A Guide to Choosing Absolute Bank Capital Requirem

AguidetochoosingabsolutebankcapitalrequirementsMarkCarey*FederalReserveBoard,MailStop19,20551Washington,DC,USAAbstractResamplingimplementationofastress-scenarioapproachtoestimatingportfoliodefaultlossdistributionsisproposedasthebasisforestimatesoftheappropriateabsolutelevelofeco-nomiccapitalallocationsforportfoliocreditrisk.Estimatesarepresentedforstressscenariosofvaryingseverityandimplicationsofdifferenttimehorizonsareanalyzed.Resultsforanum-eraireportfolioarequitesensitivetosuchvariations.Althoughtheanalysisisframedintermsofrecentproposalstoreviseregulatorycapitalrequirementsforbanks,theargumentsandre-sultsarealsorelevantforbankersmakingcapitalstructuredecisions.PublishedbyElsevierScienceB.V.JELclassification:G11;G28;G10;G20Keywords:Riskmanagement;Creditrisk;Bankregulation;Capitalrequirements1.IntroductionTheinternalratings-based(IRB)approachrecentlyproposedbytheBaselCom-mitteeonBankingSupervision(BCBS)seekstomakebankregulatorycapitalrequirementsforcreditriskapproximateeconomiccapitalrequirements(BaselCom-mitteeonBankingSupervision,2001).Thatis,undercertainassumptions(Gordy,2000b),IRBcapitalrequirementswouldvaryacrossbanksaccordingtotheriskinessoftheirportfoliosinamannerthatwouldmaketheestimatedlikelihoodofinsol-vencyduetocreditlossesapproximatelythesameforallbanksthatareatthereg-ulatoryminimum.Requiredcapitalwouldbelargerforbankswithportfoliosposinggreaterrisksoflargelossesandviceversa.JournalofBanking&Finance26(2002)929–951*Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](M.Carey).0378-4266/02/$-seefrontmatterPublishedbyElsevierScienceB.V.PII:S0378-4266(02)00210-8TheIRBcapitalformulaforcreditrisktakesasinputsloanandportfoliocharac-teristicsandproducescapitalrequirements.Designingsuchaformulainvolvesdeci-sionsabout(1)thedimensionsofcreditrisktobeincluded,thatis,whichloanandportfoliocharacteristicsshouldappearasvariablesintheformula;(2)therelativevariationsincapitalrequirementsasloanandportfoliocharacteristicsvaryfromthoseofareferenceornumeraireloanorportfolio;and(3)theabsolutelevelofcap-italrequiredforthenumeraireportfolio.Carey(2001)examinesthedimensionsofcreditriskandBaselCommitteeonBankingSupervision(2001)examinesissuesofrelativevariation.Thispaperfocusesontheabsolutelevelofcapitalforcreditrisk.Takingthenum-erairetobeaportfoliooffullydrawnloanseachwithaone-yearprobabilityofde-fault(PD)of1%,alossgivendefault(LGD)of50%,andaremainingtimetomaturityofthreeyears,theBaselCommitteeonBankingSupervision(2001)pro-posalsuggeststhattheabsolutedollaramountofcapitalrequiredforsuchaportfo-lioshouldbe10%oftheamountoftheloan.BaselCommitteeonBankingSupervision(2001)isnotclearaboutthebasisforthiscalibration,buttwomethodsofcalibrationhavebeensuggestedbyvariousobservers,abottom-upandatop-downmethod.Inthebottom-upmethod,aneconomicanalysisoftherelationshipbetweenportfolioriskandPDs,LGDs,etc.isconducted.Debatefocusesontheas-sumptionsoftheanalysisandonthechoiceofaportfoliocreditlossdistributionper-centile.Inthetop-downmethod,policymakersmakeajudgmentalchoiceofatargetcapitalratioforthebankingsystemasawhole.Giventhecharacteristicsofbankportfolios,theparametersoftheIRBformulaarecalibratedtohitthesystemictar-get.Unfortunately,resultsofthetop-downmethodcanbedifficulttorelatetobasicpolicyobjectives,suchaslikelybankinsolvencyrates.Adrawbackofextantbottom-upanalysesisthatvalidityofmanyofthesupport-ingassumptionsisdifficulttoassess.Mostimportantly,assumptionsaboutthesen-sitivityofcreditlossestosystematicriskfactorsarehardtoevaluatebecausesuchsensitivitiesusuallycannotbeestimatedwithconfidence.Suchassumptionscanhaveamajorimpactonestimatesofabsolutecapitalrequirementsproducedbyconven-tionalcreditvalueatrisk(VaR)models.Thispaperpresentsabottom-upanalysisoftheappropriateabsolutelevelofcapitalinwhichkeyassumptionsarerelativelytransparentandeasytorelatetotheobjectivesofbankregulatorsandbankmanagers.Thepapermakesthreecontri-butions.First,portfoliocreditlossdistributionsareestimatedusinganon-paramet-ric,stress-scenarioapproach(seeKupiec(1998)andShepheard-WalwynandRohner(2000)forotherstress-scenarioapproachesandJorion(2001)forageneraldiscus-sionofstresstesting).Frequencydistributionsoflossratesarecomputedbysimulat-inglossesonalargenumberofportfolios.LossratesforeachsimulatedportfolioarecomputedbysamplingwithreplacementfrompopulationsbasedonparticularyearsofMoody’sdatabaseofdefaultingandnon-defaultingbondissuers,withrealisticallyrandomloansizesandLGDs.IfloansizesandLGDswerefixedinsteadofrandom,theestimatedportfoliolossdistributionswouldapproximatetransformedbinomialdistributionsinwhichanag-gregateannualborrowerdefaultrateisthekeyparameter,soIdescribethispaper’s930M.Carey/JournalofBanking&Finance26(2002)929–951approachasinvolvingmodifiedbinomiallossdistributions.Becauseaggregatede-faultratescanberelatedtotheseverityofeconomicdownturnsand(inthispaper’ssetup)lossdistributionpercentilesrepresentbanksurvivalrates,policymakersmaysetcapitaltolimitbankfailurestosomeacceptableestimatedrateinaneconomicscenarioof