欧洲央行-缓冲风险：通过压力测试设定周期性和结构性银行资本要求（英）

EUROPEANCENTRALBANKEUROSYSTEMCyrilCouaillier,ValerioScaloneRisk-tobuffer:settingcyclicalandstructuralbankscapitalrequirementsthroughstresstestsDisclaimer:ThispapershouldnotbereportedasrepresentingtheviewsoftheEuropeanCentralBank(ECB).TheviewsexpressedarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheECB.AbstractInthispaper,weproposeanewframeworktojointlycalibratecyclicalandstructuralcapitalrequirements.Forthis,weintegrateanon-linearmacroeconomicmodelandastresstestmodel.Inthemacroeconomicmodel,theseverityofthescenariosofcyclicalrisk.Risk-relatedscenariosareusedasinputsforthestresstestmodel.Banks’structuralrequirement.Additionallossesassociatedwiththecurrentriskscenarioareusedtosetthecyclicalrequirement.Thisapproachprovidesatransparentmethodtostrikethebalancebetweencyclicalandstructuralrequirements.Keywords:Financialvulnerability,macroprudentialpolicy,non-linearmodels,capitalrequire-Non-TechnicalSummaryAftertheGlobalFinancialCrisis,theBaselIIIregulationsubstantiallyraisedbankcapitalrequirementsandintroducedadistinctionbetweenstructuralandcyclicalrequirements.Struc-turalrequirementsaimatmakingbanksmoreresilienttorisksrelatedtostructuralfeaturesofthebankingsystem(interconnection,designoftherealestatemarket,etc.).Cyclicalrequire-bothtypesofrequirements.Thecomputingbankcapitallossesunderthisscenarioand(iii)calibratingcapitalrequirementstocoverthosepotentiallosses.However,ifcyclicalandstructuralrequirementsarecalibratedusingparallelstresstestsbasedonsimilarscenarios,diferentrequiremensametypeofvulnerability,resultinginadoublecountingofriskincapitalrequirements.Forinstance,anadversescenariousedforstructurleadtooverlapswithcyclicalrequirements.ConverseToclarifyhowtojointlysetcyclicalandstructuralrequirementsviaStresstest,thepaperintroducesaconceptualframeworkcalled”Risk-to-Bufer”.Thisframeworkleveragesanon-establishadirectlinkbetweenthecyclicalrisklevelandthecalibratedcyclicalrequirement.Astructuralrequirementcanbecalibratedwithrespecttoastandardrisklevel(”referencerisk”).Acyclicalrequirementisthencalibratedwithrespecttothetothecurrentcyclicalrisk.Overall,whosedynamicsareamplifiedwiththelevelofcyclicalrisks;scenarioisusedtosetthecurrentcyclicalriskscenariodeterminethecyclicalrequirement.Thepaperalsopresentsapracticalillustrationofthisframeworkusingaamultivariatenon-linearratio(thereafterDSR)ofnon-financialprivatesectorisusedasameasureofcyclicalrisk.Theisameasureoffinancialvulnerability.Estimationsshowthattheresponsetohousingandoutputshocksareamplifiedunderhighcyclicalrisks.First,wesimulatethesetwoshockstobuildtherisk-relatedadversescenarios.Second,inordertoprojectblossesunderthediferentscenarios,thecyclicalandstructuralrequirementsaccordingtotheprojectedcapitallosses.Inthisway,wecancalibrateastructuralrequirementandcyclicalrequirementsforthediferentphasesofthefinancialcycle(e.g.medianrisk,highrisk).Overall,theproposedRisk-to-Buferframeworkaimsatprovidingaformalmechanismtolinkthelevelofcyclicalrisktothecalibrationofthecyclicalrequirementthroughstresstests,therebyreducingtheriskofdoublecountingandenhancingtheefectivenessandtransparencyofcapitalregulationinthebankingsector.TheRisk-to-Bufercanbeusedtocalibratebothmicroandmacro-prudentialrequirements.Also,theframeworkprovidesatransparentmethodtostrikethebalancebetweencyclicalandstructuralrequirements:itdirectlydependsonthelevelofcyclicalriskpolicymakersuseasareferencetosetthestrreferencelevelofcyclicalrisk,thelowerthestructuralrequirementandthehighertheroleofthecyclicalrequirements.Finally,thisapproachcanprovideausefulframeworkforthediscussionovera”neutral”cycli-calrequirement,byprovidingaclearmeasureofthebalancebetweenstructural1IntroductionSincetheglobalfinancialcrisis,prudentialauthoritieshavesubstantiallyreformedthecapitalregulationframeworkforbanks.Anewsetofrules,labelledtheBaselIIIframework,havebeenintroducedtostrengthenbanksresilienceagainstrisk.1Tothisextent,oneofthenoveltiesofBaselIIIconsistedinintroducingadistinctionbetween:i)cyclicalrequirementsthatevolvewiththefinancialcycleandensurebanksresilienceagainstrisksrelatedtotheevolutionconditions,ii)structuralrequirementsremainingconstantthroughthecycleandcoverrelatedtothestructureofthebankingsystem.2Stresstestmodelsarekeyanalyticaltoolsusedstructuralrequirements.Throughasetofeconometricandaccountingequations,thesemod-aformalframeworktomapprojectedcapitallossesintocyclicalandstructuralrequirementsismissing.Besides,ifcyclicalandstructuralrequirementsarecalibratedusingparallelstresstestofvulnerability,resultinginadoublecountingofriskinsettingcapitalrequirements.3Lackof1TheBaselCommitteeonBankingSupervision(BCBS)hasagreedonasetofreformsconcerningrequirementsforbanks.2Cyclicalrequirementsaremeanttoensureresilienceincaseofmaterialisationoftheso-calledcyclicalrisks:e.g.over-indebtednessofprivateagentscausingmassivedeleveragingepisodesorover-evaluationofassetpricestriggeringsubstantialdownwardcorrectionofassetprices.ThemainexampleisrepresentedbytheCounter-CyclicalBufer(CCyB),thatisquarterlysetbythemacroprudentialauthoritiesinacounter-cyclicalfashion.Thisrequirementincreasesduringtheupwardphaseofthefinancialcyclewhencyclicalrisksaccumulate,anddecreaseswhenrisksmaterialise,sothatbanksarelessconstrainedintheircreditsupplyandcansupportcreditinthedescendingphaseofthefinancialcycle.Besides,highercapitalratiolevelsallowbankstoabsorblosses,withoutenforcinggeneraldeleveraging.Structuralrequirementscoverinsteadrisksthatdonotevolvewiththefinancialcycle.Theserequirementsensureresilienceofbanksinperiodsofeconomicdistress,buttheydonotcoverlossesderivingfromthefinancialcycleevolution.Theserequirementsaresetaccordingtobanks’structurallong-termfeaturesandwithalowerfrequencywithrespecttothecyclicalrequirements.First,somerequirementscoverrisksconcerningidiosyncraticbanks’features,i.e.microprudentialstructuralrequirements.ExamplesofthoserequirementsaretheP2GandP2Rrequirements,setbytheSingleSupervisoryMechanism(SSM)atEuropeanlevel.Theserequirementsarecalibratedconsideringtheindividualcharacteristicsofbanks(e.g.businessmodel,internalgovernance).Macroprudentialstructuralrequirementsaresetconsideringthestructuralfeaturesofthebankingsystemasawhole,assuchastheCapitalConservationBuferandtheG-SIBbufersrequirements.Theircalibrationdoesnotevolveaccordingtheevolutionofthefinancialcyclenoritisperformedwithquarterlyfrequency,oppositetothecaseforcyclicalbufers.3Ononehand,stresstestsareusedforthecalibrationofstructuralrequirements,asP2GsetbytheECBonthebasisoftheresultsoftheEuropeanBankingAuthority(EBA)Banksstresstests.Ontheotherhand,stresstestscanalsobeusedforthecalibrationofthecountercyclicalbufers(CCyB)atnationallevel.4Tothisextent,policymakershaveidentifiedtheneedtodesignframeworkstosetdiferentrequirementsviastresstests.First,BankofEnglandclarifiedtheuseofstresstestlossestocalibratetheCounter-cyclicalThe”Risk-to-Bufer”conceptualframeworkInthefirstpartofthispaper,wepresentanewconceptualframework,theRisk-to-Bufer,tojointlycalibratecyclicalandstructuralseveritydependsonthelevelofcyclicalrisk.Thankstothemodel,weobtaina”reference”-onthecurrentlevelofthecyclicalrisk.Viathestresstestmodethereference-riskscenario.Thecyclicalrequirementiscalibratedbasedonthe(additional)cyclicalrisklosses.Inthisfashion,structuralandcyclicalrequirementscoverdiferenttypesofvulnerabilities,addressingtheriskofdouble-counting.Ourapproachisarticulatedinthreesteps.fshockshitstheeconomyunderdiferentrislevelofcyclicalrisk(e.g.minimumrisk,medianrisk)tocapturedynamicsunderastandardriskenvironment,andasecondscenarioisproducedatthecamplificationroleplayedbythecurrentcyclicalrisk.correspondingcapitalratioprojections.HigherriskscenariosareassociatedwithlargercapitalThird,theprojectedlossesareusedtocalibrriskscenarioisusedtosetthestructuralrequirement,whereastheadditionthecurrentcyclicalriskscenariosetsthecyclicalrequirement.Assuch,thislatterevolveswiththelevelofcyclicalrisk.Shouldthecurrentrisklevelbelowerthanthe”reference”risk(e.g.theoneusedtocalibratethestructuralrequirement),thecyclicalrequirementwouldbesettozero.Inthisway,thesumofbothrequirementswouldnotfallbelowthestructuralrequirement,whichactsasabackstopforcapitalrequirements.Importantly,thechoiceofthe”referencerisk”leveldirectlyafectsthelevelofthestructuralrequirementandinturnofthecyclicalrequirement: thehigherthereferencerisk,thehigherthestructuralrequirementandthelowerthespacetaken BuferandthePRAbuferinthePolicyStatement—PS15/20,Pillar2A:Reconcilingcapitalrequirementsandmacroprudentialbufers,July2020.Second,USFedclarifiedtheuseofthestressCapitalBufer(SCB),asabufersetbasedonthestresstestslossesandintegratingthepreviousCapitalConservationBufer,whichactsasa丑oorinsettingthenewSCB,setto2.5%atitsminimumlevel,seetheFinalrule.bythecyclicalrequirement.Assuch,theRisk-to-BuferframeworkofersatransparentwayforApplicationoftheconceptualframeworkInthesecondpartofthepaperweprovideapracticalillustrationofourframework.ThismodelisaMultivariateSmoothTransitionregimeswitchingmodel(Aueandhousingpricesfortheeuroarea.6ThankstoitsmultivariatestructureandtoaCholeskiisameasureofcyclicsectors(henceforthNFPS),i.e.firmsandhouseholds.Thisratioiscomputedasthefractionofincomethatagentsusetorepaytheirdebt(Drehmannetal.(2015)).TheDSRcapturestheineachyearofourprojectitheseverityoftheGDPdownturnconsideredinthe2018EBAstresstest,i.e.-7.8percentagerisklevelsandfindthattheimpactoftheadverseshockssubstantoftheDSR,i.e.withthecyclicalrisk.fromregressionestimatedontheresultsoftheEuropeanBankingAuthority(EBA)2018Banks5Spreadbetween10yearsinterestrateandshorttermrate6AsimilarmodelestimatedontheUSisusedinCouaillierandScalone(2020)toestimatethehowfinancialvulnerabilityafectsthepropagationofhousingandcreditshocks.7Forthesakeofsimplicity,inthisworkwefocusonauniquemeasureofcyclicalrisks,butothermeasuresofthecyclicalriskscouldbeusedasstatevariablevariable,assuchasCredit-to-GDPgap(Borioetal.(2014))orcreditgrowth.Inrobustnessexercises,wefindthatthistypeofamplificationistherealsowhenalternativeriskmeasuresareused.Forrobustness,diferentscenarioscouldbegeneratedbyusingdiferentcyclicalriskmeasures.averageCET1ratioofthebankingsystemaGDP).9WefindthatunderhighrisktheaggregatereductionofCET1withrespecttothethan6timeslargerthanundertheLowRisk(0.6pp).Undermediumrisk,theCET1ratiothestructuralrequirementissetequaltothelossobtainedwiththeDSRatitshistoricalmini-mum(0.6%).Whenthecurrentriskisatitsmaximum(median)level,thecyclicalrequirementissetto3.2%(1.2%).Shouldpolicymakersusethemedianhistoricalriskasthereferencelevelofrequirementwouldbeequalto1.8%.Inthmaximum,thecyclicalmaximumriskscenario.InthefirstcalibrationapproachtherelativeimportanceofcyclicalrequireLiteratureWejointwostreamsofliterature.First,bankingmodelsandstresstestmodelsBudniketal.(2019);Camaraetal.(2015);Co伍netandLin(2010);DeesandHenry(2017);ricequationslinki8TheCoreEquityTier1,orCET1,isthepurestformofbankcapital,typicallycomposedofcommonequityandretainedearnings,andtheoneonwhichstructuralandcyclicalbufersapply.9Inthiswork,weadoptamacroprudentialperspective,focusingonthesystemicdimension,i.e.settinghomogeneouscapitalrequirementsacrossbanks.Indoingso,wesetcapitalrequirementswithrespecttotheaveragebanks’losses,obtainedinastresstestmodelthatdoesnottakeintoaccounthowidiosyncraticfeaturesofbanksafectbanks’balancesheetdynamics.Thesameapproachcouldbeappliedtostresstestexerciseswhereidiosyncraticcharacteristicsofbanks(i.e.size,businessmodels)afectingcapitalratiodynamics,producingheterogeneousefectsacrossbanks(Hirtleetal.(2016)).andlosses.Inourpaperweindirectlyinferthisrelationbyusingpseudo-data(simulationsfromtheEBAstresstestmodels).Jointlywithanon-linearmacro-economicmodel,thisreduced-fromstresstestcanbeusedtoprojecttheaveragebankscapitalshortfallunderdiferentrisk-relatedmacroeconomicscenarios,withthefinalgoaltosetcyclicalandstructuralrequirements.Second,non-linearmacromodelsareestimatedtoassessonthepropagationofeconomicshocks(Aikmanetal.(2020);AlpandaandZubairy(2019);BarnichonandMatthes(2016);Barnichonetal.(2016);Carrieroetal.(2018);ChengandChiu(2020);CouaillierandScalone(2020)).Inourwork,wedetectnon-linearamplificationofrealandfinancialshocksfortheeuroarea,forwhichwefindresultsoveraeconomictheory(GuerrieriandIacoviello(2017);KiyotakiandMoore(1997)).TheuseofparallelscenariosisalsoconsideredinParlatoreandPhilipaframeworktostudytheoptimaldesignofthestresstesresilienceandprovideadviceonthebestpolicy.Inourwolinearmacroeconomicmodel.Thisapproachallowstomapeachriskleveltoadiferentcapitalwork.InSection3,wepresenttheillustrativemacroeconomicmodelandwereporttheestimatedresults.Section4housestheapplicationofourmodelforcalibratingrequirements.Section52TheRisk-to-BuferframeworkInthissectionweintroducetheconceptualframework.Thisframeworkmapstherisklevelstotheirrequirements,generatingaformallinkbetween:i)areferencerisklevelandthestructuralrequirement;ii)ahighercyclicalriskandthecyclicalrequirement.First,weshowthelogicbehindtheuseofstresstestsinsettingcapitalrequirements,highlightingthepossibleoverlapsbetweendiferentrequirementswhenparallelstresstestsarerun.Second,wepresewepresenthowthedifertocapitalrequirements.2.1Stresstestinrequirementcalibrationbanks’balancesheetvariables(e.g.capitalratios,banks’profits)conditionalontheevolutionCapitali;t=g(Macrot),(1)whereCapitali;tisthecapitalratioofbankiattimet,Macrotaretheprojectionofmacroeco-MacroeconomicvariablesMacrotaregeneratedthroughamacroeconomicmodelg()producingMacrot=f(Shockst).(2)goalofthepolicymakerifadversescenariomaterialisation,theprojectedcapitallossesCapitali;tcanbeusedtocalibratecapitalrequirementsBuffersi;t:Buffersi;t=h(Capitali;t).(3)banks(Buffersi;t=Bufferst)andissetequaltotheaveragebanks’finalcapitallosswithrespecttothestartingpointoftheprojection.11 Bufferst=h(g(f(Shockst))).(4)10Thosescenariosusuallymimicstrongdownturns,e.g.theglobalfinancialcrisis(GFC)ortheEuro-AreaSovereigndebtcrisis.11Alternativemappingfunctionscouldbeconsidered,e.g.computingshortfallswithrespecttosomeexogenousfixedlevels.Thisstandardapproach,widelyusedinpolicy-making,mayraisekeyissues.First,thestackrequirementscancalibratedbydiferentinstitutio2.2Generatingscenariosrelatedtothelevelofriskfadversescenariosacrossdiferentlevelsofrisk(e.g.lowrisk,mediumrisk,highrisk):Macro=f(shockst,CycRiskt)(5)whereCycRisktisthestatevariablemeasuringthelevelofcyclicalriskandtheshockstistheshocks,inlinewiththetheoreticalliteratureonthefinancialaccelerator(Bernankeetal.(1996);KiyotakiandMoore(1997))andtheempiricalliteratureonsuchamplifications(Aikmanetal.(2020);Carrieroetal.(2018);Jord、2.3Acapitallossforeachrisklevelcapitalratiosprojections(capital,sk)andmapthemintocapitalrequirements.Theleftpanel12Forexample,somerequirementsarefixedatinternationallevel(e.g.CapitalConservationbufer),otherrequirementsarefixedatnationallevels(Counter-cyclicalbufers).Besidesmicroprudentialrequirementsaretypicallysetbythemicroprudentialsupervisoratthebank’slevel,whereasthemacroprudentialrequirementsapplytoawholebankingsystemandaresetbytheregulator.13Astudyonhowtochooseshocksisbeyondthescopeofourwork.Inpractice,shocksareselectedinlightofriskanalysis.Figure1:IllustrationofthemethodologyNote:Themethodologyisbasedontheuseofmultiplescenariosgeneratedwiththesamesetofshocksindiferentstatesoftheeconomy.Dynamicsarestatedependent:thelowrisk(blue),themedianrisk(yellow)andthehighrisk(red)scenarioshavediferentseverity.Strongerseverityscenarioswillcauselargercapitallosses.Thestructuralandcyclicalrequirementsarethensetwithrespecttothosescenarios.First,dependingontheirpreferences,policymakerssetthestructuralrequirementtocoverthelossesunderthe”reference”riskscenario,e.g.theminimumrisklevel(righthandsidebar)orthemedianrisklevel(lefthandsidebar).Second,thecyclicalrequirementissettocovertheadditionallossesrelatedtothecurrentrisklevel.atedusingthehistoricalminimum,medianandmaximumofthestatevariable.Higherriskis2.4FromcapitallossestorequirementsstructuralrequirementisseBuffers=h(g(f(Shockst,ReferenceRisk).(6)Thecyclicalrequirementsissettothelevelofadditionallossesgeneratedunderthecurrentrisk-h(g(f(Shockst,ReferenceRisk).(7)Whenthecurrentcyclicalriskevolves,thecyclicalrequirementchangesinlinewiththelevelofcyclicalrisk.Ifthecurrentriskgoesbelowthereferencelevel,thecyclicalrequirementwillbesettozero.Conversely,ifthecurrentlevelattainsitshistoricalmaximum,thecyclicalriskrequirementwillbeequaltotheadditionalshortfallsgeneratedunderthemostseveweconsidertwoalternativesettings(rightpanelofFigure1).Inonesetting,thepolicymakerchoosestheminimumriskasthereferencerithelossesderivingfromtheriskamplificationbyusingthecyclicalrequirement(theredpartintherightbarofFigure1,whereasthestructuralrequirement(thebluepart)wouldbeequaltothelossunderthelowriskscenario.Inthiscase,underthemediumrisk(akintoa”neutral”stateoftheeconomy),thecyclicalrequirementispositive,e.g.inthiscasethe”neutral”cyclicalrequirementispositive.14undermediumriskarecoveredbythestructuralrequirement.Accordingtothissetting,thecyclicalrequirementcoversonlytheaUnderthefirstsetting,thecyclicalcomponentofthetotalrequirementspaceismorerele-vant.Inthissetting,authoritieshavemorefire-powertocounter-actthenegativeefectsofriskmaterialisationbyreleasingahigherlevelofcyclicalrequirement.Thenexttwosectionsprovideanillustrationofthisframework,basedonEuropeandataanda3Illustration:thenon-linearmacroeconomicmodelandtheinteractionvariableusedinthebenchmarkestimation.Third,wepresenttheimpulseshockandoutputshock).Indoingthat,wehighlightthesubstantialstateefectsrelatedtolevelofcyclicalrisk:bothhousingandoutputshocksaremorerecessionaryunderhighcyclicalrisk.Thisfeatureofthemodelallowsproducingscenarios,that,giventhesamesetofinitialshocks,14Tothisextent,intheUnitedKingdomandsomeeuroareajurisdictions,theneutralleveloftheCounter-Cyclicalbuferissettopositivevalues.thestructuralandthecyclicalrequirement.3.1TheeconometricmodelThemacroeconomicmodelisaMultivarbachandGorodnichenko(2013);TenreyroandThwaites(2016)),estimatedbyusingLocaluchamodel,astatevariabletransitionsbetweentwopolarregimes,afectingtheeffYt+h=F(zt-1)(Q+Σ=1β,lYt-l)(8)+(1-F(zt-1))(Q+Σ=1β,lYt-l)(8)+uh,t,whereYtisthe(n,1)vectorofendogenousvariablesattimet,zvariableattimet-1anduh,tisthe(n,1)vectoroferrorsathorizonhattimet.ThestateefectisgivenbyF(zt),thatisthescalarfunctiongoverningthetransitionbetweenthehightheinterval[0,1]andincreasesinzt.Higher(loto1(0),makingYt+hdependingmoreonthefirst(second)lineotransitionfunctionisthelogistictransformationoftheoriginalzt:deviationoftheobservedstatevariab15Thehigherθ,thefasterF(zt)goestoward0and1,i.e.convergingtodummy-regimeswitching.16zt>visequivalenttoF(zt)>0.5.Definingvasthep-thquantileofthehistoricaltimeseriesofztforcesF(zt)tospendp%ofthetimebelow0.5,i.e.inthelowregime.calibrations.andKim(2011),inordertoaccountfortheautocorrelationintimeseries.17.3.2Estimationofthemacroeconomicmodelin且ation(HICP),unemploymentrate,short-termrate(3-monthsEURIBOR),houseprices,theThestatevariabletocaptureagents’vulnerabilityistheDebtServiceratio(DSR)oftheNon-FinancialPrivateSector,ascomputedbyDrehmannetal.(2015):DSRt=(10)whereYtisincome,Dtisdebt,itistheefectivelendingrate,mistheaveragematurity.Theadebtofmmaturityinequalportion.19AhigherDSRimpliesthmorelikelytobeinfinancialdistress. 17WeconstructallpossibleoverlappingtuplesofmconsecutivedatesinthematrixYofendogenousvariables,alongwiththecorrespondingblockofregressorsforeachselecteddates,ateachhorizonofregression.Wethendrawinthissetofblockstoconstructthebootstrappedtimeseries.Wesetm=5inlinewithHorowitz(2019)),inthatmshouldbeproportionalton1/3.Wethusselectblocksoffiveconsecutivedatestobuildthebootstraptimeseries.Inarobustnessexercise,wealsoapplythebootstrap-after-bootstrapmethod,whichcorrectsforbiasinbootstrapestimates(seeKilian(1998);KilianandKim(2011))18Ourestimationresultsarerobusttotheuseofshadowshorttermrate(WuandXia(2016)).19TheuseofDebtServiceRatioallowsdirectlycapturingdiferentkeydimensionoffinancialvulnerabilityassuchastheevolutionofthecostofdebt,theamountofdebtintheeconomyandthecapacitytorepaythedebtviaincome.Thisindicatorexpressedindiferenceiswidelyusedinmacroprudentialanalysistodetectthebuild-upofcyclicalrisks(Langetal.(2019))20Structuralidentificationisnotmandatorytodesignadversescenarios,whichcanalsobeproducedthroughreducedformshocks.Nonetheless,providingastructuralinterpretationtothesetofshockscanhelptointerpretthenon-lineardynamicsfoundinthemodel.theselattertakeonequartertoreacttofinancialshocksvariablesreactingtypiunemploymentrate.ThisorderingisoverallstandardandinlinewithAikmanetal.(2020);Cesa-Bianchi(2013);GoodhartandHofmann(2008).Thesignoftheresponsesandthestatede