金融风险Measuring market risk VaR approach（PPT 58）

www.cnshu.cn中国最大的资料库下载3.Measuringmarketrisk:VaRapproach3.1Introduction3.2UnderstandingVaR3.3Riskmetrics3.4Historicsimulation3.5Mote-Carlosimulation3.6BISstandardizedmodelwww.cnshu.cn中国最大的资料库下载3.1IntroductionJ.P.MorganG30BISInvolvingprobabilitycomponentalongwithlossseveritycomponentinriskmeasurement,dealingwiththelimitationofsensitiveapproachesVaRRevolutionExtensiontoCreditandOperationalriskandthereforeintegratedriskmanagementwww.cnshu.cn中国最大的资料库下载AdvantagesofVaRapproach(oversensitivityapproach)completemeasureofrisk,Measuringriskusingthesameunit:dollarAggregateviewofaportfolioriskaccountingforleverageandcorrelationeffectsintegratednature,notonlyderivativesbutalsoallotherfinancialinstruments,andcanbebroadenedfrommarketrisktoothertypesoffinancialriskone-numberindicator.www.cnshu.cn中国最大的资料库下载3.2UnderstandingVaRQuestionsleadingustoVaRmeasureDefiningValueatRiskKeyelementsofcalculatingVaRWhatdoesPDFcurvetell?Approachestoprobabilitydistribution(typesofVaR)WorkingoutVaRthroughariskfactorwww.cnshu.cn中国最大的资料库下载QuestionsleadingustoVaRmeasureAsaportfoliomanager,youmaybeaskedbyyourbossfollowingquestions:Q1:Givenamarketchangeorshock,howmuchcouldyourportfoliosuffer?Q2:Ifitturnsouttobeabaddaytomorrow,whatistheworstlossofyourinvestment?Thefirstisasensitivityquestion,andyoucangiveaclearanswerafteryoudoasensitivitymeasureasweshowedinpreviouslectures.Thesecondisnotaclearquestion!Beforeyoutrytoanswerityouhavetoaskback“Whatdoyoumeanpreciselyby‘abadday’?”,or“Howbadthedayyousupposeittobe?”www.cnshu.cn中国最大的资料库下载SensitivityQfollowedbyprobabilityQ—Q1leadingtoVaRmeasureExampleofsensitivityQ:Givena25bpsyieldrise,howmuchcouldyourinvestmentportfolio(P=1m,MD=2ys)suffer?A:dP=-D[dR/(1+R)]P=-(MD)×(dR)×(P)=-2×0.0025×1,000,000=-$5,000.Youmaybefurtherasked:Howlikelycoulditbethecase?Ormoreprecisely,giventhenormalmarketcondition,howlikelywouldyourportfoliosuffernotmorethanthatamountofmoneyoveratargetholdingperiod?—AVaRquestion!Morefrequently,thequestionisputinanotherway:Whatistheworstlossyourportfoliocouldsufferoveratargetholdingperiodwithprobabilityofagivenlevel(say1%)undernormalmarketcondition?—AstandardVaRquestion!www.cnshu.cn中国最大的资料库下载Define“badday”andcompleteQ2—Q2leadingtoVaRmeasureOneeasywaytodefinea“badday”istodefinethelosssizeorseverity.Butthiswillmakethequestionmakenosense.Itisreasonable(andmeaningful)todefinea“badday”insuchawaythatthedayissobad,orthelossissoseverethatsuchaday(orloss)occursundernormalmarketconditiononlyonceoutofevery20(tobedefined)tradingdays,putanotherway,thechance(probability)oftheoccurrence(loss)isonly5%(tobedefined).Ifitturnsouttobeabaddaytomorrow,whatwillbetheworstlossofyourinvestment,giventhatdayhappensonceoutofevery20tradingdays?—AstandardVaRquestion!www.cnshu.cn中国最大的资料库下载DefiningValueatRiskDefinition:TheworstlossoveragiventargetholdingperiodatagivenconfidencelevelundernormalmarketconditionTwopre-specifiedvariables:HoldingPeriod(1day,1weekormore),ConfidenceLevel(95%,99%,orevenhigher)VaRisananswerto”Undernormalmarketcondition,whatistheworstlosscouldmyinvestmentportfoliosufferwithaprobabilityof5%withinonetradingday?”Iam95%(99/%)surethattheinvestmentportfoliowillsuffernotmorethan$5,000($20,000)lossover1dayundernormalmarketcondition.www.cnshu.cn中国最大的资料库下载KeyelementsofcalculatingVaRHoldingperiodConfidencelevelProbabilitydistributionofreturnProbabilitydensityfunction,PDF,inthecaseofcontinuousrandomvariableWorkingouttheprobabilitydistributionofreturnisthemostdifficultpartoftheVaRworkwww.cnshu.cn中国最大的资料库下载Holdingperiod:DEARandMore-than-one-dayVaRHoldingperiodisthetargettimehorizonduringwhichyouholdyourinvestmentposition,alsotargetmeasuringperiod.One-dayVaR,orDailyVaRisusuallycalculated,especiallyinthecaseofRiskmetricsmodel.ItisusuallytermedDailyEarningatRisk,DEAR.More-than-one-dayVaRcanbederivedfromDEARfromfollowingformula(Undertheassumptionthatmarketvalidityisconstantovertime):N-DayVaR=DEAR×NBISrequires10-dayVaR.www.cnshu.cn中国最大的资料库下载ConfidencelevelProbabilityofthelossDefiningthe“badday”:frequencyofthebaddayLevelofconfidenceoveryourlossforecast(riskestimate)Confidenceinterval,statisticallytermed.95%Riskmetricsvs.99%BISrequirementThehighertheCL,thebiggertheVaRnumber.WhatcouldhappenifCLissettoeither100%or0%?—Answersarerightstatementsbutnonsense!www.cnshu.cn中国最大的资料库下载WhatdoesPDFcurvetell?aEbE-σEE+σProbabilityDistributionofarandomvariableXX=randomreturn(orvalue,L/G)ofinvestmentE=expectedreturn,theprobabilityweightedaveragevalueofallpossibleoutcomesoftherandomvariableσ=SD,√variance,measureofdispersion,expectedsurprisesVarianceistheprobabilityweightedsumofthesquareddeviationsofalltheoutcomesfromtheirexpectedvalue,orsimply,theexpectedsquareddeviationoftherateofreturnfromitsexpectation.PDF1:F(a)=P(X≤a)PDF2:N(a)=P(X≤a)XXArea=P(X≤a)Area=P(a≤X≤b)Area=P(X≥b)=1-F(b)68.26%www.cnshu.cn中国最大的资料库下载WhatdoesPDFcurvetell?aEba=E-σEb=E+σProbabilityDistributionofarandomvariableXPDFtellstheprobabilitythattherandomvariable(X)doesnotexceedthespecifiedcriticalvaluea:F(a)=P(X≤a),whichcanbeillustratedbyth