金融时间序列分析2030192236

JournalofFinancialIntermediation15(2006)362–394fiAnanalysisofVaR-basedcapitalrequirementsDomenicoCuocoa,∗,HongLiubaFinanceDepartment,TheWhartonSchool,UniversityofPennsylvania,3620LocustWalk,Philadelphia,PA19104-6367bJohnM.OlinSchoolofBusiness,WashingtonUniversityinSt.Louis,St.Louis,MO63130Received25May2005Availableonline1December2005AbstractWestudythebehaviorofafinancialinstitutionsubjecttocapitalrequirementsbasedonself-reportedVaRmeasures,asintheBaselCommittee’sInternalModelsApproach.Weviewthesecapitalrequirementsandtheassociatedbacktestingprocedureasamechanismdesignedtoinducefinancialinstitutionstorevealtheriskoftheirinvestmentsandtosupportthisriskwithadequatelevelsofcapital.Accordingly,weconsiderthesimultaneouschoiceofanoptimaldynamicreportingandinvestmentstrategy.Overall,wefindthatVaR-basedcapitalrequirementscanbeveryeffectivenotonlyincurbingportfolioriskbutalsoininducingrevelationofthisrisk.©2005PublishedbyElsevierInc.JELclassification:D91;D92;G11;C61Keywords:Bankingregulation;Capitalrequirements;BaselCapitalAccord;InternalModelsApproach;Value-at-Risk;Portfolioconstraints1.IntroductionFinancialinstitutionsarerequiredbyregulatorstomaintainminimumlevelsofcapital.Thisregulationisnormallyjustifiedasaresponsetothenegativeexternalitiesarisingfrom*Correspondingauthor.Fax:[phone].E-mailaddresses:[e-mail](D.Cuoco),[e-mail](H.Liu).1042-9573/$–seefrontmatter©2005PublishedbyElsevierInc.doi:10.1016/j.jfi.2005.07.001D.Cuoco,H.Liu/JournalofFinancialIntermediation15(2006)362–394363bankfailuresandtotherisk-shiftingincentivescreatedbydepositinsurance.1The1988BaselCapitalAccordimposeduniformcapitalrequirementsbasedonrisk-adjustedassets,definedasthesumofassetpositionsmultipliedbyasset-specificriskweights.Theseriskweightswereintendedtoreflectprimarilytheasset’screditrisk.2In1996theAccordwasamendedtoincludeadditionalminimumcapitalreservestocovermarketrisk,definedastheriskarisingfrommovementsinthemarketpricesoftradingpositions(BaselCommitteeonBankingSupervision,1996a).The1996Amendment’sInternalModelsApproach(IMA)determinescapitalrequire-mentsonthebasisoftheoutputofthefinancialinstitutions’internalriskmeasurementsystems.FinancialinstitutionsarerequiredtoreportdailytheirValue-at-Risk(VaR)atthe99%confidenceleveloveraone-dayhorizonandoveratwo-weekhorizon(tentradingdays).3Theminimumcapitalrequirementonagivendayisthenequaltothesumofachargetocover“creditrisk”(oridiosyncraticrisk)andachargetocover“generalmarketrisk,”wherethecredit-riskchargeisequalto8%ofrisk-adjustedassetsandthemarket-riskchargeisequaltoamultipleoftheaveragereportedtwo-weekVaRsinthelast60tradingdays.4US-regulatedbanksandOTCderivativesdealersaresubjecttocapitalrequirementsdeterminedonthebasisoftheIMA.Therelianceonthefinancialinstitution’sself-reportedVaRstodeterminecapitalre-quirementscreatesanadverseselectionproblem,sincetheinstitutionhasanincentivetounderreportitstrueVaRinordertoreducecapitalrequirements.TheproceduresuggestedbytheBaselCommitteetoaddressthisproblemrelieson“backtesting”(BaselCommitteeonBankingSupervision,1996c):regulatorsshouldevaluateonaquarterlybasisthefre-quencyof“exceptions”(thatis,thefrequencyofdailylossesexceedingthereportedVaRs)inthemostrecenttwelve-monthperiodandthemultiplicativefactorusedtodeterminethemarketriskchargeshouldbeincreased(accordingtoagivenscalevaryingbetween3and4)ifthefrequencyofexceptionsishigh.5Additionalcorrectiveactionsinresponsetoahigh1SeeBergeretal.(1995),FreixasandSantomero(2002)orSantos(2002)forareviewofthetheoreticaljustificationsforbankcapitalrequirements.2Gordy(2003)showshowthecreditriskweightsmightbedeterminedinthecontextofasingle-factorcreditriskmodel.3Simplystated,VaRisthemaximumlossofatradingportfoliooveragivenhorizon,atagivenconfidencelevel(i.e.,aquantileoftheprojectedprofit/lossdistributionatthegivenhorizon).Toavoidaduplicationofrisk-measurementsystems,financialinstitutionsareallowedtoderivetheirtwo-weekVaRmeasurebyscalingupthedailyVaRbythesquarerootoften(see:BaselCommitteeonBankingSupervision,1996b,p.4).4Moreprecisely,themarket-riskchargeisequaltothelargerof:(i)theaveragereportedtwo-weekVaRsinthelast60tradingdaystimesamultiplicativefactorand(ii)thelast-reportedtwo-weekVaR.However,sincethemultiplicativefactorisnotlessthan3(seebelow),theaverageofthereportedVaRsinthelast60tradingdaystimesthefactortypicallyexceedsthelast-reportedVaR.5ThereasonbacktestingisbasedonadailyVaRmeasureinspiteofthefactthatthemarketriskchargeisbasedonatwo-weekVaRmeasureisthatVaRmeasuresaretypicallycomputedignoringportfoliorevisionsovertheVaRhorizon.AccordingtotheBaselCommittee,“itisoftenarguedthatvalue-at-riskmeasurescannotbecomparedagainstactualtradingoutcomes,sincetheactualoutcomeswillinevitablybe‘contaminated’bychangesinportfoliocompositionduringtheholdingperiod.[...]Thisargumentispersuasivewithregardtotheuseofvalue-at-riskmeasuresbasedonpriceshockscalibratedtolongerholdingperiods.Thatis,comparingtheten-day,99thpercentileriskmeasuresfromtheinternalmodelscapitalrequirementwithactualten-daytradingoutcomes