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Investment Securities
 12 Months Ended
Dec. 31, 2018
Investments, Debt and Equity Securities [Abstract]  
Investment Securities
Investments Securities

White Mountains’s portfolio of investment securities held for general investment purposes consists of fixed maturity investments, short-term investments, common equity securities and other long-term investments, which are all 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 and other securities, which at the time of purchase, mature or become available for use within one year.  Short-term investments are carried at amortized or accreted cost, which approximated fair value as of December 31, 2018 and 2017.
Other long-term investments consist primarily of unconsolidated entities, private equity funds and hedge funds.
 
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 and dividend income from its common equity securities and other long-term investments.
The following table presents pre-tax net investment income for 2018, 2017 and 2016:
 
 
Year Ended December 31,
Millions
 
2018
 
2017
 
2016
Fixed maturity investments
 
$
35.1

 
$
44.9

 
$
28.5

Short-term investments
 
8.0

 
1.8

 
.9

Common equity securities
 
15.1

 
10.6

 
4.0

Other long-term investments
 
3.8

 
1.2

 
1.1

Total investment income
 
62.0

 
58.5

 
34.5

Third-party investment expenses
 
(3.0
)
 
(2.5
)
 
(2.4
)
Net investment income, pre-tax
 
$
59.0


$
56.0


$
32.1



Net Realized and Unrealized Investment Gains (Losses)

The following table presents net realized and unrealized investment gains (losses) for 2018, 2017 and 2016:
 
 
Year Ended December 31,
Millions
 
2018
 
2017
 
2016
Net realized investment (losses) gains, pre-tax
 
$
(12.9
)
 
$
24.1

 
$
270.0

Net unrealized investment (losses) gains, pre-tax
 
(95.4
)
 
109.2

 
(297.4
)
Net realized and unrealized investment (losses) gains, pre-tax
 
(108.3
)

133.3


(27.4
)
Income tax benefit (expense) attributable to net realized and
   unrealized investment (losses) gains
 
18.2

 
(12.9
)
 
2.7

Net realized and unrealized investment (losses) gains, after-tax
 
$
(90.1
)
 
$
120.4

 
$
(24.7
)


For the years ended December 31, 2018, 2017 and 2016, all of White Mountains’s net realized and unrealized investment gains (losses) were recorded in the statements of operations. There were no investments gains (losses) recorded in other comprehensive income.

Net Realized Investment Gains (Losses)
The following tables present net realized investment gains (losses) for 2018, 2017 and 2016:
 
 
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

 
 
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
 
$
(1.9
)
 
$
.3

 
$
(1.6
)
Short-term investments
 
.4

 
—

 
.4

Common equity securities
 
268.5

 
—

 
268.5

Other long-term investments
 
2.7

 
—

 
2.7

Net realized investment gains, pre-tax
 
269.7

 
.3

 
270.0

Income tax expense attributable to net realized investment gains
 
(45.6
)
 
—

 
(45.6
)
Net realized investment gains, after-tax
 
$
224.1

 
$
.3

 
$
224.4


Net Unrealized Investment Gains (Losses)
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 2018, 2017 and 2016:
 
 
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

 
 
Year Ended December 31, 2016
Millions
 
Net
Unrealized Losses
 
Net Foreign
Exchange Gains (Losses)
 
Total Net Unrealized
Losses Reflected in
Earnings
Fixed maturity investments
 
$
(14.6
)
 
$
2.1

 
$
(12.5
)
Common equity securities
 
(257.4
)
 
(3.3
)
 
(260.7
)
Other long-term investments
 
(22.7
)
 
(1.5
)
 
(24.2
)
Net unrealized investment losses, pre-tax
 
(294.7
)
 
(2.7
)
 
(297.4
)
Income tax benefit attributable to net unrealized investment losses
 
48.3

 
—

 
48.3

Net unrealized investment losses, after-tax
 
$
(246.4
)
 
$
(2.7
)
 
$
(249.1
)


White Mountains recognized gross realized investment gains of $49.4 million, $61.5 million and $283.7 million and gross realized investment losses of $62.3 million, $37.4 million and $13.7 million on sales of investment securities during 2018, 2017 and 2016.
The following table presents total gains (losses) included in earnings attributable to unrealized investment gains (losses) for Level 3 investments for the years ended December 31, 2018, 2017 and 2016:
 
 
Year Ended December 31,
Millions
 
2018
 
2017
 
2016
Fixed maturity investments
 
$
—

 
$
—

 
$
0.1

Other long-term investments
 
22.6

 
(15.4
)
 
(14.3
)
Total net unrealized investment gains (losses), pre-tax - Level 3 investments
 
$
22.6

 
$
(15.4
)
 
$
(14.2
)

Investment Holdings

The following tables present 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, 2018 and 2017.
 
 
December 31, 2018
Millions
 
Cost or
Amortized
Cost
 
Gross
Unrealized
Gains
 
Gross
Unrealized
Losses
 
Net Foreign
Currency
Gains
 
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


 
 
December 31, 2017
Millions
 
Cost or
Amortized
Cost
 
Gross
Unrealized
Gains
 
Gross
Unrealized
Losses
 
Net Foreign
Currency
Gains
 
Carrying
Value
U.S. Government and agency obligations
 
$
297.8

 
$
—

 
$
(1.3
)
 
$
—

 
$
296.5

Debt securities issued by corporations
 
867.6

 
2.9

 
(4.3
)
 
14.7

 
880.9

Mortgage and asset-backed securities
 
697.2

 
1.6

 
(4.1
)
 
—

 
694.7

Municipal obligations
 
252.0

 
3.7

 
(.8
)
 
—

 
254.9

Foreign government, agency and provincial
   obligations
 
2.6

 
—

 
—

 
.1

 
2.7

Total fixed maturity investments
 
$
2,117.2

 
$
8.2

 
$
(10.5
)
 
$
14.8

 
$
2,129.7



The weighted average duration of White Mountains’s fixed income portfolio was approximately 3.4 years when including short-term investments and approximately 4.0 years when excluding short-term investments as of December 31, 2018.
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, 2018. 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, 2018
Millions
 
Cost or Amortized Cost
 
Carrying Value
Due in one year or less
 
$
84.8

 
$
84.4

Due after one year through five years
 
500.8

 
496.2

Due after five years through ten years
 
222.4

 
218.0

Due after ten years
 
144.0

 
145.4

Mortgage and asset-backed securities
 
136.1

 
133.5

Total
 
$
1,088.1

 
$
1,077.5



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, 2018 and 2017:
 
 
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

 
 
December 31, 2017
Millions
 
Cost or
Amortized Cost
 
Gross Unrealized
Gains
 
Gross Unrealized
Losses
 
Net Foreign
Currency Losses
 
Carrying
Value
Common equity securities
 
$
739.7

 
$
129.4

 
$
(3.0
)
 
$
—

 
$
866.1

Other long-term investments
 
$
246.6

 
$
6.8

 
$
(39.7
)
 
$
(4.9
)
 
$
208.8



Proceeds from the sales and maturities of investments, excluding short-term investments, totaled $2.2 billion, $2.8 billion and $3.7 billion for the years ended December 31, 2018, 2017 and 2016.

Investments Held on Deposit or as Collateral

As of December 31, 2018 and 2017, investments of $254.3 million and $204.6 million, were held in trusts required to be maintained in relation to HG Global’s reinsurance agreements with BAM. White Mountains’s insurance subsidiaries are required to maintain deposits with certain insurance regulatory agencies in order to maintain their insurance licenses. The fair value of such deposits, which represent BAM’s state deposits and are included within the investment portfolio, totaled $6.1 million and $6.0 million as of December 31, 2018 and 2017.

Fair Value Measurements as of December 31, 2018
Fair value measurements are categorized into a hierarchy that distinguishes between inputs based on market data from independent sources (“observable inputs”) and a reporting entity’s internal assumptions based upon the best information available when external market data is limited or unavailable (“unobservable inputs”). Quoted prices in active markets for identical assets or liabilities have the highest priority (“Level 1”), followed by observable inputs other than quoted prices, including prices for similar but not identical assets or liabilities (“Level 2”) and unobservable inputs, including the reporting entity’s estimates of the assumptions that market participants would use, having the lowest priority (“Level 3”). As of December 31, 2018 and 2017, White Mountains used quoted market prices or other observable inputs to determine fair value for approximately 87% and 94% of the investment portfolio. See Note 1 — “Basis of Presentation and Significant Accounting Policies”.
Fair Value Measurements by Level
The following tables present White Mountains’s fair value measurements for investments as of December 31, 2018 and 2017 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, 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

 
—

 
 
 
 
 
 
 
 
 
Mortgage and asset-backed securities
 
133.5

 
—

 
133.5

 
—

Municipal obligations
 
280.3

 
—

 
280.3

 
—

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 primarily invest in international equities.
(4) Consists of unconsolidated entities, private equity funds and one hedge fund 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, 2017
Millions
 
Fair Value
 
Level 1
 
Level 2
 
Level 3
Fixed maturity investments:
 
 

 
 

 
 

 
 

U.S. Government and agency obligations
 
$
296.5

 
$
296.5

 
$
—

 
$
—

 
 
 
 
 
 
 
 
 
Debt securities issued by corporations:
 
 

 
 

 
 

 
 

Consumer
 
185.1

 
—

 
185.1

 
—

Communications
 
127.8

 
—

 
127.8

 
—

Financials
 
114.8

 
—

 
114.8

 
—

Utilities
 
108.9

 
—

 
108.9

 
—

Materials
 
95.5

 
—

 
95.5

 
—

Healthcare
 
94.3

 
—

 
94.3

 
—

Technology
 
80.5

 
—

 
80.5

 
—

Energy
 
48.1

 
—

 
48.1

 
—

Industrial
 
25.9

 
—

 
25.9

 
—

Total debt securities issued by corporations
 
880.9

 
—

 
880.9

 
—

 
 
 
 
 
 
 
 
 
Mortgage and asset-backed securities
 
694.7

 
—

 
694.7

 
—

Municipal obligations
 
254.9

 
—

 
254.9

 
—

Foreign government, agency and provincial obligations
 
2.7

 
—

 
2.7

 
—

Total fixed maturity investments
 
2,129.7

 
296.5

 
1,833.2

 
—

 
 
 
 
 
 
 
 
 
Short-term investments (1)
 
176.1

 
151.0

 
25.1

 
—

 
 
 
 
 
 
 
 
 
Common equity securities:
 
 

 
 

 
 

 
 

Exchange traded funds (2)
 
569.7

 
508.1

 
61.6

 
—

Healthcare
 
17.1

 
17.1

 
—

 
—

Financials
 
16.3

 
16.3

 
—

 
—

Technology
 
15.1

 
15.1

 
—

 
—

Industrial
 
11.9

 
11.9

 
—

 
—

Communications
 
10.9

 
10.9

 
—

 
—

Consumer
 
10.7

 
10.7

 
—

 
—

Energy
 
3.8

 
3.8

 
—

 
—

Other (3)
 
210.6

 
—

 
210.6

 
—

Total common equity securities
 
866.1

 
593.9

 
272.2

 
—

Other long-term investments (4)
 
77.2

 
—

 
—

 
77.2

Other long-term investments — NAV(5)
 
135.3

 
—

 
—

 
—

Total investments
 
$
3,384.4

 
$
1,041.4

 
$
2,130.5

 
$
77.2


(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 primarily invests in international equities.
(4) Excludes carrying value of $(3.7) related to foreign currency forward contracts.
(5) Consists of unconsolidated entities, private equity funds and one hedge 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 ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of December 31, 2018 and 2017:
 
 
Fair Value at December 31,
Millions
 
2018
 
2017
AAA
 
$
8.9

 
$
1.6

AA
 
88.7

 
42.6

A
 
270.5

 
192.5

BBB
 
142.4

 
465.2

BB
 
—

 
161.7

B
 
—

 
17.3

Debt securities issued by corporations (1)
 
$
510.5

 
$
880.9

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

Mortgage and Asset-backed Securities

The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of December 31, 2018 and 2017:
 
 
December 31, 2018
 
December 31, 2017
Millions
 
Fair Value
 
Level 2
 
Level 3
 
Fair Value
 
Level 2
 
Level 3
Mortgage-backed securities:
 
 

 
 

 
 

 
 

 
 

 
 

Agency:
 
 

 
 

 
 

 
 

 
 

 
 

FNMA
 
$
53.6

 
$
53.6

 
$
—

 
$
84.5

 
$
84.5

 
$
—

FHLMC
 
38.1

 
38.1

 
—

 
62.0

 
62.0

 
—

GNMA
 
23.7

 
23.7

 
—

 
46.3

 
46.3

 
—

Total agency (1)
 
115.4

 
115.4

 
—

 
192.8

 
192.8

 
—

Non-agency:
 
 

 
 

 
 

 
 

 
 

 
 

Commercial
 
—

 
—

 
—

 
70.5

 
70.5

 
—

Total non-agency
 
—

 
—

 
—

 
70.5

 
70.5

 
—

 
 
 
 
 
 
 
 
 
 
 
 
 
Total mortgage-backed securities
 
115.4

 
115.4

 
—

 
263.3

 
263.3

 
—

Other asset-backed securities:
 
 

 
 
 
 
 
 

 
 
 
 
Vehicle receivables
 
9.2

 
9.2

 
—

 
142.4

 
142.4

 
—

Credit card receivables
 
8.9

 
8.9

 
—

 
206.0

 
206.0

 
—

Other
 
—

 
—

 
—

 
83.0

 
83.0

 
—

Total other asset-backed securities
 
18.1

 
18.1

 
—

 
431.4

 
431.4

 
—

Total mortgage and asset-backed securities
 
$
133.5

 
$
133.5

 
$
—

 
$
694.7

 
$
694.7

 
$
—

(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).

White Mountains considers sub-prime mortgage-backed securities as those that have underlying loan pools that exhibit weak credit characteristics, or those that are issued from dedicated sub-prime shelves or dedicated second-lien shelf registrations (i.e., White Mountains considers investments backed primarily by second-liens to be sub-prime risks regardless of credit scores or other metrics). As of December 31, 2018, White Mountains did not hold any mortgage-backed securities categorized as sub-prime.
White Mountains considers mortgage-backed securities as “non-prime” (also called “Alt A” or “A-”) if they are backed by collateral that has overall credit quality between prime and sub-prime based on White Mountains’s review of the characteristics of their underlying mortgage loan pools, such as credit scores and financial ratios. As of December 31, 2018, White Mountains did not hold any mortgage-backed securities classified as non-prime.


Other Long-Term Investments

The following table presents the carrying values of White Mountains’s other long-term investments as of December 31, 2018 and 2017:
 
 
Carrying Value at December 31,
Millions
 
2018
 
2017
PassportCard/DavidShield (1)
 
$
75.0

 
$
21.0

Kudu
 
30.7

 
—

Other unconsolidated entities (1)(2)
 
60.0

 
62.2

Total unconsolidated entities(1)(2)
 
165.7

 
83.2

Private equity funds and hedge funds
 
146.1

 
125.3

Foreign currency forward contracts
 
—

 
(3.7
)
Other
 
13.8

 
4.0

Total other long-term investments
 
$
325.6

 
$
208.8

(1) See Fair Value Measurements by Level table.
(2) Includes White Mountains's non-controlling interests in certain private common equity securities, limited liability companies and convertible preferred securities.

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 NAV of the funds. As of December 31, 2018, White Mountains held investments in 12 private equity funds and one hedge fund.  The largest investment in a single fund was $54.3 million as of December 31, 2018 and $54.9 million as of December 31, 2017.
The following table presents investments in private equity funds and hedge funds by investment objective and sector as of December 31, 2018 and 2017:
 
 
December 31, 2018
 
December 31, 2017
Millions
 
Fair Value
 
Unfunded
Commitments
 
Fair Value
 
Unfunded
Commitments
 
 
 
 
 
 
 
 
 
Private equity funds
 
 

 
 

 
 

 
 

Manufacturing/Industrial
 
$
42.9

 
$
10.5

 
$
43.3

 
$
10.4

Aerospace/Defense/Government
 
27.6

 
34.9

 
15.8

 
12.9

Direct lending
 
13.0

 
17.7

 
7.1

 
23.1

Financial services
 
8.3

 
13.6

 
4.2

 
11.7

Total private equity funds
 
91.8

 
76.7

 
70.4

 
58.1

 
 
 
 
 
 
 
 
 
Hedge funds
 
 

 
 

 
 

 
 

Long/short banks and financial
 
54.3

 
—

 
54.9

 
—

Total hedge funds
 
54.3

 
—

 
54.9

 
—

Total private equity funds and hedge funds
   included in other long-term investments
 
$
146.1

 
$
76.7

 
$
125.3

 
$
58.1


Investments in private equity funds are generally subject to a lock-up period during which investors may not request a redemption. Distributions prior to the expected termination date of the fund may be limited to dividends or proceeds arising from the liquidation of the fund’s underlying investments. In addition, certain private equity funds have the option to extend the lock-up period.
The following table presents investments in private equity funds that were subject to lock-up periods as of December 31, 2018:
Millions
 
1 – 3 years
 
3 – 5 years
 
5 – 10 years
 
>10 years
 
Total
Private equity funds — expected lock-up period remaining
 
$
1.8

 
$
5.5

 
$
63.2

 
$
21.3

 
$
91.8



Investors in private equity funds are generally subject to indemnification obligations outside of the capital commitment period and prior to the winding up of the fund. As of December 31, 2018 and 2017, 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. As of December 31, 2018, White Mountains held one active hedge fund with a fair value of $54.3 million. The hedge fund is subject to a semi-annual restriction on redemptions and an advance notice period requirement of 45 days.

Rollforward of Fair Value Measurements by Level

White Mountains uses quoted market prices where available as the inputs to estimate fair value for its investments in active markets. Such measurements are considered to be either Level 1 or Level 2 measurements, depending on whether the quoted market price inputs are for identical securities (Level 1) or similar securities (Level 2). Level 3 measurements for fixed maturity investments, common equity securities and other long-term investments as of December 31, 2018 and 2017 consist of securities for which the estimated fair value has not been determined based upon quoted market price inputs for identical or similar securities.
The following tables present the changes in White Mountains’s fair value measurements by level for the years ended December 31, 2018 and 2017:
 
 
 
 
 
 
Level 3 Investments
 
Unconsolidated Entities, Private Equity Funds and Hedge Funds 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)  
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 — “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.


 
 
 
 
 
 
Level 3 Investments
 
Unconsolidated Entities, Private Equity Funds and Hedge Funds Measured at NAV (3)
 
 
 
Millions
 
Level 1
Investments
 
Level 2
Investments
 
Fixed
Maturity Investments
 
Other Long- term
Investments
 
 
Total
Balance at December 31, 2016
 
$
279.5

 
$
2,093.8

 
$
—

 
$
91.4

 
$
82.6

 
$
2,547.3

(1)(2)(5) 
Net realized and unrealized gains (losses)
 
82.7

 
69.6

 
—

 
(15.3
)
 
20.4

 
157.4

(4) 
Amortization/accretion
 
—

 
(9.1
)
 
—

 
—

 
—

 
(9.1
)
 
Purchases
 
1,209.3

 
2,007.9

 
31.2

 
3.1

 
81.0

 
3,332.5

 
Sales
 
(681.1
)
 
(2,070.3
)
 
(12.5
)
 
(2.0
)
 
(48.7
)
 
(2,814.6
)
 
Deconsolidation of SSIE
 
—

 
(5.2
)
 
—

 
—

 
—

 
(5.2
)
 
Transfers in
 
—

 
18.7

 
—

 
—

 
—

 
18.7

 
Transfers out
 
—

 
—

 
(18.7
)
 
—

 
—

 
(18.7
)
 
Balance at December 31, 2017
 
$
890.4

 
$
2,105.4

 
$
—

 
$
77.2

 
$
135.3

 
$
3,208.3

(1)(2) 

(1) Excludes carrying value of $(3.7) and $(1.2) as of December 31, 2017 and 2016 associated with foreign currency forward contracts.
(2) Excludes carrying value of $176.1 and $175.0 as of December 31, 2017 and 2016 classified as short-term investments, of which $0.1 is classified as held for sale at December 31, 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 — “Basis of Presentation and Significant Accounting Policies”.
(4) Excludes realized and unrealized losses associated with foreign currency forward contracts and short-term investments of $23.8 and $0.3 for the year ended December 31, 2017.
(5) Includes carrying value of $6.6 of fixed maturity investments at December 31, 2016 that is classified as assets held for sale related to SSIE.

Fair Value Measurements — Transfers Between Levels - For Years Ended December 31, 2018 and 2017
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 2018, 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 2017, three fixed maturity investments classified as a Level 3 measurement in the prior period were transferred to Level 2 measurement because quoted market prices for similar securities that were considered reliable and could be validated against an alternative source were available as of December 31, 2017. These measurements comprise “Transfers out” of Level 3 and “Transfers in” to Level 2 of $18.7 million for the period ended December 31, 2017.

Significant Unobservable Inputs

The following tables present significant unobservable inputs used in estimating the fair value of other long-term investments, other than private equity funds and hedge funds, classified within Level 3 as of December 31, 2018 and 2017. The fair value of investments in certain unconsolidated entities, private equity funds and hedge funds are generally estimated using the NAV of the funds.

$ in Millions, Except Share Price
 
December 31, 2018
Description
 
Valuation Technique(s)
 
Fair Value (1)
 
Unobservable Input
PassportCard/DavidShield
 
Discounted cash flow
 
$75.0
 
Discount rate
-
18.0%
 
 
 
 
 
 
Exit multiple
-
1.00
Compare.com
 
Discounted cash flow
 
$16.9
 
Discount rate
-
22.0%
 
 
 
 
 
 
Exit multiple
-
2.75
YOUSURE Tarifvergleich GmbH (“durchblicker”)
 
Discounted cash flow
 
$15.5
 
Discount rate
-
23.0%
 
 
 
 
 
 
Exit multiple
-
2.25
Captricity, Inc.
 
Discounted cash flow
 
$14.5
 
Discount rate
-
23.0%
 
 
 
 
 
 
Exit multiple
-
3.75
Galvanic Applied Sciences
 
Multiple of EBITDA
 
$3.1
 
EBITDA multiple
-
6.00
Private debt instrument
 
Discounted cash flow
 
$10.0
 
Discount rate
-
9.62%
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

$ in Millions, Except Share Price
 
December 31, 2017
Description
 
Valuation Technique(s)
 
Fair Value (1)
 
Unobservable Input
PassportCard
 
Discounted cash flow
 
$21.0
 
Discount rate
-
25.0%
 
 
 
 
 
 
Exit multiple
-
1.00
Compare.com
 
Discounted cash flow
 
$22.1
 
Discount rate
-
35.0%
 
 
 
 
 
 
Exit multiple
-
1.75
durchblicker
 
Discounted cash flow
 
$11.3
 
Discount rate
-
21.0%
 
 
 
 
 
 
Exit multiple
-
1.75
Captricity, Inc.
 
Discounted cash flow
 
$14.5
 
Discount rate
-
30.0%
 
 
 
 
 
 
Exit multiple
-
3.50
Galvanic Applied Sciences
 
Multiple of EBITDA
 
$0.6
 
EBITDA multiple
-
6.00
OneTitle Holdings LLC
 
Share price of most recent transaction
 
$3.6
 
Share price
-
$2.52
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.