Common-risk-factors-in-the-returns-on-stocks-and-b

JournalofFinancialEconomics33(1993)3-56.North-HollandCommonriskfactorsinthereturnsonstocksandbonds*EugeneF.FamaandKennethR.FrenchUniversityofChicago,Chicago,IL60637,USAReceivedJuly1992,finalversionreceivedSeptember1992Thispaperidentifiesfivecommonriskfactorsinthereturnsonstocksandbonds.Therearethreestock-marketfactors:anoverallmarketfactorandfactorsrelatedtofirmsizeandbook-to-marketequity.Therearetwobond-marketfactors,relatedtomaturityanddefaultrisks.Stockreturnshavesharedvariationduetothestock-marketfactors,andtheyarelinkedtobondreturnsthroughsharedvariationinthebond-marketfactors.Exceptforlow-gradecorporates,thebortd-marketfactorscapturethecommonvariationinbondreturns.Mostimportant,thefivefactorsseemtoexplainaveragereturnsonstocksandbonds.1.IntroductionThecross-sectionofaveragereturnsonU.S.commonstocksshowslittlerelationtoeitherthemarketpsoftheSharpe(1964tLintner(1965)asset-pricingmodelortheconsumptionpsoftheintertemporalasset-pricingmodelofBreeden(1979)andothers.[See,forexample,Reinganum(1981)andHreeden,Gibbons,andLitzenberger(1989).]Ontheotherhand,variablesthathavenospecialstandinginasset-pricingtheoryshowreliablepowertoexplainthecross-sectionofaveragereturns.Thelistofempiricallydeterminedaverage-returnvariablesincludessize(ME,stockpricetimesnumberofshares),leverage,earnings/price(EIP),andbook-to-marketequity(theratioofthebookvalueofafirm'scommonstock,BE,toitsmarketvalue,ME).[SeeBanz(1981),Bhandari(1988),Basu(1983),andRosenberg,Reid,andL,anstein(1985).]Correspondenceto:EugeneF.Fama,GraduateSchoolofBusiness,UniversityofChicago,1101East58thStreet,Chicago,IL60637.USA.*ThecommentsofDavidBooth,JohnCochrane,Nai-TuChen,WayneFerson,JosefLakonishok,MarkMitchell.G.WilliamSchwert,JayShanken.andRexSinquefieldaregratefullyacknowledged.ThisresearchissupportedbytheNationalScienceFoundation(Fama)andtheCenterforResearchinSecuritiesPrices(French).0304-405X93,$05001993-ElsevlerSclencePubltshersBVAllr~ghtsreserved4E.F.FamaandK.R.French.CommonriskfactorsinstockandbondreturnsFamaandFrench(1992a)studythejointrolesofmarket8,size,E/P,leverage,andbook-to-marketequityinthecross-sectionofaveragestockreturns.Theyfindthatusedaloneorincombinationwithothervariables,8(theslopeintheregressionofastock'sreturnonamarketreturn)haslittleinformationaboutaveragereturns.Usedalone,size,EJP,leverage,andbook-to-marketequityhaveexplanatorypower.Imcombinations,size(ME)andbook-to-marketequity(BEIME)seemtoabsorbtheapparentrolesofleverageandE/Pinaveragereturns.Thebottom-lineresultisthattwoempiricallydeterminedvariables,sizeandbook-to-marketequity,doagoodjobexplainingthecross-sectionofaveragereturnsonNYSE,Amex,andNASDAQstocksforthe1963-1990period.Thispaperextendstheasset-pricingtestsinFamaandFrench(1992a)inthreeways.(a)Weexpandthesetof(assetreturnstobeexplained.Theonlyassetscon-sideredinFamaandFrench(1992a)arecommonstocks.Ifmarketsareintegrated,asinglemodelshouldalsoexplainbondreturns.ThetestshereincludeU.S.governmentandcorporatebondsaswellasstocks.(b)Wealsoexpandthesetofvariablesusedtoexplainreturns.Thesizeandbook-to-marketvariablesinFamaandFrench(1992a)aredirectedatstocks.Weextendthelisttoterm-structurevariablesthatarelikelytoplayaroleinbondreturns.Thegoalistoexaminewhethervariablesthatareimportantinbondreturnshelptoexplainstockreturns,andviceversa.Thenotionisthatifmarketsareintegrated,thereisprobablysomeoverlapbetweenthereturnprocessesforbondsandstocks.(c)Perhapsmostimportant,theapproachtotestingasset-pricingmodelsisdifferent.FamaandFrench(1992a)usethecross-sectionregressionsofFamaandMacBeth(1973);thecross-sectionofstockreturnsisregressedonvariableshypothesizedtoexplainaveragereturns.Itwouldbedifficulttoaddbondstothecross-sectionregressionssinceexplanatoryvariableslikesizeandbook-to-marketequityhavenoobviousmeaningforgovernmentandcorporatebonds.Thispaperusesthetime-seriesregressionapproachofBlack,Jensen,andScholes(1972).Monthlyreturnsonstocksandbondsareregressedonthereturnstoamarketportfolioofstocksandmimickingportfoliosforsize,book-to-marketequity(BEIME),andterm-structureriskfactorsinreturns.Thetime-seriesregressionslopesarefactorloadingsthat,unlikesizeorBEIME,haveaclearinterpretationasrisk-factorsensitivitiesforbondsaswellasforstocks.Thetime-seriesregressionsarealsoconvenientforstudyingtwoimportantasset-pricingissues.(a)Oneofourcentralthemesisthatifassetsarepricedrationally,variablesthatarerelatedtoaveragereturns,suchassizeandbook-to-marketequity,mustproxyforsensitivitytocommon(sharedandthusundiversifiable)riskfactorsinE.F.FamaandK.R.French,Commonriskfactorsinsrockandbondreturns5returns.Thetime-seriesregressionsgivedirectevidenceonthisissue.Inparticu-lar,theslopesandR2valuesshowwhethermimickingportfoliosforriskfactorsrelatedtosizeandBEIMEcapturesharedvariationinstockandbondreturnsnotexplainedbyotherfactors.(b)Thetime-seriesregressionsuseexcessreturns(monthlystockorbondreturnsminustheone-monthTreasurybillrate)asdependentvariablesandeitherexcessreturnsorreturnsonzero-investmentportfoliosasexplanatoryvariables.Insuchregressions,awell-specifiedasset-pr