2 Common risk factors in the returns on stocks and

3/4/20201國立東華大學財務金融學系CommonRiskFactorsinStockandBondReturnsEugeneFamaandKennethFrenchJournalofFinancialEconomics33(1993)3-56.蕭朝興3/4/20202國立東華大學財務金融學系前言本文從三方面來延伸FamaandFrench(1992)的資產定價檢定探討的資產包含了債券與股票包含了股票市場與債券市場的變數來解釋報酬研究方法：ThetimeseriesregressionapproachofBlack,JensenandScholes(1972)R(t)–Rf(t)=a+b．[RM(t)–Rf(t)]+s．SMB(t)+h．HML(t)+e(t)3/4/20203國立東華大學財務金融學系R(t)–Rf(t)=RiskPremium=MarketRiskPremium+RiskPremiumassociatedwithfirmsize+RiskPremiumassociatedwithBM如何判斷共同風險因子能捕捉報酬的共同變異?RegressionslopeandR2前言3/4/20204國立東華大學財務金融學系如何判斷資產定價模式是否設定良好?截距項（a）是否顯著異於0？當截距項顯著異於0時，表示報酬的變異中，該資產定價模式有無法解釋的部分R(t)–{Rf(t)+b．[RM(t)–Rf(t)]+s．SMB(t)+h．HML(t)}=a+e(t)三因子模式所預期的報酬率前言3/4/2020國立東華大學財務金融學系5模型與變數設定—解釋變數部分3/4/20206國立東華大學財務金融學系1.Breakingpoint(Size)Formationdate—AttheendofJuneofyeart,1963-1991WhyJune?Look-aheadBias.Dataavailable:AttheendofJune.Size—step1:AllNYSEstocksonCRSPrankedonSZstep2:ThemedianNYSEsizeisthenusedtosplitAmexandNASDAQstocksintotwogroups(SandB)3/4/20207國立東華大學財務金融學系1.Breakingpoint(BM)Dataavailable:AttheendofDecemberofyeart-1BreakNYSE,Amex,andNASDAQstocksintothreeBMgroupsbasedonthebreakpointsforthebottom30%(Low),40%(Median)andtop30%(High)oftherankedvaluesofBMforNYSEstocks.Notusenegative-BEfirms.Reasonstosortfirmsinto3groupsonBMandonly2groupsonSZ.SurvivorshipBias3/4/20208國立東華大學財務金融學系2.ConstructSixPortfoliosThroughIndependentSort(A)B/MLowMediaHighsizeSmallS/LS/MS/HBigB/LB/MB/HMonthlyvalued-weightedreturnonthesixportfoliosarecalculatedfromJulyofyearttoJuneofyeart+1andportfolioarereformedagainonJuneofyeart+1.3/4/20209國立東華大學財務金融學系2.ConstructSixPortfoliosThroughIndependentSources(B)SMB=1/3(S/L+S/M+S/H-B/L-B/M-B/H)MimickingthecommonriskfactorinreturnrelatedtosizeHML=½(S/H+B/H-S/L-B/L)MimickingthecommonriskfactorinreturnrelatedtoBMPurpose:toreducethecorrelationbetweenHMLandSMB3/4/2020國立東華大學財務金融學系10Theplayingfield---TheEmpiricalResults3/4/202011國立東華大學財務金融學系Table1–DescriptiveStatistics3/4/202012國立東華大學財務金融學系Table1–DescriptiveStatisticsBecauseweuseNYSEbreakpointstoformthe25size-BE/MEportfolios,theportfoliosinthesmallestsizequintilehavethemoststocks(mostlysmallAmexandNASDAQstocks).Incontrast,theportfoliosinthelargestsizequintilehavethefeweststocksbutthelargestfractionsofvalue.ThefiveportfoliosinthelargestMEquintileaverageabout74%oftotalvalue.3/4/202013國立東華大學財務金融學系Table2(A)—SummaryStatistics3/4/202014國立東華大學財務金融學系Table2(A)—SummaryStatisticsHighvolatility—capturesubstantialcommonvariationinreturnsHighaveragepremium(Mean)—explainmuchcross-sectionalvariationinaveragereturnsTakeSMBasanexample:TheaverageSMBreturn0.27%permonth(t=1.73)meanstheaveragepremiumforthesize-relatedfactorinreturns.Sumoftheinterceptandresidualsfromtheregression:3/4/202015國立東華大學財務金融學系Table2(B)—DependentvariablesThereisanegativerelationbetweensizeandaveragereturn,andthereisastrongerpositiverelationbetweenaveragereturnandbook-to-marketequity.Becausestockreturnshavehighstandarddeviations(around6%permonthforthesize-BMportfolios),largeaveragereturnsoftenarenotreliablydifferentfrom0.3/4/202016國立東華大學財務金融學系Table4–Stock-MarketFactors3/4/202017國立東華大學財務金融學系Table4–Stock-MarketFactorsTheonlyR2valuesnear0.9areforthebig-stocklow-book-to-marketportfolios.Forsmall-stockandhigh-BE/MEportfolios,R2valueslessthan0.8or0.7aretherule.Thesearethestockportfoliosforwhichthesizeandbook-to-marketfactors,SMBandHML,willhavetheirbestshotatshowingmarginalexplanatorypower.3/4/202018國立東華大學財務金融學系Table5—Stock-marketFactors(B)TheR2valuesarenothighenough.ItleavescommonvariationinstockreturnsthatispickedupbythemarketportfolioinTable4.3/4/202019國立東華大學財務金融學系Table6—Stock-marketFactors(C)3/4/202020國立東華大學財務金融學系Table6—Stock-marketFactors(C)AddingSMBandHMLtotheregressionscollapsestheβsforstockstoward1.0;lowβsmoveuptoward1.0andhighβsmovedown.HMLclearlycapturessharedvariationinstockreturns,relatedtobook-to-marketequity,thatismissedbythemarketandbySMB3/4/202021國立東華大學財務金融學系Table6—Stock-marketFactors(C)R2sarequitehigh3/4/202022國立東華大學財務金融學系RobustTestJointtestsontheregressionintercepts.(Table9)Diagnostics.(Equation2,page42)Januaryseasonals.(Table10)Split-sampletests.PortfoliosformonE/P,D/P.(Table11)【说明结果不是特例，而是具有通用性】3/4/202023國立東華大學財務金融學系Table9三因子模型的a呈现大幅度衰减3/4/202024國立東華大學財務金融學系Table93/4/202025國立東華大學財務金融學系Diagnostics-Januaryseasonals研究目的-檢測5-factormodel是否能捕捉“元月效應”?股票報酬在元月時特別高，尤其是小型股判斷方式-其中,JAN=1,元月0,其他月份當5-factormodel的殘差項不能被元月效應所解釋時，表示5-factormodel已包含了元月效應()()RtabJANte投資組合的超額報酬5factorsexplanatoryreturn5-factorregressionresiduals3/4/202026國立東華大學財務金融學系Table10-以“excessreturns”當應變數3/4/202027國立東華大學財務金融學系Table10-以”Regressionresiduals”當應變數大幅縮小，雖顯著，仍表示元月效應仍大量被五因子解釋。3/4/202028國立東華大學財務金融學系Diagnostics-spilt-sampletests研究目的：檢測SMB與HML能解釋與size、BE/ME有關的股票共同變異，並非是“以左手來預測右手”的情形Explanatoryreturnsdependentreturns角色互相交換3/4/202029國立東華大學財務金融學系Diagnostics-portfoliosformedonE/P研究目的：3-factormodel亦能解釋以其他變數(與報酬有關)所形成之投資組合報酬率與Size-BE/MEportfolios的建構程序相同E/P與BE/ME有很強的正向關係LowBE/ME:growthstocks持續有高的盈餘，因此能產生比淨值還高的市價highBE/ME:valuestocks持續有低的盈餘，使得市價比淨值還低12t第t-1年會計年度結束時的盈餘E/P第t-1年月底的市值3/4/202030國立東華大學財務金融學系