现代资产组合理论和资本资产定价模型分析

ModernPortfolioTheoryTheFactorModelsandTheArbitragePricingTheoryChapter8ByDingzhaoyongReturn-generatingProcessandFactorModels•Return-generatingprocess–Isastatisticalmodelthatdescribehowreturnonasecurityisproduced.–ThetaskofidentifyingtheMarkowitzefficientsetcanbegreatlysimplifiedbyintroducingthisprocess.–Themarketmodelisakindofthisprocess,andtherearemanyothers.Return-generatingProcessandFactorModels•Factormodels–Thesemodelsassumethatthereturnonasecurityissensitivetothemove-mentsofvariousfactorsorindices.–Inattemptingtoaccuratelyestimateexpectedreturns,variances,andcovariancesforsecurities,multiple-factormodelsarepotentiallymoreusefulthanthemarketmodel.Return-generatingProcessandFactorModels–Implicitintheconstructionofafactormodelistheassumptionthatthereturnsontwosecuritieswillbecorrelatedonlythroughcommonreactionstooneormoreofthespecifiedinthemodel.Anyaspectofasecurity’sreturnunexplainedbythefactormodelisuncorrelatedwiththeuniqueelementsofreturnsonothersecurities.Return-generatingProcessandFactorModels–Afactormodelisapowerfultoolforportfoliomanagement.«Itcansupplytheinformationneededtocalculateexpectedreturns,variances,andcovariancesforeverysecurity,whicharethenecessaryconditionsfordeterminingthecurvedMarkowitzefficientset.«Itcanalsobeusedtocharacterizeaportfolio’ssensitivitytomovementinthefactors.Return-generatingProcessandFactorModels•Factormodelssupplythenecessarylevelofabstractionincalculatingcovariances.–Theproblemofcalculatingcovariancesamongsecuritiesrisesexponentiallyasthenumberofsecuritiesanalyzedincrease.–Practically,abstractionisanessentialstepinidentifyingtheMarkowitzset.Return-generatingProcessandFactorModels•Factormodelsprovideinvestmentmanagerswithaframeworktoidentifyimportantfactorsintheeconomyandthemarketplaceandtoassesstheextenttowhichdifferentsecuritiesandportfolioswillrespondtochangesinthesefactors.–Aprimarygoalofsecurityanalysisistodeterminethesefactorsandthesensitivitiesofsecurityreturntomovementsinthesefactors.One-FactorModels•Theone-factormodelsrefertothereturn-generatingprocessforsecuritiesinvolvesasinglefactor.Thesefactorsmaybeoneofthefollowings:–ThepredictedgrowthrateinGDP–Theexpectedreturnonmarketindex–Thegrowthrateofindustrialproduc-tion,etc.One-FactorModels•AnexamplePage295:Figure11.1GDPforfactorzerothegrowthGDPpredictedWidgettoofysensitivittperiodinWidgetonreturnspecificoeuniquethetperiodinGDPinreturnofratepredictedthetperiodinWidgetonreturnthe:whereabeGDPrebGDParttttttOne-FactorModels•Generalizingtheexample–Assumptions«Therandomerrortermandthefactorareuncorrelated.(Why?)«Therandomerrortermsofanytwosecuritiesareuncorrelated.(Why?)ittiiiteFbarOne-FactorModels–Expectedreturn–Variance–CovarianceFbariii2222eiFiib2FjiijbbOne-FactorModels•Twoimportantfeaturesofone-factormodel–Thetangencyportfolioiseasytoget.«Thereturnsonallsecuritiesrespondtoasinglecommonfactorgreatersimplifiesthetaskofidentifyingthetangencyportfolio.«Thecommonresponsivenessofsecuritiestothefactoreliminatestheneedtoestimatedirectlythecovariancesbetweenthesecurities.«Thenumberofestimates:3N+2One-FactorModels–Thefeatureofdiversificationistrueofanyone-factormodel.«Factorrisk:«Nonfactorrisk:«Diversificationleadstoanaveragingoffactorrisk«Diversificationreducesnonfactorrisk)(22Fib2eiOne-FactorModelsNNNXbXbbeNeeNieiepNieiiepNiiipepFpp22221122212221222211:whereMultiple-FactorModels•Thehealthoftheeconomyeffectsmostfirms,buttheeconomyisnotasimple,monolithicentity.Severalcommoninfluenceswithpervasiveeffectsmightbeidentified–ThegrowthrateofGDP–Thelevelofinterestrate–Theinflationrate–ThelevelofoilpriceMultiple-FactorModels•Two-FactorModels–Assumethatthereturn-generatingprocesscontainstwofactors.ittitiiiteFbFbar2211tttteINFbGDPbar21Multiple-FactorModels«Thesecondequationprovidesatwo-factormodelofacompany’sstock,whosereturnsareaffectedbyexpectationsconcerningboththegrowthrateinGDPandtherateofinflation.«Page301:Figure11.2«Tothisscatterofpointsisfitatwo-dimensionalplanebyusingthestatisticaltechniqueofmultiple-regressionanalysis.Multiple-FactorModels–Fourparametersneedtobeestimatedforeachsecuritywiththetwo-factormodel:ai,bi1,bi2,andthestandarddeviationoftherandomerrorterm.–Foreachofthefactors,twoparametersneedtobeestimated.Theseparametersaretheexpectedvalueofeachfactorandthevarianceofeachfactor.Finally,thecovariancebetweenfactors.Multiple-FactorModels–Expectedreturn–Variance–Covariance2211FbFbariiii22121222221212),(2eiiiFiFiiFFCOVbbbb),()(21122122222111FFCOVbbbbbbbbjijiFjiFjiijMultiple-FactorModels–Thetangencyportfolio«Theinvestorcanproceedtouseanoptimizertoderivethecurveefficientset.–Diversification«Diversificationleadstoanaveragingoffactorrisk.«Diversificationcansubstantiallyreducenonfactorrisk.«Forawell-diversifiedportfolio,nonfactorriskwillbeinsignificant.Multiple-FactorModelspttptppNiititNiiitNiiiNiiiNiittitiiiNiitipteFbFbaeXFbXFbXaXeFbFbaXrXr221112121111122111)(Multi