R-Forecasting and Asset Pricing Anomalies

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1、Robust-H∞ForecastingandAssetPricingAnomaliesAaronTornell∗UCLAandNBERFirstdraft:August1998Thisdraft:December2001JELClassificationNo.C61,E44,G12AbstractWepresentaRobust-H∞modelthathelpsrationalizewellknownassetpricinganomalies,suchasthepredictabilityofexcessreturns,excessvolatility,andtheequity-premi

2、umpuzzle.Aswithrationalexpectations(RE),agents’forecastsarebasedonarigorousoptimizationalgorithmthatdoesnotpre-sumemisperceptions—itsimplydepartsfromsomeoftheimplicitassumptionsthatunderlieRE.Agentsfeartheexistenceofmisspecificationanddesignstrategiesthatwillberobustagainstaverylargeclassofmisspeci

3、fications.Thenewelementisthatuncertaintycannotbemodeledviaprobabilitydistribu-tions.Weconsideranassetpricingmodelwhereuncertaintyisrepresentedbyunknown-butboundeddisturbancesequences,asintheH∞-controlliterature.Agentsmustfilterthe‘persistent’componentofasequenceofdividendobservationsinordertomakecon

4、sumptionandportfoliodecisions.WefindthatH∞forecastsaremoresensitivetonewsthanREforecastsandequilibriumpricesexhibittheanomaliespreviouslymentioned.∗Thispaperwascirculatedunderthetitle“H∞ForecastingandExcessVolatilityofAssetPrices.”IthankforhelpfulcommentsCostasAzariadis,OlivierBlanchard,BryanEllick

5、son,DrewFudenberg,LarsHansen,MichaelHarrison,KenJudd,MonikaPiazzesi,EduaroSchwartz,JimStock,JohnTaylorandseminarparticipantsatHarvard,MITandtheNBERassetpricinggroup.IespeciallythankTamerBasarandTomSargent.ForexcellentresearchassistanceIthankKitMingYan.Allerrorsaremyown.1.IntroductionTherearesevera

6、lstylizedfactsinmacroeconomicsthatcannoteasilybeexplainedbyrationalexpectationsmodelswithstandardtime-additivepreferences.Prominentexamplesaretheexcessvolatilityofassetprices,thepredictabilityofexcessreturns,andtheequitypremiumandrisk-freeratepuzzles.Inordertorationalizetheseanomaliesresearchersha

7、veextendedthebenchmarkmodelindifferentdirec-tions.Onestrategyhasbeentokeeprationalexpectations(RE),buttoconsidermorecomplexpreferencesthatgeneratetime-varyingriskpremia,ortointroduceimperfectionsincreditmarkets.1T