Chap007最优风险资产组合

INVESTMENTS|BODIE,KANE,MARCUSCopyright©2011byTheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinCHAPTER7OptimalRiskyPortfolios最优风险资产组合INVESTMENTS|BODIE,KANE,MARCUS7-2TheInvestmentDecision投资决策•Top-downprocesswith3steps:自上而下1.Capitalallocationbetweentheriskyportfolioandrisk-freeasset首先分配份额：安全、风险资产间2.Assetallocationacrossbroadassetclasses各类资产间的配置3.Securityselectionofindividualassetswithineachassetclass每类资产内部的证券选择INVESTMENTS|BODIE,KANE,MARCUS7-3DiversificationandPortfolioRisk分散化与组合风险•Marketrisk市场风险–Systematicornondiversifiable系统风险也是不可分散风险•Firm-specificrisk公司风险–Diversifiableornonsystematic可分散风险、非系统性风险INVESTMENTS|BODIE,KANE,MARCUS7-4Figure7.1PortfolioRiskasaFunctionoftheNumberofStocksinthePortfolio组合风险作为组合内股票数量的函数INVESTMENTS|BODIE,KANE,MARCUS7-5Figure7.2PortfolioDiversification组合分散化INVESTMENTS|BODIE,KANE,MARCUS7-6PortfolioDiversification:Intuition组合分散化:直觉INVESTMENTS|BODIE,KANE,MARCUS7-7CovarianceandCorrelation协方差与相关系数•Portfolioriskdependsonthecorrelationbetweenthereturnsoftheassetsintheportfolio组合风险依赖于组合资产回报之间的相关系数•Covarianceandthecorrelationcoefficientprovideameasureofthewayreturnsoftwoassetsvary协方差与相关系数可以提供资产间回报变化相互关联的方式INVESTMENTS|BODIE,KANE,MARCUS7-8Two-SecurityPortfolio:Return二资产组合收益情况PortfolioReturnBondWeightBondReturnEquityWeightEquityReturnpDEDEPDDEErrwrwrwwrr()()()pDDEEErwErwErINVESTMENTS|BODIE,KANE,MARCUS7-9=VarianceofSecurityD=VarianceofSecurityE=CovarianceofreturnsforSecurityDandSecurityETwo-SecurityPortfolio:Risk二资产组合风险情况EDEDEEDDrrCov2E2DEDrrCov,INVESTMENTS|BODIE,KANE,MARCUS7-10Two-SecurityPortfolio:Risk风险情况•Anotherwaytoexpressvarianceoftheportfolio:表达组合方差的另一种办法2(,)(,)2(,)PDDDDEEEEDEDEwwCovrrwwCovrrwwCovrrINVESTMENTS|BODIE,KANE,MARCUS7-11D,E=Correlationcoefficientofreturns相关系数Cov(rD,rE)=DEDED=StandarddeviationofreturnsforSecurityD标准差DE=StandarddeviationofreturnsforSecurityE标准差ECovariance协方差INVESTMENTS|BODIE,KANE,MARCUS7-12Rangeofvaluesfor1,2+1.0-1.0If=1.0,thesecuritiesareperfectlypositivelycorrelated完全正相关If=-1.0,thesecuritiesareperfectlynegativelycorrelated完全负相关CorrelationCoefficients:PossibleValues相关系数的可能值INVESTMENTS|BODIE,KANE,MARCUS7-13CorrelationCoefficients相关系数•WhenρDE=1,thereisnodiversification如果相关系数为1就没有风险分散效果•WhenρDE=-1,aperfecthedgeispossible如果相关系数为-1，可以做出完全对冲效果DDEEPwwDEDDEww1INVESTMENTS|BODIE,KANE,MARCUS7-14Table7.2ComputationofPortfolioVarianceFromtheCovarianceMatrix从协方差矩阵中算出组合方差INVESTMENTS|BODIE,KANE,MARCUS7-15Three-AssetPortfolio三资产组合112233()()()()pErwErwErwEr23232222212123,2323,1312,121222INVESTMENTS|BODIE,KANE,MARCUS7-16Figure7.3PortfolioExpectedReturnasaFunctionofInvestmentProportions组合期望收益对投资比例的函数INVESTMENTS|BODIE,KANE,MARCUS7-17Figure7.4PortfolioStandardDeviationasaFunctionofInvestmentProportions组合标准差对投资比例的函数INVESTMENTS|BODIE,KANE,MARCUS7-18TheMinimumVariancePortfolio最小方差投资组合•Theminimumvarianceportfolioistheportfoliocomposedoftheriskyassetsthathasthesmalleststandarddeviation,theportfoliowithleastrisk.•最小方差组合是风险资产组合成为具有最小方差（或者标准差）的投资组合•Whencorrelationislessthan+1,theportfoliostandarddeviationmaybesmallerthanthatofeitheroftheindividualcomponentassets.相关系数小于1时会有分散化效果•Whencorrelationis-1,thestandarddeviationoftheminimumvarianceportfolioiszero.相关系数等于-1时最小方差组合标准差为0INVESTMENTS|BODIE,KANE,MARCUS7-19Figure7.5PortfolioExpectedReturnasaFunctionofStandardDeviation组合期望收益对标准差的函数INVESTMENTS|BODIE,KANE,MARCUS7-20•Theamountofpossibleriskreductionthroughdiversificationdependsonthecorrelation.可能降低的风险取决于相关系数•Theriskreductionpotentialincreasesasthecorrelationapproaches-1.为-1时最低–If=+1.0,noriskreductionispossible.没分散–If=0,σPmaybelessthanthestandarddeviationofeithercomponentasset.可能比任何一种资产都低–If=-1.0,arisklesshedgeispossible.完全消除风险CorrelationEffects相关系数效应INVESTMENTS|BODIE,KANE,MARCUS7-21Figure7.6TheOpportunitySetoftheDebtandEquityFundsandTwoFeasibleCALs债券和股权基金的投资可行集与两条资本配置线INVESTMENTS|BODIE,KANE,MARCUS7-22TheSharpeRatio夏普比•MaximizetheslopeoftheCALforanypossibleportfolio,P.最大化CAL的斜率•Theobjectivefunctionistheslope:•TheslopeisalsotheSharperatio.•斜率就是夏普比()PfPPErrSINVESTMENTS|BODIE,KANE,MARCUS7-23Figure7.7TheOpportunitySetoftheDebtandEquityFundswiththeOptimalCALandtheOptimalRiskyPortfolio债券与股权的投资可行集-最优CAL与最优风险组合INVESTMENTS|BODIE,KANE,MARCUS7-24Figure7.8DeterminationoftheOptimalOverallPortfolio决定最优组合INVESTMENTS|BODIE,KANE,MARCUS7-25Figure7.9TheProportionsoftheOptimalOverallPortfolio最优组合的成分INVESTMENTS|BODIE,KANE,MARCUS7-26MarkowitzPortfolioSelectionModel马克维茨资产组合选择模型•SecuritySelection证券选择–Thefirststepistodeterminetherisk-returnopportunitiesavailable.第一步是决定风险收益的投资机会–Allportfoliosthatlieontheminimum-variancefrontierfromtheglobalminimum-varianceportfolioandupwardprovidethebestrisk-returncombinations最小方差边界上的全局最优方差组合，向上的半条线是最优组合INVESTMENTS|BODIE,KANE,MARCUS7-27Figure7.10TheMinimum-VarianceFrontierofRiskyAssets风险资产的最小方差边界INVESTMENTS|BODIE,KANE,MARCUS7-28MarkowitzPortfolioSelectionModel马克维茨资产组合选择模型•WenowsearchfortheCALwiththehighestreward-to-variabilityratio•我们选择与最小方差边界上半部分相切的那一根资本配置线作为最优资本配置线INVESTMENTS|BODIE,KANE,MAR