Management’s discussion and analysis levels.
Net charge-offs continued to improve as a result of improvement in delinquencies and home prices.
Auto: Auto loans at December 31, 2013, were $52.8 billion, compared with $49.9 billion at December 31, 2012.
Loan balances increased due to new originations, partially offset by paydowns and payoffs.
Delinquencies and nonaccrual loans improved compared with December 31, 2012.
Net charge-offs decreased from the prior year due to prior year incremental charge-offs reported in accordance with regulatory guidance on certain loans discharged under Chapter 7 bankruptcy.
Loss levels are considered low as a result of favorable trends in both loss frequency and loss severity, mainly due to enhanced underwriting standards and a strong used car market.
The auto loan portfolio reflected a high concentration of prime-quality credits.
Business banking: Business banking loans at December 31, 2013, were $19.0 billion, compared with $18.9 billion at December 31, 2012.  Business Banking loans primarily include loans that are collateralized, often with personal loan guarantees, and may also include Small Business Administration guarantees.
Nonaccrual loans showed improvement from December 31, 2012.
Net charge-offs declined for the year ended December 31, 2013, compared with the year ended December 31, 2012.
Student and other: Student and other loans at December 31, 2013, were $11.6 billion, compared with $12.2 billion at December 31, 2012.
The decrease was primarily due to runoff of the student loan portfolio.
Other loans primarily include other secured and unsecured consumer loans.
Nonaccrual loans increased compared with December 31, 2012, while net charge-offs decreased for the year ended December 31, 2013, compared with the prior year.
Purchased credit-impaired loans: PCI loans at December 31, 2013, were $53.1 billion, compared with $59.7 billion at December 31, 2012.
This portfolio represents loans acquired in the Washington Mutual transaction, which were recorded at fair value at the time of acquisition.
PCI HELOCs originated by Washington Mutual were generally revolving loans for a 10-year period, after which time the HELOC converts to an interest-only loan with a balloon payment at the end of the loan’s term.
Substantially all undrawn HELOCs within the revolving period have been blocked.
As of December 31, 2013, approximately 19% of the option ARM PCI loans were delinquent and approximately 54% have been modified into fixed-rate, fully amortizing loans.
Substantially all of the remaining loans are making amortizing payments, although such payments are not necessarily fully amortizing.
This latter group of loans are subject to the risk of payment shock due to future payment recast.
Default rates generally increase on option ARM loans when payment recast results in a payment increase.
The expected increase in default rates is considered in the Firm’s quarterly impairment assessment.
The cumulative amount of unpaid interest added to the unpaid principal balance of the option ARM PCI pool was $724 million and $879 million at December 31, 2013, and December 31, 2012, respectively.
The Firm estimates the following balances of option ARM PCI loans will undergo a payment recast that results in a payment increase: $487 million in 2014, $810 million in 2015 and $710 million in 2016.
The following table provides a summary of lifetime principal loss estimates included in both the nonaccretable difference and the allowance for loan losses.
Summary of lifetime principal loss estimates
## Table 0 ##
(a) Includes the original nonaccretable difference established in purchase accounting of $30.5 billion for principal losses only plus additional principal losses recognized subsequent to acquisition through the provision and allowance for loan losses.
The remaining nonaccretable difference for principal losses only was $3.8 billion and $5.8 billion at December 31, 2013 and 2012, respectively.
(b) Life-to-date (“LTD”) liquidation losses represent both realization of loss upon loan resolution and any principal forgiven upon modification.
LTD liquidation losses included $53 million of write-offs of prime mortgages for the year ended December 31, 2013.
Lifetime principal loss estimates declined from December 31, 2012, to December 31, 2013, reflecting improvement in home prices and delinquencies.
The decline in lifetime principal loss estimates during the year ended December 31, 2013, resulted in a $1.5 billion reduction of the PCI allowance for loan losses ($1.0 billion related to option ARM loans, $200 million to subprime mortgage, $150 million to home equity loans and $150 million to prime mortgage).
In addition, for the year ended December 31, 2013, PCI write-offs of $53 million were recorded against the prime mortgage allowance for loan losses.
For further information about the Firm’s PCI loans, including write-offs, see Note 14 on pages 258–283 of this Annual Report.
As a result of reserve actions and PCI prime mortgage write-offs, the allowance for loan loss for the PCI portfolio declined from $5.7 billion at December 31, 2012, to $4.2 billion at December 31, 2013.
The allowance for loan losses decreased from $1.5 billion to $494 million for the option ARM portfolio, from $1.9 billion to $1.7 billion for prime mortgage, from $380 million to $180 million for subprime mortgage and from $1.9 billion to $1.8 billion for the home equity portfolio from December 31, 2012 to December 31, 2013.
The Firm does not estimate the fair value of consumer lending-related commitments.
In many cases, the Firm can reduce or cancel these commitments by providing the borrower notice or, in some cases, without notice as permitted by law.
For a further discussion of the valuation of lending-related commitments, see page 198 of this Note.
Trading assets and liabilities Trading assets include debt and equity instruments owned by JPMorgan Chase (“long” positions) that are held for client market-making and client-driven activities, as well as for certain risk management activities, certain loans managed on a fair value basis and for which the Firm has elected the fair value option, and physical commodities inventories that are generally accounted for at the lower of cost or market (market approximates fair value).
Trading liabilities include debt and equity instruments that the Firm has sold to other parties but does not own (“short” positions).
The Firm is obligated to purchase instruments at a future date to cover the short positions.
Included in trading assets and trading liabilities are the reported receivables (unrealized gains) and payables (unrealized losses) related to derivatives.
Trading assets and liabilities are carried at fair value on the Consolidated Balance Sheets.
Balances reflect the reduction of securities owned (long positions) by the amount of identical securities sold but not yet purchased (short positions).
Trading assets and liabilities – average balances Average trading assets and liabilities were as follows for the periods indicated.
## Table 1 ##
Note 4 – Fair value option The fair value option provides an option to elect fair value as an alternative measurement for selected financial assets, financial liabilities, unrecognized firm commitments, and written loan commitments not previously carried at fair value.
Elections Elections were made by the Firm to: ?
Mitigate income statement volatility caused by the differences in the measurement basis of elected instruments (for example, certain instruments elected were previously accounted for on an accrual basis) while the associated risk management arrangements are accounted for on a fair value basis; ?
Eliminate the complexities of applying certain accounting models (e. g. , hedge accounting or bifurcation accounting for hybrid instruments); and/or ?
Better reflect those instruments that are managed on a fair value basis.
Elections include the following: ?
Loans purchased or originated as part of securitization warehousing activity, subject to bifurcation accounting, or managed on a fair value basis.  ?
Securities financing arrangements with an embedded derivative and/or a maturity of greater than one year.  ?
Owned beneficial interests in securitized financial assets that contain embedded credit derivatives, which would otherwise be required to be separately accounted for as a derivative instrument.  ?
Certain investments that receive tax credits and other equity investments acquired as part of the Washington Mutual transaction.  ?
Structured notes issued as part of CIB’s client-driven activities.
(Structured notes are predominantly financial instruments that contain embedded derivatives. )
?
Long-term beneficial interests issued by CIB’s consolidated securitization trusts where the underlying assets are carried at fair value.
Determination of instrument-specific credit risk for items for which a fair value election was made The following describes how the gains and losses included in earnings during December 31, 2013, 2012 and 2011, which were attributable to changes in instrument-specific credit risk, were determined.  ?
Loans and lending-related commitments: For floating- rate instruments, all changes in value are attributed to instrument-specific credit risk.
For fixed-rate instruments, an allocation of the changes in value for the period is made between those changes in value that are interest rate-related and changes in value that are credit-related.
Allocations are generally based on an analysis of borrower-specific credit spread and recovery information, where available, or benchmarking to similar entities or industries.  ?
Long-term debt: Changes in value attributable to instrument-specific credit risk were derived principally from observable changes in the Firm’s credit spread.  ?
Resale and repurchase agreements, securities borrowed agreements and securities lending agreements: Generally, for these types of agreements, there is a requirement that collateral be maintained with a market value equal to or in excess of the principal amount loaned; as a result, there would be no adjustment or an immaterial adjustment for instrument-specific credit risk related to these agreements.
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, 2013 and 2012, for loans, long-term debt and long-term beneficial interests for which the fair value option has been elected.
## Table 2 ##
(a) There were no performing loans that were ninety days or more past due as of December 31, 2013 and 2012, respectively.
(b) Remaining contractual principal is not applicable to nonprincipal-protected notes.
Unlike principal-protected structured notes, for which the Firm is obligated to return a stated amount of principal at the maturity of the note, nonprincipal-protected structured notes do not obligate the Firm to return a stated amount of principal at maturity, but to return an amount based on the performance of an underlying variable or derivative feature embedded in the note.
(c) Where the Firm issues principal-protected zero-coupon or discount notes, the balance reflected as the remaining contractual principal is the final principal payment at maturity.
(d) During 2013, certain loans that resulted from restructurings that were previously classified as performing were reclassified as nonperforming loans.
Prior periods were revised to conform with the current presentation.
At December 31, 2013 and 2012, the contractual amount of letters of credit for which the fair value option was elected was $4.5 billion and $4.5 billion, respectively, with a corresponding fair value of $(99) million and $(75) million, respectively.
For further information regarding off-balance sheet lending-related financial instruments, see Note 29 on pages 318–324 of this Annual Report.

Tables referenced above, in order (Table 0 first):
<table><tr><td>December 31,(in billions)</td><td colspan="2">Lifetime lossestimates<sup>(a)</sup></td><td colspan="2">LTD liquidationlosses<sup>(b)</sup></td></tr><tr><td></td><td>2013</td><td>2012</td><td>2013</td><td>2012</td></tr><tr><td>Home equity</td><td>$14.7</td><td>$14.9</td><td>$12.1</td><td>$11.5</td></tr><tr><td>Prime mortgage</td><td>3.8</td><td>4.2</td><td>3.3</td><td>2.9</td></tr><tr><td>Subprime mortgage</td><td>3.3</td><td>3.6</td><td>2.6</td><td>2.2</td></tr><tr><td>Option ARMs</td><td>10.2</td><td>11.3</td><td>8.8</td><td>8.0</td></tr><tr><td>Total</td><td>$32.0</td><td>$34.0</td><td>$26.8</td><td>$24.6</td></tr></table>
<table><tr><td>Year ended December 31, (in millions)</td><td>2013</td><td>2012</td><td>2011</td></tr><tr><td>Trading assets – debt and equity instruments</td><td>$340,449</td><td>$349,337</td><td>$393,890</td></tr><tr><td>Trading assets – derivative receivables</td><td>72,629</td><td>85,744</td><td>90,003</td></tr><tr><td>Trading liabilities – debt and equity instruments<sup>(a)</sup></td><td>77,706</td><td>69,001</td><td>81,916</td></tr><tr><td>Trading liabilities – derivative payables</td><td>64,553</td><td>76,162</td><td>71,539</td></tr></table>
<table><tr><td></td><td colspan="4">2013</td><td colspan="4">2012</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>$5,156</td><td></td><td>$1,491</td><td>$-3,665</td><td>$4,217</td><td></td><td>$960</td><td>$-3,257</td></tr><tr><td>Loans<sup>(d)</sup></td><td>209</td><td></td><td>154</td><td>-55</td><td>293</td><td></td><td>236</td><td>-57</td></tr><tr><td>Subtotal</td><td>5,365</td><td></td><td>1,645</td><td>-3,720</td><td>4,510</td><td></td><td>1,196</td><td>-3,314</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>33,069</td><td></td><td>29,295</td><td>-3,774</td><td>44,084</td><td></td><td>40,581</td><td>-3,503</td></tr><tr><td>Loans<sup>(d)</sup></td><td>1,618</td><td></td><td>1,563</td><td>-55</td><td>2,034</td><td></td><td>1,927</td><td>-107</td></tr><tr><td>Total loans</td><td>$40,052</td><td></td><td>$32,503</td><td>$-7,549</td><td>$50,628</td><td></td><td>$43,704</td><td>$-6,924</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>$15,797</td><td><sup>(c)</sup></td><td>$15,909</td><td>$112</td><td>$16,541</td><td><sup>(c)</sup></td><td>$16,391</td><td>$-150</td></tr><tr><td>Nonprincipal-protected debt<sup>(b)</sup></td><td>NA</td><td></td><td>12,969</td><td>NA</td><td>NA</td><td></td><td>14,397</td><td>NA</td></tr><tr><td>Total long-term debt</td><td>NA</td><td></td><td>$28,878</td><td>NA</td><td>NA</td><td></td><td>$30,788</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>$1,996</td><td>NA</td><td>NA</td><td></td><td>$1,170</td><td>NA</td></tr><tr><td>Total long-term beneficial interests</td><td>NA</td><td></td><td>$1,996</td><td>NA</td><td>NA</td><td></td><td>$1,170</td><td>NA</td></tr></table>

Question: What's the average of the Home equity for Lifetime lossestimates(a) in the years where Loans reported as trading assets for Contractual principal outstanding is positive?
Answer: 14.8
Reasoning program: add(14.7,14.9), divide(#0,2)