UIUC商学院课件.ppt

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1、Copyright©1996-2005byNeilD.Pearson.Allrightsreserved.Delta-Normal(Variance-Covariance)MethodforanEquityPortfolioNeilD.PearsonCopyright©1996-2005byNeilD.Pearson.Allrightsreserved.SummaryofDelta-NormalmethodAssume:Normaldistributionsformarketfactorsportfoliovalueisgivenbylinear(delta)appr

2、oximationchangesinportfoliovalueareNormallydistributedUsemathematicsof(multivariate)NormaldistributiontodeterminedistributionofchangesinportfoliovalueFromdistribution/density,computeorreadoffvalue-at-riskCopyright©1996-2005byNeilD.Pearson.Allrightsreserved.FocusofDelta-NormalmethodOnce

3、wedeterminethedistributionofchangesinportfoliovalue,wecandeterminethe“cutoff”thatleavesprobabilitypinleft-handtailCopyright©1996-2005byNeilD.Pearson.Allrightsreserved.Equityportfolioexample$110millioninwell-diversifiedportfoliooflargecap.U.S.equities,perfectlycorrelatedwithS&P500500FT-S

4、E100indexfuturescontractsShort200S&P500contracts600writtenFT-SE100indexcalloptionswithstrikelevelof5,875800writtenS&P500indexcallswithstrikelevelof1,100Netvalue=110million-valueofwrittenoptions=USD101,485,220Copyright©1996-2005byNeilD.Pearson.Allrightsreserved.Indexandexchangeratelevels

5、Indexes:S&P500isat1,097.6FT-SE100isat5,862.3Exchangerate:USD1.6271/GBPCopyright©1996-2005byNeilD.Pearson.Allrightsreserved.Portfoliovalueasfunctionof2indexesInthisfigure,theexchangerateisheldfixedatlevelofUSD1.6271/GBPCopyright©1996-2005byNeilD.Pearson.Allrightsreserved.Port.valueasfunc

6、tionofS&P500Copyright©1996-2005byNeilD.Pearson.Allrightsreserved.Port.valueasfunctionofFT-SE100Copyright©1996-2005byNeilD.Pearson.Allrightsreserved.RiskmappingComputingportfoliostandarddeviationcanbedifficultrisksofsomeinstruments(e.g.,options)changeaslevelofstockpriceschangeActualportf

7、oliosoftenincludemanypositionstherecanbe100’sor1,000’sofdifferentpositionstoestimatecovariancematrixofthousandsofinstrumentsisnotfeasibleIndividualstocksare“mapped”topositionsinalimitednumberofmarketindexes“Mapping”theportfolioComplicatedactualportfolio:toocomplicatedtodirectl