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1、JournalofFinancialEconomics24(1989)289-317.North-HollandTIME-VARYINGCONDITIONALCOVARIANCESINTESTSOFASSETPRICINGMODELSCampbellR.HARVEY*DukeUniversity,Durham,NC27706,USAReceivedOctober1988,finalversionreceivedJune1989Thispaperproposestestsofassetpricing
2、modelsthatallowfortimevariationinconditionalcovariances.Theevidenceindicatesthattheconditionalcovariancesdochangethroughtime.Estimatesoftheexpectedexcessreturnonthemarketdividedbythevarianceofthemarket(reward-to-riskratio)arepresentedfortheSharpe—Lint
3、nerCAPM,aswellasanumberoftestsofthemodelspecification.Thepatternsofthepricingerrorsthroughtimesuggestthemodel'sinabilitytocapturethedynamicbehaviorofassetsreturns.1.IntroductionManyassetpricingmodels(CAPMs)imposetherestrictionthatexpectedreturnsarelin
4、earlyrelatedtoassetrisk.TheconditionalversionoftheSharpe(1964)andLintner(1965)CAPMimposestherestrictionthatconditionallyexpectedreturnsonassetsarelinearlyrelatedtotheconditionallyexpectedreturnonamarket-wideportfolioinexcessofarisk-freereturn.Thecoeff
5、i-cientinthelinearrelationistheasset'sbetaortheratiooftheconditionalcovarianceoftheasset'sreturnwiththemarkettotheconditionalvarianceofthemarket.TestsoftheunconditionalversionoftheCAPMsuchasBlack,Jensen,andScholes(1972),FamaandMacBeth(1973),Gibbons(19
6、82),andStambaugh(1982)assumethatexpectedreturnsareconstant,themarketportfolioisobservable,andassets'betasarestationaryoverafixedperiod.Cross-sectionaltestsareconductedbyregressingunconditionalexpectedreturnsonuncondi-tionalbetas.Thesetestsarecarriedou
7、tonfive-orten-yearsubperiodsbecause*IhavebenefitedfromdiscussionswithDouglasBreeden,WernerDeBondt,WayneFerson,JoelHasbrouck,RogerHuang,KennethSingleton,ThomasSmith,S.Viswanathan,andGuofuZhou.IamespeciallyindebtedtoWilliamSchwert,theeditor,andJohnCampb
8、ell,thereferee,fortheirmanyconstructivesuggestions.IhavealsobenefitedfromthecommentsofseminarparticipantsatDukeUniversity,theJohnsonSymposiumattheUniversityofWisconsin-Madi-son,andtheWesternandEuropeanFinanceAssociationmeetings.0304-405X/89/$3