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1、THEJOURNALOFFINANCE•VOL.LXVII,NO.2•APRIL2012AreStocksReallyLessVolatileintheLongRun?LUBOˇSPˇASTORandROBERTF.STAMBAUGH´∗ABSTRACTAccordingtoconventionalwisdom,annualizedvolatilityofstockreturnsisloweroverlonghorizonsthanovershorthorizons,duetomeanreversioninducedbyr
2、eturnpre-dictability.Incontrast,wefindthatstocksaresubstantiallymorevolatileoverlonghorizonsfromaninvestor’sperspective.Thisperspectiverecognizesthatparametersareuncertain,evenwithtwocenturiesofdata,andthatobservablepredictorsimper-fectlydelivertheconditionalexpect
3、edreturn.Meanreversioncontributesstronglytoreducinglong-horizonvariancebutismorethanoffsetbyvariousuncertaintiesfacedbytheinvestor.Thesameuncertaintiesreducedesiredstockallocationsoflong-horizoninvestorscontemplatingtarget-datefunds.CONVENTIONALWISDOMVIEWSSTOCKret
4、urnsaslessvolatileoverlongerinvest-menthorizons.Thisviewseemsconsistentwithvariousempiricalestimates.Forexample,usingtwocenturiesofU.S.equityreturns,Siegel(2008)reportsthatvariancesrealizedoverinvestmenthorizonsofseveraldecadesaresub-stantiallylowerthanshort-horiz
5、onvariancesonaper-yearbasis.Suchevi-dencepertainstounconditionalvariance,butasimilarmessageisdeliveredbystudiesthatconditionvarianceoninformationusefulinpredictingreturns.CampbellandViceira(2002,2005),forexample,reportestimatesofconditionalvariancesthatdecreasewit
6、htheinvestmenthorizon.Wefindthatstocksareactuallymorevolatileoverlonghorizonsfromaninvestor’sperspective.Investorsconditiononavailableinformationbutrealizetheirknowledgeislimitedintwokeyrespects.First,evenafterobserving206yearsofdata(1802to2007),investorsdonotknowt
7、hevaluesoftheparametersofthereturn-generatingprocess,especiallytheparametersrelatedtotheconditionalexpectedreturn.Second,investorsrecognizethatobservable∗PastorisattheUniversityofChicagoBoothSchoolofBusiness,NBER,andCEPR.Stam-´baughisattheWhartonSchooloftheUnivers
8、ityofPennsylvaniaandNBER.WearegratefulforcommentsfromJohnCampbell,PeterChristoffersen,DarrellDuffie,GeneFama,WayneFer-son,MichaelHalling,CamHarvey,Anthon
