《2-historicalsimulation,value-at-risk,andexpectedshortfall.》.pdf

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1、2HistoricalSimulation,Value-at-Risk,andExpectedShortfall1ChapterOverviewThemainobjectivesofthischapteraretwofold.FirstwewanttointroducethemostcommonlyusedmethodforcomputingVaR,HistoricalSimulation,andwediscusstheprosandconsofthismethod.WethendiscusstheprosandconsoftheVaRriskmeasureitse

2、lfandconsidertheExpectedShortfall(ES)alternative.Thechapterisorganizedasfollows:lWeintroducetheHistoricalSimulation(HS)methodanddiscussitsprosandpar-ticularlyitscons.lWeconsideranextensionofHS,oftenreferredtoasWeightedHistoricalSimula-tion(WHS).WecompareHSandWHSduringthe1987crash.lWeth

3、enstudytheperformanceofHSandRiskMetricsduringthe2008–2009finan-cialcrisis.lWesimulateartificialreturndataandassesstheHSVaRonthisdata.lFinallywecomparetheVaRriskmeasurewithapotentiallymoreinformativealter-native,ES.TheoverallconclusionfromthischapteristhatHSisproblematicforcomputingVaR.Th

4、iswillmotivatethedynamicmodelsconsideredlater.ThesemodelscanbeusedtocomputeExpectedShortfalloranyotherdesiredriskmeasure.2HistoricalSimulationThissectiondefinestheHSapproachtoValue-at-Riskandthendiscussestheprosandconsoftheapproach.ElementsofFinancialRiskManagement.DOI:10.1016/B978-0-12

5、-374448-7.00002-6c2012Elsevier,Inc.Allrightsreserved.22Background2.1DefiningHistoricalSimulationLettodaybedayt.Consideraportfolioofnassets.IfwetodayownNi;tunitsorsharesofassetithenthevalueoftheportfoliotodayisXnVPF;tDNi;tSi;tiD1Usingtoday’sportfolioholdingsbuthistoricalassetpriceswecanc

6、omputethehistoryof“pseudo”portfoliovaluesthatwouldhavematerializediftoday’sportfo-lioallocationhadbeenusedthroughtime.Forexample,yesterday’spseudoportfoliovalueisXnVPF;t1DNi;tSi;t1iD1Thisisapseudovaluebecausetheunitsofeachassetheldtypicallychangesovertime.Thepseudologreturncannowbede

7、finedas
RPF;tDlnVPF;t=VPF;t1Armedwiththisdefinition,wearenowreadytodefinetheHistoricalSimulationapproachtoriskmanagement.TheHStechniqueisdeceptivelysimple.Considertheavailabilityofapastsequenceofmdailyhypotheticalportfolioreturns,calculatedusingpastpricesoftheunderlyingassetsoftheport