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时间:2019-07-10
《The Two-Parameter Portfolio__ Model》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、TheTwo-ParameterPortfolioModel”FoundationsofFinance”Chapter7October12,20101/22OutlineTheFrameworkTheTwo-ParameterPortfolioModelTheGeometryoftheEfficientSetTheEffectofDiversificationAnExtendedModelSomeEmpiricalPuzzles2/22TheFrameworkConsideroneinvestor’sdecision,whi
2、chisanatomisticcompetitorinfrictionlessmarketsTwoperiod:t=1,hehaswealthw1,whichhemustallocatetocurrentconsumptionc1andtoaninvestmentw1 c1insomeportfolioofsecuritiest=2,thevalueofhisportfolioprovideshisconsumptionc2ThenhisproblemisMaxU(c1;c˜2)s:t:c˜2=(w1 c1)(1+R˜p
3、)whereR˜pisthereturnontheportfoliopfromtime1totime23/22TheTwo-ParameterPortfolioModelSupposeU(c1;c˜2)=u(c1)+u(˜c2),thenwhatisu(˜c2)?ThroughTaylorexpansion01002u(˜c2)=u(E(˜c2))+u(E(˜c2))(˜c2 E(˜c2))+u(E(˜c2))(˜c2 E(˜c2))+R32thenhisexpectedutility:1002E(u(˜c2))=u(E
4、(˜c2))+u(E(˜c2))(˜c2))+E(R3)2Howitwillbecometwo-parameterportfoliomodel,ormean-variancemodel?4/22TheTwo-ParameterPortfolioModelForarbitrarydistributions,themean-variancemodelcanbemotivatedbyassumingquadraticutilityquadraticutility:u(c)=10c 2c2,thenR=03butithasun
5、desirablepropertiesofsatiationandincreasingabsoluteriskaversionForarbitrarypreferences,themean-variancemodelcanbemotivatedbyassumingtheratesofreturnaremultivariatenormallydistributedthenE(R3)canbeexpressedasfunctionsofthemeanandvariancenormaldistributionarealsost
6、ableunderaddition5/22TheTwo-ParameterPortfolioModelAssumenormaldistribution1002E(u(˜c2))=u(E(˜c2))+u(E(˜c2))(˜c2)+E(R3)2E(˜c2)=(w1 c1)(1+E(R˜p))(˜c2)=(w1 c1)(R˜p)Wheninvestorisrisk-averse,u0(c)>0u00(c)<0,so,givenE(R˜p),investorprefersless(R˜p)ofportfoliotomor
7、e;given(R˜p),heprefersmoreE(R˜p)toless.Efficientportfolioset:Nootherportfoliowiththesameorhigherexpectedreturnhaslowerstandarddeviationofreturn.6/22TheTwo-ParameterPortfolioModelGeometricinterpretation:7/22TheGeometryoftheEfficientSetConsiderthecombinationsoftwose
8、curitiesR˜p=xR˜q+(1 x)R˜sE(R˜p)=xE(R˜q)+(1 x)E(R˜s)(R˜p)=(x22(R˜q)+(1 x)22(R˜s)+2x(1 x)corr(R˜q;R˜s)(R˜q)(R˜s))1=2wherecov(R˜q;R˜s)corr(R˜q;R˜s)=(R˜q)(R
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