RAROC at Bank of America From Theory to Practice

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JournalofAppliedCorporateFinanceSUMMER1996VOLUME9.2RAROCatBankofAmerica:FromTheorytoPracticebyEdwardZaik,JohnWalter,andGabrielaKelling,BankofAmerica,andChristopherJames,UniversityofFlorida RAROCATBANKOFbyEdwardZaik,JohnWalter,andGabrielaKelling,BankofAmerica,AMERICA:FROMwithChristopherJames,THEORYTOPRACTICEUniversityofFloridaincethelate1980s,anumberoflargeU.S.mancethatmanagementcanusetocomparetheSbankshaveinvestedheavilyinsystemseconomicasopposedtotheaccountingprofitabilitydesignedtomeasuretherisksassociatedofbusinesseswithdifferentsourcesofriskandwiththeirdifferentlinesofbusiness.Thedifferentcapitalrequirements.immediatepurposeofsuchriskmeasurementsys-TheuseofRAROCbymajormoney-centerandtemsistoprovidebankmanagementswithamoreregionalbankstoformulatecapitalstructuretargetsreliablewaytodeterminetheamountofcapitalandtoevaluateperformanceisamajordeparturenecessarytosupporteachoftheirmajoractivities,fromtraditionalpractice.Bankshavelongreliedonandthustodeterminetheequitycapitalrequiredbymeasuressuchasreturnonassets(ROA)andreturnthebankasawhole.onbookequity(ROE)toevaluatetheirownperfor-Thisrecentinterestinmeasuringriskispartlyamance,bothattheconsolidatedlevelandforresponsetothegreaterregulatoryemphasisonindividualoperatingunits.Andcapitaladequacycapitaladequacythathascomewithimplementationhasbeendeterminedprimarilybybanks’abilitytooftheBaselrisk-basedcapitalrequirementsissuedmeetminimumcapitalrequirementssetbyregula-in1988andthepassageofFDICIAin1991.Eventors.Neithertheregulatoryrequirementsnorcon-moreimportantthansuchregulatorychanges,how-ventionally-appliedROAorROEmeasuresaread-ever,arefundamentalchangesinthebusinessofjustedinanysystematicwayfordifferencesinthebankingthathaveforcedbankmanagementstoseekrisksofthebank’svariousactivities.TheBaselbetterwaystomeasureoperatingperformance.Asguidelines,forexample,effectivelyassignthesametheprogressivederegulation(capitalrequirementscapitalrequirementtoallcommercialloans,regard-aside)oftheindustrycontinues,banksarechoosinglessoftheirdegreeofrisk,whilerequiringnotoprovideanincreasinglydiversesetofproductscapitalfortakingdepositsandpositionsinTreasuryandservices.Therealinnovationinthesenewbonds.Followingtheregulators’example,manyperformanceevaluationmethodsliesintheirabilitybankmanagements—atleastuntilfairlyrecently—toallocatebanks’capitalamongtheirexpandinghavebeencontenttousetheBaselguidelinesasaarrayofnontraditional,fee-basedactivities—manybasisforassigningcapitaltobusinessunits,andtoofwhichdonotinvolveanydirectuseofcapitalatmeasuretheROEsofthoseunitsonthatbasis.Butall.Theultimategoaloftheserisk-basedcapitalbankers’increasingrecognitionoftheshortcomingsallocationsystems,whichareoftenlumpedtogetherofthesetraditionalmeasuresispromptinggrowthundertheacronymRAROC(“riskadjustedreturnonintheuseofRAROCanditsrisk-basedmethodsforcapital”),istoprovideauniformmeasureofperfor-allocatingcapital.83BANKOFAMERICAJOURNALOFAPPLIEDCORPORATEFINANCEJOURNALOFAPPLIEDCORPORATEFINANCE Assuggested,then,itisprimarilychangesinimplementingaRAROCsystemintoanorganiza-thebusinessenvironment,notregulatoryman-tionaslargeanddiversifiedasthepresent-dayBdates,thataredrivingbankstomakechangesinofA,andthepromisethatRAROCholdsoutfortheircapitalallocationandperformancemeasure-creatingandreinforcingavalue-basedcorporatementsystems.Theincreaseincompetitionthatculture.hascomewithderegulationhassqueezedprofitmarginsinmosttraditionalbankingactivities,RAROCANDFINANCIALTHEORYthusdrivingthequestfornewsourcesofrevenueandprofit.AndtheresultinggreaterdiversityofDevelopmentoftheRAROC“methodology”bankbusinessesiscausingbankerstodevotewasstartedinthelate1970sbyagroupatBankersmoreattentiontomanagingtherelativelyunfa-Trust.Theiroriginalintentwastomeasuretheriskmiliarrisksassociatedwiththosebusinesses.Butofthebank’screditportfolio,andtheamountofperhapsthemostpowerfulimpetustobankers’equitycapitalnecessarytolimittheexposureoftheuseofmoresystematicriskmeasuresiscomingbank’sdepositors(andotherdebtholders)toafromincreasinglyactivistinstitutionalinvestors.specifiedprobabilityofloss.Sincethen,anumberSuchinvestors,togetherwiththeoperationoftheofotherlargebankshavedevelopedRAROC(orcorporatetakeovermarket,areexertingtremen-RAROC-like)systems,inmostcaseswiththeaimofdouspressureonmanagementstorealizethequantifyingtheamountofequitycapitalnecessarypotentialforaddingshareholdervaluewithintosupportalloftheiroperatingactivities,fee-basedtheirorganizations.Theclearexpectationforandtradingactivitiesaswellastraditionallending.theseRAROCsystemsisthatbettermeasurementBankofAmerica’spolicyistocapitalizeeachmethodswillproducebetterperformancebyofitsbusinessunitsinamannerconsistentwithaholdingmanagersaccountablefortheamountofAAcreditratingbasedontheunit’s“stand-alone”investorcapitaltheyareputtingatrisk.risk,butalsoincludinganadjustmentforanyInthisarticle,weexaminehowrisk-basedinternaldiversificationbenefitsprovidedbythecapitalallocationmodelsworkbydescribingtheunit.(Aswediscussinmoredetaillater,thestand-RAROCsystemdevelopedbyBankofAmerica.Inaloneriskofabusinessunitismeasuredbythe1993,BofA’sRiskandCapitalAnalysisGroupwasexpected,orforward-looking,volatilityofitsoper-chargedwiththetaskofdevelopingandinstitutingatingvalue.)Eachoftheseindividualcapitalalloca-asinglecorporate-widesystemtoallocatecapitaltotionsarethenaggregatedtoarriveattheoptimalallthebank’sactivities.Since1994,thatsystemhaslevelofequitycapitalfortheentirebank.beenprovidingquarterlyreportsofrisk-adjustedRAROCsystemsallocatecapitalfortwobasicreturnsoncapitalforeachofthebank’s37businessreasons:(1)riskmanagementand(2)performanceunits.By1995,BofAhadalsodevelopedtheevaluation.Forriskmanagementpurposes,thecapabilitytocalculateRAROCdowntothelevelofoverridinggoalofallocatingcapitaltoindividualindividualproducts,transactions,andcustomerre-businessunitsistodeterminethebank’soptimallationships.Thethree-yearprocessofdevelopingcapitalstructure—theproportionofequitytoassetsandimplementingasystemtomeasureeconomicthatminimizesthebank’soverallcostoffunding.returnsprovidesaninterestingcasestudyintheThisprocessinvolvesestimatinghowmuchtheriskapplicationoffinancialtheorytorealbusiness(orvolatility)ofeachbusinessunitcontributestoproblems.thetotalriskofthebank,andhencetothebank’sWebeginbydiscussingthefinancialtheoryoverallcapitalrequirements.ofallocatingequitycapitalamongdifferentbusi-Forperformanceevaluationpurposes,RAROCnessesinthecontextofBankofAmerica’sobjec-systemsassigncapitaltobusinessunitsaspartofativesformeasuringrisk-adjustedcapital.Thenweprocessofdeterminingtherisk-adjustedrateofprovideadetailedlookatthemeasurementsys-returnand,ultimately,the“economicprofit”ofeachtemitself,includingeachofthefourdifferentbusinessunit.Theobjectiveinthiscaseistomea-sourcesofrisk—credit,country,market,andbusi-sureabusinessunit’scontributiontoshareholderness(ornonportfolio)risk—thattogetherdeter-value,andthustoprovideabasisforeffectiveminetheamountofcapitalassignedtoanactivity.capitalbudgetingandincentivecompensationatThirdandlast,wediscussthechallengesofthebusinessunitlevel.84VOLUME9NUMBER2SUMMER1996 Themostpowerfulimpetustobankers’useofmoresystematicriskmeasuresiscomingfromincreasinglyactivistinstitutionalinvestors.TheclearexpectationfortheseRAROCsystemsisthatbettermeasurementmethodswillproducebetterperformancebyholdingmanagersaccountablefortheamountofinvestorcapitaltheyareputtingatrisk.RAROCandRiskManagementthecostsandbenefitsofholdingequitycapitalinthecontextofthesemarketfrictions.Inbanking,asinWhatguidancedoescorporatefinancetheorymostindustries,thetaxshieldprovidedbytax-providemanagersinhowtoallocatecapital?Firstdeductibleinterestpayments(asopposedtonon-let’sconsidertheissueofriskmanagementanddeductibledividends)createsanincentivetomakeoptimalcapitalstructure.Allocatingequitycapitalonextensiveuseofdebtfinancing.Banks’accesstothebasisoftheriskofindividualbusinessunitsmayfixed-ratedepositinsurancealsomakesdebtintheseempointlesstothosefamiliarwithModiglianiandformofdepositsalow-costsourceoffunding.WhenMiller’sPropositionI—theso-calledcapitalstructurecombinedwiththisfederalinsurancesubsidy,de-irrelevancetheorem.ThekeyinsightoftheM&Mpositors’furtherreductionoftheirrequiredinteresttheoryisthat,ina“frictionless”capitalmarket(oneratesfortheliquidityandconvenienceofdemandwithperfectinformation,andwithouttaxes,bank-andtimedepositsisanaddedincentiveforbankstoruptcycosts,orconflictsbetweenmanagersandusethisformofleverage.shareholders),howacorporationfinancesitself—Anotherimportantmotiveforincreasinglever-whetherpredominantlywithdebtorwithequity—age,orreducingequity,isthepotentialforhighwillnotaffectthevalueofthefirminanysystematicleveragetostrengthenmanagement’sincentivetoorpredictableway.Thelogicbehindthisconclusionoperateasefficientlyaspossible,tomakenecessaryissimple:Becauseindividualinvestorscancreatecutbackstorestoreprofitability,andtorejectall“homemade”leverageanddiversifymost“firm-investmentprojectsthatdonotpromisetoreturnspecific”corporateriskssimplybyadjustingtheirtheircostofcapital.Thisincentivebenefitofhighownportfolios,theywillnotrewardcorporationsleveragecanbesignificantinindustrieswithexcessthatundertaketheseactivitiesontheirbehalfbycapital.Giventheovercapacityintheirtraditionalloweringtheirrequiredratesofreturn.Ifoneacceptsbusinesses,manybankstodayarechoosingtopaythisconclusion,thereislittletobegainedfromriskouttheirexcesscapitalintheformoflargestockmanagementor,byextension,fromdevotingre-repurchases—decisionsthatarealmostinvariablysourcestodeterminingtheappropriateamountofrewardedbythestockmarket.equitycapitalforabank—muchlessforindividualSuchbenefitsofincreasingfinancialleveragebusinessunitswithinthebank.must,ofcourse,beweighedagainstthecosts.IntheBut,ofcourse,noself-respectingbankerwouldextremecase,highleveragecanleadtodefaultandacceptthepropositionthatcapitalmarketsoperateacostlyreorganization.Buttherearealsosignificantwithoutfrictions.Indeed,banksandotherfinancialcoststobanksthatcanariseincasesoffinancialintermediariesoftenaddvaluepreciselythroughdistressthataremuchlessextreme.Foronething,theirabilitytoreducemarketfrictionsthatputoffFDICIAimposesheavycosts(intheformofin-publicbondholders—frictionssuchaslimitedpubliccreasedregulatoryoversight)onbanksthatviolateinformationandthepossibilityofcostlyrenegotia-theminimumcapitalstandards.Butthemostserioustionsoftroubledcredits.Nevertheless,theM&Mdeterrenttohighleverageinbankingisthepossibil-frameworkprovidesausefulstartingpointintheityforliquidityconstraintstocausemajordisruptionsfollowingsense:Intheprocessofdemonstratingofabank’soperatingactivities.whycapitalstructuredoesn’tmatter,italsosuggestsAsRobertMertonandAndrePeroldpointedoutthewaysinwhichthecapitalstructurechoicecaninarecentarticleinthisjournal,1banksandotherincreasevalue—namely,by(1)reducingtaxespaidfinancialfirmscanbedistinguishedfromindustrialbyinvestorsorthecompany;(2)reducinginforma-companiesbythefactthattheircustomersareoftentioncosts;(3)reducingthecostsoffinancialtroublealsotheirlargestliabilityholders.Forexample,a(orliquidityconstraints);and(4)strengtheningbank’sdepositors,swapcounterparties,andletter-managers’incentivestoinvestinallpositiveNPVof-creditbeneficiariesallhaveliabilityclaimsontheprojectswhilerejectingallothers.bank.Andbecausethesecustomersplaceapre-Financetheorythussuggeststhat,indesigningmiumvalueonassurancesofperformanceontheiracapitalallocationsystem,thefirststepistoidentifycontracts,theyshowastrongpreferenceforbanks1.“TheoryofRiskCapitalforFinancialFirms,”JournalofAppliedCorporateFinance,Vol.6No.3(Fall1993).85JOURNALOFAPPLIEDCORPORATEFINANCE withahighcreditquality.Asaconsequence,ahighmorelikelytobeinfluencedbythevolatilityofthecreditratingisgenerallyheldtobeessentialforaunderlyingvariablesthataffectbankstockpricesbanktobeamajorswapsdealer,tounderwritethanbyyear-to-yearchangesinbankearningsandsecurities,ortocompeteeffectivelyinthecorporatebookcapital.bankingmarket.2And,justasabank’soverallcapitalshouldInsum,thesensitivityofbanks’customerstodependonthevolatilityofitsmarketvalue,capitalbanks’creditratingsislikelytomeanrevenueallocationstoindividualbusinessunitsofthebankforgoneandthusamajorlossofoperatingvalueforshouldbemadeonthebasisofthe“contribution”ofthosebankswhosecreditqualityfallsbelowacertaineachbusinessunittotheoverallvolatilityofthelevel.Inrecognitionofthispotentialcostofhighbank’smarketvalue.5Formanyofthefee-basedleverage,BofAhasestablishedcapitalstandardsthatactivitiesofbanks,thisislikelytomeanassigningareconsistentwithmaintainingaAAcreditratingonconsiderablymorecapitalthansuchoperationsitsseniordebentures—and,assuggestedearlier,allrequireintheirday-to-dayexecution.TakethecasesofitsbusinessesareimplicitlycapitalizedtoaAAofsecuritiesunderwritingandtheissuanceofcom-standard.mitments.AlthoughneitherrequiresmuchcapitalDefiningRisk:VolatilityofBookCapitalorforday-to-dayfundingofoperations(whatMertonMarketValue?Uptothispoint,wehavenotedthatandPeroldrefertoas“cashcapital”),bothrequirethetheRAROCsystemassignsequitycapitalprimarilyimplicitbackingofsignificantamountsofthebank’saccordingtothe“stand-alone”riskofabusinessunit,capital(“riskcapital”).andthatsuchriskisinturnafunctionofthevolatilityTakingAccountofInternalDiversificationofthebusinessunit’svalue.Butthisraisesatheoreti-Benefits.Butwhiletheassignmentofriskcapitalcalissuethathasconsiderablepracticalimport:Inwillmeanlargercapitalallocationstofee-basedsettingacapitalstructuretargetforabank,howdoesactivitiesthanundertraditionalmeasurementsys-onemeasurethevolatilityofitsvalue—orthetems,thereisalsooneoffsettingfactor—thevolatilityofthevalueofitsindividualunits?Isittheextenttowhich“nonsynchronous”cyclesinavolatilityofthebank’sstockprice,orofsomeproxygivenactivity’sprofitsandoperatingvalueserveformarketvaluesuchasabusinessunit’seconomictoreduceswingsinthebank’soverallmarketcashflows?Orisitthevolatilityofthebank’svalue.Tomeasuretherisk“contribution”ofaunitreportedearningsandbookcapital—themainfocustotheentirebank,onemusttakeintoaccountnotoftheregulators—thatiscriticalindeterminingonlythe“stand-alone”volatilityofabusiness,butcapitaladequacy?alsohowanindividualbusinessunit’smarketGiventherationaleformanagingthecapitalvaluevarieswiththevalueofotherunitswithinpositionofabankjustpresented—inparticular,thethebank.Forexample,abusinesswhoseoperat-needtomaintainahighcreditratingtosupporttheingcashflowsarestronglycorrelatedwiththebank’soff-balance-sheetactivities—therelevantprofitsoftherestofthebankwillrequirealargermeasureofriskfordeterminingcapitaladequacyisamountofcapitalthanwillabusiness(ofthethevolatilityofabank’smarketvalue,notthesamevolatility)whoseprofitsmoveinvolatilityofitsbookorregulatorycapital.3Banks’countercyclicalfashion.Thelogicforthisdiversi-abilitytosmooththeirreportedearningsusingtheficationadjustmentisstraightforward:theloanlossprovisionandotherreservesiswellunder-countercyclicalbusinesshasdiversificationben-stoodbyinstitutionalinvestorsandthebondratingefitsforthebankasawholethatenablethebankagencies.4Forthisreason,bankcreditratingsaretooperatewithlessequitycapital.2.Thisargumentalsosuggeststhatiftheimportanceofahighcreditratingflowvolatilityislesslikelytobeatargetofariskmanagementprogramthanforvarieswiththetypeofbusiness,thecapitalrequirementswillvary.Requiringallnonfinancialfirms.businessestobecapitalizedataparticularlevelmaycreateanadditionalburden4.Forevidenceofthemarket’sabilitytoseethroughaccountingearningstoforthosebusinessesthatrequirealowercreditrating.cash,seeinthisissuethecommentsbythebanksecuritiesanalystsin“Roundtable3.BofA,likemostbanks,focusesonthevolatilityinthemarketvalueofitsonCurrentIssuesinCommercialBanking:StrategicPlanning,Performancecommonstockwhenevaluatingcapitaladequacy.AnalternativeobjectiveofriskMeasurement,andIncentiveCompensation.”managementisvolatilityinthecashflowsorearnings.Theideahereisthat,given5.Asapracticalmatter,manyofabank’sbusinessesdonotmarktheirthecostsofexternalfinancing,theabilityoftheenterprisetoengageinpositiveportfoliostomarketonaregularbasis.Asaresult,trackingthevolatilityofmarketnetpresentvaluemaybeimpairedbyadverseshockstocashfloworearnings.But,valuesisnotpossible.Forthosebusinesses,volatilityineconomicearningsmustgiventheongoingaccessbyfinancialfirmstothecapitalmarkets,managingcashbeusedasasurrogateforvolatilityofmarketvalues.86VOLUME9NUMBER2SUMMER1996 Maximizingshareholderwealthrequiresthatabankundertakeallnewprojectsthatexceedthecostofcapital.IfmanagersarerewardedsolelyonthebasisofROE,orRAROC,theyarelikelytorejectvalue-increasingprojectsthatwilllowertheiraveragereturns.RAROC,EconomicProfit,andPerformanceReconcilingRAROCwiththeCAPM.AtBankMeasurementofAmerica,thecapitalchargeforeachbusinessisobtainedbymultiplyingeconomiccapitalbytheInadditiontoriskmanagementandcapitalsame,corporate-widecostofequitycapital(orthestructureplanning,RAROCsystemsareusedtoso-called“hurdlerate”).Thispracticeappearstobeevaluatetheperformanceofbusinessunits.Inthisatoddswiththestandarddiscountedcashflowcontext,therisk-adjustedreturnoncapitalservesmethodprescribedbymodernfinancetheory.InasamorereliablemeasurethantraditionalROE.accordancewiththewidely-usedCapitalAssetPric-Ifabusinessunit’sRAROCishigherthanthecostingModel(CAPM),thecostofcapitalforeachofequity—shareholders’minimumrequiredrateactivityshouldreflectthe“systematic”riskofthatofreturn—thentheunitisjudgedtobecreatingactivity.Bysystematicriskwemeanthe“covari-valueforshareholders.ButifRAROCisbelowtheance”ofthatoperation’svalue(asmeasuredbyitscostofequity,theunitisreducingshareholderbeta)withthevalueofthemarketportfolio.value.BofA’sdecisiontouseacommonhurdlerateButthisisnotthelaststepintheanalysis.Theforallbusinessunitswasmotivatedbyanumberofuseofratesofreturn—whetherRAROCortraditionalconsiderations.OneisthedifficultyofestimatingmeasureslikeROEorROA—doesnotprovideabetasforindividuallinesofbusinesswithfewstand-basisformeasuringhowmuchvalueisbeingcreatedalonecompetitors.Andgiventhelackofobjectiveordestroyedbyanoperation.Indeed,theexclusivedata,the“influencecosts”arisingfromdisputesuseofRAROC,oranyrate-of-return,toevaluateamongmanagersassesseddifferentcostsofcapitalperformancecanleadtocorporate-widewerelikelytobesignificant.Butyetanother,andunderinvestment.Maximizingshareholderwealthprobablythedecisive,factorinourchoiceofasinglerequiresthatabankundertakeallnewprojectsthathurdleratewasourjudgmentthatamoretheoreti-exceedthecostofcapital.IfmanagersarerewardedcallypreciseuseoftheCAPMwouldnotleadtosolelyonthebasisofROE,orRAROC,theyarelikelymaterialdifferencesinresults.Asnoted,ourRAROCtorejectvalue-increasingprojectsthatwilllowersystemeffectivelyconfersdiversificationbenefitsontheiraveragereturns.individualbusinessunitsintheformofreducedToavoidthisproblemandcreatetherightcapitalallocations.Andthisinturnmeansthattheinvestmentincentivesformanagers,performancerisk“contributions”ofindividualunitsarebasedonshouldbeevaluatedaccordingtothe“residual“internalbetas,”ifyouwill.Thatistosay,theunitsincome”—orwhatBofAcallsthe“economicarenotbeingchargedforthatportionoftheiroverallprofit”—oftheactivity.Economicprofitiscalculatedriskthatisdiversifiedawaybythestructureoftheasearnings(netoftaxes,interestpayments,andbankasawhole.And,totheextentthatabankasexpectedcreditlosses)lessachargeforthecostoflargeanddiversifiedasBofAcanbeviewedasaequitycapital.Theobjectiveofthiscalculation,surrogateforthebroadmarket,thenthisapplicationagain,istoprovideameasureofthevalueaddedbyofRAROCmayendupproducingresultsverysimilaraparticularactivity—onethatallowstheoperatingtothosegeneratedbyaCAPMsystemwithmultipleperformanceof“off-balance-sheet”activititestobediscountrates.6comparedtothatoftraditionalasset-basedactivities.TheGoalforManagers:IncreasingEconomicThevalueaddedassociatedwitheachactivitycanProfit.AlthoughBofAappliesacommonhurdlethenbeusedasabasisformanagerialincentiveratetoallitsdifferentbusinessestodeterminecompensationaswellasaguidetomanagersinwhethertheyareaddingvalueforshareholders,determiningwhethertoexpandthatactivitythroughbusinessmanagersarerewardedforincrementaladditionalinvestment.improvementsineconomicprofit.Theobjectiveis6.Theobjectiveofallocatingmorecapitaltoriskieractivitiesistoensurethatallocationprocessistomaketheinternalbetasforequityinvestmentsthesametherisk(asmeasuredbyaninternalbeta)ofanequityinvestmentineachactivityacrosstheprojects.Inaddition,itcanbeshownthatifthebankholdsanefficientlyissimilar.Thisprocessensuresthateventhoughriskonan“unlevered”basismaydiversifiedportfolioofbusinesses,theinternalbetaswillbeidenticaltothebetasvarywidelyacrossthevariousactivitiesofthebank,onaleveredbasistheriskofofeachactivitywiththemarket.Totheextentthatthebankdoesnotholdanvariousactivitiesisthesame.efficientlydiversifiedportfolioofbusinesses,thehighertheR2ofthebanksstockAsatechnicalmatter,ifthebankholdsawelldiversifiedportfolioofreturnswiththemarketreturnstheclosertheinternalbetaswillbetomarket-basedbusinesses,thecostofequitywillbeidenticalsincetheeffectofthecapitalbetas.87JOURNALOFAPPLIEDCORPORATEFINANCE to“leveltheplayingfield”forlinemanagers,ensur-linesofbusiness.SincesuccessfulcompletionofingthatsomeoperatingheadsarenotrewardedforthisfirstpassinMarchof1994,theBankhasbeeninheritinghighlyprofitableoperationswhilepro-progressivelyintegratingRAROCconceptsintoex-vidingstrongerencouragementforturnaroundsitu-istingmanagementreportingsystems.ations.BeforesayingmoreabouttheimplementationTosummarize,then,corporatefinancetheoryprocess,wenowprovideanoverviewoftheriskimpliesthatcapitalshouldbeallocatedonthebasismeasurementandcapitalallocationframeworkthatofeachbusiness’scontributiontotheoverallvolatil-wasputinplace.ityorriskofthebank’smarketvalueofequity.Inaddition,performanceshouldbeevaluatedontheTheFrameworkbasisoftheeconomicvalueaddedbythebank’sactivities.WenowturntoadiscussionofhowthisRiskisdefinedasanyphenomenonthatcreatesframeworkisbeingappliedintherealworld.potentialvolatilityinthemarketvalueofthefirm.Thepurposeofriskcapitalistoprovidecomprehen-RAROCATBANKOFAMERICAsivecoverageoflossesfortheorganizationasawhole.By“comprehensive,”wemeancoverageofUntillate1993,theprimaryprofitabilitymea-allsourcesofriskwithaveryhighdegreeofsureinmanagementreportsatBankofAmericawasconfidence.returnonassets—thatis,netincomedividedbytotalBankofAmericahasidentifiedfourmajorcat-assets.Forseveralyearspriortothis,theBankhadegoriesofriskassociatedwithitsvariousactivities:struggledwithlittlesuccesstomeasureperformanceCreditriskistheriskoflossduetoborroweronarisk-adjustedbasis.Likemanyotherbanks,Bofdefault.Inadditiontodefaultriskonloans,creditriskAhadattemptedtoapplyRiskBasedCapitalGuide-alsoincludesatradingcounterparty’sfailuretopaylinestoprofitabilitymeasurement.Usingtheregula-onacontractualobligation.toryrequirementstodeterminetheequitylevelsofCountryriskisdefinedastheriskoflossoncross-eachbusiness,thebankhaddevelopedacompli-borderandsovereignexposuresduetogovernmen-catedprocessforassigningdifferentrisk-basedtalactions.Suspensionofhardcurrencypayments,hurdleratestoeachbusinessforcapitalbudgetingradicaldevaluationofthecurrency,andnationaliza-andperformanceevaluation.But,becauseofthetionofassetsheldasinvestmentsaresomeexamplesdifficultyofreconcilingregulatoryequityrequire-ofsuchgovernmentactions.mentswithaportfolio-basedriskframework,thisMarketriskistheriskoflossduetochangesintheapproachmetwithconsiderableinternalresistance.marketpriceoftheBank’sassetsandobligations.InNovember1993,effortstoredefineperfor-Examplesofmarketriskareforeignexchangerisk,mancemeasurementweregivenhighpriority.Theinterestraterisk,andoptionsriskonmortgagesandRisk&CapitalAnalysisdepartmentwasformedanddeposits.giventheresponsibilityofdevelopingtheoverallBusinessriskistheuncertaintyoftherevenuesandframeworkforrisk-adjustedprofitabilitymeasure-expensesassociatedwithnon-portfolioactivitiesment.Seniormanagementpressedforquickimple-suchasorigination,servicing,anddataprocessing.mentation(infact,theoveralldevelopmentprocessBusinessriskisafunctionofgeneralindustryfactors,wasallottedjustfourmonths).Theinitialstaffingofcompany-specificfactors,andexternalfactorssuchthedepartmentincludedamanagerandfourfinan-astechnologicaladvancesandregulatorychanges.cialanalysts.Togainaccesstostate-of-the-artindus-Riskcanbemeasuredalongtwodimensions:trypractices,Risk&CapitalAnalysisalsoengagedexpectedlossandunexpectedloss.AsillustratedinOliver,Wyman&CompanytoassistintheinitialFigure1,expectedlossistheaveragerateoflossdevelopmentofRAROCatBofA.expectedfromaportfolio.Inthecaseofcreditrisk,Theshort-termobjectiveoftheRAROCprojectexpectedlossesarereflectedinloanratesandfees;wastodevelopacomprehensiveandconsistentandbecausetheyareintendedtobecoveredbymethodologyforattributingcapitaltothebank’soperatingearnings,suchlossesarereportedin“firsttier”businessunits.Followingapilottestinrequiredloanlossprovisionsonabank’sP&L.IftheBank’sU.S.CorporateGroup,aninitialsetoflossesalwaysequalledtheirexpectedlevels,thereRAROCcalculationswasperformedfor37differentwouldbenoneedforcapitaltoprotectagainstsuch88VOLUME9NUMBER2SUMMER1996 Byassigninglevelsofcapitalbasedonanticipatedfuturerisksratherthanhistoricalrisks,oursystemisdesignedtoencouragemanagerstomakechangesinthebusinessmixoftheirunit,orinthecompositionofthecreditportfolio,thatimprovetherisk-rewardprofileofthebankwhileincreasingtheirownRAROCandeconomicprofit.FIGURE1EXPECTEDLOSSANDUNEXPECTEDLOSSlosses.Althoughtheconceptofexpectedlossap-TimeHorizonforMeasuringRisk.Overwhatpliesmostdirectlytocreditriskandcountryrisk,ittimeperiodshouldrisksbemeasured?Intheory,thecanalsobeappliedtootherrisktypes.choiceoftimehorizonformeasuringriskisarbitrary.UnexpectedlossisthevolatilityofreturnsorOnecouldusevolatilitymeasuredoverfive-yearorlosses(asmeasuredbythestandarddeviationofeventen-yearintervalswiththeaimofcapturing“fullthosereturnsorlosses)aroundtheirexpectedlevels.cycles”inrisk.Ontheotherhand,itishardtogetItisunexpectedlossthatcreatestheneedforreliabledataforsuchlongperiods,particularlyoneconomiccapital;and,foreachofthefoursourcesunfamiliarbusinesses;andonemaybeabletogetofriskassociatedwithagivenbusinessunit,itisreasonablyprecisemeasurementsusingvolatilityunexpectedlossthatdetermineseconomiccapital.overmuchshorterperiodsoftime.CapitalizationandConfidenceLevels.HowAtBofA,wehavechosentocalculatebothmuchprotectionagainstunexpectedlossesisenough?expectedandunexpectedlossusingacommonone-AtBankofAmerica,thetotalamountofeconomicyeartimehorizontoensureconsistencyacrossthecapitalattributedtoallofthebusinessunitsistheorganization.Thischoiceoftimehorizonissome-amountthatisestimatedtoguaranteethesolvencywhatofacompromisebetweenacredit-andmarket-ofthebankata99.97%confidencelevel.Putalittleriskperspective.Ifthetimehorizonisnotconsistent,differently,capitalisassignedtoallbusinessunitsinthencomparabilityofreturnmeasuresislost.7sufficientamounttocovercatastrophiclossesinallAnotherkeyconsiderationwastoensurethatbut3outof10,000possiblescenarios.Toensureourmeasuresofriskarebothascurrentandasconsistentcapitalizationacrossthebank,thiscom-forwardlookingaspossible.Capitalassignmentsaremonstandardisappliedtoallfourriskcategoriesforupdatedquarterlytoreflecttheriskinherentintheallbusinessunits.businessgiventhecompositionandcreditqualityofSeniormanagement’schoiceofthe99.97%thecurrentportfolio.Byassigninglevelsofcapitalcoveragelevel(or,alternatively,a.03%probabilitybasedonanticipatedfuturerisksratherthanhistori-ofdefault)wasdeterminedbyevaluatingtheimplicitcalrisks,oursystemisdesignedtoencouragerisksanddefaultratesofpublicdebtprojectedovermanagerstomakeshiftsinthebusinessmixoftheiraone-yearhorizon(moreaboutthisbelow).Theunit,orchangesinthecompositionofthecreditconclusionofthisanalysiswasthata99.97%cover-portfolio,thatimprovetherisk-rewardprofileoftheagelevelwassufficienttoreducetheriskofthebankbankwhileincreasingtheirownRAROCandeco-totheaveragelevelsforAAratedcompanies.nomicprofit.7.Asnoted,theaveragedefaultrateforAAfirmswasapproximately.03%overfallfrom99.97%to99.00%orless;andthustheamountofcapitalrequiredwouldthathorizon.Measuredovera10-yearhorizon,thedefaultprobabilityforAAloansnotnecessarilyincreaseasaconsequenceoflengtheningthehorizon.wouldbe1.00%ormore.But,inthatcase,ourrequiredconfidencelevelwould89JOURNALOFAPPLIEDCORPORATEFINANCE CapitalandProbabilityDistributions.Toindividualfacilityortransaction.Suchabottom-up,achievethetargetedconfidencelevelforthecapitali-orbuildingblock,approachallowscapitaltobezationofanybusiness,itisnecessarytoconsidernotaggregatedordisaggregatedatvariouslevelsandinonlythevolatilityofthatbusiness’sresults,butalsovariouswayswithoutdistortingtheresults.Fortheprobabilitydistributionofpotentialoutcomes.Isexample,capitalcanbeassignednotonlytolinesofthedistributiona“normal,”bell-shapedcurve,inbusinessbutalso,inmanycases,toindividualwhichhighandlowoutcomesareroughlysymmetri-productsthatcutacrossthedifferentbusinessunits.cal?Oristhedistributionhighly“skewed,”withCreditrisk,ortheriskoflossduetoborrowerlossestendingtobecomeverylargeattheextremedefaults,isattributedtoallunitswithborrowerorendofthedistribution?Theprobabilitydistributioncounterpartyexposure(commercialborrowers,con-isimportantbecauseitwilldeterminethenumberofsumerborrowersandtradingcounterparties).Forstandarddeviationsofunexpectedlossestoachievecommercialportfolios,bothcreditandcountryriskthe99.97%confidenceinterval.capitalarecalculatedattheindividualloanlevel.Forexample,forrisksthatcanbecharacter-Thisallowsforthefinestpossiblegradationofrisk.izedashavingnormaldistributions(suchasinter-Inthecaseofconsumerloans,thesheervolumeofestrate,foreignexchange,andother“market”suchloansmakesitcost-effectivetoperformcreditrisks),capitalcoverageof3.4standarddeviationsisriskcalculationsonlydowntothe“sub-portfolio”consistentwitha99.97%confidenceinterval.Forlevel.Sub-portfoliosaredefinedtoberelativelycreditlosses,bycontrast,theempiricaldatasuggesthomogenousgroupsofloanswiththeprimarystrati-thatthedistributionisnotnormal,buthighlyskewed.ficationbasedontheproductandriskclassification.Andthe(verysmall)possibilityofverylargelossesThetotalamountofcreditcapitaldependsonrequirescapitalcoverageofcreditrisksof6stan-anumberoffactors.Themostimportantarethedarddeviationstoachievethesame99.97%confi-internalcreditratingoftheborrowerandthedollardenceinterval.amountofexposure.OtherfactorsthatcomeintoRiskContribution.Aswenotedinthetheoryconsiderationaretheamountofunutilizedcommit-sectionofthispaper,theamountofcapitalthatisment,thetypeofcollateralsupportingthecredit,theattributedtoeachbusinessunitreflectsthatunit’sinstrumenttype,thesizeoftheexposurerelativeto“contribution”tothevariabilityofthebank’soverallthetotalportfolio,andtheindustryoftheborrower.return.Therearetwoimportantfactorsindetermin-(FormoredetailonBofA’smethodformeasuringingabusiness’sriskcontribution:(1)thetotal,orcreditrisk,seetheAppendix.)“stand-alone,”volatilityofitsreturns;and(2)theCountryriskistheriskofloss—independentofextentofthecorrelationofthatunit’sreturnswiththetheborrower’sfinancialcondition—onforeignex-returnsoftheoverallbank.Themorevolatiletheposuresarisingfromgovernmentactions.Countryunit’sperformance,allelseequal,thelargertheriskisattributedtoallbusinessunitswithcross-assignmentofcapital.But,totheextentthatitsborderandsovereignexposures.Becausecountryreturnsarelessthanperfectlycorrelated,itseco-andcreditriskarecloselyrelated,BofA’scountrynomiccapitalisreduced(bymultiplyingaunit’sriskapproachcloselyparallelsitscreditriskmethod-stand-aloneeconomiccapitalbyacoefficientthatisology.Thekeydifferenceisthattheriskratingofthelessthan1.0).Thisapproach,asnotedearlier,iscountryisusedinplaceofthecustomer’sinternaldesignedtocapturethediversificationbenefitofriskrating.Thecountryriskofacross-borderholdingaportfolioofbusinesses,andtogiveeachexposureistreatedasequivalenttoadirectloantooftheindividualbusinesses“credit”fortheamountthegovernmentwheretheloanisdomiciled.ofdiversificationitprovides.MarketriskistheriskoflossduetochangesinthemarketpricesoftradedassetsandobligationsofMeasuringandCapitalizingthebank.ItarisesmostobviouslyfromanoutrightTheFourSourcesofRiskpositionorfromanexplicitderivative.AtBofA,twogeneralprocessesareusedtomeasuremarketrisk.TheriskmeasurementsandcapitalassignmentsFormosttradingactivity,marketriskismeasuredforeachofthefoursourcesofriskaremadeattheusinga“valueatrisk”(orVAR)framework.Forlowestleveloftheorganizationthatthedatawillproductswithoptionsriskexposure,suchasmort-support—insomecases,downtothelevelofthegagesandhomeequityloans,themarketriskis90VOLUME9NUMBER2SUMMER1996 Useofeconomicprofitisdesignedtopromotenotonlygreaterefficiencyinexistingoperations,butalsostrategicinvestmentdecisions—thatis,decisionstoemploymore(orless)capitalinthebusiness—thatareconsistentwithmaximizingshareholdervalue.estimatedusingMonteCarlosimulation.MarketriskCalculatingEconomicProfit.Thefinalstepincapitaliscalculatedatthetradingunitorportfoliotheanalysisisthecalculationofeconomicprofit.level,withadjustmentsmadetoaccountfordiversi-Theeconomicprofitofabusinessunitisits“re-ficationassociatedwiththecorrelationbetweensidual”earnings—whatisleftoveraftersubtractingtradingrooms.thecostofeconomiccapitalfromrisk-adjustednetBusinessriskincludesalltherisksthatthebankincome.Thecostofeconomiccapitalistheex-issubjecttoasaresultofoperatingasagoing-pectedreturnorhurdleraterequiredbyinvestorsconcernbusiness(butexcludingthethreeportfolio(and,forreasonsdiscussedearlier,BofAhasriskslistedabove).BofA’scurrentmethodforchosentoapplythesame,corporate-widecostofmeasuringbusinessriskisbasedonaveragecapitali-equitytoallbusinessunits).zationratiosfornon-financialfirmsinretailandThevirtueofeconomicprofitasaperformancewholesaleindustries.Alsonowbeingconsidered,measureisthatitcapturesboththereturngeneratedhowever,arealternativeapproaches(notably,useofbyabusinessandtheamountofeconomiccapitalperformancevolatilitymeasures)forpossibleimple-investedinthebusiness.Useofeconomicprofitismentationbytheendofthisyear.thusdesignedtopromotenotonlygreaterefficiencyinexistingoperations,butalsostrategicinvestmentBusinessUnitCalculationsdecisions—thatis,decisionstoemploymore(orless)capitalinthebusiness—thatareconsistentwithTheriskmeasuresdescribedaboveprovidethemaximizingshareholdervalue.Useofeconomicbasisforassigningcapitaltoeachofthebank’s37profitmightreveal,forexample,thatsomebusi-businessunits.SuchcapitalassignmentsinturnnesseswithveryhighreturnsmaybecontributingallowforperiodiccalculationsofRAROCandeco-lesstoshareholdervaluethanotherbusinesseswithnomicprofit.Everyquarteramanagementbriefinglowerreturnsbutsignificantlymoreinvestedcapital.bookofRAROCandeconomicprofitperformanceAnexclusivefocusonRAROC,aswenotedearlier,isdistributedtoseniormanagement,businessman-islikelytoleadtounderinvestmentinvalue-addingagers,andseniorfinanceofficers.ThisbookshowsprojectsthatbringdowntheoverallRAROC.resultsforthecurrentquarter,aneight-quartertrend,andaprojectionoftheplanfortheentireTHEFUTUREbankandits37businessgroups.ReportsandgraphicsarepresentedthatallowcomparisonsofAsmentionedearlier,theinitialaimoftheRAROC,economicprofit,andcapitalinvestedacrossRAROCprojectwastodevelopaframeworkforallbusinessgroups.attributingcapitaltothebank’s37“firsttier”businessCalculatingRAROC.ThecalculationofRAROCunits.Thisgoalwasaccomplishedbytakingatop-isrelativelysimpleoncealltheriskcalculationshavedownapproach.Thatis,ratherthandevelopingthebeencompleted.RAROCiscomputedbydividingcompleteframeworkforaparticularbusinessunitrisk-adjustednetincomebythetotalamountofandthenmovingontothenext,theinitialeffortcuteconomiccapitalassignedbasedontheriskcalcu-acrosstheentireorganization.lation.ThestartingpointforthenumeratorisBofA’sThisapproachservedtwopurposes.First,ital-managementreportingsystem.Theexistingman-lowedearlytestingoftheframework’sabilitytobeagementreportingsystemallocatesincomeandadaptedtoavarietyofdifferentkindsofportfoliosexpenseitemsdowntotheunitlevel.Thissystemandbusinesses.Second,andperhapsmoreimpor-reportsnotonlydirectrevenuesandexpenses,buttant,thisapproachgreatlyincreasedthelevelofin-alsotransferpricingallocations,chargesforinternalformationaboutandacceptanceoftheconceptwithinservices,andoverheadandtaxallocations.theorganization.InformationabouttheconceptualRisk-adjustednetincomeisthendeterminedbybasisofRAROCwasdisseminatedthroughoutthetakingthefinancialdataallocatedtothebusinessesbankthroughaseriesofmanagementcommunica-andadjustingtheincomestatementforexpectedloss.tions.And,toensurethatthemessagewasbeingAsecondadjustmentisalsorequiredtotakeintoheardandunderstood,thecommunicationeffortconsiderationtheeffectsonthenetinterestmarginofincludedindividualmeetingswithbusinessmanag-thechangeinthecapitalaccountasthefocusisshifteders,formalone-and-a-halfdaytrainingclasses,andfrombookprofitabilitytoeconomicprofitability.specializedsessionstargetedforspecificaudiences.91JOURNALOFAPPLIEDCORPORATEFINANCE AkeyfactorinthesuccessoftheRAROCprojectsystemreportsmonthlyRAROCandeconomicprofittodatewasBofA’smergerwithContinentalBankforcommercialcustomersand,insodoing,allowsin1994.Forseveralyearspriortothemerger,theprofitabilityofcustomerandindustrysegmentsContinentalhadbeenrelyingheavilyonaRAROCtobeanalyzedonaworldwidebasis.systemtomanagetheprofitabilityofitscommercialAnotherareaslatedforpossibleimplementa-lendingbusinessand,asaconsequence,RAROCtionofRAROCisincentivecompensation.Whileawasalreadywellintegratedintoitscultureandfinaldecisionhasnotbeenmade,BankofAmericamanagementpractices.AndRAROC’seffectivenessisexploringtyingincentivebonusesfarmoredirectlyatContinentalstronglyinfluencedthepushforatoeconomicprofitperformance.similarsystematBankofAmericaandaccelerateditsInsum,theRAROCperformancemeasurementadoptionasakeydecisiontool.systemhasbecomeakeydecision-makingtoolatOverthelongerterm,thegoaloftheRAROCBankofAmerica.WithaRAROCprocessinplace,projectatBofAistosupportandpromotetheuseseniormanagementcanevaluatethebankasaofRAROCinbusinessdecisionsatalllevelsoftheportfolioofbusinessesandmakeresourceallocationorganization.Althoughmeasurementoforganiza-decisionsthatimprovethebank’srisk/rewardpro-tionalprofitabilityisclearlyimportant,itiscriticalfile.Atthelevelofthebusinessunitsandbelow,thethattheRAROCframeworkalsobeappliedtonewperformancemeasurementsystemholdsoutevaluatetheprofitabilityofcustomersegments,moreaccountabilityandstrongerincentivestomaxi-productcategories,portfoliomanagementinitia-mizeshareholdervalue.Indeed,whenproperlytives,andindividualtransactions.Asoneindicationappliedandimplementedthroughouttheorganiza-ofsuccessinthiseffort,RAROCmeasuresarenowtion,RAROCanditscompanionmeasureeconomicincludedincustomerprofitabilityanalysisforwhole-profithavethepowertobuildandsustainavalue-salebankingrelationships.Aglobalprofitabilitybasedcorporateculture.EDWARDZAIKGABRIELAKELLINGisSeniorVicePresidentandheadoftheRiskandCapitalAnalysisisFinancialConsultantintheRiskandCapitalAnalysisGroupGroupatBankofAmerica.atBankofAmerica.JOHNWALTERCHRISTOPHERJAMESisVicePresidentintheRiskandCapitalAnalysisGroupatBankistheWilliamH.Dial/SunBankProfessorofFinanceattheofAmerica.UniversityofFlorida.92VOLUME9NUMBER2SUMMER1996 APPENDIXMEASURINGCREDITRISKThemeasurementofcreditriskrequireseconomiclossesassociatedwiththedefaultevent.estimatesofexpectedloss,unexpectedloss,andTheytakeintoconsiderationthetimingandfinallyunexpectedlosscontribution.Thecapitalpresentvaluesofrecoverystreamsaswellastheleveliscalculatedbasedontheunexpectedlosslegalcostsandcostofcarryondefaultedcredits.contributionandthecoverageleveldesired.Ingeneralterms,severityisafunctionofcollateral,Thefirststepistocalculateexpectedloss,theseniority,andotherstructuralfactors.Estimatesofaveragelossesanticipatedfromagivencreditseverityrateshavebeendrawnfromhistoricalexposuremeasuredonaperannumbasis.Forexperience.Theyaredifferentiatedforthemajorindividualcredits,expectedlossismodelledandcollateralclasses,suchasaccountsreceivable,computedastheproductofthreevariables—inventory,cash,securities,equipment,realestatedefaultprobability,loanequivalencyexposure,andunsecured.andseverity.Algebraically,theformulaissimple:UnexpectedcreditlossesareestimatedbycalculatingthedeviationoflossesfromtheirExpectedLoss=DefaultProbability×Exposure×Severitymean.Thestandarddeviationoflosseswilldeter-minetheamountofcapitalthatwouldberequiredDefaultprobabilityisthemoststraightfor-onastand-alonebasis.wardofthethreecomponents.ItistheprobabilityUnexpectedlossesarederivedusingthethatacustomerwilldefaultonitsobligationswithinstandarddeviationformulaforbinomialevents,thenextyear.Defaultratesaresetforaoneyearwiththedefaultrateastherandombinomialhorizon;however,forveryshort-termcredits,thevariable.Everyloancanbethoughtofasarandomdefaultratesareadjusteddownwardstoreflectthebinomialvariable—eithertheborrowerdefaultslowerrisk.Forcommercialfacilities,thedefaultordoesnotdefault.Besidesthedefaultrate,otherrateistiedtothecustomer’sinternalcreditrating,variablesintheunexpectedlosscalculationin-whileforconsumerportfoliositistiedtothecreditcludeexposure,severity,andthevolatilityofscoreordelinquencybucket.Thesedefaultratesseverity.havebeenestimatedfromstatisticalanalysisoftheUltimately,unexpectedlosscontributionde-Bank’slossexperience.terminesthelevelofattributedeconomiccapital.Theloanequivalentexposureforeachfacil-Aspreviouslystated,BofAassignscapitalbasedityistheexpectedoutstandingbalanceiftheonthecontributionbythatloanorbusinesstothefacilitydefaults.TheaverageutilizationratesonBank’soverallunexpectedloss.defaultedcreditstendtobemuchhigherthantheUnexpectedlosscontributiontakesintonorm.Onanintuitivelevel,fewbusinessesdefaultconsiderationthecorrelationofthecreditwiththewithoutfirstdrawingonavailablecreditlinestooverallportfolio,aswellasthesizeofthecreditmeetincreasingcashneeds.Theconceptofloaninrelationtotheportfolio.Anindividualloancanequivalencyisalsousedtoderiveexposurebeveryriskyonastand-alonebasis,butitsfactorsforoff-balance-sheetassets,suchasstandbyadditiontoaportfoliocanreducetheaggregateandcommerciallettersofcreditandswapsandriskifthecorrelationoflossesbetweentheloanderivatives.ThefactorsusedatBofAarefunc-andtherestoftheportfolioislessthanone.tionsofboththeinstrumenttypeandtheinternalCorrelationfactorsfocusonwhetherthecreditratingoftheborrower.facilityisdomesticorforeign,andtheindustrySeverityistheconsequenceofdefault.Itisanclass.Furtherdevelopmentsofthecorrelationestimateoftheaveragelossesincurredonafactorswillbemadetoincludeageographicdefaultedloanexpressedasapercentofthevariable.Amultipleisappliedtotheunexpectedoutstandingbalanceatthetimeofdefault.Thelosscontributiontodeterminethelevelofeco-severityestimatesareintendedtocaptureallnomiccapitalthatwillprovidea99.97%coverage.93JOURNALOFAPPLIEDCORPORATEFINANCE 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