the table below reflects the estimated effects on pension expense of certain changes in annual assumptions , using 2012 estimated expense as a baseline . change in assumption ( a ) estimated increase to 2012 pension expense ( in millions ) .
for december 31 , 2011 and december 31 , 2010 , what was the average unpaid principal balance outstanding of loans sold as a participant in these programs , in billions?
( a ) the impact is the effect of changing the specified assumption while holding all other assumptions constant . our pension plan contribution requirements are not particularly sensitive to actuarial assumptions . investment performance has the most impact on contribution requirements and will drive the amount of permitted contributions in future years . also , current law , including the provisions of the pension protection act of 2006 , sets limits as to both minimum and maximum contributions to the plan . we do not expect to be required by law to make any contributions to the plan during 2012 . we maintain other defined benefit plans that have a less significant effect on financial results , including various nonqualified supplemental retirement plans for certain employees . recourse and repurchase obligations as discussed in note 3 loan sale and servicing activities and variable interest entities in the notes to consolidated financial statements in item 8 of this report , pnc has sold commercial mortgage and residential mortgage loans directly or indirectly in securitizations and whole-loan sale transactions with continuing involvement . one form of continuing involvement includes certain recourse and loan repurchase obligations associated with the transferred assets in these transactions . commercial mortgage loan recourse obligations we originate , close , and service certain multi-family commercial mortgage loans which are sold to fnma under fnma 2019s delegated underwriting and servicing ( 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 , 2011 and december 31 , 2010 , the unpaid principal balance outstanding of loans sold as a participant in these programs was $ 13.0 billion and $ 13.2 billion , respectively . the potential maximum exposure under the loss share arrangements was $ 4.0 billion at both december 31 , 2011 and december 31 , 2010 . we maintain a reserve for estimated losses based on our exposure . the reserve for losses under these programs totaled $ 47 million and $ 54 million as of december 31 , 2011 and december 31 , 2010 , 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 . 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 whole-loan sale transactions . as discussed in note 3 in the notes to consolidated financial statements in item 8 of this report , agency securitizations consist of mortgage loans sale transactions with fnma , fhlmc , and the government national mortgage association ( gnma ) program , while non-agency securitizations and whole-loan sale transactions consist of mortgage loans sale transactions with private investors . our historical exposure and activity associated with agency securitization repurchase obligations has primarily been related to transactions with fnma and fhlmc , as indemnification and repurchase losses associated with federal housing agency ( fha ) and department of veterans affairs ( va ) -insured and uninsured loans pooled in gnma securitizations historically have been minimal . repurchase obligation activity associated with residential mortgages is reported in the residential mortgage banking segment . pnc 2019s repurchase obligations also include certain brokered home equity loans/lines that were sold to a limited number of private investors in the financial services industry by national city prior to our acquisition . pnc is no longer engaged in the brokered home equity lending business , and our exposure under these loan repurchase obligations is limited to repurchases of the whole-loans sold in these transactions . repurchase activity associated with brokered home equity lines/loans are reported in the non-strategic assets portfolio segment . loan covenants and representations and warranties are established through loan sale agreements with various investors to provide assurance that pnc has sold loans to the pnc financial services group , inc . 2013 form 10-k 69 .