优化风险投资组合.ppt

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1、OptimalRiskyPortfolio优化风险投资组合InvestmentsSlidesbyZengqfChapter6SWUNCopyright©2005byZENGQINGFEN,SWUN本章主要内容TopicsCovered§1分散投资与组合风险!§2最小方差组合!§3有效边界!§4最优风险投资组合§5资产在股票、债券及短期国债间的配置组合理论总结§1分散化与组合风险RiskReductionwithDiversificationNumberofSecuritiesSt.DeviationMarketRi

2、skUniqueRiskFigure7.2PortfolioDiversificationrp=W1r1+W2r2W1=ProportionoffundsinSecurity1W2=ProportionoffundsinSecurity2r1=ExpectedreturnonSecurity1r2=ExpectedreturnonSecurity2两种风险资产组合后如何降低了风险？Two-SecurityPortfolio:Returnp2=w1212+w2222+2W1W2Cov(r1r2)Two-Secu

3、rityPortfolio:RiskCov(r1r2)=1,212完全正相关的资产组合的等于各证券的加权平均.此时组合的标准差必定大于0问题当相关系数=-1时，两资产组合的标准差等于？要想构建标准差为0的组合，两资产权重如何分配？计算组合方差：利用协方差矩阵概念练习:利用协方差矩阵计算组合方差2p=W1212+W2212+2W1W2rp=W1r1+W2r2+W3r3Cov(r1r2)+W3232Cov(r1r3)+2W1W3Cov(r2r3)+2W2W3Three-SecurityPortfoli

4、orp=Weightedaverageofthensecuritiesp2=(Considerallpairwisecovariancemeasures)InGeneral,Forann-SecurityPortfolio:§2最小方差组合(两风险资产)债券股票E（r）8%13%标准差12%20%协方差72相关系数0.3风险收益分析预期收益(%)标准差(%)相关系数协方差股票E13200.372债券B812股权重债权重预期收益方差标准差018144120.10.98.5133.611.55854660.20.8

5、9131.211.45425690.30.79.5136.811.69615320.40.610150.412.26376780.430.5710.15156.0412.49159720.450.5510.25160.212.65701390.480.5210.4167.0412.92439550.50.510.517213.1148770.550.4510.75185.813.63084740.60.411201.614.19859150.70.311.5239.215.46609190.80.212284.81

6、6.87601850.90.112.5338.418.3956517101340020Table7.3ExpectedReturnandStandardDeviationwithVariousCorrelationCoefficientsTwo-SecurityPortfolioswithDifferentCorrelations=113%E(r)St.Dev20%=.3=-1=-1资产组合的机会集合最小方差组合%812%Therelationshipdependsoncorrelationcoeffic

7、ient.-1.0<<+1.0Thesmallerthecorrelation,thegreatertheriskreductionpotential.Ifr=+1.0,noriskreductionispossible.CorrelationEffects最小方差组合风险收益分析预期收益(%)标准差(%)相关系数协方差股票E13200.372债券B812股权重债权重预期收益方差标准差018144120.10.98.5133.611.55854660.2(精确0.18)0.89131.211.45425690.3

8、0.79.5136.811.69615320.40.610150.412.26376780.430.5710.15156.0412.49159720.450.5510.25160.212.65701390.480.5210.4167.0412.92439550.50.510.517213.1148770.550.4510.75185.813.63084740