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Investment Securities (Tables) | 12 Months Ended
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Dec. 31, 2016
Investments, Debt and Equity Securities [Abstract] |
Par Value to Fair Value Reconciliation of Surplus Notes [Table Text Block] | Below is a table illustrating the valuation adjustments taken to arrive at the estimated fair value of the OneBeacon Surplus Notes as of December 31, 2016 and 2015:
|  | Type of Surplus Note |  | Total as of December 31, 2016 |  | Total as of December 31, 2015
Millions |  | Seller Priority |  | Pari Passu |
Par Value |  | $ | 57.9 |  |  | $ | 43.1 |  |  | $ | 101.0 |  |  | $ | 101.0 |
Fair value adjustments to reflect: |  |  |  |  |  |  |  |
Current market rates on public debt and contract-based repayments(1) |  | 6.2 |  |  | (1.1 | ) |  | 5.1 |  |  | (15.1 | )
Regulatory approval (2) |  | (.2 | ) |  | (15.4 | ) |  | (15.6 | ) |  | (24.2 | )
Liquidity adjustment (3) |  | (12.8 | ) |  | (5.8 | ) |  | (18.6 | ) |  | (10.2 | )
Total adjustments |  | (6.8 | ) |  | (22.3 | ) |  | (29.1 | ) |  | (49.5 | )
Fair value(4) |  | $ | 51.1 |  |  | $ | 20.8 |  |  | $ | 71.9 |  |  | $ | 51.5 |
(1) Represents the value of the surplus notes, at current market yields on comparable publicly traded debt, and assuming issuer is allowed to make principal and interest payments when its financial capacity is available, as measured by statutory capital in excess of a 250% RBC score under the NAIC’s risk-based capital standards for property and casualty companies. The favorable year-over-year change in impact is due principally to the narrowing of non-investment grade credit spreads as well as the time value of money benefit from moving one year closer to modeled cash receipts. (2) Represents anticipated delay in securing regulatory approvals of interest and principal payments to reflect graduated changes in Issuer's statutory surplus. The monetary impact of the anticipated delay is measured based on credit spreads of public securities with roughly equivalent percentages of discounted payments missed. The favorable year-over-year change in impact is driven primarily by the narrowing of non-investment grade credit spreads, which causes the anticipated delay in securing regulatory approval to be less punitive, partially offset by the change in estimates and assumptions regarding the timeline, amounts, and process necessary to obtain regulatory approval for principal and interest payments described below. (3) Represents impact of liquidity spread to account for OneBeacon’s sole ownership of the OneBeacon Surplus Notes, lack of a trading market and unique nature of the ongoing regulatory approval process. The unfavorable year-over-year change in impact is due largely to the increased fair value of the notes as well as a higher effective duration resulting from a lower overall yield to maturity; there was no change in the magnitude of the liquidity spread in 2016. (4) The increase in the fair value of the OneBeacon Surplus Notes during the year ended December 31, 2016 was driven primarily by the narrowing of non-investment grade credit spreads, partially offset by the impact of a change in estimates and assumptions regarding the timing of regulatory approval of principal and interest payments on the notes.
Pre-tax net investment income | Pre-tax net investment income for 2016, 2015 and 2014 consisted of the following:
|  | Year Ended December 31,
Millions |  | 2016 |  | 2015 |  | 2014
Investment income: |  |  |  |  |  |
Fixed maturity investments |  | $ | 77.3 |  |  | $ | 52.6 |  |  | $ | 51.3 |
Short-term investments |  | 1.1 |  |  | .2 |  |  | .1 |
Common equity securities |  | 7.5 |  |  | 10.1 |  |  | 16.6 |
Other long-term investments |  | 4.0 |  |  | 3.3 |  |  | 4.4 |
Total investment income |  | 89.9 |  |  | 66.2 |  |  | 72.4 |
Third-party investment expenses |  | (3.1 | ) |  | (5.4 | ) |  | (12.9 | )
Net investment income, pre-tax |  | $ | 86.8 |  |  | $ | 60.8 |  |  | $ | 59.5 |
Net Realized and Unrealized Investment Gains and Losses | Net realized and unrealized investment gains (losses) consisted of the following:
|  | Year Ended December 31,
Millions |  | 2016 |  | 2015 |  | 2014
Net realized investment gains, pre-tax |  | $ | 280.3 |  |  | $ | 77.3 |  |  | $ | 166.8 |
Net unrealized investment (losses) gains, pre-tax |  | (270.0 | ) |  | 148.1 |  |  | (88.3 | )
Net realized and unrealized investment gains, pre-tax |  | 10.3 |  |  | 225.4 |  |  | 78.5 |
Income tax expense attributable to net realized and unrealized investment gains |  | (8.8 | ) |  | (35.2 | ) |  | (18.0 | )
Net realized and unrealized investment gains, after tax |  | $ | 1.5 |  |  | $ | 190.2 |  |  | $ | 60.5 |
Net unrealized investment gains (losses) for Level 3 investments | The following table summarizes the amount of total gains (losses) included in earnings attributable to net unrealized investment gains (losses) for Level 3 investments for the years ended December 31, 2016, 2015 and 2014.
|  | Year Ended December 31,
Millions |  | 2016 |  | 2015 |  | 2014
Fixed maturity investments |  | $ | .1 |  |  | $ | (1.1 | ) |  | $ | 1.9 |
Common equity securities |  | — |  |  | (9.0 | ) |  | 5.8 |
Other long-term investments |  | 6.1 |  |  | (13.0 | ) |  | — |
Total net unrealized investment gains (losses), pre-tax - Level 3 investments |  | $ | 6.2 |  |  | $ | (23.1 | ) |  | $ | 7.7 |
Net realized and unrealized investment gains, after-tax, as recorded on the statements of operations and comprehensive income (losses) | The components of White Mountains’s net realized and unrealized investment gains (losses), after-tax, as recorded on the statements of operations and comprehensive income were as follows:
|  | Year Ended December 31,
Millions |  | 2016 |  | 2015 |  | 2014
Net change in pre-tax unrealized investment (losses) gains on investments in unconsolidated affiliates |  | $ | — |  |  | $ | (39.2 | ) |  | $ | 81.2 |
Income tax benefit (expense) |  | — |  |  | 2.9 |  |  | (5.9 | )
Net change in unrealized investment (losses) gains on investments in unconsolidated affiliates, after tax |  | — |  |  | (36.3 | ) |  | 75.3 |
Reversal of accumulated other comprehensive income related to change in accounting for the investment in Symetra |  | — |  |  | 1.4 |  |  | — |
Total investment (losses) gains through accumulated other comprehensive income |  | — |  |  | (34.9 | ) |  | 75.3 |
Net realized and unrealized investment gains, after-tax |  | 1.5 |  |  | 190.2 |  |  | 60.5 |
Total investment gains recorded during the period, after-tax |  | $ | 1.5 |  |  | $ | 155.3 |  |  | $ | 135.8 |
Realized Gain (Loss) on Investments | Net realized investment gains for 2016, 2015 and 2014 consisted of the following:
|  | Year ended December 31, 2016
Millions |  | Net realized (losses) gains |  | Net foreign exchange gains |  | Total net realized (losses) gains reflected in earnings
Fixed maturity investments |  | $ | (2.1 | ) |  | $ | .4 |  |  | $ | (1.7 | )
Short-term investments |  | .4 |  |  | — |  |  | .4 |
Common equity securities |  | 280.7 |  |  | — |  |  | 280.7 |
Other long-term investments |  | .9 |  |  | — |  |  | .9 |
Net realized investment gains, pre-tax |  | 279.9 |  |  | .4 |  |  | 280.3 |
Income tax expense attributable to net realized investment gains |  | (49.5 | ) |  | — |  |  | (49.5 | )
Net realized investment gains, after-tax |  | $ | 230.4 |  |  | $ | .4 |  |  | $ | 230.8 |
|  | Year ended December 31, 2015
Millions |  | Net realized gains |  | Net foreign exchange gains |  | Total net realized gains reflected in earnings
Fixed maturity investments |  | $ | 1.9 |  |  | $ | — |  |  | $ | 1.9 |
Common equity securities |  | 64.4 |  |  | .4 |  |  | 64.8 |
Other long-term investments |  | 10.6 |  |  | — |  |  | 10.6 |
Net realized investment gains, pre-tax |  | 76.9 |  |  | .4 |  |  | 77.3 |
Income tax expense attributable to net realized investment gains |  | (22.8 | ) |  | — |  |  | (22.8 | )
Net realized investment gains, after-tax |  | $ | 54.1 |  |  | $ | .4 |  |  | $ | 54.5 |
|  | Year ended December 31, 2014
Millions |  | Net realized gains |  | Net foreign exchange gains |  | Total net realized gains reflected in earnings
Fixed maturity investments |  | $ | 5.8 |  |  | $ | — |  |  | $ | 5.8 |
Common equity securities |  | 138.0 |  |  | — |  |  | 138.0 |
Other long-term investments |  | 23.0 |  |  | — |  |  | 23.0 |
Net realized investment gains, pre-tax |  | 166.8 |  |  | — |  |  | 166.8 |
Income tax expense attributable to net realized investment gains |  | (28.4 | ) |  | — |  |  | (28.4 | )
Net realized investment gains, after-tax |  | $ | 138.4 |  |  | $ | — |  |  | $ | 138.4 |
Unrealized Gain (Loss) on Investments | The following table summarizes net unrealized investment gains (losses) and changes in the carrying value of investments measured at fair value:
|  | Year ended December 31, 2016
Millions |  | Net unrealized losses |  | Net foreign exchange gains (losses) |  | Total net unrealized losses reflected in earnings
Fixed maturity investments |  | $ | (12.1 | ) |  | $ | 2.1 |  |  | $ | (10.0 | )
Common equity securities |  | (254.6 | ) |  | (3.3 | ) |  | (257.9 | )
Other long-term investments |  | (.6 | ) |  | (.3 | ) |  | (.9 | )
Forward contracts |  | — |  |  | (1.2 | ) |  | (1.2 | )
Net unrealized investment losses, pre-tax |  | (267.3 | ) |  | (2.7 | ) |  | (270.0 | )
Income tax benefit attributable to net unrealized investment losses |  | 40.7 |  |  | — |  |  | 40.7 |
Net unrealized investment losses, after-tax |  | $ | (226.6 | ) |  | $ | (2.7 | ) |  | $ | (229.3 | )
|  | Year ended December 31, 2015
Millions |  | Net unrealized (losses) gains |  | Net foreign exchange losses |  | Total net unrealized (losses) gains reflected in earnings
Fixed maturity investments |  | $ | (15.6 | ) |  | $ | — |  |  | $ | (15.6 | )
Common equity securities |  | 207.6 |  |  | (3.7 | ) |  | 203.9 |
Other long-term investments |  | (39.1 | ) |  | (1.1 | ) |  | (40.2 | )
Net unrealized investment gains (losses), pre-tax |  | 152.9 |  |  | (4.8 | ) |  | 148.1 |
Income tax expense attributable to net unrealized investment gains (losses) |  | (12.3 | ) |  | (.1 | ) |  | (12.4 | )
Net unrealized investment gains (losses), after-tax |  | $ | 140.6 |  |  | $ | (4.9 | ) |  | $ | 135.7 |
|  | Year ended December 31, 2014
Millions |  | Net unrealized gains (losses) |  | Net foreign exchange losses |  | Total net unrealized gains (losses) reflected in earnings
Fixed maturity investments |  | $ | 11.3 |  |  | $ | — |  |  | $ | 11.3 |
Common equity securities |  | (83.0 | ) |  | (7.7 | ) |  | (90.7 | )
Other long-term investments |  | (7.6 | ) |  | (1.3 | ) |  | (8.9 | )
Net unrealized investment losses, pre-tax |  | (79.3 | ) |  | (9.0 | ) |  | (88.3 | )
Income tax benefit attributable to net unrealized investment losses |  | 9.9 |  |  | .5 |  |  | 10.4 |
Net unrealized investment losses, after-tax |  | $ | (69.4 | ) |  | $ | (8.5 | ) |  | $ | (77.9 | )
Investment holdings, fixed maturity investments | The cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains, and carrying values of White Mountains’s fixed maturity investments as of December 31, 2016 and 2015, were as follows:
|  | December 31, 2016
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency gains |  | Carrying value
US Government and agency obligations |  | $ | 281.7 |  |  | $ | .1 |  |  | $ | (3.5 | ) |  | $ | — |  |  | $ | 278.3 |
Debt securities issued by corporations |  | 1,512.6 |  |  | 8.4 |  |  | (13.7 | ) |  | 2.1 |  |  | 1,509.4 |
Municipal obligations |  | 308.8 |  |  | 1.9 |  |  | (1.7 | ) |  | — |  |  | 309.0 |
Mortgage and asset-backed securities |  | 2,141.7 |  |  | 2.6 |  |  | (11.4 | ) |  | — |  |  | 2,132.9 |
Foreign government, agency and provincial obligations |  | 12.9 |  |  | .3 |  |  | — |  |  | — |  |  | 13.2 |
Preferred stocks |  | 8.3 |  |  | 5.7 |  |  | — |  |  | — |  |  | 14.0 |
Total fixed maturity investments |  | 4,266.0 |  |  | 19.0 |  |  | (30.3 | ) |  | 2.1 |  |  | 4,256.8 |
Fixed maturity investments reclassified to assets held for sale related to SSIE |  |  |  |  |  |  |  |  |  | (6.6 | )
Total fixed maturity investments |  |  |  |  |  |  |  |  |  | $ | 4,250.2 |
|  | December 31, 2015
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency gains (losses) |  | Carrying value
US Government and agency obligations |  | $ | 160.4 |  |  | $ | — |  |  | $ | (.4 | ) |  | $ | — |  |  | $ | 160.0 |
Debt securities issued by corporations |  | 1,001.0 |  |  | 4.3 |  |  | (5.3 | ) |  | — |  |  | 1,000.0 |
Municipal obligations |  | 227.8 |  |  | 2.2 |  |  | (1.2 | ) |  | — |  |  | 228.8 |
Mortgage and asset-backed securities |  | 1,170.6 |  |  | 2.0 |  |  | (5.6 | ) |  | — |  |  | 1,167.0 |
Foreign government, agency and provincial obligations |  | 1.0 |  |  | .2 |  |  | — |  |  | — |  |  | 1.2 |
Preferred stocks |  | 78.3 |  |  | 4.4 |  |  | — |  |  | — |  |  | 82.7 |
Total fixed maturity investments |  | 2,639.1 |  |  | 13.1 |  |  | (12.5 | ) |  | $ | — |  |  | 2,639.7 |
Fixed maturity investments reclassified to assets held for sale related to SSIE |  |  |  |  |  |  |  |  |  | (9.5 | )
Total fixed maturity investments |  |  |  |  |  |  |  |  |  | $ | 2,630.2 |
Schedule of contractual maturities of fixed maturities | The cost or amortized cost and carrying value of White Mountains’s fixed maturity investments as of December 31, 2016 is presented below by contractual maturity. 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, 2016
Millions |  | Cost or amortized cost |  | Carrying value
Due in one year or less |  | $ | 212.8 |  |  | $ | 213.3 |
Due after one year through five years |  | 1,272.6 |  |  | 1,270.2 |
Due after five years through ten years |  | 462.8 |  |  | 458.4 |
Due after ten years |  | 167.8 |  |  | 168.0 |
Mortgage and asset-backed securities |  | 2,141.7 |  |  | 2,132.9 |
Preferred stocks |  | 8.3 |  |  | 14.0 |
Total |  | $ | 4,266.0 |  |  | $ | 4,256.8 |
Investment holdings, equity securities, convertible fixed maturities and other long-term investments | The cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains (losses), and carrying values of White Mountains’s common equity securities and other long-term investments as of December 31, 2016 and 2015 were as follows:
|  | December 31, 2016
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency losses |  | Carrying value
Common equity securities |  | $ | 440.8 |  |  | $ | 35.9 |  |  | $ | (2.4 | ) |  | $ | — |  |  | $ | 474.3 |
Other long-term investments |  | $ | 314.9 |  |  | $ | 40.3 |  |  | $ | (28.0 | ) |  | $ | (3.9 | ) |  | $ | 323.3 |
|  | December 31, 2015
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency losses |  | Carrying value
Common equity securities |  | $ | 822.5 |  |  | $ | 302.8 |  |  | $ | (11.4 | ) |  | $ | — |  |  | $ | 1,113.9 |
Other long-term investments |  | $ | 304.5 |  |  | $ | 32.0 |  |  | $ | (18.4 | ) |  | $ | (2.3 | ) |  | $ | 315.8 |
Fair value measurements by level, investment securities | The following tables summarize White Mountains’s fair value measurements for investments as of December 31, 2016 and 2015 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. The fair value measurements for derivative assets associated with White Mountains’s variable annuity business are presented in Note 9.
|  | December 31, 2016
Millions |  | Fair value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 278.3 |  |  | $ | 268.8 |  |  | $ | 9.5 |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |
Consumer |  | 385.6 |  |  | — |  |  | 385.6 |  |  | — |
Health Care |  | 244.2 |  |  | — |  |  | 244.2 |  |  | — |
Utilities |  | 180.3 |  |  | — |  |  | 180.3 |  |  | — |
Financials |  | 176.0 |  |  | — |  |  | 176.0 |  |  | — |
Industrial |  | 146.4 |  |  | — |  |  | 146.4 |  |  | — |
Communications |  | 131.4 |  |  | — |  |  | 131.4 |  |  | — |
Materials |  | 102.6 |  |  | — |  |  | 102.6 |  |  | — |
Technology |  | 89.4 |  |  | — |  |  | 89.4 |  |  | — |
Energy |  | 53.5 |  |  | — |  |  | 53.5 |  |  | — |
Total debt securities issued by corporations: |  | 1,509.4 |  |  | — |  |  | 1,509.4 |  |  | — |
Mortgage and asset-backed securities |  | 2,132.9 |  |  | — |  |  | 2,132.9 |  |  | — |
Municipal obligations |  | 309.0 |  |  | — |  |  | 309.0 |  |  | — |
Foreign government, agency and provincial obligations |  | 13.2 |  |  | .6 |  |  | 12.6 |  |  | — |
Preferred stocks |  | 14.0 |  |  | — |  |  | 14.0 |  |  | — |
Total fixed maturity investments (4) |  | 4,256.8 |  |  | 269.4 |  |  | 3,987.4 |  |  | — |
Short-term investments (4)(5) |  | 287.1 |  |  | 274.4 |  |  | 12.7 |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Exchange traded funds (1) |  | 321.6 |  |  | 270.4 |  |  | 51.2 |  |  | — |
Health Care |  | 20.9 |  |  | 20.9 |  |  | — |  |  | — |
Consumer |  | 12.9 |  |  | 12.9 |  |  | — |  |  | — |
Financials |  | 11.6 |  |  | 11.6 |  |  | — |  |  | — |
Technology |  | 11.0 |  |  | 11.0 |  |  | — |  |  | — |
Communications |  | 10.5 |  |  | 10.5 |  |  | — |  |  | — |
Energy |  | 3.7 |  |  | 3.7 |  |  | — |  |  | — |
Industrial |  | 2.2 |  |  | 2.2 |  |  | — |  |  | — |
Other |  | 79.9 |  |  | — |  |  | 79.9 |  |  | — |
Total common equity securities |  | 474.3 |  |  | 343.2 |  |  | 131.1 |  |  | — |
Other long-term investments (2)(3) |  | 177.7 |  |  | — |  |  | — |  |  | 177.7 |
Total investments (2)(3)(4) |  | $ | 5,195.9 |  |  | $ | 887.0 |  |  | $ | 4,131.2 |  |  | $ | 177.7 |
(1) 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. (2) Excludes carrying value of $3.5 associated with other long-term investment limited partnerships accounted for using the equity method and $(1.2) related to foreign currency forward contracts. Excludes carrying value of $12.3 associated with a tax advantaged federal affordable housing development fund accounted for using the proportional amortization method. (3) Excludes carrying value of $131.0 associated with hedge funds and private equity funds for which fair value is measured at NAV using the practical expedient. (4) Includes carrying value of $6.6 in fixed maturity investments and $0.1 in short-term investments that are classified as assets held for sale related to SSIE. (5) Short-term investments are measured at amortized cost, which approximates fair value.
|  | December 31, 2015
Millions |  | Fair value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 160.0 |  |  | $ | 133.4 |  |  | $ | 26.6 |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |  |  |  |
Consumer |  | 253.3 |  |  | — |  |  | 253.3 |  |  | — |
Financials |  | 175.9 |  |  | — |  |  | 175.9 |  |  | — |
Health Care |  | 151.3 |  |  | — |  |  | 151.3 |  |  | — |
Industrial |  | 135.6 |  |  | — |  |  | 135.6 |  |  | — |
Energy |  | 82.0 |  |  | — |  |  | 82.0 |  |  | — |
Utilities |  | 61.5 |  |  | — |  |  | 61.5 |  |  | — |
Technology |  | 60.0 |  |  | — |  |  | 60.0 |  |  | — |
Communications |  | 49.2 |  |  | — |  |  | 49.2 |  |  | — |
Materials |  | 31.2 |  |  | — |  |  | 31.2 |  |  | — |
Total debt securities issued by corporations: |  | 1,000.0 |  |  | — |  |  | 1,000.0 |  |  | — |
Mortgage and asset-backed securities |  | 1,167.0 |  |  | — |  |  | 1,167.0 |  |  | — |
Municipal obligations |  | 228.8 |  |  | — |  |  | 228.8 |  |  | — |
Foreign government, agency and provincial obligations |  | 1.2 |  |  | .6 |  |  | .6 |  |  | — |
Preferred stocks |  | 82.7 |  |  | — |  |  | 12.7 |  |  | 70.0 |
Total fixed maturity investments (4) |  | 2,639.7 |  |  | 134.0 |  |  | 2,435.7 |  |  | 70.0 |
Short-term investments (4)(5) |  | 211.3 |  |  | 211.3 |  |  | — |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Financials |  | 653.2 |  |  | 653.2 |  |  | — |  |  | — |
Exchange traded funds(1) |  | 183.3 |  |  | 162.0 |  |  | 21.3 |  |  | — |
Consumer |  | 70.0 |  |  | 70.0 |  |  | — |  |  | — |
Communications |  | 43.7 |  |  | 43.7 |  |  | — |  |  | — |
Health Care |  | 35.7 |  |  | 35.7 |  |  | — |  |  | — |
Technology |  | 27.0 |  |  | 27.0 |  |  | — |  |  | — |
Industrial |  | 26.6 |  |  | 26.6 |  |  | — |  |  | — |
Other |  | 74.4 |  |  | — |  |  | 74.4 |  |  | — |
Total common equity securities |  | 1,113.9 |  |  | 1,018.2 |  |  | 95.7 |  |  | — |
Other long-term investments (2)(3) |  | 169.5 |  |  | — |  |  | — |  |  | 169.5 |
Total investments (2)(3)(4) |  | $ | 4,134.4 |  |  | $ | 1,363.5 |  |  | $ | 2,531.4 |  |  | $ | 239.5 |
(1) 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. (2) Excludes carrying value of $3.8 associated with other long-term investment limited partnerships accounted for using the equity method. Excludes carrying value of $14.7 associated with a tax advantaged federal affordable housing development fund accounted for using the proportional amortization method. (3) Excludes carrying value of $127.8 associated with hedge funds and private equity funds for which fair value is measured at NAV using the practical expedient. (4) Includes carrying value of $9.5 in fixed maturity investments and $0.1 in short-term investments that are classified as assets held for sale related to SSIE. (5) Short-term investments are measured at amortized cost, which approximates fair value.
Debt securities issued by corporations, credit ratings | The following table summarizes the ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2016 and 2015:
|  | Fair Value at December 31,
Millions |  | 2016 |  | 2015
AA |  | $ | 100.9 |  |  | $ | 95.2 |
A |  | 381.9 |  |  | 397.7 |
BBB |  | 786.5 |  |  | 507.1 |
BB |  | 214.0 |  |  | — |
B |  | 26.1 |  |  | — |
Debt securities issued by corporations(1) |  | $ | 1,509.4 |  |  | $ | 1,000.0 |
(1) | Credit ratings are assigned based on the following hierarchy: 1) Standard & Poors Financial Services LLC (“Standard & Poor’s”) and 2) Moody’s Investor Services (“Moody’s”)
Mortgage-backed, asset-backed securities | The following table summarizes the carrying value of White Mountains’s mortgage and asset-backed securities as of December 31, 2016 and December 31, 2015:
|  | December 31, 2016 |  | December 31, 2015
Millions |  | Fair Value |  | Level 2 |  | Level 3 |  | Fair Value |  | Level 2 |  | Level 3
Mortgage-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Agency: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
GNMA |  | $ | 283.9 |  |  | $ | 283.9 |  |  | $ | — |  |  | $ | 265.5 |  |  | $ | 265.5 |  |  | $ | — |
FNMA |  | 278.3 |  |  | 278.3 |  |  | — |  |  | 42.2 |  |  | 42.2 |  |  | — |
FHLMC |  | 89.8 |  |  | 89.8 |  |  | — |  |  | 22.8 |  |  | 22.8 |  |  | — |
Total Agency (1) |  | 652.0 |  |  | 652.0 |  |  | — |  |  | 330.5 |  |  | 330.5 |  |  | — |
Non-agency: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Residential |  | 205.3 |  |  | 205.3 |  |  | — |  |  | 133.2 |  |  | 133.2 |  |  | — |
Commercial |  | 127.5 |  |  | 127.5 |  |  | — |  |  | 140.4 |  |  | 140.4 |  |  | — |
Total Non-agency |  | 332.8 |  |  | 332.8 |  |  | — |  |  | 273.6 |  |  | 273.6 |  |  | — |
Total mortgage-backed securities |  | 984.8 |  |  | 984.8 |  |  | — |  |  | 604.1 |  |  | 604.1 |  |  | — |
Other asset-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |
Vehicle receivables |  | 479.5 |  |  | 479.5 |  |  | — |  |  | 269.7 |  |  | 269.7 |  |  | — |
Credit card receivables |  | 438.3 |  |  | 438.3 |  |  | — |  |  | 217.7 |  |  | 217.7 |  |  | — |
Other |  | 230.3 |  |  | 230.3 |  |  | — |  |  | 75.5 |  |  | 75.5 |  |  | — |
Total other asset-backed securities |  | 1,148.1 |  |  | 1,148.1 |  |  | — |  |  | 562.9 |  |  | 562.9 |  |  | — |
Total mortgage and asset-backed securities |  | $ | 2,132.9 |  |  | $ | 2,132.9 |  |  | $ | — |  |  | $ | 1,167.0 |  |  | $ | 1,167.0 |  |  | $ | — |
(1) | Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).
Schedule of security issuance years of investments in non-agency RMBS and non-agency CMBS securities | The security issuance years of White Mountains’s investments in non-agency RMBS and non-agency CMBS securities as of December 31, 2016 are as follows:
|  |  |  |  |  |  |  | Security Issuance Year |  |  |  |  |  |  |  |
Millions |  | Fair Value |  | 2004 |  | 2005 |  | 2006 |  | 2007 |  | 2008 |  | 2009 |  | 2010 |  | 2011 |  | 2012 |  | 2013 |  | 2014 |  | 2015 |  | 2016
Non-agency RMBS |  | $ | 205.3 |  |  | $ | 19.4 |  |  | $ | 5.7 |  |  | $ | 3.0 |  |  | $ | — |  |  | $ | 2.7 |  |  | $ | — |  |  | $ | 7.4 |  |  | $ | 9.9 |  |  | $ | 5.0 |  |  | $ | 15.3 |  |  | $ | 53.3 |  |  | $ | 48.3 |  |  | $ | 35.3 |
Non-agency CMBS |  | 127.5 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 4.3 |  |  | — |  |  | 18.1 |  |  | 11.5 |  |  | 23.4 |  |  | 44.4 |  |  | $ | 25.8 |
Total |  | $ | 332.8 |  |  | $ | 19.4 |  |  | $ | 5.7 |  |  | $ | 3.0 |  |  | $ | — |  |  | $ | 2.7 |  |  | $ | — |  |  | $ | 11.7 |  |  | $ | 9.9 |  |  | $ | 23.1 |  |  | $ | 26.8 |  |  | $ | 76.7 |  |  | $ | 92.7 |  |  | $ | 61.1 |
Non-agency residential mortgage securities, collateral quality and tranche levels | The classification of the underlying collateral quality and the tranche levels of White Mountains’s non-agency RMBS securities are as follows as of December 31, 2016:
Millions |  | Fair Value |  | Super Senior(1) |  | Senior(2) |  | Subordinate(3)
Prime |  | $ | 205.3 |  |  | $ | 150.6 |  |  | $ | 54.7 |  |  | $ | — |
Non-prime |  | — |  |  | — |  |  | — |  |  | — |
Sub-prime |  | — |  |  | — |  |  | — |  |  | — |
Total non-agency RMBS |  | $ | 205.3 |  |  | $ | 150.6 |  |  | $ | 54.7 |  |  | $ | — |
(1) | At issuance, Super Senior, or in the case of resecuritization, the underlying securities, were rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch Ratings (“Fitch”) and were senior to other “AAA” or “Aaa” bonds.
(2) | At issuance, Senior, or in the case of resecuritization, the underlying securities, were rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch and were senior to non-“AAA” or non-“Aaa” bonds.
(3) | At issuance, Subordinate were not rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch and were junior to “AAA” or “Aaa” bonds.
Non-agency commercial mortgage securities, type of interest rate and tranche levels | The amount of fixed and floating rate securities and their tranche levels of White Mountains’s non-agency CMBS securities are as follows as of December 31, 2016:
Millions |  | Fair Value |  | Super Senior(1) |  | Senior(2) |  | Subordinate(3)
Fixed rate CMBS |  | $ | 116.0 |  |  | $ | 8.7 |  |  | $ | 59.1 |  |  | $ | 48.2 |
Floating rate CMBS |  | 11.5 |  |  | — |  |  | — |  |  | 11.5 |
Total non-agency CMBS |  | $ | 127.5 |  |  | $ | 8.7 |  |  | $ | 59.1 |  |  | $ | 59.7 |
(1) | At issuance, Super Senior, or in the case of resecuritization, the underlying securities, were rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch and were senior to other “AAA” or “Aaa” bonds.
(2) | At issuance, Senior, or in the case of resecuritization, the underlying securities, were rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch and were senior to non-“AAA” or non-“Aaa” bonds.
(3) | At issuance, Subordinate were not rated “AAA” by Standard & Poor’s, “Aaa” by Moody’s or “AAA” by Fitch and were junior to “AAA” or “Aaa” bonds
Other long-term investments | The following table summarizes investments in hedge funds and private equity funds by investment objective and sector as of December 31, 2016 and 2015:
|  | December 31, 2016 |  | December 31, 2015
Millions |  | Fair Value |  | Unfunded Commitments |  | Fair Value |  | Unfunded Commitments
Hedge funds |  |  |  |  |  |  |  |  |  |  |  |
Long/short banks and financial |  | $ | 36.5 |  |  | $ | — |  |  | $ | 12.8 |  |  | $ | — |
Long/short equity REIT |  | 19.9 |  |  | — |  |  | 20.6 |  |  | — |
Other |  | 3.4 |  |  | — |  |  | 3.6 |  |  | — |
Total hedge funds |  | 59.8 |  |  | — |  |  | 37.0 |  |  | — |
Private equity funds |  |  |  |  |  |  |  |  |  |  |  |
Aerospace/Defense/Government |  | 19.4 |  |  | 25.9 |  |  | 19.8 |  |  | 30.3 |
Manufacturing/Industrial |  | 15.9 |  |  | 22.4 |  |  | 24.9 |  |  | 2.5 |
Energy infrastructure & services |  | 14.1 |  |  | 3.2 |  |  | 20.7 |  |  | 3.4 |
Multi-sector |  | 11.4 |  |  | 2.0 |  |  | 14.8 |  |  | 2.1 |
Healthcare |  | 3.5 |  |  | .4 |  |  | 3.8 |  |  | .4 |
Private equity secondaries |  | 3.0 |  |  | 2.1 |  |  | 4.4 |  |  | 2.1 |
Direct lending/Mezzanine debt |  | 1.8 |  |  | 35.7 |  |  | — |  |  | — |
Financial Services |  | 1.0 |  |  | 5.0 |  |  | — |  |  | — |
Insurance |  | .8 |  |  | 41.3 |  |  | 2.0 |  |  | 41.3 |
Real estate |  | .3 |  |  | .1 |  |  | .4 |  |  | .1 |
Total private equity funds |  | 71.2 |  |  | 138.1 |  |  | 90.8 |  |  | 82.2 |
Total hedge and private equity funds included in other long-term investments |  | $ | 131.0 |  |  | $ | 138.1 |  |  | $ | 127.8 |  |  | $ | 82.2 |
Fair value of hedge funds subject to restrictions on redemption frequency and advance notice period requirements for investments in active hedge funds | The following summarizes the December 31, 2016 fair value of hedge funds subject to restrictions on redemption frequency and advance notice period requirements for investments in active hedge funds:
Millions |  | Notice Period
Redemption frequency |  | 30-59 days notice |  | 60-89 days notice |  | 90-119 days notice |  | Total
Monthly |  | $ | — |  |  | $ | — |  |  | $ | — |  |  | $ | — |
Quarterly |  | 15.9 |  |  | — |  |  | — |  |  | 15.9 |
Semi-annual |  | 21.6 |  |  | 19.9 |  |  | — |  |  | 41.5 |
Annual |  | — |  |  | — |  |  | 2.4 |  |  | 2.4 |
Total |  | $ | 37.5 |  |  | $ | 19.9 |  |  | $ | 2.4 |  |  | $ | 59.8 |
Fair Value of private equity funds subject to lock-up periods | As of December 31, 2016, investments in private equity funds were subject to lock-up periods as follows:
Millions |  | 1-3 years |  | 3 – 5 years |  | 5 – 10 years |  | >10 years |  | Total
Private Equity Funds — expected lock-up period remaining |  | $ | 14.8 |  |  | $ | 3.5 |  |  | $ | 50.0 |  |  | $ | 2.9 |  |  | $ | 71.2 |
Rollforward of fair value investments by level | The following tables summarize the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2016 and 2015:
|  |  |  |  |  | Level 3 Investments |  |  |  |  |
Millions |  | Level 1 Investments |  | Level 2 Investments |  | Fixed maturity investments |  | Common equity securities |  | Other long-term investments |  | Hedge Funds and Private Equity Funds measured at NAV(3) |  | Total |
Balance at January 1, 2016 |  | $ | 1,152.2 |  |  | $ | 2,531.4 |  |  | $ | 70.0 |  |  | $ | — |  |  | $ | 169.5 |  |  | $ | 127.8 |  |  | $ | 4,050.9 |  | (1)(2)(4)
Total net realized and unrealized investment gains (losses) |  | 11.3 |  |  | .2 |  |  | .1 |  |  | — |  |  | 6.1 |  |  | (6.1 | ) |  | 11.6 |  |
Amortization/Accretion |  | .1 |  |  | (19.4 | ) |  | — |  |  | — |  |  | — |  |  | — |  |  | (19.3 | ) |
Purchases |  | 2,243.7 |  |  | 3,979.8 |  |  | 120.8 |  |  | — |  |  | 2.2 |  |  | 35.2 |  |  | 6,381.7 |  |
Sales |  | (2,794.8 | ) |  | (2,491.5 | ) |  | (72.9 | ) |  | — |  |  | (.1 | ) |  | (25.9 | ) |  | (5,385.2 | ) |
Transfers in |  | — |  |  | 118.0 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 118.0 |  |
Transfers out |  | — |  |  | — |  |  | (118.0 | ) |  | — |  |  | — |  |  | — |  |  | (118.0 | ) |
Balance at December 31, 2016 |  | $ | 612.5 |  |  | $ | 4,118.5 |  |  | $ | — |  |  | $ | — |  |  | $ | 177.7 |  |  | $ | 131.0 |  |  | $ | 5,039.7 |  | (1)(2)(4)
(1) | Excludes carrying value of $3.5 and $3.8 as of December 31, 2016 and January 1, 2016 associated with other long-term investments accounted for using the equity method and $(1.2) related to foreign currency forward contracts. Excludes carrying value of $12.3 and $14.7 at December 31, 2016 and January 1, 2016 associated with a tax advantaged federal affordable housing development fund accounted for using the proportional amortization method.
(2) | Excludes carrying value of $287.1 and $211.3 as of December 31, 2016 and January 1, 2016 classified as short-term investments, of which $0.1 and $0.1 is classified as held for sale at December 31, 2016 and January 1, 2016.
(3) | Investments for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Summary of Significant Accounting Policies”.
(4) | Includes carrying value of $6.6 and $9.5 of fixed maturity investments at December 31, 2016 and January 1, 2016 that is classified as assets held for sale related to SSIE.
|  |  |  |  |  | Level 3 Investments |  |  |  |  |
Millions |  | Level 1 Investments |  | Level 2 Investments |  | Fixed maturity investments |  | Common equity securities |  | Other long-term investments |  | Hedge Funds and Private Equity Funds measured at NAV(3) |  | Total |
Balance at January 1, 2015 |  | $ | 550.6 |  |  | $ | 2,372.9 |  |  | $ | 76.4 |  |  | $ | 39.5 |  |  | $ | 125.9 |  |  | $ | 178.3 |  | (1) | $ | 3,343.6 |  | (1)(2)
Total net realized and unrealized investment gains (losses) |  | 263.0 |  |  | (13.7 | ) |  | (1.1 | ) |  | 7.8 |  |  | (20.0 | ) |  | (9.2 | ) |  | 226.8 |  | (3)(4)
Amortization/Accretion |  | — |  |  | (19.6 | ) |  | — |  |  | — |  |  | — |  |  | — |  |  | (19.6 | ) |
Purchases |  | 814.5 |  |  | 1,436.0 |  |  | 35.3 |  |  | — |  |  | 76.5 |  |  | 14.8 |  |  | 2,377.1 |  |
Sales |  | (825.7 | ) |  | (1,286.0 | ) |  | — |  |  | (43.7 | ) |  | (12.9 | ) |  | (41.8 | ) |  | (2,210.1 | ) |
Symetra transfer |  | 394.5 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 394.5 |  |
Effect of redemption of Prospector hedge funds |  | (43.5 | ) |  | — |  |  | — |  |  | (3.6 | ) |  | — |  |  | (14.3 | ) |  | (61.4 | ) |
Transfers in |  | — |  |  | 41.8 |  |  | — |  |  | — |  |  | — |  |  | — |  |  | 41.8 |  |
Transfers out |  | (1.2 | ) |  | — |  |  | (40.6 | ) |  | — |  |  | — |  |  | — |  |  | (41.8 | ) |
Balance at December 31, 2015 |  | $ | 1,152.2 |  |  | $ | 2,531.4 |  |  | $ | 70.0 |  |  | $ | — |  |  | $ | 169.5 |  |  | $ | 127.8 |  | (1) | $ | 4,050.9 |  | (1)(2)
(1) | Excludes carrying value of $3.8 and $5.2 as of December 31, 2015 and January 1, 2015 associated with other long-term investment limited partnerships accounted for using the equity method. Excludes carrying value of $14.7 and $16.8 at December 31, 2015 and January 1, 2015 associated with a tax advantaged federal affordable housing development fund accounted for using the proportional amortization method.
(2) | Excludes carrying value of $211.3 and $376.8 as of December 31, 2015 and January 1, 2015 classified as short-term investments.
(3) | Excludes $0.8 of net realized and unrealized investment losses associated with the Prospector Funds and consolidation of investment-related liabilities.
(4) | Includes unrealized investment gains of $258.8 associated with the Symetra transfer from investments in unconsolidated affiliates to common equity securities.
(5) Includes carrying value of $10.1 and $9.5 of fixed maturity investments at January 1, 2015 and December 31, 2015 that is classified as assets held for sale related to SSIE.
Schedule of significant unobservable inputs used in estimating the fair value of investment securities | The following summarizes significant unobservable inputs used in estimating the fair value of investment securities, other than hedge funds and private equity funds, classified within Level 3 as of December 31, 2016 and December 31, 2015. The fair value of investments in hedge funds and private equity funds are generally estimated using the NAV of the funds.
Description |  | December 31, 2016
$ in millions, except share price |  | Valuation Technique(s) |  | Fair Value (1) |  | Unobservable Input
Private equity security |  | Share price of most recent transaction |  | $21.0 |  | Share price | - | $1.00
Private equity security |  | Discounted cash flow |  | $22.1 |  | Discount rate | - | 25.0%
Private equity security |  | Share price of most recent transaction |  | $3.2 |  | Share price | - | $2.52
Private convertible preferred security |  | Multiple of EBITDA |  | $3.6 |  | EBITDA multiple | - | 6.00
Private convertible preferred security |  | Share price of most recent transaction |  | $27.0 |  | Share price | - | $3.83
Community reinvestment vehicle |  | Member share of GAAP net equity |  | $14.3 |  | GAAP net equity |  | $14.3
Private equity security |  | Discounted cash flow/ Option pricing method |  | $9.3 |  | Discount rate | - | 21.0%
|  |  |  |  |  | Time until expiration | - | 4 years
|  |  |  | Volatility/Standard deviation | - | 50.0%
|  |  |  | Risk free rate | - | 1.00%
OneBeacon Surplus Notes: |  |  |  |  |  |
- Seller priority |  | Discounted cash flow |  | $51.1 |  | Discount rate (2) | - | 9.6%
|  |  |  | Timing of interest payments (4) | - | 2020
|  |  |  | Timing of principal payments (4) | - | 2030
- Pari passu |  | Discounted cash flow |  | $20.8 |  | Discount rate (3) | - | 15.0%
|  |  |  | Timing of interest payments (5) | - | 2021
|  |  |  | Timing of principal payments (5) | - | 2035
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs. (2) Stochastic modeling supporting the fair value estimation indicates that the average percentage of discounted payments missed on the seller priority note is roughly equivalent to that of a conventional debt security with a credit rating of ‘B’. The corresponding credit spread increased by an additional 250 basis points to reflect both a liquidity discount for a private debt instrument and regulatory payment approval uncertainty, was added to the treasury rate to determine the discount rate for the seller priority note. (3) Stochastic modeling supporting the fair value estimation indicates that the average percentage of discounted payments missed on the pari passu note is roughly equivalent to that of a conventional debt security with a credit rating of ‘CCC’. The corresponding credit spread increased by an additional 250 basis points to reflect both a liquidity discount for a private debt instrument and regulatory payment approval uncertainty, was added to the treasury rate to determine the discount rate for the seller priority note. (4) As of December 31, 2016, OneBeacon has assumed for the purpose of estimating fair value that all accrued but unpaid interest on the seller priority note since the date of issuance is paid in 2020, with regular annual interest payments beginning thereafter. Principal repayments are assumed to begin on a graduated basis in 2030. (5) As of December 31, 2016, OneBeacon has assumed for the purpose of estimating fair value that regular annual interest payments on the pari passu note begin in 2021. All accrued but unpaid interest since the date of issuance is assumed to be paid in 2025. Principal repayments are assumed to begin on a graduated basis in 2035.
Description |  | December 31, 2015
$ in millions, except share price |  | Valuation Technique(s) |  | Fair Value(1) |  | Unobservable Input
Preferred Stock |  | Par value (2) |  | $70.0 |  | Issuer’s intent to call | - | $70.0
Private equity security |  | Share price of most recent transaction |  | $21.0 |  | Share price | - | $1.00
Private equity security |  | Share price of most recent transaction |  | $33.8 |  | Share price | - | $1.03
Private equity security |  | Share price of most recent transaction |  | $3.0 |  | Share price | - | $2.52
Private convertible preferred security |  | Multiple of EBITDA |  | $5.7 |  | EBITDA multiple | - | 6.00
Private convertible preferred security |  | Share price of most recent transaction |  | $27.0 |  | Share price | - | $3.83
Community reinvestment vehicle |  | Member share of GAAP net equity |  | $14.3 |  | GAAP net equity |  | $14.3
Private equity security |  | Option pricing method |  | $9.6 |  |  |  |
|  |  |  |  |  | Time until expiration | - | 4 years
|  |  |  | Volatility/Standard deviation | - | 60.0%
|  |  |  | Risk free rate | - | 1.15%
OneBeacon Surplus Notes (7): |  |  |  |  |  |
- Seller priority |  | Discounted cash flow |  | $38.0 |  | Discount rate (3) | - | 13.0%
|  |  |  | Timing of interest payments (5) | - | 2020
|  |  |  | Timing of principal payments (5) | - | 2025
- Pari passu |  | Discounted cash flow |  | $13.5 |  | Discount rate (4) | - | 22.4%
|  |  |  | Timing of interest payments (6) | - | 2020
|  |  |  | Timing of principal payments (6) | - | 2030
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs. (2) Valuation based on the issuer’s intent as of December 31, 2015 to call the security in the near term. (3) Stochastic modeling supporting the fair value estimation indicates that the average percentage of discounted payments missed on the seller priority note is roughly equivalent to that of a conventional debt security with a credit rating of ‘B’. The corresponding credit spread increased by an additional 250 basis points to reflect both a liquidity discount for a private debt instrument and regulatory payment approval uncertainty, was added to the treasury rate to determine the discount rate for the seller priority note. (4) Stochastic modeling supporting the fair value estimation indicates that the average percentage of discounted payments missed on the pari passu note is roughly equivalent to that of a conventional debt security with a credit rating of ‘CCC’. The corresponding credit spread increased by an additional 250 basis points to reflect both a liquidity discount for a private debt instrument and regulatory payment approval uncertainty, was added to the treasury rate to determine the discount rate for the seller priority note. (5) As of December 31, 2015, OneBeacon assumed for the purpose of estimating fair value that all accrued but unpaid interest on the seller priority note since the date of issuance was paid in 2020, with regular annual payments beginning thereafter. Principal repayments were assumed to begin on a graduated basis in 2025. (6) As of December 31, 2015, OneBeacon assumed for the purpose of estimating fair value that all accrued but unpaid interest on the pari passu note since the date of issuance was paid in 2020, with regular annual payments beginning thereafter. Principal repayments were assumed to begin on a graduated basis in 2030. (7) The decrease in the fair value of the OneBeacon Surplus Notes during the twelve months ended December 31, 2015 was primarily due to widening of non-investment grade credit spreads.
Other Investments Not Readily Marketable [Table Text Block] | Other long-term investments consist of the following as of December 31, 2016 and 2015:
|  | Carrying Value at
Millions |  | December 31, 2016 |  | December 31, 2015
Hedge funds and private equity funds, at fair value (1) |  | $ | 131.0 |  |  | $ | 127.8 |
Private equity securities and limited liability companies, at fair value (1) |  | 72.0 |  |  | 82.1 |
OneBeacon Surplus Notes, at fair value(1) |  | 71.9 |  |  | 51.5 |
Private convertible preferred securities, at fair value (1) |  | 30.6 |  |  | 32.7 |
Tax advantaged federal affordable housing development fund (2) |  | 12.3 |  |  | 14.7 |
Partnership investments accounted for under the equity method |  | 3.5 |  |  | 3.8 |
Other |  | 2.0 |  |  | 3.2 |
Total other-long term investments |  | $ | 323.3 |  |  | $ | 315.8 |
(1) See Fair Value Measurements by Level table. (2) Fund accounted for using the proportional amortization method.

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- Definition Tabular disclosure of the realized and unrealized gains and losses reported in the statement of income which have resulted from the sale and holding of marketable securities, respectively, as well as the sale or disposal of cost method investments. Such amounts would include realized gains and losses on the sale or disposal of trading, available-for-sale, and held-to-maturity securities, unrealized gains and losses on trading securities, unrealized gains and losses on available-for-sale and held-to-maturity securities transferred to the trading securities category, realized gains and losses on the sale or disposal of cost method investments, and losses recognized for other than temporary impairments (OTTI) of such investments. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 9 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27357-111563 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 25 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=65884222&loc=d3e22054-111558 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 9 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27357-111563 Reference 4: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 10 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27405-111563 Reference 5: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 9 -Subparagraph (e) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27357-111563 Reference 6: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 5.M) -URI http://asc.fasb.org/extlink&oid=65877573&loc=d3e87990-122713 + Details
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