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

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

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

3、rformanceofHSandRiskMetricsduringthe2008–2009finan-cialcrisis.lWesimulateartificialreturndataandassesstheHSVaRonthisdata.lFinallywecomparetheVaRriskmeasurewithapotentiallymoreinformativealter-native,ES.TheoverallconclusionfromthischapteristhatHSisproblematicforcomputingVaR.Thiswillmotivatethed

4、ynamicmodelsconsideredlater.ThesemodelscanbeusedtocomputeExpectedShortfalloranyotherdesiredriskmeasure.2HistoricalSimulationThissectiondefinestheHSapproachtoValue-at-Riskandthendiscussestheprosandconsoftheapproach.ElementsofFinancialRiskManagement.DOI:10.1016/B978-0-12-374448-7.00002-6c2012El

5、sevier,Inc.Allrightsreserved.22Background2.1DefiningHistoricalSimulationLettodaybedayt.Consideraportfolioofnassets.IfwetodayownNi;tunitsorsharesofassetithenthevalueoftheportfoliotodayisXnVPF;tDNi;tSi;tiD1Usingtoday’sportfolioholdingsbuthistoricalassetpriceswecancomputethehistoryof“pseudo”port

6、foliovaluesthatwouldhavematerializediftoday’sportfo-lioallocationhadbeenusedthroughtime.Forexample,yesterday’spseudoportfoliovalueisXnVPF;t1DNi;tSi;t1iD1Thisisapseudovaluebecausetheunitsofeachassetheldtypicallychangesovertime.Thepseudologreturncannowbedefinedas
RPF;tDlnVPF;t=VPF;t1Armedwi

7、ththisdefinition,wearenowreadytodefinetheHistoricalSimulationapproachtoriskmanagement.TheHStechniqueisdeceptivelysimple.Considertheavailabilityofapastsequenceofmdailyhypotheticalportfolioreturns,calculatedusingpastpricesoftheunderlyingassetsoftheport