207056-PDF-ENG

9-207-056JANUARY28,2007________________________________________________________________________________________________________________ProfessorMalcolmBakerpreparedthisnoteasthebasisforclassdiscussion.Copyright©2007PresidentandFellowsofHarvardCollege.Toordercopiesorrequestpermissiontoreproducematerials,call1-800-545-7685,writeHarvardBusinessSchoolPublishing,Boston,MA02163,orgoto—electronic,mechanical,photocopying,recording,orotherwise—withoutthepermissionofHarvardBusinessSchool.MALCOLMBAKERMultifactorModelsTherearetwopartstothisexercise.Thefirstistoevaluatetheperformanceoffourmutualfunds.And,thesecondistoestimatethecostofcapitalfortwofirms.BenchmarkingBothpartsoftheexerciseareaboutchoosinganappropriatebenchmark,eitherforevaluatingpastinvestmentreturnsorassessinganewproject.Ideally,abenchmarkshouldreflecttheopportunitycost,orthebestalternativeinvestment.Ifaninvestmentmanager’spastreturnssignificantlyexceedanappropriatebenchmark,thenwecanconcludethatheorshehadlegitimatestockpickingskill.Similarly,iftheexpectedreturnonanewinvestmentprojectexceedsanappropriatebenchmark,thenwecanconcludethatitisworthundertaking.In1998,theSECrequiredallmutualfundstodesignateabenchmarktopresentalongsidehistoricalreturns.Thevastmajorityofequityfundsuseoneofthefollowingbenchmarks:S&P500,Russell1000orLargeCapValue,Russell1000orLargeCapGrowth,S&PMidCap400,RussellMidCap,RussellMidCapGrowth,RussellMidCapValue,S&PSmallCap600,Russell2000,Russell2000orSmallCapGrowth,orRussell2000orSmallCapValue.1(Monthlyreturnsontheseportfolios,onthevalue-weightedmarket,onlong-termgovernmentbonds,andonTreasurybillsareshowninExhibit1fortheperiodfromJanuary2000throughDecember2004.)Academicresearchalsoprovidessomeguidanceonappropriatebenchmarks.Forexample,undertheassumptionsofthecapitalassetpricingmodel(CAPM),diversifiedinvestorsusethefollowingformulatobenchmarkperformance:()fmfRRR−+β,whereRfreferstotherisk-freerateofreturn;Rm—Rfreferstothereturnonthemarketportfolioinexcessoftherisk-freerate;andβistheslopecoefficientinaregressionoffirmorfundreturnsinexcessoftheriskfreerateonRm—Rf.Thismodelcanbeusedeitherprospectively,withexpectationsoffuturereturnsandβ,orretrospectively,withpastrealizationsofreturnsandβoveraperiod.1SeeBerkSensoyandStevenKaplan,2005,“DoMutualFundsTimeTheirBenchmarks,”UniversityofChicagoWorkingPaper,fordetails.ThisdocumentisauthorizedforuseonlybyZhiyuanJiang([e-mail]).Copyingo[e-mail]800-988-0886foradditionalcopies.207-056MultifactorModels2AnotherexampleistheFama-French3-FactorModel,whichaddstwo“factors”totheCAPM:2()sSMBhHMLRRRfmf++−+β,whereHML,or“HighminusLow”book-to-marketratio,andSMB,or“SmallminusBig”marketcapitalization,areportfoliosconstructedbyGeneFamaandKenFrenchtomeasuretherelativereturnsofstockswithhighandlowratiosofbook-to-marketvalueandwithhighandlowmarketcapitalization.3Athirdexampleisacommonlyused4-FactorModel,whichaddsstockpricemomentuminadditiontoHMLandSMB.4()mMOMsSMBhHMLRRRfmf+++−+β,whereMOMisaportfoliothatmeasurestherelativereturnsofstockswithhighandlowreturnsinthepastyear.Inprinciple,morefactorportfolioscouldbeaddedtothemodel.(MonthlyreturnsonHML,SMB,MOM,and10industryportfoliosareshowninExhibit2fortheperiodfromJanuary2000throughDecember2004.)AswiththeCAPM,the3-and4-factormodelscanbeusedeitherprospectivelyorretrospectively.Whenusedprospectively,estimatesofthefutureexpectedreturnstoeachfactorportfolioarerequired.TheCAPMonlyrequiresestimatesofexpectedβandmarketriskpremium,whilethe4-factormodelalsorequiresestimatesofexpectedcoefficientsh,s,anduandthreeadditionalfactorpremia.Themarketriskpremiumistheexpectedfuturereturnofthemarketportfoliolessthereturnontherisk-freeasset.TheotherfactorpremiaaretheexpectedfuturereturnsontheHML,SMB,andMOMportfolios.(Averageannualreturnsonthevalue-weightedmarket,long-termgovernmentbonds,HML,SMB,MOM,and10industryportfoliosareshowninExhibit3fortheperiodfrom1963through2004.)Whetherthesenewfactorsare“risk”factorsisasubjectofdebate.IntheCAPM,lowβstocksreducetheriskofdiversifiedportfolios.Moregeneralassetpricingmodelsdoallowformorethanoneriskfactor.5But,thereisnoanalogoustheoreticalreasonwhyinvestorswouldacceptlowerreturnsonfirmsthatmovetogetherwithlargemarketcapitalizationstocksandlowbook-to-marketstocks,forexample.PerformanceEvaluation1.EvaluatetheperformanceofTRowePriceBlueChipGrowth(Ticker:TRBCX),GoldmanSachsCORELargeCapGrowth(Ticker:GLCGX),DiversifiedSpecialEquityInv(Ticker:DVPEX),andDFATax-ManagedU.S.SmallCapValue(Ticker:DTMVX)overtheperiodfromJanuary2000throughDecember2004.UsetheCAPM,amultifactormodel,andany2SeeEugeneFamaandKennethFrench,1993,“CommonRiskFactorsintheReturnsonStocksandBonds,”JournalofFinancialEconomics,and“ValidityandRoleoftheCapitalAssetPricingModel,”Chapter8.3inPrinciplesofCorporateFinance(8thed.),byRichardBrealey,StewartMyers,andFranklinAllen,McGraw-Hill/