sensitivity of portfolio var and cvar to portfolio return characteristics

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1、SensitivityofportfolioVaRandCVaRtoportfolioreturncharacteristicsStoyanV.StoyanovFinAnalytica,Inc.,USAandUniversityofKarlsruhe,Germany,KITe-mail:stoyan.stoyanov@finanalytica.comSvetlozarT.Rachev∗UniversityofKarlsruhe,Germany,KITandUniversityofCaliforniaSantaBarbara,USAChiefScientist,FinAnalytica,Inc

2、.e-mail:zari.rachev@statistik.uni-karlsruhe.deFrankJ.FabozziYaleSchoolofManagemente-mail:frank.fabozzi@yale.edu∗ProfRachevgratefullyacknowledgesresearchsupportbygrantsfromDivisionofMathematical,LifeandPhysicalSciences,CollegeofLettersandScience,UniversityofCalifornia,SantaBarbara,theDeutschenForsc

3、hungsgemeinschaftandtheDeutscherAkademischerAustauschDienst.1AbstractRiskmanagementthroughmarginalrebalancingisimportantforinstitutionalinvestorsduetothesizeoftheirportfolios.WeconsidertheproblemofimprovingmarginallyportfolioVaRandCVaRthroughamarginalchangeintheportfolioreturncharacteristics.Westu

4、dytherelativesignificanceofstandarddeviation,mean,tailthickness,andskewnessinaparametricsettingassumingaStudent’storastabledistributionforportfolioreturns.WealsocarryoutanempiricalstudywiththeconstituentsofDAX30,CAC40,andSMI.Ouranalysisleadstopracticalimplicationsforinstitutionalinvestorsandregulat

5、ors.Keywords:value-at-risk,conditionalvalue-at-risk,Student’stdistribu-tion,stabledistributions,marginalrebalancingJELClassification:G11,G3221IntroductionIntheliterature,therehasbeenadebateaboutthepropertiesofvariousriskmeasuresandwhichriskmeasureisbestfromapracticalviewpoint.Fromahistoricalperspec

6、tive,variancewassuggestedasaproxyforriskbyMarkowitz(1952)asapartofaframeworkforportfolioselectionthatisstillwidelyusedbypractitioners.Thedisadvantagesofvarianceasameasureofriskarewelldocumentedintheliterature–varianceisnotatrueriskmeasurebecauseitpenalizessymmetricallybothprofitandloss.Sinceriskisa

7、nasymmetricphenomenon,atrueriskmeasureshouldfocusonthedownsideonly;theupsidepotentialshouldbeirrelevantfromariskmanagementperspective.Ariskmeasurewhichhasbeenwidelyacceptedsincethe1990sisthevalue-at-risk(VaR).Itw