ASSET ALLOCATION_MANAGEMENT STYLE AND PERFORMANCE

ASSETALLOCATION:MANAGEMENTSTYLEANDPERFORMANCEMEASUREMENTAnAssetclassfactormodelcanhelpmakeorderoutofchaosWilliamF.Sharpe*ReprintedfromtheJournalofPortfolioManagement,Winter1992,pp.7-19.ThiscopyrightedmaterialhasbeenreprintedwithpermissionfromTheJournalofPortfolioManagement.Copyright©InstitutionalInvestor,Inc.,488MadisonAvenue,NewYork,N.Y.10022,aCapitalCities/ABC,Inc.Company.Phone[phone].Itiswidelyagreedthatassetallocationaccountsforalargepartofthevariabilityinthereturnonatypicalinvestor'sportfolio.Thisisespeciallytrueiftheoverallportfolioisinvestedinmultiplefunds,eachincludinganumberofsecurities.Assetallocationisgenerallydefinedastheallocationofaninvestor'sportfolioamonganumberofmajorassetclasses.Clearlysuchageneralizationcannotbemadeoperationalwithoutdefiningsuchclasses.Onceasetofassetclasseshasbeendefined,itisimportanttodeterminetheexposuresofeachcomponentofaninvestor'soverallportfoliotomovementsintheirreturns.Suchinformationcanbeaggregatedtodeterminetheinvestor'soveralleffectiveassetmix.Ifitdoesnotconformtothedesiredmix,appropriatealterationscanthenbemade.Onceaprocedureformeasuringexposurestovariationsinreturnsofmajorassetclassesisinplace,itispossibletodeterminehoweffectivelyindividualfundmanagershaveperformedtheirfunctionsandtheextent(ifany)towhichvaluehasbeenaddedthroughactivemanagement.Finally,theeffectivenessoftheinvestor'soverallassetallocationcanbecomparedwiththatofoneormorebenchmarkassetmixes.Aneffectivewaytoaccomplishallthesetasksistouseanassetclassfactormodel.Afterdescribingthecharacteristicsofsuchamodel,weillustrateapplicationsofamodelwithtwelveassetclassestoanalyzetheperformanceofasetofopen-endmutualfundsbetween1985and1989.ASSETCLASSFACTORMODELSFactormodelsarecommonininvestmentanalysis.Equation(1)isagenericrepresentation:Rirepresentsthereturnonasseti,Fi1representsthevalueoffactor1,Fi2thevalueoffactor2,Finthevalueofthen'th(last)factorandeithenon-factorcomponentofthereturnoni.Allthesevaluesare(potentially)unknownbefore-the-fact,asindicatedbythetildes.Theremainingvalues(bi1throughbin)representthesensitivitiesofRitofactorsFi1throughFin.Akeyassumptionmakesamodelofthissortmorethansimplyanexerciseindatadescription:Thenon-factorreturnforoneasset(ei)isassumedtobeuncorrelatedwiththatofeveryother(e.g.ej).Ineffect,thefactorsaretheonlysourcesofcorrelationamongreturns.Anassetclassfactormodelcanbeconsideredaspecialcaseofthegenerictype.Insuchamodeleachfactorrepresentsthereturnonanassetclassandthesensitivities(bijvalues)arerequiredtosumto1(100%).Ineffect,thereturnonanassetiisrepresentedasthereturnonaportfolio(shownbythesumofthetermsinthebracketedexpression)investedinthenassetclassesplusaresidualcomponent(ei).Forexpositoryconvenience,thesumofthetermsinthebracketscanbetermedthereturnattributabletostyleandtheresidualcomponent(ei)thereturnduetoselection.Indeed,akeycontributionofthisapproachistheseparationofreturnintothesetwomaincomponents.EVALUATINGASSETCLASSFACTORMODELSTheusefulnessofanassetclassfactormodeldependsontheassetclasseschosenforitsimplementation.Whilenotstrictlynecessary,itisdesirablethatsuchassetclassesbe1)mutuallyexclusive,2)exhaustiveand3)havereturnsthatdiffer.Pragmatically,eachshouldrepresentamarket-capitalizationweightedportfolioofsecurities;nosecurityshouldbeincludedinmorethanoneassetclass;asmanysecuritiesaspossibleshouldbeincludedinthechosenassetclasse;andtheassetclassreturnsshouldeitherhavelowcorrelationswithoneanotheror,incasesinwhichcorrelationsarehigh,differentstandarddeviations.Whiletheappropriatemeasureoftheefficacyofanyspecificimplementationdependsontheusestowhichthemodelistobeput,factormodelsaretypicallyevaluatedonthebasisoftheirabilitytoexplainthereturnsoftheassetsinquestion(i.e.theRis).Ausefulmetricistheproportionofvarianceexplainedbytheselectedassetclasses.Usingthetraditionaldefinition,forasseti:Theright-handsideofequation(2)equals1minustheproportionofvarianceunexplained.TheresultingR-squaredvaluethusindicatestheproportionofthevarianceofRiexplainedbythenassetclasses1.Itisimportanttorecognizethatthismeasureindicatesonlytheextenttowhichaspecificmodelfitsthedataathand.Abettertestoftheusefulnessofanyimplementationisitsabilitytoexplainperformanceout-of-sample.Forthisreasonitisimportanttoconsidernotonlytheabilityofamodeltoexplainagivensetofdatabutalsoitsparsimony.Otherthingsequal(e.g.R-squaredvalues),thefewertheassetclasses,themorelikelyisthemodeltorepresentcontinuingfundamentalrelationshipswithpredictivecontent2.Toevaluatetheexposuresoffundstochangesinthereturnsofkeyassetclasses,theappropriatemeasureisthecollectiveabilityofasetofsuchclassestoexplainthetime-seriesvariabilityinthereturnsonatypicalfund(e.g.mutualfundorseparately-managedinstitutionalaccount).Notethatthiscriteriondiffersfromthatoftenappliedinevaluatingfactormodelsdesignedtodescribespecificportionsoftheoverallcapitalmarket.Forexample,whenconstructinganequityfactormodel,onemightconsidertheabilityoftheselectedfactorstoexplainthetime-seriesvariationinthereturnsofatypicalstock.Moststockmarketmodelsincludefactorsrepresentingret