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Investment Securities (Tables) | 12 Months Ended
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Dec. 31, 2019
Investments, Debt and Equity Securities [Abstract] |
Pre-tax net investment income | The following table presents pre-tax net investment income for 2019, 2018 and 2017:
|  | Year Ended December 31,
Millions |  | 2019 |  | 2018 |  | 2017
Fixed maturity investments |  | $ | 32.4 |  |  | $ | 35.1 |  |  | $ | 44.9 |
Short-term investments |  | 5.0 |  |  | 8.0 |  |  | 1.8 |
Common equity securities |  | 13.5 |  |  | 15.1 |  |  | 10.6 |
Other long-term investments |  | 30.1 |  |  | 3.8 |  |  | 1.2 |
Total investment income |  | 81.0 |  |  | 62.0 |  |  | 58.5 |
Third-party investment expenses |  | (1.3 | ) |  | (3.0 | ) |  | (2.5 | )
Net investment income, pre-tax |  | $ | 79.7 |  |  | $ | 59.0 |  |  | $ | 56.0 |
Net Realized and Unrealized Investment Gains and Losses | The following table presents net realized and unrealized investment gains (losses) for 2019, 2018 and 2017:
|  | Year Ended December 31,
Millions |  | 2019 |  | 2018 |  | 2017
Net realized investment gains (losses), pre-tax (1) |  | $ | 96.6 |  |  | $ | (12.9 | ) |  | $ | 24.1 |
Net unrealized investment gains (losses), pre-tax (2) |  | 336.6 |  |  | (95.4 | ) |  | 109.2 |
Net realized and unrealized investment gains (losses), pre-tax |  | 433.2 |  |  | (108.3 | ) |  | 133.3 |
Income tax (expense) benefit attributable to net realized and unrealized investment gains (losses) |  | (87.0 | ) |  | 18.2 |  |  | (12.9 | )
Net realized and unrealized investment gains (losses), after-tax |  | $ | 346.2 |  |  | $ | (90.1 | ) |  | $ | 120.4 |
(1) Excludes $67.5 realized gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.” (2) Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”
Realized Gain (Loss) on Investments | The following tables present net realized investment gains (losses) for the years ended 2019, 2018 and 2017:
|  | Year Ended December 31, 2019
Millions |  | Net Realized Gains |  | Net Foreign Exchange Gains (Losses) |  | Total Net Realized Gains Reflected in Earnings
Fixed maturity investments |  | $ | 4.9 |  |  | $ | — |  |  | $ | 4.9 |
Short-term investments |  | .2 |  |  | — |  |  | .2 |
Common equity securities |  | 85.9 |  |  | — |  |  | 85.9 |
Other long-term investments (1) |  | 5.6 |  |  | — |  |  | 5.6 |
Net realized investment gains, pre-tax |  | 96.6 |  |  | — |  |  | 96.6 |
Income tax expense attributable to net realized investment gains |  | (10.6 | ) |  | — |  |  | (10.6 | )
Net realized investment gains, after-tax |  | $ | 86.0 |  |  | $ | — |  |  | $ | 86.0 |
(1) Excludes $67.5 realized gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”
|  | Year Ended December 31, 2018
Millions |  | Net Realized (Losses) Gains |  | Net Foreign Exchange Gains (Losses) |  | Total Net Realized (Losses) Gains Reflected in Earnings
Fixed maturity investments |  | $ | (29.8 | ) |  | $ | 18.2 |  |  | $ | (11.6 | )
Short-term investments |  | (.8 | ) |  | — |  |  | (.8 | )
Common equity securities |  | 6.6 |  |  | — |  |  | 6.6 |
Other long-term investments |  | .1 |  |  | (7.2 | ) |  | (7.1 | )
Net realized investment (losses) gains, pre-tax |  | (23.9 | ) |  | 11.0 |  |  | (12.9 | )
Income tax benefit attributable to net realized investment (losses) gains |  | 9.1 |  |  | — |  |  | 9.1 |
Net realized investment (losses) gains, after-tax |  | $ | (14.8 | ) |  | $ | 11.0 |  |  | $ | (3.8 | )
|  | Year Ended December 31, 2017
Millions |  | Net Realized (Losses) Gains |  | Net Foreign Exchange Gains (Losses) |  | Total Net Realized Gains (Losses) Reflected in Earnings
Fixed maturity investments |  | $ | (1.6 | ) |  | $ | 4.1 |  |  | $ | 2.5 |
Short-term investments |  | (.3 | ) |  | — |  |  | (.3 | )
Common equity securities |  | 18.1 |  |  | 6.0 |  |  | 24.1 |
Other long-term investments |  | 19.1 |  |  | (21.3 | ) |  | (2.2 | )
Net realized investment gains (losses), pre-tax |  | 35.3 |  |  | (11.2 | ) |  | 24.1 |
Income tax expense attributable to net realized investment gains (losses) |  | (8.9 | ) |  | — |  |  | (8.9 | )
Net realized investment gains (losses), after-tax |  | $ | 26.4 |  |  | $ | (11.2 | ) |  | $ | 15.2 |
Unrealized Gain (Loss) on Investments | The following tables present net unrealized investment gains (losses) and changes in the carrying value of investments measured at fair value for the years ended 2019, 2018 and 2017:
|  | Year Ended December 31, 2019
Millions |  | Net Unrealized Gains |  | Net Foreign Exchange Losses |  | Total Net Unrealized Gains Reflected in Earnings
Fixed maturity investments |  | $ | 38.6 |  |  | $ | — |  |  | $ | 38.6 |
Common equity securities |  | 109.8 |  |  | — |  |  | 109.8 |
Other long-term investments (1) |  | 188.5 |  |  | (.3 | ) |  | 188.2 |
Net unrealized investment gains (losses), pre-tax |  | 336.9 |  |  | (.3 | ) |  | 336.6 |
Income tax expense attributable to net unrealized investment gains |  | (76.4 | ) |  | — |  |  | (76.4 | )
Net unrealized investment gains (losses), after-tax |  | $ | 260.5 |  |  | $ | (.3 | ) |  | $ | 260.2 |
(1) Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions.”
|  | Year Ended December 31, 2018
Millions |  | Net Unrealized (Losses) Gains |  | Net Foreign Exchange (Losses) Gains |  | Total Net Unrealized (Losses) Gains Reflected in Earnings
Fixed maturity investments |  | $ | (8.3 | ) |  | $ | (14.8 | ) |  | $ | (23.1 | )
Common equity securities |  | (105.5 | ) |  | — |  |  | (105.5 | )
Other long-term investments |  | 30.2 |  |  | 3.0 |  |  | 33.2 |
Net unrealized investment losses, pre-tax |  | (83.6 | ) |  | (11.8 | ) |  | (95.4 | )
Income tax benefit attributable to net unrealized investment losses |  | 9.1 |  |  | — |  |  | 9.1 |
Net unrealized investment losses, after-tax |  | $ | (74.5 | ) |  | $ | (11.8 | ) |  | $ | (86.3 | )
|  | Year Ended December 31, 2017
Millions |  | Net Unrealized Gains (Losses) |  | Net Foreign Exchange Gains (Losses) |  | Total Net Unrealized Gains (Losses) Reflected in Earnings
Fixed maturity investments |  | $ | 13.8 |  |  | $ | 12.7 |  |  | $ | 26.5 |
Common equity securities |  | 99.3 |  |  | — |  |  | 99.3 |
Other long-term investments |  | (15.6 | ) |  | (1.0 | ) |  | (16.6 | )
Net unrealized investment gains, pre-tax |  | 97.5 |  |  | 11.7 |  |  | 109.2 |
Income tax expense attributable to net unrealized investment gains |  | (4.0 | ) |  | — |  |  | (4.0 | )
Net unrealized investment gains, after-tax |  | $ | 93.5 |  |  | $ | 11.7 |  |  | $ | 105.2 |
Net unrealized investment gains (losses) for Level 3 investments | The following table presents total gains (losses) included in earnings attributable to net unrealized investment gains (losses) for Level 3 investments for the years ended December 31, 2019, 2018 and 2017 for investments held as of December 31, 2019, 2018 and 2017:
|  | Year Ended December 31,
Millions |  | 2019 |  | 2018 |  | 2017
Other long-term investments |  | $ | 181.9 |  |  | $ | 22.6 |  |  | $ | (15.4 | )
Investment holdings, fixed maturity investments | The following tables present the cost or amortized cost, gross unrealized investment gains (losses) and carrying values of White Mountains’s fixed maturity investments as of December 31, 2019 and 2018.
|  | December 31, 2019
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Carrying Value
U.S. Government and agency obligations |  | $ | 231.7 |  |  | $ | 1.0 |  |  | $ | (.2 | ) |  | $ | 232.5 |
Debt securities issued by corporations |  | 454.9 |  |  | 12.5 |  |  | (.2 | ) |  | 467.2 |
Municipal obligations |  | 284.7 |  |  | 12.5 |  |  | (.1 | ) |  | 297.1 |
Mortgage and asset-backed securities |  | 206.6 |  |  | 2.7 |  |  | (.3 | ) |  | 209.0 |
Total fixed maturity investments |  | $ | 1,177.9 |  |  | $ | 28.7 |  |  | $ | (.8 | ) |  | $ | 1,205.8 |
|  | December 31, 2018
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Carrying Value
U.S. Government and agency obligations |  | $ | 154.0 |  |  | $ | .1 |  |  | $ | (.9 | ) |  | $ | 153.2 |
Debt securities issued by corporations |  | 519.0 |  |  | 1.0 |  |  | (9.5 | ) |  | 510.5 |
Municipal obligations |  | 279.0 |  |  | 2.4 |  |  | (1.1 | ) |  | 280.3 |
Mortgage and asset-backed securities |  | 136.1 |  |  | .1 |  |  | (2.7 | ) |  | 133.5 |
Total fixed maturity investments |  | $ | 1,088.1 |  |  | $ | 3.6 |  |  | $ | (14.2 | ) |  | $ | 1,077.5 |
Schedule of contractual maturities of fixed maturities | The following table presents the cost or amortized cost and carrying value of White Mountains’s fixed maturity investments by contractual maturity as of December 31, 2019. Actual maturities could differ from contractual maturities because borrowers may have the right to call or prepay certain obligations with or without call or prepayment penalties.
|  | December 31, 2019
Millions |  | Cost or Amortized Cost |  | Carrying Value
Due in one year or less |  | $ | 190.0 |  |  | $ | 190.8 |
Due after one year through five years |  | 481.6 |  |  | 489.3 |
Due after five years through ten years |  | 165.3 |  |  | 173.2 |
Due after ten years |  | 134.4 |  |  | 143.5 |
Mortgage and asset-backed securities |  | 206.6 |  |  | 209.0 |
Total |  | $ | 1,177.9 |  |  | $ | 1,205.8 |
Investment holdings, equity securities, convertible fixed maturities and other long-term investments | The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency losses, and carrying values of White Mountains’s common equity securities and other long-term investments as of December 31, 2019 and 2018:
|  | December 31, 2019
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Net Foreign Currency Losses |  | Carrying Value
Common equity securities |  | $ | 553.3 |  |  | $ | 130.6 |  |  | $ | — |  |  | $ | — |  |  | $ | 683.9 |
Other long-term investments |  | $ | 667.4 |  |  | $ | 255.2 |  |  | $ | (64.1 | ) |  | $ | (2.2 | ) |  | $ | 856.3 |
|  | December 31, 2018
Millions |  | Cost or Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Net Foreign Currency Losses |  | Carrying Value
Common equity securities |  | $ | 904.7 |  |  | $ | 51.0 |  |  | $ | (30.1 | ) |  | $ | — |  |  | $ | 925.6 |
Other long-term investments |  | $ | 330.3 |  |  | $ | 52.2 |  |  | $ | (54.9 | ) |  | $ | (2.0 | ) |  | $ | 325.6 |
Fair value measurements by level, investment securities | The following tables present White Mountains’s fair value measurements for investments as of December 31, 2019 and 2018 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, foreign governments, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations and common equity securities by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated these asset classes into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate and S&P 500 indices.
|  | December 31, 2019
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 232.5 |  |  | $ | 232.5 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |
Financials |  | 144.8 |  |  | — |  |  | 144.8 |  |  | — |
Industrial |  | 59.0 |  |  | — |  |  | 59.0 |  |  | — |
Healthcare |  | 52.6 |  |  | — |  |  | 52.6 |  |  | — |
Consumer |  | 50.9 |  |  | — |  |  | 50.9 |  |  | — |
Energy |  | 44.9 |  |  | — |  |  | 44.9 |  |  | — |
Technology |  | 41.2 |  |  | — |  |  | 41.2 |  |  | — |
Communications |  | 31.3 |  |  | — |  |  | 31.3 |  |  | — |
Utilities |  | 25.0 |  |  | — |  |  | 25.0 |  |  | — |
Materials |  | 17.5 |  |  | — |  |  | 17.5 |  |  | — |
Total debt securities issued by corporations |  | 467.2 |  |  | — |  |  | 467.2 |  |  | — |
Municipal obligations |  | 297.1 |  |  | — |  |  | 297.1 |  |  | — |
Mortgage and asset-backed securities |  | 209.0 |  |  | — |  |  | 209.0 |  |  | — |
Total fixed maturity investments |  | 1,205.8 |  |  | 232.5 |  |  | 973.3 |  |  | — |
Short-term investments (1) |  | 201.2 |  |  | 189.4 |  |  | 11.8 |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Exchange traded funds (2) |  | 536.4 |  |  | 521.6 |  |  | 14.8 |  |  | — |
Other (3) |  | 147.5 |  |  | 25.9 |  |  | 121.5 |  |  | 0.1 |
Total common equity securities |  | 683.9 |  |  | 547.5 |  |  | 136.3 |  |  | 0.1 |
Other long-term investments |  | 654.0 |  |  | — |  |  | — |  |  | 654.0 |
Other long-term investments — NAV(4) |  | 202.3 |  |  | — |  |  | — |  |  | — |
Total investments |  | $ | 2,947.2 |  |  | $ | 969.4 |  |  | $ | 1,121.4 |  |  | $ | 654.1 |
(1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement. (3) Primarily consists of two investments in unit trusts that predominantly invest in international equities and an open-end mutual fund that invests in domestic large-cap companies. (4) Consists of private equity funds, one hedge fund and ILS funds for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
|  | December 31, 2018
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 153.2 |  |  | $ | 153.2 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |  |  |  |
Financials |  | 143.4 |  |  | — |  |  | 143.4 |  |  | — |
Consumer |  | 68.5 |  |  | — |  |  | 68.5 |  |  | — |
Technology |  | 60.5 |  |  | — |  |  | 60.5 |  |  | — |
Energy |  | 57.6 |  |  | — |  |  | 57.6 |  |  | — |
Healthcare |  | 55.0 |  |  | — |  |  | 55.0 |  |  | — |
Industrial |  | 47.6 |  |  | — |  |  | 47.6 |  |  | — |
Communications |  | 31.8 |  |  | — |  |  | 31.8 |  |  | — |
Materials |  | 26.3 |  |  | — |  |  | 26.3 |  |  | — |
Utilities |  | 19.8 |  |  | — |  |  | 19.8 |  |  | — |
Total debt securities issued by corporations |  | 510.5 |  |  | — |  |  | 510.5 |  |  | — |
Municipal obligations |  | 280.3 |  |  | — |  |  | 280.3 |  |  | — |
Mortgage and asset-backed securities |  | 133.5 |  |  | — |  |  | 133.5 |  |  | — |
Total fixed maturity investments |  | 1,077.5 |  |  | 153.2 |  |  | 924.3 |  |  | — |
Short-term investments (1) |  | 214.2 |  |  | 204.4 |  |  | 9.8 |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Exchange traded funds (2) |  | 675.3 |  |  | 617.0 |  |  | 58.3 |  |  | — |
Healthcare |  | 14.0 |  |  | 14.0 |  |  | — |  |  | — |
Financials |  | 13.5 |  |  | 13.5 |  |  | — |  |  | — |
Communications |  | 12.7 |  |  | 12.7 |  |  | — |  |  | — |
Industrial |  | 11.4 |  |  | 11.4 |  |  | — |  |  | — |
Technology |  | 7.4 |  |  | 7.4 |  |  | — |  |  | — |
Consumer |  | 6.2 |  |  | 6.2 |  |  | — |  |  | — |
Energy |  | 4.1 |  |  | 4.1 |  |  | — |  |  | — |
Materials |  | 3.1 |  |  | 3.1 |  |  | — |  |  | — |
Other (3) |  | 177.9 |  |  | — |  |  | 177.9 |  |  | — |
Total common equity securities |  | 925.6 |  |  | 689.4 |  |  | 236.2 |  |  | — |
Other long-term investments |  | 138.7 |  |  | — |  |  | — |  |  | 138.7 |
Other long-term investments — NAV (4) |  | 186.9 |  |  | — |  |  | — |  |  | — |
Total investments |  | $ | 2,542.9 |  |  | $ | 1,047.0 |  |  | $ | 1,170.3 |  |  | $ | 138.7 |
(1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a Level 2 measurement. (3) Consists of two investments in unit trusts that predominantly invest in international equities. (4) Consists of private equity funds, one hedge fund, White Mountains’s non-controlling equity interest in Kudu prior to consolidation and one unconsolidated entity for which fair value is measured at NAV using the practical expedient. Investments for which fair value is measured at NAV are not classified within the fair value hierarchy.
Debt securities issued by corporations, credit ratings | The following table presents the ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2019 and 2018:
|  | Fair Value at December 31,
Millions |  | 2019 |  | 2018
AAA |  | $ | 9.5 |  |  | $ | 8.9 |
AA |  | 73.9 |  |  | 88.7 |
A |  | 288.5 |  |  | 270.5 |
BBB |  | 95.3 |  |  | 142.4 |
Debt securities issued by corporations (1) |  | $ | 467.2 |  |  | $ | 510.5 |
(1) | Credit ratings are based upon issuer credit ratings provided by Standard & Poor’s Financial Services LLC (“Standard & Poor’s”), or if unrated by Standard & Poor’s, long-term obligation ratings provided by Moody’s Investor Service, Inc
Mortgage-backed, asset-backed securities | The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of December 31, 2019 and 2018:
|  | December 31, 2019 |  | December 31, 2018
Millions |  | Fair Value |  | Level 2 |  | Level 3 |  | Fair Value |  | Level 2 |  | Level 3
Mortgage-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Agency: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
FNMA |  | $ | 88.6 |  |  | $ | 88.6 |  |  | $ | — |  |  | $ | 53.6 |  |  | $ | 53.6 |  |  | $ | — |
FHLMC |  | 60.5 |  |  | 60.5 |  |  | — |  |  | 38.1 |  |  | 38.1 |  |  | — |
GNMA |  | 30.8 |  |  | 30.8 |  |  | — |  |  | 23.7 |  |  | 23.7 |  |  | — |
Total agency (1) |  | 179.9 |  |  | 179.9 |  |  | — |  |  | 115.4 |  |  | 115.4 |  |  | — |
Total mortgage-backed securities |  | 179.9 |  |  | 179.9 |  |  | — |  |  | 115.4 |  |  | 115.4 |  |  | — |
Other asset-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |
Vehicle receivables |  | 15.1 |  |  | 15.1 |  |  | — |  |  | 9.2 |  |  | 9.2 |  |  | — |
Credit card receivables |  | 14.0 |  |  | 14.0 |  |  | — |  |  | 8.9 |  |  | 8.9 |  |  | — |
Total other asset-backed securities |  | 29.1 |  |  | 29.1 |  |  | — |  |  | 18.1 |  |  | 18.1 |  |  | — |
Total mortgage and asset-backed securities |  | $ | 209.0 |  |  | $ | 209.0 |  |  | $ | — |  |  | $ | 133.5 |  |  | $ | 133.5 |  |  | $ | — |
(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).
Other Investments Not Readily Marketable | The following table presents the carrying values of White Mountains’s other long-term investments as of December 31, 2019 and 2018:
|  | Carrying Value at
Millions |  | December 31, 2019 |  | December 31, 2018
Kudu’s Participation Contracts (1)(2) |  | $ | 266.5 |  |  | $ | — |
MediaAlpha (1)(3) |  | 180.0 |  |  | — |
PassportCard/DavidShield (1) |  | 90.0 |  |  | 75.0 |
Elementum (1) |  | 55.1 |  |  | — |
Other unconsolidated entities (1)(4) |  | 31.2 |  |  | 60.0 |
Kudu (5) |  | — |  |  | 30.7 |
Total unconsolidated entities (1) |  | 622.8 |  |  | 165.7 |
Private equity funds and hedge funds |  | 161.1 |  |  | 146.1 |
Insurance-linked securities funds |  | 41.2 |  |  | — |
Other |  | 31.2 |  |  | 13.8 |
Total other long-term investments |  | $ | 856.3 |  |  | $ | 325.6 |
(1) See Fair Value Measurements by Level table. (2) Includes Kudu’s non-controlling equity interests in the form of revenue and earnings participation contracts. As of December 31, 2019, White Mountains consolidates Kudu. See Note 2 — “Significant Transactions”. (3) The MediaAlpha Transaction was completed on February 26, 2019. See Note 2 — “Significant Transactions”. (4) Includes White Mountains’s non-controlling equity interests in certain private common equity securities, limited liability companies and convertible preferred securities. (5) Includes White Mountains’s non-controlling equity interest in Kudu prior to consolidation. See Note 2 — “Significant Transactions”.
Other long-term investments | The following table presents investments and unfunded commitments in private equity funds and hedge funds by investment objective and sector as of December 31, 2019 and 2018:
|  | December 31, 2019 |  | December 31, 2018
Millions |  | Fair Value |  | Unfunded Commitments |  | Fair Value |  | Unfunded Commitments
Private equity funds |  |  |  |  |  |  |  |  |  |  |  |
Manufacturing/Industrial |  | $ | 57.7 |  |  | $ | 4.1 |  |  | $ | 42.9 |  |  | $ | 10.5 |
Aerospace/Defense/Government |  | 33.8 |  |  | 23.3 |  |  | 27.6 |  |  | 34.9 |
Financial services |  | 15.0 |  |  | 22.8 |  |  | 8.3 |  |  | 13.6 |
Direct lending |  | — |  |  | — |  |  | 13.0 |  |  | 17.7 |
Total private equity funds |  | 106.5 |  |  | 50.2 |  |  | 91.8 |  |  | 76.7 |
Hedge funds |  |  |  |  |  |  |  |  |  |  |  |
Long/short banks and financial |  | 54.6 |  |  | — |  |  | 54.3 |  |  | — |
Total hedge funds |  | 54.6 |  |  | — |  |  | 54.3 |  |  | — |
Total private equity funds and hedge funds included in other long-term investments |  | $ | 161.1 |  |  | $ | 50.2 |  |  | $ | 146.1 |  |  | $ | 76.7 |
Fair Value of private equity funds subject to lock-up periods | The following table presents investments in private equity funds that were subject to lock-up periods as of December 31, 2019:
Millions |  | 1 – 3 years |  | 3 – 5 years |  | 5 – 10 years |  | >10 years |  | Total
Private equity funds — expected lock-up period remaining |  | $ | 4.8 |  |  | $ | 51.9 |  |  | $ | 40.2 |  |  | $ | 9.6 |  |  | $ | 106.5 |
Rollforward of fair value investments by level | The following tables present the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2019 and 2018:
|  |  |  |  |  | Level 3 Investments |  | Other Long-term Investments Measured at NAV (3) |  |  |
Millions |  | Level 1 Investments |  | Level 2 Investments |  | Common Equity Securities |  | Other Long-term Investments(2) |  |  | Total
Balance at December 31, 2018 |  | $ | 842.6 |  |  | $ | 1,160.5 |  |  | $ | — |  |  | $ | 138.7 |  |  | $ | 186.9 |  |  | $ | 2,328.7 |  | (1)
Net realized and unrealized gains |  | 163.0 |  |  | 76.1 |  |  | — |  |  | 181.2 |  |  | 12.7 |  |  | 433.0 |  | (2)4)
Amortization/accretion |  | .2 |  |  | (1.8 | ) |  | — |  |  | — |  |  | — |  |  | (1.6 | ) |
Purchases |  | 165.3 |  |  | 404.5 |  |  | .1 |  |  | 185.4 |  |  | 110.8 |  |  | 866.1 |  |
Sales |  | (391.1 | ) |  | (529.7 | ) |  | — |  |  | — |  |  | (29.5 | ) |  | (950.3 | ) |
Effect of Kudu Transaction |  | — |  |  | — |  |  | — |  |  | 141.8 |  |  | (71.7 | ) |  | 70.1 |  |
Transfers in |  | — |  |  | — |  |  | — |  |  | 10.9 |  |  | 4.0 |  |  | 14.9 |  |
Transfers out |  | — |  |  | — |  |  | — |  |  | (4.0 | ) |  | (10.9 | ) |  | (14.9 | ) |
Balance at December 31, 2019 |  | $ | 780.0 |  |  | $ | 1,109.6 |  |  | $ | .1 |  |  | $ | 654.0 |  |  | $ | 202.3 |  |  | $ | 2,746.0 |  | (1)
(1) Excludes carrying value of $201.2 and $214.2 as of December 31, 2019 and 2018 classified as short-term investments.
(2) | Includes $114.7 unrealized investment gain associated with the MediaAlpha Transaction, which is recorded in a separate line item in the statement of operations titled Realized gain and unrealized investment gain from the MediaAlpha Transaction. See Note 2 — “Significant Transactions”.
(3) Includes private equity funds, hedge funds, ILS funds and unconsolidated entities 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”. (4) Excludes realized and unrealized losses associated with short-term investments of $0.2 for the year ended December 31, 2019.
|  |  |  |  |  | Level 3 Investments |  | Other Long-term Investments Measured at NAV (3) |  |  |
Millions |  | Level 1 Investments |  | Level 2 Investments |  | Other Long- term Investments |  |  | Total
Balance at December 31, 2017 |  | $ | 890.4 |  |  | $ | 2,105.4 |  |  | $ | 77.2 |  |  | $ | 135.3 |  |  | $ | 3,208.3 |  | (1)(2)
Net realized and unrealized (losses) gains |  | (64.9 | ) |  | (64.4 | ) |  | 16.2 |  |  | 13.3 |  |  | (99.8 | ) | (4)
Amortization/accretion |  | .2 |  |  | (2.7 | ) |  | — |  |  | — |  |  | (2.5 | ) |
Purchases |  | 514.7 |  |  | 783.8 |  |  | 45.3 |  |  | 50.5 |  |  | 1,394.3 |  |
Sales |  | (497.8 | ) |  | (1,661.6 | ) |  | — |  |  | (12.2 | ) |  | (2,171.6 | ) |
Transfers in |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |
Transfers out |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |
Balance at December 31, 2018 |  | $ | 842.6 |  |  | $ | 1,160.5 |  |  | $ | 138.7 |  |  | $ | 186.9 |  |  | $ | 2,328.7 |  | (2)
(1) Excludes carrying value of $(3.7) as of December 31, 2017 associated with foreign currency forward contracts. (2) Excludes carrying value of $214.2 and $176.1 as of December 31, 2018 and 2017 classified as short-term investments.
(3) | Includes private equity funds, hedge funds and unconsolidated entities 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”.
(4) Excludes realized and unrealized losses associated with foreign currency forward contracts, foreign currency on cash and open trades and short-term investments of $3.5, $4.2 and $0.8 for the year ended December 31, 2018.
Schedule of significant unobservable inputs used in estimating the fair value of investment securities | The following tables present significant unobservable inputs used in estimating the fair value of other long-term investments, other than private equity funds, hedge funds and ILS funds, classified within Level 3 as of December 31, 2019 and 2018. The fair value of investments in private equity funds, hedge funds and ILS funds are generally estimated using the NAV of the funds.
$ in Millions |  | December 31, 2019
Description |  | Valuation Technique(s) |  | Fair Value (1) |  | Unobservable Inputs
|  |  |  |  |  | Discount Rate (2) |  | Terminal Cash Flow Exit Multiple (x) or Terminal Revenue Growth Rate (%) (2)
Kudu’s Participation Contracts |  | Discounted cash flow |  | $266.5 |  | 15% - 22% |  | 6x - 12x
MediaAlpha |  | Discounted cash flow |  | $180.0 |  | 15% |  | 4%
PassportCard/DavidShield |  | Discounted cash flow |  | $90.0 |  | 22% |  | 4%
Elementum Holdings, L.P. |  | Discounted cash flow |  | $55.1 |  | 20% |  | 4%
Private debt instruments |  | Discounted cash flow |  | $23.7 |  | 4% - 9% |  | N/A
All other |  | Discounted cash flow |  | $23.7 |  | 25% - 32% |  | 4%
Compare.com |  | Estimated net realizable value |  | $2.5 |  | Net asset value: |  | $2.5
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs. (2) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal cash flow exit multiples or terminal revenue growth rates in isolation would result in higher (lower) fair value measurements.
$ in Millions |  | December 31, 2018
Description |  | Valuation Technique(s) |  | Fair Value (1) |  | Unobservable Inputs
|  |  |  |  |  | Discount Rate (2) |  | Terminal Revenue Exit Multiple (x) (2)
PassportCard/DavidShield |  | Discounted cash flow |  | $75.0 |  | 18% |  | 1x
Compare.com |  | Discounted cash flow |  | $16.9 |  | 22% |  | 3x
Private debt instrument |  | Discounted cash flow |  | $10.0 |  | 9% |  | N/A
All other |  | Discounted cash flow |  | $30.0 |  | 23% |  | 2x - 4x
Galvanic Applied Sciences |  | Multiple of EBITDA |  | $3.1 |  | EBITDA multiple: |  | 6x
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs. (2) Increases (decreases) to the discount rates in isolation would result in lower (higher) fair value measurements, while increases (decreases) to the terminal revenue exit multiples in isolation would result in higher (lower) fair value measurements.

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