 |  |  | — |
Debt |  | 44.2 |  |  | — |
Reinsurance payable |  | 512.8 |  |  | — |
Contingent consideration |  | 22.5 |  |  | — |
Accounts payable on unsettled investment purchases |  | 1.9 |  |  | — |
Other liabilities |  | 73.0 |  |  | — |
Total P&C Insurance and Reinsurance liabilities |  | 2,133.1 |  |  | — |
Specialty Insurance Distribution (NSM) |  |  |  |
Debt |  | 270.7 |  |  | 272.6 |
Premiums payable |  | 137.9 |  |  | 113.4 |
Contingent consideration |  | 7.3 |  |  | 14.6 |
Other liabilities |  | 89.7 |  |  | 91.2 |
Total Specialty Insurance Distribution liabilities |  | 505.6 |  |  | 491.8 |
Asset Management (Kudu) |  |  |  |
Debt |  | 94.5 |  |  | 86.3 |
Other liabilities |  | 31.1 |  |  | 10.0 |
Total Asset Management liabilities |  | 125.6 |  |  | 96.3 |
Other Operations |  |  |  |
Debt |  | 19.4 |  |  | 17.5 |
Accrued incentive compensation |  | 50.1 |  |  | 70.1 |
Other liabilities |  | 42.6 |  |  | 46.3 |
Total Other Operations liabilities |  | 112.1 |  |  | 133.9 |
Total liabilities |  | 3,171.9 |  |  | 1,013.5 |
Equity |  |  |  |
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 3,109,182 and 3,102,011 shares and paid-in surplus |  | 3.1 |  |  | 3.1 |
Paid-in surplus |  | 594.1 |  | 592.1
Retained earnings |  | 3,378.6 |  |  | 3,311.2 |
Accumulated other comprehensive gain (loss), after-tax: |  |  |  |
Net unrealized foreign currency translation and interest rate swap gains (losses) |  | 2.4 |  |  | (.4) |
Total White Mountains’s common shareholders’ equity |  | 3,978.2 |  |  | 3,906.0 |
Non-controlling interests |  | 129.8 |  |  | (88.1) |
Total equity |  | 4,108.0 |  |  | 3,817.9 |
Total liabilities and equity |  | $ | 7,279.9 |  |  | $ | 4,831.4 |

See Notes to Consolidated Financial Statements
2

WHITE MOUNTAINS INSURANCE GROUP, LTD.
CONSOLIDATED STATEMENTS OF OPERATIONS
(Unaudited)

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Revenues: |  |  |  |  |  |  |  |
Financial Guarantee (HG Global/BAM) |  |  |  |  |  |  |  |
Earned insurance premiums |  | $ | 6.5 |  |  | $ | 5.6 |  |  | $ | 12.9 |  |  | $ | 11.0 |
Net investment income |  | 4.3 |  |  | 4.9 |  |  | 8.8 |  |  | 10.4 |
Net realized and unrealized investment gains (losses) |  | 6.3 |  |  | 14.4 |  |  | (11.6) |  |  | 20.5 |
Other revenues |  | .3 |  |  | 1.2 |  |  | .6 |  |  | 1.7 |
Total Financial Guarantee revenues |  | 17.4 |  |  | 26.1 |  |  | 10.7 |  |  | 43.6 |
P&C Insurance and Reinsurance (Ark) |  |  |  |  |  |  |  |
Earned insurance premiums |  | 117.8 |  |  | — |  |  | 222.4 |  |  | — |
Net investment income |  | .4 |  |  | — |  |  | 1.2 |  |  | — |
Net realized and unrealized investment gains |  | 8.9 |  |  | — |  |  | 10.0 |  |  | — |
Other revenues |  | 3.4 |  |  | — |  |  | 6.0 |  |  | — |
Total P&C Insurance and Reinsurance revenues |  | 130.5 |  |  | — |  |  | 239.6 |  |  | — |
Specialty Insurance Distribution (NSM) |  |  |  |  |  |  |  |
Commission revenues |  | 68.0 |  |  | 63.0 |  |  | 127.6 |  |  | 116.0 |
Other revenues |  | 16.3 |  |  | 13.1 |  |  | 31.5 |  |  | 25.1 |
Total Specialty Insurance Distribution revenues |  | 84.3 |  |  | 76.1 |  |  | 159.1 |  |  | 141.1 |
Asset Management (Kudu) |  |  |  |  |  |  |  |
Net investment income |  | 8.4 |  |  | 5.6 |  |  | 16.6 |  |  | 12.9 |
Net realized and unrealized investment gains (losses) |  | 27.8 |  |  | 16.5 |  |  | 43.6 |  |  | (8.3) |
Other revenues |  | — |  |  | — |  |  | .1 |  |  | .1 |
Total Asset Management revenues |  | 36.2 |  |  | 22.1 |  |  | 60.3 |  |  | 4.7 |
Other Operations |  |  |  |  |  |  |  |
Net investment income |  | 4.0 |  |  | 9.1 |  |  | 11.1 |  |  | 19.2 |
Net realized and unrealized investment gains (losses) |  | 16.6 |  |  | 107.0 |  |  | 18.7 |  |  | (61.0) |
Net realized and unrealized investment gains from investment in MediaAlpha |  | 113.0 |  |  | 15.0 |  |  | 71.3 |  |  | 45.0 |
Commission revenues |  | 2.3 |  |  | 1.9 |  |  | 4.6 |  |  | 4.0 |
Other revenues |  | 22.4 |  |  | 2.3 |  |  | 29.5 |  |  | 3.8 |
Total Other Operations revenues |  | 158.3 |  |  | 135.3 |  |  | 135.2 |  |  | 11.0 |
Total revenues |  | $ | 426.7 |  |  | $ | 259.6 |  |  | $ | 604.9 |  |  | $ | 200.4 |

3

CONSOLIDATED STATEMENTS OF OPERATIONS (CONTINUED)
(Unaudited)

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Expenses: |  |  |  |  |  |  |  |
Financial Guarantee (HG Global/BAM) |  |  |  |  |  |  |  |
Insurance acquisition expenses |  | $ | 1.6 |  |  | $ | 2.1 |  |  | $ | 3.5 |  |  | $ | 3.8 |
General and administrative expenses |  | 13.9 |  |  | 12.7 |  |  | 30.3 |  |  | 27.4 |
Total Financial Guarantee expenses |  | 15.5 |  |  | 14.8 |  |  | 33.8 |  |  | 31.2 |
P&C Insurance and Reinsurance (Ark) |  |  |  |  |  |  |  |
Loss and loss adjustment expenses |  | 52.6 |  |  | — |  |  | 118.6 |  |  | — |
Insurance and reinsurance acquisition expenses |  | 34.0 |  |  | — |  |  | 70.7 |  |  | — |
Other underwriting expenses |  | 19.1 |  |  | — |  |  | 30.3 |  |  | — |
General and administrative expenses |  | 5.7 |  |  | — |  |  | 32.3 |  |  | — |
Interest expense |  | 1.3 |  |  | — |  |  | 2.4 |  |  | — |
Total P&C Insurance and Reinsurance expenses |  | 112.7 |  |  | — |  |  | 254.3 |  |  | — |
Specialty Insurance Distribution (NSM) |  |  |  |  |  |  |  |
General and administrative expenses |  | 47.3 |  |  | 48.5 |  |  | 93.3 |  |  | 88.1 |
Broker commission expenses |  | 21.6 |  |  | 21.0 |  |  | 40.5 |  |  | 39.3 |
Change in fair value of contingent consideration |  | .2 |  |  | (1.7) |  |  | .2 |  |  | (2.3) |
Amortization of other intangible assets |  | 8.2 |  |  | 6.3 |  |  | 16.8 |  |  | 11.1 |
Loss on assets held for sale |  | — |  |  | — |  |  | 28.7 |  |  | — |
Interest expense |  | 5.9 |  |  | 5.7 |  |  | 11.8 |  |  | 10.0 |
Total Specialty Insurance Distribution expenses |  | 83.2 |  |  | 79.8 |  |  | 191.3 |  |  | 146.2 |
Asset Management (Kudu) |  |  |  |  |  |  |  |
General and administrative expenses |  | 3.2 |  |  | 2.8 |  |  | 5.7 |  |  | 5.3 |
Amortization of other intangible assets |  | .1 |  |  | .1 |  |  | .2 |  |  | .2 |
Interest expense |  | 1.5 |  |  | 1.5 |  |  | 7.3 |  |  | 2.9 |
Total Asset Management expenses |  | 4.8 |  |  | 4.4 |  |  | 13.2 |  |  | 8.4 |
Other Operations |  |  |  |  |  |  |  |
Cost of sales |  | 17.9 |  |  | 2.2 |  |  | 21.9 |  |  | 4.2 |
General and administrative expenses |  | 29.5 |  |  | 25.3 |  |  | 65.2 |  |  | 42.8 |
Amortization of other intangible assets |  | .4 |  |  | .2 |  |  | .9 |  |  | .4 |
Interest expense |  | .4 |  |  | .2 |  |  | .7 |  |  | .5 |
Total Other Operations expenses |  | 48.2 |  |  | 27.9 |  |  | 88.7 |  |  | 47.9 |
Total expenses |  | 264.4 |  |  | 126.9 |  |  | 581.3 |  |  | 233.7 |
Pre-tax income (loss) from continuing operations |  | 162.3 |  |  | 132.7 |  |  | 23.6 |  |  | (33.3) |
Income tax (expense) benefit |  | (29.8) |  |  | (24.1) |  |  | (20.3) |  |  | 1.4 |
Net income (loss) from continuing operations |  | 132.5 |  |  | 108.6 |  |  | 3.3 |  |  | (31.9) |
Net (loss) gain from sale of discontinued operations, net of tax |  | — |  |  | (1.0) |  |  | 18.7 |  |  | (.1) |
Net income (loss) |  | 132.5 |  |  | 107.6 |  |  | 22.0 |  |  | (32.0) |
Net loss attributable to non-controlling interests |  | 6.0 |  |  | 7.8 |  |  | 41.2 |  |  | 18.6 |
Net income (loss) attributable to White Mountains’s common shareholders |  | $ | 138.5 |  |  | $ | 115.4 |  |  | $ | 63.2 |  |  | $ | (13.4) |

See Notes to Consolidated Financial Statements
4

WHITE MOUNTAINS INSURANCE GROUP, LTD.
CONSOLIDATED STATEMENTS OF COMPREHENSIVE INCOME
(Unaudited)

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Net income (loss) attributable to White Mountains’s common shareholders |  | $ | 138.5 |  |  | $ | 115.4 |  |  | $ | 63.2 |  |  | $ | (13.4) |
Other comprehensive income (loss), net of tax |  | 1.0 |  |  | .5 |  |  | 2.8 |  |  | (2.9) |
Comprehensive income (loss) |  | 139.5 |  |  | 115.9 |  |  | 66.0 |  |  | (16.3) |
Other comprehensive income attributable to non-controlling interests |  | (.1) |  |  | (.2) |  |  | (.2) |  |  | (.2) |
Comprehensive income (loss) attributable to White Mountains’s common shareholders |  | $ | 139.4 |  |  | $ | 115.7 |  |  | $ | 65.8 |  |  | $ | (16.5) |

Earnings (loss) per share attributable to White Mountains’s common shareholders: |  |  |  |
Basic (loss) earnings per share |  |  |  |  |  |  |  |
Continuing operations |  | $ | 44.56 |  |  | $ | 37.46 |  |  | $ | 14.32 |  |  | $ | (4.25) |
Discontinued operations |  | — |  |  | (.32) |  |  | 6.03 |  |  | (.03) |
Total consolidated operations |  | $ | 44.56 |  |  | $ | 37.14 |  |  | $ | 20.35 |  |  | $ | (4.28) |
Diluted (loss) earnings per share |  |  |  |  |  |  |  |
Continuing operations |  | $ | 44.56 |  |  | $ | 37.46 |  |  | $ | 14.32 |  |  | $ | (4.25) |
Discontinued operations |  | — |  |  | (.32) |  |  | 6.03 |  |  | (.03) |
Total consolidated operations |  | $ | 44.56 |  |  | $ | 37.14 |  |  | $ | 20.35 |  |  | $ | (4.28) |
Dividends declared and paid per White Mountains’s common share |  | $ | — |  |  | $ | — |  |  | $ | 1.00 |  |  | $ | 1.00 |

See Notes to Consolidated Financial Statements.
5

WHITE MOUNTAINS INSURANCE GROUP, LTD.
CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY
(Unaudited)

|  | White Mountains’s Common Shareholders’ Equity |  |  |  |
Millions |  | Common shares and paid-in surplus |  | Retained earnings |  | AOCI, after tax |  | Total |  | Non-controlling interest |  | Total Equity
Balance at March 31, 2021 |  | $ | 597.9 |  |  | $ | 3,226.7 |  |  | $ | 1.3 |  |  | $ | 3,825.9 |  |  | $ | 110.0 |  |  | $ | 3,935.9 |
Net income (loss) |  | — |  |  | 138.5 |  |  | — |  |  | 138.5 |  |  | (6.0) |  |  | 132.5 |
Net change in foreign currency translation and other |  | — |  |  | — |  |  | .9 |  |  | .9 |  |  | .1 |  |  | 1.0 |
Total comprehensive income (loss) |  | — |  |  | 138.5 |  |  | .9 |  |  | 139.4 |  |  | (5.9) |  |  | 133.5 |
Dividends to non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | (.6) |  |  | (.6) |
Issuances of common shares |  | 1.7 |  |  | — |  |  | — |  |  | 1.7 |  |  | — |  |  | 1.7 |
Issuances of shares of non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | 6.1 |  |  | 6.1 |
BAM member surplus contribution, net of tax |  | — |  |  | — |  |  | — |  |  | — |  |  | 16.3 |  |  | 16.3 |
Amortization of restricted share awards |  | 3.5 |  |  | — |  |  | — |  |  | 3.5 |  |  | — |  |  | 3.5 |
Recognition of equity-based compensation expense of subsidiaries |  | 1.3 |  |  | — |  |  | — |  |  | 1.3 |  |  | .3 |  |  | 1.6 |
Net contributions and dilution from other non-controlling interests |  | (7.2) |  |  | 13.4 |  |  | .2 |  |  | 6.4 |  |  | (6.5) |  |  | (.1) |
Acquisition of non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | 10.1 |  |  | 10.1 |
Balance at June 30, 2021 |  | $ | 597.2 |  |  | $ | 3,378.6 |  |  | $ | 2.4 |  |  | $ | 3,978.2 |  |  | $ | 129.8 |  |  | $ | 4,108.0 |

|  | White Mountains’s Common Shareholders’ Equity |  |  |  |
Millions |  | Common shares and paid-in surplus |  | Retained earnings |  | AOCI, after tax |  | Total |  | Non-controlling interest |  | Total Equity
Balance at March 31, 2020 |  | $ | 589.3 |  |  | $ | 2,498.0 |  |  | $ | (10.6) |  |  | $ | 3,076.7 |  |  | $ | (117.6) |  |  | $ | 2,959.1 |
Net income (loss) |  | — |  |  | 115.4 |  |  | — |  |  | 115.4 |  |  | (7.8) |  |  | 107.6 |
Net change in foreign currency translation and other |  | — |  |  | — |  |  | .3 |  |  | .3 |  |  | .1 |  |  | .4 |
Total comprehensive income (loss) |  | — |  |  | 115.4 |  |  | .3 |  |  | 115.7 |  |  | (7.7) |  |  | 108.0 |
Dividends to non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | (.9) |  |  | (.9) |
Issuances of common shares |  | 1.3 |  |  | — |  |  | — |  |  | 1.3 |  |  | — |  |  | 1.3 |
Repurchases and retirements of common shares |  | (6.5) |  |  | (24.1) |  |  | — |  |  | (30.6) |  |  | — |  |  | (30.6) |
BAM member surplus contributions, net of tax |  | — |  |  | — |  |  | — |  |  | — |  |  | 21.5 |  |  | 21.5 |
Amortization of restricted share awards |  | 3.6 |  |  | — |  |  | — |  |  | 3.6 |  |  | — |  |  | 3.6 |
Net contributions and dilution from other non-controlling interests |  | (.7) |  |  | — |  |  | — |  |  | (.7) |  |  | 2.0 |  |  | 1.3 |
Balance at June 30, 2020 |  | $ | 587.0 |  |  | $ | 2,589.3 |  |  | $ | (10.3) |  |  | $ | 3,166.0 |  |  | $ | (102.7) |  |  | $ | 3,063.3 |

See Notes to Consolidated Financial Statements.
6

CONSOLIDATED STATEMENTS OF CHANGES IN EQUITY (CONTINUED)
(Unaudited)

|  | White Mountains’s Common Shareholders’ Equity |  |  |  |
Millions |  | Common shares and paid-in surplus |  | Retained earnings |  | AOCI, after tax |  | Total |  | Non-controlling interest |  | Total Equity
Balance at January 1, 2021 |  | $ | 595.2 |  |  | $ | 3,311.2 |  |  | $ | (.4) |  |  | $ | 3,906.0 |  |  | $ | (88.1) |  |  | $ | 3,817.9 |
Net income (loss) |  | — |  |  | 63.2 |  |  | — |  |  | 63.2 |  |  | (41.2) |  |  | 22.0 |
Net change in foreign currency translation and other |  | — |  |  | — |  |  | 2.6 |  |  | 2.6 |  |  | .2 |  |  | 2.8 |
Total comprehensive income (loss) |  | — |  |  | 63.2 |  |  | 2.6 |  |  | 65.8 |  |  | (41.0) |  |  | 24.8 |
Dividends declared on common shares |  | — |  |  | (3.1) |  |  | — |  |  | (3.1) |  |  | — |  |  | (3.1) |
Dividends to non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | (1.2) |  |  | (1.2) |
Issuances of common shares |  | 1.7 |  |  | — |  |  | — |  |  | 1.7 |  |  | — |  |  | 1.7 |
Issuance of shares of non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | 6.1 |  |  | 6.1 |
Repurchases and retirements of common shares |  | (1.4) |  |  | (6.1) |  |  | — |  |  | (7.5) |  |  | — |  |  | (7.5) |
BAM member surplus contributions, net of tax |  | — |  |  | — |  |  | — |  |  | — |  |  | 30.1 |  |  | 30.1 |
Amortization of restricted share awards |  | 7.5 |  |  | — |  |  | — |  |  | 7.5 |  |  | — |  |  | 7.5 |
Recognition of equity-based compensation expense of subsidiaries |  | 1.8 |  |  | — |  |  | — |  |  | 1.8 |  |  | .3 |  |  | 2.1 |
Net contributions and dilution from other non-controlling interests |  | (7.6) |  |  | 13.4 |  |  | .2 |  |  | 6.0 |  |  | (6.7) |  |  | (.7) |
Acquisition of non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | 230.3 |  |  | 230.3 |
Balance at June 30, 2021 |  | $ | 597.2 |  |  | $ | 3,378.6 |  |  | $ | 2.4 |  |  | $ | 3,978.2 |  |  | $ | 129.8 |  |  | $ | 4,108.0 |

|  | White Mountains’s Common Shareholders’ Equity |  |  |  |
Millions |  | Common shares and paid-in surplus |  | Retained earnings |  | AOCI, after tax |  | Total |  | Non-controlling interest |  | Total Equity
Balance at January 1, 2020 |  | $ | 596.3 |  |  | $ | 2,672.4 |  |  | $ | (7.2) |  |  | $ | 3,261.5 |  |  | $ | (116.8) |  |  | $ | 3,144.7 |
Net loss |  | — |  |  | (13.4) |  |  | — |  |  | (13.4) |  |  | (18.6) |  |  | (32.0) |
Net change in foreign currency translation and other |  | — |  |  | — |  |  | (3.1) |  |  | (3.1) |  |  | .1 |  |  | (3.0) |
Total comprehensive loss |  | — |  |  | (13.4) |  |  | (3.1) |  |  | (16.5) |  |  | (18.5) |  |  | (35.0) |
Dividends declared on common shares |  | — |  |  | (3.2) |  |  | — |  |  | (3.2) |  |  | — |  |  | (3.2) |
Dividends to non-controlling interests |  | — |  |  | — |  |  | — |  |  | — |  |  | (1.4) |  |  | (1.4) |
Issuances of common shares |  | 1.3 |  |  | — |  |  | — |  |  | 1.3 |  |  | — |  |  | 1.3 |
Repurchases and retirements of common shares |  | (18.6) |  |  | (66.5) |  |  | — |  |  | (85.1) |  |  | — |  |  | (85.1) |
BAM member surplus contributions, net of tax |  | — |  |  | — |  |  | — |  |  | — |  |  | 31.5 |  |  | 31.5 |
Amortization of restricted share awards |  | 8.7 |  |  | — |  |  | — |  |  | 8.7 |  |  | — |  |  | 8.7 |
Net contributions and dilution from other non-controlling interests |  | (.7) |  |  | — |  |  | — |  |  | (.7) |  |  | 2.5 |  |  | 1.8 |
Balance at June 30, 2020 |  | $ | 587.0 |  |  | $ | 2,589.3 |  |  | $ | (10.3) |  |  | $ | 3,166.0 |  |  | $ | (102.7) |  |  | $ | 3,063.3 |

See Notes to Consolidated Financial Statements.
7

WHITE MOUNTAINS INSURANCE GROUP, LTD.
CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited)

|  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020
Cash flows from operations: |  |  |  |
Net income (loss) |  | $ | 22.0 |  |  | $ | (32.0) |
Adjustments to reconcile net income to net cash used for operations: |  |  |  |
Net realized and unrealized investment (gains) losses |  | (60.7) |  |  | 48.8 |
Net realized and unrealized investment gains from investment in MediaAlpha |  | (71.3) |  |  | (45.0) |
Deferred income tax expense (benefits) |  | 21.9 |  |  | (2.7) |
Net (gain) loss from sale of discontinued operations, net of tax |  | (18.7) |  |  | .1 |
Amortization of restricted share and option awards |  | 7.5 |  |  | 8.7 |
Amortization and depreciation |  | 28.0 |  |  | 17.4 |
Other operating items: |  |  |  |
Net change in reinsurance recoverables |  | 2.0 |  |  | — |
Net change in insurance premiums receivable |  | (352.3) |  |  | — |
Net change in commissions receivable |  | (8.4) |  |  | (3.0) |
Net change in ceded unearned premiums |  | 54.1 |  |  | — |
Net change in loss and loss adjustment expense reserves |  | 64.0 |  |  | — |
Net change in premiums payable |  | 24.5 |  |  | 28.1 |
Net change in unearned insurance premiums |  | 406.0 |  |  | 20.2 |
Net change in deferred acquisition costs |  | (81.5) |  |  | (2.9) |
Net change in reinsurance payable |  | (15.5) |  |  | — |
Net change in restricted cash |  | 15.9 |  |  | 40.0 |
Investments in Kudu Participation Contracts |  | (11.3) |  |  | (57.4) |
Net change in other assets and liabilities, net |  | (12.3) |  |  | (59.2) |
Net cash provided from (used for) operations |  | 13.9 |  |  | (38.9) |
Cash flows from investing activities: |  |  |  |
Net change in short-term investments |  | (9.9) |  |  | 84.0 |
Sales of fixed maturity and convertible investments |  | 127.2 |  |  | 244.2 |
Maturities, calls and paydowns of fixed maturity and convertible investments |  | 86.4 |  |  | 93.7 |
Sales of common equity securities |  | 176.8 |  |  | 108.0 |
Distributions and redemptions of other long-term investments and settlements of forward contracts |  | 58.1 |  |  | 64.1 |
Release of cash pre-funded/placed in escrow for Ark Transaction |  | 646.3 |  |  | — |
Purchases of consolidated subsidiaries, net of cash acquired of $52.2 and $11.9 |  | 10.6 |  |  | (120.3) |
Purchases of other long-term investments |  | (130.2) |  |  | (42.3) |
Purchases of common equity securities |  | (103.7) |  |  | (33.7) |
Purchases of fixed maturity and convertible investments |  | (764.3) |  |  | (293.4) |
Other investing activities, net |  | (7.0) |  |  | (15.3) |
Net cash provided from investing activities |  | 90.3 |  |  | 89.0 |
Cash flows from financing activities: |  |  |  |
Draw down of debt and revolving line of credit |  | 105.3 |  |  | 69.4 |
Repayment of debt and revolving line of credit |  | (95.6) |  |  | (1.1) |
Cash dividends paid to the Company’s common shareholders |  | (3.2) |  |  | (3.2) |
Common shares repurchased |  | — |  |  | (78.5) |
Distribution to non-controlling interest shareholders |  | (1.2) |  |  | (1.2) |
Contingent consideration payments related to acquisitions of subsidiaries |  | (7.5) |  |  | (6.4) |
Acquisition of subsidiary shares from non-controlling interest shareholders |  | (.4) |  |  | — |
Capital contributions to non-controlling interest shareholders |  | — |  |  | 2.2 |
Capital contributions from BAM members |  | 30.1 |  |  | 31.5 |
Acquisition of subsidiary shares by non-controlling interest shareholders |  | 6.1 |  |  | — |
Fidus Re premium payment |  | (5.0) |  |  | (1.6) |
Other financing activities, net |  | (16.9) |  |  | (9.8) |
Net cash provided from financing activities |  | 11.7 |  |  | 1.3 |
Effect of exchange rate changes on cash |  | (.4) |  |  | (1.1) |
Net change in cash during the period - continuing operations, including the effect of exchange rate changes |  | 115.5 |  |  | 50.3 |
Cash balances at beginning of period (includes restricted cash balances of $78.4 and $56.3) |  | 211.2 |  |  | 161.0 |
Cash balances at end of period (includes restricted cash balances of $94.3 and $96.3) |  | $ | 326.7 |  |  | $ | 211.3 |
Supplemental cash flows information: |  |  |  |
Interest paid |  | $ | (14.5) |  |  | $ | (6.7) |
Net income tax payments |  | $ | (2.1) |  |  | $ | — |

See Notes to Consolidated Financial Statements
8

NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (Unaudited)
Note 1. Basis of Presentation and Significant Accounting Policies
Basis of Presentation
The Company is an exempted Bermuda limited liability company whose principal businesses are conducted through its subsidiaries and other affiliates. The Company’s headquarters is located at 26 Reid Street, Hamilton, Bermuda HM 11, its principal executive office is located at 23 South Main Street, Suite 3B, Hanover, New Hampshire 03755-2053 and its registered office is located at Clarendon House, 2 Church Street, Hamilton, Bermuda HM 11. The Company’s website is located at www.whitemountains.com. The information contained on White Mountains’s website is not incorporated by reference into, and is not a part of, this report.
The accompanying consolidated financial statements have been prepared in accordance with generally accepted accounting principles in the United States (“GAAP”) and include the accounts of White Mountains Insurance Group, Ltd. (the “Company” or the “Registrant”), its subsidiaries (collectively with the Company, “White Mountains”) and other entities required to be consolidated under GAAP.
Consolidation Principles
Under GAAP, the Company is required to consolidate any entity in which it holds a controlling financial interest. A controlling financial interest is usually in the form of an investment representing the majority of the subsidiary’s voting interests. However, a controlling financial interest may also arise from a financial interest in a variable interest entity (“VIE”) through arrangements that do not involve ownership of voting interests. The Company consolidates a VIE if it determines that it is the primary beneficiary. The primary beneficiary is defined as the entity who holds a variable interest that gives it both the power to direct the VIE’s activities that most significantly impact its economic performance and the obligation to absorb losses of, or the right to receive returns from, the VIE that could potentially be significant to the VIE.
Intercompany transactions have been eliminated in consolidation. These interim financial statements include all adjustments considered necessary by management to fairly state the financial position, results of operations and cash flows of White Mountains. These interim financial statements may not be indicative of financial results for the full year and should be read in conjunction with the Company’s 2020 Annual Report on Form 10-K.
Business Combinations
White Mountains accounts for purchases of businesses using the acquisition method, which requires the measurement of assets acquired, including goodwill and other intangible assets, and liabilities assumed, including contingent liabilities, at their estimated fair values as of the acquisition date. The acquisition date fair values represent management’s best estimates and are based upon established valuation techniques, reasonable assumptions and, where appropriate, valuations performed by independent third parties. In circumstances where additional information is required in order to determine the acquisition date fair value of balance sheet amounts, provisional amounts may be recorded as of the acquisition date and may be subject to subsequent adjustment throughout the measurement period, which is up to one year from the acquisition date. Measurement period adjustments are recognized in the period in which they are determined. The results of operations and cash flows of businesses acquired are included in the consolidated financial statements from the date of acquisition. White Mountains accounts for purchases of other intangible assets that do not meet the definition of a business as asset acquisitions. Asset acquisitions are recognized at the amount of consideration paid, which is deemed to equal fair value.
Use of Estimates
The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities as of the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ from those estimates.
Fair Value Measurement s
Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (“observable inputs”) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (“unobservable inputs”). Quoted prices in active markets for identical assets or liabilities have the highest priority (“Level 1”), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (“Level 2”) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (“Level 3”).
9

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 June 30, 2021, White Mountains’s reportable segments were HG Global/BAM, Ark, NSM, Kudu and Other Operations.
The HG Global/BAM segment consists of HG Global Ltd. and its wholly-owned subsidiaries (“HG Global”) and the consolidated results of Build America Mutual Assurance Company (“BAM”) (collectively, “HG Global/BAM”). BAM is the first and only mutual municipal bond insurance company in the United States. By insuring the timely payment of principal and interest, BAM provides market access to, and lowers interest expense for, issuers of municipal bonds used to finance essential public purposes such as schools, utilities and transportation facilities. BAM is owned by and operated for the benefit of its members, the municipalities that purchase BAM’s insurance for their debt issuances. HG Global was established to fund the startup of BAM and, through its wholly-owned subsidiary, HG Re Ltd. (“HG Re”), to provide up to 15%-of-par, first loss reinsurance protection for policies underwritten by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. HG Global, together with its subsidiaries, funded the initial capitalization of BAM through the purchase of $503.0 million of surplus notes issued by BAM, consisting of $203.0 million of Series A Notes and $300.0 million of Series B Notes (the “BAM Surplus Notes”). As of June 30, 2021 and December 31, 2020, White Mountains owned 96.9% of HG Global’s preferred equity and 88.4% of its common equity. White Mountains does not have an ownership interest in BAM. However, White Mountains is required to consolidate BAM’s results in its financial statements because BAM is a VIE for which White Mountains is the primary beneficiary. BAM’s results are attributed to non-controlling interests.
The Ark segment consists of Ark Insurance Holdings Limited and its subsidiaries (collectively, “Ark”). Ark writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”). Beginning in January 2021, Ark began writing certain classes of its business through Group Ark Insurance Limited (“GAIL”), Ark’s wholly-owned Class 4 Bermuda-based insurance and reinsurance company.
As of June 30, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% on a fully-diluted, fully-converted basis, taking account of management’s equity incentives). If the additional $200.0 million of equity capital that White Mountains has agreed to contribute to Ark 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). The remaining shares are owned by employees. In the future, management rollover shareholders could earn additional shares in the company if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing. See Note 2 — “Significant Transactions”.
The NSM segment consists of NSM Insurance HoldCo, LLC and its subsidiaries (collectively, “NSM”). NSM is a full-service managing general underwriting agency (“MGU”) and program administrator for specialty property and casualty insurance. The company places insurance in niche sectors such as specialty transportation, real estate, social services and pet. On behalf of its insurance carrier partners, NSM typically manages all aspects of the placement process, including product development, marketing, underwriting, policy issuance and claims. NSM earns commissions based on the volume and profitability of the insurance that it places. NSM does not take insurance risk. As of June 30, 2021 and December 31, 2020, White Mountains owned 96.6% of the basic units outstanding of NSM (87.5% and 89.6% on a fully diluted, fully converted basis). See Note 2 — “Significant Transactions”.
The Kudu segment consists of Kudu Investment Management, LLC and its subsidiaries (collectively “Kudu”). Kudu provides capital solutions for boutique asset managers for a variety of purposes including generational ownership transfers, management buyouts, acquisition and growth finance and legacy partner liquidity. Kudu also provides strategic assistance to investees from time to time. Kudu’s capital solutions typically are structured as minority preferred equity stakes with distribution rights, generally tied to gross revenues and designed to generate immediate strong, stable cash yields. As of June 30, 2021 and December 31, 2020, White Mountains owned 99.3% and 99.1% of the basic units outstanding (84.8% and 85.4% on a fully diluted, fully converted basis).
The Other Operations segment consists of the Company and its wholly-owned subsidiary, White Mountains Capital, LLC, (“WM Capital”) its other intermediate holding companies, its wholly-owned investment management subsidiary, White Mountains Advisors LLC (“WM Advisors”), investment assets managed by WM Advisors, its interests in MediaAlpha, Inc. (“MediaAlpha”), PassportCard Limited (“PassportCard”) and DavidShield Life Insurance Agency (2000) Ltd. (“DavidShield”) (collectively, “PassportCard/ DavidShield”), Elementum Holdings LP (“Elementum”), and certain other consolidated and unconsolidated entities and certain other assets. See Note 2 — “Significant Transactions”.
10

Discontinued Operations and Assets Held for Sale
In the first quarter of 2021, White Mountains recorded a gain on sale of discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) in 2016.
On April 12, 2021, NSM sold the Fresh Insurance Services Group Limited (“Fresh Insurance”) motor business, which was classified as held for sale at March 31, 2021. The transaction did not meet the criteria to be classified as discontinued operations. See Note 19 — “Held for Sale and Discontinued Operations”.
Significant Accounting Policies
In addition to the following, refer to the Notes to Consolidated Financial Statements in the Company’s 2020 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s significant accounting policies.
Ark Insurance Operations
Ark writes a diversified portfolio of reinsurance and insurance, including property, marine & energy, specialty, accident & health and casualty, through the Syndicates. Beginning in January 2021, Ark began writing certain classes of its business through GAIL.
For the years of account prior to White Mountains’s transaction with Ark, a significant proportion of the Syndicates’ underwriting capital was provided by other third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts through Ark’s corporate member. The TPC Providers’ economic participation in the Syndicates for the remaining open years of account prior to White Mountains’s transaction with Ark is approximately 51% of the total net result of the Syndicates. Captions within results of operations and other comprehensive income are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.
Ark’s premiums written comprise premiums on insurance contracts incepted during the year as well as premium adjustments related to prior years of account. Insurance premiums are recognized as revenues over the loss exposure or coverage period in proportion to the level of insurance protection provided. In most cases, premiums are earned ratably over the term of the contract with unearned premiums calculated on a monthly pro-rata basis. Premiums earned are presented net of amounts ceded to reinsurers. Premiums receivable, representing amounts due from insureds, are presented net of an allowance for uncollectible premiums, including expected credit losses, both dispute and credit related. The allowance is based upon Ark’s ongoing review of amounts outstanding, historical loss data, including delinquencies and write-offs, current and forecasted economic conditions and other relevant factors. Credit risk is partially mitigated by Ark’s ability to cancel the policy if the policyholder does not pay the premium.
Deferred acquisition costs comprise brokerage and taxes which are directly attributable to and vary with the production of business. These costs are deferred and amortized to the extent they related to successful contract acquisitions over the applicable premium recognition period.
Losses and loss adjustment expenses (“LAE”) are charged against income as incurred. Unpaid losses and LAE, including estimates for amounts incurred but not reported (“IBNR”) are based on estimates of the ultimate costs of settling claims, including the effects of inflation and other societal and economic factors. Unpaid loss and LAE reserves represent management’s best estimate of ultimate losses and LAE, net of estimated salvage and subrogation recoveries, if applicable. Such estimates are regularly reviewed and updated and any resulting adjustments are reflected in current results of operations. The process of estimating loss and LAE involves a considerable degree of judgment by management and the ultimate amount of expense to be incurred could be considerably greater than or less than the amounts currently reflected in the financial statements.
Reinsurance recoverables represent amounts of paid losses and loss adjustment expenses, case reserves and IBNR amounts ceded to reinsurers under reinsurance treaties. Amounts recoverable from reinsurers are estimated in a manner consistent with the associated claim liability. Ark reports its reinsurance recoverables net of an allowance for estimated uncollectible reinsurance, including expected credit losses. The allowance is based upon its ongoing review of amounts outstanding, length of collection periods, changes in reinsurer credit standing, disputes, applicable coverage defenses and other relevant factors.
11

Derivatives
From time to time, White Mountains holds derivative financial instruments for risk management purposes. White Mountains recognizes all derivatives as either assets or liabilities, measured at fair value, on the consolidated balance sheet. Changes in the fair value of derivative instruments that meet the criteria for hedge accounting are recognized in other comprehensive income and reclassified into current period pre-tax income when the hedged items are recognized therein. Changes in the fair value of derivative instruments that do not meet the criteria for hedge accounting are recognized in current period pre-tax income.
As of June 30, 2021 and December 31, 2020, NSM holds an interest rate swap derivative instrument that meets the criteria for hedge accounting. See Note 9 — “Derivatives”.
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 the Lloyd’s underwriting capacity, trade names, customer relationships and contracts, information technology platforms and insurance licenses.
Reinsurance Contracts Accounted for as Deposits
Reinsurance contracts that do not meet the risk transfer requirements necessary to be accounted for as reinsurance are accounted for using the deposit method. Under the deposit method, ceded premiums paid are not recognized through income but rather treated as a deposit. BAM entered into ceded reinsurance agreements with Fidus Re Ltd. (“Fidus Re”) during the second quarter of 2018 and the first quarter of 2021, which are both accounted for using the deposit method. See Note 10 — “Municipal Bond Guarantee Insurance”. The nonrefundable consideration paid by BAM to Fidus Re is charged to financing expense within general and administrative expenses.
Ark has an aggregate excess of loss contract with SiriusPoint Ltd. (“SiriusPoint”), formerly Third Point Reinsurance Ltd., which is accounted for using the deposit method and recorded within other assets. Ark earns an annual crediting rate of 3.0%, which is recorded within other revenue. During the three months ended June 30, 2021, Ark negotiated a reduction of $31.7 million, including accrued interest, to the aggregate excess of loss contract with SiriusPoint. As of June 30, 2021, the carrying value of Ark’s deposit in SiriusPoint, including accrued interest, was $20.1 million.
Cash and Restricted Cash
Cash includes amounts on hand and demand deposits with banks and other financial institutions. Amounts presented in the statement of cash flows are shown net of balances acquired and sold in the purchase or sale of the Company’s consolidated subsidiaries.
Cash balances that are not immediately available for general corporate purposes, including fiduciary accounts held by NSM on behalf of insurance carriers and the interest reserve account that Kudu maintains under its credit facility, are classified as restricted.
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Note 2. Significant Transactions
MediaAlpha
On October 30, 2020, MediaAlpha completed an initial public offering (the “MediaAlpha IPO”). In the offering, White Mountains sold 3.6 million shares at $19.00 per share ($17.67 per share net of underwriting fees) and received total proceeds of $63.8 million. White Mountains also received $55.0 million of net proceeds related to a dividend recapitalization at MediaAlpha.
Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet.
As of December 31, 2020, White Mountains owned 20.5 million MediaAlpha shares, representing a 35.0% ownership interest (32.3% on a fully-diluted, fully converted basis). At the December 31, 2020 closing price of $39.07 per share, the fair value of White Mountains’s remaining investment in MediaAlpha was $802.2 million.
On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160.3 million.
As of June 30, 2021, White Mountains owned 16.9 million shares, representing a 28.4% basic ownership interest (26.3% fully-diluted/fully-converted basis). At the June 30, 2021 closing price of $42.10 per share, the fair value of White Mountains’s investment in MediaAlpha was $713.2 million. At this level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $5.50 per share increase or decrease in White Mountains’s book value per share. At the July 2021 month-end closing price of $33.40 per share, the fair value of White Mountains’s investment in MediaAlpha was $565.8 million. See Note 16 — “Equity-Method Eligible Investments”.
Ark
On October 1, 2020, White Mountains entered into a subscription and purchase agreement (the “Ark SPA”) with Ark and certain selling shareholders (collectively with Ark, the “Ark Sellers”). Certain Ark Sellers also entered into a related management warranty deed (together with the Ark SPA, the “Ark Acquisition Agreement”) pursuant to which they made certain warranties about the Ark business (collectively the “Ark Transaction”). Under the terms of the Ark SPA, White Mountains agreed to contribute $605.4 million of equity capital to Ark, at a pre-money valuation of $300.0 million, and purchase $40.9 million of shares from the Ark Sellers. White Mountains also agreed to contribute up to an additional $200.0 million of equity capital to Ark in 2021. In accordance with the Ark SPA, in the fourth quarter of 2020, White Mountains pre-funded/placed in escrow a total of $646.3 million in preparation for closing the Ark Transaction, including $280.0 million funded directly to Lloyd’s on behalf of Ark under the terms of a Deposit Trust Deed and $366.3 million placed in escrow, which is reflected on the balance sheet within the Other Operations segment as of December 31, 2020.
On January 1, 2021, White Mountains completed the Ark Transaction in accordance with the terms of the Ark SPA. As of June 30, 2021, White Mountains owned 72.0% of Ark on a basic shares outstanding basis (63.0% on a fully-diluted, fully-converted basis, taking account of management’s equity incentives). If the additional $200.0 million of equity capital that White Mountains has agreed to contribute to Ark 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). The remaining shares are owned by employees. In the future, management rollover shareholders could earn additional shares in the company if and to the extent that White Mountains achieves certain multiple of invested capital return thresholds. If fully earned, these additional shares would represent 12.5% of the shares outstanding at closing.
White Mountains and Ark have agreed to extend the deadline for Ark to call the additional $200 million of capital to September 15, 2021.
White Mountains recognized total assets acquired related to the Ark Transaction of $2.5 billion, including goodwill and other intangible assets of $292.5 million, and total liabilities of $1.7 billion, including contingent consideration of $22.5 million and non-controlling interest of $220.2 million. Ark incurred transaction costs of $25.3 million in the first quarter of 2021.
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The following presents additional details of the assets acquired and liabilities assumed as of the January 1, 2021 acquisition date:

Millions |  | As of January 1, 2021 |
Investments |  | $ | 594.3 |
Cash |  | 52.0 | (1)
Reinsurance recoverables |  | 433.4 |
Insurance premiums receivable |  | 236.7 |
Ceded unearned premiums |  | 170.2 |
Value of in-force business acquired |  | 71.7 |
Other assets |  | 88.9 |
Loss and loss adjustment expense reserves |  | (696.0) |
Unearned insurance premiums |  | (326.1) |
Debt |  | (46.4) |
Ceded reinsurance payable |  | (528.3) |
Other liabilities |  | (25.9) |
Net tangible assets acquired |  | 24.5 |
Goodwill |  | 116.8 |
Other intangible assets - syndicate underwriting capacity |  | 175.7 |
Deferred tax liability on other intangible assets |  | (33.4) |
Net assets acquired |  | $ | 283.6 |

(1) Cash excludes the White Mountains cash contribution of $605.4 as part of the Ark transaction.
The acquisition date fair values of assets and liabilities, including insurance reserves and intangible assets, are provisional and are subject to revision within one year of the acquisition date.
The values of net tangible assets acquired and the resulting goodwill, other intangible assets and contingent consideration were recorded at fair value using Level 3 inputs. The majority of the tangible assets acquired and liabilities assumed were recorded at their carrying values, as their carrying values approximated their fair values due to their short-term nature. The fair values of goodwill, other intangible assets and the contingent consideration liability were internally estimated primarily based on the income approach. The income approach estimates fair value based on the present value of the cash flows that the assets are expected to generate in the future. White Mountains developed internal estimates for the expected future cash flows and discount rates used in the present value calculations.
The value of in-force business acquired represents the estimated profits relating to the unexpired contracts, net of related prepaid reinsurance at the acquisition date through the expiration date of the contracts. The value of the syndicate underwriting capacity intangible asset was estimated using net cash flows attributable to Ark’s rights to write business in the Lloyd’s market. The value of the in-force business acquired and the syndicate underwriting capacity were estimated using a discounted cash flow method. Significant inputs to the valuation models include estimates of growth in premium revenues, investment returns, claim costs, expenses and discount rates based on a weighted average cost of capital.
In evaluating the fair value of Ark’s loss and loss adjustment expense reserves, White Mountains determined that the risk-free rate of interest was approximately equal to the risk factor reflecting the uncertainty within the reserves and that no adjustment was necessary.
Ark’s segment income and expenses for the three and six months ended June 30, 2021 are presented in Note 15 - “Segment Information.” Pro forma financial information for Ark for the three and six months ended June 30, 2020 has not been presented because as a private U.K. domiciled company Ark does not have quarterly financial reporting requirements and therefore quarterly financial information is not available for periods prior to the January 1, 2021 acquisition date.
NSM
On May 18, 2018, NSM acquired 100% of Fresh Insurance, which is an insurance broker that offers non-standard personal lines products in the United Kingdom. NSM paid $49.6 million of upfront cash consideration for Fresh Insurance. NSM borrowed $51.0 million to fund the transaction. During the nine months ended September 30, 2019, NSM paid a purchase price adjustment of an additional $0.7 million of consideration. The purchase price is subject to additional adjustments based upon growth in EBITDA during two earnout periods, one which ended in February 2020 and one ending in February 2022. NSM did not make any payments related to the first Fresh Insurance earnout period.
On April 12, 2021, NSM sold Fresh Insurance’s motor business for net proceeds of £1.1 million (approximately $1.5 million based upon the foreign exchange spot rate as of the transaction date). As of March 31, 2021, the Fresh Insurance motor business was classified as held for sale and NSM recognized a loss of $28.7 million in the first quarter of 2021. See Note 19 — “Held for Sale and Discontinued Operations”.
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On December 3, 2018, NSM acquired all the net assets of KBK Insurance Group, Inc. (“KBK”), a specialized MGU focused on the towing and transportation space. NSM paid $60.0 million of upfront cash consideration for KBK. White Mountains contributed $29.0 million to NSM and NSM borrowed $30.1 million to fund the transaction. As of March 31, 2019, White Mountains determined that the relative values of goodwill and other intangible assets from the KBK transaction were $32.6 million and $32.7 million, reflecting acquisition date fair values, and recorded a liability of $5.9 million relating to the fair value of contingent consideration made in connection with the acquisition. The purchase price is subject to adjustments based upon growth in EBITDA during three earnout periods, one which ended in December 2019, one which ended in December 2020 and one ending in December 2021. In the first quarter of 2021 and 2020, NSM paid $6.7 million and $6.4 million related to the first and second KBK earnout periods. As of June 30, 2021, the KBK contingent consideration liability was $6.6 million.
On April 7, 2020, NSM acquired 100% of Kingsbridge Group Limited (“Kingsbridge”), a leading provider of commercial lines insurance and consulting services for the professional contractor and freelancer markets in the United Kingdom. NSM paid £107.2 million (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 of $4.1 million. During the fourth quarter of 2020, NSM recognized pre-tax income of $4.1 million for the change in fair value of the Kingsbridge contingent consideration liability and a foreign currency translation unrealized gain of $0.3 million. As of June 30, 2021, the Kingsbridge contingent consideration liability was $0.1 million.
The contingent consideration liabilities related to NSM’s acquisitions are subject to adjustments based upon EBITDA, EBITDA projections, and present value factors for acquired entities. For the three and six months ended June 30, 2021, NSM recognized pre-tax loss of $0.2 million and $0.2 million for the change in the fair value of its contingent consideration liabilities. For the three and six months ended June 30, 2020, NSM recognized pre-tax income of $1.7 million and $2.3 million for the change in the fair value of its contingent consideration liabilities. Any future adjustments to contingent consideration liabilities under the agreements will be recognized through pre-tax income. As of June 30, 2021 and December 31, 2020, NSM recorded total contingent consideration liabilities of $7.3 million and $14.6 million.
PassportCard/DavidShield
On January 24, 2018, White Mountains acquired a 50.0% ownership interest in DavidShield, its joint venture partner in PassportCard. DavidShield is a managing general agency that is the leading provider of expatriate medical insurance in Israel and uses the same card-based delivery system as PassportCard. As part of the transaction, White Mountains reorganized its equity stake in PassportCard so that White Mountains and its partner in DavidShield would each own 50.0% of both businesses. To facilitate the transaction, White Mountains provided financing to its partner in the form of a non-interest bearing loan that is secured by the partner’s equity in PassportCard and DavidShield. The gross purchase price for the 50.0% interest in DavidShield was $41.8 million, or $28.3 million net of the financing provided for the restructuring.
On May 7, 2020, White Mountains made an additional $15.0 million investment in PassportCard/DavidShield to support operations through the ongoing COVID-19 pandemic. The transaction increased White Mountains’s ownership interest from 50.0% to 53.8%, but had no impact on the governance structure of the companies, including White Mountains’s board representation or other investor rights. The governance structures for both PassportCard and DavidShield were designed to give White Mountains and its co-investor equal power to make the decisions that most significantly impact the operations of PassportCard and DavidShield.
As a result of the transaction, White Mountains’s re-evaluated its accounting treatment for PassportCard and DavidShield. Because White Mountains does not have the unilateral power to direct the operations of PassportCard or DavidShield, White Mountains does not hold a controlling financial interest in either PassportCard or DavidShield and does not consolidate either entity. White Mountains’s ownership interest gives White Mountains the opportunity to exert significant influence over the significant financial and operating activities of PassportCard and DavidShield. Accordingly, PassportCard and DavidShield meet the criteria to be accounted for under the equity method. White Mountains has taken the fair value option for its investment in PassportCard and DavidShield. Changes in the fair value of PassportCard and DavidShield are recorded in realized and unrealized investment gains. White Mountains’s maximum exposure to loss on its equity investment in PassportCard/DavidShield and the non-interest bearing loan to its partner is limited to the total carrying value of $104.0 million.
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Note 3. Investment Securities
White Mountains’s portfolio of investment securities held for general investment purposes consists of fixed maturity investments, short-term investments, common equity securities, its investment in MediaAlpha and other long-term investments, which are classified as trading securities. Trading securities are reported at fair value as of the balance sheet date. Net realized and unrealized investment gains (losses) on trading securities are reported in pre-tax revenues.
White Mountains’s fixed maturity investments are generally valued using industry standard pricing methodologies. Key inputs include benchmark yields, benchmark securities, reported trades, issuer spreads, bids, offers, credit ratings and prepayment speeds. Income on mortgage and asset-backed securities is recognized using an effective yield based on anticipated prepayments and the estimated economic life of the securities. When actual prepayments differ significantly from anticipated prepayments, the estimated economic life is recalculated and the remaining unamortized premium or discount is amortized prospectively over the remaining economic life.
Realized investment gains (losses) resulting from sales of investment securities are accounted for using the specific identification method. Premiums and discounts on all fixed maturity investments are amortized or accreted to income over the anticipated life of the investment. Short-term investments consist of interest-bearing money market funds, certificates of deposit and other securities, which at the time of purchase, mature or become available for use within one year. Short-term investments are carried at fair value as of June 30, 2021 and December 31, 2020.
Other long-term investments consist primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, insurance-linked securities funds (“ILS funds”) and private debt investments.
Net Investment Income
White Mountains’s net investment income is comprised primarily of interest income associated with White Mountains’s fixed maturity investments and short-term investments, dividend income from common equity securities, distributions from its investment in MediaAlpha and distributions from other long-term investments.
The following table presents pre-tax net investment income for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Fixed maturity investments |  | $ | 7.2 |  |  | $ | 7.3 |  |  | $ | 13.7 |  |  | $ | 15.4 |
Short-term investments |  | (1.1) |  |  | .1 |  |  | .5 |  |  | .9 |
Common equity securities |  | — |  |  | 2.2 |  |  | — |  |  | 6.0 |
Investment in MediaAlpha |  | — |  |  | 2.5 |  |  | — |  |  | 5.0 |
Other long-term investments |  | 11.3 |  |  | 7.8 |  |  | 25.1 |  |  | 15.8 |
Amount attributable to TPC Providers |  | .3 |  |  | — |  |  | (.6) |  |  | — |
Total investment income |  | 17.7 |  |  | 19.9 |  |  | 38.7 |  |  | 43.1 |
Third-party investment expenses |  | (.6) |  |  | (.3) |  |  | (1.0) |  |  | (.6) |
Net investment income, pre-tax |  | $ | 17.1 |  |  | $ | 19.6 |  |  | $ | 37.7 |  |  | $ | 42.5 |

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Net Realized and Unrealized Investment Gains (Losses)
The following table presents net realized and unrealized investment gains (losses) for the three and six months ended June 30, 2021 and 2020:

|  |  | Three Months Ended |  | Six Months Ended
|  |  | June 30, |  | June 30,
Millions |  |  | 2021 |  | 2020 |  | 2021 |  | 2020
Fixed maturity investments |  |  | $ | 9.0 |  |  | $ | 30.0 |  |  | $ | (16.4) |  |  | $ | 32.2 |
Short-term investments |  |  | 1.6 |  |  | — |  |  | .3 |  |  | .4 |
Common equity securities |  |  | 5.1 |  |  | 98.3 |  |  | 6.1 |  |  | (42.5) |
Investment in MediaAlpha |  |  | 113.0 |  |  | 15.0 |  |  | 71.3 |  |  | 45.0 |
Other long-term investments |  |  | 47.4 |  |  | 9.6 |  |  | 75.5 |  |  | (38.9) |
Amount attributable to TPC Providers |  |  | (3.5) |  |  | — |  |  | (4.8) |  |  | — |
Net realized and unrealized investment gains (losses) (1) |  |  | 172.6 |  |  | 152.9 |  |  | 132.0 |  |  | (3.8) |
Less: net (losses) gains on investment securities sold during the period |  |  | (.1) |  |  | 2.2 |  |  | (.3) |  |  | (6.5) |
Net realized and unrealized investment gains on investment securities held at the end of the period |  |  | $ | 172.7 |  |  | $ | 150.7 |  |  | $ | 132.3 |  |  | $ | 2.7 |

(1) For the three months ended June 30, 2021 and 2020, includes $(0.2) and $0.4 of realized and unrealized investment (losses) gains related to foreign currency exchange. For the six months ended June 30, 2021 and 2020, includes $(0.4) and $0.0 of realized and unrealized investment (losses) related to foreign currency exchange.
The following table presents total gains included in earnings attributable to net unrealized investment gains for Level 3 investments for the three and six months ended June 30, 2021 and 2020 for investments still held at the end of the period:

|  | Three Months Ended |  |  | Six Months Ended
|  | June 30, |  |  | June 30,
Millions |  | 2021 |  | 2020 |  |  | 2021 |  | 2020
Other long-term investments |  | $ | 32.3 |  |  | $ | 25.3 |  |  |  | $ | 49.0 |  |  | $ | 15.9 |
Total net unrealized investment gains, pre-tax - Level 3 investments |  | $ | 32.3 |  |  | $ | 25.3 |  |  |  | $ | 49.0 |  |  | $ | 15.9 |

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 June 30, 2021 and December 31, 2020:

|  | June 30, 2021
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Net Foreign Currency Losses |  | Carrying Value
U.S. Government and agency obligations |  | $ | 252.9 |  |  | $ | 1.8 |  |  | $ | (.5) |  |  | $ | — |  |  | $ | 254.2 |
Debt securities issued by corporations |  | 846.9 |  |  | 15.7 |  |  | (2.3) |  |  | (.1) |  |  | 860.2 |
Municipal obligations |  | 270.3 |  |  | 19.1 |  |  | (.4) |  |  | — |  |  | 289.0 |
Mortgage and asset-backed securities |  | 222.6 |  |  | 4.4 |  |  | (.9) |  |  | — |  |  | 226.1 |
Collateralized loan obligations |  | 128.2 |  |  | — |  |  | (.3) |  |  | (.1) |  |  | 127.8 |
Total fixed maturity investments |  | $ | 1,720.9 |  |  | $ | 41.0 |  |  | $ | (4.4) |  |  | $ | (.2) |  |  | $ | 1,757.3 |

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|  | December 31, 2020
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  |  |  | Carrying Value
U.S. Government and agency obligations |  | $ | 173.2 |  |  | $ | 3.1 |  |  | $ | — |  |  |  |  | $ | 176.3 |
Debt securities issued by corporations |  | 522.8 |  |  | 24.7 |  |  | (.1) |  |  |  |  | 547.4 |
Municipal obligations |  | 244.0 |  |  | 21.0 |  |  | — |  |  |  |  | 265.0 |
Mortgage and asset-backed securities |  | 211.7 |  |  | 6.8 |  |  | — |  |  |  |  | 218.5 |
Total fixed maturity investments |  | $ | 1,151.7 |  |  | $ | 55.6 |  |  | $ | (.1) |  |  |  |  | $ | 1,207.2 |

The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of June 30, 2021. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.

|  | June 30, 2021
Millions |  | Cost or Amortized Cost |  | Carrying Value
Due in one year or less |  | $ | 124.2 |  |  | $ | 125.3 |
Due after one year through five years |  | 772.0 |  |  | 782.2 |
Due after five years through ten years |  | 357.4 |  |  | 368.8 |
Due after ten years |  | 116.5 |  |  | 127.2 |
Mortgage and asset-backed securities and collateralized loan obligations |  | 350.8 |  |  | 353.9 |
Total fixed maturity investments |  | $ | 1,720.9 |  |  | $ | 1,757.4 |

The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of common equity securities, White Mountains’s investment in MediaAlpha and other long-term investments as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Net Foreign Currency (Losses) Gains |  | Carrying Value
Common equity securities |  | $ | 136.4 |  |  | $ | 6.0 |  |  | $ | — |  |  | $ | (.4) |  |  | $ | 142.0 |
Investment in MediaAlpha |  | $ | — |  |  | $ | 713.2 |  |  | $ | — |  |  | $ | — |  |  | $ | 713.2 |
Other long-term investments |  | $ | 979.0 |  |  | $ | 166.1 |  |  | $ | (64.6) |  |  | $ | .9 |  |  | $ | 1,081.4 |

|  | December 31, 2020
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Net Foreign Currency Gains |  | Carrying Value
Investment in MediaAlpha |  | $ | — |  |  | $ | 802.2 |  |  | $ | — |  |  | $ | — |  |  | $ | 802.2 |
Other long-term investments |  | $ | 767.4 |  |  | $ | 95.8 |  |  | $ | (78.1) |  |  | $ | 1.7 |  |  | $ | 786.8 |

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Fair Value Measurements
As of June 30, 2021 and December 31, 2020, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 75% and 73% of the investment portfolio.
Fair Value Measurements by Level
The following tables present White Mountains’s fair value measurements for investments as of June 30, 2021 and December 31, 2020 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated this asset class into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate.

|  | June 30, 2021
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 254.2 |  |  | $ | 254.2 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |
Financials |  | 230.8 |  |  | — |  |  | 230.8 |  |  | — |
Consumer |  | 150.4 |  |  | — |  |  | 150.4 |  |  | — |
Technology |  | 97.1 |  |  | — |  |  | 97.1 |  |  | — |
Industrial |  | 96.1 |  |  | — |  |  | 96.1 |  |  | — |
Healthcare |  | 92.4 |  |  | — |  |  | 92.4 |  |  | — |
Utilities |  | 67.4 |  |  | — |  |  | 67.4 |  |  | — |
Communications |  | 50.3 |  |  | — |  |  | 50.3 |  |  | — |
Energy |  | 44.0 |  |  | — |  |  | 44.0 |  |  | — |
Materials |  | 31.7 |  |  | — |  |  | 31.7 |  |  | — |
Total debt securities issued by corporations |  | 860.2 |  |  | — |  |  | 860.2 |  |  | — |
Municipal obligations |  | 289.0 |  |  | — |  |  | 289.0 |  |  | — |
Mortgage and asset-backed securities |  | 226.1 |  |  | — |  |  | 226.1 |  |  | — |
Collateralized loan obligations |  | 127.8 |  |  | — |  |  | 127.8 |  |  | — |
Total fixed maturity investments |  | 1,757.3 |  |  | 254.2 |  |  | 1,503.1 |  |  | — |
Short-term investments |  | 532.5 |  |  | 507.4 |  |  | 25.1 |  |  | — |
Common equity securities (1) |  | 142.0 |  |  | — |  |  | 142.0 |  |  | — |
Investment in MediaAlpha |  | 713.2 |  |  | 713.2 |  |  | — |  |  | — |
Other long-term investments |  | 679.6 |  |  | — |  |  | 5.2 |  |  | 674.4 |
Other long-term investments — NAV (2) |  | 401.8 |  |  | — |  |  | — |  |  | — |
Total other long-term investments |  | 1,081.4 |  |  | — |  |  | 5.2 |  |  | 674.4 |
Total investments |  | $ | 4,226.4 |  |  | $ | 1,474.8 |  |  | $ | 1,675.4 |  |  | $ | 674.4 |

(1) Consist of investments in listed funds that predominantly invest in international equities.
(2) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
19

|  | December 31, 2020
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 176.3 |  |  | $ | 176.3 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |
Financials |  | 133.9 |  |  | — |  |  | 133.9 |  |  | — |
Consumer |  | 81.9 |  |  | — |  |  | 81.9 |  |  | — |
Industrial |  | 66.9 |  |  | — |  |  | 66.9 |  |  | — |
Technology |  | 66.7 |  |  | — |  |  | 66.7 |  |  | — |
Healthcare |  | 51.5 |  |  | — |  |  | 51.5 |  |  | — |
Communications |  | 44.5 |  |  | — |  |  | 44.5 |  |  | — |
Energy |  | 35.8 |  |  | — |  |  | 35.8 |  |  | — |
Materials |  | 33.9 |  |  | — |  |  | 33.9 |  |  | — |
Utilities |  | 32.3 |  |  | — |  |  | 32.3 |  |  | — |
Total debt securities issued by corporations |  | 547.4 |  |  | — |  |  | 547.4 |  |  | — |
Municipal obligations |  | 265.0 |  |  | — |  |  | 265.0 |  |  | — |
Mortgage and asset-backed securities |  | 218.5 |  |  | — |  |  | 218.5 |  |  | — |
Total fixed maturity investments |  | 1,207.2 |  |  | 176.3 |  |  | 1,030.9 |  |  | — |
Short-term investments |  | 142.9 |  |  | 142.9 |  |  | — |  |  | — |
Investment in MediaAlpha |  | 802.2 |  |  | 802.2 |  |  | — |  |  | — |
Other long-term investments |  | 614.2 |  |  | — |  |  | — |  |  | 614.2 |
Other long-term investments — NAV (1) |  | 172.6 |  |  | — |  |  | — |  |  | — |
Total other long-term investments |  | 786.8 |  |  | — |  |  | — |  |  | 614.2 |
Total investments |  | $ | 2,939.1 |  |  | $ | 1,121.4 |  |  | $ | 1,030.9 |  |  | $ | 614.2 |

(1) Consists of private equity funds and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
Debt Securities Issued by Corporations
The following table presents the credit ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of June 30, 2021 and December 31, 2020:

|  | Fair Value at
Millions |  | June 30, 2021 |  | December 31, 2020
AAA |  | $ | 12.7 |  |  | $ | 10.6 |
AA |  | 80.1 |  |  | 57.9 |
A |  | 437.3 |  |  | 318.3 |
BBB |  | 320.0 |  |  | 159.6 |
BB |  | 1.1 |  |  | 1.0 |
Other |  | 9.0 |  |  | — |
Debt securities issued by corporations (1) |  | $ | 860.2 |  |  | $ | 547.4 |

(1) Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc.
20

Mortgage and Asset-backed Securities and Collateralized Loan Obligations
The following table presents the fair value of White Mountains’s mortgage and asset-backed securities and collateralized loan obligations as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
Millions |  | Fair Value |  | Level 2 |  | Level 3 |  | Fair Value |  | Level 2 |  | Level 3
Mortgage-backed securities: |  |  |  |  |  |  |  |  |  |  |  |
Agency: |  |  |  |  |  |  |  |  |  |  |  |
FNMA |  | $ | 106.7 |  |  | $ | 106.7 |  |  | $ | — |  |  | $ | 88.7 |  |  | $ | 88.7 |  |  | $ | — |
FHLMC |  | 70.3 |  |  | 70.3 |  |  | — |  |  | 70.1 |  |  | 70.1 |  |  | — |
GNMA |  | 32.8 |  |  | 32.8 |  |  | — |  |  | 40.6 |  |  | 40.6 |  |  | — |
Total agency (1) |  | 209.8 |  |  | 209.8 |  |  | — |  |  | 199.4 |  |  | 199.4 |  |  | — |
Non-agency: Residential |  | .6 |  |  | .6 |  |  | — |  |  | — |  |  | — |  |  | — |
Total non-agency |  | .6 |  |  | .6 |  |  | — |  |  | — |  |  | — |  |  | — |
Total mortgage-backed securities |  | 210.4 |  |  | 210.4 |  |  | — |  |  | 199.4 |  |  | 199.4 |  |  | — |
Other asset-backed securities: |  |  |  |  |  |  |  |  |  |  |  |
Credit card receivables |  | 11.3 |  |  | 11.3 |  |  | — |  |  | 11.3 |  |  | 11.3 |  |  | — |
Vehicle receivables |  | 4.4 |  |  | 4.4 |  |  | — |  |  | 7.8 |  |  | 7.8 |  |  | — |
Total other asset-backed securities |  | 15.7 |  |  | 15.7 |  |  | — |  |  | 19.1 |  |  | 19.1 |  |  | — |
Total mortgage and asset-backed securities |  | 226.1 |  | 226.1 |  | — |  |  | 218.5 |  |  | 218.5 |  |  | — |
Collateralized loan obligations |  | 127.8 |  |  | 127.8 |  |  | — |  |  | — |  |  | — |  |  | — |
Total mortgage and asset-backed securities and collateralized loan obligations |  | $ | 353.9 |  |  | $ | 353.9 |  |  | $ | — |  |  | $ | 218.5 |  |  | $ | 218.5 |  |  | $ | — |

(1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed
by a government sponsored entity (i.e., FNMA, FHLMC).
As of June 30, 2021, White Mountains’s investment portfolio included $127.8 million of collateralized loan obligations that are within the senior tranches of their respective fund securitization structures. All of White Mountains’s collateral loan obligations were rated AAA or AA as of June 30, 2021.
Investment in MediaAlpha
Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and is presented as a separate line item on the balance sheet.
At the June 30, 2021 closing price of $42.10 per share, the fair value of White Mountains’s investment in MediaAlpha was $713.2 million. See Note 2 — “Significant Transactions”.
21

Other Long-Term Investments
The following table presents the carrying values of White Mountains’s other long-term investments as of June 30, 2021 and December 31, 2020:

|  | Fair Value at
Millions |  | June 30, 2021 |  | December 31, 2020
Kudu’s Participation Contracts |  | $ | 455.5 |  |  | $ | 400.6 |
PassportCard/DavidShield |  | 95.0 |  |  | 95.0 |
Elementum Holdings L.P. |  | 56.7 |  |  | 55.1 |
Other unconsolidated entities (1) |  | 39.0 |  |  | 42.4 |
Total unconsolidated entities |  | 646.2 |  |  | 593.1 |
Private equity funds and hedge funds |  | 142.3 |  |  | 121.2 |
Lloyd’s trust deposits |  | 105.0 |  |  | — |
Bank loan fund |  | 100.4 |  |  | — |
ILS funds |  | 54.1 |  |  | 51.4 |
Private debt investments |  | 20.2 |  |  | 21.1 |
Other |  | 13.2 |  |  | — |
Total other long-term investments |  | $ | 1,081.4 |  |  | $ | 786.8 |

(1) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities and Simple Agreement for Future Equity (“SAFE”) investments.
Private Equity Funds and Hedge Funds
White Mountains invests in private equity funds and hedge funds, which are included in other long-term investments. The fair value of these investments is generally estimated using the net asset value (“NAV”) of the funds. As of June 30, 2021, White Mountains held investments in thirteen private equity funds and one hedge fund. The largest investment in a single private equity fund or hedge fund was $24.9 million as of June 30, 2021 and $29.1 million as of December 31, 2020.
The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
Millions |  | Fair Value |  | Unfunded Commitments |  | Fair Value |  | Unfunded Commitments
Private equity funds |  |  |  |  |  |  |  |
Aerospace/Defense/Government |  | $ | 70.8 |  |  | $ | 14.0 |  |  | $ | 69.1 |  |  | $ | 15.3 |
Financial services |  | 54.0 |  |  | 30.0 |  |  | 23.5 |  |  | 30.4 |
Real estate |  | 4.3 |  |  | 3.0 |  |  | — |  |  | — |
Manufacturing/Industrial |  | .1 |  |  | — |  |  | 28.6 |  |  | — |
Total private equity funds |  | 129.2 |  |  | 47.0 |  |  | 121.2 |  |  | 45.7 |
Hedge funds |  |  |  |  |  |  |  |
European small/mid cap |  | 13.1 |  |  | — |  |  | — |  |  | — |
Total hedge funds |  | 13.1 |  |  | — |  |  | — |  |  | — |
Total private equity funds and hedge funds included in other long-term investments |  | $ | 142.3 |  |  | $ | 47.0 |  |  | $ | 121.2 |  |  | $ | 45.7 |

22

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 June 30, 2021:

Millions |  | 1 – 3 years |  | 3 – 5 years |  | 5 – 10 years |  | >10 years |  | Total
Private equity funds — expected lock-up period remaining |  | $.3 |  | $24.3 |  | $84.8 |  | $19.8 |  | $129.2

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 June 30, 2021 and December 31, 2020, White Mountains is not aware of any indemnification claims relating to its investments in private equity funds.
Redemption of investments in most hedge funds is subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. White Mountains’s hedge fund investment is subject to a perpetual two-year restriction on redemption frequency from the initial investment in the fund and a 90-days advanced notice period requirement.
Lloyd’s Trust Deposits
White Mountains’s other long-term investments include Lloyd’s Trust Deposits, which consists of overseas deposits and Canadian comingled pooled funds. The Lloyd’s Trust Deposits invest primarily in short-term government securities, agency securities and corporate bonds held in trusts that are managed by Lloyd's of London. These investments are required of Lloyd's syndicates to protect policyholders in overseas markets and are pledged into Lloyd’s trust accounts to provide a portion of the capital needed to support obligations at Lloyd’s. The fair value of the Lloyd’s Trust Deposits is generally estimated using the NAV of the funds. As of June 30, 2021, White Mountains held Lloyd’s Trust Deposits with a fair value of $105.0 million.
Bank Loan Fund
White Mountains’s other long-term investments include a bank loan fund with a fair value of $100.4 million as of June 30, 2021. The fair value of this investment is estimated using the NAV of the fund. The bank loan fund’s investment objective is to provide, on an unleveraged basis, high current income consistent with preservation of capital and low duration. The bank loan fund primarily invests in a broad portfolio of U.S. dollar-denominated, non-investment grade, floating-rate senior secured loans and may invest in other financial instruments, such as secured and unsecured corporate debt, credit default swaps, reverse repurchase agreements and synthetic indices and cash and cash equivalents.
The investment in the bank loan fund is subject to restrictions on redemption frequency and advance notice periods for redemptions. Amounts requested for redemptions remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period. White Mountains may redeem all or a portion of its bank loan fund investment as of any calendar month-end upon 15 calendar days advanced written notice.
Insurance-Linked Securities Funds
White Mountains’s other long-term investments include ILS fund investments. The fair value of these investments is generally estimated using the NAV of the funds. As of June 30, 2021, White Mountains held investments in ILS funds with a fair value of $54.1 million.
Investments in ILS funds are generally subject to restrictions, including lock-up periods where no redemptions or withdrawals are allowed, non-renewal clauses, restrictions on redemption frequency and advance notice periods for redemptions. From time to time, natural catastrophe, liquidity, market or other events will occur that make the determination of fair value for underlying investments in ILS funds less certain due to the potential for loss development. In such circumstances, the impacted investments may be subject to additional lock-up provisions.
ILS funds are typically subject to monthly and annual restrictions on redemptions and advance redemption notice period requirements that range between 30 and 90 days. Amounts requested for redemption remain subject to market fluctuations until the redemption effective date, which generally falls at the end of the defined redemption period.
One of the ILS funds in White Mountains’s portfolio requires shareholders to provide advance redemption notice on or before September 15 of each calendar year. Amounts requested for redemption in this fund remain subject to market fluctuation until the underlying investment has fully matured or been commuted, which may be up to a period of three years from the start of each calendar year.
23

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 June 30, 2021 and 2020 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities.
The following tables present the changes in White Mountains’s fair value measurements by level for the six months ended June 30, 2021 and 2020:

|  |  |  |  | Level 3 Investments | Other Long-term Investments Measured at NAV (1) |  |  |
Millions | Level 1 Investments | Level 2 Investments |  |  | Other Long-term Investments |  | Total |
Balance at December 31, 2020 | $ | 978.5 |  | $ | 1,030.9 |  |  |  | $ | 614.2 |  | $ | 172.6 |  |  | $ | 2,796.2 |  | (2)
Net realized and unrealized gains (losses) | 69.5 |  | (8.5) |  |  |  | 48.9 |  | 26.6 |  |  | 136.5 |  | (3)
Amortization/Accretion | (.1) |  | (3.6) |  |  |  | — |  | — |  |  | (3.7) |  |
Purchases | 92.7 |  | 780.5 |  |  |  | 13.2 |  | 123.2 |  |  | 1,009.6 |  |
Sales | (173.2) |  | (217.2) |  |  |  | (11.5) |  | (56.4) |  |  | (458.3) |  |
Effect of Ark Transaction | — |  | 68.2 |  |  |  | 9.6 |  | 135.8 |  |  | 213.6 |  |
Transfers in | — |  | — |  |  |  | — |  | — |  |  | — |  |
Transfers out | — |  | — |  |  |  | — |  | — |  |  | — |  |
Balance at June 30, 2021 | $ | 967.4 |  | $ | 1,650.3 |  |  |  | $ | 674.4 |  | $ | 401.8 |  |  | $ | 3,693.9 |  | (2)

(1) Consists of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies”.
(2) Excludes carrying value of $532.5 and $142.9 as of June 30, 2021 and December 31, 2020 classified as short-term investments.
(3) Excludes realized and unrealized gains associated with short-term investments of $0.3 and includes amounts attributable to TPC Providers of $4.8 for the six months ended June 30, 2021.

|  |  |  |  |  | Level 3 Investments | Other Long-term Investments Measured at NAV (1) |  |
Millions | Level 1 Investments | Level 2 Investments |  | Common equity securities |  | Other Long-term Investments and Investment in MediaAlpha Pre-IPO | Total |
Balance at December 31, 2019 | $ | 780.0 |  | $ | 1,109.6 |  |  | $ | .1 |  |  | $ | 654.0 |  | $ | 202.3 |  | $ | 2,746.0 |  | (2)
Net realized and unrealized (losses) gains | (13.9) |  | 3.6 |  |  | — |  |  | 15.6 |  | (9.5) |  | (4.2) |  | (3)
Amortization/Accretion | — |  | (1.9) |  |  | — |  |  | — |  | — |  | (1.9) |  |
Purchases | 113.0 |  | 214.2 |  |  | — |  |  | 78.6 |  | 21.2 |  | 427.0 |  |
Sales | (214.0) |  | (231.9) |  |  | — |  |  | (8.1) |  | (56.0) |  | (510.0) |  |
Transfers in | — |  | — |  |  | — |  |  | — |  | — |  | — |  |
Transfers out | — |  | — |  |  | — |  |  | — |  | — |  | — |  |
Balance at June 30, 2020 | $ | 665.1 |  | $ | 1,093.6 |  |  | $ | .1 |  |  | $ | 740.1 |  | $ | 158.0 |  | $ | 2,656.9 |  | (2)

(1) Includes private equity funds, a hedge fund and ILS funds for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies”.
(2) Excludes carrying value of $117.6 and $201.2 as of June 30, 2020 and December 31, 2019 classified as short-term investments.
(3) Excludes realized and unrealized losses associated with short-term investments of $0.4 for the six months ended June 30, 2020.
24

Fair Value Measurements — Transfers Between Levels - Six-months ended June 30, 2021 and 2020
Transfers between levels are recorded using the fair value measurement as of the end of the quarterly period in which the event or change in circumstance giving rise to the transfer occurred.
During the six months ended June 30, 2021 and 2020, there were no fixed maturity investments or other long-term investments classified as Level 3 measurements in the prior period that were transferred to Level 2 measurements.
During the first six months of 2021 and 2020, there were no fixed maturity investments or other long-term investments classified as Level 2 measurements in the prior period that were transferred to Level 3 measurements.
Significant Unobservable Inputs
The following tables present significant unobservable inputs used in estimating the fair value of White Mountains’s other long-term investments, classified within Level 3 as of June 30, 2021 and December 31, 2020. The tables below exclude $35.5 million and $27.6 million of Level 3 other long-term investments primarily valued based on recent or expected transaction prices. The fair value of investments in private equity funds, hedge funds, Lloyd’s trust deposits, bank loans funds and ILS funds are generally estimated using the NAV of the funds.

$ in Millions |  | June 30, 2021
Description |  | Valuation Technique(s) (1) |  | Fair Value (2) |  | Unobservable Inputs
|  |  |  |  |  | Discount Rate (3)(4) |  | Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4)
Kudu’s Participation Contracts (5) |  | Discounted cash flow |  | $455.5 |  | 18% - 23% |  | 7x - 13x
PassportCard/DavidShield |  | Discounted cash flow |  | $95.0 |  | 23% |  | 4%
Elementum Holdings, L.P. |  | Discounted cash flow |  | $56.7 |  | 17% |  | 4%
Private debt investments |  | Discounted cash flow |  | $10.9 |  | 3% - 8% |  | N/A
Other |  | Discounted cash flow |  | $20.8 |  | 20% - 24% |  | 4%

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.
(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.
(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values.
(4) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.
(5) In the six months ended June 30, 2021, Kudu deployed a total of $10.9 in TIG Advisors LLC and $0.4 in TK Partners LLC, existing Kudu Participation Contracts.

$ in Millions |  | December 31, 2020
Description |  | Valuation Technique(s) (1) |  | Fair Value (2) |  | Unobservable Inputs
|  |  |  |  |  | Discount Rate (3)(4) |  | Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (4)
Kudu’s Participation Contracts (5) |  | Discounted cash flow |  | $400.6 |  | 18% - 23% |  | 7x - 12x
PassportCard/DavidShield (6) |  | Discounted cash flow |  | $95.0 |  | 23% |  | 4%
Elementum Holdings, L.P. |  | Discounted cash flow |  | $55.1 |  | 17% |  | 4%
Private debt investments |  | Discounted cash flow |  | $17.1 |  | 4% - 8% |  | N/A
Other |  | Discounted cash flow |  | $18.8 |  | 20% - 24% |  | 4%

(1) Key inputs to the discounted cash flow analysis generally include projections of future revenue and earnings, discount rates and terminal exit multiples or growth rates.
(2) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.
(3) Since Kudu’s Participation Contracts are not subject to corporate taxes within Kudu Investment Management, LLC, pre-tax discount rates are applied to pre-tax cash flows in determining fair values.
(4) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.
(5) In 2020, Kudu deployed a total of $118.2 in new Kudu Participation Contracts, including Creation Investments Capital, Sequoia Financial Group, Channel Capital and Ranger Investment Management.
(6) In 2020, White Mountains made an additional $15.0 investment in PassportCard/DavidShield. See Note 2 — “Significant Transactions”.
25

Note 4. Goodwill and Other Intangible Assets
White Mountains accounts for purchases of businesses using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. The acquisition date fair values of certain assets and liabilities, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date.
The following table presents the acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by segment as of June 30, 2021 and December 31, 2020:

$ in Millions |  | Weighted Average Economic Life (in years) |  | June 30, 2021 |  | December 31, 2020
| Acquisition Date Fair Value |  | Accumulated Amortization |  | Impairments and Amounts Allocated to Held for Sale |  | Net Carrying Value |  | Acquisition Date Fair Value |  | Accumulated Amortization |  | Impairments |  | Net Carrying Value
Goodwill: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ark |  | N/A |  | $ | 116.8 |  |  | $ | — |  |  | $ | — |  |  | $ | 116.8 |  |  | $ | — |  |  | $ | — |  |  | $ | — |  |  | $ | — |
NSM (1) |  | N/A |  | 508.1 |  |  | — |  |  | 30.2 |  |  | 477.9 |  |  | 506.4 |  |  | — |  |  | — |  |  | 506.4 |
Kudu |  | N/A |  | 7.6 |  |  | — |  |  | — |  |  | 7.6 |  |  | 7.6 |  |  | — |  |  | — |  |  | 7.6 |
Other Operations |  | N/A |  | 27.1 |  |  | — |  |  | — |  |  | 27.1 |  |  | 11.5 |  |  | — |  |  | — |  |  | 11.5 |
Total goodwill |  |  |  | 659.6 |  |  | — |  |  | 30.2 |  |  | 629.4 |  |  | 525.5 |  |  | — |  |  | — |  |  | 525.5 |
Other intangible assets: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ark |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Underwriting Capacity | N/A |  | 175.7 |  |  | — |  |  | — |  |  | 175.7 |  |  | — |  |  | — |  |  | — |  |  | — |
NSM (1) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Customer relationships |  | 8.9 |  | 136.4 |  |  | 46.3 |  |  | 3.5 |  |  | 86.6 |  |  | 136.2 |  |  | 36.7 |  |  | 3.5 |  |  | 96.0 |
Trade names |  | 16 |  | 65.5 |  |  | 10.0 |  |  | 1.0 |  |  | 54.5 |  |  | 65.4 |  |  | 8.3 |  |  | 1.0 |  |  | 56.1 |
Information technology platform |  | 0 |  | 3.1 |  |  | 1.4 |  |  | 1.7 |  |  | — |  |  | 3.1 |  |  | 1.4 |  |  | 1.7 |  |  | — |
Renewal rights |  | 12 |  | 82.5 |  |  | 10.4 |  |  | — |  |  | 72.1 |  |  | 82.5 |  |  | 4.9 |  |  | — |  |  | 77.6 |
Other |  | 3.4 |  | 1.7 |  |  | 1.2 |  |  | — |  |  | .5 |  |  | 1.7 |  |  | 1.0 |  |  | — |  |  | .7 |
Subtotal |  |  |  | 289.2 |  |  | 69.3 |  |  | 6.2 |  |  | 213.7 |  |  | 288.9 |  |  | 52.3 |  |  | 6.2 |  |  | 230.4 |
Kudu |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  | 7 |  | 2.2 |  |  | .7 |  |  | — |  |  | 1.5 |  |  | 2.2 |  |  | .6 |  |  | — |  |  | 1.6 |
Other Operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  | 9.6 |  | 3.6 |  |  | .5 |  |  | — |  |  | 3.1 |  |  | 3.6 |  |  | .3 |  |  | — |  |  | 3.3 |
Customer relationships |  | 10.7 |  | 14.2 |  |  | 2.1 |  |  | — |  |  | 12.1 |  |  | 14.2 |  |  | 1.4 |  |  | — |  |  | 12.8 |
Insurance Licenses |  | N/A |  | 8.6 |  |  | — |  |  | — |  |  | 8.6 |  |  | 8.6 |  |  | — |  |  | — |  |  | 8.6 |
Other |  | 5.4 |  | .3 |  |  | .2 |  |  | — |  |  | .1 |  |  | .3 |  |  | .1 |  |  | — |  |  | .2 |
Subtotal |  |  |  | 26.7 |  |  | 2.8 |  |  | — |  |  | 23.9 |  |  | 26.7 |  |  | 1.8 |  |  | — |  |  | 24.9 |
Total other intangible assets | 493.8 |  |  | 72.8 |  |  | 6.2 |  |  | 414.8 |  |  | 317.8 |  |  | 54.7 |  |  | 6.2 |  |  | 256.9 |
Total goodwill and other intangible assets | $ | 1,153.4 |  |  | $ | 72.8 |  |  | $ | 36.4 |  |  | 1,044.2 |  |  | $ | 843.3 |  |  | $ | 54.7 |  |  | 6.2 |  |  | 782.4 |
Goodwill and other intangible assets attributed to non-controlling interests |  | (115.9) |  |  |  |  |  |  |  |  | (28.1) |
Goodwill and other intangible assets included in White Mountains’s common shareholders’ equity |  | $ | 928.3 |  |  |  |  |  |  |  |  | $ | 754.3 |

(1) As of June 30, 2021, NSM’s goodwill and intangible assets included $1.5 and $0.2 of the effect of foreign currency translation. As of December 31, 2020, NSM’s goodwill and intangible assets included $13.4 and $1.6 of the effect of foreign currency translation.
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The goodwill recognized for the entities shown above is attributed to expected future cash flows. The acquisition date fair values of other intangible assets with finite lives are estimated using income approach techniques, which use future expected cash flows to develop a discounted present value amount.
The multi-period-excess-earnings method estimates fair value using the present value of the incremental after-tax cash flows attributable solely to the other intangible asset over its remaining life. This approach was used to estimate the fair value of other intangible assets associated with the underwriting capacity, trade names, customer relationships and contracts and information technology.
The relief-from-royalty method was used to estimate fair value for other intangible assets that relate to rights that could be obtained via a license from a third-party owner. Under this method, the fair value is estimated using the present value of license fees avoided by owning rather than leasing the asset. This technique was used to estimate the fair value of domain names, certain trademarks and brand names.
The with-or-without method estimates the fair value of an other intangible asset that provides an incremental benefit. Under this method, the fair value of the other intangible asset is calculated by comparing the value of the entity with and without the other intangible asset. This approach was used to estimate the fair value of favorable lease terms.
The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for
acquisitions completed from January 1, 2020 through June 30, 2021:

$ in Millions |  |  |  |
Acquisition of subsidiary/ asset |  | Goodwill and Other intangible asset (1) |  | Acquisition Date
Kingsbridge |  | $ | 131.7 |  |  | April 7, 2020
Ark |  | $ | 292.5 |  |  | January 1, 2021
Other Operations |  | $ | 31.0 |  |  | Various

(1) Acquisition date fair values include the effect of adjustments during the measurement period and excludes the effect of foreign currency translation subsequent to the acquisition date.
On at least an annual basis beginning no later than the interim period included in the one-year anniversary of an acquisition, White Mountains evaluates goodwill and other intangible assets for potential impairment. Between annual evaluations, White Mountains considers changes in circumstances or events subsequent to the most recent evaluation that may indicate that an impairment may exist and, if necessary will perform an interim review for potential impairment.
On April 12, 2021, NSM sold Fresh Insurance’s motor business. In connection with the sale, White Mountains recognized a loss of $28.7 million during the three months ended March 31, 2021. See Note 19 — “Held for Sale and Discontinued Operations”. During the three months ended June 30, 2020, White Mountains recognized impairments of other intangible assets of $6.2 million. The impairments related to NSM’s write-off of intangible assets in its U.K. vertical. The impairments related to lower premium volumes, including due to the impact of the COVID-19 pandemic, and certain reorganization initiatives in the U.K. vertical. There were no other impairments of other intangible assets and no impairments of goodwill for the three and six months ended June 30, 2021 and 2020.
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The following tables present the change in goodwill and other intangible assets for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30,
|  | 2021 |  | 2020
Millions |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets
Beginning balance |  | $ | 613.4 |  |  | $ | 423.6 |  |  | $ | 1,037.0 |  |  | $ | 392.4 |  |  | $ | 254.4 |  |  | $ | 646.8 |
Acquisition of businesses |  | 15.8 |  | (1) | — |  |  | 15.8 |  |  | 125.1 |  | (2) | — |  |  | 125.1 |
Foreign currency translation |  | .2 |  |  | (.1) |  |  | .1 |  |  | .7 |  |  | .1 |  |  | .8 |
Impairments |  | — |  |  | — |  |  | — |  |  | — |  |  | (6.2) |  |  | (6.2) |
Amortization |  | — |  |  | (8.7) |  |  | (8.7) |  |  | — |  |  | (6.6) |  |  | (6.6) |
Ending balance |  | $ | 629.4 |  |  | $ | 414.8 |  |  | $ | 1,044.2 |  |  | $ | 518.2 |  |  | $ | 241.7 |  |  | $ | 759.9 |

(1) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Other Operations had not yet been finalized at June 30, 2021.
(2) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge had not yet been finalized at June 30, 2020.

|  | Six Months Ended June 30,
|  | 2021 |  | 2020
Millions |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets
Beginning balance |  | $ | 525.5 |  |  | $ | 256.9 |  |  | $ | 782.4 |  |  | $ | 394.7 |  |  | $ | 260.0 |  |  | $ | 654.7 |
Ark Transaction |  | 116.8 |  |  | 175.7 |  |  | 292.5 |  |  | — |  |  | — |  |  | — |
Acquisition of businesses |  | 15.8 |  | (3) | — |  |  | 15.8 |  |  | 125.1 |  | (4) | — |  |  | 125.1 |
Foreign currency translation |  | 1.7 |  |  | .1 |  |  | 1.8 |  |  | (1.8) |  |  | (.4) |  |  | (2.2) |
Impairments |  | — |  |  | — |  |  | — |  |  | — |  |  | (6.2) |  |  | (6.2) |
Loss on assets held for sale (1) |  | (30.2) |  |  | — |  |  | (30.2) |  |  | — |  |  | — |  |  | — |
Measurement period adjustments (2) |  | (.2) |  |  | — |  |  | (.2) |  |  | .2 |  |  | — |  |  | .2 |
Amortization |  | — |  |  | (17.9) |  |  | (17.9) |  |  | — |  |  | (11.7) |  |  | (11.7) |
Ending balance |  | $ | 629.4 |  |  | $ | 414.8 |  |  | $ | 1,044.2 |  |  | $ | 518.2 |  |  | $ | 241.7 |  |  | $ | 759.9 |

(1) Relates to the sale of NSM’s Fresh Insurance’s motor business recorded in the first quarter of 2021. This amount excludes $1.5 of net proceeds related to the sale.
(2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the six months ended June 30, 2021, adjustments primarily relate to the acquisition within the Other Operations segment.
(3) The relatives fair values of goodwill and other intangible assets recognized in connection with the acquisition within Other Operations had not yet been finalized at June 30, 2021.
(4) The relatives fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge had not yet been finalized at June 30, 2020.
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Note 5. Loss and Loss Adjustment Expense Reserves
Ark establishes loss and LAE reserves that are estimates of amounts needed to pay claims and related expenses in the future for insured events that have already occurred. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain.
Loss and LAE reserves typically comprise case reserves for claims reported and reserves for losses that have occurred but for which claims have not yet been reported, referred to as IBNR reserves. IBNR reserves include a provision for expected future development on case reserves. Case reserves are estimated based on the experience and knowledge of claims staff regarding the nature and potential cost of each claim and are adjusted as additional information becomes known or payments are made. IBNR reserves are typically derived by subtracting paid loss and LAE and case reserves from estimates of ultimate losses and LAE. Actuaries estimate ultimate loss and LAE using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made.
Ultimate loss and LAE are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate loss and LAE with respect to any line of business, past experience with respect to that line of business is the primary resource, but cannot be relied upon in isolation. Ark’s own experience, particularly claims development experience, such as trends in case reserves, payments on and closings of claims, as well as changes in business mix and coverage limits, is the most important information for estimating its reserves. Ultimate loss and LAE for major losses and catastrophes are estimated based on the known and expected exposures to the loss event, rather than simply relying on the extrapolation of reported and settled claims.
Uncertainties in estimating ultimate loss and LAE are magnified by the time lag between when a claim actually occurs and when it is reported and eventually settled. This time lag is sometimes referred to as the “claim-tail”. The claim-tail for most property coverages is typically short (usually a few days up to a few months). The claim-tail for liability/casualty coverages can be quite long as claims are often reported and ultimately paid or settled years after the related loss events occur. During the long claims reporting and settlement period, additional facts regarding coverages written in prior accident years, as well as about actual claims and trends may become known and, as a result, Ark may adjust its reserves. If management determines that an adjustment is appropriate, the adjustment is booked in the accounting period in which such determination is made. Accordingly, should reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted.
In determining ultimate loss and LAE, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. Because of the factors previously discussed, the process requires the use of informed judgment and is inherently uncertain.
Ark performs an actuarial review of its recorded reserves each quarter, using several generally accepted actuarial methods to evaluate its loss reserves, each of which has its own strengths and weaknesses. Management places more or less reliance on a particular method based on the facts and circumstances at the time the reserve estimates are made.
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The following table summarizes the loss and LAE reserve activity of Ark’s insurance and reinsurance subsidiaries for the three and six months ended June 30, 2021:

Millions |  | Three Months Ended June 30, 2021 |  | Six Months Ended June 30, 2021
Gross beginning balance |  | $ | 751.9 |  |  | $ | 696.0 |
Less: beginning reinsurance recoverable on unpaid losses |  | (447.5) |  |  | (433.4) |
Net loss and LAE reserves |  | 304.4 |  |  | 262.6 |
Loss and LAE incurred relating to: |  |  |  |
Current year losses |  | 61.6 |  |  | 127.1 |
Prior year losses |  | (9.0) |  |  | (8.5) |
Total incurred losses and LAE |  | 52.6 |  |  | 118.6 |
Foreign currency translation adjustment to loss and LAE reserves |  | (2.9) |  |  | (2.2) |
Loss and LAE paid relating to: |  |  |  |
Current year losses |  | (1.1) |  |  | (2.5) |
Prior year losses |  | (18.3) |  |  | (41.8) |
Total loss and LAE payments |  | (19.4) |  |  | (44.3) |
Net ending balance |  | 334.7 |  |  | 334.7 |
Plus: ending reinsurance recoverable on unpaid losses |  | 425.3 |  |  | 425.3 |
Gross ending balance |  | $ | 760.0 |  |  | $ | 760.0 |

Ark’s GAAP combined ratio in the second quarter and first six months of 2021 included $9.0 million (8 points) and $8.5 million (4 points) of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business.
See Note 10 — “Municipal Bond Guarantee Insurance” for loss and LAE reserve balances related to White Mountains financial guarantee business.
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Note 6. Third Party Reinsurance
In the normal course of business, Ark may seek to limit losses that may arise from catastrophes or other events by reinsuring certain risks with third party reinsurers. Ark remains liable for risks reinsured in the event that the reinsurer does not honor its obligations under reinsurance contracts. The following table summarizes the effects of reinsurance on written and earned premiums and on losses and LAE for Ark.

|  | Three Months Ended June 30, 2021 |  | Six Months Ended June 30, 2021 |  |
Millions |  |  |  |
Written premiums: |  |  |  |  |  |
Gross |  | $ | 328.1 |  |  | $ | 732.6 |  |  |
Ceded |  | (65.9) |  |  | (128.0) |  |  |
Net written premiums |  | $ | 262.2 |  |  | $ | 604.6 |  |  |
Earned premiums: |  |  |  |  |  |
Gross |  | $ | 174.9 |  |  | $ | 337.5 |  |  |
Ceded |  | (57.1) |  |  | (115.1) |  |  |
Net earned premiums |  | $ | 117.8 |  |  | $ | 222.4 |  |  |
Losses and LAE: |  |  |  |  |  |
Gross |  | $ | 63.6 |  |  | $ | 179.2 |  |  |
Ceded |  | (11.0) |  |  | (60.6) |  |  |
Net Losses and LAE |  | $ | 52.6 |  |  | $ | 118.6 |  |  |

As of June 30, 2021, Ark had $425.3 million and $6.0 million of reinsurance recoverables on unpaid and paid losses. As reinsurance contracts do not relieve Ark of its obligation to its policyholders, Ark seeks to reduce the credit risk associated with reinsurance balances by avoiding over-reliance on specific reinsurers through the application of concentration limits and thresholds. Ark is selective with its reinsurers, placing reinsurance with only those reinsurers having a strong financial condition. Ark monitors the financial strength of its reinsurers on an ongoing basis.
As of June 30, 2021, Ark’s reinsurance recoverables on unpaid losses of $425.3 million included $314.6 million related to TPC Providers, which are collateralized. Of the remaining $110.7 million of reinsurance recoverables on unpaid losses, 87.6% are from reinsurers with an A.M. Best Company, Inc (“A.M. Best”) rating of at least “A-” (Excellent, which is the fourth highest of 16 financial strength ratings), and an additional 7.5% are collateralized.
See Note 10 — “Municipal Bond Guarantee Insurance” for third-party reinsurance balances related to White Mountains financial guarantee business.
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Note 7. Debt
The following table presents White Mountains’s debt outstanding as of June 30, 2021 and December 31, 2020:

Millions |  | June 30, 2021 |  | Effective Rate | (1) |  | December 31, 2020 |  | Effective Rate | (1) |
Ark Alesco Notes, carrying value |  | $ | 30.0 |  |  |  |  | $ | — |  |  |  |
Ark Dekania Note, carrying value |  | 14.2 |  |  |  |  | — |  |  |  |
Ark Subordinated Notes, carrying value |  | 44.2 |  |  | 4.8% |  | — |  |  |  |
NSM Bank Facility |  | 276.6 |  |  | 7.6% | (2) |  | 277.4 |  |  | 7.5% | (2) |
Unamortized issuance cost |  | (7.2) |  |  |  |  | (6.1) |  |  |  |
NSM Bank Facility, carrying value |  | 269.4 |  |  |  |  | 271.3 |  |  |  |
Other NSM debt, carrying value |  | 1.3 |  |  | 3.5% |  | 1.3 |  |  | 2.5% |
Kudu Credit Facility |  | 102.0 |  |  | 5.6% |  | — |  |  |  |
Unamortized issuance cost |  | (7.5) |  |  |  |  | — |  |  |  |
Kudu Credit Facility, carrying value |  | 94.5 |  |  |  |  | — |  |  |  |
Kudu Bank Facility |  | — |  |  |  |  | 89.2 |  |  | 8.3% |
Unamortized issuance cost |  | — |  |  |  |  | (2.9) |  |  |  |
Kudu Bank Facility, carrying value |  | — |  |  |  |  | 86.3 |  |  |  |
Other Operations debt |  | 19.8 |  |  | 7.4% |  | 18.0 |  |  | 7.4% |
Unamortized issuance cost |  | (.4) |  |  |  |  | (.5) |  |  |  |
Other Operations, carrying value |  | 19.4 |  |  |  |  | 17.5 |  |  |  |
Total debt |  | $ | 428.8 |  |  |  |  | $ | 376.4 |  |  |  |

(1) Effective rate includes the effect of the amortization of debt issuance costs.
(2) NSM’s effective rate excludes the effect of the interest rate swap on the hedged portion of the debt. The weighted average interest rate for the quarter ended June 30, 2021 and December 31, 2020, excluding the effect of amortization of debt issuance costs, was 7.0% and 7.0%. The weighted average interest rate for the quarter ended June 30, 2021 and December 31, 2020 on the total NSM Bank Facility including both the effect of the amortization of debt issuance costs and the effect of the interest rate swap was 8.5% and 8.4%.
Ark Subordinated Notes
In March 2007, Ark issued $30.0 million face value of floating rate unsecured junior subordinated deferrable interest notes to Alesco Preferred Funding XII Ltd., Alesco Preferred Funding XIII Ltd. and Alesco Preferred Funding XIV Ltd (the “Ark Alesco Notes”) and a €12.0 million floating rate subordinated note to Dekania Europe CDO II plc (the “Ark Dekania Note”) (together, the “Ark Subordinated Notes”). The Alesco Notes, which mature in June 2037, accrue interest at a floating rate equal to the three-month U.S. LIBOR plus 4.6%. The Ark Dekania Note, which matures in June 2027, accrues interest at a floating rate equal to the three-month EURIBOR plus 4.6%. As of June 30, 2021, the Ark Alesco Notes had an outstanding balance of $30.0 million and the Ark Dekania Note had an outstanding balance of €12.0 million (approximately $14.2 million based upon the foreign exchange spot rate as of June 30, 2021).
Ark Stand By Letter of Credit Facility
Ark has a secured stand by letter of credit facility (the “Ark LOC Facility”) with three lenders, Lloyds Bank plc, National Westminster Bank plc and ING Bank N.V, London Branch to provide capital support for the Syndicates. As of June 30, 2021, the utilized level of the facility was $45.0 million, with the ability to increase up to $150.0 million, subject to formal approval by Lloyd’s. The Ark LOC Facility has a termination date of December 31, 2025. During the three and six months ended June 30, 2021, Ark did not borrow or make any repayments under the Ark LOC Facility.
The Ark LOC Facility, which provides funds at Lloyd’s, is secured by all property of the loan parties and contains various affirmative, negative and financial covenants that White Mountains considers to be customary for such borrowings, including a minimum tangible net worth covenant.
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NSM Bank Facility
NSM maintains a secured credit facility (the “NSM Bank Facility”) with Ares Capital Corporation. In both 2021 and 2020, NSM amended the terms of the facility. On April 7, 2020, NSM amended the NSM Bank Facility to increase the total commitment from $234.0 million, comprised of term loans of $224.0 million and a revolving credit loan commitment of $10.0 million, to $291.4 million, comprised of term loans of $276.4 million, including £42.5 million (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. In connection with the April 7, 2020 amendment, the reference rates for USD denominated borrowings increased. The USD-LIBOR rate floor increased to 1.25% and the margin over USD-LIBOR increased from a range of 4.25% to 4.75% to a range of 5.50% to 6.00%.
On June 2, 2021, NSM amended the NSM Bank Facility to reduce the margin over the reference interest rate for USD LIBOR loans from a range of 5.5% to 6.00% to a range of 4.50% to 5.00%, and reduce the margin over the reference rate for GBP loans from a range of 6.0% to 6.50% to a range of 5.00% to 5.50%. The amendment also increased the revolving credit loan commitment to $40.0 million and added a $50.0 million delayed-draw term loan commitment. The amendment also changed the reference interest rate for the GBP loan from GBP-LIBOR to SONIA. The maturity dates of the term loans and the revolving credit loans were not changed as part of the amendment. The term loans under the NSM Bank Facility mature on May 11, 2026, and the revolving loan matures on November 11, 2025. The reference interest rates under the NSM Bank Facility are generally subject to a 1.25% rate floor.
Under GAAP, if the terms of a debt instrument are amended, unless there is greater than 10% change in the expected discounted future cash flows of such instrument, the instrument’s carrying value does not change. White Mountains has determined that the impact of the 2021 and 2020 amendments to the NSM Bank Facility was less than 10% on the expected discounted future cash flows.
The following table presents the change in debt under the NSM Bank Facility for the three and six months ended June 30, 2021 and 2020:

NSM Bank Facility |  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Beginning balance |  | $ | 277.3 |  |  | $ | 220.7 |  |  | $ | 277.4 |  |  | $ | 221.3 |
Term loans |  |  |  |  |  |  |  |
Borrowings (1) |  | — |  |  | 52.4 |  |  | — |  |  | 52.4 |
Repayments |  | (.7) |  |  | — |  |  | (1.4) |  |  | (.6) |
Foreign currency translation |  | — |  |  | .3 |  |  | .6 |  |  | .3 |
Revolving credit loan |  |  |  |  |  |  |  |
Borrowings |  | — |  |  | — |  |  | — |  |  | — |
Repayments |  | — |  |  | — |  |  | — |  |  | — |
Ending balance |  | 276.6 |  |  | 273.4 |  |  | $ | 276.6 |  |  | $ | 273.4 |

(1) Borrowings for both the three and six months ended June 30, 2020 included $52.4 for the funding of the acquisition of Kingsbridge.
As of June 30, 2021, the term loans had an outstanding balance of $276.6 million, including £42.1 million (approximately $58.1 million based upon the foreign exchange spot rate as of June 30, 2021) 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. See Note 9 — “Derivatives”.
As of June 30, 2021, $146.8 million of the outstanding term loans were hedged by the swap and $129.8 million of the outstanding term loans were unhedged.
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The following table presents the NSM weighted average interest rate for the six months ended June 30, 2021 and 2020:

NSM Weighted Average Interest Rate |  | Six Months Ended June 30,
|  | 2021 |  | 2020
Millions |  | Weighted Average |  | Interest Expense (1) |  | Weighted Average Interest rate |  | Weighted Average |  | Interest Expense (1) |  | Weighted Average Interest rate
Term loan - hedged |  | $ | 147.4 |  |  | $ | 6.8 |  |  | 9.2 | % |  | $ | 148.5 |  |  | $ | 6.4 |  |  | 8.6 | %
Term loan - unhedged |  | 129.9 |  | 5.0 |  | 7.7 | % |  | 123.8 |  | 3.6 |  | 5.8 | %
Total NSM Facility |  | $ | 277.3 |  |  | $ | 11.8 |  |  | 8.5 | % |  | $ | 272.3 |  |  | $ | 10.0 |  |  | 7.3 | %

(1) Interest expense includes the amortization of debt issuance costs and the effect of the interest rate swap and excludes interest expense related to the Other NSM Debt.
The NSM Bank Facility is secured by all property of the loan parties and contains various affirmative, negative and financial covenants that White Mountains considers to be customary for such borrowings, including a maximum consolidated total leverage ratio covenant.
Other NSM Debt
NSM also has a secured term loan related to its U.K. vertical. As of June 30, 2021, the secured term loan had an outstanding balance of $1.4 million and a maturity date of December 31, 2022.
Kudu Credit Facility and Kudu Bank Facility
On December 23, 2019, Kudu entered into a secured credit facility with Monroe Capital Management Advisors, LLC (the “Kudu Bank Facility”). On March 23, 2021, Kudu replaced the Kudu Bank Facility and entered into a secured revolving credit facility (the “Kudu Credit Facility”) with Massachusetts Mutual Life Insurance Company to fund new investments and related transaction expenses. The maximum borrowing capacity of the Kudu Credit Facility is $300.0 million, which includes the initial advanced amount of $102.0 million. The Kudu Credit Facility matures on March 23, 2036. In connection with the replacement of the Kudu Bank Facility, Kudu recognized a total loss of $4.1 million, representing debt issuance costs and prepayment fees, which are included within interest expense for the year to date period ended June 30, 2021.
Interest on the Kudu Credit Facility accrues at a floating interest rate equal to the greater of the three-month USD-LIBOR and 0.25%, plus in each case, the applicable spread of 4.30%. The Kudu Credit Facility requires Kudu to maintain an interest reserve account, which is included in restricted cash. As of June 30, 2021, the interest reserve account is $4.0 million. The Kudu Credit Facility requires Kudu to maintain a ratio of outstanding balance to the sum of fair market value of participation contracts and cash held in certain accounts (the “LTV Percentage”) of less than 50% in years 0-3, 40% in years 4-6, 25% in years 7-8, 15% in years 9-10, and 0% thereafter. As of June 30, 2021, Kudu has a 23.2% LTV Percentage.
Kudu may borrow undrawn balances within the initial three year availability period, subject to customary terms and conditions, to the extent the amount borrowed under the Kudu Credit Facility does not exceed the borrowing base which is equal to 35% of the fair value of Kudu’s qualifying participation contracts. When considering White Mountains’s remaining equity commitment to Kudu, the available undrawn balance was $70.7 million as of June 30, 2021.
During the three months ended June 30, 2021, Kudu did not make any borrowings or repayments on the Kudu Credit Facility. During the six months ended June 30, 2021, Kudu borrowed $3.0 million and repaid the outstanding Kudu Bank Facility balance of $92.2 million. As of June 30, 2021, the Kudu Credit Facility had an undrawn balance of $198.0 million.
The Kudu Credit Facility is secured by all property of the loan parties and contains various affirmative and negative covenants that White Mountains considers to be customary for such borrowings.
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Other Operations Debt
As of June 30, 2021, debt in White Mountains’s Other Operations segment consisted of three 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 the three months ended June 30, 2021, White Mountains’s Other Operations segment had no borrowings and made repayments of $0.2 million on the term loans and $0.3 million on the revolving credit loan, under the first credit facility. During the six months ended June 30, 2021, White Mountains’s Other Operations segment had borrowings and repayments of $0.3 million on the revolving credit loan and made repayments of $0.8 million on the term loans, under the first credit facility. As of June 30, 2021, the first credit facility had an outstanding balance of $8.3 million.
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 the three and six months ended June 30, 2021, White Mountains’s Other Operations segment had no borrowings. During the three and six months ended June 30, 2021, White Mountains’s Other Operations made repayments of $0.2 million and $0.4 million on the term loans, under the second credit facility. As of June 30, 2021, the second credit facility had an outstanding balance of $8.5 million.
The third credit facility has a maximum borrowing capacity of $4.0 million, which is comprised of a revolving credit loan commitment, with a maturity date of October 26, 2021. During the three and six months ended June 30, 2021, White Mountains’s Other Operations segment had no borrowings and made repayments of $0.5 million, under the third credit facility. As of June 30, 2021, the third credit facility had an outstanding balance of $3.0 million.
Compliance
At June 30, 2021, White Mountains was in compliance in all material respects with the covenants under all of its debt instruments.
Note 8. Income Taxes
The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law and taxes are imposed, the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035, pursuant to the Bermuda Exempted Undertakings Tax Protection Act of 1966. The Company has subsidiaries and branches that operate in various other jurisdictions around the world that are subject to tax in the jurisdictions in which they operate. The jurisdictions in which the Company’s subsidiaries and branches are subject to tax are Ireland, Israel, Luxembourg, the United Kingdom and the United States.
White Mountains’s income tax expense related to pre-tax income from continuing operations for the three months ended June 30, 2021 represented an effective tax rate of 18.4%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by income generated in jurisdictions with lower tax rates than the United States partially offset by additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities. On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19.0% to 25.0% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective.
White Mountains’s income tax expense related to pre-tax income from continuing operations for the six months ended June 30, 2021 represented an effective tax rate of 86.0%. The effective tax rate was higher than the U.S. statutory rate of 21.0%, driven primarily by the additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities in relation to White Mountains’s pre-tax income in the first six months of 2021.
White Mountains’s income tax (expense) related to pre-tax income (loss) from continuing operations for the three and six months ended June 30, 2020 represented an effective tax rate of 18.2% and 4.2%. The effective tax rate was different from the U.S. statutory rate of 21.0%, driven primarily by income generated in jurisdictions with lower tax rates than the United States and state income taxes.
In arriving at the effective tax rate for the three and six months ended June 30, 2021 and 2020, White Mountains forecasted all income and expense items including the change in unrealized investment gains (losses) and realized investment gains (losses) for the years ending December 31, 2021 and 2020.
White Mountains records a valuation allowance against deferred tax assets if it becomes more likely than not that all or a portion of a deferred tax asset will not be realized. Changes in valuation allowances from period to period are included in income tax expense in the period of change. In determining whether or not a valuation allowance, or change therein, is warranted, White Mountains considers factors such as prior earnings history, expected future earnings, carryback and carryforward periods and strategies that if executed would result in the realization of a deferred tax asset.
With few exceptions, White Mountains is no longer subject to U.S. federal, state, or non-U.S. income tax examinations by tax authorities for years before 2015.
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Note 9. 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 June 30, 2021, the variable rate received by NSM under the swap agreement was 1.00%. Over the term of the swap, the notional amount decreases in accordance with the principal repayments NSM expects to make on its term loans.
As of June 30, 2021, $146.8 million of the outstanding term loans were hedged by the swap. For the three and six months ended June 30, 2021, the weighted average effective interest rate on the outstanding term loans that were hedged, including the effect of the amortization of debt issuance costs and the effect of the interest rate swap, was 9.2%.
NSM’s obligations under the swap are secured by the same collateral securing the NSM Bank Facility on a pari passu basis. NSM does not currently hold any collateral deposits from or provide any collateral deposits to the swap counterparty.
NSM evaluated the effectiveness of the swap to hedge its interest rate risk associated with its variable rate debt and concluded at the swap inception date that the swap was highly effective in hedging that risk. NSM evaluates the effectiveness of the hedging relationship on an ongoing basis.
For the three and six months ended June 30, 2021, White Mountains recognized net interest expense of $0.6 million and $1.3 million for the periodic net settlement payments on the swap. For the three and six months ended June 30, 2020, White Mountains recognized net interest expense of $0.7 million and $1.2 million for the periodic net settlement payments on the swap. As of June 30, 2021 and December 31, 2020, the estimated fair value of the swap and the accrual of the periodic net settlement payments recorded in other liabilities was $6.6 million and $8.2 million. There was no ineffectiveness in the hedge for the three and six months ended June 30, 2021 and 2020. For the three and six months ended June 30, 2021, the $0.6 million and $1.6 million change in the fair value of the swap is included within White Mountains’s accumulated other comprehensive income (loss). For the three and six months ended June 30, 2020, the $0.4 million and $(2.8) 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 GBP-LIBOR rate at the measurement date exceeds 1.25%, NSM will receive payments from the counterparty equal to the GBP-LIBOR rate, less the 1.25% cap rate. As of June 30, 2021, the GBP-LIBOR rate was 0.08%.
NSM accounts for the interest rate caps as derivatives at fair value, with changes in fair value recognized in current period earnings within interest expense. For the three and six months ended June 30, 2021 and June 30, 2020, White Mountains recognized a negligible amount related to the change in fair value on the interest rate caps within interest expense. As of June 30, 2021 and December 31, 2020, the estimated fair value of the caps recorded in other assets was less than $0.1 million.
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Note 10. Municipal Bond Guarantee Insurance
HG Global was established to fund the startup of BAM, a mutual municipal bond insurer. HG Global, together with its subsidiaries, provided the initial capitalization of BAM through the purchase of $503.0 million of BAM Surplus Notes.
Reinsurance Treaties
FLRT
BAM is a party to a first loss reinsurance treaty (“FLRT”) with HG Re under which HG Re provides first loss protection up to 15%-of-par outstanding on each municipal bond insured by BAM. For capital appreciation bonds, par is adjusted to the estimated equivalent par value for current interest paying bonds. In return, BAM cedes up to 60% of the risk premium charged for insuring the municipal bond, which is net of a ceding commission. The FLRT is a perpetual agreement, with an initial term through the end of 2022.
Fidus Re
BAM is party to two collateralized financial guarantee excess of loss reinsurance agreements that serve to increase BAM’s claims paying resources and are provided by Fidus Re, a Bermuda based special purpose insurer created in 2018 solely to provide reinsurance protection to BAM.
In the second quarter of 2018, Fidus Re was initially capitalized by the issuance of $100.0 million of insurance linked securities (the “Fidus Re 2018 Agreement”. The proceeds from issuance were placed in a collateral trust supporting Fidus Re’s obligations to BAM. The insurance linked securities were issued by Fidus Re with an initial term of 12 years and are callable five years after the date of issuance. Under the Fidus Re 2018 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $165.0 million on a portion of BAM’s financial guarantee portfolio (the “2018 Covered Portfolio”) up to a total reimbursement of $100.0 million. The Fidus Re 2018 Agreement does not provide coverage for losses in excess of $276.1 million. The 2018 Covered Portfolio consists of approximately 38% of BAM’s portfolio of financial guaranty policies issued through June 30, 2021.
In the first quarter of 2021, Fidus Re issued an additional $150.0 million of insurance linked securities (the “Fidus Re 2021 Agreement”) with an initial term of 12 years and are callable five years after the date of issuance. Under the Fidus Re 2021 Agreement, Fidus Re reinsures 90% of aggregate losses exceeding $135.0 million on a portion of BAM’s financial guarantee portfolio (the “2021 Covered Portfolio”) up to a total reimbursement of $150.0 million. The Fidus Re 2021 Agreement does not provide coverage for losses in excess of $301.7 million. The 2021 Covered Portfolio consists of approximately 39% of BAM’s portfolio of financial guaranty policies issued through June 30, 2021.
The Fidus Re Agreements are accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as they do not meet the risk transfer requirements necessary to be accounted for as reinsurance.
XOLT
In January 2020, BAM entered into an excess of loss reinsurance agreement (the “XOLT”) with HG Re. Under the XOLT, HG Re provides last dollar protection for exposures on municipal bonds insured by BAM in excess of NYDFS single issuer limits. The XOLT is subject to an aggregate limit equal to the lesser of $75.0 million or the assets held in the Supplemental Trust at any point in time. The agreement is accounted for using deposit accounting and any related financing expenses are recorded in general and administrative expenses as the agreement does not meet the risk transfer requirements necessary to be accounted for as reinsurance.
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Collateral Trusts
HG Re’s obligations under the FLRT are limited to the assets in two collateral trusts: a Regulation 114 Trust and a supplemental collateral trust (the “Supplemental Trust” and together with the Regulation 114 Trust, the “Collateral Trusts”). Losses required to be reimbursed under the FLRT are subject to an aggregate limit equal to the assets held in the Collateral Trusts at any point in time.
On a monthly basis, BAM deposits cash equal to ceded premiums, net of ceding commissions, due to HG Re under the FLRT directly into the Regulation 114 Trust. The Regulation 114 Trust target balance is equal to gross ceded unearned premiums and unpaid ceded loss and LAE expenses, if any. If, at the end of any quarter, the Regulation 114 Trust balance is below the target balance, funds will be withdrawn from the Supplemental Trust and deposited into the Regulation 114 Trust in an amount equal to the shortfall. If, at the end of any quarter, the Regulation 114 Trust balance is above 102% of the target balance, funds will be withdrawn from the Regulation 114 Trust and deposited into the Supplemental Trust. The Regulation 114 Trust balance as of June 30, 2021 and December 31, 2020 was $233.8 million and $222.8 million.
The Supplemental Trust target balance is $603.0 million, less the amount of cash and securities in the Regulation 114 Trust in excess of its target balance (the “Supplemental Trust Target Balance”). If, at the end of any quarter, the Supplemental Trust balance exceeds the Supplemental Trust Target Balance, such excess may be distributed to HG Re. The distribution will be made first as an assignment of accrued interest on the BAM Surplus Notes and second in cash and/or fixed income securities.
As the BAM Surplus Notes are repaid over time, the BAM Surplus Notes will be replaced in the Supplemental Trust by cash and fixed income securities. The Supplemental Trust balance as of June 30, 2021 and December 31, 2020 was $602.7 million and $604.3 million.
As of June 30, 2021 and December 31, 2020, the Collateral Trusts held assets of $836.4 million and $827.1 million, which included $442.3 million and $434.5 million of cash and investments, $388.2 million and $388.2 million of BAM Surplus Notes and $5.9 million and $4.4 million of interest receivable on the BAM Surplus Notes.
BAM Surplus Notes
Through 2024, the interest rate on the BAM Surplus Notes is a variable rate equal to the one-year U.S. Treasury rate plus 300 basis points, set annually. During 2021, the interest rate on the BAM Surplus Notes is 3.1%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. BAM is required to seek regulatory approval to pay interest and principal on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS.
In December 2020, BAM made a $30.1 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $21.5 million was a repayment of principal held in the Supplemental Trust, $0.2 million was a payment of accrued interest held inside the Supplemental Trust and $8.4 million was a payment of accrued interest held outside the Supplemental Trust.
In January 2020, BAM made a one-time $65.0 million cash payment of principal and interest on the BAM Surplus Notes held by HG Global. Of this payment, $47.9 million was a repayment of principal held in the Supplemental Trust, $0.9 million was a payment of accrued interest held inside the Supplemental Trust and $16.2 million was a payment of accrued interest held outside the Supplemental Trust.
During the three and six months ended June 30, 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest.
As of June 30, 2021 and December 31, 2020, the principal balance on the BAM Surplus Notes was $388.2 million and $388.2 million and total interest receivable on the BAM Surplus Notes was $161.8 million and $155.7 million.
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Insured Obligations and Premiums
The following table presents a schedule of BAM’s insured obligations as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
Contracts outstanding |  | 11,629 |  |  | 10,997 |
Remaining weighted average contract period outstanding (in years) |  | 10.6 |  | 10.7
Contractual debt service outstanding (in millions): |  |  |  |
Principal |  | $ | 81,574.5 |  |  | $ | 75,287.7 |
Interest |  | 37,871.2 |  |  | 36,448.8 |
Total debt service outstanding |  | $ | 119,445.7 |  |  | $ | 111,736.5 |
Gross unearned insurance premiums (in millions) |  | $ | 250.9 |  |  | $ | 237.5 |

The following table presents a schedule of BAM’s future premium revenues as of June 30, 2021:

Millions |  | June 30, 2021
July 1, 2021 - December 31, 2021 |  | $ | 12.1 |
January 1, 2022 - March 31, 2022 |  | 5.9 |
April 1, 2022 - June 30, 2022 |  | 5.8 |
July 1, 2022 - September 30, 2022 |  | 5.8 |
October 1, 2022 - December 31, 2022 |  | 5.7 |
Total 2022 |  | 23.2 |
2023 |  | 21.9 |
2024 |  | 20.3 |
2025 |  | 18.8 |
2026 |  | 17.4 |
2027 and thereafter |  | 137.2 |
Total gross unearned insurance premiums |  | $ | 250.9 |

The following table presents a schedule of written premiums and earned premiums included in White Mountains’s HG Global/BAM segment for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30, |  |  |  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020 |  |  |  |  |  | 2021 |  | 2020
Written premiums: |  |  |  |  |  |  |  |  |  |  |  |
Direct |  | $ | 13.8 |  |  | $ | 21.3 |  |  |  |  |  |  | $ | 21.8 |  |  | $ | 31.0 |
Assumed |  | — |  |  | .2 |  |  |  |  |  |  | 4.5 |  |  | .2 |
Gross written premiums |  | $ | 13.8 |  |  | $ | 21.5 |  |  |  |  |  |  | $ | 26.3 |  |  | $ | 31.2 |
Earned premiums: |  |  |  |  |  |  |  |  |  |  |  |
Direct |  | $ | 5.6 |  |  | $ | 4.7 |  |  |  |  |  |  | $ | 10.9 |  |  | $ | 9.2 |
Assumed |  | .9 |  |  | .9 |  |  |  |  |  |  | 2.0 |  |  | 1.8 |
Gross earned premiums |  | $ | 6.5 |  |  | $ | 5.6 |  |  |  |  |  |  | $ | 12.9 |  |  | $ | 11.0 |

In the second quarter of 2020, BAM assumed a municipal bond guarantee contract with a par value of $36.9 million through an endorsement to the facultative quota share reinsurance agreement.
In January 2021, BAM entered into a 100% facultative quota share reinsurance agreement under which it assumed a portfolio of municipal bond guarantee contracts with a par value of $0.8 billion.
None of the contracts assumed were non-performing and no loss reserves have been established for any of the contracts, either as of the transaction dates or as of June 30, 2021. The agreements, which cover future claims exposure only, meet the risk transfer criteria under ASC 944-20, Insurance Activities and accordingly have been accounted for as reinsurance.
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Note 11. Earnings Per Share
White Mountains calculates earnings per share using the two-class method, which allocates earnings between common shares and unvested restricted common shares. Both classes of shares participate equally in dividends and earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares.
The following table presents the Company’s computation of earnings per share from continuing operations for the three and six months ended June 30, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations”.

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
|  | 2021 |  | 2020 |  | 2021 |  | 2020
Basic and diluted earnings per share numerators (in millions): |  |  |  |  |  |  |  |
Net income (loss) attributable to White Mountains’s common shareholders |  | $ | 138.5 |  |  | $ | 115.4 |  |  | $ | 63.2 |  |  | $ | (13.4) |
Less: total income (loss) from discontinued operations, net of tax |  | — |  |  | (1.0) |  |  | 18.7 |  |  | (.1) |
Net income (loss) from continuing operations attributable to White Mountains’s common shareholders |  | $ | 138.5 |  |  | $ | 116.4 |  |  | $ | 44.5 |  |  | $ | (13.3) |
Allocation of (earnings) losses to participating restricted common shares (1) |  | (1.7) |  |  | (1.6) |  |  | (.5) |  |  | .1 |
Basic and diluted earnings (losses) per share numerators |  | $ | 136.8 |  |  | $ | 114.8 |  |  | $ | 44.0 |  |  | $ | (13.2) |
Basic earnings per share denominators (in thousands): |  |  |  |  |  |  |  |
Total average common shares outstanding during the period |  | 3,107.8 |  |  | 3,107.5 |  |  | 3,104.0 |  |  | 3,142.8 |
Average unvested restricted common shares(2) |  | (37.8) |  |  | (43.1) |  |  | (35.1) |  |  | (38.5) |
Basic earnings (losses) per share denominator |  | 3,070.0 |  |  | 3,064.4 |  |  | 3,068.9 |  |  | 3,104.3 |
Diluted earnings per share denominator (in thousands): |  |  |  |  |  |  |  |
Total average common shares outstanding during the period |  | 3,107.8 |  |  | 3,107.5 |  |  | 3,104.0 |  |  | 3,142.8 |
Average unvested restricted common shares (2) |  | (37.8) |  |  | (43.1) |  |  | (35.1) |  |  | (38.5) |
Diluted earnings (losses) per share denominator |  | 3,070.0 |  |  | 3,064.4 |  |  | 3,068.9 |  |  | 3,104.3 |
Basic and diluted earnings per share (in dollars) - continuing operations: |  |  |  |  |  |  |  |
Distributed earnings - dividends declared and paid |  | $ | — |  |  | $ | — |  |  | $ | 1.00 |  |  | $ | 1.00 |
Undistributed earnings (losses) |  | 44.56 |  |  | 37.46 |  |  | 13.32 |  |  | (5.25) |
Basic and diluted earnings (losses) per share |  | $ | 44.56 |  |  | $ | 37.46 |  |  | $ | 14.32 |  |  | $ | (4.25) |

(1) Restricted shares issued by White Mountains receive dividends, and therefore, are considered participating securities.
(2) Restricted shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans”.
The following table presents the undistributed net earnings (losses) from continuing operations for the three and six months ended June 30, 2021 and 2020. See Note 19 — “Held for Sale and Discontinued Operations”.

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Undistributed net earnings (losses) - continuing operations: |  |  |  |  |  |  |  |
Net loss attributable to White Mountains’s common shareholders, net of restricted common share amounts |  | $ | 136.8 |  |  | $ | 114.8 |  |  | $ | 44.0 |  |  | $ | (13.2) |
Dividends declared, net of restricted common share amounts (1) |  | — |  |  | — |  |  | (3.1) |  |  | (3.1) |
Total undistributed net earnings (losses), net of restricted common share amounts |  | $ | 136.8 |  |  | $ | 114.8 |  |  | $ | 40.9 |  |  | $ | (16.3) |

(1) Restricted shares issued by White Mountains receive dividends, and are therefore considered participating securities.
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Note 12. Employee Share-Based Incentive Compensation Plans
White Mountains’s Long-Term Incentive Plan (the “WTM Incentive Plan”) provides for grants of various types of share-based and non-share-based incentive awards to key employees of White Mountains. As of June 30, 2021, White Mountains’s share-based compensation incentive awards consist of performance shares and restricted shares.
Performance Shares
Performance shares are designed to reward employees for meeting company-wide performance targets. Performance shares are conditional grants of a specified maximum number of common shares or an equivalent amount of cash. Awards generally vest at the end of a three-year service period, are subject to the attainment of pre-specified performance goals, and are valued based on the market value of common shares at the time awards are paid. Performance shares earned under the WTM Incentive Plan are typically paid in cash but may be paid in common shares. Compensation expense is recognized for the vested portion of the awards over the related service periods. The level of payout ranges from zero to two times the number of shares initially granted, depending on White Mountains’s financial performance. Performance shares become payable at the conclusion of a performance cycle (typically 3 years) if pre-defined financial targets are met. The performance measures used for determining performance share payouts are growth in White Mountains’s adjusted book value per share and intrinsic value per share. Intrinsic value per share is generally calculated by adjusting adjusted book value per share for differences between the adjusted book value of certain assets and liabilities and White Mountains’s estimate of their underlying intrinsic values.
The following table presents the performance share activity for the three and six months ended June 30, 2021 and 2020 for performance shares granted under the WTM Incentive Plan:

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
|  | 2021 |  | 2020 |  | 2021 |  | 2020
Millions, except share amounts |  | Target Performance Shares Outstanding |  | Accrued Expense |  | Target Performance Shares Outstanding |  | Accrued Expense |  | Target Performance Shares Outstanding |  | Accrued Expense |  | Target Performance Shares Outstanding |  | Accrued Expense
Beginning of period |  | 40,784 |  |  | $ | 38.2 |  |  | 42,458 |  |  | $ | 9.8 |  |  | 42,458 |  |  | $ | 56.3 |  |  | 42,473 |  |  | $ | 43.7 |
Shares paid (1) |  | — |  |  | — |  |  | — |  |  | — |  |  | (14,117) |  |  | (34.6) |  |  | (14,070) |  |  | (27.7) |
New grants |  | 475 |  |  | — |  |  | — |  |  | — |  |  | 13,475 |  |  | — |  |  | 14,055 |  |  | — |
Forfeitures and cancellations (2) |  | (7) |  |  | (.2) |  |  | — |  |  | — |  |  | (564) |  |  | .2 |  |  | — |  |  | .4 |
Expense recognized |  | — |  |  | 7.7 |  |  | — |  |  | 6.0 |  |  | — |  |  | 23.8 |  |  | — |  |  | (.6) |
End of period |  | 41,252 |  |  | $ | 45.7 |  |  | 42,458 |  |  | $ | 15.8 |  |  | 41,252 |  |  | $ | 45.7 |  |  | 42,458 |  |  | $ | 15.8 |

(1) WTM performance share payments in 2021 for the 2018-2020 performance cycle, which were paid in cash in March 2021 at 200% of target. WTM performance share payments in 2020 for the 2017-2019 performance cycle, which were paid in cash in March 2020, ranged from 174% to 180% of target.
(2) Amounts include changes in assumed forfeitures, as required under GAAP.
During the three months ended June 30, 2021, White Mountains granted 475 performance shares for the 2021-2023 performance cycle. During the six months ended June 30, 2021, White Mountains granted 13,475 performance shares for the 2021-2023 performance cycle. During the six months ended June 30, 2020, White Mountains granted 14,055 performance shares for the 2020-2022 performance cycle.
All performance shares earned were settled in cash. If all the outstanding WTM performance shares had vested on June 30, 2021, the total additional compensation cost to be recognized would have been $33.4 million, based on accrual factors (common share price and payout assumptions) as of June 30, 2021.
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The following table presents performance shares outstanding and accrued expense for performance shares awarded under the WTM Incentive Plan as of June 30, 2021 for each performance cycle:

|  | Six Months Ended June 30, 2021
Millions, except share amounts |  | Target Performance Shares Outstanding |  | Accrued Expense
Performance cycle: |  |  |  |
2019 – 2021 |  | 14,850 |  |  | $ | 28.4 |
2020 – 2022 |  | 13,555 |  |  | 15.6 |
2021 – 2023 |  | 13,475 |  |  | 2.5 |
Sub-total |  | 41,880 |  |  | 46.5 |
Assumed forfeitures |  | (628) |  |  | (.8) |
June 30, 2021 |  | 41,252 |  |  | $ | 45.7 |

Restricted Shares
Restricted shares are grants of a specified number of common shares that generally vest at the end of a 34-month service period. The following table presents the unrecognized compensation cost associated with the outstanding restricted share awards for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
|  | 2021 |  | 2020 |  | 2021 |  | 2020
Millions, except share amounts |  | Restricted Shares |  | Unamortized Issue Date Fair Value |  | Restricted Shares |  | Unamortized Issue Date Fair Value |  | Restricted Shares |  | Unamortized Issue Date Fair Value |  | Restricted Shares |  | Unamortized Issue Date Fair Value
Non-vested, |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Beginning of period |  | 37,805 |  |  | $ | 26.2 |  |  | 43,105 |  |  | $ | 26.6 |  |  | 43,105 |  |  | $ | 15.2 |  |  | 43,395 |  |  | $ | 16.7 |
Issued |  | 475 |  |  | .5 |  |  | — |  |  | — |  |  | 13,475 |  |  | 16.1 |  |  | 14,055 |  |  | 15.1 |
Vested |  | — |  |  | — |  |  | — |  |  | — |  |  | (17,717) |  |  | — |  |  | (14,345) |  |  | — |
Forfeited |  | — |  |  | — |  |  | — |  |  | — |  |  | (583) |  |  | (.6) |  |  | — |  |  | — |
Expense recognized |  | — |  |  | (3.5) |  |  | — |  |  | (3.6) |  |  | — |  |  | (7.5) |  |  | — |  |  | (8.8) |
End of period |  | 38,280 |  |  | $ | 23.2 |  |  | 43,105 |  |  | $ | 23.0 |  |  | 38,280 |  |  | $ | 23.2 |  |  | 43,105 |  |  | $ | 23.0 |

During the three months ended June 30, 2021, White Mountains issued 475 restricted shares that vest on January 1, 2024. During the six months ended June 30, 2021, White Mountains issued 13,475 restricted shares that vest on January 1, 2024. During the six months ended June 30, 2020, White Mountains issued 14,055 restricted shares that vest on January 1, 2023. The unamortized issue date fair value as of June 30, 2021 is expected to be recognized ratably over the remaining vesting periods.
42

Note 13. Leases
White Mountains has entered into lease agreements, primarily for office space. These leases are classified as operating leases, with lease expense recognized on a straight-line basis over the term of the lease. Lease incentives, such as free rent or landlord reimbursements for leasehold improvements, are recognized at lease inception and amortized on a straight-line basis over the term of the lease. Lease expense and the amortization of leasehold improvements are recognized within general and administrative expenses. Lease payments related to options to extend or renew the lease term are excluded from the calculation of lease liabilities unless White Mountains is reasonably certain of exercising those options.
As of June 30, 2021 and December 31, 2020, the right of use (“ROU”) asset was $44.3 million and $37.6 million and lease liabilities were $47.3 million and $38.3 million.
The following table summarizes net lease expense recognized in White Mountains’s consolidated statement of operations for the three and six months ended June 30, 2021 and 2020:

Millions |  | Three Months Ended June 30, |  | Six Months Ended June 30,
Lease Cost |  | 2021 |  | 2020 |  | 2021 |  | 2020
Lease cost |  | $ | 2.6 |  |  | $ | 2.1 |  |  | $ | 4.5 |  |  | $ | 4.1 |
Less: sublease income |  | .1 |  |  | .1 |  |  | .2 |  |  | .2 |
Net lease cost |  | $ | 2.5 |  |  | $ | 2.0 |  |  | $ | 4.3 |  |  | $ | 3.9 |

The following table presents the contractual maturities of the lease liabilities associated with White Mountains’s operating lease agreements as of June 30, 2021:

Millions |  | As of June 30, 2021
Remainder of 2021 |  | $ | 4.0 |
2022 |  | 10.8 |
2023 |  | 9.8 |
2024 |  | 8.5 |
2025 |  | 6.7 |
Thereafter |  | 16.3 |
Total undiscounted lease payments |  | 56.1 |
Less: present value adjustment |  | 8.8 |
Operating lease liability |  | $ | 47.3 |

43

The following tables present lease related assets and liabilities by reportable segment as of June 30, 2021 and December 31, 2020:

|  | As of June 30, 2021
Millions |  | HG/BAM |  | Ark |  | NSM |  | Kudu |  | Other Operations |  | Total |  | Weighted Average Incremental Borrowing Rate (1)
ROU lease asset |  | $ | 8.5 |  |  | $ | 7.1 |  |  | $ | 14.0 |  |  | $ | 6.9 |  |  | $ | 7.8 |  |  | $ | 44.3 |  |  | 5.0%
Lease liability |  | $ | 9.2 |  |  | $ | 7.1 |  |  | $ | 15.3 |  |  | $ | 7.1 |  |  | $ | 8.6 |  |  | $ | 47.3 |  |

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.

|  | As of December 31, 2020
Millions |  | HG/BAM |  | NSM |  | Kudu |  | Other Operations |  | Total |  | Weighted Average Incremental Borrowing Rate (1)
ROU lease asset |  | $ | 10.1 |  |  | $ | 17.1 |  |  | $ | 2.0 |  |  | $ | 8.4 |  |  | $ | 37.6 |  |  | 4.6%
Lease liability |  | $ | 10.1 |  |  | $ | 17.1 |  |  | $ | 2.0 |  |  | $ | 9.1 |  |  | $ | 38.3 |  |

(1) The present value of the remaining lease payments was determined by discounting the lease payments using the incremental borrowing rate.
Note 14. 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 June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
$ in Millions |  | Non-controlling Percentage |  | Non-controlling Equity |  | Non-controlling Percentage |  | Non-controlling Equity
Non-controlling interests, excluding BAM |  |  |  |  |  |  |  |
HG Global |  | 3.1 | % |  | $ | 11.1 |  |  | 3.1 | % |  | $ | 13.5 |
Ark |  | 28.0 | % |  | 213.1 |  |  | — | % |  | — |
NSM |  | 3.4 | % |  | 15.9 |  |  | 3.4 | % |  | 17.0 |
Kudu |  | .7 | % |  | 2.5 |  |  | .7 | % |  | 2.3 |
Other |  | various |  | 12.4 |  |  | various |  | 2.4 |
Total, excluding BAM |  |  |  | 255.0 |  |  |  |  | 35.2 |
BAM |  | 100.0 | % |  | (125.2) |  |  | 100.0 | % |  | (123.3) |
Total non-controlling interests |  |  |  | $ | 129.8 |  |  |  |  | $ | (88.1) |

44

Note 15. Segment Information
As of June 30, 2021, White Mountains conducted its operations through five segments: (1) HG Global/BAM, (2) Ark, (3) NSM, (4) Kudu and (5) Other Operations. A discussion of White Mountains’s consolidated investment operations is included after the discussion of operations by segment.
As a result of the Ark Transaction, White Mountains began consolidating Ark in its financial statements as of January 1, 2021.
White Mountains has made its segment determination based on consideration of the following criteria: (i) the nature of the business activities of each of the Company’s subsidiaries and affiliates; (ii) the manner in which the Company’s subsidiaries and affiliates are organized; (iii) the existence of primary managers responsible for specific subsidiaries and affiliates; and (iv) the organization of information provided to the chief operating decision makers and the Board of Directors. Significant intercompany transactions among White Mountains’s segments have been eliminated herein.
The following tables present the financial information for White Mountains’s segments:

Millions |  | HG Global/ BAM |  | Ark |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Three Months Ended June 30, 2021 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Earned insurance premiums |  | $ | 6.5 |  |  | $ | 117.8 |  |  | $ | — |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 124.3 |
Net investment income |  | 4.3 |  |  | .4 |  |  | — |  |  | 8.4 |  |  |  |  | 4.0 |  |  | 17.1 |
Net realized and unrealized investment gains |  | 6.3 |  |  | 8.9 |  |  | — |  |  | 27.8 |  |  |  |  | 16.6 |  |  | 59.6 |
Net realized and unrealized investment losses from investment in MediaAlpha |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 113.0 |  |  | 113.0 |
Commission revenues |  | — |  |  | — |  |  | 68.0 |  |  | — |  |  |  |  | 2.3 |  |  | 70.3 |
Other revenue |  | .3 |  |  | 3.4 |  |  | 16.3 |  |  | — |  |  |  |  | 22.4 |  |  | 42.4 |
Total revenues |  | 17.4 |  |  | 130.5 |  |  | 84.3 |  |  | 36.2 |  |  |  |  | 158.3 |  |  | 426.7 |
Loss and loss adjustment expenses |  | — |  |  | 52.6 |  |  | — |  |  | — |  |  |  |  | — |  |  | 52.6 |
Insurance acquisition expenses |  | 1.6 |  |  | 34.0 |  |  | — |  |  | — |  |  |  |  | — |  |  | 35.6 |
Cost of sales |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 17.9 |  |  | 17.9 |
General and administrative expenses |  | 13.9 |  |  | 24.8 |  |  | 47.3 |  |  | 3.2 |  |  |  |  | 29.5 |  |  | 118.7 |
Broker commission expense |  | — |  |  | — |  |  | 21.6 |  |  | — |  |  |  |  | — |  |  | 21.6 |
Change in fair value of contingent consideration liabilities |  | — |  |  | — |  |  | .2 |  |  | — |  |  |  |  | — |  |  | .2 |
Amortization of other intangible assets |  | — |  |  | — |  |  | 8.2 |  |  | .1 |  |  |  |  | .4 |  |  | 8.7 |
Interest expense |  | — |  |  | 1.3 |  |  | 5.9 |  |  | 1.5 |  |  |  |  | .4 |  |  | 9.1 |
Total expenses |  | 15.5 |  |  | 112.7 |  |  | 83.2 |  |  | 4.8 |  |  |  |  | 48.2 |  |  | 264.4 |
Pre-tax income |  | $ | 1.9 |  |  | $ | 17.8 |  |  | $ | 1.1 |  |  | $ | 31.4 |  |  |  |  | $ | 110.1 |  |  | $ | 162.3 |

45

Millions |  | HG Global/ BAM |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Three Months Ended June 30, 2020 |  |  |  |  |  |  |  |  |  |  |  |
Earned insurance premiums |  | $ | 5.6 |  |  | $ | — |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 5.6 |
Net investment income |  | 4.9 |  |  | — |  |  | 5.6 |  |  |  |  | 9.1 |  |  | 19.6 |
Net realized and unrealized investment gains |  | 14.4 |  |  | — |  |  | 16.5 |  |  |  |  | 107.0 |  |  | 137.9 |
Net unrealized investment gains from investment in MediaAlpha |  | — |  |  | — |  |  | — |  |  |  |  | 15.0 |  |  | 15.0 |
Commission revenues |  | — |  |  | 63.0 |  |  | — |  |  |  |  | 1.9 |  |  | 64.9 |
Other revenue |  | 1.2 |  |  | 13.1 |  |  | — |  |  |  |  | 2.3 |  |  | 16.6 |
Total revenues |  | 26.1 |  |  | 76.1 |  |  | 22.1 |  |  |  |  | 135.3 |  |  | 259.6 |
Insurance acquisition expenses |  | 2.1 |  |  | — |  |  | — |  |  |  |  | — |  |  | 2.1 |
Cost of sales |  | — |  |  | — |  |  | — |  |  |  |  | 2.2 |  |  | 2.2 |
General and administrative expenses |  | 12.7 |  |  | 48.5 |  |  | 2.8 |  |  |  |  | 25.3 |  |  | 89.3 |
Broker commission expense |  | — |  |  | 21.0 |  |  | — |  |  |  |  | — |  |  | 21.0 |
Change in fair value of contingent consideration liabilities |  | — |  |  | (1.7) |  |  | — |  |  |  |  | — |  |  | (1.7) |
Amortization of other intangible assets |  | — |  |  | 6.3 |  |  | .1 |  |  |  |  | .2 |  |  | 6.6 |
Interest expense |  | — |  |  | 5.7 |  |  | 1.5 |  |  |  |  | .2 |  |  | 7.4 |
Total expenses |  | 14.8 |  |  | 79.8 |  |  | 4.4 |  |  |  |  | 27.9 |  |  | 126.9 |
Pre-tax income (loss) |  | $ | 11.3 |  |  | $ | (3.7) |  |  | $ | 17.7 |  |  |  |  | $ | 107.4 |  |  | $ | 132.7 |

Millions |  | HG Global/ BAM |  | Ark |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Six Months Ended June 30, 2021 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Earned insurance premiums |  | $ | 12.9 |  |  | $ | 222.4 |  |  | $ | — |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 235.3 |
Net investment income |  | 8.8 |  |  | 1.2 |  |  | — |  |  | 16.6 |  |  |  |  | 11.1 |  |  | 37.7 |
Net realized and unrealized investment (losses) gains |  | (11.6) |  |  | 10.0 |  |  | — |  |  | 43.6 |  |  |  |  | 18.7 |  |  | 60.7 |
Net realized and unrealized investment losses from investment in MediaAlpha |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 71.3 |  |  | 71.3 |
Commission revenues |  | — |  |  | — |  |  | 127.6 |  |  | — |  |  |  |  | 4.6 |  |  | 132.2 |
Other revenue |  | .6 |  |  | 6.0 |  |  | 31.5 |  |  | .1 |  |  |  |  | 29.5 |  |  | 67.7 |
Total revenues |  | 10.7 |  |  | 239.6 |  |  | 159.1 |  |  | 60.3 |  |  |  |  | 135.2 |  |  | 604.9 |
Loss and loss adjustment expenses |  | — |  |  | 118.6 |  |  | — |  |  | — |  |  |  |  | — |  |  | 118.6 |
Insurance acquisition expenses |  | 3.5 |  |  | 70.7 |  |  | — |  |  | — |  |  |  |  | — |  |  | 74.2 |
Cost of sales |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 21.9 |  |  | 21.9 |
General and administrative expenses |  | 30.3 |  |  | 62.6 |  |  | 93.3 |  |  | 5.7 |  |  |  |  | 65.2 |  |  | 257.1 |
Broker commission expense |  | — |  |  | — |  |  | 40.5 |  |  | — |  |  |  |  | — |  |  | 40.5 |
Change in fair value of contingent consideration liabilities |  | — |  |  | — |  |  | .2 |  |  | — |  |  |  |  | — |  |  | .2 |
Amortization of other intangible assets |  | — |  |  | — |  |  | 16.8 |  |  | .2 |  |  |  |  | .9 |  |  | 17.9 |
Loss on assets held for sale |  | — |  |  | — |  |  | 28.7 |  |  | — |  |  |  |  | — |  |  | 28.7 |
Interest expense |  | — |  |  | 2.4 |  |  | 11.8 |  |  | 7.3 |  |  |  |  | .7 |  |  | 22.2 |
Total expenses |  | 33.8 |  |  | 254.3 |  |  | 191.3 |  |  | 13.2 |  |  |  |  | 88.7 |  |  | 581.3 |
Pre-tax (loss) income |  | $ | (23.1) |  |  | $ | (14.7) |  |  | $ | (32.2) |  |  | $ | 47.1 |  |  |  |  | $ | 46.5 |  |  | $ | 23.6 |

46

Millions |  | HG Global/ BAM |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Six Months Ended June 30, 2020 |  |  |  |  |  |  |  |  |  |  |  |
Earned insurance premiums |  | $ | 11.0 |  |  | $ | — |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 11.0 |
Net investment income |  | 10.4 |  |  | — |  |  | 12.9 |  |  |  |  | 19.2 |  |  | 42.5 |
Net realized and unrealized investment gains (losses) |  | 20.5 |  |  | — |  |  | (8.3) |  |  |  |  | (61.0) |  |  | (48.8) |
Net unrealized investment gains from investment in MediaAlpha |  | — |  |  | — |  |  | — |  |  |  |  | 45.0 |  |  | 45.0 |
Commission revenues |  | — |  |  | 116.0 |  |  | — |  |  |  |  | 4.0 |  |  | 120.0 |
Other revenue |  | 1.7 |  |  | 25.1 |  |  | .1 |  |  |  |  | 3.8 |  |  | 30.7 |
Total revenues |  | 43.6 |  |  | 141.1 |  |  | 4.7 |  |  |  |  | 11.0 |  |  | 200.4 |
Insurance acquisition expenses |  | 3.8 |  |  | — |  |  | — |  |  |  |  | — |  |  | 3.8 |
Cost of sales |  | — |  |  | — |  |  | — |  |  |  |  | 4.2 |  |  | 4.2 |
General and administrative expenses |  | 27.4 |  |  | 88.1 |  |  | 5.3 |  |  |  |  | 42.8 |  |  | 163.6 |
Broker commission expense |  | — |  |  | 39.3 |  |  | — |  |  |  |  | — |  |  | 39.3 |
Change in fair value of contingent consideration liabilities |  | — |  |  | (2.3) |  |  | — |  |  |  |  | — |  |  | (2.3) |
Amortization of other intangible assets |  | — |  |  | 11.1 |  |  | .2 |  |  |  |  | .4 |  |  | 11.7 |
Interest expense |  | — |  |  | 10.0 |  |  | 2.9 |  |  |  |  | .5 |  |  | 13.4 |
Total expenses |  | 31.2 |  |  | 146.2 |  |  | 8.4 |  |  |  |  | 47.9 |  |  | 233.7 |
Pre-tax income (loss) |  | $ | 12.4 |  |  | $ | (5.1) |  |  | $ | (3.7) |  |  |  |  | $ | (36.9) |  |  | $ | (33.3) |

In compliance with ASC 606, Revenues from Contracts with Customers, the following tables present White Mountains’s total revenues by revenue source for the three and six months ended June 30, 2021 and 2020:

Millions |  | HG Global/BAM |  | Ark |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Three Months Ended June 30, 2021 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Commission and other revenue |  |  |  |  |  |  |  |  |  |  |  |  |  |
Specialty Transportation |  | $ | — |  |  | $ | — |  |  | $ | 26.5 |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 26.5 |
Real Estate |  | — |  |  | — |  |  | 9.3 |  |  | — |  |  |  |  | — |  |  | 9.3 |
Social Services |  | — |  |  | — |  |  | 9.3 |  |  | — |  |  |  |  | — |  |  | 9.3 |
Pet |  | — |  |  | — |  |  | 18.5 |  |  | — |  |  |  |  | — |  |  | 18.5 |
United Kingdom |  | — |  |  | — |  |  | 13.8 |  |  | — |  |  |  |  | — |  |  | 13.8 |
Other |  | — |  |  | — |  |  | 6.9 |  |  | — |  |  |  |  | 2.3 |  |  | 9.2 |
Total commission and other revenue |  | — |  |  | — |  |  | 84.3 |  |  | — |  |  |  |  | 2.3 |  |  | 86.6 |
Product and service revenues |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 22.8 |  |  | 22.8 |
Revenues from contracts with customers |  | — |  |  | — |  |  | 84.3 |  |  | — |  |  |  |  | 25.1 |  |  | 109.4 |
Other (1) |  | 17.4 |  |  | 130.5 |  |  | — |  |  | 36.2 |  |  |  |  | 133.2 |  |  | 317.3 |
Total revenues |  | $ | 17.4 |  |  | $ | 130.5 |  |  | $ | 84.3 |  |  | $ | 36.2 |  |  |  |  | $ | 158.3 |  |  | $ | 426.7 |

(1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.
47

Millions |  | HG Global/BAM |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Three Months Ended June 30, 2020 |  |  |  |  |  |  |  |  |  |  |  |
Commission and other revenue |  |  |  |  |  |  |  |  |  |  |  |
Specialty Transportation |  | $ | — |  |  | $ | 23.8 |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 23.8 |
Real Estate |  | — |  |  | 15.4 |  |  | — |  |  |  |  | — |  |  | 15.4 |
Social Services |  | — |  |  | 7.3 |  |  | — |  |  |  |  | — |  |  | 7.3 |
Pet |  | — |  |  | 13.2 |  |  | — |  |  |  |  | — |  |  | 13.2 |
United Kingdom |  | — |  |  | 12.4 |  |  | — |  |  |  |  | — |  |  | 12.4 |
Other |  | — |  |  | 4.0 |  |  | — |  |  |  |  | 1.8 |  |  | 5.8 |
Total commission and other revenue |  | — |  |  | 76.1 |  |  | — |  |  |  |  | 1.8 |  |  | 77.9 |
Product revenues |  | — |  |  | — |  |  | — |  |  |  |  | 2.3 |  |  | 2.3 |
Revenues from contracts with customers |  | — |  |  | 76.1 |  |  | — |  |  |  |  | 4.1 |  |  | 80.2 |
Other (1) |  | 26.1 |  |  | — |  |  | 22.1 |  |  |  |  | 131.2 |  |  | 179.4 |
Total revenues |  | $ | 26.1 |  |  | $ | 76.1 |  |  | $ | 22.1 |  |  |  |  | $ | 135.3 |  |  | $ | 259.6 |

(1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.

Millions |  | HG Global/BAM |  | Ark |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Six Months Ended June 30, 2021 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Commission and other revenue |  |  |  |  |  |  |  |  |  |  |  |  |  |
Specialty Transportation |  | $ | — |  |  | $ | — |  |  | $ | 47.3 |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 47.3 |
Real Estate |  | — |  |  | — |  |  | 19.0 |  |  | — |  |  |  |  | — |  |  | 19.0 |
Social Services |  | — |  |  | — |  |  | 16.0 |  |  | — |  |  |  |  | — |  |  | 16.0 |
Pet |  | — |  |  | — |  |  | 35.7 |  |  | — |  |  |  |  | — |  |  | 35.7 |
United Kingdom |  | — |  |  | — |  |  | 26.9 |  |  | — |  |  |  |  | — |  |  | 26.9 |
Other |  | — |  |  | — |  |  | 14.2 |  |  | — |  |  |  |  | 4.6 |  |  | 18.8 |
Total commission and other revenue |  | — |  |  | — |  |  | 159.1 |  |  | — |  |  |  |  | 4.6 |  |  | 163.7 |
Product and service revenues |  | — |  |  | — |  |  | — |  |  | — |  |  |  |  | 29.3 |  |  | 29.3 |
Revenues from contracts with customers |  | — |  |  | — |  |  | 159.1 |  |  | — |  |  |  |  | 33.9 |  |  | 193.0 |
Other (1) |  | 10.7 |  |  | 239.6 |  |  | — |  |  | 60.3 |  |  |  |  | 101.3 |  |  | 411.9 |
Total revenues |  | $ | 10.7 |  |  | $ | 239.6 |  |  | $ | 159.1 |  |  | $ | 60.3 |  |  |  |  | $ | 135.2 |  |  | $ | 604.9 |

1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.
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Millions |  | HG Global/BAM |  | NSM |  | Kudu |  |  |  | Other Operations |  | Total
Six Months Ended June 30, 2020 |  |  |  |  |  |  |  |  |  |  |  |
Commission and other revenue |  |  |  |  |  |  |  |  |  |  |  |
Specialty Transportation |  | $ | — |  |  | $ | 44.2 |  |  | $ | — |  |  |  |  | $ | — |  |  | $ | 44.2 |
Real Estate |  | — |  |  | 26.7 |  |  | — |  |  |  |  | — |  |  | 26.7 |
Social Services |  | — |  |  | 13.6 |  |  | — |  |  |  |  | — |  |  | 13.6 |
Pet |  | — |  |  | 25.1 |  |  | — |  |  |  |  | — |  |  | 25.1 |
United Kingdom (2) |  | — |  |  | 22.4 |  |  | — |  |  |  |  | — |  |  | 22.4 |
Other |  | — |  |  | 9.1 |  |  | — |  |  |  |  | 4.0 |  |  | 13.1 |
Total commission and other revenue |  | — |  |  | 141.1 |  |  | — |  |  |  |  | 4.0 |  |  | 145.1 |
Product revenues |  | — |  |  | — |  |  | — |  |  |  |  | 4.4 |  |  | 4.4 |
Revenues from contracts with customers |  | — |  |  | 141.1 |  |  | — |  |  |  |  | 8.4 |  |  | 149.5 |
Other (1) |  | 43.6 |  |  | — |  |  | 4.7 |  |  |  |  | 2.6 |  |  | 50.9 |
Total revenues |  | $ | 43.6 |  |  | $ | 141.1 |  |  | $ | 4.7 |  |  |  |  | $ | 11.0 |  |  | $ | 200.4 |

(1) Other consists of premiums, investment income, investment gains and losses and other revenues outside the scope of ASC 606, Revenues from Contracts with Customers.
(2) Includes the results of Kingsbridge from April 7, 2020, the date of the Kingsbridge transaction.
Note 16. Equity-Method Eligible Investments
White Mountains’s equity method eligible investments include White Mountains’s investment in MediaAlpha, certain other unconsolidated entities, including Kudu’s Participation Contracts, private equity funds and hedge funds in which White Mountains has the ability to exert significant influence over the investee’s operating and financial policies.
The following table presents the basic ownership interests and carrying values of White Mountains’s equity method eligible investments as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
Millions |  | Basic Ownership Interest |  | Carrying Value |  | Basic Ownership Interest |  | Carrying Value
Investment in MediaAlpha |  | 28.4 | % |  | $ | 713.2 |  |  | 35.0 | % |  | $ | 802.2 |
Kudu Participation Contracts |  | 3.2 - 32.7% |  | 455.5 |  |  | 3.2 - 35.0% |  | 400.6 |
PassportCard/DavidShield |  | 53.8 | % |  | 95.0 |  |  | 53.8 | % |  | 95.0 |
Elementum Holdings, L.P. |  | 29.7 | % |  | 56.7 |  |  | 28.9 | % |  | 55.1 |
Other equity method eligible investments, at fair value |  | Under 50.0% |  | 100.9 |  |  | Under 50.0% |  | 132.2 |
Other equity method eligible investments, at fair value |  | 50.0% and over |  | 16.6 |  |  | 50.0% and over |  | 15.2 |

For the three and six months ended June 30, 2021, White Mountains received dividend and income distributions from equity method eligible investments of $11.0 million, and $24.7 million, which were recorded within net investment income in the consolidated statement of operations. For the three and six months ended June 30, 2020, White Mountains received dividend and income distributions from equity method eligible investments of $10.0 million, and $21.4 million, which were recorded within net investment income in the consolidated statement of operations.
Subsequent to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha is accounted for at fair value based on the publicly traded share price of MediaAlpha’s common stock and White Mountains presents its investment in MediaAlpha as a separate line item on the balance sheet. See Note 2 — “Significant Transactions”. For the six months ended June 30, 2021 and 2020, MediaAlpha was considered a significant subsidiary.
49

The following tables present summarized financial information for MediaAlpha as of June 30, 2021 and 2020:

Millions |  | June 30, 2021 |  | December 31, 2020 |  |
Balance sheet data: |  |  |  |  |  |
Total assets |  | $ | 236.4 |  |  | $ | 210.3 |  |  |
Total liabilities |  | $ | 315.6 |  |  | $ | 315.5 |  |  |

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Income statement data: |  |  |  |  |  |  |  |
Total revenues |  | $ | 157.4 |  |  | $ | 123.6 |  |  | $ | 330.9 |  |  | $ | 243.1 |
Total expenses |  | $ | 157.8 |  |  | $ | 113.5 |  |  | $ | 331.1 |  |  | $ | 224.1 |
Net income |  | $ | (.4) |  |  | $ | 10.1 |  |  | $ | (.2) |  |  | $ | 19.0 |

Note 17. Fair Value of Financial Instruments
White Mountains records its financial instruments at fair value with the exception of debt obligations, which are recorded as debt at face value less unamortized original issue discount. See Note 7 — “Debt”.
The following table presents the fair value and carrying value of these financial instruments as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021 |  | December 31, 2020
Millions |  | Fair Value |  | Carrying Value |  | Fair Value |  | Carrying Value
Ark Subordinated Notes |  | $ | 41.5 |  |  | $ | 44.2 |  |  | $ | — |  |  | $ | — |
NSM Bank Facility |  | $ | 265.9 |  |  | $ | 269.4 |  |  | $ | 279.3 |  |  | $ | 271.3 |
Other NSM debt |  | $ | 1.3 |  |  | $ | 1.3 |  |  | $ | 1.3 |  |  | $ | 1.3 |
Kudu Credit Facility |  | $ | 109.3 |  |  | $ | 94.5 |  |  | $ | — |  |  | $ | — |
Kudu Bank Facility |  | $ | — |  |  | $ | — |  |  | $ | 89.3 |  |  | $ | 86.3 |
Other Operations debt |  | $ | 21.0 |  |  | $ | 19.4 |  |  | $ | 18.8 |  |  | $ | 17.5 |

The fair value estimates for the Ark Subordinated Notes, NSM Bank Facility, the Other NSM debt, the Kudu Credit Facility, the Kudu Bank Facility and Other Operations debt have been determined based on a discounted cash flow approach and are considered to be Level 3 measurements.
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Note 18. Commitments and Contingencies
Legal Contingencies
White Mountains is subject to litigation and arbitration in the normal course of business. White Mountains considers the requirements of ASC 450 when evaluating its exposure to litigation and arbitration. ASC 450 requires that accruals be established for litigation and arbitration if it is probable that a loss has been incurred and it can be reasonably estimated. ASC 450 also requires that litigation and arbitration be disclosed if it is probable that a loss has been incurred or if there is a reasonable possibility that a loss may have been incurred. White Mountains does not have any current litigation that may have a material adverse effect on White Mountains’s financial condition, results of operations or cash flows.
The following description presents significant legal contingencies, ongoing non-claims related litigation or arbitration as of June 30, 2021:
Esurance
On October 7, 2011, the Company completed the sale of its Esurance Holdings, Inc. and its subsidiaries and Answer Financial Inc. and its subsidiaries (collectively, “Esurance”) to The Allstate Corporation (“Allstate”) pursuant to a Stock Purchase Agreement dated as of May 17, 2011. Subject to specified thresholds and limits, the Company remains contingently liable to Allstate for specified matters related to the pre-closing period, including (a) losses of Esurance arising from extra-contractual claims and claims in excess of policy limits, (b) certain corporate reorganizations effected to remove entities from Esurance that were not being sold in the transaction, and (c) certain tax matters, including certain net operating losses being less than stated levels.
Sirius Group Tax Contingency
In the first quarter of 2021, White Mountains recorded a $17.6 million gain within discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius International Insurance Group, Ltd. (“Sirius Group”) in 2016. The liability related to certain interest deductions claimed by Sirius Group that had been disputed by the Swedish Tax Agency (STA). In April 2021, the STA informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal (and that the interest deductions should not be disallowed). In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor.
Note 19. Held for Sale and Discontinued Operations
Sirius Group
As of December 31, 2020, White Mountains recorded a liability of $18.7 million, related to the tax indemnification provided in connection with the sale of Sirius Group in 2016. For the six months ended June 30, 2021, White Mountains recorded a gain of $17.6 million in discontinued operations to reverse the liability accrued as of December 31, 2020 and $1.1 million gain related to foreign currency translation. See Note 18 — “Commitments and Contingencies”.
NSM
On April 12, 2021, NSM completed the sale of the Fresh Insurance motor business for net proceeds of £1.1 million (approximately $1.5 million based upon the foreign exchange spot rate as of the transaction date). The assets and liabilities included in the transaction, were measured at their estimated fair values, net of disposal and classified as held for sale at March 31, 2021. However, the transaction did not meet the criteria to be classified as discontinued operations. In the first quarter of 2021, NSM recorded a loss of $28.7 million related to the sale.
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Earnings Per Share from Discontinued Operations
White Mountains calculates earnings per share using the two-class method, which allocates earnings between common and unvested restricted common shares. Both classes of shares participate equally in earnings on a per share basis. Basic earnings per share amounts are based on the weighted average number of common shares outstanding adjusted for unvested restricted common shares. Diluted earnings per share amounts are also impacted by the net effect of potentially dilutive common shares outstanding.
The following table presents the Company’s computation of earnings per share for discontinued operations for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
|  | 2021 |  | 2020 |  | 2021 |  | 2020
Basic and diluted earnings per share numerators (in millions): |  |  |  |  |  |  |  |
Net income (loss) attributable to White Mountains’s common shareholders |  | $ | 138.5 |  |  | $ | 115.4 |  |  | $ | 63.2 |  |  | $ | (13.4) |
Less: total income (loss) from continuing operations, net of tax |  | 138.5 |  |  | 116.4 |  |  | 44.5 |  |  | (13.3) |
Net (loss) gain from discontinued operations attributable to White Mountains’s common shareholders |  | $ | — |  |  | $ | (1.0) |  |  | $ | 18.7 |  |  | $ | (.1) |
Allocation of earnings to participating restricted common shares (1) |  | — |  |  | — |  |  | (.2) |  |  | — |
Basic and diluted earnings(losses) per share numerators (2) |  | $ | — |  |  | $ | (1.0) |  |  | $ | 18.5 |  |  | $ | (.1) |
Basic earnings per share denominators (in thousands): |  |  |  |  |  |  |  |
Total average common shares outstanding during the period |  | 3,107.8 |  |  | 3,107.5 |  |  | 3,104.0 |  |  | 3,142.8 |
Average unvested restricted common shares (3) |  | (37.8) |  |  | (43.1) |  |  | (35.1) |  |  | (38.5) |
Basic earnings per share denominator |  | 3,070.0 |  |  | 3,064.4 |  |  | 3,068.9 |  |  | 3,104.3 |
Diluted earnings per share denominator (in thousands): |  |  |  |  |  |  |  |
Total average common shares outstanding during the period |  | 3,107.8 |  |  | 3,107.5 |  |  | 3,104.0 |  |  | 3,142.8 |
Average unvested restricted common shares (3) |  | (37.8) |  |  | (43.1) |  |  | (35.1) |  |  | (38.5) |
Diluted earnings per share denominator |  | 3,070.0 |  |  | 3,064.4 |  |  | 3,068.9 |  |  | 3,104.3 |
Basic and diluted earnings (losses) per share (in dollars) - discontinued operations: |  | $ | — |  |  | $ | (.32) |  |  | $ | 6.03 |  |  | $ | (.03) |

(1) Restricted shares issued by White Mountains contain dividend participation features, and therefore, are considered participating securities.
(2) Net earnings attributable to White Mountains’s common shareholders, net of restricted share amounts, is equal to undistributed earnings for the three and six months ended June 30, 2021 and 2020.
(3) Restricted common shares outstanding vest upon a stated date. See Note 12 — “Employee Share-Based Incentive Compensation Plans”.
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Item 2. Management’s Discussion and Analysis of Financial Condition and Results of Operations.
The following discussion contains “forward-looking statements”. White Mountains intends statements that are not historical in nature, which are hereby identified as forward-looking statements, to be covered by the safe harbor provisions of the Private Securities Litigation Reform Act of 1995. White Mountains cannot promise that its expectations in such forward-looking statements will turn out to be correct. White Mountains’s actual results could be materially different from and worse than its expectations. See “FORWARD-LOOKING STATEMENTS” on page 90 for specific important factors that could cause actual results to differ materially from those contained in forward-looking statements.
The following discussion also includes twelve non-GAAP financial measures: (i) adjusted book value per share, (ii) BAM’s gross written premiums and member surplus contributions (“MSC”) from new business, (iii) Ark’s adjusted loss and loss adjustment expense ratio, (iv) Ark’s adjusted insurance acquisition expense ratio, (v) Ark’s adjusted other underwriting expense ratio, (vi) Ark’s adjusted combined ratio (vii) NSM’s earnings before interest, taxes, depreciation and amortization (“EBITDA”), (viii) NSM’s adjusted EBITDA, (ix) Kudu’s EBITDA, (x) Kudu’s adjusted EBITDA, (xi) total consolidated portfolio returns excluding MediaAlpha and (xii) adjusted capital, that have been reconciled from their most comparable GAAP financial measures on page 84. White Mountains believes these measures to be useful in evaluating White Mountains’s financial performance and condition.
RESULTS OF OPERATIONS FOR THE THREE AND SIX MONTHS ENDED JUNE 30, 2021 AND 2020
Overview
White Mountains reported book value per share of $1,279 and adjusted book value per share of $1,292 as of June 30, 2021. Book value per share and adjusted book value per share both increased 4% in the second quarter of 2021 and 2% in the first six months of 2021, including dividends, driven primarily by results of operations as well as the increase in the MediaAlpha share price. Book value per share and adjusted book value per share both increased 4% in the second quarter of 2020, driven primarily by the rebound in the equity markets during the quarter. Book value per share decreased 0.2% and adjusted book value per share increased 0.4% in the first six months of 2020, including dividends.
Results in the second quarter and first six months of 2021 were driven primarily by $113 million and $71 million of net realized and unrealized investment gains from White Mountains’s investment in MediaAlpha, resulting from increases in the MediaAlpha share price (from $39.07 as of December 31, 2020 and from $35.43 as of March 31, 2021) to $42.10 as of June 30, 2021. Results in the first six months of 2021 also included realized investment gains on shares sold in a secondary offering completed by MediaAlpha. On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares at $46.00 per share ($44.62 per share net of underwriting fees). In the secondary offering, White Mountains sold 3.6 million shares for net proceeds of $160 million. As of June 30, 2021, White Mountains owned 16.9 million shares of MediaAlpha, representing a 28% basic ownership interest (26% on a fully-diluted/fully-converted basis). At the June 30 closing price of $42.10 per share, the value of White Mountains’s investment in MediaAlpha was $713 million. At this level of ownership, each $1.00 per share increase or decrease in the share price of MediaAlpha will result in an approximate $5.50 per share increase or decrease in White Mountains’s book value per share and adjusted book value per share.
Gross written premiums and MSC collected in the HG Global/BAM segment totaled $30 million and $56 million in the second quarter and first six months of 2021, compared to $43 million and $63 million in the second quarter and first six months of 2020. BAM insured municipal bonds with par value of $5.1 billion and $8.7 billion in the second quarter and first six months of 2021, compared to $4.1 billion and $7.1 billion in the second quarter and first six months of 2020. Total pricing was 59 and 65 basis points in the second quarter first six months of 2021, compared to 105 and 89 basis points in the second quarter and first six months of 2020. BAM’s total claims paying resources were $1,165 million as of June 30, 2021, compared to $987 million as of December 31, 2020 and $957 million as of June 30, 2020. In the first quarter of 2021, BAM completed a reinsurance agreement with Fidus Re, Ltd. (“Fidus Re”) that increased BAM’s claims paying resources by $150 million. In July 2021, S&P Global Ratings completed its annual review and affirmed BAM’s “AA/stable” rating.
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Ark’s GAAP combined ratio was 90% and 99% in the second quarter and first six months of 2021. Ark’s adjusted combined ratio, which adds back amounts ceded to insurance and reinsurance groups that provide third party underwriting capital, was 84% and 96% in the second quarter and first six months of 2021. The adjusted combined ratio in the second quarter and first six months of 2021 included 10 points and 5 points of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business, and 6 points and 12 points of catastrophe losses. In the second quarter of 2021 Ark reported gross written premiums of $328 million, net written premiums of $262 million and net earned premiums of $118 million. Ark’s gross written premiums in the second quarter of 2021 were up 78% from the second quarter of 2020 (prior to White Mountains’s ownership of Ark), with risk-adjusted rate change approximately up 7%. In the first six months of 2021, Ark reported gross written premiums of $733 million, net written premiums of $605 million and net earned premiums of $222 million. Ark’s gross written premiums in the first six months of 2021 were up 93% from the first six months of 2020 (prior to White Mountains’s ownership of Ark), with risk-adjusted rate change up approximately 9%. Ark reported pre-tax income (loss) of $18 million and $(15) million in the second quarter and first six months of 2021. Ark’s pre-tax loss for the first six months of 2021 included $25 million of transaction expenses related to White Mountains’s transaction with Ark.
NSM reported pre-tax income of $1 million, adjusted EBITDA of $19 million, and commission and other revenues of $84 million in the second quarter of 2021, compared to pre-tax loss of $4 million, adjusted EBITDA of $18 million, and commission and other revenues of $76 million in the second quarter of 2020. NSM reported pre-tax loss of $32 million, adjusted EBITDA of $33 million, and commission and other revenues of $159 million in the first six months of 2021, compared to pre-tax loss of $5 million, adjusted EBITDA of $29 million, and commission and other revenues of $141 million in the first six months of 2020. On April 12, 2021, NSM sold its Fresh Insurance motor business, which resulted in a loss of $29 million recorded in the first quarter of 2021. Results in the first six months of 2021 and the first six months of 2020, from the date of acquisition, include the results of Kingsbridge, a leading provider of commercial lines insurance and consulting services to the contingent workforce in the United Kingdom, which was acquired on April 7, 2020.
Kudu reported pre-tax income of $31 million and adjusted EBITDA of $5 million in the second quarter of 2021, compared to pre-tax income of $18 million and adjusted EBITDA of $4 million in the second quarter of 2020. Pre-tax income in the second quarter of 2021 included $28 million of unrealized gains on Kudu’s participation contracts, compared to $17 million of unrealized gains on Kudu’s participation contracts in the second quarter of 2020. Kudu reported pre-tax income of $47 million and adjusted EBITDA of $11 million in the first six months of 2021, compared to pre-tax loss of $4 million and adjusted EBITDA of $9 million in the first six months of 2020. Pre-tax income in the first six months of 2021 included $44 million of unrealized gains on Kudu’s participation contracts, compared to $8 million of unrealized losses on Kudu’s participation contracts in the first six months of 2020, which reflected the impact of the market dislocation from the COVID-19 pandemic on Kudu’s underlying asset management firms. As of June 30, 2021, Kudu has deployed $398 million in 13 investment management firms, with an average cash yield to Kudu at inception of 10.3%. The firms have total assets under management of approximately $52 billion, spanning a range of asset classes, including real estate, wealth management, hedge funds, private equity and alternative credit strategies.
White Mountains’s pre-tax total return on invested assets was 5.0% in the second quarter of 2021. This return included $113 million of net unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 2.4% in the second quarter of 2021. Excluding MediaAlpha, investment returns in the second quarter of 2021 were driven primarily by favorable other long-term investments results and the impact of the flattening of the yield curve on the fixed income portfolio. White Mountains’s pre-tax total return on invested assets was 6.5% in the second quarter of 2020. This return included $18 million of net investment income and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 6.4% in the second quarter of 2020. Excluding MediaAlpha, investment returns in the second quarter of 2020 were driven primarily by a rebound in equity markets following the decline experienced in the first quarter of 2020 in reaction to the COVID-19 pandemic.
White Mountains’s pre-tax total return on invested assets was 4.7% in the first six months of 2021. This return included $71 million of net realized and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 3.1% in the first six months of 2021. Excluding MediaAlpha, investment returns in the first six months of 2021 were driven primarily by favorable other long-term investment results. White Mountains’s pre-tax total return on invested assets was 1.7% in the first six months of 2020. This return included $50 million of net investment income and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was flat in the first six months of 2020. Excluding MediaAlpha, returns in the first six months of 2020 were driven primarily by the decline in interest rates and favorable other long-term investments results, offset by the overall decline in equity markets over the period.
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Adjusted Book Value Per Share
The following table presents White Mountains’s book value per share and reconciles it to adjusted book value per share, a non-GAAP measure. See NON-GAAP FINANCIAL MEASURES on page 84.

|  | June 30, 2021 |  | March 31, 2021 |  | December 31, 2020 |  | June 30, 2020
Book value per share numerators (in millions): |  |  |  |  |  |  |  |
White Mountains’s common shareholders’ equity - GAAP book value per share numerator |  | $ | 3,978.2 |  |  | $ | 3,825.9 |  |  | $ | 3,906.0 |  |  | $ | 3,166.0 |
Time value of money discount on expected future payments on the BAM Surplus Notes (1) |  | (132.8) |  |  | (137.7) |  |  | (142.5) |  |  | (146.7) |
HG Global’s unearned premium reserve (1) |  | 201.5 |  |  | 195.3 |  |  | 190.0 |  |  | 173.8 |
HG Global’s net deferred acquisition costs (1) |  | (56.3) |  |  | (54.2) |  |  | (52.4) |  |  | (47.0) |
Adjusted book value per share numerator |  | $ | 3,990.6 |  |  | $ | 3,829.3 |  |  | $ | 3,901.1 |  |  | $ | 3,146.1 |
Book value per share denominators (in thousands of shares): |  |  |  |  |  |  |  |
Common shares outstanding - GAAP book value per share denominator |  | 3,109.2 |  |  | 3,107.3 |  |  | 3,102.0 |  |  | 3,101.8 |
Unearned restricted common shares |  | (20.6) |  |  | (23.4) |  |  | (14.8) |  |  | (23.1) |
Adjusted book value per share denominator |  | 3,088.6 |  |  | 3,083.9 |  |  | 3,087.2 |  |  | 3,078.7 |
GAAP book value per share |  | $ | 1,279.49 |  |  | $ | 1,231.27 |  |  | $ | 1,259.18 |  |  | $ | 1,020.71 |
Adjusted book value per share |  | $ | 1,292.03 |  |  | $ | 1,241.71 |  |  | $ | 1,263.64 |  |  | $ | 1,021.91 |
Year-to-date dividends paid per share |  | $ | 1.00 |  |  | $ | 1.00 |  |  | $ | 1.00 |  |  | $ | 1.00 |

(1) Amount reflects White Mountains’s preferred share ownership in HG Global of 96.9%.
Goodwill and Other Intangible Assets
The following table presents a summary of goodwill and other intangible assets that are included in White Mountains’s book value as of June 30, 2021, December 31, 2020, and June 30, 2020:

Millions |  | June 30, 2021 |  |  |  |  |  | December 31, 2020 |  | June 30, 2020 |
Goodwill: |  |  |  |  |  |  |  |  |  |  |
Ark |  | $ | 116.8 |  |  |  |  |  |  | $ | — |  |  | $ | — |  |
NSM |  | 477.9 |  |  |  |  |  |  | 506.4 |  |  | 504.9 |  | (3)
Kudu |  | 7.6 |  |  |  |  |  |  | 7.6 |  |  | 7.6 |  |
Other Operations |  | 27.1 |  | (2) |  |  |  |  | 11.5 |  |  | 5.7 |  |
Total goodwill |  | 629.4 |  |  |  |  |  |  | 525.5 |  |  | 518.2 |  |
Other intangible assets: |  |  |  |  |  |  |  |  |  |  |
Ark |  | 175.7 |  |  |  |  |  |  | — |  |  | — |  |
NSM |  | 213.7 |  |  |  |  |  |  | 230.4 |  |  | 223.7 |  |
Kudu |  | 1.5 |  |  |  |  |  |  | 1.6 |  |  | 1.8 |  |
Other Operations |  | 23.9 |  |  |  |  |  |  | 24.9 |  |  | 16.2 |  |
Total other intangible assets |  | 414.8 |  |  |  |  |  |  | 256.9 |  |  | 241.7 |  |
Total goodwill and other intangible assets (1) |  | 1,044.2 |  |  |  |  |  |  | 782.4 |  |  | 759.9 |  |
Goodwill and other intangible assets attributed to non-controlling interests |  | (115.9) |  |  |  |  |  |  | (28.1) |  |  | (25.9) |  |
Goodwill and other intangible assets included in White Mountains’s common shareholders’ equity |  | $ | 928.3 |  |  |  |  |  |  | $ | 754.3 |  |  | $ | 734.0 |  |

(1) See Note 4 — “Goodwill and Other Intangible Assets” for details of goodwill and other intangible assets.
(2) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition within Other Operations had not yet been finalized at June 30, 2021.
(3) The relative fair values of goodwill and other intangible assets recognized in connection with the acquisition of Kingsbridge had not yet been finalized at June 30, 2020.
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Summary of Consolidated Results
The following table presents White Mountains’s consolidated financial results for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended |  | Six Months Ended |
|  | June 30, |  | June 30, |
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020 |
Revenues |  |  |  |  |  |  |  |  |
Financial Guarantee revenues |  | $ | 17.4 |  |  | $ | 26.1 |  |  | $ | 10.7 |  |  | $ | 43.6 |  |
P&C Insurance and Reinsurance revenues |  | 130.5 |  |  | — |  |  | 239.6 |  |  | — |  |
Specialty Insurance Distribution revenues |  | 84.3 |  |  | 76.1 |  |  | 159.1 |  |  | 141.1 |  |
Asset Management revenues |  | 36.2 |  |  | 22.1 |  |  | 60.3 |  |  | 4.7 |  |
Other Operations revenues |  | 158.3 |  |  | 135.3 |  |  | 135.2 |  |  | 11.0 |  |
Total revenues |  | 426.7 |  |  | 259.6 |  |  | 604.9 |  |  | 200.4 |  |
Expenses |  |  |  |  |  |  |  |  |
Financial Guarantee expenses |  | 15.5 |  |  | 14.8 |  |  | 33.8 |  |  | 31.2 |  |
P&C Insurance and Reinsurance expenses |  | 112.7 |  |  | — |  |  | 254.3 |  |  | — |  |
Specialty Insurance Distribution expenses |  | 83.2 |  |  | 79.8 |  |  | 191.3 |  |  | 146.2 |  |
Asset Management expenses |  | 4.8 |  |  | 4.4 |  |  | 13.2 |  |  | 8.4 |  |
Other Operations expenses |  | 48.2 |  |  | 27.9 |  |  | 88.7 |  |  | 47.9 |  |
Total expenses |  | 264.4 |  |  | 126.9 |  |  | 581.3 |  |  | 233.7 |  |
Pre-tax income (loss) |  |  |  |  |  |  |  |  |
Financial Guarantee pre-tax income (loss) |  | 1.9 |  |  | 11.3 |  |  | (23.1) |  |  | 12.4 |  |
P&C Insurance and Reinsurance pre-tax income (loss) |  | 17.8 |  |  | — |  |  | (14.7) |  |  | — |  |
Specialty Insurance Distribution pre-tax income (loss) |  | 1.1 |  |  | (3.7) |  |  | (32.2) |  |  | (5.1) |  |
Asset Management pre-tax income (loss) |  | 31.4 |  |  | 17.7 |  |  | 47.1 |  |  | (3.7) |  |
Other Operations pre-tax income (loss) |  | 110.1 |  |  | 107.4 |  |  | 46.5 |  |  | (36.9) |  |
Total pre-tax income (loss) |  | 162.3 |  |  | 132.7 |  |  | 23.6 |  |  | (33.3) |  |
Income tax (expense) benefit |  | (29.8) |  |  | (24.1) |  |  | (20.3) |  |  | 1.4 |  |
Net income (loss) from continuing operations |  | 132.5 |  |  | 108.6 |  |  | 3.3 |  |  | (31.9) |  |
Net (loss) gain from sale of discontinued operations, net of tax |  | — |  |  | (1.0) |  |  | 18.7 |  |  | (.1) |  |
Net income (loss) |  | 132.5 |  |  | 107.6 |  |  | 22.0 |  |  | (32.0) |  |
Net loss attributable to non-controlling interests |  | 6.0 |  |  | 7.8 |  |  | 41.2 |  |  | 18.6 |  |
Net income (loss) attributable to White Mountains’s common shareholders |  | 138.5 |  |  | 115.4 |  |  | 63.2 |  |  | (13.4) |  |
Other comprehensive income (loss), net of tax |  | 1.0 |  |  | .5 |  |  | 2.8 |  |  | (2.9) |  |
Comprehensive income (loss) |  | 139.5 |  |  | 115.9 |  |  | 66.0 |  |  | (16.3) |  |
Comprehensive income attributable to non-controlling interests |  | (.1) |  |  | (.2) |  |  | (.2) |  |  | (.2) |  |
Comprehensive income (loss) attributable to White Mountains’s common shareholders |  | $ | 139.4 |  |  | $ | 115.7 |  |  | $ | 65.8 |  |  | $ | (16.5) |  |

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I. Summary of Operations By Segment
As of June 30, 2021,White Mountains conducted its operations through five segments: (1) HG Global/BAM, (2) Ark, (3) NSM, (4) Kudu and (5) Other Operations. A discussion of White Mountains’s consolidated investment operations is included after the discussion of operations by segment. White Mountains’s segment information is presented in Note 15 — “Segment Information” to the Consolidated Financial Statements.
As a result of the Ark Transaction, White Mountains began consolidating Ark in its financial statements as of January 1, 2021. See Note 2 — “Significant Transactions”.
HG Global/BAM
The following tables present the components of pre-tax income (loss) included in White Mountains’s HG Global/BAM segment related to the consolidation of HG Global, which includes HG Re and its other wholly-owned subsidiaries, and BAM for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30, 2021
Millions |  | HG Global |  | BAM |  | Eliminations |  | Total
Direct written premiums |  | $ | — |  |  | $ | 13.8 |  |  | $ | — |  |  | $ | 13.8 |
Assumed written premiums |  | 11.8 |  |  | — |  |  | (11.8) |  |  | — |
Gross written premiums |  | 11.8 |  |  | 13.8 |  |  | (11.8) |  |  | 13.8 |
Ceded written premiums |  | — |  |  | (11.8) |  |  | 11.8 |  |  | — |
Net written premiums |  | $ | 11.8 |  |  | $ | 2.0 |  |  | $ | — |  |  | $ | 13.8 |
Earned insurance premiums |  | $ | 5.3 |  |  | $ | 1.2 |  |  | $ | — |  |  | $ | 6.5 |
Net investment income |  | 1.7 |  |  | 2.6 |  |  | — |  |  | 4.3 |
Net investment income - BAM Surplus Notes |  | 3.0 |  |  | — |  |  | (3.0) |  |  | — |
Net realized and unrealized investment gains |  | 2.4 |  |  | 3.9 |  |  | — |  |  | 6.3 |
Other revenue |  | .1 |  |  | .2 |  |  | — |  |  | .3 |
Total revenues |  | 12.5 |  |  | 7.9 |  |  | (3.0) |  |  | 17.4 |
Insurance acquisition expenses |  | 1.3 |  |  | .3 |  |  | — |  |  | 1.6 |
General and administrative expenses |  | .5 |  |  | 13.4 |  |  | — |  |  | 13.9 |
Interest expense - BAM Surplus Notes |  | — |  |  | 3.0 |  |  | (3.0) |  |  | — |
Total expenses |  | 1.8 |  |  | 16.7 |  |  | (3.0) |  |  | 15.5 |
Pre-tax income (loss) |  | $ | 10.7 |  |  | $ | (8.8) |  |  | $ | — |  |  | $ | 1.9 |
Supplemental information: |  |  |  |  |  |  |  |
MSC collected (1) |  | $ | — |  |  | $ | 16.3 |  |  | $ | — |  |  | $ | 16.3 |

(1) MSC are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.
57

|  | Three Months Ended June 30, 2020
Millions |  | HG Global |  | BAM |  | Eliminations |  | Total
Direct written premiums |  | $ | — |  |  | $ | 21.3 |  |  | $ | — |  |  | $ | 21.3 |
Assumed (ceded) written premiums |  | 18.3 |  |  | .2 |  |  | (18.3) |  |  | .2 |
Gross written premiums |  | 18.3 |  |  | 21.5 |  |  | (18.3) |  |  | 21.5 |
Ceded written premiums |  | — |  |  | (18.3) |  |  | 18.3 |  |  | — |
Net written premiums |  | $ | 18.3 |  |  | $ | 3.2 |  |  | $ | — |  |  | $ | 21.5 |
Earned insurance premiums |  | $ | 4.6 |  |  | $ | 1.0 |  |  | $ | — |  |  | $ | 5.6 |
Net investment income |  | 2.0 |  |  | 2.9 |  |  | — |  |  | 4.9 |
Net investment income - BAM Surplus Notes |  | 4.7 |  |  | — |  |  | (4.7) |  |  | — |
Net realized and unrealized investment gains |  | 10.7 |  |  | 3.7 |  |  | — |  |  | 14.4 |
Other revenue |  | .1 |  |  | 1.1 |  |  | — |  |  | 1.2 |
Total revenues |  | 22.1 |  |  | 8.7 |  |  | (4.7) |  |  | 26.1 |
Insurance acquisition expenses |  | 1.2 |  |  | .9 |  |  | — |  |  | 2.1 |
General and administrative expenses |  | .5 |  |  | 12.2 |  |  | — |  |  | 12.7 |
Interest expense - BAM Surplus Notes |  | — |  |  | 4.7 |  |  | (4.7) |  |  | — |
Total expenses |  | 1.7 |  |  | 17.8 |  |  | (4.7) |  |  | 14.8 |
Pre-tax income (loss) |  | $ | 20.4 |  |  | $ | (9.1) |  |  | $ | — |  |  | $ | 11.3 |
Supplemental information: |  |  |  |  |  |  |  |
MSC collected (1) |  | $ | — |  |  | $ | 21.5 |  |  | $ | — |  |  | $ | 21.5 |

(1) MSC are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.

|  | Six Months Ended June 30, 2021
Millions |  | HG Global |  | BAM |  | Eliminations |  | Total
Direct written premiums |  | $ | — |  |  | $ | 21.8 |  |  | $ | — |  |  | $ | 21.8 |
Assumed written premiums |  | 22.5 |  |  | 4.5 |  |  | (22.5) |  |  | 4.5 |
Gross written premiums |  | 22.5 |  |  | 26.3 |  |  | (22.5) |  |  | 26.3 |
Ceded written premiums |  | — |  |  | (22.5) |  |  | 22.5 |  |  | — |
Net written premiums |  | $ | 22.5 |  |  | $ | 3.8 |  |  | $ | — |  |  | $ | 26.3 |
Earned insurance premiums |  | $ | 10.6 |  |  | $ | 2.3 |  |  | $ | — |  |  | $ | 12.9 |
Net investment income |  | 3.5 |  |  | 5.3 |  |  | — |  |  | 8.8 |
Net investment income - BAM Surplus Notes |  | 6.0 |  |  | — |  |  | (6.0) |  |  | — |
Net realized and unrealized investment losses |  | (7.5) |  |  | (4.1) |  |  | — |  |  | (11.6) |
Other revenue |  | .2 |  |  | .4 |  |  | — |  |  | .6 |
Total revenues |  | 12.8 |  |  | 3.9 |  |  | (6.0) |  |  | 10.7 |
Insurance acquisition expenses |  | 2.8 |  |  | .7 |  |  | — |  |  | 3.5 |
General and administrative expenses |  | 1.1 |  |  | 29.2 |  |  | — |  |  | 30.3 |
Interest expense - BAM Surplus Notes |  | — |  |  | 6.0 |  |  | (6.0) |  |  | — |
Total expenses |  | 3.9 |  |  | 35.9 |  |  | (6.0) |  |  | 33.8 |
Pre-tax income (loss) |  | $ | 8.9 |  |  | $ | (32.0) |  |  | $ | — |  |  | $ | (23.1) |
Supplemental information: |  |  |  |  |  |  |  |
MSC collected (1) |  | $ | — |  |  | 30.1 |  |  | $ | — |  |  | $ | 30.1 |

(1) MSC are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.
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|  | Six Months Ended June 30, 2020
Millions |  | HG Global |  | BAM |  | Eliminations |  | Total
Direct written premiums |  | $ | — |  |  | $ | 31.0 |  |  | $ | — |  |  | $ | 31.0 |
Assumed (ceded) written premiums |  | 26.6 |  |  | .2 |  |  | (26.6) |  |  | .2 |
Gross written premiums |  | 26.6 |  |  | 31.2 |  |  | (26.6) |  |  | 31.2 |
Ceded written premiums |  | — |  |  | (26.6) |  |  | 26.6 |  |  | — |
Net written premiums |  | $ | 26.6 |  |  | $ | 4.6 |  |  | $ | — |  |  | $ | 31.2 |
Earned insurance premiums |  | $ | 9.0 |  |  | $ | 2.0 |  |  | $ | — |  |  | $ | 11.0 |
Net investment income |  | 4.3 |  |  | 6.1 |  |  | — |  |  | 10.4 |
Net investment income - BAM Surplus Notes |  | 9.5 |  |  | — |  |  | (9.5) |  |  | — |
Net realized and unrealized investment gains |  | 12.1 |  |  | 8.4 |  |  | — |  |  | 20.5 |
Other revenue |  | .1 |  |  | 1.6 |  |  | — |  |  | 1.7 |
Total revenues |  | 35.0 |  |  | 18.1 |  |  | (9.5) |  |  | 43.6 |
Insurance acquisition expenses |  | 2.2 |  |  | 1.6 |  |  | — |  |  | 3.8 |
General and administrative expenses |  | 1.0 |  |  | 26.4 |  |  | — |  |  | 27.4 |
Interest expense - BAM Surplus Notes |  | — |  |  | 9.5 |  |  | (9.5) |  |  | — |
Total expenses |  | 3.2 |  |  | 37.5 |  |  | (9.5) |  |  | 31.2 |
Pre-tax income (loss) |  | $ | 31.8 |  |  | $ | (19.4) |  |  | $ | — |  |  | $ | 12.4 |
Supplemental information: |  |  |  |  |  |  |  |
MSC collected (1) |  | $ | — |  |  | $ | 31.5 |  |  | $ | — |  |  | $ | 31.5 |

(1) MSC are recorded directly to BAM’s equity, which is recorded as non-controlling interest on White Mountains’s balance sheet.
HG Global/BAM Results—Three Months Ended June 30, 2021 versus Three Months Ended June 30, 2020
BAM is required to prepare its financial statements on a statutory accounting basis for the NYDFS and does not report stand-alone GAAP financial results. BAM is owned by its members, the municipalities that purchase BAM’s insurance for their debt issuances. BAM charges an insurance premium on each municipal bond insurance policy it writes. A portion of the premium is MSC and the remainder is a risk premium. In the event of a municipal bond refunding, a portion of the MSC from 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, and 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.
Gross written premiums and MSC collected in the HG Global/BAM segment totaled $30 million in the second quarter of 2021, compared to $43 million in the second quarter of 2020. BAM insured $5.1 billion of municipal bonds, $4.8 billion of which were in the primary market, in the second quarter of 2021, compared to $4.1 billion of municipal bonds, $3.2 billion of which were in the primary market, in the second quarter of 2020.
Total pricing, which reflects both gross written premiums and MSC from new business, decreased to 59 basis points in the second quarter of 2021, compared to 105 basis points in the second quarter of 2020. See “NON-GAAP FINANCIAL MEASURES” on page 84. The decrease in total pricing was driven primarily by a decrease in pricing in the primary and secondary markets in the second quarter of 2021 and a decrease in the amount of par insured in the secondary market. Pricing in the primary market decreased to 51 basis points in the second quarter of 2021, compared to 62 basis points in the second quarter of 2020. Pricing in the secondary and assumed reinsurance markets, which is more transaction specific than pricing in the primary market, decreased to 175 basis points in the second quarter of 2021, compared to 256 basis points in the second quarter of 2020. Demand remained strong for insured bonds of double-A rated issuers.
59

The following table presents the gross par value of primary and secondary market policies issued, the gross par value of assumed reinsurance, the gross written premiums and MSC collected and total pricing for the three months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30,
$ in Millions |  | 2021 |  | 2020
Gross par value of primary market policies issued |  | $ | 4,815.5 |  |  | $ | 3,196.1 |
Gross par value of secondary market policies issued |  | 312.1 |  |  | 878.5 |
Gross par value of assumed reinsurance |  | — |  |  | 36.9 |
Total gross par value of market policies issued |  | $ | 5,127.6 |  |  | $ | 4,111.5 |
Gross written premiums |  | $ | 13.7 |  |  | $ | 21.5 |
MSC collected |  | 16.3 |  |  | 21.5 |
Total gross written premiums and MSC collected |  | $ | 30.0 |  |  | $ | 43.0 |
Present value of future installment MSC collections |  | — |  |  | .3 |
Gross written premium adjustments on existing installment policies |  | .1 |  |  | — |
Gross written premiums and MSC from new business |  | $ | 30.1 |  |  | $ | 43.3 |
Total pricing |  | 59 bps |  | 105 bps

HG Global reported pre-tax income of $11 million in the second quarter of 2021, compared to pre-tax income of $20 million in the second quarter of 2020. The change in pre-tax income was driven primarily by lower investment returns on HG Global’s investment portfolio, as the interest rate decline in the second quarter of 2021 was less than the interest rate decline in the second quarter of 2020, and a decrease in interest income on the BAM Surplus Notes. Results in the second quarter of 2021 include $3 million of interest income on the BAM Surplus Notes, compared to $5 million in the second quarter of 2020. Interest income on the BAM Surplus Notes decreased due to both a decrease in the balance of the BAM Surplus Notes and a decrease in the interest rate earned on the BAM Surplus Notes in the second quarter of 2021, compared to the second quarter of 2020.
BAM is a mutual insurance company that is owned by its members. BAM’s results are consolidated into White Mountains’s GAAP financial statements and attributed to non-controlling interests. White Mou ntains reported $9 million of GAAP pre-tax loss from BAM in both the second quarter of 2021 and 2020. Results in the second quarter of 2021 include $3 million of interest expense on the BAM Surplus Notes and $13 million of general and administrative expenses, compared to $5 million of interest expense and $12 million of general and administrative expenses in the second quarter of 2020.
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COVID-19
BAM expects that investor concerns about the impact of the COVID-19 pandemic should continue to result in both increased insured penetration in the primary market and opportunities in the secondary market. The COVID-19 pandemic is negatively impacting the finances of municipalities to varying degrees, and, over time, financial stress could emerge. BAM’s existing credit portfolio is of high quality and structured to be resilient during economic slowdowns. BAM views consumption-based tax-backed credits (sales, hotel, excise), transportation-related credits (airports, mass transportation, ports and toll roads) and higher education-related credits as those most likely to be affected by pandemic-related impacts on the economy. Combined, these sectors total approximately 16% of BAM’s outstanding insured par. All BAM-insured bond payments due through August 1, 2021 have been made by insureds. BAM currently has no insured bonds on its insured credit watchlist.
HG Global/BAM Results—Six Months Ended June 30, 2021 versus Six Months Ended June 30, 2020
Gross written premiums and MSC collected in the HG Global/BAM segment totaled $56 million in the first six months of 2021, compared to $63.0 million in the first six months of 2020. BAM insured $8.7 billion of municipal bonds, $7.4 billion of which were in the primary market, in the first six months of 2021, compared to $7.1 billion of municipal bonds, $5.7 billion of which were in the primary market, in the first six months of 2020. In the first quarter of 2021, BAM completed an assumed reinsurance transaction to reinsure municipal bonds with a par value of $805 million.
Total pricing, which reflects both gross written premiums and MSC from new business, decreased to 65 basis points in the first six months of 2021, compared to 89 basis points in the first six months of 2020. See “NON-GAAP FINANCIAL MEASURES” on page 84. The decrease in total pricing was driven primarily by a decrease in pricing in the secondary and assumed reinsurance markets in the first six months of 2021. Pricing in the primary market decreased to 54 basis points in the first six months of 2021, compared to 56 basis points in the first six months of 2020. Pricing in the secondary and assumed reinsurance markets, which is more transaction specific than pricing in the primary market, decreased to 131 basis points in the first six months of 2021, compared to 223 basis points in the first six months of 2020. Demand remained strong for insured bonds of double-A rated issuers.
The following table presents the gross par value of primary and secondary market policies issued, the gross par value of assumed reinsurance, the gross written premiums and MSC collected and total pricing for the six months ended June 30, 2021 and 2020:

|  | Six Months Ended June 30,
$ in Millions |  | 2021 |  | 2020
Gross par value of primary market policies issued |  | $ | 7,357.5 |  |  | $ | 5,704.2 |
Gross par value of secondary market policies issued |  | 489.2 |  |  | 1,347.0 |
Gross par value of assumed reinsurance |  | 805.5 |  |  | 36.9 |
Total gross par value of market policies issued |  | $ | 8,652.2 |  |  | $ | 7,088.1 |
Gross written premiums |  | 26.2 |  |  | $ | 31.2 |
MSC collected |  | 30.1 |  |  | 31.5 |
Total gross written premiums and MSC collected |  | $ | 56.3 |  |  | $ | 62.7 |
Present value of future installment MSC collections |  | — |  |  | .3 |
Gross written premium adjustments on existing installment policies |  | .1 |  |  | — |
Gross written premiums and MSC from new business |  | $ | 56.4 |  |  | $ | 63.0 |
Total pricing |  | 65 bps |  | 89 bps

61

HG Global reported pre-tax income of $9 million in the first six months of 2021, compared to pre-tax income of $32 million in the first six months of 2020. The change in pre-tax income was driven primarily by lower investment returns on HG Global’s investment portfolio, as interest rates rose in the first six months of 2021 and declined in the first six months of 2020, and a decrease in interest income on the BAM Surplus Notes. Results in the first six months of 2021 include $6 million of interest income on the BAM Surplus Notes, compared to $10 million in the first six months of 2020. Interest income on the BAM Surplus Notes decreased due to both a decrease in the balance of the BAM Surplus Notes and a decrease in the interest rate earned on the BAM Surplus Notes in the first six months of 2021, compared to the first six months of 2020.
White Mou ntains reported $32 million of GAAP pre-tax loss from BAM in the first six months of 2021, compared to $19 million in the first six months of 2020. The increase in pre-tax loss was driven primarily by lower investment returns on BAM’s investment portfolio, as interest rates rose in the first six months of 2021 and declined in the first six months of 2020, partially offset by lower interest expense on the BAM Surplus Notes. Results in the first six months of 2021 include $6 million of interest expense on the BAM Surplus Notes and $29 million of general and administrative expenses, compared to $10 million of interest expense and $26 million of general and administrative expenses in the first six months of 2020.
Claims Paying Resources
BAM’s “claims paying resources” represents the capital and other financial resources BAM has available to pay claims and, as such, is a key indication of BAM’s financial strength.
BAM’s claims paying resources were $1,165 million as of June 30, 2021, compared to $987 million as of December 31, 2020 and $957 million as of June 30, 2020. In the first quarter of 2021, BAM completed a reinsurance agreement with Fidus Re, a special-purpose insurer created solely to provide collateralized reinsurance protection to BAM, that increased BAM’s claims paying resources by $150 million. The reinsurance agreement with Fidus Re 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.
The following table presents BAM’s total claims paying resources as of June 30, 2021, December 31, 2020 and June 30, 2020:

Millions |  | June 30, 2021 |  | December 31, 2020 |  | June 30, 2020 |  |
Policyholders’ surplus |  | $ | 323.1 |  |  | $ | 324.7 |  |  | $ | 345.1 |  |  |
Contingency reserve |  | 97.4 |  |  | 86.4 |  |  | 76.9 |  |  |
Qualified statutory capital |  | 420.5 |  |  | 411.1 |  |  | 422.0 |  |  |
Net unearned premiums |  | 47.4 |  |  | 45.2 |  |  | 42.4 |  |  |
Present value of future installment premiums and MSC |  | 13.8 |  |  | 14.0 |  |  | 14.6 |  |  |
HG Re, Ltd. collateral trusts at statutory value |  | 433.0 |  |  | 417.0 |  |  | 378.1 |  |  |
Fidus Re, Ltd. collateral trust at statutory value |  | 250.0 |  |  | 100.0 |  |  | 100.0 |  |  |
Claims paying resources |  | $ | 1,164.7 |  |  | $ | 987.3 |  |  | $ | 957.1 |  |  |

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HG Global/BAM Balance Sheets
The following tables present amounts from HG Global, which includes HG Re and its other wholly-owned subsidiaries, and BAM that are contained within White Mountains’s consolidated balance sheet as of June 30, 2021 and December 31, 2020:

|  | June 30, 2021
Millions |  | HG Global |  | BAM |  | Eliminations and Segment Adjustment |  | Total
Assets |  |  |  |  |  |  |  |
Fixed maturity investments |  | $ | 415.4 |  |  | $ | 469.2 |  |  | $ | — |  |  | $ | 884.6 |
Short-term investments |  | 24.9 |  |  | 20.0 |  |  | — |  |  | 44.9 |
Total investments |  | 440.3 |  |  | 489.2 |  |  | — |  |  | 929.5 |
Cash |  | 4.4 |  |  | 16.2 |  |  | — |  |  | 20.6 |
BAM Surplus Notes |  | 388.2 |  |  | — |  |  | (388.2) |  |  | — |
Accrued interest receivable on BAM Surplus Notes |  | 161.8 |  |  | — |  |  | (161.8) |  |  | — |
Deferred acquisition costs |  | 58.1 |  |  | 30.5 |  |  | (58.1) |  |  | 30.5 |
Insurance premiums receivable |  | 4.3 |  |  | 6.9 |  |  | (4.3) |  |  | 6.9 |
Accrued investment income |  | 2.0 |  |  | 3.0 |  |  | — |  |  | 5.0 |
Other assets |  | .1 |  |  | 14.2 |  |  | (.3) |  |  | 14.0 |
Total assets |  | $ | 1,059.2 |  |  | $ | 560.0 |  |  | $ | (612.7) |  |  | $ | 1,006.5 |
Liabilities |  |  |  |  |  |  |  |
BAM Surplus Notes(1) |  | $ | — |  |  | $ | 388.2 |  |  | $ | (388.2) |  |  | $ | — |
Accrued interest payable on BAM Surplus Notes(2) |  | — |  |  | 161.8 |  |  | (161.8) |  |  | — |
Preferred dividends payable to White Mountains’s subsidiaries(3) |  | 371.2 |  |  | — |  |  | — |  |  | 371.2 |
Preferred dividends payable to non-controlling interests |  | 13.1 |  |  | — |  |  | — |  |  | 13.1 |
Unearned insurance premiums |  | 208.0 |  |  | 42.9 |  |  | — |  |  | 250.9 |
Accrued incentive compensation |  | .8 |  |  | 15.3 |  |  | — |  |  | 16.1 |
Accounts payable on unsettled investment purchases |  | — |  |  | — |  |  | — |  |  | — |
Other liabilities |  | 1.1 |  |  | 77.0 |  |  | (62.7) |  |  | 15.4 |
Total liabilities |  | 594.2 |  |  | 685.2 |  |  | (612.7) |  |  | 666.7 |
Equity |  |  |  |  |  |  |  |
White Mountains’s common shareholders’ equity |  | 453.9 |  |  | — |  |  | — |  |  | 453.9 |
Non-controlling interests |  | 11.1 |  |  | (125.2) |  |  | — |  |  | (114.1) |
Total equity |  | 465.0 |  |  | (125.2) |  |  | — |  |  | 339.8 |
Total liabilities and equity |  | $ | 1,059.2 |  |  | $ | 560.0 |  |  | $ | (612.7) |  |  | $ | 1,006.5 |

(1) Under GAAP, the BAM Surplus Notes are classified as debt by the issuer. Under statutory accounting principles, they are classified as policyholders’ surplus.
(2) Under GAAP, interest accrues daily on the BAM Surplus Notes. Under statutory accounting principles, interest is not accrued on the BAM Surplus Notes until it has been approved for payment by insurance regulators.
(3) 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 are added back to White Mountains’s common shareholders’ equity within the HG Global/BAM segment.
63

|  | December 31, 2020
Millions |  | HG Global |  | BAM |  | Eliminations and Segment Adjustment |  | Total Segment
Assets |  |  |  |  |  |  |  |
Fixed maturity investments |  | $ | 415.9 |  |  | $ | 443.6 |  |  | $ | — |  |  | $ | 859.5 |
Short-term investments |  | 16.5 |  |  | 43.9 |  |  | — |  |  | 60.4 |
Total investments |  | 432.4 |  |  | 487.5 |  |  | — |  |  | 919.9 |
Cash |  | 23.8 |  |  | 19.0 |  |  | — |  |  | 42.8 |
BAM Surplus Notes |  | 388.2 |  |  | — |  |  | (388.2) |  |  | — |
Accrued interest receivable on BAM Surplus Notes |  | 155.7 |  |  | — |  |  | (155.7) |  |  | — |
Deferred acquisition costs |  | 54.1 |  |  | 27.8 |  |  | (54.1) |  |  | 27.8 |
Insurance premiums receivable |  | 4.4 |  |  | 6.9 |  |  | (4.4) |  |  | 6.9 |
Accrued investment income |  | 2.0 |  |  | 3.0 |  |  | — |  |  | 5.0 |
Other assets |  | — |  |  | 15.8 |  |  | (.4) |  |  | 15.4 |
Total assets |  | $ | 1,060.6 |  |  | $ | 560.0 |  |  | $ | (602.8) |  |  | $ | 1,017.8 |
Liabilities |  |  |  |  |  |  |  |
BAM Surplus Notes(1) |  | $ | — |  |  | $ | 388.2 |  |  | $ | (388.2) |  |  | $ | — |
Accrued interest payable on BAM Surplus Notes(2) |  | — |  |  | 155.7 |  |  | (155.7) |  |  | — |
Preferred dividends payable to White Mountains’s subsidiaries(3) |  | 363.9 |  |  | — |  |  | — |  |  | 363.9 |
Preferred dividends payable to non-controlling interests |  | 12.7 |  |  | — |  |  | — |  |  | 12.7 |
Unearned insurance premiums |  | 196.1 |  |  | 41.4 |  |  | — |  |  | 237.5 |
Other liabilities |  | 2.2 |  |  | 98.0 |  |  | (58.9) |  |  | 41.3 |
Total liabilities |  | 574.9 |  |  | 683.3 |  |  | (602.8) |  |  | 655.4 |
Equity |  |  |  |  |  |  |  |
White Mountains’s common shareholders’ equity |  | 472.2 |  |  | — |  |  | — |  |  | 472.2 |
Non-controlling interests |  | 13.5 |  |  | (123.3) |  |  | — |  |  | (109.8) |
Total equity |  | 485.7 |  |  | (123.3) |  |  | — |  |  | 362.4 |
Total liabilities and equity |  | $ | 1,060.6 |  |  | $ | 560.0 |  |  | $ | (602.8) |  |  | $ | 1,017.8 |

(1) Under GAAP, the BAM Surplus Notes are classified as debt by the issuer. Under statutory accounting principles, they are classified as policyholders’ surplus.
(2) Under GAAP, interest accrues daily on the BAM Surplus Notes. Under statutory accounting principles, interest is not accrued on the BAM Surplus Notes until it has been approved for payment by insurance regulators.
(3) 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 are added back to White Mountains’s common shareholders’ equity within the HG Global/BAM segment.
64

Ark
On January 1, 2021, White Mountains completed the Ark Transaction. See Note 2 — “Significant Transactions”.
In connection with the Ark Transaction, White Mountains committed to contribute up to an additional $200 million of equity capital to Ark in 2021. White Mountains and Ark have agreed to extend the deadline for Ark to call the additional $200 million of capital to September 15, 2021.
In July 2021, Ark issued €39 million (approximately $46 million based upon the foreign exchange spot rate as of the transaction date) of subordinated debt and it continues to make progress on the balance of its planned capital raise.
Ark writes a diversified portfolio of insurance and reinsurance, including property, marine & energy, specialty, accident & health and casualty, through Lloyd’s Syndicates 4020 and 3902 (the “Syndicates”). Beginning in January 2021, Ark began writing certain classes of its business through GAIL.
The following table presents the components of pre-tax loss included in White Mountains’s Ark segment for the three and six months ended June 30, 2021:

Millions |  | Three Months Ended June 30, 2021 |  | Six Months Ended June 30, 2021
Earned insurance and reinsurance premiums |  | $ | 117.8 |  |  | $ | 222.4 |
Net investment income |  | .4 |  |  | 1.2 |
Net realized and unrealized investment gains |  | 8.9 |  |  | 10.0 |
Other revenues |  | 3.4 |  |  | 6.0 |
Total revenues |  | 130.5 |  |  | 239.6 |
Losses and LAE |  | 52.6 |  |  | 118.6 |
Insurance and reinsurance acquisition expenses |  | 34.0 |  |  | 70.7 |
Other underwriting expenses |  | 19.1 |  |  | 30.3 |
General and administrative expenses |  | 5.7 |  |  | 32.3 |
Interest expense |  | 1.3 |  |  | 2.4 |
Total expenses |  | 112.7 |  | 254.3
Pre-tax income (loss) |  | $ | 17.8 |  |  | $ | (14.7) |

For the years of account prior to the Ark Transaction, a significant proportion of the Syndicates’ underwriting capital was provided by other third-party insurance and reinsurance groups (“TPC Providers”) using whole account reinsurance contracts through Ark’s corporate member. The TPC Providers’ economic participation in the Syndicates for the remaining open years of account prior to the Ark Transaction is approximately 51% of the total net result of the Syndicates. Captions within Ark’s results of operations are shown net of amounts relating to the TPC Providers share of the Syndicates’ results, including investment results.
65

Ark Results—Three Months Ended June 30, 2021
Ark’s GAAP combined ratio was 90% in the second quarter of 2021. The GAAP combined ratio included 8 points of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business, and 6 points of catastrophe losses.
Ark’s adjusted combined ratio was 84% in the second quarter of 2021. The adjusted combined ratio included 10 points of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business, and 6 points of catastrophe losses.
Ark reported pre-tax income of $18 million in the second quarter of 2021.
The following table presents Ark’s loss and loss adjustment expense, insurance acquisition expense, other underwriting expense and combined ratios on both a GAAP-basis and an adjusted basis, which adds back amounts ceded to TPC Providers, for the three months ended June 30, 2021:

|  | Three Months Ended June 30, 2021
$ in Millions |  | GAAP |  | Third Party Capital Share (1) |  | Adjusted
Insurance premiums: |  |  |  |  |  |
Gross written premiums |  | $ | 328.1 |  |  | $ | — |  |  | $ | 328.1 |
Net written premiums |  | $ | 262.2 |  |  | $ | (3.0) |  |  | $ | 259.2 |
Net earned premiums |  | $ | 117.8 |  |  | $ | 15.7 |  |  | $ | 133.5 |
Insurance expenses: |  |  |  |  |  |
Loss and loss adjustment expenses |  | $ | 52.6 |  |  | $ | 6.6 |  |  | $ | 59.2 |
Insurance acquisition expenses |  | 34.1 |  |  | — |  |  | 34.1 |
Other underwriting expenses |  | 19.1 |  |  | (.1) |  |  | 19.0 |
Total insurance expenses |  | $ | 105.8 |  |  | $ | 6.5 |  |  | $ | 112.3 |
Ratios: |  |  |  |  |  |
Loss and loss adjustment expense |  | 44.7 | % |  |  |  | 44.3 | %
Insurance acquisition expense |  | 28.9 | % |  |  |  | 25.5 | %
Other underwriting expense |  | 16.2 | % |  |  |  | 14.2 | %
Combined Ratio |  | 89.8 | % |  |  |  | 84.0 | %

(1) See “NON-GAAP FINANCIAL MEASURES” on page 84.
Gross Written Premiums
The following table presents Ark’s gross written premiums by line of business for the three months ended June 30, 2021 and the three months ended June 30, 2020, which was prior to White Mountains’s ownership of Ark. White Mountains believes this is useful in understanding the underwriting growth in the newly acquired business. Gross written premiums increased 78% to $328 million in the second quarter of 2021, compared to the second quarter of 2020, with risk adjusted rate change up approximately 7%.

|  | For the Three Months Ended
Millions |  | June 30, 2021 |  | June 30, 2020
Property |  | $ | 176.7 |  |  | $ | 87.4 |
Specialty |  | 68.8 |  |  | 35.3 |
Marine & Energy |  | 50.2 |  |  | 40.3 |
Casualty |  | 17.5 |  |  | (.3) |
Accident & Health |  | 14.9 |  |  | 22.1 |
Total Gross Written Premium |  | $ | 328.1 |  |  | $ | 184.8 |

66

Ark Results—Six Months Ended June 30, 2021
Ark’s GAAP combined ratio was 99% in the first six months of 2021. The GAAP combined ratio included 10 points of catastrophe losses, of which 7 points related to Winter Storm Uri, and 4 points of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business.
Ark’s adjusted combined ratio was 96% in the first six months of 2021. The adjusted combined ratio included 12 points of catastrophe losses, of which 8 points related to Winter Storm Uri, and 5 points of favorable prior year development, primarily related to the Property, Energy and Accident & Health lines of business.
Ark reported pre-tax loss of $15 million in the first six months of 2021, which included $25 million of transaction expenses related to the Ark Transaction.
The following table presents Ark’s loss and loss adjustment expense, insurance acquisition expense, other underwriting expense and combined ratios on both a GAAP-basis and an adjusted basis, which adds back amounts ceded to TPC Providers, for the six months ended June 30, 2021:

|  | Six Months Ended June 30, 2021
$ in Millions |  | GAAP |  | Third Party Capital Share (1) |  | Adjusted
Insurance premiums: |  |  |  |  |  |
Gross written premiums |  | $ | 732.6 |  |  | $ | — |  |  | $ | 732.6 |
Net written premiums |  | $ | 604.6 |  |  | $ | (8.0) |  |  | $ | 596.6 |
Net earned premiums |  | $ | 222.4 |  |  | $ | 46.9 |  |  | $ | 269.3 |
Insurance expenses: |  |  |  |  |  |
Loss and loss adjustment expenses |  | $ | 118.6 |  |  | $ | 38.2 |  |  | $ | 156.8 |
Insurance acquisition expenses |  | 70.8 |  |  | — |  |  | 70.8 |
Other underwriting expenses |  | 30.3 |  |  | 1.2 |  |  | 31.5 |
Total insurance expenses |  | $ | 219.7 |  |  | $ | 39.4 |  |  | $ | 259.1 |
Ratios: |  |  |  |  |  |
Loss and loss adjustment expense |  | 53.3 | % |  |  |  | 58.2 | %
Insurance acquisition expense |  | 31.8 | % |  |  |  | 26.3 | %
Other underwriting expense |  | 13.6 | % |  |  |  | 11.7 | %
Combined Ratio |  | 98.7 | % |  |  |  | 96.2 | %

(1) See “NON-GAAP FINANCIAL MEASURES” on page 84.
67

Gross Written Premiums
The following table presents Ark’s gross written premiums by line of business for the first six months ended June 30, 2021 and 2020, which was prior to White Mountains’s ownership of Ark. White Mountains believes this is useful in understanding the underwriting growth in the newly acquired business. Gross written premiums increased 93% to $733 million in the first six months of 2021, compared to the first six months of 2020, with risk adjusted rate change up approximately 9%.

|  | For the Six Months Ended
Millions |  | June 30, 2021 |  | June 30, 2020
Property |  | $ | 280.3 |  |  | $ | 131.9 |
Marine & Energy |  | 190.2 |  |  | 94.4 |
Specialty |  | 178.5 |  |  | 69.6 |
Accident & Health |  | 52.8 |  |  | 64.6 |
Casualty |  | 30.8 |  |  | 20.0 |
Total Gross Written Premium |  | $ | 732.6 |  |  | $ | 380.5 |

Catastrophe Risk Management
Ark has exposure to losses caused by unpredictable catastrophic events. Covered unpredictable catastrophic events include natural and other disasters, such as hurricanes, windstorms, earthquakes, floods, wildfires and severe winter weather. Catastrophes can also include public health crises, terrorist attacks, explosions, infrastructure failures and cyber-attacks. The extent of a catastrophe loss is a function of both the severity of the event and total amount of insured exposure affected by the event. During 2020, Ark incurred $24 million of natural catastrophe losses and $28 million of COVID-19 related losses after reinstatement premiums and amounts ceded to third-party reinsurers but before amounts ceded to TPC Providers.
Ark seeks to manage its exposure to catastrophic losses by limiting the aggregate insured value of policies in geographic areas with exposure to catastrophic events by estimating potential losses for many different catastrophe scenarios and by buying reinsurance, including retrocessional coverages. To manage and analyze aggregate insured values and potential losses, Ark uses a variety of tools, including external and internal catastrophe modeling software packages.
Based upon its business plan for 2021, Ark estimates that its two largest modeled probable maximum loss natural catastrophe scenarios on a net occurrence basis at a 1-in-250-year return period are U.S. windstorm and U.S. earthquake. In each case, the estimated net impact of a 1-in-250-year return period loss is expected to be less than 25% of total tangible capital (shareholders equity and subordinated debt). The net impact is before income tax but after reinstatement premiums, amounts ceded to third party reinsurers and amounts ceded to TPC Providers. In addition, Ark also has significant exposure to Japanese earthquake, Japanese windstorm, European windstorm and U.S. wildfire.
Ark’s estimates of potential losses are dependent on many variables, including assumptions about demand surge and storm surge, loss adjustment expenses, insurance-to-value and storm intensity in the aftermath of weather-related catastrophes utilized to model the event, the relationship of the actual event to the modeled event and the quality of data provided by ceding companies (in the case of our reinsurance operations). Accordingly, if the assumptions about the variables are incorrect, the losses Ark might incur from an actual catastrophe could be materially higher than the expectation of losses generated from modeled catastrophe scenarios. There could also be unmodelled losses which exceed the amounts estimated for U.S. windstorm and U.S. earthquake. For a further discussion, see “Risk Factors – Unpredictable catastrophic events could adversely affect our results of operations and financial condition” in White Mountains’s Annual Report on Form 10-K for the year ended December 31, 2020.
68

NSM
The following table presents the components of GAAP net loss, EBITDA and adjusted EBITDA included in White Mountains’s NSM segment for the three and six months ended June 30, 2021 and 2020. NSM’s pre-tax loss for the six months ended June 30,2021 included a loss of $29 million related to the sale of its Fresh Insurance’s motor business. See Note 2 — “Significant Transactions”.

|  | Three Months Ended June 30, |  | Six Months Ended June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Commission revenues |  | $ | 68.0 |  |  | $ | 63.0 |  |  | $ | 127.6 |  |  | $ | 116.0 |
Broker commission expenses |  | 21.6 |  |  | 21.0 |  |  | 40.5 |  |  | 39.3 |
Gross profit |  | 46.4 |  |  | 42.0 |  |  | 87.1 |  |  | 76.7 |
Other revenues |  | 16.3 |  |  | 13.1 |  |  | 31.5 |  |  | 25.1 |
General and administrative expenses |  | 47.3 |  |  | 48.5 |  |  | 93.3 |  |  | 88.1 |
Change in fair value of contingent consideration |  | .2 |  |  | (1.7) |  |  | .2 |  |  | (2.3) |
Amortization of other intangible assets |  | 8.2 |  |  | 6.3 |  |  | 16.8 |  |  | 11.1 |
Loss on assets held for sale |  | — |  |  | — |  |  | 28.7 |  |  | — |
Interest expense |  | 5.9 |  |  | 5.7 |  |  | 11.8 |  |  | 10.0 |
GAAP pre-tax income (loss) |  | 1.1 |  |  | (3.7) |  |  | (32.2) |  |  | (5.1) |
Income tax expense (benefit) |  | 1.2 |  |  | (2.2) |  |  | (6.8) |  |  | (2.9) |
GAAP net loss |  | (.1) |  |  | (1.5) |  |  | (25.4) |  |  | (2.2) |
Add back: |  |  |  |  |  |  |  |
Interest expense |  | 5.9 |  |  | 5.7 |  |  | 11.8 |  |  | 10.0 |
Income tax expense (benefit) |  | 1.2 |  |  | (2.2) |  |  | (6.8) |  |  | (2.9) |
General and administrative expenses — depreciation |  | 1.2 |  |  | .8 |  |  | 2.3 |  |  | 1.7 |
Amortization of other intangible assets |  | 8.2 |  |  | 6.3 |  |  | 16.8 |  |  | 11.1 |
EBITDA (1) |  | 16.4 |  |  | 9.1 |  |  | (1.3) |  |  | 17.7 |
Add back: |  |  |  |  |  |  |  |
Change in fair value of contingent consideration liabilities |  | .2 |  |  | (1.7) |  |  | .2 |  |  | (2.3) |
Non-cash equity-based compensation expense |  | .5 |  |  | — |  |  | 1.1 |  |  | — |
Impairments of intangible assets |  | — |  |  | 6.2 |  |  | — |  |  | 6.2 |
Loss on assets held for sale |  | — |  |  | — |  |  | 28.7 |  | — |
Acquisition-related transaction expenses |  | .2 |  |  | 3.3 |  |  | .2 |  |  | 5.0 |
Investments made in the development of new business lines |  | .1 |  |  | .4 |  |  | .1 |  |  | .4 |
Restructuring expenses |  | 1.6 |  |  | .7 |  |  | 4.4 |  |  | 1.5 |
Adjusted EBITDA (1) |  | $ | 19.0 |  |  | $ | 18.0 |  |  | $ | 33.4 |  |  | $ | 28.5 |

(1) See “NON-GAAP FINANCIAL MEASURES” on page 84.
NSM Results—Three Months Ended June 30, 2021 versus Three Months Ended June 30, 2020
NSM reported pre-tax income of $1 million, adjusted EBITDA of $19 million and commission and other revenues of $84 million in the second quarter of 2021, compared to pre-tax loss of $4 million, adjusted EBITDA of $18 million and commission and other revenues of $76 million in the second quarter of 2020. The increase in NSM’s pre-tax results in the second quarter of 2021, compared to the second quarter of 2020 was driven primarily by growth in the pet, social services and specialty transportation verticals, partially offset by a decline in the real estate vertical. NSM’s general and administrative expenses were $47 million in the second quarter of 2021, compared to $49 million in the second quarter of 2020. The decrease in NSM’s general and administrative expenses in the second quarter of 2021, compared to the second quarter of 2020 was driven primarily by a $6 million impairment of intangible assets related to NSM’s U.K. vertical in the second quarter of 2020.
69

NSM’s business consists of over 16 active programs that are broadly categorized into six market verticals. The following table presents the controlled premium and commission and other revenues by vertical for the three months ended June 30, 2021 and 2020:

|  | Three Months Ended June 30,
|  | 2021 |  | 2020 |  |
$ in Millions |  | Controlled Premium (1) |  | Commission and Other Revenues |  | Controlled Premium (1) |  | Commission and Other Revenues |  |  |  |
Specialty Transportation |  | $ | 92.7 |  |  | $ | 26.5 |  |  | $ | 84.6 |  |  | $ | 23.8 |  |  |  |  |
Real Estate |  | 42.2 |  |  | 9.3 |  |  | 65.6 |  |  | 15.4 |  |  |  |  |
Social Services |  | 38.0 |  |  | 9.3 |  |  | 29.2 |  |  | 7.3 |  |  |  |  |
Pet |  | 45.3 |  |  | 18.5 |  |  | 32.0 |  |  | 13.2 |  |  |  |  |
United Kingdom |  | 50.3 |  |  | 13.8 |  |  | 41.6 |  |  | 12.4 |  |  |  |  |
Other |  | 40.5 |  |  | 6.9 |  |  | 27.4 |  |  | 4.0 |  |  |  |  |
Total |  | $ | 309.0 |  |  | $ | 84.3 |  |  | $ | 280.4 |  |  | $ | 76.1 |  |  |  |  |

(1) Controlled Premium are total premiums placed by NSM during the period.
Specialty Transportation: NSM’s specialty transportation controlled premium and commission and other revenues increased 10% and 11% in the second quarter of 2021, compared to the second quarter of 2020, driven primarily by the impact of higher commission levels in collector car and the trucking business. The higher commission levels in collector car will continue to flow through this program’s results over the balance of the year.
Real Estate: NSM’s real estate controlled premium and commission and other revenues decreased 36% and 40%, respectively, in the second quarter of 2021, compared to the second quarter of 2020, driven primarily by declines in both rate and units in the coastal condominium program, partially offset by growth in units in NSM’s excess and surplus habitational program. The declines in the coastal condominium program were driven primarily by lower insurance carrier capacity available for the program as NSM transitions to a new insurance carrier platform. Until additional capacity is raised, the impact of lower capacity in the coastal condominium program will continue to flow through this program’s results through the balance of the year.
Social Services: NSM’s social services controlled premium and commission and other revenues increased 30% and 27%, respectively, in the second quarter of 2021, compared to the second quarter of 2020, driven primarily by substantial growth in units resulting from the lifting of COVID-19 lockdowns.
Pet: NSM’s pet controlled premium and commission and other revenues increased 42% and 40%, respectively, in the second quarter of 2021, compared to the second quarter of 2020 driven primarily by substantial growth in units. The increase in commission and other revenues was slightly less than premium as lower rate affinity business grew faster than direct market business.
United Kingdom: NSM’s United Kingdom controlled premium and commission and other revenues increased 21% and 11%, respectively, in the second quarter of 2021, compared to the second quarter of 2020, driven primarily by growth in units in the MGA business as COVID-19 pandemic restrictions in the United Kingdom began to lift. Commission and other revenues increased less than controlled premium as lower rate MGA controlled premium increased significantly more than higher rate brokerage controlled premium.
Other: NSM’s other controlled premium and commission and other revenues increased 48% and 68%, respectively, in the second quarter of 2021, compared to the second quarter of 2020, driven primarily by increases in the workers compensation and staffing markets resulting from the lifting of COVID-19 lockdowns. Commission and other revenues increased more than controlled premium due to favorable product mix shifts into higher rate workers compensation.
COVID-19
The COVID-19 pandemic negatively impacted certain programs (e.g., lower volumes in the non-standard auto and outdoor leisure businesses in the United Kingdom) while others have been positively impacted (e.g., higher volumes in pet). Results at NSM could still be negatively impacted in the coming quarters, but White Mountains does not currently anticipate dramatic impacts over the fullness of time.
70

NSM Results—Six Months Ended June 30, 2021 versus Six Months Ended June 30, 2020
NSM reported pre-tax loss of $32 million, adjusted EBITDA of $33 million and commission and other revenues of $159 million in the first six months of 2021, compared to pre-tax loss of $5 million, adjusted EBITDA of $29 million and commission and other revenues of $141 million in the first six months of 2020. NSM’s pre-tax loss in the first quarter of 2021 includes a loss of $29 million related to the sale of its Fresh Insurance motor business. Results in the first six months of 2021 and the first six months of 2020, from the date of acquisition, include the results of Kingsbridge, a leading provider of commercial lines insurance and consulting services to the contingent workforce in the United Kingdom, which was acquired on April 7, 2020. See Note 2 — “Significant Transactions”. NSM’s general and administrative expenses were $93 million in the first six months of 2021, compared to $88 million in the first six months of 2020. The increase in NSM’s general and administrative expenses in the first six months of 2021, compared to the first six months of 2020 was driven primarily by the acquisition of Kingsbridge and additional investments in collector car and pet to support growth, partially offset by a $6 million impairment of intangible assets related to NSM’s U.K. vertical in the second quarter of 2020.
The following table presents the controlled premium and commission and other revenues by vertical for the six months ended June 30, 2021 and 2020:

|  | Six Months Ended June 30,
|  | 2021 |  | 2020 |  |
$ in Millions |  | Controlled Premium (1) |  | Commission and Other Revenues |  | Controlled Premium (1) |  | Commission and Other Revenues |  |  |  |
Specialty Transportation |  | $ | 167.5 |  |  | $ | 47.3 |  |  | $ | 158.8 |  |  | $ | 44.2 |  |  |  |  |
Real Estate |  | 85.1 |  |  | 19.0 |  |  | 114.1 |  |  | 26.7 |  |  |  |  |
Social Services |  | 65.1 |  |  | 16.0 |  |  | 53.7 |  |  | 13.6 |  |  |  |  |
Pet |  | 89.0 |  |  | 35.7 |  |  | 61.3 |  |  | 25.1 |  |  |  |  |
United Kingdom |  | 102.6 |  |  | 26.9 |  |  | 80.4 |  |  | 22.4 |  |  |  |  |
Other |  | 79.9 |  |  | 14.2 |  |  | 63.3 |  |  | 9.1 |  |  |  |  |
Total |  | $ | 589.2 |  |  | $ | 159.1 |  |  | $ | 531.6 |  |  | $ | 141.1 |  |  |  |  |

(1) Controlled Premium are total premiums placed by NSM during the period.
Specialty Transportation: NSM’s specialty transportation controlled premium and commission and other revenues increased 5% and 7%, respectively, in the first six months of 2021, compared to the first six months of 2020, driven primarily by the impact of higher commission levels in collector car. The higher commission levels in collector car will continue to flow through this program’s results over the balance of the year.
Real Estate: NSM’s real estate controlled premium and commission and other revenues decreased 25% and 29%, respectively, in the first six months of 2021, compared to the first six months of 2020, driven primarily by declines in both rate and units in the coastal condominium program, partially offset by growth in units in NSM’s excess and surplus habitational program. The declines in the coastal condominium program were driven primarily by lower insurance carrier capacity available for the program as NSM transitions to a new insurance carrier platform. Until additional capacity is raised, the impact of lower capacity in the coastal condominium program will continue to flow through this program’s results through the balance of the year.
Social Services: NSM’s social services controlled premium and commission and other revenues increased 21% and 18%, respectively, in the first six months of 2021, compared to the first six months of 2020, driven primarily by rate increases and growth in units resulting from the lifting of COVID-19 lockdowns, slightly offset by a shift in product mix.
Pet: NSM’s pet controlled premium and commission and other revenues increased 45% and 42%, respectively, in the first six months of 2021, compared to the first six months of 2020, driven primarily by substantial growth in units. The increase in commission and other revenues was slightly less than premium as lower rate affinity business grew faster than direct market business.
United Kingdom: NSM’s United Kingdom controlled premium and commission and other revenues increased 28% and 20%, respectively, in the first six months of 2021, compared to the first six months of 2020, driven primarily by the acquisition of Kingsbridge and growth in the MGA business. Excluding Kingsbridge, which was acquired in April 2020, United Kingdom controlled premium increased 11% in the first six months of 2021, compared to the first six months of 2020, as the COVID-19 pandemic restrictions in the United Kingdom began to lift and growth in units increased in the MGA business. Excluding Kingsbridge, commission and other revenues declined 3% due to the sale of the Fresh Insurance motor business in April 2021, and changes in product mix, as lower rate MGA controlled premium increased and higher rate brokerage controlled premium decreased.
Other: NSM’s other controlled premium and commission and other revenues increased 26% and 56%, respectively in the first six months of 2021, compared to the first six months of 2020, driven primarily by increases in the workers compensation and staffing markets resulting from the lifting of COVID-19 lockdowns. Commission and other revenues increased more than controlled premium due to favorable product mix shifts into higher rate workers compensation and an increase in contingent commissions.
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Kudu
During the six months ended June 30, 2021, Kudu deployed $11 million in an existing portfolio company. As of June 30, 2021, Kudu has deployed a total of $398 million in 13 asset management firms, with an average cash yield to Kudu at inception of 10.3%. The firms have combined assets under management of approximately $52 billion, spanning a range of asset classes, including real estate, real assets, wealth management, hedge funds, private equity and alternative credit strategies.
On March 23, 2021, Kudu replaced its existing secured bank facility with the Kudu Credit Facility. Subject to maximum LTV levels, the maximum borrowing capacity of the Kudu Credit Facility is $300 million (which includes the initial advanced amount of $102 million). See Note 7 — “Debt”.
The following table presents the components of GAAP net income (loss), EBITDA and adjusted EBITDA included in White Mountains’s Kudu segment for the three and six months ended June 30, 2021 and 2020:

|  |  |  | Three Months Ended June 30, |  | Six Months Ended June 30, |  |
Millions |  |  |  | 2021 |  | 2020 |  | 2021 |  | 2020 |  |
Net investment income |  |  |  | $ | 8.4 |  |  | $ | 5.6 |  |  | $ | 16.6 |  |  | $ | 12.9 |  |  |
Net unrealized investment gains (losses) |  |  |  | 27.8 |  |  | 16.5 |  |  | 43.6 |  |  | (8.3) |  |  |
Other revenues |  |  |  | — |  |  | — |  |  | .1 |  |  | .1 |  |  |
Total revenues |  |  |  | 36.2 |  |  | 22.1 |  |  | 60.3 |  |  | 4.7 |  |  |
General and administrative expenses |  |  |  | 3.2 |  |  | 2.8 |  |  | 5.7 |  |  | 5.3 |  |  |
Amortization of other intangible assets |  |  |  | .1 |  |  | .1 |  |  | .2 |  |  | .2 |  |  |
Interest expense |  |  |  | 1.5 |  |  | 1.5 |  |  | 7.3 |  |  | 2.9 |  |  |
Total expenses |  |  |  | 4.8 |  |  | 4.4 |  |  | 13.2 |  |  | 8.4 |  |  |
GAAP pre-tax income (loss) |  |  |  | 31.4 |  |  | 17.7 |  |  | 47.1 |  |  | (3.7) |  |  |
Income tax expense (benefit) |  |  |  | 9.7 |  |  | 4.8 |  |  | 17.5 |  |  | (.6) |  |  |
GAAP net income (loss) |  |  |  | 21.7 |  |  | 12.9 |  |  | 29.6 |  |  | (3.1) |  |  |
Add back: |  |  |  |  |  |  |  |  |  |  |  |
Interest expense |  |  |  | 1.5 |  |  | 1.5 |  |  | 7.3 |  |  | 2.9 |  |  |
Income tax expense (benefit) |  |  |  | 9.7 |  |  | 4.8 |  |  | 17.5 |  |  | (.6) |  |  |
Amortization of other intangible assets |  |  |  | .1 |  |  | .1 |  |  | .2 |  |  | .2 |  |  |
EBITDA (1) |  |  |  | 33.0 |  |  | 19.3 |  |  | 54.6 |  |  | (.6) |  |  |
Add back: |  |  |  |  |  |  |  |  |  |  |  |
Net unrealized investment (gains) losses |  |  |  | (27.8) |  |  | (16.5) |  |  | (43.6) |  |  | 8.3 |  |  |
Non-cash equity-based compensation expense |  |  |  | .1 |  |  | — |  |  | .2 |  |  | — |  |  |
Acquisition-related transaction expenses |  |  |  | — |  |  | .9 |  |  | — |  |  | 1.5 |  |  |
Adjusted EBITDA (1) |  |  |  | $ | 5.3 |  |  | $ | 3.7 |  |  | $ | 11.2 |  |  | $ | 9.2 |  |  |

(1) See “NON-GAAP FINANCIAL MEASURES” on page 84.
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Kudu Results—Three Months Ended June 30, 2021 versus Three Months Ended June 30, 2020
Kudu reported pre-tax income of $31 million, adjusted EBITDA of $5 million and total revenues of $36 million in the second quarter of 2021, compared to pre-tax income of $18 million, adjusted EBITDA of $4 million and total revenues of $22 million in the second quarter of 2020. Pre-tax income in the second quarter of 2021 included $28 million of unrealized gains on Kudu’s Participation Contracts, compared to $17 million of unrealized gains on Kudu’s participation contracts in the second quarter of 2020. The increase in unrealized gains on Kudu’s Participation Contracts was driven primarily by asset growth and the performance of Kudu’s portfolio of asset managers. The increases in net investment income were driven primarily by amounts earned from the $111 million (including approximately $2 million of transaction costs) in new deployments that Kudu made subsequent to the first quarter of 2020.
COVID-19
Over time, Kudu’s revenues will fluctuate with increases and decreases in assets under management and fee levels at Kudu’s underlying asset management business, which are impacted by increases and decreases in financial markets, such as those experienced during 2020 in response to the COVID-19 pandemic. Kudu’s portfolio diversification, in particular its emphasis on private capital and its de-emphasis on long-only strategies, should continue to provide some downside protection to financial market declines.
Kudu Results—Six Months Ended June 30, 2021 versus Six Months Ended June 30, 2020
Kudu reported pre-tax income of $47 million, adjusted EBITDA of $11 million and total revenues of $60 million in the first six months of 2021, compared to pre-tax loss of $4 million, adjusted EBITDA of $9 million and total revenues of $5 million in the first six months of 2020. Pre-tax income in the first six months of 2021 included $44 million of unrealized gains on Kudu’s Participation Contracts, driven primarily by asset growth and the performance of Kudu’s portfolio of asset managers. Pre-tax income in the first six months of 2020 included $8 million of unrealized losses on Kudu’s participation contracts, which reflected the impact of the market dislocation from the COVID-19 pandemic on Kudu’s underlying asset management firms. The increases in net investment income were driven primarily by amounts earned from the $132 million (including approximately $3 million of transaction costs) in new deployments that Kudu made in 2020 and 2021.
Other Operations
The following table presents a summary of White Mountains’s financial results from its Other Operations segment for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
Millions |  | 2021 |  | 2020 |  | 2021 |  | 2020
Net investment income |  | $ | 4.0 |  |  | $ | 9.1 |  |  | $ | 11.1 |  |  | $ | 19.2 |
Net realized and unrealized investment gains (losses) |  | 16.6 |  |  | 107.0 |  |  | 18.7 |  |  | (61.0) |
Net realized and unrealized investment gains from investment in MediaAlpha |  | 113.0 |  |  | 15.0 |  |  | 71.3 |  |  | 45.0 |
Commission revenues |  | 2.3 |  |  | 1.9 |  |  | 4.6 |  |  | 4.0 |
Other revenues |  | 22.4 |  |  | 2.3 |  |  | 29.5 |  |  | 3.8 |
Total revenues |  | 158.3 |  |  | 135.3 |  |  | 135.2 |  |  | 11.0 |
Cost of sales |  | 17.9 |  |  | 2.2 |  |  | 21.9 |  |  | 4.2 |
General and administrative expenses |  | 29.5 |  |  | 25.3 |  |  | 65.2 |  |  | 42.8 |
Amortization of other intangible assets |  | .4 |  |  | .2 |  |  | .9 |  |  | .4 |
Interest expense |  | .4 |  |  | .2 |  |  | .7 |  |  | .5 |
Total expenses |  | 48.2 |  |  | 27.9 |  |  | 88.7 |  |  | 47.9 |
Pre-tax income (loss) |  | $ | 110.1 |  |  | $ | 107.4 |  |  | $ | 46.5 |  |  | $ | (36.9) |

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Other Operations Results—Three Months Ended June 30, 2021 versus Three Months Ended June 30, 2020
White Mountains’s Other Operations segment reported pre-tax income of $110 million in the second quarter of 2021, compared to $107 million in the second quarter of 2020. White Mountains’s Other Operations segment reported net realized and unrealized investment gains from its investment in MediaAlpha of $113 million in the second quarter of 2021, compared to $15 million in the second quarter of 2020. White Mountains’s Other Operations segment reported net realized and unrealized investment gains of $17 million in the second quarter of 2021, compared to $107 million in the second quarter of 2020. White Mountains’s Other Operations segment reported net investment income of $4 million in the second quarter of 2021, compared to $9 million in the second quarter of 2020. See Summary of Investment Results on page 75.
The Other Operations segment reported $22 million of other revenues in the second quarter of 2021, compared to $2 million in the second quarter of 2020. The Other Operations segment reported $18 million of cost of sales in the second quarter of 2021, compared to $2 million in the second quarter of 2020. The increases in other revenues and cost of sales were driven primarily by an acquisition within the Other Operations segment.
The Other Operations segment reported general and administrative expenses of $30 million in the second quarter of 2021, compared to $25 million in the second quarter of 2020. The increase in general and administrative expenses was driven primarily by higher incentive compensation costs, due to an increase in White Mountains’s share price and a higher assumed harvest percentage on outstanding performance shares in periods subsequent to the MediaAlpha IPO.
Other Operations Results—Six Months Ended June 30, 2021 versus Six Months Ended June 30, 2020
White Mountains’s Other Operations segment reported pre-tax income (loss) of $47 million in the first six months of 2021, compared to $(37) million in the first six months of 2020. White Mountains’s Other Operations segment reported net realized and unrealized investment gains from its investment in MediaAlpha of $71 million in the first six months of 2021, compared to $45 million in the first six months of 2020. White Mountains’s Other Operations segment reported net realized and unrealized investment gains (losses) of $19 million in the first six months of 2021, compared to $(61) million in the first six months of 2020. White Mountains’s Other Operations segment reported net investment income of $11 million in the first six months of 2021, compared to $19 million in the first six months of 2020. See Summary of Investment Results on page 75.
The Other Operations segment reported $30 million of other revenues in the first six months of 2021, compared to $4 million in the first six months of 2020. The Other Operations segment reported $22 million of cost of sales in the first six months of 2021, compared to $4 million in the first six months of 2020. The increases in other revenues and cost of sales were driven primarily by a new acquisition within the Other Operations segment.
The Other Operation segment reported general and administrative expenses of $65 million in the first six months of 2021, compared to $43 million in the first six months of 2020. The increase in general and administrative expenses was driven primarily by higher incentive compensation costs, due to an increase in White Mountains’s share price and a higher assumed harvest percentage on outstanding performance shares in periods subsequent to the MediaAlpha IPO.
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II. Summary of Investment Results
White Mountains’s total investment results include results from all segments. For purposes of discussing rates of return, all percentages are presented gross of management fees and trading expenses and are calculated before any adjustments for TPC Providers in order to produce a better comparison to benchmark returns.
The following table presents the pre-tax investment return for White Mountains’s consolidated portfolio for the three and six months ended June 30, 2021 and 2020:
Gross Investment Returns and Benchmark Returns
Prior to the MediaAlpha IPO, White Mountains’s investment in MediaAlpha was presented within other long-term investments. Subsequent to the MediaAlpha IPO, White Mountains presents its investment in MediaAlpha in a separate line item on the balance sheet. Amounts for periods prior to the MediaAlpha IPO have been reclassified to be comparable to the current period.
The following table presents White Mountains’s returns for the three and six months ended June 30, 2021 and 2020:

|  | Three Months Ended |  | Six Months Ended
|  | June 30, |  | June 30,
|  | 2021 |  | 2020 |  | 2021 |  | 2020
Fixed income investments |  | 0.8 | % |  | 2.8 | % |  | (0.1) | % |  | 3.6 | %
Bloomberg Barclays U.S. Intermediate Aggregate Index |  | 0.8 | % |  | 2.1 | % |  | (0.8) | % |  | 4.7 | %
Common equity securities |  | 3.6 | % |  | 19.2 | % |  | 5.5 | % |  | (5.8) | %
Investment in MediaAlpha |  | 18.8 | % |  | 8.3 | % |  | 8.7 | % |  | 27.9 | %
Other long-term investments |  | 5.7 | % |  | 2.7 | % |  | 10.0 | % |  | (3.3) | %
Total common equity securities, investment in MediaAlpha and other long-term investments |  | 10.0 | % |  | 10.1 | % |  | 10.9 | % |  | (0.5) | %
Total common equity securities and other long-term investments |  | 5.4 | % |  | 10.4 | % |  | 9.4 | % |  | (4.3) | %
S&P 500 Index (total return) |  | 8.5 | % |  | 20.5 | % |  | 15.3 | % |  | (3.1) | %
Total consolidated portfolio |  | 5.0 | % |  | 6.5 | % |  | 4.7 | % |  | 1.7 | %
Total consolidated portfolio - excluding MediaAlpha |  | 2.4 | % |  | 6.4 | % |  | 3.1 | % |  | — | %

Investment Returns—Three and Six Months Ended June 30, 2021 versus Three and Six Months Ended June 30, 2020
White Mountains’s pre-tax total return on invested assets was 5.0% in the second quarter of 2021. This return included $113 million of net unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 2.4% in the second quarter of 2021. Excluding MediaAlpha, investment returns in the second quarter of 2021 were driven primarily by favorable other long-term investments results and the impact of the flattening of the yield curve on the fixed income portfolio. White Mountains’s pre-tax total return on invested assets was 6.5% in the second quarter of 2020. This return included $18 million of net investment income and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 6.4% in the second quarter of 2020. Excluding MediaAlpha, investment returns in the second quarter of 2020 were driven primarily by a rebound in equity markets following the decline experienced in the first quarter of 2020 in reaction to the COVID-19 pandemic.
White Mountains’s pre-tax total return on invested assets was 4.7% in the first six months of 2021. This return included $71 million of net realized and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was 3.1% in first six months of 2021. Excluding MediaAlpha, investment returns in the first six months of 2021 were driven primarily by favorable other long-term investment results. White Mountains’s pre-tax total return on invested assets was 1.7% in the first six months of 2020. This return included $50 million of net investment income and unrealized investment gains from White Mountains’s investment in MediaAlpha. Excluding MediaAlpha, the total return on invested assets was flat in the first six months of 2020. Excluding MediaAlpha, returns in the first six months of 2020 were driven primarily by the decline in interest rates and favorable other long-term investments results, offset by the overall decline in equity markets over the period.
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Fixed Income Results
White Mountains’s fixed income portfolio, including short-term investments, was $2.3 billion and $1.4 billion as of June 30, 2021 and December 31, 2020. The increase was driven primarily by the inclusion of invested assets acquired in the Ark Transaction. The duration of White Mountains’s fixed income portfolio, including short-term investments, was 2.6 years and 3.2 years as of June 30, 2021 and December 31, 2020. White Mountains’s fixed income portfolio includes fixed maturity investments and short-term investments in the Collateral Trusts of $440 million and $432 million as of June 30, 2021 and December 31, 2020.
White Mountains’s fixed income portfolio returned 0.8% in the second quarter of 2021, compared to 2.8% in the second quarter of 2020, in line with and outperforming the Bloomberg Barclays U.S. Intermediate Aggregate Index returns of 0.8% and 2.1% for the comparable periods. White Mountains’s fixed income portfolio returned -0.1% in the first six months of 2021, compared to 3.6% in the first six months of 2020, outperforming and underperforming the Bloomberg Barclays U.S. Intermediate Aggregate Index returns of -0.8% and 4.7% for the comparable periods.
The results in the second quarter of 2021 were driven primarily by the impact of White Mountains’s overweight positioning to investment grade corporate bonds as longer-term interest rates declined during the quarter. The results in the first six months of 2021 were driven primarily by the short duration positioning of White Mountains’s fixed income portfolio as interest rates increased during the period. The results in the second quarter of 2020 were driven primarily by the impact of White Mountains’s overweight positioning to investment grade corporate bonds as credit spreads tightened significantly during the quarter. The results in the first six months of 2020 were driven primarily by the short duration positioning of White Mountains’s fixed income portfolio as interest rates declined significantly during the period.
Common Equity Securities, Investment in MediaAlpha and Other Long-Term Investments Results
White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments was $1.9 billion and $1.6 billion as of June 30, 2021 and December 31, 2020, which represented 46% and 54% of total invested assets. See Note 3 — “Investment Securities”. The change was driven primarily by the inclusion of invested assets relating to the Ark Transaction, partially offset by a decline in White Mountains’s investment in MediaAlpha resulting from the MediaAlpha secondary offering in the first quarter of 2021.
White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned 10.0% in the second quarter of 2021, which included $113 million of net unrealized investment gains from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 5.4% in the second quarter of 2021. White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned 10.1% in the second quarter of 2020, which included $18 million of net investment income and unrealized investment gains from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 10.4% in the second quarter of 2020.
White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned 10.9% in the first six months of 2021, which included $71 million of net realized and unrealized investment gains from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned 9.4% in the first six months of 2021. White Mountains’s portfolio of common equity securities, its investment in MediaAlpha and other long-term investments returned -0.5% in the first six months of 2020, which included $50 million of net investment income and unrealized investment gains from MediaAlpha. White Mountains’s portfolio of common equity securities and other long-term investments returned -4.3% in the first six months of 2020.
During the second half of 2020, White Mountains sold its portfolio of common equity securities, including its portfolio of ETFs and international common equity securities, in anticipation of funding the Ark Transaction. Following the Ark Transaction, White Mountains’s portfolio of common equity securities consists of international listed funds held by Ark. As of June 30, 2021, the fair value of White Mountains’s international listed funds was $142 million.
White Mountains’s portfolio of common equity securities returned 3.6% in the second quarter of 2021, compared to 19.2% in the second quarter of 2020, underperforming the S&P 500 Index returns of 8.5% and 20.5% for the comparable periods. White Mountains’s portfolio of common equity securities returned 5.5% in the first six months of 2021, compared to -5.8% in the first six months of 2020, underperforming the S&P 500 Index returns of 15.3% and -3.1% for the comparable periods. The results for the second quarter and first six months of 2021 and 2020 were driven primarily by relative underperformance in White Mountains’s non-U.S. common equity positions versus the S&P 500 Index for these periods.
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Historically, White Mountains’s portfolio of ETFs was designed to provide investment results that generally corresponded to the performance of the S&P 500 Index. White Mountains’s portfolio of ETFs was fully liquidated as of December 31, 2020. In the second quarter and first six months of 2020, White Mountains’s portfolio of ETFs essentially earned the effective index return, before expenses. White Mountains also maintained relationships with a small number of third-party registered investment advisers (the “actively managed common equity portfolio”), who primarily invested in non-U.S. equity securities through unit trusts. At the end of the third quarter of 2020, White Mountains fully redeemed its actively managed common equity portfolio. White Mountains’s actively managed common equity portfolio returned 15.6% in the second quarter of 2020, underperforming the S&P 500 Index return of 20.5%. White Mountains’s actively managed common equity portfolio returned -15.0% in the first six months of 2020, underperforming the S&P 500 Index returns of -3.1%.
White Mountains maintains a portfolio of other long-term investments that consists primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, ILS funds and private debt investments. White Mountains’s portfolio of other long-term investments was $1.1 billion and $787 million as of June 30, 2021 and December 31, 2020. The change in other long-term investments was driven primarily by the inclusion of invested assets held by Ark, the addition of a bank loan fund and an increase in the fair value of Kudu’s Participation Contracts.
White Mountains’s other long-term investments portfolio returned 5.7% in the second quarter of 2021, compared to 2.7% in the second quarter of 2020. Investment returns for the second quarter of 2021 were driven primarily by $36 million of net investment income and unrealized investment gains from Kudu’s Participation Contracts, driven primarily by asset growth and performance from Kudu’s underlying asset management firms, and $13 million of net investment income and realized and unrealized investment gains from private equity funds. Investment returns in the second quarter of 2020 included $22 million of net investment income and unrealized investment gains from Kudu’s Participation Contracts, primarily driven by the impact of the market rebound in the second quarter of 2020 on Kudu’s underlying asset management businesses.
White Mountains’s other long-term investments portfolio returned 10.0% in the first six months of 2021, compared to
-3.3% in the first six months of 2020. Investment returns for the first six months of 2021 were driven primarily by $60 million of net investment income and unrealized investment gains from Kudu’s Participation Contracts, driven primarily by asset growth and performance of Kudu’s underlying asset management firms, and $28 million of net investment income and realized and unrealized investment gains from private equity funds. Investment returns in the first six months of 2020 were driven by a $10 million decrease in the fair value of White Mountains’s investment in PassportCard/DavidShield, where the global slowdown in travel activity in reaction to the COVID-19 pandemic caused a significant decline in premiums and revenues, and a $8 million decrease in the fair value of Kudu’s Participation Contracts, driven by the impact of the market dislocation from the COVID-19 pandemic in the first quarter of 2020 on Kudu’s underlying asset management businesses.
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Foreign Currency Exposure
As of June 30, 2021, White Mountains had foreign currency exposure on $260 million of net assets primarily related to NSM’s U.K.-based operations, Kudu’s non-U.S. Participation Contracts, Ark’s non-U.S. business and certain other foreign consolidated and unconsolidated entities.
The following table presents the fair value of White Mountains’s foreign denominated net assets by segment as of June 30, 2021:

Currency $ in Millions |  | NSM |  | Kudu |  | Other Segment |  | Ark |  | Total Fair Value |  | % of Total Shareholders’ Equity |  |  |  |  |  |  |  |
GBP |  | $ | 122.4 |  |  | $ | — |  |  | $ | — |  |  | $ | 21.0 |  |  | $ | 143.4 |  |  | 3.5 | % |  |  |  |  |  |  |  |  |  |  |
AUD |  | — |  |  | 44.4 |  |  | — |  |  | 11.7 |  |  | 56.1 |  |  | 1.4 | % |  |  |  |  |  |  |  |  |  |  |
EUR |  | — |  |  | — |  |  | 21.0 |  |  | .2 |  |  | 21.2 |  |  | .5 | % |  |  |  |  |  |  |  |  |  |  |
CAD |  | — |  |  | — |  |  |  |  | 27.8 |  |  | 27.8 |  |  | .7 | % |  |  |  |  |  |  |  |  |  |  |
All other |  | — |  |  | — |  |  | 11.5 |  |  | — |  |  | 11.5 |  |  | .3 | % |  |  |  |  |  |  |  |  |  |  |
Total |  | $ | 122.4 |  |  | $ | 44.4 |  |  | $ | 32.5 |  |  | $ | 60.7 |  |  | $ | 260.0 |  |  | 6.4 | % |  |  |  |  |  |  |  |  |  |  |

Income Taxes
The Company and its Bermuda domiciled subsidiaries are not subject to Bermuda income tax under current Bermuda law. In the event there is a change in the current law and taxes are imposed, the Company and its Bermuda domiciled subsidiaries would be exempt from such tax until March 31, 2035 pursuant to the Bermuda Exempted Undertakings Tax Protection Act of 1966. The Company has subsidiaries and branches that operate in various other jurisdictions around the world that are subject to tax in the jurisdictions in which they operate. The jurisdictions in which the Company’s subsidiaries and branches are subject to tax are Ireland, Israel, Luxembourg, the United Kingdom and the United States.
White Mountains’s income tax expense related to pre-tax income from continuing operations for the three months ended June 30, 2021 represented an effective tax rate of 18%. The effective tax rate was different from the U.S. statutory rate of 21%, driven primarily by income generated in jurisdictions with lower tax rates than the United States partially offset by additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities. On June 10, 2021, the U.K. enacted an increase in its corporate tax rate from 19% to 25% for periods after April 1, 2023. On June 30, 2021, White Mountains increased its net U.K. deferred tax liability to reflect the higher tax rate on temporary differences projected to reverse after the new rate becomes effective.
White Mountains’s income tax expense related to pre-tax income from continuing operations for the six months ended June 30, 2021 represented an effective tax rate of 86%. The effective tax rate was higher than the U.S. statutory rate of 21%, driven primarily by the additional tax expense related to the revaluation of U.K. deferred tax assets and liabilities in relation to White Mountains’s pre-tax income in the first six months of 2021.
White Mountains’s income tax benefit related to pre-tax loss from continuing operations for the second quarter and first six months of June 30, 2020 represented an effective tax rate of 18% and 4%. The effective tax rate was different from the U.S. statutory rate of 21%, driven primarily by income generated in jurisdictions with lower tax rates than the United States and state income taxes. See Note 8 — “Income Taxes”.
Discontinued Operations
In the first quarter of 2021, White Mountains recorded an $18 million gain within discontinued operations as a result of reversing a liability arising from the tax indemnification provided in connection with the sale of Sirius Group in 2016. The liability related to certain interest deductions claimed by Sirius Group that had been disputed by the Swedish Tax Agency (STA). In April 2021, the STA informed the Swedish Administrative Court of Appeal that Sirius Group should prevail in its appeal (and that the interest deductions should not be disallowed). In June 2021, the Swedish Administrative Court of Appeal ruled in Sirius Group’s favor.
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LIQUIDITY AND CAPITAL RESOURCES
Operating Cash and Short-term Investments
Holding Company Level
The primary sources of cash for the Company and certain of its intermediate holding companies are expected to be distributions from its insurance, reinsurance and other operating subsidiaries, net investment income, proceeds from sales, repayments and maturities of investments, capital raising activities and, from time to time, proceeds from sales of operating subsidiaries. The primary uses of cash are expected to be general and administrative expenses, purchases of investments, payments to tax authorities, payments on and repurchases/retirements of its debt obligations, dividend payments to holders of the Company’s common shares, distributions to non-controlling interest holders of consolidated subsidiaries, contributions to operating subsidiaries and, from time to time, purchases of operating subsidiaries and repurchases of the Company’s common shares.
Operating Subsidiary Level
The primary sources of cash for White Mountains’s insurance, reinsurance and other operating subsidiaries are expected to be premium and fee collections, commissions, net investment income, proceeds from sales, repayments and maturities of investments, contributions from holding companies and capital raising activities. The primary uses of cash are expected to be claim payments, policy acquisition costs, general and administrative expenses, broker commission expenses, insurance acquisition expenses, loss payments, costs of sales, purchases of investments, payments to tax authorities, payments on and repurchases/retirements of its debt obligations, distributions made to holding companies, distributions to non-controlling interest holders and, from time to time, purchases of operating subsidiaries.
Both internal and external forces influence White Mountains’s financial condition, results of operations and cash flows. Claim settlements, premium and fee levels, loss payments, cost of sales and investment returns may be impacted by changing rates of inflation and other economic conditions. Some time may lapse between the occurrence of an insured loss, the reporting of the loss to White Mountains’s operating subsidiaries and the settlement of the liability for that loss. The exact timing of the payment of losses and benefits cannot be predicted with certainty. White Mountains’s insurance and reinsurance operating subsidiaries maintain portfolios of invested assets with varying maturities and a substantial amount of cash and short-term investments to provide adequate liquidity for the payment of claims.
Management believes that White Mountains’s cash balances, cash flows from operations and routine sales and maturities of investments are adequate to meet expected cash requirements for the foreseeable future on both a holding company and insurance, reinsurance and other operating subsidiary level.
Dividend Capacity
The following is a description of the dividend capacity of White Mountains’s insurance, reinsurance and other operating subsidiaries:
HG Global/BAM
As of June 30, 2021, HG Global had $619 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 the six months ended June 30, 2021, HG Global declared and paid a $22 million preferred dividend, of which White Mountains received $21 million. As of June 30, 2021, HG Global has accrued $384 million of dividends payable to holders of its preferred shares, $371 million of which is payable to White Mountains and is eliminated in consolidation. As of June 30, 2021, HG Global and its subsidiaries had $1 million of cash outside of HG Re.
HG Re is a Special Purpose Insurer subject to regulation and supervision by the BMA, but it 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 June 30, 2021, HG Re had $753 million of statutory capital and surplus and $836 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.
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The Supplemental Trust Target Balance is $603 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 June 30, 2021, the Collateral Trusts held assets of $836 million, which included $442 million of cash and investments, $388 million of BAM Surplus Notes and $6 million of interest receivable on the BAM Surplus Notes.
As of June 30, 2021, HG Re had $3 million of cash and investments and $118 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 is 3.1%. Beginning in 2025, the interest rate will be fixed at the higher of the then current variable rate or 8.0%. BAM is required to seek regulatory approval to pay interest and principal on the BAM Surplus Notes only to the extent that its remaining qualified statutory capital and other capital resources continue to support its outstanding obligations, its business plan and its “AA/stable” rating from Standard & Poor’s. No payment of principal or interest on the BAM Surplus Notes may be made without the approval of the NYDFS.
During the three and six months ended June 30, 2021, BAM made no repayments of the BAM Surplus Notes or accrued interest. 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, $48 million was a repayment of principal held in the Supplemental Trust, $1 million was a payment of accrued interest held in the Supplemental Trust and $16 million was a payment of accrued interest held outside the Supplemental Trust. See Note 10 — “Municipal Bond Guarantee Insurance”.
Ark
Group Ark Insurance Ltd. (“GAIL”), a class 4 licensed Bermuda insurer has the ability to declare or pay dividends or make capital distributions during any 12-month period without the prior approval of Bermuda regulatory authorities on the condition that any such declaration or payment of dividends or capital distributions does not cause a breach of any of its regulatory solvency and liquidity requirements. During 2021, GAIL has the ability, subject to meeting all appropriate liquidity and solvency requirements, to make dividend or capital distributions without the prior approval of regulatory authorities, subject to meeting all appropriate liquidity and solvency requirements, of $20 million, which is equal to 15% of its December 31, 2020 statutory capital, excluding earned surplus. The amount of dividends available to be paid by GAIL in any given year is also subject to cash flow and earnings generated by GAIL's business. During the six months ended June 30, 2021, GAIL did not pay a dividend to its immediate parent.
As of June 30, 2021, Ark and its intermediate holding companies had $5 million of net unrestricted cash, short-term investments and fixed maturity investments outside of its regulated and unregulated insurance and reinsurance operating subsidiaries. During the six months ended June 30, 2021, Ark did not pay any dividends to its immediate parent.
NSM
During the six months ended June 30, 2021, NSM distributed $2 million to unitholders, substantially all of which was paid to White Mountains. As of June 30, 2021, NSM had $64 million of net unrestricted cash and short-term investments.
Kudu
During the six months ended June 30, 2021, Kudu distributed $5 million to unitholders, substantially all of which was paid to White Mountains. As of June 30, 2021, Kudu had $10 million of net unrestricted cash and short-term investments.
Other Operations
During the six months ended June 30, 2021, White Mountains paid a $3 million common share dividend. As of June 30, 2021, the Company and its intermediate holding companies had $594 million of net unrestricted cash, short-term investments and fixed maturity investments, $713 million of MediaAlpha common stock and $159 million of private equity funds and ILS funds.
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Financing
The following table presents White Mountains’s capital structure as of June 30, 2021 and December 31, 2020:

$ in Millions |  | June 30, 2021 |  | December 31, 2020
Ark Alesco Notes |  | $ | 30.0 |  |  | $ | — |
Ark Dekania Note |  | 14.2 |  |  | — |
Ark Subordinated Notes (1) |  | 44.2 |  |  | — |
NSM Bank Facility (1)(2) |  | 269.4 |  |  | 271.3 |
Other NSM debt (1)(2) |  | 1.3 |  |  | 1.3 |
Kudu Credit Facility (1)(2) |  | 94.5 |  |  | — |
Kudu Bank Facility (1)(2) |  | — |  |  | 86.3 |
Other Operations debt (1)(2) |  | 19.4 |  |  | 17.5 |
Total debt |  | 428.8 |  |  | 376.4 |
Non-controlling interests—excluding BAM |  | 255.0 |  |  | 35.2 |
Total White Mountains’s common shareholders’ equity |  | 3,978.2 |  |  | 3,906.0 |
Total capital |  | 4,662.0 |  |  | 4,317.6 |
Time-value discount on expected future payments on the BAM Surplus Notes (3) |  | (132.8) |  |  | (142.5) |
HG Global’s unearned premium reserve (3) |  | 201.5 |  |  | 190.0 |
HG Global’s net deferred acquisition costs (3) |  | (56.3) |  |  | (52.4) |
Total adjusted capital |  | $ | 4,674.4 |  |  | $ | 4,312.7 |
Total debt to total adjusted capital |  | 9.2 | % |  | 8.7 | %

(1) See Note 7 — “Debt” for details of debt arrangements.
(2) Net of unamortized issuance costs
(3) Amount reflects White Mountains’s preferred share ownership in HG Global of 96.9%.
Management believes that White Mountains has the flexibility and capacity to obtain funds externally through debt or equity financing on both a short-term and long-term basis. However, White Mountains can provide no assurance that, if needed, it would be able to obtain additional debt or equity financing on satisfactory terms, if at all.
It is possible that, in the future, one or more of the rating agencies may lower White Mountains’s existing ratings. If one or more of its ratings were lowered, White Mountains could incur higher borrowing costs on future borrowings and its ability to access the capital markets could be impacted.
Covenant Compliance
As of June 30, 2021, White Mountains was in compliance in all material respects with all of the covenants under all of its debt instruments.
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Share Repurchases
White Mountains’s board of directors has authorized the Company to repurchase its common shares from time to time, subject to market conditions. The repurchase authorizations do not have a stated expiration date. As of June 30, 2021, 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 approved by its board of directors.
During the six months ended June 30, 2021, White Mountains repurchased and retired 7,161 of its common shares for $7 million, at an average share price of $1,039, which was approximately 80% of White Mountains’s June 30, 2021 adjusted book value per share. All of the shares White Mountains repurchased in the first six months of 2021 were to satisfy employee income tax withholding pursuant to employee benefit plans.
During the six months ended June 30, 2020, White Mountains repurchased and retired 99,087 of its common shares for $85 million, at an average share price of $859, which was approximately 84% of White Mountains’s June 30, 2020 adjusted book value per share. Of the shares White Mountains repurchased in the first six months of 2020, 5,899 were to satisfy employee income tax withholding pursuant to employee benefit plans, which do not reduce the board authorization.
Cash Flows
Detailed information concerning White Mountains’s cash flows during the six months ended June 30, 2021 and 2020 follows:
Cash flows from operations for the six months ended June 30, 2021 and June 30, 2020
Net cash provided from (used for) operations was $14 million in the six months ended June 30, 2021, compared to $(39) million in the six months ended June 30, 2020. The increase in cash provided from (used for) operations was primarily driven by a decrease in the deployments in Kudu’s participation contracts in the first six months ended June 30 2021, compared to the first six months ended June 30, 2020, partially offset by Ark’s transaction expenses during the six months ended June 30, 2021. As of June 30, 2021, the Company and its intermediate holding companies had $594 million of net unrestricted cash, short-term investments and fixed maturity investments, $713 million of MediaAlpha common stock and $159 million of private equity funds and ILS funds.
Cash flows from investing and financing activities for the six months ended June 30, 2021
Financing and Other Capital Activities
During the six months ended June 30, 2021, the Company declared and paid a $3 million cash dividend to its common shareholders.
During the six months ended June 30, 2021, White Mountains repurchased and retired 7,161 of its common shares for $7 million, all of which were repurchased under employee benefit plans for statutory withholding tax payments.
During the six months ended June 30, 2021, BAM received $30 million in MSC.
During the six months ended June 30, 2021, HG Global declared and paid $22 million of preferred dividends, of which $21 million was paid to White Mountains.
During the six months ended June 30, 2021, NSM distributed $2 million to unitholders, substantially all of which was paid to White Mountains.
During the six months ended June 30, 2021, NSM repaid $1 million in term loans under the NSM Bank Facility.
During the six months ended June 30, 2021, Kudu distributed $5 million to unitholders, substantially all of which was paid to White Mountains.
During the six months ended June 30, 2021, Kudu borrowed $3 million in term loans under the Kudu Bank Facility.
On March 23, 2021, Kudu entered into the Kudu Credit Facility with an initial draw of $102 million, of which $92 million was used to repay the outstanding principal balance on its term loans under the Kudu Bank Facility.
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Acquisitions and Dispositions
On January 1, 2021 White Mountains completed the Ark Transaction, which included contributing $605 million of equity capital to Ark, at a pre-money valuation of $300 million, and purchasing $41 million of shares from certain selling shareholders. In the fourth quarter of 2020, White Mountains prefunded/placed in escrow a total of $646 million in preparation for closing the Ark Transaction.
On March 23, 2021, MediaAlpha completed a secondary offering of 8.05 million shares. In the secondary offering, White Mountains sold 3.6 million shares at $46.00 per share ($44.62 per share net of underwriting fees) for net proceeds of $160 million.
Cash flows from investing and financing activities for the six months ended June 30, 2020
Financing and Other Capital Activities
During the six months ended June 30, 2020, the Company declared and paid a $3 million cash dividend to its common shareholders.
During the six months ended June 30, 2020, White Mountains repurchased and retired 99,087 of its common shares for $85 million, 5,899 of which were repurchased under employee benefit plans for statutory withholding tax payments.
During the six months ended June 30, 2020, BAM received $32 million in MSC.
During the six months ended June 30, 2020, BAM repaid $48 million of principal and paid $17 million of accrued interest on the BAM Surplus Notes.
During the six months ended June 30, 2020, HG Global declared and paid $23 million of preferred dividends, of which $22 million was paid to White Mountains.
During the six months ended June 30, 2020, NSM borrowed £43 million (approximately $52 million based upon the foreign exchange spot rate at the date of acquisition) in term loans under the NSM Bank Facility for the Kingsbridge transaction.
During the six months ended June 30, 2020, Kudu borrowed $17 million in term loans under the Kudu Bank Facility and made no repayments.
Acquisitions and Dispositions
On April 7, 2020, NSM acquired 100% of Kingsbridge for £107 million (approximately $132 million based upon the foreign exchange spot rate at the date of acquisition) in upfront cash. White Mountains contributed $80 million to NSM and NSM borrowed £43 million (approximately $52 million based upon the foreign exchange spot rate at the date of acquisition) to fund the transaction.
On May 7, 2020 White Mountains made an additional $15 million investment in PassportCard/DavidShield.
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NON-GAAP FINANCIAL MEASURES
This report includes 12 non-GAAP financial measures that have been reconciled to their most comparable GAAP financial measures.
Adjusted book value per share
Adjusted book value per share is a non-GAAP financial measure, which is derived by adjusting (i) the GAAP book value per share numerator and (ii) the common shares outstanding denominator, as described below.
The GAAP book value per share numerator is adjusted (i) to include a discount for the time value of money arising from the modeled timing of cash payments of principal and interest on the BAM Surplus Notes and (ii) to add back the unearned premium reserve, net of deferred acquisition costs, at HG Global.
Under GAAP, White Mountains is required to carry the BAM Surplus Notes, including accrued interest, at nominal value with no consideration for time value of money. Based on a debt service model that forecasts operating results for BAM through maturity of the BAM Surplus Notes, the present value of the BAM Surplus Notes, including accrued interest and using an 8% discount rate, was estimated to be $137 million, $142 million, $147 million and $151 million less than the nominal GAAP carrying values as of June 30, 2021, March 31, 2021, December 31, 2020 and June 30, 2020, respectively.
The value of HG Global’s unearned premium reserve, net of deferred acquisition costs, was $150 million, $146 million, $142 million, and $131 million as of June 30, 2021, March 31, 2021, December 31, 2020 and June 30, 2020, respectively.
White Mountains believes these adjustments are useful to management and investors in analyzing the intrinsic value of HG Global, including the value of the BAM Surplus Notes and the value of the in-force business at HG Re, HG Global’s reinsurance subsidiary.
The denominator used in the calculation of adjusted book value per share equals the number of common shares outstanding, adjusted to exclude unearned restricted common shares, the compensation cost of which, at the date of calculation, has yet to be amortized. Restricted common shares are earned on a straight-line basis over their vesting periods. The reconciliation of GAAP book value per share to adjusted book value per share is included on page 55.
BAM’s gross written premiums and MSC from new business
BAM’s gross written premiums and MSC from new business is a non-GAAP financial measure, which is derived by adjusting gross written premiums and MSC collected (i) to include the present value of future installment MSC not yet collected and (ii) to exclude the impact of gross written premium adjustments related to policies closed in prior periods. White Mountains believes these adjustments are useful to management and investors in evaluating the volume and pricing of new business closed during the period. The reconciliation from GAAP gross written premiums to gross written premiums and MSC from new business is included on page 60.
Ark’s adjusted loss and loss adjustment expense, insurance acquisition expense, other underwriting expense and combined ratios
Ark’s adjusted loss and loss adjustment expense ratio, adjusted insurance acquisition expense ratio, adjusted other underwriting expense ratio and adjusted combined ratio are non-GAAP financial measures, which are derived by adjusting the GAAP ratios to add back amounts ceded to TPC Providers for the Syndicates. The impact of these reinsurance arrangements relate to years of account prior to the Ark Transaction. White Mountains believes these adjustments are useful to management and investors in evaluating Ark’s results on a fully aligned basis. The reconciliation from the GAAP ratios to the adjusted ratios is included on page 66.
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NSM’s earnings before interest, taxes, depreciation and amortization (“EBITDA”) and NSM’s adjusted EBITDA
NSM’s EBITDA and adjusted EBITDA are non-GAAP financial measures. EBITDA is a non-GAAP financial measure that excludes interest expense on debt, income tax expense (benefit), depreciation and amortization of other intangible assets from GAAP net income (loss). Adjusted EBITDA is a non-GAAP financial measure that excludes certain other items in GAAP net income (loss) in addition to those excluded from EBITDA. The adjustments relate to (i) change in fair value of contingent consideration liabilities, (ii) non-cash equity-based compensation expense, (iii) impairments of intangible assets, (iv) loss on assets held for sale, (v) acquisition-related transaction expenses, (vi) investments made in the development of new business lines and (vii) restructuring expenses. A description of each follows:
•Change in fair value of contingent consideration liabilities - Contingent consideration liabilities are amounts payable to the sellers of businesses purchased by NSM that are contingent on the earnings of such businesses in periods subsequent to their acquisition. Under GAAP, contingent consideration liabilities are initially recorded at fair value as part of purchase accounting, with the periodic change in the fair value of these liabilities recorded as income or an expense.
•Non-cash equity-based compensation expense - Represents non-cash expenses related to NSM’s management compensation emanating from the grants of equity units.
•Impairments of intangible assets - Represents expense related to NSM’s write-off of intangible assets. For the periods presented, the impairments related primarily to NSM’s write-off of intangible assets in its U.K. vertical. The impairments related to lower premium volumes, including due to the impact of the COVID-19 pandemic, and certain reorganization initiatives in the U.K. vertical.
•Loss on assets held for sale - Represents the loss on the net assets held for sale related to the Fresh Insurance’s motor business.
•Acquisition-related transaction expenses - Represents costs directly related to NSM’s transactions to acquire businesses, such as transaction-related compensation, banking, accounting and external lawyer fees, which are not capitalized and are expensed under GAAP.
•Investments made in the development of new business lines - Represents the net loss related to the start-up of newly established lines of business, which NSM views as investments.
•Restructuring expenses - Represents expenses associated with eliminating redundant work force and facilities that often arise as a result of NSM’s post-acquisition integration strategies. For the periods presented, this adjustment relates primarily to NSM’s expenses incurred in certain reorganization initiatives in the U.K. vertical.
White Mountains believes that these non-GAAP financial measures are useful to management and investors in evaluating NSM’s performance. The reconciliation of NSM’s GAAP net income (loss) to EBITDA and adjusted EBITDA is included on page 69.
Kudu’s EBITDA and Kudu’s adjusted EBITDA
Kudu's EBITDA and adjusted EBITDA are non-GAAP financial measures. EBITDA is a non-GAAP financial measure that excludes interest expense on debt, income tax expense (benefit), depreciation and amortization of other intangible assets from GAAP net income (loss). Adjusted EBITDA is a non-GAAP financial measure that excludes certain other items in GAAP net income (loss) in addition to those excluded from EBITDA. The adjustments relate to (i) net unrealized investment gains (losses) on Kudu's Participation Contracts, (ii) non-cash equity-based compensation expense and (iii) acquisition-related transaction expenses. A description of each adjustment follows:
•Net unrealized investment (gains) losses - Represents net unrealized investment gains and losses on Kudu's Participation Contracts, which are recorded at fair value under GAAP.
•Non-cash equity-based compensation expense - Represents non-cash expenses related to Kudu's management compensation that are settled with equity units in Kudu.
•Acquisition-related transaction expenses - Represents costs directly related to Kudu's transactions to acquire Participation Contracts, such as external lawyer, banker, consulting and placement agent fees, which are not capitalized and are expensed under GAAP.
White Mountains believes that these non-GAAP financial measures are useful to management and investors in evaluating Kudu’s performance. The reconciliation of Kudu’s GAAP net income (loss) to EBITDA and adjusted EBITDA is included on page 72.
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Total consolidated portfolio return excluding MediaAlpha
Total consolidated portfolio return excluding MediaAlpha is a non-GAAP financial measure that removes the net investment income and net realized and unrealized investment gains (losses) from White Mountains’s investment in MediaAlpha. White Mountains believes this measure to be useful to management and investors by showing the underlying performance of White Mountains’s investment portfolio without regard to MediaAlpha. A reconciliation from GAAP to the reported percentages is as follows:

|  |  |  | Three Months Ended June 30, 2021 |  | Three Months Ended June 30, 2020
|  |  |  |  |  |  |  | GAAP Return |  | Remove MediaAlpha |  | Return - Excluding MediaAlpha |  | GAAP Return |  | Remove MediaAlpha |  | Return - Excluding MediaAlpha
Total consolidated portfolio return |  |  |  |  |  |  |  | 5.0 | % |  | (2.6) | % |  | 2.4 | % |  | 6.5 | % |  | (0.1) | % |  | 6.4 | %

|  |  |  | Six Months Ended June 30, 2021 |  | Six Months Ended June 30, 2020
|  |  |  |  |  |  |  | GAAP Return |  | Remove MediaAlpha |  | Return - Excluding MediaAlpha |  | GAAP Return |  | Remove MediaAlpha |  | Return - Excluding MediaAlpha
Total consolidated portfolio return |  |  |  |  |  |  |  | 4.7 | % |  | (1.6) | % |  | 3.1 | % |  | 1.7 | % |  | (1.7) | % |  | — | %

Adjusted capital
Total capital at White Mountains is comprised of White Mountains’s common shareholders’ equity, debt and non-controlling interests other than non-controlling interests attributable to BAM. Total adjusted capital is a non-GAAP financial measure, which is derived by adjusting total capital (i) to include a discount for the time value of money arising from the expected timing of cash payments of principal and interest on the BAM Surplus Notes and (ii) to add back the unearned premium reserve, net of deferred acquisition costs, at HG Global. The reconciliation of total capital to total adjusted capital is included on page 81.
CRITICAL ACCOUNTING ESTIMATES
Refer to the Company’s 2020 Annual Report on Form 10-K for a complete discussion regarding White Mountains’s critical accounting estimates. The following describes changes to White Mountains’s critical accounting estimates since December 31, 2020 as of June 30, 2021.
I. Fair Value Measurements
General
White Mountains records certain assets and liabilities at fair value in its consolidated financial statements, with changes therein recognized in current period earnings. In addition, White Mountains discloses estimated fair value for certain liabilities measured at historical or amortized cost. 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 the 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 its estimates of fair value, 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.
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Invested Assets
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 June 30, 2021, approximately 75% 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 fixed maturity investments, primarily its investments in U.S. Treasuries and short-term investments, which include U.S. Treasury Bills, its investment in MediaAlpha subsequent to the MediaAlpha IPO, and common equity securities. 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, mortgage and asset-backed securities and collateralized loan obligations. Investments valued using Level 2 inputs also include certain common equity listed funds 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
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.
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Other Long-Term Investments
As of June 30, 2021, White Mountains owned a portfolio of other long-term investments valued at $1.1 billion, that consisted primarily of unconsolidated entities, including Kudu’s Participation Contracts, private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, ILS funds and private debt investments. As of June 30, 2021, $674 million of White Mountains’s other long-term investments consisting primarily of unconsolidated entities, including Kudu’s Participation Contracts and private debt investments, 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 June 30, 2021, $402 million of White Mountains’s other long-term investments, consisting of private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund, and 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 its 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.
As of June 30, 2021, White Mountains’s most significant other long-term investments that are valued using Level 3 measurements include Kudu’s Participation Contracts and PassportCard/DavidShield.
Valuation of Kudu’s Participation Contracts
Kudu’s Participation Contracts comprise non-controlling equity interests in the form of revenue and earnings participation contracts. On a quarterly basis, White Mountains values each of Kudu’s Participation Contracts using discounted cash flow models. The valuation models include key inputs such as projections of future revenues and earnings of Kudu’s clients, a discount rate and a terminal cash flow exit multiple. The expected future cash flows are based on management judgment, considering current performance, budgets and projected future results. The discount rates reflect the weighted average cost of capital, considering comparable public company data, adjusted for risks specific to the business and industry. The terminal exit multiple is generally based on expectations of annual cash flow to Kudu from each of its clients in the terminal year of the cash flow model. In determining fair value, White Mountains considers factors such as performance of underlying products and vehicles, expected client growth rates, new fund launches, fee rates by products, capacity constraints, operating cash flow of underlying manager and other qualitative factors, including the assessment of key personnel.
As of June 30, 2021, the combined fair value of Kudu’s Participation Contracts was $456 million. The inputs to each discounted cash flow analysis vary depending on the nature of each client. As of June 30, 2021, White Mountains concluded that pre-tax discount rates in the range of 18% to 23%, and terminal cash flow exit multiples in the range of 7 to 13 times were appropriate for the valuations of Kudu’s Participation Contracts.
With a discounted cash flow analysis, small changes to inputs in a valuation model may result in significant changes to fair value. The following table presents the estimated effect on the fair value of Kudu’s Participation Contracts as of June 30, 2021, resulting from increases and decreases to the discount rates and terminal cash flow exit multiples used in the discounted cash flow analysis:

$ in Millions |  | Discount Rate(1)
Terminal Exit Multiple |  | -2% |  | -1% |  | 18% - 23% |  | +1% |  | +2% |  |  |
+2 |  | $ | 541 |  |  | $ | 511 |  |  | $ | 485 |  |  | $ | 459 |  |  | $ | 435 |  |  |  |
+1 |  | $ | 523 |  |  | $ | 495 |  |  | $ | 470 |  |  | $ | 445 |  |  | $ | 423 |  |  |  |
7x - 13x |  | $ | 506 |  |  | $ | 480 |  |  | $ | 456 |  |  | $ | 432 |  |  | $ | 411 |  |  |  |
-1 |  | $ | 489 |  |  | $ | 464 |  |  | $ | 441 |  |  | $ | 419 |  |  | $ | 399 |  |  |  |
-2 |  | $ | 472 |  |  | $ | 449 |  |  | $ | 428 |  |  | $ | 408 |  |  | $ | 389 |  |  |  |

(1) 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.
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Valuation PassportCard/DavidShield
On a quarterly basis, White Mountains values its investment in PassportCard/DavidShield using a discounted cash flow model. The discounted cash flow valuation model includes key inputs such as projections of future revenues and earnings, a discount rate and a terminal revenue growth rate. The expected future cash flows are based on management judgment, considering current performance, budgets and projected future results. The discount rate reflects the weighted average cost of capital, considering comparable public company data, adjusted for risks specific to the business and industry. The terminal revenue growth rate is based on company, industry and macroeconomic expectations of perpetual revenue growth subsequent to the end of the discrete period in the discounted cash flow analysis.
When making its fair value selection, which is within a range of reasonable values derived from the discounted cash flow model, White Mountains considers all available information, including any relevant market multiples and multiples implied by recent transactions, facts and circumstances specific to PassportCard/DavidShield’s businesses and industries, and any infrequent or unusual results for the period.
White Mountains concluded that an after-tax discount rate of 23% and a terminal revenue growth rate of 4% was appropriate for the valuation of its investment in PassportCard/DavidShield as of June 30, 2021. Utilizing these assumptions, White Mountains determined that the fair value of its investment in PassportCard/DavidShield was $95 million as of June 30, 2021.
Premiums and commission revenues from leisure travel insurance placed by PassportCard declined dramatically in the twelve months ended December 31, 2020 due to the COVID-19 pandemic. This decline was modestly offset by increased revenues from international private medical insurance placed by DavidShield. PassportCard/DavidShield expects these trends to continue until global travel resumes. During the third quarter of 2020, PassportCard/DavidShield curtailed its global expansion efforts in response to the impact of the COVID-19 pandemic.
In the first quarter of 2021, sustained progress with COVID-19 vaccinations in Israel and abroad led to the Israeli airport reopening in March, which resulted in increased leisure travel and the placement of leisure travel insurance by PassportCard. Revenues from private medical insurance placed by DavidShield remained strong in the first six months of 2021.
With a discounted cash flow analysis, small changes to inputs in a valuation model may result in significant changes to fair value. The following table presents the estimated effect on the fair value of White Mountains’s investment in PassportCard/DavidShield as of June 30, 2021, resulting from changes in key inputs to the discounted cash flow analysis, including the discount rate and terminal revenue growth rate:

$ in Millions |  | Discount Rate
Terminal Revenue Growth Rate |  | 21% |  | 22% |  | 23% |  | 24% |  | 25% |  |  |
4.5% |  | $ | 113 |  |  | $ | 104 |  |  | $ | 96 |  |  | $ | 89 |  |  | $ | 82 |  |  |  |
4.0% |  | $ | 112 |  |  | $ | 103 |  |  | $ | 95 |  |  | $ | 88 |  |  | $ | 81 |  |  |  |
3.5% |  | $ | 110 |  |  | $ | 102 |  |  | $ | 94 |  |  | $ | 87 |  |  | $ | 81 |  |  |  |

Other Long-term Investments - NAV
White Mountains’s portfolio of other long-term investments includes investments in private equity funds, a hedge fund, Lloyd’s trust deposits, a bank loan fund and ILS funds, which are valued at fair value using NAV as a practical expedient. White Mountains employs a number of procedures to assess the reasonableness of the fair value measurements for other long-term investments measured at NAV, 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 valuation inputs to be unobservable. The fair value of White Mountains’s other long-term investments measured at NAV are generally determined using the fund manager’s NAV. In the event that White Mountains believes the fair value 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.
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FORWARD-LOOKING STATEMENTS
This report may contain “forward-looking statements” within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934. All statements, other than statements of historical facts, included or referenced in this report which address activities, events or developments which White Mountains expects or anticipates will or may occur in the future are forward-looking statements. The words “could”, “will”, “believe”, “intend”, “expect”, “anticipate”, “project”, “estimate”, “predict” and similar expressions are also intended to identify forward-looking statements. These forward-looking statements include, among others, statements with respect to White Mountains’s:
•change in book value or adjusted book value per share or return on equity;
•business strategy;
•financial and operating targets or plans;
•incurred loss and loss adjustment expenses and the adequacy of its loss and loss adjustment expense reserves and related reinsurance;
•projections of revenues, income (or loss), earnings (or loss) per share, EBITDA, adjusted EBITDA, dividends, market share or other financial forecasts of White Mountains or its businesses;
•expansion and growth of its business and operations; and
•future capital expenditures.
These statements are based on certain assumptions and analyses made by White Mountains in light of its experience and perception of historical trends, current conditions and expected future developments, as well as other factors believed to be appropriate in the circumstances. However, whether actual results and developments will conform to its expectations and predictions is subject to risks and uncertainties that could cause actual results to differ materially from expectations, including:
• the risks that are described from time to time in White Mountains’s filings with the Securities and Exchange Commission, including but not limited to White Mountains’s Annual Report on Form 10-K for the fiscal year ended December 31, 2020;
• claims arising from catastrophic events, such as hurricanes, earthquakes, floods, fires, terrorist attacks or severe winter weather;
• recorded loss reserves subsequently proving to have been inadequate;
• the market value of White Mountains’s investment in MediaAlpha;
• the trends and uncertainties from the COVID-19 pandemic, including judicial interpretations on the extent of insurance coverage provided by insurers for COVID-19 pandemic related claims;
•business opportunities (or lack thereof) that may be presented to it and pursued;
• actions taken by rating agencies, such as financial strength or credit ratings downgrades or placing ratings on negative watch;
• the continued availability of capital and financing;
• deterioration of general economic, market or business conditions, including due to outbreaks of contagious disease (including the COVID-19 pandemic) and corresponding mitigation efforts;
• competitive forces, including the conduct of other insurers;
• changes in domestic or foreign laws or regulations, or their interpretation, applicable to White Mountains, its competitors or its customers; and
• other factors, most of which are beyond White Mountains’s control.
Consequently, all of the forward-looking statements made in this report are qualified by these cautionary statements, and there can be no assurance that the actual results or developments anticipated by White Mountains will be realized or, even if substantially realized, that they will have the expected consequences to, or effects on, White Mountains or its business or operations. White Mountains assumes no obligation to publicly update any such forward-looking statements, whether as a result of new information, future events or otherwise.
Item 3.Quantitative and Qualitative Disclosures About Market Risk.
Refer to White Mountains’s 2020 Annual Report on Form 10-K and in particular Item 7A. - “Quantitative and Qualitative Disclosures About Market Risk”.
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Item 4.Controls and Procedures.
The Principal Executive Officer (“PEO”) and the Principal Financial Officer (“PFO”) of White Mountains have evaluated the effectiveness of its disclosure controls and procedures (as defined in Rule 13a-15(e) and 15d-15(e) of the Exchange Act) as of the end of the period covered by this report. Based on that evaluation, the PEO and PFO have concluded that White Mountains’s disclosure controls and procedures are effective.
There were no significant changes with respect to the Company’s internal control over financial reporting or in other factors that materially affected, or are reasonably likely to materially affect, internal control over financial reporting during the quarter ended June 30, 2021.
Part II.OTHER INFORMATION
Item 1.Legal Proceedings.
None.
Item 1A. Risk Factors.
There have been no material changes to any of the risk factors previously disclosed in the Registrant’s 2020 Annual Report
on Form 10-K.
Item 2.Issuer Purchases of Equity Securities.

Months |  | Total Number of Shares Purchased |  | Average Price Paid per Share |  | Total Number of Shares Purchased as Part of Publicly Announced Plans (1) |  | Maximum Number of Shares that May Yet Be Purchased Under the Plans (1)
April 1 - April 30, 2021 |  | — |  |  | $ | — |  |  | — |  |  | 542,517 |
May 1 - May 31, 2021 |  | — |  |  | $ | — |  |  | — |  |  | 542,517 |
June 1 - June 30, 2021 |  | — |  |  | $ | — |  |  | — |  |  | 542,517 |
Total |  | — |  |  | $ | — |  |  | — |  |  | 542,517 |

(1) White Mountains’s board of directors has authorized the Company to repurchase its common shares, from time to time, subject to market conditions. The repurchase authorizations do not have a stated expiration date.
Item 3. Defaults Upon Senior Securities.
None.
Item 4.Mine Safety Disclosures.
None.
Item 5.Other Information.
None.
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Item 6.Exhibits.

(a) |  | Exhibit number |  |  |  | Name
|  | 2 |  |  | — |  |  | Plan of Reorganization (incorporated by reference herein to the Company’s Registration Statement on S-4 (No. 333-87649) dated September 23, 1999)
|  | 3.1 |  |  | — |  |  | Memorandum of Continuance of the Company (incorporated by reference herein to Exhibit (3)(i) of the Company’s Current Report on Form 8-K dated November 1, 1999)
|  | 3.2 |  |  | — |  |  | Amended and Restated Bye-Laws of the Company (incorporated by reference herein to Exhibit 3 of the Company’s Report on Form 10-Q dated May 2, 2017)
|  | 10 |  |  | — |  |  | FIFTH AMENDMENT dated as of June 2, 2021, among NSM INSURANCE GROUP, LLC, a Delaware limited liability company, NSM INSURANCE HOLDCO, LLC, a Delaware limited liability company, NSM UK HOLDINGS LTD, a company incorporated in England and Wales, the other LOAN PARTIES party hereto, ARES CAPITAL CORPORATION, a Maryland corporation, as administrative agent, the LENDERS party hereto and the L/C ISSUERS party hereto. *
|  | 31.1 |  | — |  |  | Principal Executive Officer Certification Pursuant to Rule 13a-14 (a) of the Securities Exchange Act of 1934, as Amended. *
|  | 31.2 |  | — |  |  | Principal Financial Officer Certification Pursuant to Rule 13a-14 (a) of the Securities Exchange Act of 1934, as Amended. *
|  | 32.1 |  | — |  |  | Principal Executive Officer Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002. *
|  | 32.2 |  | — |  |  | Principal Financial Officer Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002. *
|  | 101 |  | — |  |  | XBRL Instance Document - the instance document does not appear in the Interactive Data File because its XBRL tags are embedded within the Inline XBRL document.

* | Included herein

SIGNATURES
Pursuant to the requirements of the Securities Exchange Act of 1934, the Registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.

|  |  | WHITE MOUNTAINS INSURANCE GROUP, LTD.
|  |  | (Registrant)
Date: | August 6, 2021 |  |  | By: /s/ Michaela J. Hildreth
|  |  |  | Michaela J. Hildreth
|  |  |  | Managing Director and Chief Accounting Officer

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