THE GOLDMAN SACHS GROUP, INC.  AND SUBSIDIARIES Management’s Discussion and Analysis Equities.
Includes client execution activities related to making markets in equity products and commissions and fees from executing and clearing institutional client transactions on major stock, options and futures exchanges worldwide, as well as OTC transactions.
Equities also includes our securities services business, which provides financing, securities lending and other prime brokerage services to institutional clients, including hedge funds, mutual funds, pension funds and foundations, and generates revenues primarily in the form of interest rate spreads or fees.
The table below presents the operating results of our Institutional Client Services segment.
## Table 0 ##
1.
Net revenues related to the Americas reinsurance business were $317 million for 2013.
In April 2013, we completed the sale of a majority stake in our Americas reinsurance business and no longer consolidate this business.2015 versus 2014.
Net revenues in Institutional Client Services were $15.15 billion for 2015, essentially unchanged compared with 2014.
Net revenues in Fixed Income, Currency and Commodities Client Execution were $7.32 billion for 2015, 13% lower than 2014.
Excluding a gain of $168 million in 2014 related to the extinguishment of certain of our junior subordinated debt, net revenues in Fixed Income, Currency and Commodities Client Execution were 12% lower than 2014, reflecting significantly lower net revenues in mortgages, credit products and commodities.
The decreases in mortgages and credit products reflected challenging market-making conditions and generally low levels of activity during 2015.
The decline in commodities primarily reflected less favorable market-making conditions compared with 2014, which included a strong first quarter of 2014.
These decreases were partially offset by significantly higher net revenues in interest rate products and currencies, reflecting higher volatility levels which contributed to higher client activity levels, particularly during the first quarter of 2015.
Net revenues in Equities were $7.83 billion for 2015, 16% higher than 2014.
Excluding a gain of $121 million ($30 million and $91 million included in equities client execution and securities services, respectively) in 2014 related to the extinguishment of certain of our junior subordinated debt, net revenues in Equities were 18% higher than 2014, primarily due to significantly higher net revenues in equities client execution across the major regions, reflecting significantly higher results in both derivatives and cash products, and higher net revenues in securities services, reflecting the impact of higher average customer balances and improved securities lending spreads.
Commissions and fees were essentially unchanged compared with 2014.
The firm elects the fair value option for certain unsecured borrowings.
The fair value net gain attributable to the impact of changes in our credit spreads on these borrowings was $255 million ($214 million and $41 million related to Fixed Income, Currency and Commodities Client Execution and equities client execution, respectively) for 2015, compared with a net gain of $144 million ($108 million and $36 million related to Fixed Income, Currency and Commodities Client Execution and equities client execution, respectively) for 2014.
During 2015, the operating environment for Institutional Client Services was positively impacted by diverging central bank monetary policies in the United States and the Euro area in the first quarter, as increased volatility levels contributed to strong client activity levels in currencies, interest rate products and equity products, and marketmaking conditions improved.
However, during the remainder of the year, concerns about global growth and uncertainty about the U. S.  Federal Reserve’s interest rate policy, along with lower global equity prices, widening high-yield credit spreads and declining commodity prices, contributed to lower levels of client activity, particularly in mortgages and credit, and more difficult market-making conditions.
If macroeconomic concerns continue over the long term and activity levels decline, net revenues in Institutional Client Services would likely be negatively impacted.
Operating expenses were $13.94 billion for 2015, 28% higher than 2014, due to significantly higher net provisions for mortgage-related litigation and regulatory matters, partially offset by decreased compensation and benefits expenses.
Pre-tax earnings were $1.21 billion in 2015, 72% lower than 2014.
Difference between aggregate fair value and aggregate remaining contractual principal balance outstanding The following table reflects the difference between the aggregate fair value and the aggregate remaining contractual principal balance outstanding as of December 31, 2018 and 2017, for loans, long-term debt and long-term beneficial interests for which the fair value option has been elected.
## Table 1 ##
(a) There were no performing loans that were ninety days or more past due as of December 31, 2018 and 2017.
(b) Remaining contractual principal is not applicable to nonprincipal-protected structured notes and long-term beneficial interests.
Unlike principal-protected structured notes and long-term beneficial interests, for which the Firm is obligated to return a stated amount of principal at maturity, nonprincipalprotected structured notes and long-term beneficial interests do not obligate the Firm to return a stated amount of principal at maturity, but for structured notes to return an amount based on the performance of an underlying variable or derivative feature embedded in the note.
However, investors are exposed to the credit risk of the Firm as issuer for both nonprincipal-protected and principal-protected notes.
(c) Where the Firm issues principal-protected zero-coupon or discount notes, the balance reflects the contractual principal payment at maturity or, if applicable, the contractual principal payment at the Firm’s next call date.
At December 31, 2018 and 2017, the contractual amount of lending-related commitments for which the fair value option was elected was $6.9 billion and $7.4 billion, respectively, with a corresponding fair value of $(82) million and $(76) million, respectively.
For further information regarding off-balance sheet lending-related financial instruments, refer to Note 27.
Structured note products by balance sheet classification and risk component The following table presents the fair value of structured notes, by balance sheet classification and the primary risk type.
## Table 2 ##
Net investment hedge gains and losses The following table presents hedging instruments, by contract type, that were used in net investment hedge accounting relationships, and the pre-tax gains/(losses) recorded on such instruments for the years ended December 31, 2018, 2017 and 2016.
## Table 3 ##
(a) Certain components of hedging derivatives are permitted to be excluded from the assessment of hedge effectiveness, such as forward points on foreign exchange forward contracts.
The Firm elects to record changes in fair value of these amounts directly in other income.
(b) Excludes amounts reclassified from AOCI to income on the sale or liquidation of hedged entities.
For additional information, refer to Note 23.
(c) The prior period amounts have been revised to conform with the current period presentation.
(d) Represents the effective portion of changes in value of the related hedging derivative.
The Firm did not recognize any ineffectiveness on net investment hedges directly in income during 2017 and 2016.
Gains and losses on derivatives used for specified risk management purposes The following table presents pre-tax gains/(losses) recorded on a limited number of derivatives, not designated in hedge accounting relationships, that are used to manage risks associated with certain specified assets and liabilities, including certain risks arising from the mortgage pipeline, warehouse loans, MSRs, wholesale lending exposures, and foreign currency denominated assets and liabilities.
## Table 4 ##
(a) Primarily represents interest rate derivatives used to hedge the interest rate risk inherent in the mortgage pipeline, warehouse loans and MSRs, as well as written commitments to originate warehouse loans.
Gains and losses were recorded predominantly in mortgage fees and related income.
(b) Relates to credit derivatives used to mitigate credit risk associated with lending exposures in the Firm’s wholesale businesses.
These derivatives do not include credit derivatives used to mitigate counterparty credit risk arising from derivative receivables, which is included in gains and losses on derivatives related to market-making activities and other derivatives.
Gains and losses were recorded in principal transactions revenue.
(c) Primarily relates to derivatives used to mitigate foreign exchange risk of specified foreign currency-denominated assets and liabilities.
Gains and losses were recorded in principal transactions revenue.
(d) The prior period amounts have been revised to conform with the current period presentation.
Gains and losses on derivatives related to market-making activities and other derivatives The Firm makes markets in derivatives in order to meet the needs of customers and uses derivatives to manage certain risks associated with net open risk positions from its market-making activities, including the counterparty credit risk arising from derivative receivables.
All derivatives not included in the hedge accounting or specified risk management categories above are included in this category.
Gains and losses on these derivatives are primarily recorded in principal transactions revenue.
Refer to Note 6 for information on principal transactions revenue.
Credit derivatives Credit derivatives are financial instruments whose value is derived from the credit risk associated with the debt of a third-party issuer (the reference entity) and which allow one party (the protection purchaser) to transfer that risk to another party (the protection seller).
Credit derivatives expose the protection purchaser to the creditworthiness of the protection seller, as the protection seller is required to make payments under the contract when the reference entity experiences a credit event, such as a bankruptcy, a failure to pay its obligation or a restructuring.
The seller of credit protection receives a premium for providing protection but has the risk that the underlying instrument referenced in the contract will be subject to a credit event.
The Firm is both a purchaser and seller of protection in the credit derivatives market and uses these derivatives for two primary purposes.
First, in its capacity as a market-maker, the Firm actively manages a portfolio of credit derivatives by purchasing and selling credit protection, predominantly on corporate debt obligations, to meet the needs of customers.
Second, as an end-user, the Firm uses credit derivatives to manage credit risk associated with lending exposures (loans and unfunded commitments) and derivatives counterparty exposures in the Firm’s wholesale businesses, and to manage the credit risk arising from certain financial instruments in the Firm’s market-making businesses.
Following is a summary of various types of credit derivatives.
Notes to consolidated financial statements Note 6 – Noninterest revenue and noninterest expense The Firm records noninterest revenue from certain contracts with customers under ASC 606, Revenue from Contracts with Customers, in investment banking fees, deposit-related fees, asset management, administration, and commissions, and components of card income.
Contracts in the scope of ASC 606 are often terminable on demand and the Firm has no remaining obligation to deliver future services.
For arrangements with a fixed term, the Firm may commit to deliver services in the future.
Revenue associated with these remaining performance obligations typically depends on the occurrence of future events or underlying asset values, and is not recognized until the outcome of those events or values are known.
The adoption of the revenue recognition guidance in the first quarter of 2018, required gross presentation of certain costs previously offset against revenue, predominantly associated with certain distribution costs (previously offset against asset management, administration and commissions), with the remainder associated with certain underwriting costs (previously offset against investment banking fees).
Adoption of the guidance did not result in any material changes in the timing of revenue recognition.
This guidance was adopted retrospectively and, accordingly, prior period amounts were revised, which resulted in an increase in both noninterest revenue and noninterest expense.
The Firm did not apply any practical expedients.
For additional information, refer to Note 1.
Investment banking fees This revenue category includes debt and equity underwriting and advisory fees.
As an underwriter, the Firm helps clients raise capital via public offering and private placement of various types of debt and equity instruments.
Underwriting fees are primarily based on the issuance price and quantity of the underlying instruments, and are recognized as revenue typically upon execution of the client’s transaction.
The Firm also manages and syndicates loan arrangements.
Credit arrangement and syndication fees, included within debt underwriting fees, are recorded as revenue after satisfying certain retention, timing and yield criteria.
The Firm also provides advisory services, by assisting its clients with mergers and acquisitions, divestitures, restructuring and other complex transactions.
Advisory fees are recognized as revenue typically upon execution of the client’s transaction.
## Table 5 ##
Investment banking fees are earned primarily by CIB.
Refer to Note 31 for segment results.
Principal transactions Principal transactions revenue is driven by many factors, including the bid-offer spread, which is the difference between the price at which the Firm is willing to buy a financial or other instrument and the price at which the Firm is willing to sell that instrument.
It also consists of the realized (as a result of the sale of instruments, closing out or termination of transactions, or interim cash payments) and unrealized (as a result of changes in valuation) gains and losses on financial and other instruments (including those accounted for under the fair value option) primarily used in client-driven market-making activities and on private equity investments.
In connection with its clientdriven market-making activities, the Firm transacts in debt and equity instruments, derivatives and commodities (including physical commodities inventories and financial instruments that reference commodities).
Principal transactions revenue also includes certain realized and unrealized gains and losses related to hedge accounting and specified risk-management activities, including: (a) certain derivatives designated in qualifying hedge accounting relationships (primarily fair value hedges of commodity and foreign exchange risk), (b) certain derivatives used for specific risk management purposes, primarily to mitigate credit risk and foreign exchange risk, and (c) other derivatives.
For further information on the income statement classification of gains and losses from derivatives activities, refer to Note 5.
In the financial commodity markets, the Firm transacts in OTC derivatives (e. g. , swaps, forwards, options) and ETD that reference a wide range of underlying commodities.
In the physical commodity markets, the Firm primarily purchases and sells precious and base metals and may hold other commodities inventories under financing and other arrangements with clients.
The following table presents all realized and unrealized gains and losses recorded in principal transactions revenue.
This table excludes interest income and interest expense on trading assets and liabilities, which are an integral part of the overall performance of the Firm’s client-driven marketmaking activities.
Refer to Note 7 for further information on interest income and interest expense.
Trading revenue is presented primarily by instrument type.
The Firm’s clientdriven market-making businesses generally utilize a variety of instrument types in connection with their market-making and related risk-management activities; accordingly, the trading revenue presented in the table below is not representative of the total revenue of any individual line of business.
Notes to consolidated financial statements Securities lending indemnifications Through the Firm’s securities lending program, counterparties’ securities, via custodial and non-custodial arrangements, may be lent to third parties.
As part of this program, the Firm provides an indemnification in the lending agreements which protects the lender against the failure of the borrower to return the lent securities.
To minimize its liability under these indemnification agreements, the Firm obtains cash or other highly liquid collateral with a market value exceeding 100% of the value of the securities on loan from the borrower.
Collateral is marked to market daily to help assure that collateralization is adequate.
Additional collateral is called from the borrower if a shortfall exists, or collateral may be released to the borrower in the event of overcollateralization.
If a borrower defaults, the Firm would use the collateral held to purchase replacement securities in the market or to credit the lending client or counterparty with the cash equivalent thereof.
Derivatives qualifying as guarantees The Firm transacts certain derivative contracts that have the characteristics of a guarantee under U. S.  GAAP.
These contracts include written put options that require the Firm to purchase assets upon exercise by the option holder at a specified price by a specified date in the future.
The Firm may enter into written put option contracts in order to meet client needs, or for other trading purposes.
The terms of written put options are typically five years or less.
Derivatives deemed to be guarantees also includes stable value contracts, commonly referred to as “stable value products”, that require the Firm to make a payment of the difference between the market value and the book value of a counterparty’s reference portfolio of assets in the event that market value is less than book value and certain other conditions have been met.
Stable value products are transacted in order to allow investors to realize investment returns with less volatility than an unprotected portfolio.
These contracts are typically longer-term or may have no stated maturity, but allow the Firm to elect to terminate the contract under certain conditions.
The notional value of derivatives guarantees generally represents the Firm’s maximum exposure.
However, exposure to certain stable value products is contractually limited to a substantially lower percentage of the notional amount.
The fair value of derivative guarantees reflects the probability, in the Firm’s view, of whether the Firm will be required to perform under the contract.
The Firm reduces exposures to these contracts by entering into offsetting transactions, or by entering into contracts that hedge the market risk related to the derivative guarantees.
The following table summarizes the derivatives qualifying as guarantees as of December 31, 2018 and 2017.

Tables referenced above, in order (Table 0 first):
<table><tr><td></td><td>Year Ended December</td></tr><tr><td><i>$ in millions</i></td><td>2015</td><td>2014</td><td>2013</td></tr><tr><td>Fixed Income, Currency and Commodities Client Execution</td><td>$ 7,322</td><td>$ 8,461</td><td>$ 8,651</td></tr><tr><td>Equities client execution<sup>1</sup></td><td>3,028</td><td>2,079</td><td>2,594</td></tr><tr><td>Commissions and fees</td><td>3,156</td><td>3,153</td><td>3,103</td></tr><tr><td>Securities services</td><td>1,645</td><td>1,504</td><td>1,373</td></tr><tr><td>Total Equities</td><td>7,829</td><td>6,736</td><td>7,070</td></tr><tr><td>Total net revenues</td><td>15,151</td><td>15,197</td><td>15,721</td></tr><tr><td>Operating expenses</td><td>13,938</td><td>10,880</td><td>11,792</td></tr><tr><td>Pre-tax earnings</td><td>$ 1,213</td><td>$ 4,317</td><td>$ 3,929</td></tr></table>
<table><tr><td></td><td colspan="4">2018</td><td colspan="4">2017</td></tr><tr><td>December 31, (in millions)</td><td>Contractual principal outstanding</td><td></td><td>Fair value</td><td>Fair value over/(under) contractual principal outstanding</td><td>Contractual principal outstanding</td><td></td><td>Fair value</td><td>Fair value over/(under) contractual principal outstanding</td></tr><tr><td>Loans<sup>(a)</sup></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Nonaccrual loans</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Loans reported as trading assets</td><td>$4,240</td><td></td><td>$1,350</td><td>$- 2,890</td><td>$4,219</td><td></td><td>$1,371</td><td>$- 2,848</td></tr><tr><td>Loans</td><td>39</td><td></td><td>—</td><td>- 39</td><td>39</td><td></td><td>—</td><td>- 39</td></tr><tr><td>Subtotal</td><td>4,279</td><td></td><td>1,350</td><td>- 2,929</td><td>4,258</td><td></td><td>1,371</td><td>- 2,887</td></tr><tr><td>All other performing loans</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Loans reported as trading assets</td><td>42,215</td><td></td><td>40,403</td><td>- 1,812</td><td>38,157</td><td></td><td>36,590</td><td>- 1,567</td></tr><tr><td>Loans</td><td>3,186</td><td></td><td>3,151</td><td>- 35</td><td>2,539</td><td></td><td>2,508</td><td>- 31</td></tr><tr><td>Total loans</td><td>$49,680</td><td></td><td>$44,904</td><td>$- 4,776</td><td>$44,954</td><td></td><td>$40,469</td><td>$- 4,485</td></tr><tr><td>Long-term debt</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Principal-protected debt</td><td>$32,674</td><td><sup>(c)</sup></td><td>$28,718</td><td>$- 3,956</td><td>$26,297</td><td><sup>(c)</sup></td><td>$23,848</td><td>$- 2,449</td></tr><tr><td>Nonprincipal-protected debt<sup>(b)</sup></td><td>NA</td><td></td><td>26,168</td><td>NA</td><td>NA</td><td></td><td>23,671</td><td>NA</td></tr><tr><td>Total long-term debt</td><td>NA</td><td></td><td>$54,886</td><td>NA</td><td>NA</td><td></td><td>$47,519</td><td>NA</td></tr><tr><td>Long-term beneficial interests</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Nonprincipal-protected debt<sup>(b)</sup></td><td>NA</td><td></td><td>$28</td><td>NA</td><td>NA</td><td></td><td>$45</td><td>NA</td></tr><tr><td>Total long-term beneficial interests</td><td>NA</td><td></td><td>$28</td><td>NA</td><td>NA</td><td></td><td>$45</td><td>NA</td></tr></table>
<table><tr><td></td><td colspan="4">December 31, 2018</td><td colspan="4">December 31, 2017</td></tr><tr><td>(in millions)</td><td>Long-term debt</td><td>Short-term borrowings</td><td>Deposits</td><td>Total</td><td>Long-term debt</td><td>Short-term borrowings</td><td>Deposits</td><td>Total</td></tr><tr><td>Risk exposure</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Interest rate</td><td>$24,137</td><td>$62</td><td>$12,372</td><td>$36,571</td><td>$22,056</td><td>$69</td><td>$8,058</td><td>$30,183</td></tr><tr><td>Credit</td><td>4,009</td><td>995</td><td>—</td><td>5,004</td><td>4,329</td><td>1,312</td><td>—</td><td>5,641</td></tr><tr><td>Foreign exchange</td><td>3,169</td><td>157</td><td>38</td><td>3,364</td><td>2,841</td><td>147</td><td>38</td><td>3,026</td></tr><tr><td>Equity</td><td>21,382</td><td>5,422</td><td>7,368</td><td>34,172</td><td>17,581</td><td>7,106</td><td>6,548</td><td>31,235</td></tr><tr><td>Commodity</td><td>372</td><td>34</td><td>1,207</td><td>1,613</td><td>230</td><td>15</td><td>4,468</td><td>4,713</td></tr><tr><td>Total structured notes</td><td>$53,069</td><td>$6,670</td><td>$20,985</td><td>$80,724</td><td>$47,037</td><td>$8,649</td><td>$19,112</td><td>$74,798</td></tr></table>
<table><tr><td></td><td colspan="2">2018</td><td colspan="2">2017</td><td colspan="2">2016</td></tr><tr><td>Year ended December 31,(in millions)</td><td>Amounts recorded in income<sup>(a)(b)</sup></td><td>Amounts recorded inOCI</td><td>Amounts recorded in income<sup>(a)(b)(c)</sup></td><td>Amounts recorded inOCI<sup>(d)</sup></td><td>Amounts recorded in income<sup>(a)(b)(c)</sup></td><td>Amounts recorded inOCI<sup>(d)</sup></td></tr><tr><td>Foreign exchange derivatives</td><td>$11</td><td>$1,219</td><td>$-152</td><td>$-1,244</td><td>$-280</td><td>$262</td></tr></table>
<table><tr><td></td><td colspan="5">Derivatives gains/(losses)recorded in income</td></tr><tr><td>Year ended December 31,(in millions)</td><td>2018</td><td>2017</td><td></td><td>2016</td><td></td></tr><tr><td>Contract type</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Interest rate<sup>(a)</sup></td><td>$79</td><td>$331</td><td></td><td>$1,174</td><td></td></tr><tr><td>Credit<sup>(b)</sup></td><td>- 21</td><td>- 74</td><td></td><td>- 282</td><td></td></tr><tr><td>Foreign exchange<sup>(c)</sup></td><td>117</td><td>- 107</td><td><sup>(d)</sup></td><td>- 20</td><td><sup>(d)</sup></td></tr><tr><td>Total</td><td>$175</td><td>$150</td><td><sup>(d)</sup></td><td>$872</td><td><sup>(d)</sup></td></tr></table>
<table><tr><td>Year ended December 31,(in millions)</td><td>2018</td><td>2017</td><td>2016</td></tr><tr><td>Underwriting</td><td></td><td></td><td></td></tr><tr><td>Equity</td><td>$1,684</td><td>$1,466</td><td>$1,200</td></tr><tr><td>Debt</td><td>3,347</td><td>3,802</td><td>3,277</td></tr><tr><td>Total underwriting</td><td>5,031</td><td>5,268</td><td>4,477</td></tr><tr><td>Advisory</td><td>2,519</td><td>2,144</td><td>2,095</td></tr><tr><td>Total investment banking fees</td><td>$7,550</td><td>$7,412</td><td>$6,572</td></tr></table>

Question: What's the current increasing rate of Principal-protected debt for Fair value?
Answer: 0.20421
Reasoning program: subtract(28718,23848), divide(#0,23848)