英文原文：10TheMarkowitzInvestmentPortfolioSelectionModelThefirstninechaptersofthisbookpresentedthebasicprobabilitytheorywithwhichanystudentofinsuranceandinvestmentsshouldbefamiliar.Inthisfinalchapter,wediscussanimportantapplicationofthebasictheory:theNobelPrizewinninginvestmentportfolioselectionmodelduetoHarryMarkowitz.Thismaterialisnotdiscussedinotherprobabilitytextsofthislevel;however,itisaniceapplicationofthebasictheoryanditisveryaccessible.TheMarkowitzportfolioselectionmodelhasaprofoundeffectontheinvestmentindustry.Indeed,thepopularityofindexfunds(mutualfundsthattracktheperformanceofanindexsuchastheS&P500anddonotattemptto“beatthemarket”)canbetracedtoasurprisingconsequenceoftheMarkowitzmodel:thateveryinvestor,regardlessofrisktolerance,shouldholdthesameportfolioofriskysecurities.Thisresulthascalledintoquestiontheconventionalwisdomthatitispossibletobeatthemarketwiththe“right”investmentmanagerandinsodoinghasrevolutionizedtheinvestmentindustry.OurpresentationoftheMarkowitzmodelisorganizedinthefollowingway.Webeginbyconsideringportfoliosoftwosecurities.Animportantexampleofaportfolioofthistypeisoneconsistingofastockmutualfundandabondmutualfund.Seenfromthisperspective,theportfolioselectionproblemwithtwosecuritiesisequivalenttotheproblemofassetallocationbetweenstocksandbonds.Wethenconsiderportfoliosoftworiskysecuritiesandarisk-freeasset,theprototypebeingaportfolioofastockmutualfund,abondmutualfund,andamoney-marketfund.Finally,weconsiderportfolioselectionwhenanunlimitednumberofsecuritiesisavailableforinclusionintheportfolio.WeconcludethischapterbybrieflydiscussinganimportantconsequenceoftheMarkowitzmodel,namely,theNobelPrizewinningcapitalassetpricingmodelduetoWilliamSharpe.TheCAPM,asitisreferredto,givesaformulaforthefairreturnonariskysecuritywhentheoverallmarketisinequilibrium.LiketheMarkowitzmodel,theCAPMhashadaprofoundinfluenceonportfoliomanagementpractice.10.1PortfoliosofTwoSecuritiesInthissection,weconsiderportfoliosconsistingofonlytwosecurities,1Sand2S.Thesetwosecuritiescouldbeastockmutualfundandabondmutualfund,inwhichcasetheportfolioselectionproblemamountstoassetallocation,ortheycouldbesomethingelse.Ourobjectiveistodeterminethe“bestmix”of1Sand2Sintheportfolio.PortfolioOpportunitySetLet'sbeginbydescribingthesetofpossibleportfoliosthatcanbeconstructedfrom1Sand2S.Supposethatthecurrentvalueofourportfolioisddollarsandlet1dand2dbethedollaramountsinvestedin1Sand2S,respectively.Let1Rand2Rbethesimplereturnson1Sand2SoverafuturetimeperiodthatbeginsnowandendsatafixedfuturepointintimeandletRbethecorrespondingsimplereturnfortheportfolio.Then,ifnochangesaremadetotheportfoliomixduringthetimeperiodunderconsideration,2211111RdRdRd.Hence,thereturnontheportfoliooverthegiventimeperiodis211RxxRR,whereddx1isthefractionoftheportfoliocurrentlyinvestedin1S.Consequently,byvaryingx,wecanchangethereturncharacteristicsoftheportfolio.Nowif1Sand2Sareriskysecurities,aswewillassumethroughoutthissection,then1R,2R,andRareallrandomvariables.Supposethat1Rand2Rarebothnormallydistributedandtheirjointdistributionhasabivariatenormaldistribution.Thismayappeartobeastrongassumption.However,dataonstockpricereturnssuggestthat,asafirstapproximation,itisnotunreasonable.Then,fromthepropertiesofthenormaldistribution,itfollowsthatRisnormallydistributedandthatthedistributionsof1R,2R,andRarecompletelycharacterizedbyt...
