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Investment Securities
 12 Months Ended
Dec. 31, 2018
Investments, Debt and Equity Securities [Abstract]  
Investment Securities
Investment Securities
Our investment securities portfolio consists of: (i) an available-for-sale securities portfolio and a held-to-maturity securities portfolio, both of which represent interest-earning investment securities; and (ii) a non-marketable and other equity securities portfolio, which primarily represents investments managed as part of our funds management business as well as public equity securities held as a result of equity warrant assets exercised.
Available-for-Sale Securities
The major components of our AFS investment securities portfolio at December 31, 2018 and 2017 are as follows:
 
 
December 31, 2018
(Dollars in thousands)
 
Amortized
Cost
 
Unrealized
Gains
 
Unrealized
Losses
 
Carrying
Value
Available-for-sale securities, at fair value:
 
 
 
 
 
 
 
 
U.S. Treasury securities
 
$
4,762,182

 
$
11,638

 
$
(35,562
)
 
$
4,738,258

U.S. agency debentures
 
1,090,426

 
61

 
(6,370
)
 
1,084,117

Foreign government debt securities
 
5,815

 
—

 
(3
)
 
5,812

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
Agency-issued collateralized mortgage obligations—fixed rate
 
1,922,618

 
—

 
(42,400
)
 
1,880,218

Agency-issued collateralized mortgage obligations—variable rate
 
81,270

 
383

 
(15
)
 
81,638

Total available-for-sale securities
 
$
7,862,311

 
$
12,082

 
$
(84,350
)
 
$
7,790,043

 
 
December 31, 2017
(Dollars in thousands)
 
Amortized
Cost
 
Unrealized
Gains
 
Unrealized
Losses
 
Carrying
Value
Available-for-sale securities, at fair value:
 
 
 
 
 
 
 
 
U.S. Treasury securities
 
$
6,865,068

 
$
1,113

 
$
(25,679
)
 
$
6,840,502

U.S. agency debentures
 
1,569,195

 
3,569

 
(5,636
)
 
1,567,128

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
Agency-issued collateralized mortgage obligations—fixed rate
 
2,292,311

 
258

 
(25,534
)
 
2,267,035

Agency-issued collateralized mortgage obligations—variable rate
 
372,481

 
1,375

 
(126
)
 
373,730

Equity securities
 
31,953

 
40,525

 
(209
)
 
72,269

Total available-for-sale securities
 
$
11,131,008

 
$
46,840

 
$
(57,184
)
 
$
11,120,664


The following table summarizes sale activity of available-for-sale securities as recorded in the line item “Gains on investment securities, net," a component of noninterest income:
 
 
Year ended December 31,
(Dollars in thousands)
 
2018
 
2017
 
2016
Sales proceeds
 
$
474,482

 
$
580,871

 
$
2,892,460

Net realized gains and losses:
 

 

 

Gross realized gains
 
127

 
5,113

 
15,051

Gross realized losses
 
(867
)
 
(10,302
)
 
(2,856
)
Net realized (losses) gains
 
$
(740
)
 
$
(5,189
)
 
$
12,195


The following tables summarize our unrealized losses on our AFS securities portfolio into categories of less than 12 months, or 12 months or longer as of December 31, 2018 and 2017:
 
 
December 31, 2018
 
 
Less than 12 months
 
12 months or longer (1)
 
Total
(Dollars in thousands)
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
Available-for-sale securities:
 
 
 
 
 
 
 
 
 
 
 
 
U.S. Treasury securities
 
$
494,287

 
$
(3,785
)
 
$
3,568,119

 
$
(31,777
)
 
$
4,062,406

 
$
(35,562
)
U.S. agency debentures
 
443,790

 
(1,602
)
 
591,216

 
(4,768
)
 
1,035,006

 
(6,370
)
Foreign government debt securities
 
5,812

 
(3
)
 
—

 
—

 
5,812

 
(3
)
Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
 
 
Agency-issued collateralized mortgage obligations—fixed rate
 
13,430

 
(22
)
 
1,866,788

 
(42,378
)
 
1,880,218

 
(42,400
)
Agency-issued collateralized mortgage obligations—variable rate
 
—

 
—

 
13,516

 
(15
)
 
13,516

 
(15
)
Total temporarily impaired securities (1)
 
$
957,319

 
$
(5,412
)
 
$
6,039,639

 
$
(78,938
)
 
$
6,996,958

 
$
(84,350
)
 
(1)
As of December 31, 2018, we identified a total of 200 investments that were in unrealized loss positions, of which 162 investments totaling $6.0 billion with unrealized losses of $78.9 million have been in an impaired position for a period of time greater than 12 months. As of December 31, 2018, we do not intend to sell any of our impaired securities prior to recovery of our adjusted cost basis, and it is more likely than not that we will not be required to sell any of our securities prior to recovery of our adjusted cost basis. Based on our analysis as of December 31, 2018, we deem all impairments to be temporary, and therefore changes in value for our temporarily impaired securities as of the same date are included in other comprehensive income. Market valuations and impairment analyses on assets in the AFS securities portfolio are reviewed and monitored on a quarterly basis.
 
 
December 31, 2017
 
 
Less than 12 months
 
12 months or longer (1)
 
Total
(Dollars in thousands)
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
Available-for-sale securities:
 
 
 
 
 
 
 
 
 
 
 
 
U.S. Treasury securities
 
$
5,968,914

 
$
(23,397
)
 
$
323,966

 
$
(2,282
)
 
$
6,292,880

 
$
(25,679
)
U.S. agency debentures
 
736,541

 
(2,289
)
 
336,196

 
(3,347
)
 
1,072,737

 
(5,636
)
Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
 
 
Agency-issued collateralized mortgage obligations—fixed rate
 
2,193,277

 
(25,534
)
 
—

 
—

 
2,193,277

 
(25,534
)
Agency-issued collateralized mortgage obligations—variable rate
 
13,843

 
(3
)
 
53,186

 
(123
)
 
67,029

 
(126
)
Equity securities
 
624

 
(209
)
 
—

 
—

 
624

 
(209
)
Total temporarily impaired securities (1)
 
$
8,913,199

 
$
(51,432
)
 
$
713,348

 
$
(5,752
)
 
$
9,626,547

 
$
(57,184
)
 
(1)
As of December 31, 2017, we identified a total of 268 investments that were in unrealized loss positions, of which 46 investments totaling $713.3 million with unrealized losses of $5.8 million have been in an impaired position for a period of time greater than 12 months.
The following table summarizes the fixed income securities, carried at fair value, classified as AFS as of December 31, 2018 by the remaining contractual principal maturities. For U.S. Treasury securities, U.S. agency debentures and foreign government debt securities, the expected maturity is the actual contractual maturity of the notes. Expected maturities for mortgage-backed securities may differ significantly from their contractual maturities because mortgage borrowers have the right to prepay outstanding loan obligations with or without penalties. Mortgage-backed securities classified as AFS typically have original contractual maturities from 10 to 30 years whereas expected average lives of these securities tend to be significantly shorter and vary based upon structure and prepayments in lower interest rate environments.
 
 
December 31, 2018
(Dollars in thousands)
 
Total
 
One Year
or Less
 
After One
Year to
Five Years
 
After Five
Years to
Ten Years
 
After
Ten Years
U.S. Treasury securities
 
$
4,738,258

 
$
1,765,333

 
$
2,524,484

 
$
448,441

 
$
—

U.S. agency debentures
 
1,084,117

 
665,750

 
418,367

 
—

 
—

Foreign government debt securities
 
5,812

 
—

 
5,812

 
—

 
—

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
Agency-issued collateralized mortgage obligations—fixed rate
 
1,880,218

 
—

 
—

 
16,030

 
1,864,188

Agency-issued collateralized mortgage obligations—variable rate
 
81,638

 
—

 
—

 
—

 
81,638

Total
 
$
7,790,043

 
$
2,431,083

 
$
2,948,663

 
$
464,471

 
$
1,945,826

Held-to-Maturity Securities
The components of our HTM investment securities portfolio at December 31, 2018 and 2017 are as follows:
 
 
December 31, 2018
(Dollars in thousands)
 
Amortized
Cost
 
Unrealized
Gains
 
Unrealized
Losses
 
Fair Value
Held-to-maturity securities, at cost:
 
 
 
 
 
 
 
 
U.S. agency debentures (1)
 
$
640,990

 
$
2,148

 
$
(4,850
)
 
$
638,288

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
Agency-issued mortgage-backed securities
 
8,103,638

 
5,011

 
(157,767
)
 
7,950,882

Agency-issued collateralized mortgage obligations—fixed rate
 
2,183,204

 
—

 
(62,272
)
 
2,120,932

Agency-issued collateralized mortgage obligations—variable rate
 
214,483

 
608

 
(14
)
 
215,077

Agency-issued commercial mortgage-backed securities
 
2,769,706

 
6,969

 
(64,374
)
 
2,712,301

Municipal bonds and notes
 
1,575,421

 
2,304

 
(26,969
)
 
1,550,756

Total held-to-maturity securities
 
$
15,487,442

 
$
17,040

 
$
(316,246
)
 
$
15,188,236

 
(1)
Consists of pools of Small Business Investment Company debentures issued and guaranteed by the U.S. Small Business Administration, an independent agency of the United States.
 
 
December 31, 2017
(Dollars in thousands)
 
Amortized
Cost
 
Unrealized
Gains
 
Unrealized
Losses
 
Fair Value
Held-to-maturity securities, at cost:
 
 
 
 
 
 
 
 
U.S. agency debentures (1)
 
$
659,979

 
$
3,167

 
$
(1,601
)
 
$
661,545

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
Agency-issued mortgage-backed securities
 
6,304,969

 
4,854

 
(43,528
)
 
6,266,295

Agency-issued collateralized mortgage obligations—fixed rate
 
2,829,979

 
23

 
(54,372
)
 
2,775,630

Agency-issued collateralized mortgage obligations—variable rate
 
255,782

 
733

 
(34
)
 
256,481

Agency-issued commercial mortgage-backed securities
 
1,868,985

 
694

 
(25,563
)
 
1,844,116

Municipal bonds and notes
 
743,761

 
3,452

 
(3,000
)
 
744,213

Total held-to-maturity securities
 
$
12,663,455

 
$
12,923

 
$
(128,098
)
 
$
12,548,280

 
(1)
Consists of pools of Small Business Investment Company debentures issued and guaranteed by the U.S. Small Business Administration, an independent agency of the United States.
 
The following tables summarize our unrealized losses on our HTM securities portfolio into categories of less than 12 months and 12 months or longer as of December 31, 2018 and 2017:
 
 
December 31, 2018
 
 
Less than 12 months
 
12 months or longer (1)
 
Total
(Dollars in thousands)
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
Held-to-maturity securities:
 
 
 
 
 
 
 
 
 
 
 
 
U.S. agency debentures
 
$
291,432

 
$
(2,915
)
 
$
66,624

 
$
(1,935
)
 
$
358,056

 
$
(4,850
)
Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
 
 
Agency-issued mortgage-backed securities
 
2,493,156

 
(34,956
)
 
3,972,690

 
(122,811
)
 
6,465,846

 
(157,767
)
Agency-issued collateralized mortgage
    obligations—fixed rate
 
16,952

 
(109
)
 
2,103,980

 
(62,163
)
 
2,120,932

 
(62,272
)
Agency-issued collateralized mortgage
    obligations—variable rate
 
3,364

 
(1
)
 
8,101

 
(13
)
 
11,465

 
(14
)
Agency-issued commercial mortgage-backed
    securities
 
177,697

 
(1,580
)
 
1,600,277

 
(62,794
)
 
1,777,974

 
(64,374
)
Municipal bonds and notes
 
868,751

 
(17,075
)
 
340,413

 
(9,894
)
 
1,209,164

 
(26,969
)
Total temporarily impaired securities (1)
 
$
3,851,352

 
$
(56,636
)
 
$
8,092,085

 
$
(259,610
)
 
$
11,943,437

 
$
(316,246
)
 

(1)
As of December 31, 2018, we identified a total of 1244 investments that were in unrealized loss positions, of which 695 investments totaling $8.1 billion with unrealized losses of $259.6 million have been in an impaired position for a period of time greater than 12 months. As of December 31, 2018, we do not intend to sell any of our impaired securities prior to recovery of our adjusted cost basis, and it is more likely than not that we will not be required to sell any of our securities prior to recovery of our adjusted cost basis, which is consistent with our classification of these securities. Based on our analysis as of December 31, 2018, we deem all impairments to be temporary. Market valuations and impairment analyses on assets in the HTM securities portfolio are reviewed and monitored on a quarterly basis.
 
 
December 31, 2017
 
 
Less than 12 months
 
12 months or longer (1)
 
Total
(Dollars in thousands)
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
 
Fair Value of
Investments
 
Unrealized
Losses
Held-to-maturity securities:
 
 
 
 
 
 
 
 
 
 
 
 
U.S. agency debentures
 
$
104,688

 
$
(1,601
)
 
$
—

 
$
—

 
$
104,688

 
$
(1,601
)
Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
 
 
Agency-issued mortgage-backed securities
 
4,270,377

 
(34,092
)
 
408,913

 
(9,436
)
 
4,679,290

 
(43,528
)
Agency-issued collateralized mortgage obligations—fixed rate
 
1,011,709

 
(13,631
)
 
1,741,614

 
(40,741
)
 
2,753,323

 
(54,372
)
Agency-issued collateralized mortgage
  obligations—variable rate
 
—

 
—

 
9,812

 
(34
)
 
9,812

 
(34
)
Agency-issued commercial mortgage-backed securities
 
979,361

 
(11,566
)
 
773,712

 
(13,997
)
 
1,753,073

 
(25,563
)
Municipal bonds and notes
 
344,796

 
(2,103
)
 
32,844

 
(897
)
 
377,640

 
(3,000
)
Total temporarily impaired securities (1)
 
$
6,710,931

 
$
(62,993
)
 
$
2,966,895

 
$
(65,105
)
 
$
9,677,826

 
$
(128,098
)
 
(1)
As of December 31, 2017, we identified a total of 753 investments that were in unrealized loss positions, of which 237 investments totaling $3.0 billion with unrealized losses of $65.1 million have been in an impaired position for a period of time greater than 12 months.
The following table summarizes the remaining contractual principal maturities on fixed income investment securities classified as HTM as of December 31, 2018. For U.S. agency debentures, the expected maturity is the actual contractual maturity of the notes. Expected maturities for mortgage-backed securities may differ significantly from their contractual maturities because mortgage borrowers have the right to prepay outstanding loan obligations with or without penalties. Mortgage-backed securities classified as HTM typically have original contractual maturities from 10 to 30 years whereas expected average lives of these securities tend to be significantly shorter and vary based upon structure and prepayments in lower interest rate environments.
 
 
December 31, 2018
 
 
Total
 
One Year
or Less
 
After One Year to
Five Years
 
After Five Years to
Ten Years
 
After
Ten Years
(Dollars in thousands)
 
Amortized Cost
 
Fair Value
 
Amortized Cost
 
Fair Value
 
Amortized Cost
 
Fair Value
 
Amortized Cost
 
Fair Value
 
Amortized Cost
 
Fair Value
U.S. agency debentures
 
$
640,990

 
$
638,288

 
$
—

 
$
—

 
$
104,550

 
$
104,105

 
$
536,440

 
$
534,183

 
$
—

 
$
—

Residential mortgage-backed securities:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Agency-issued mortgage-backed securities
 
8,103,638

 
7,950,883

 
—

 
—

 
155,257

 
152,524

 
885,622

 
859,609

 
7,062,759

 
6,938,750

Agency-issued collateralized mortgage obligations - fixed rate
 
2,183,204

 
2,120,932

 
—

 
—

 
—

 
—

 
483,043

 
466,458

 
1,700,161

 
1,654,474

Agency-issued collateralized mortgage obligations - variable rate
 
214,483

 
215,077

 
—

 
—

 
—

 
—

 
—

 
—

 
214,483

 
215,077

Agency-issued commercial mortgage-backed securities
 
2,769,706

 
2,712,301

 
—

 
—

 
—

 
—

 
—

 
—

 
2,769,706

 
2,712,301

Municipal bonds and notes
 
1,575,421

 
1,550,755

 
9,725

 
9,720

 
75,379

 
74,670

 
307,184

 
300,766

 
1,183,133

 
1,165,599

Total
 
$
15,487,442

 
$
15,188,236

 
$
9,725

 
$
9,720

 
$
335,186

 
$
331,299

 
$
2,212,289

 
$
2,161,016

 
$
12,930,242

 
$
12,686,201

Non-marketable and Other Equity Securities
The major components of our non-marketable and other equity securities portfolio at December 31, 2018 and 2017 are as follows:
(Dollars in thousands)
 
December 31, 2018
 
December 31, 2017
Non-marketable and other equity securities:
 
 
 
 
Non-marketable securities (fair value accounting):
 
 
 
 
Consolidated venture capital and private equity fund investments (1)
 
$
118,333

 
$
128,111

Unconsolidated venture capital and private equity fund investments (2)
 
201,098

 
98,548

Other investments without a readily determinable fair value (3)
 
25,668

 
27,680

Other equity securities in public companies (fair value accounting) (4)
 
20,398

 
310

Non-marketable securities (equity method accounting) (5):
 
 
 
 
Venture capital and private equity fund investments
 
129,485

 
89,809

Debt funds
 
5,826

 
21,183

Other investments
 
121,721

 
111,198

Investments in qualified affordable housing projects, net (6)
 
318,575

 
174,214

Total non-marketable and other equity securities
 
$
941,104

 
$
651,053

 
(1)
The following table shows the amounts of venture capital and private equity fund investments held by the following consolidated funds and our ownership percentage of each fund at December 31, 2018 and 2017 (fair value accounting):
 
 
December 31, 2018
 
December 31, 2017
(Dollars in thousands)
 
Amount
 
Ownership %
 
Amount
 
Ownership %
Strategic Investors Fund, LP
 
$
12,452

 
12.6
%
 
$
14,673

 
12.6
%
Capital Preferred Return Fund, LP
 
53,957

 
20.0

 
54,147

 
20.0

Growth Partners, LP
 
50,845

 
33.0

 
58,372

 
33.0

CP I, LP
 
1,079

 
10.7

 
919

 
10.7

Total consolidated venture capital and private equity fund investments
 
$
118,333

 
 
 
$
128,111

 
 


(2)
The carrying value represents investments in 213 and 235 funds (primarily venture capital funds) at December 31, 2018 and December 31, 2017, respectively, where our ownership interest is typically less than 5% of the voting interests of each such fund and in which we do not have the ability to exercise significant influence over the partnerships operating activities and financial policies. Effective January 1, 2018, we adopted ASU 2016-01, Recognition and Measurement of Financial Assets and Financial Liabilities which eliminated the concept of cost method accounting. On a prospective basis, we will carry our unconsolidated venture capital and private equity fund investments at fair value based on the fund investments' net asset values per share as obtained from the general partners of the investments. For each fund investment, we adjust the net asset value per share for differences between our measurement date and the date of the fund investment’s net asset value by using the most recently available financial information from the investee general partner, for example September 30th for our December 31st consolidated financial statements, adjusted for any contributions paid, distributions received from the investment, and significant fund transactions or market events during the reporting period. We recorded a cumulative adjustment to opening retained earnings on January 1, 2018 for the difference between fair value and cost for these fund investments. The estimated fair value and carrying value of these venture capital and private equity fund investments was $201.1 million as of December 31, 2018. As of December 31, 2017, these investments were carried at cost and had a carrying value of $98.5 million.

(3)
Effective January 1, 2018, we adopted ASU 2016-01, Recognition and Measurement of Financial Assets and Financial Liabilities which eliminated the concept of cost method accounting. On a prospective basis, we have elected the measurement alternative and will report our other investments in the line item "Other investments without a readily determinable fair value". These investments include direct equity investments in private companies. The carrying value is based on the price at which the investment was acquired plus or minus changes resulting from observable price changes in orderly transactions for identical or similar investments. We consider a range of factors when adjusting the fair value of these investments, including, but not limited to, the term and nature of the investment, local market conditions, values for comparable securities, current and projected operating performance, exit strategies, financing transactions subsequent to the acquisition of the investment and a discount for certain investments that have lock-up restrictions or other features that indicate a discount to fair value is warranted.
The following table shows the carrying amount of other investments without a readily determinable fair value at December 31, 2018, and the amounts recognized in earnings for the year ended December 31, 2018 and on a cumulative basis:

(Dollars in thousands)
 
Year ended December 31, 2018
 
Cumulative Adjustments
Measurement alternative:
 
 
 
 
Carrying value at December 31, 2018
 
$
25,668

 
 
Carrying value adjustments:
 
 
 
 
Impairment
 
$
—

 
$
—

Downward changes for observable prices
 
1,963

 
1,963

Upward changes for observable prices
 
1,711

 
1,711

(4)
Investments classified as other equity securities (fair value accounting) represent shares held in public companies as a result of exercising public equity warrant assets and direct equity investments in public companies held by our consolidated funds. Effective January 1, 2018, we adopted ASU 2016-01, which requires equity securities to be measured at fair value with changes in the fair value recognized through net income. Prior to January 1, 2018 we reported equity securities in public companies that we held as a result of exercising public equity warrant assets in available-for-sale securities. On a prospective basis, these equity securities will be reported in non-marketable and other equity securities.

(5)
The following table shows the carrying value and our ownership percentage of each investment at December 31, 2018 and 2017 (equity method accounting):
 
 
December 31, 2018
 
December 31, 2017
(Dollars in thousands)
 
Amount
 
Ownership %
 
Amount
 
Ownership %
Venture capital and private equity fund investments:
 
 
 
 
 
 
 
 
Strategic Investors Fund II, LP
 
$
4,670

 
8.6
%
 
$
6,342

 
8.6
%
Strategic Investors Fund III, LP
 
17,396

 
5.9

 
18,758

 
5.9

Strategic Investors Fund IV, LP
 
28,974

 
5.0

 
25,551

 
5.0

Strategic Investors Fund V funds
 
28,189

 
Various

 
16,856

 
Various

CP II, LP (i)
 
7,122

 
5.1

 
6,700

 
5.1

Other venture capital and private equity fund investments
 
43,134

 
Various

 
15,602

 
Various

 Total venture capital and private equity fund investments
 
$
129,485

 


 
$
89,809

 
 
Debt funds:
 
 
 
 
 
 
 
 
Gold Hill Capital 2008, LP (ii)
 
$
3,901

 
15.5
%
 
$
18,690

 
15.5
%
Other debt funds
 
1,925

 
Various

 
2,493

 
Various

Total debt funds
 
$
5,826

 
 
 
$
21,183

 
 
Other investments:
 
 
 
 
 
 
 
 
SPD Silicon Valley Bank Co., Ltd.
 
$
76,412

 
50.0
%
 
$
75,337

 
50.0
%
Other investments
 
45,309

 
Various

 
35,861

 
Various

Total other investments
 
$
121,721

 
 
 
$
111,198

 
 
 

(i)
Our ownership includes direct ownership interest of 1.3 percent and indirect ownership interest of 3.8 percent through our investments in Strategic Investors Fund II, LP.
(ii)
Our ownership includes direct ownership interest of 11.5 percent in the fund and an indirect interest in the fund through our investment in Gold Hill Capital 2008, LLC of 4.0 percent.

(6)
The following table presents the balances of our investments in qualified affordable housing projects and related unfunded commitments included as a component of "other liabilities" on our consolidated balance sheets at December 31, 2018 and 2017:
(Dollars in thousands)
 
December 31, 2018
 
December 31, 2017
Investments in qualified affordable housing projects, net
 
$
318,575

 
$
174,214

Other liabilities
 
205,685

 
100,891


The following table presents other information relating to our investments in qualified affordable housing projects for the years ended December 31, 2018, 2017 and 2016:
 
 
Year ended December 31,
(Dollars in thousands)
 
2018
 
2017
 
2016
Tax credits and other tax benefits recognized
 
$
24,047

 
$
17,296

 
$
15,404

Amortization expense included in provision for income taxes (i)
 
18,876

 
17,362

 
12,145

 
 
(i)
All investments are amortized using the proportional amortization method and amortization expense is included in the provision for income taxes. Included in amortization expense for the year ended December 31, 2017 is a one-time cumulative effect adjustment of $3.8 million due to the decrease in value of deductions in the 2018 tax year and going forward, due to the TCJ Act federal corporate income tax rate reduction.
The following table presents the net gains and losses on non-marketable and other equity securities in 2018, 2017 and 2016 as recorded in the line item “Gains on investment securities, net," a component of noninterest income:
 
 
Year ended December 31,
(Dollars in thousands)
 
2018
 
2017
 
2016
Net gains (losses) on non-marketable and other equity securities:
 
 
 
 
 
 
Non-marketable securities (fair value accounting):
 
 
 
 
 
 
Consolidated venture capital and private equity fund investments
 
$
20,999

 
$
27,186

 
$
5,964

Unconsolidated venture capital and private equity fund investments (1)
 
39,075

 
21,377

 
17,816

Other investments without a readily determinable fair value (1)
 
3,206

 
3,842

 
(45
)
Other equity securities in public companies (fair value accounting) (1)
 
(25,483
)
 
241

 
(90
)
Non-marketable securities (equity method accounting):
 
 
 
 
 
 
Venture capital and private equity fund investments
 
49,341

 
14,472

 
4,070

Debt funds
 
541

 
8,950

 
948

Other investments
 
1,155

 
(6,276
)
 
10,882

Total net gains on non-marketable and other equity securities
 
$
88,834

 
$
69,792

 
$
39,545

Less: Realized net losses on the sales and OTTI of non-marketable and other equity securities (2)
 
(26,097
)
 
(355
)
 
(4,524
)
Net gains on non-marketable and other equity securities still held
 
$
114,931

 
$
70,147

 
$
44,069

 
 
(1)
Prior period amounts are not determined in a manner consistent with the current period presentation due to the adoption of ASU 2016-01.
(2)
Realized gains and losses include sales and OTTI of non-marketable and other equity securities. Includes losses of $20.8 million in losses on sales and $5.3 million of OTTI for the period ended December 31, 2018. Includes gains of $3.8 million and $0.2 million on sales and $4.2 million and $4.7 million of OTTI for the periods ended December 31, 2017 and 2016, respectively.