高盛因子模型

1,ProjectpresentationLinearFactorModelandMoreHongCaiOctober14,2010,2,OUTLINE,IntroductiontoLinearFactorModelsIntroductiontoBARRA-TypeLinearFactorModelsBARRA-TypeChineseEquityLinearFactorModelsBeyondBARRA-TypeLinearFactorModelsSummary,3,IntroductiontoLinearFactorModels,Alinearfactormodel(LFM)isananalyticaldeviceborrowedfromtheworldofstatisticsandemployssingleormultiple,mostlymultiple,factorslinearlyinitscomputationstoexplainmarketphenomenaand/orequilibriumassetprices,especiallyinequitymarket.LFMscanbeusedtoexplaineitheranindividualsecurityoraportfolioofsecuritiesbycomparingthefactorstoanalyzerelationshipsbetweenvariablesandthesecuritysresultingperformance.LFMsarealsousedtoconstructportfolioswithcertaincharacteristics,suchasrisk,ortotrackindexes.Theycanbedividedintothreecategories:macroeconomic,fundamentalandstatisticalmodels.,MajorApplicationofLFMsPredictreturnsofanindividualsecurityoraportfolioofsecurities.Generateestimatesofabnormalreturns(so-calledAlphaModel)Identifyrisksensitivities.Estimatethevariabilityandconvertibilityofreturns(Further,VaRcomputationbyDelta-Normalmethod).Usedinvarioustradingstrategies,likeStat-Arb,Quant/AlgoTrading(suchasmomentum,liquidityandetc).,4,LinearFactorModelSpecification,Thegeneralformofthelinear(multiple)factormodelisRit=i+1if1t+2if2t+KifKt+itwhere:Rit=returnorexcessreturnonasseti(i=1,n)fkt=kthcommonfactor(k=1,K)ki=factorloadingonassetiforkthfactorit=assetspecificfactorforasseti,AssumptionsThefactorrealizations,ft,areI(0)withunconditionalmoments.Theassetspecificerrorterms,it,areuncorrelatedwitheachofthecommonfactors,fkt.Theerrorterms,it,areseriallyuncorrelatedandcontemporaneouslyuncorrelatedacrossassets.,5,ThreeTypesofLinearFactorModels,MacroeconomicfactormodelsUseobservableeconomictimeserieslikeinterestratesandinflationasmeasuresofpervasiveorcommonfactorsinassetreturns.Examples:SharpesSingleIndexModel,CAPM,andAPT.Factorvariables,ft,areobservablebutfactorloadings,i,mustbeestimates.FundamentalfactormodelsUseobservablefirmorassetspecificattributessuchasfirmsize,dividendyield,andindustryclassificationtodeterminecommonfactorsinassetreturns.Examples:Fama-FrenchFactorModelandBARRAFactorModel.InFama-French-TypeFactorModel,firmattributesareusedtocreatefactormimickingportfoliosthatareusedtoproxythefactorvariablesft.Factorloadings,i,mustbeestimated.InBARRA-TypeFactorModel,factorloadings,i,arefirmattributesandobservable.Thefactorvariables,ft,mustbeestimated.StatisticalfactormodelsTreatsthecommonfactorsasunobservableorlatentvariables.Examples:FactorAnalysisandPrincipleComponentAnalysis.Bothfactorvariables,ft,andfactorloadings,imustbeestimated.,6,IntroductiontoBARRAsModels,BARRA,whohaddevelopedBARRAsModels,isaninvestmentconsultingfirmspecializinginquantitativeriskmanagementtools.Thefactorsarethemodelsstatisticallyderivedbuildingblockstocapturethesourcesofequitymarketreturns.TheBARRAUSE3modelemploys67explanatoryfactors.Mostofthemareintuitivealthoughsomenot.Themodelisconsideredlinearbecause,ingeneral,itassumesthatthefactorsinfluencingthemarketworkinalinearfashion.BARRAdoesperformanceanalysisbyfirstestimatingthereturnstoitsfactorsandthenbylinkingthesefactorreturnswitheachmanagersactivepolicies.Eachmonth,BARRArunsabigstatisticalregressionthatsimultaneouslyproducesestimatesofthepriormonthsreturnforeachfactor.Thesefactorreturnscanbeinterpretedas“whileadjustingfortheotherfactorsintheUSE3model,thereturnforfactorXwasY%lastmonth.”Takingthedividendyieldfactorasanexample,onecansaythatnetofthe64otherfactors,thereturnattributabletodividendyieldwas1.2%lastmonth.,Now,BARRAFactorModelswillbethefocusofthepresentationduetotheirimportanceandpopularityinfinancialindustryasafactualstandard.,7,IntroductiontoBARRAsModels,BARRAsmodelisusedtopredictreturnsandriskforequity,fixedincome,cashandderivativeinstruments,atboththeassetandportfoliolevel.,MajorComponentsofBARRAsModelsBarraGlobalEquityModel(GEM2S/L)-Capturestheeffectsofglobalcommonfactors,suchastheworldmarket,styles,countries,industriesandcurrencies,onportfolioreturn.BarraEuropeEquityModel(EUE3)-ProvidesaunifiedperspectiveonriskacrossallmainEuropeanequitymarkets.EUE3capturesthecommoncharacteristicsoftheexpandedEuropeanregion,suchastheEuropemarket,styles,industries,countriesandcurrencies.BarraIntegratedModel-Offersaclearanddetailedviewofyourriskexposuresacrossmarkets,assetclassesandcurrencies.BarraMultiple-HorizonEquityModels-IncorporatedailyreturnsandinvestmenthorizonintotheprovenfactorstructureofBARRAsindustry-leadingriskmodels.BarraSingleCountryEquityModels-Covertheworldsmajorequitymarkets-offeringsourcesofriskandreturnspecifictolocalmarkets.BarraTradingModels-Idealforequitytradersmanagingriskovershorttimehorizons.,8,ProsandConsofBARRAsModels,ProsofBARRAModelsBARRAModelsisthemostcomprehensiveapproachtoequityperformanceanalysisavailable.Thelargenumberoffactorsandthestatisticalrigorofthemodeldodecomposeequityreturnsintomanyinvestmentpolicyvariables.TheseresultsusedinconjunctionwithBARRAsriskmanagementtools,createavaluablefeedbacklooptoaccentuateormitigatepoliciesasappropriate.Theassumptionoflinearityholdsatmostofcasesandmakesthemodelscapabletohandleverycomplexfactorsandassets,andthussignificantlydecreasesthecomputationloadsforportfolioanalysisandriskmanagement.,ConsofBARRAModelsTheassumptionoflinearitybreaksinsomeaccessions,likeunabletocapturetheextremebehaviorofthelargestcapitalizationstocks.UsingBARRAsmodeltocontrolriskstealsthemodelsthunderwhenitcomestoexplainingreturns.Othermethods,likereturns-basedstyleanalysisorpeergrouprankingscouldoffersmorevaluableprescriptiveinterpretation.Itisdifficulttodecidehowmanyandwhichfactorstoinclude.Also,modelswillbejudgedonhistoricalnumbers,whichmightnotaccuratelypredictfuturevalues.BARRAsmodelsassumethatallinvestmentsaremadeonamonthlybuy-and-holdbasis.Forinvestmentmanagerswithsignificantamountsofintra-monthturnover,thelimitationcannoticeablyaffecttheanalysis.,9,BARRA-TypeChineseEquityModel,TobuildBARRA-TypeChineseequitymodelisageneralquestionofmultivariateregressioninfinancialeconometrics.Moststatisticalpackages,suchasSAS,RandS-Plus,couldhandletheregressionprocesses.,KeysinbuildingBARRA-TypeChineseequitymodel:Dataaccuracy,acrucialpieceofriskmodeling,isoneofthecrucialelementsinthesuccessofBARRAsmodels.Thededicatedteamsaggregateandcleanserawdatafromvarioussources,andcreateadatabasewithgreatdepthandaccuracy.InordertomatchthestandardsetbyBARRA,extensiveeffortsmustbeimplementedindatacollectionandprocessing.Morechallengesareindataqualityanddifferentstatisticalmethodology,likemonthlyGDPgrowth,inChina.AlthoughthechoiceofriskfactorswillfollowBARRAUSE3model,significantmodificationsarerequiredduetosomespecialpropertiesofChineseequitymarket,suchasindividual-tradingdominance,hugenon-tradableshareinventory,significantgovernmentguidanceandvolatiletradingbehavior.,10,FurtherImproveChineseEquityModel,DuetothesuccessofBARRAFactorModels,manyfinancialinstitutionshadtriedtobuildtheirownBARRA-TypefactormodeltoimplementtheirproprietaryinsightstothemarketsandovercomesomeshortcomingsoftheBARRAsmodelstoachieveadditionaladvantagescomparedtogeneralusersoftheBARRAsmodels.GoldmanSachshadbuilttheirownBARRA-Typefactormodelbyincludingadditionalriskfactorsandupdatedthenewmodelwithmuchhigherfrequency.Aspecialalgorithmhadbeendevelopedtofastentheregressionprocess.Theimprovementshadbeenpositivelyapprovedinthevarioustradingstrategiesatseveralequitymarketsacrosstheworld.TheresultsofGoldmanSachsclearlydemonstratedthatitisapplicabletobuildanefficientBARRA-Typefactormodelwithreasonableresources,althoughsuchfurtherimprovementsarenotthefirstpriorityinbuildingBARRA-TypeChineseequitymodel.,11,VariousApplicationsBasedonBARRA-TypeLFMs,KeyApplicationsintendedtodevelop:PortfolioManagementPortfolioOptimizationIndexTrackingPerformanceAnalysisALPHAGenerationRiskManagementRiskFactorSensitivityAnalysisRiskNeutralityandMitigationValue-at-RiskComputation,BARRA-Typelinearmultiplefactormodelsarewidelyusedinfinancialindustryandvariousapplicationshavebeendevelopedtotakeadvantageofthepowerofthemodels.Itisinsufficienttoonlydevelopthemodelitself.,12,FullBARRA-TypeLFMDevelopment,OverallDevelopmentMethodology,PreliminaryBARRA-TypeLFMDevelopment,PreliminaryModelValidation,SmallDataSets,APIandGUIDevelopment,DateCollectionandCleanse,Feedbacks,FullModelValidation,ApplicationDevelopment,AutomationandStreamlineProcedures,13,DevelopmentProcedures,DateCollectionandCleanseDedicatedstaffwillbeinchargeofdatecollectionandcleanse.Additionalattentionmushbeenpaidtomanymacroeconomicalindicatorsduetodifferentmethodologyandpoorquality.Inadditiontotheofficialdomesticdata,estimatesfromotherdatasourcesarealsoconsidered.Focusonthedataofthelast10-15years.,PreliminaryBARRA-TypeLFMDevelopmentandValidationThepreliminarymodeldevelopmentishighlyintertwinedwiththestepofdatacollectionandcleanse.Thechoiceofriskfactorswilldecidewhatkindsofdatatobecollected,andthequalityandavailabilityofdataalsoaffectthemodelformation.Asmallsetofstocks(50-100)isselectedwithgoodbalanceintermsofmarketsize,industry,growth/valueandmoreattributes.Thedatabefore2009willbeusedtodecidethemodelstructure,whichwillbejustifiedbythedataafter2009.Inordertofastenthedevelopment,MatlabandstatisticalpackageslikeSASwillused.,14,DevelopmentProcedures,FullBARRA-TypeLFMDevelopmentandValidationMostdataacrossallChinesestockswillbeusedinfullmodeldevelopment.Inadditiontothetraditionalvalidationprocessbyusingthelatestdata,themorestringentandcomprehensivetestshavetobeenpast.Thesetestsaredesignedbymimickingtherealapplicationsofthemodel.Thewholeregressionprocessshouldbeoptimizedin15-20hrs.Ornewtoolsmustbeenintroduced.,AutomationandStreamlineProceduresDatamanagementwillbethecoreofthewholecycle.PythonorPerlwillbeusedtostreamlinethewholeprocessandscheduletheroutinejobs.Newtoolsordevelopmentplatformmightbeintroducedtofastentheregressionanddatamanagement.,15,DevelopmentProcedures,ApplicationDevelopmentApplicationsmustbedesignedontheneedsofclients.Comparedtoweb-basedapplications,astandaloneclient-sidesoftwareminimizesdatacommunicationwiththedataserverandtheleakageofhighlysensitivetradinginformation.Algorithmsmustbeoptimizedtolimitthecomputationtime.,APIandGUIDevelopmentGUIforweb-basedapplicationsandAPIforastandaloneclient-sidesoftware.GUIandAPImustberunatdedicatedservers,whichwillbeupdatedfromthedatabase.,16,ProspectsofComprehensiveFinancialServiceProvider,ChineseMarketOrientedBasedonneedsofChinesefinancialmarketandproductsCompletelylocalizedcustomsupportsFullyintegrateChinesecharacteristicswithstate-of-artofWallStreetCostEfficientSeparatemostofcommonquantitativeresearchandroutinesfromdailyinvestmentdecisionsSavemoneyandtimetobuildacompletesupportingteamLetfundmanagerandriskofficertofocusontheirmainbusinessFastenthep