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1dynamicriskaversion,stochasticdiscountfactorandassetpricing(361005)2*dynamicriskaversion,stochasticdiscountfactorandassetpricingCampbellandCochrane(1998)BrandtandWang(2001)(EquityPremiumPuzzle)SummaryThispaperwillmakeageneralizationofdynamicriskaversiononthebaseofhabit-formedconsumption-basedCAPM,andthuscanexplaintheequitypremiumpuzzleinageneralway.DifferentfromCampbellandCochrane(1998)andBrandtandWang(2001)whichbothhypothesizethesteadystate,thispapersupposestheunitrootprocessofthedynamicriskaversion.Also,thispaperdoesnotsupposetherelevantfactorsoftheformingofconsumptionhabit.Sotheresultisageneralformoftherelationshipbetweentheassetpricinganddynamicriskaversion.Markowitz(1959),Sharpe(1964)Lintner(1965)CAPMBlack(1972)CAPMCAPM1Ross(1976)(APT)Merton(1973a)ICAPMCampbell(2000)Cochrane(2000)2MehraandPrescott(1985)3BrennanandYihongXia(2000)*GFA1CAPM2)(')('11tttcucum++=b,1+tm,b)(cu33CampbellandCochrane(1998)BrandtandWang(2001)NormandinandPascal(1998)4CampbellandCochrane(1998)BrandtandWang(2001)1Pratt(1964)Amihud1980StapletonandSubrahmanyam(1990)ZeckhauserandKeeler(1970)GreenandSrivastava(1985)5Sundaresan(1983)Merton(1990)Merton(1980)KlockandPhilips19991∑∞=-0)(ttttXCUb,11)(++-=ttttRCWW,WCRaa---=--11)()(1ttttXCXCU,1fa,4FamaandFrench(1988),Heaton(1993);HeatonandLucas(1995)5Cochrane(2000).4)ln()(ttttXCXCU-=-,1=a.tX,0=∂∂ttCX),)(()(),(11++-+-=tttttttttCRCWVEXCUCWVb),)(()('1111+++-=-ttttttttCRCWVREXCUb)('),(1ttttXCUCWV-=)(')('111+++-=-ttttttXCUREXCUb.1))(')('(111=--+++ttttttRXCUXCUEb,11+tM)(')('111tttttXCUXCUM--=+++b,N)(')('ttNtNtNNtXCUXCUM--=+++b(2)tRRA=ttttttttXCCXCUXCUC-=---a)(')(=tttttCXCSS-=,a(3)ttttttCXCXRRA+≈--==aagln)1ln(lnlnagln0=-ttCX2--5-ageggln,011=-=++ttt,1+te,CampbellandCochrane(1998)6,11+teBrandtandWang(2001)1+teG1×NN,H1×Nthesensitivityfunction)(11'1+++-=tttttGEGHe,'HHtHtg,)()'(111+++--=ttttttGEGHggg1+ttGE)(mVARtitimitGBAGx++=-=∑1A1×NiBNN×1(2),=--=+++)(')('ttNtNtNNtXCUXCUMbaab--++--)()(ttNtNtNXCXC=)])ln()[ln(exp(ntntttNXCXC++---ab(4)(3)ttttCXCga-+=-lnln)ln(,(3)611)(+++-+=ttteggfgg,g1pff16)))ln(ln(exp(tNttNtNCC---++ggab(5)tttCCglnln11-=++,)))...((exp(21NttttNtNNtgggM++++++++--=ggab(6)=))(exp(1itNiitNg+=+∑+-eab(7)1=N,))(exp())(exp(11111++++++-=--=ttttttggMeabggab(6)(7),2(1)1+tM1)(11=++tttRME,11111),(cov1+++++-=tttttttttMERMMERE(8)(8),Stein71+tR))),(exp((cov),(cov11111++++++-=tttttttRgRMeab=)),(cov),(cov)))((exp((111111++++++--+-tttttttttRgRgEaeaeab),(cov),(cov1111111++++++++=ttttttttttRgRMEREaea(9)tfttRME=+118,tfR7Steinxyf))('(xfE,),cov())('()),(cov(yxxfEyxf=81)(1=+tfttRME,1+tMtfR,tfttRME11=+.7),(cov1111++++++=tttttfttRgRREea(10)0),(cov11=++tttRe,atfRa(10)000901+tg),(cov),(cov11111+++++-=ttttttttRgEgRg(10))),()')(((cov1111++++-++=tttttttfttREGGIHRREgaI1×N10VAR(m)miBAi,...2,1),,(==yG),,(Habq=tH1101NNttME+1191+te1011111)()(==×=+++++tNtttNtNttNtNttPMEPPMERME,NtttNttREPME++==18)())(())'((11qqqQPPWPPTtttTttt∑∑===--(11)tP1×KtN1Nk.)|)(),...(),(()(21yqqqqNktNtNtttMMMEP+++=W2(GMM)1))((11=++tttRMEq,tttttZZRME⊗=⊗++1))((11q,tZ12⊗130))1)(((11=⊗-++ttttZRMEq,0))1)(((11=⊗-++tttZRMEq,ttttZRMh⊗-=+++)1)(()(111qq,q))(1())'(1(1111∑∑=+=+TttTtthTWhTqq(12)Amihud,Yakov,1980,“GeneralRiskAverseandAttitudetowardRisks”,JournalofFinance,35,685-691.Black,F.,1972,“CapitalMarketEquilibriumwithRestrictedBorrowing”,JournalofBusiness,45,444-454.Black,F.andM.Scholes,1973,“ThePricingofOptionsandCorporateLiabilities”,JournalofPoliticalEconomy,81,637-654.Brandt,MichaelW.,andKevinQ.Wang,2001,“TimeVaryingRiskAversionandUnexpectedInflation”,WhartonSchoolworkingpaper.12GMMCochrane(2000)13Green(1993)9Brennan,MichaelJ.andYihongXia,2000,“StockPriceVolatilityandtheEquityPremium”.UCLAworkingpaper.Campbell,J.Y.,2000,“AssetPricingattheMillennium”,JournalofFinance,55,1515-1567.Campbell,J.Y.,AndrewW.Lo,andA.CraigM.,1997,TheEconometricsofFinancialMarkets,PrincetonUniversityPress.Campbell,J.Y.andJohnH.Cochrane,1998,“ByForceofHabit:aConsumption-BasedExplanationofAggregateStockMarketBehavior”,HarvardUniversityandNBERworkingpaper.Cochrane,JohnH.,2000,AssetPricing,PrincetonUniversityPress.Fama,E.F.andK.R.French,1988,“PermanentandTemporaryComponentsofStockPrices”,JournalofPoliticalEconomy,96,246-73.Green,RichardC.,andSanjaySrivastava,1985,“RiskAversionandArbitrage”,Journaloffinance,40,257-268.Green,WilliamH.,1993,EconometricAnalysis,Prentice-HallInc.Heaton,J.C.(1993),“TheInteractionBetweenTime-non-separablePreferencesandTimeAggregation”,Econometrica,61,353-85.Heaton,J.C.andD.J.Lucas(1992),“TheEffectsofIncompleteInsuranceMarketsandTradingCostsinaConsumption-basedAssetPricingMode”',JournalofEconomicDynamicsandControl,16,601-20.Klock,Mark,andRobertF.Philips,1999,“AModelofReturnVolatilitywithApplicationtoEstimatingRelativeRiskAversion”,ReviewofQuantitativeFinanceandAccounting,13,249-260.Lintner,J.,1965,“SecurityPrices,RisksandMaximalGainsfromDiversification”,JournalofFinance,20,587-615.Markowitz,H.,1959,“PortfolioSelection:EfficientDiversificationofInvestment”,JohnWiley,NewYork.Mehra,R.andE.Prescott,1985,“TheEquityPremiumPuzzle”,JournalofMonetaryEconomics,15,145-161.Mert