in some cases , indemnification obligations of the types described above arise under arrangements entered into by predecessor companies for which we become responsible as a result of the acquisition . pursuant to their bylaws , pnc and its subsidiaries provide indemnification to directors , officers and , in some cases , employees and agents against certain liabilities incurred as a result of their service on behalf of or at the request of pnc and its subsidiaries . pnc and its subsidiaries also advance on behalf of covered individuals costs incurred in connection with certain claims or proceedings , subject to written undertakings by each such individual to repay all amounts advanced if it is ultimately determined that the individual is not entitled to indemnification . we generally are responsible for similar indemnifications and advancement obligations that companies we acquire had to their officers , directors and sometimes employees and agents at the time of acquisition . we advanced such costs on behalf of several such individuals with respect to pending litigation or investigations during 2012 . it is not possible for us to determine the aggregate potential exposure resulting from the obligation to provide this indemnity or to advance such costs . visa indemnification our payment services business issues and acquires credit and debit card transactions through visa u.s.a . inc . card association or its affiliates ( visa ) . in october 2007 , visa completed a restructuring and issued shares of visa inc . common stock to its financial institution members ( visa reorganization ) in contemplation of its initial public offering ( ipo ) . as part of the visa reorganization , we received our proportionate share of a class of visa inc . common stock allocated to the us members . prior to the ipo , the us members , which included pnc , were obligated to indemnify visa for judgments and settlements related to the specified litigation . as a result of the acquisition of national city , we became party to judgment and loss sharing agreements with visa and certain other banks . the judgment and loss sharing agreements were designed to apportion financial responsibilities arising from any potential adverse judgment or negotiated settlements related to the specified litigation . in july 2012 , visa funded $ 150 million into their litigation escrow account and reduced the conversion rate of visa b to a shares . we continue to have an obligation to indemnify visa for judgments and settlements for the remaining specified litigation , therefore we may have additional exposure to the specified visa litigation . recourse and repurchase obligations as discussed in note 3 loan sale and servicing activities and variable interest entities , pnc has sold commercial mortgage , residential mortgage and home equity loans directly or indirectly through securitization and loan sale transactions in which we have continuing involvement . one form of continuing involvement includes certain recourse and loan repurchase obligations associated with the transferred assets . commercial mortgage loan recourse obligations we originate , close and service certain multi-family commercial mortgage loans which are sold to fnma under fnma 2019s dus program . we participated in a similar program with the fhlmc . under these programs , we generally assume up to a one-third pari passu risk of loss on unpaid principal balances through a loss share arrangement . at december 31 , 2012 and december 31 , 2011 , the unpaid principal balance outstanding of loans sold as a participant in these programs was $ 12.8 billion and $ 13.0 billion , respectively . the potential maximum exposure under the loss share arrangements was $ 3.9 billion at december 31 , 2012 and $ 4.0 billion at december 31 , 2011 . we maintain a reserve for estimated losses based upon our exposure . the reserve for losses under these programs totaled $ 43 million and $ 47 million as of december 31 , 2012 and december 31 , 2011 , respectively , and is included in other liabilities on our consolidated balance sheet . if payment is required under these programs , we would not have a contractual interest in the collateral underlying the mortgage loans on which losses occurred , although the value of the collateral is taken into account in determining our share of such losses . our exposure and activity associated with these recourse obligations are reported in the corporate & institutional banking segment . table 154 : analysis of commercial mortgage recourse obligations .

Table: in millions 2012 2011 january 1 $ 47 $ 54 reserve adjustments net 4 1 losses 2013 loan repurchases and settlements -8 ( 8 ) -8 ( 8 ) december 31 $ 43 $ 47

residential mortgage loan and home equity repurchase obligations while residential mortgage loans are sold on a non-recourse basis , we assume certain loan repurchase obligations associated with mortgage loans we have sold to investors . these loan repurchase obligations primarily relate to situations where pnc is alleged to have breached certain origination covenants and representations and warranties made to purchasers of the loans in the respective purchase and sale agreements . residential mortgage loans covered by these loan repurchase obligations include first and second-lien mortgage loans we have sold through agency securitizations , non-agency securitizations , and loan sale transactions . as discussed in note 3 loans sale and servicing activities and 228 the pnc financial services group , inc . 2013 form 10-k .

Question: by what percentage did the potential maximum exposure decrease by the end of 2012?
Answer: 2.5%
Calculation: multiply(divide(subtract(const_4, 3.9), const_4), const_100)