The Capital Asset Pricing Model Theory and Evidenc

Firstdraft:August2003Thisdraft:January2004TheCapitalAssetPricingModel:TheoryandEvidence∗EugeneF.FamaandKennethR.FrenchThecapitalassetpricingmodel(CAPM)ofWilliamSharpe(1964)andJohnLintner(1965)marksthebirthofassetpricingtheory(resultinginaNobelPrizeforSharpein1990).Fourdecadeslater,theCAPMisstillwidelyusedinapplications,suchasestimatingthecostofcapitalforfirmsandevaluatingtheperformanceofmanagedportfolios.ItisthecenterpieceofMBAinvestmentcourses.Indeed,itisoftentheonlyassetpricingmodeltaughtinthesecourses.1TheattractionoftheCAPMisthatitofferspowerfulandintuitivelypleasingpredictionsabouthowtomeasureriskandtherelationbetweenexpectedreturnandrisk.Unfortunately,theempiricalrecordofthemodelispoor–poorenoughtoinvalidatethewayitisusedinapplications.TheCAPM’sempiricalproblemsmayreflecttheoreticalfailings,theresultofmanysimplifyingassumptions.Buttheymayalsobecausedbydifficultiesinimplementingvalidtestsofthemodel.Forexample,theCAPMsaysthattheriskofastockshouldbemeasuredrelativetoacomprehensive“marketportfolio”thatinprinciplecanincludenotjusttradedfinancialassets,butalsoconsumerdurables,realestate,andhumancapital.Evenifwe∗EugeneF.Fama([e-mail])isRobertR.McCormickDistinguishedServiceProfessorofFinance,GraduateSchoolofBusiness,UniversityofChicago,Chicago,Illinois.KennethR.French([e-mail])isCarlE.andCatherineM.HeidtProfessorofFinance,TuckSchoolofBusiness,DartmouthCollege,Hanover,NewHampshire.WegratefullyacknowledgethecommentsofJohnCochrane,GeorgeConstantinides,RichardLeftwich,TobiasMoskowitz,AndreiShleifer,RenéStulz,andTimothyTaylor.1Althougheveryassetpricingmodelisacapitalassetpricingmodel,thefinanceprofessionreservestheacronymCAPMforthespecificmodelofSharpe(1964),Lintner(1965),andBlack(1972)discussedhere.Thus,throughoutthepaperwerefertotheSharpe–Lintner–BlackmodelastheCAPM.2takeanarrowviewofthemodelandlimititspurviewtotradedfinancialassets,isitlegitimatetofurtherlimitthemarketportfoliotoU.S.commonstocks(atypicalchoice),orshouldthemarketbeexpandedtoincludebonds,andotherfinancialassets,perhapsaroundtheworld?Intheend,wearguethatwhetherthemodel’sproblemsreflectweaknessesinthetheoryorinitsempiricalimplementation,thefailureoftheCAPMinempiricaltestsimpliesthatmostapplicationsofthemodelareinvalid.WebeginbyoutliningthelogicoftheCAPM,focusingonitspredictionsaboutriskandexpectedreturn.WethenreviewthehistoryofempiricalworkandwhatitsaysaboutshortcomingsoftheCAPMthatposechallengestobeexplainedbyalternativemodels.TheLogicoftheCAPMTheCAPMbuildsonthemodelofportfoliochoicedevelopedbyHarryMarkowitz(1959).InMarkowitz’smodel,aninvestorselectsaportfolioattimet-1thatproducesastochasticreturnatt.Themodelassumesinvestorsareriskaverseand,whenchoosingamongportfolios,theycareonlyaboutthemeanandvarianceoftheirone-periodinvestmentreturn.Asaresult,investorschoose“mean-variance-efficient”portfolios,inthesensethattheportfolios:1)minimizethevarianceofportfolioreturn,givenexpectedreturn,and2)maximizeexpectedreturn,givenvariance.Thus,theMarkowitzapproachisoftencalleda“mean-variancemodel.”Theportfoliomodelprovidesanalgebraicconditiononassetweightsinmean-variance-efficientportfolios.TheCAPMturnsthisalgebraicstatementintoatestablepredictionabouttherelationbetweenriskandexpectedreturnbyidentifyingaportfoliothatmustbeefficientifassetpricesaretoclearthemarketofallassets.Sharpe(1964)andLintner(1965)addtwokeyassumptionstotheMarkowitzmodeltoidentifyaportfoliothatmustbemean-variance-efficient.Thefirstassumptioniscomplete3agreement:givenmarketclearingassetpricesatt-1,investorsagreeonthejointdistributionofassetreturnsfromt-1tot.Andthisdistributionisthetrueone,thatis,thedistributionfromwhichthereturnsweusetotestthemodelaredrawn.Thesecondassumptionisthatthereisborrowingandlendingatariskfreerate,whichisthesameforallinvestorsanddoesnotdependontheamountborrowedorlent.Figure1describesportfolioopportunitiesandtellstheCAPMstory.Thehorizontalaxisshowsportfoliorisk,measuredbythestandarddeviationofportfolioreturn;theverticalaxisshowsexpectedreturn.Thecurveabc,whichiscalledtheminimumvariancefrontier,tracescombinationsofexpectedreturnandriskforportfoliosofriskyassetsthatminimizereturnvarianceatdifferentlevelsofexpectedreturn.(Theseportfoliosdonotincluderiskfreeborrowingandlending.)Thetradeoffbetweenriskandexpectedreturnforminimumvarianceportfoliosisapparent.Forexample,aninvestorwhowantsahighexpectedreturn,perhapsatpointa,mustaccepthighvolatility.AtpointT,theinvestorcanhaveanintermediateexpectedreturnwithlowervolatility.Ifthereisnoriskfreeborrowingorlending,onlyportfoliosabovebalongabcaremean-variance-efficient,sincetheseportfoliosalsomaximizeexpectedreturn,giventheirreturnvariances.Addingriskfreeborrowingandlendingturnstheefficientsetintoastraightline.Consideraportfoliothatinveststheproportionxofportfoliofundsinariskfreesecurityand1-xinsomeportfoliog.Ifallfundsareinvestedintheriskfreesecurity–thatis,theyareloanedattheriskfreerateofinterest–theresultisthepointRfinFigure1,aportfoliowithzerovarianceandariskfreerateofreturn.Combinationsofriskfreelend