8. Intertemporal Asset Pricing

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1、Long-TermPortfolioChoiceJohnY.CampbellEc2723November2011JohnY.Campbell(Ec2723)Long-TermPortfolioChoiceNovember20111/35OutlineMyopicportfoliochoice:investmentrulesthatdonotdependontheinvestmenthorizon.IEpstein-Zinutilitywitheitheriidreturnsorγ=1.Long-term

2、portfoliochoice:investmentrulesthatdodependontheinvestmenthorizon.AssumeEpstein-Zinutilityandγ6=1.ITime-varyinginterestrates(Campbell-ViceiraChapter3.)ITime-varyingriskpremia(CVChapter4.)IApplicationstothecross-sectionofstockreturns(intertemporalCAPM).IL

3、aborincome,animplicitholdingofhumancapitalwhosevaluedependsonthehorizon(CVChapters6and7.)JohnY.Campbell(Ec2723)Long-TermPortfolioChoiceNovember20112/35MyopicPortfolioChoiceMyopicPortfolioChoice(1)Whenislong-termportfoliochoiceequivalenttoshort-termportfo

4、liochoice,i.e.myopic?Assumepowerutility,lognormalassetreturns,approximateportfolioreturn(exactincontinuoustime)IPowerutilityinvestorsolvesamean-varianceproblemEasytoseethatiidreturnsimplymyopicinvestingwhennorebalancingispossibleIMeansandvariancesscalepr

5、oportionallytotheinvestmenthorizonISolutiontomean-varianceproblemisuna¤ectedbythehorizonTechnicaldi¢culty:portfolioreturnapproximationdeterioratesatlonghorizonsIButthishaslittleimpactinpractice(Barberis2000)Abiggerissue:Whatiftheinvestorcanrebalance?John

6、Y.Campbell(Ec2723)Long-TermPortfolioChoiceNovember20113/35MyopicPortfolioChoiceMyopicPortfolioChoice(2)Withpowerutility,portfoliochoicedoesnotdependonwealth,sopastreturnsirrelevantWithiidreturns,nostatevariablesSowecancon…neattentiontodeterministicportfo

7、liosharesWewanttoshowthatdeterministicαt=α,constantInvestorsolvesaK-periodmean-varianceproblem.ConsiderK=2.1γmaxEt(rp,2,t+2)+Vart(rp,2,t+2)Vart(rp,2,t+2).22JohnY.Campbell(Ec2723)Long-TermPortfolioChoiceNovember20114/35MyopicPortfolioChoiceMyopicPortfoli

8、oChoice(3)rp2,t+22rf=(rp,t+1rf)+(rp,t+2rf)12=αt(rt+1rf)+αt(1αt)σ212+αt+1(rt+2rf)+αt+1(1αt+1)σ,2Var(r)=(α2+α2)σ2tp,2,t+2tt+112Et(rp,2,t+2)+Vart(rp,2,t+2)=2rf+(αt+αt+1)(Errf+σ/2).2JohnY.Campbell(Ec2723)Long-TermPortf