美联储线性因子模型与期望收益估计

FinanceandEconomicsDiscussionSeries FederalReserveBoard,Washington,D.C.ISSN1936-2854(Print) ISSN2767-3898(Online) LinearFactorModelsandtheEstimationofExpectedReturns CisilSarisoy,PeterdeGoeij,andBasJ.M.Werker2024-014 Pleasecitethispaperas: Sarisoy,Cisil,PeterdeGoeij,andBasJ.M.Werker(2024).“LinearFactorMod-elsandtheEstimationofExpectedReturns,”FinanceandEconomicsDiscussionSe-ries2024-014.Washington:BoardofGovernorsoftheFederalReserveSystem,https://doi.org/10.17016/FEDS.2024.014. NOTE:StaffworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers. LinearFactorModelsandtheEstimationofExpectedReturns CisilSarisoy∗FederalReserveBoard PeterdeGoeijTilburgUniversityBasJ.M.WerkerTilburgUniversity January2024 Abstract Thispaperanalyzesthepropertiesofexpectedreturnestimatorsonindividualassetsimpliedbythelinearfactormodelsofassetpricing,i.e.,theproductofβandλ.Weprovidetheasymptoticpropertiesoffactor–model–basedexpectedreturnestimators,whichyieldthestandarderrorsforriskpremiumestimatorsforindividualassets.Weshowthatusingfactor-model-basedriskpremiumestimatesleadstosizableprecisiongainscomparedtousinghistoricalaverages.Finally,inferenceaboutexpectedreturnsdoesnotsufferfromasmall–betabiaswhenfactorsaretraded.Themoreprecisefactor–model–basedestimatesofexpectedreturnstranslateintosizableimprovementsinout–of–sampleperformanceofoptimalportfolios. Keywords:CrossSectionofExpectedReturns,RiskPremium,Smallβ’s. ∗WethankTorbenG.Andersen,BertilleAntoine,SvetlanaBryzgalova,FrankdeJong,JoostDriessen,StefanoGiglio,BryanKelly,FrankKleibergen,YinyingLi,PauloMaio,AdamMcCloskey,DinoPalazzo,AndrewPatton,EricRenault,EnriqueSentana,GeorgeTauchen,ViktorTodorov,BrianWeller,DachengXiu,andGuofuZhouforhelpfulcommentsanddiscussionsaswellasseminarandconferenceparticipantsatBlackRock,FederalReserveBoard,NorthwesternUniversityKelloggSchoolofManagement,ErasmusUniversityRotterdam,TilburgUniversity,andCIREQMontrealEconometricsConferenceinhonorofEricRenault.WealsothankChazzEdingtonforhisexcellentresearchassistance.TheviewsexpressedaresolelythoseoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystem,orofanyotherpersonassociatedwiththeFederalReserveSystem.Correspondingauthor:CisilSarisoy,FederalReserveBoard,Washington,D.C.20551U.S.A.E-mail:cisil.sarisoy@frb.gov. 1Introduction Estimatingexpectedreturnsonindividualassetsorportfoliosisperhapsoneofthelongeststandingchallengesinassetpricing.Onestandardapproachathandistousehistoricalaverages.However,itisknownthattheseestimatesaregenerallyverynoisy.Evenusingdailydatadoesnothelpmuch,ifatall.Thereisalonghistoryofpaperstryingtoimproveestimatesofexpectedreturnsbyusingassetpricingmodels,inwhichexpectedexcessreturnsonindividualassetsarelinearintheirexposurestotheriskfactorsimposed(β).Thecoefficientsinthislinearrelationshiparethepricesofriskforthefactors(λ).ExamplesincludeSharpe(1964)’sCAPM,Merton(1973)’sICAPM,Breeden(1979)’sCCAPM,Ross(1976)’APTandLettauandLudvigson(2001)’sconditionalCCAPM,amongmanyothers.Theliteratureoninferencebasedonfactormodelsmainlyconcentrates,inafrequentistsetting,ontheeconometricpropertiesofthepricesofrisk,λ,andevaluatingtheabilityofthemodelsinexplainingthecrosssectionofexpectedreturns.Inthispaper,thefocusisdifferent:weanalyzetheestimationoftheexpected(excess)returnsonindividualassetsorportfoliosbasedonlinearfactormodels,i.e.,theproductofexposuresβandriskpricesλ.Inordertohaveanestimateoftheexpected(excess)returnonanindividualasset,bothβandλhavetobeestimated,andthedependencebetweentheseestimatorsintroduceanontrivialnoisestructureinthestandarderrorsoftheexpected(excess)returnestimators.Jorion(1991)comparesCAPM—basedestimatorswithclassicalsampleaveragesofpastreturnsfindingtheformeroutperformingthelatterinestimatingexpectedstockre-turns.P´astorandStambaugh(1999)investigate,inaBayesiansetting,theimpactofprioruncertaintyaboutmispricinginafactormodelontheposteriorestimatesofthecostofequity.Similarly,P´astor(2000)developsBayesianapproachestoexaminetheroleofpriormispricinginportfolioallocationdecisions.Ourpapercomplementsthisearlierworkbyprovidingthefirstasymptoticanalysisfortheexpected(excess)returnestimatorsforsev- eraloften–usedfactormodels.Suchlimitingdistributionsyieldthefrequentiststandarderrorsand,accordingly,confidenceboundsfortheexpected(excess)returnofindividualassetsorportfolios.Moreover,weevaluatetheimplicationsofweaklycorrelatedfactorsontheestimationofexpected(excess)returns.Weexaminetheinferenceundervarioussettingswherethefactorsaretraded,non-tradedortheirmimickingportfoliosareusedintheestimation. First,wederivetheasymptoticpropertiesofexpected(excess)return–riskpremium–esti