ch08最优风险资产组合.ppt

1、8-1第8章 最优风险资产组合 Optimal Risky Portfolios8-2最优风险资产组合 Optimal Risky Portfolios8.1 分散化与资产组合风险8.2 两种风险资产的资产组合8.3 在股票、债券与国库券之间的资产配置8.4 马科维茨的资产组合选择模型8.5 电子表格模型8.6 具有无风险资产限制的最优资产组合8-3最优风险资产组合 Optimal Risky Portfolios从分散化如何降低资产组合投资回报的风险开始。在建立这一基点之后，我们将从资产配置和证券选择的两方面考察有效分散化策略。我们将首先考察一个不包含无风险资产的资产配置，我们将运用两个有风

2、险的共同基金：一个是长期债券基金，一个是股票基金。然后我 们将加上一个无风险资产来决定一个最优资产组合。The efficient diversification strategies at the asset allocation and security selection levels.We start with a simple example of asset allocation that excludes the risk-free asset.To that effect we use two risky mutual funds:a long-term bond fund a

3、nd a stock fund.With this example we investigate the relationship between investment proportions and the resulting portfolio expected return and standard deviation.We then add a risk-free asset to the menu and determine the optimal asset allocation.8-4分散化与风险Risk Reduction with Diversification股票数量股票数

4、量Number of Securities标准方差标准方差 St.Deviation市场风险市场风险(系统风险系统风险)Market Risk独特风险独特风险(非系统风险非系统风险)Unique Risk8-5多样化与组合风险Diversification and Portfolio risk一种股票：One-security：风险来自宏观经济 Risks come from macro econ.风险来自企业自己 Risks come from company self两种股票：Two-security 股票组合降低风险 Portfolio will reduce risk8-6R=DR=D

5、t t+(P+(Pt t-P-P0 0)/P)/P0 0E E(R)(R)=R Ri iP Pi i (I=1 to n)(I=1 to n)R Ri i:预期收益率预期收益率 expected returnexpected returnP Pi i:预期收益的概率预期收益的概率 probability of expected returnprobability of expected returnFor example:For example:E E(R)(R)=15%*0.25+10%*0.5+8%*0.25=10.75%=15%*0.25+10%*0.5+8%*0.25=10.75%R=

6、(1/M)*R=(1/M)*R Ri i (I=1 to n)(I=1 to n)如果假设未来各年的收益都如果假设未来各年的收益都相等相等 when all expected returns are samewhen all expected returns are same E E(R)(R)=R=R=（15%+10%+8%15%+10%+8%）/3=11%/3=11%单个股票收益Single Security Return 8-7 R R2 2 =P Pi i（R Ri i-E E(R)(R)）2 2 (I=1 to n)(I=1 to n)=(1/4)(15-11)=(1/4)(15-1

7、1)2 2+(1/2)(10-11)+(1/2)(10-11)2 2+(1/4)(8-11)+(1/4)(8-11)2 2=6.75=6.75 R R=（6.756.75）（1/21/2）=2.6=2.6 （R R）2 2 均方差均方差均方差均方差（R R）标准方差标准方差标准方差标准方差单个股票风险Single Security Risk8-8我们将考察一个包括两个共同基金的资产组合，一个是专门投资于长期债券的债券我们将考察一个包括两个共同基金的资产组合，一个是专门投资于长期债券的债券我们将考察一个包括两个共同基金的资产组合，一个是专门投资于长期债券的债券我们将考察一个包括两个共同基金的资产

8、组合，一个是专门投资于长期债券的债券资产组合资产组合资产组合资产组合D D，一个是专门投资于股权证券的股票基金，一个是专门投资于股权证券的股票基金，一个是专门投资于股权证券的股票基金，一个是专门投资于股权证券的股票基金 E E，表，表，表，表 8-18-1列出了影响这些基列出了影响这些基列出了影响这些基列出了影响这些基金收益率的参数，这些参数可以从真实的基金中估计得出。金收益率的参数，这些参数可以从真实的基金中估计得出。金收益率的参数，这些参数可以从真实的基金中估计得出。金收益率的参数，这些参数可以从真实的基金中估计得出。We will consider a portfolio compris

9、ed of two mutual funds,a bond We will consider a portfolio comprised of two mutual funds,a bond portfolio specializing in long-term debt securities,denoted portfolio specializing in long-term debt securities,denoted D D,and a stock,and a stock fund that specializes in equity securities,fund that spe

10、cializes in equity securities,E E.Table 8.1 lists the parameters.Table 8.1 lists the parameters describing the rate-of-return distribution of these funds.These parameters describing the rate-of-return distribution of these funds.These parameters are representative of those that can be estimated from

11、 actual funds.are representative of those that can be estimated from actual funds.两种股票组合：收益Two-Security Portfolio:Return8-9组合收益率组合收益率r rp p =W =WD Dr rD D+W WE Er rE EW WD D=投资与债券中的部分基金投资与债券中的部分基金r rD D=投资债券的收益投资债券的收益W W =Proportion of funds in Security=Proportion of funds in Security（股票）（股票）r r =Ex

12、pected return on Security=Expected return on Security（股票）（股票）两种股票组合：收益Two-Security Portfolio:ReturnWi iSi i=1=1n n=1 8-10资产组合的期望收益是资产组合中各种证券的资产组合的期望收益是资产组合中各种证券的期望收益的加权平均值期望收益的加权平均值The expected return on the portfolio is a weighted average of expected returns on the component securities with portfol

13、io proportions as weights:E(rp)=WDE(rD D)+WEE(rE E)两种股票组合：收益Two-Security Portfolio:Return8-11 s sp p2 2 =w=w2 2s s2 2+w+w2 2s sE E2 2+2w+2wD Dw wE ECov(rCov(rD,D,r rE E)s sD D2 2=债券的方差债券的方差Variance of Security Variance of Security s s s sE E2 2=股票的方差股票的方差股票的方差股票的方差Variance of SecurityVariance of Sec

14、urityCov(rCov(r，r r)=)=债券和股票收益的债券和股票收益的协方差协方差 Cov(rCov(r，r r)=Covariance of returns for)=Covariance of returns for Security Security and Security and Security 两种股票组合：风险Two-Security Portfolio:Risk8-12协方差协方差 Covariance DEDE =收益的相关系数收益的相关系数Correlation coefficient of Correlation coefficient of returns r

15、eturns Cov(rCov(r，r rE E)=)=D D D DE E E E s s s sD Ds s s sE ECov(rCov(r，r rD D)=)=D D2 2s sD D=证券证券D D收益的标准方差收益的标准方差 Standard deviation of returns for Security DStandard deviation of returns for Security Ds sE E=Standard deviation of returns for Security E=Standard deviation of returns for Securit

16、y E s sp p2 2 =w=w2 2s s2 2+w+w2 2s sE E2 2+2w+2wD Dw wE E DEDE D D E E8-13相关系数：相关系数：取值范围Correlation Coefficients:Possible Values如果如果如果如果 r r r r=1.0,=1.0,证券组合将是正相关证券组合将是正相关证券组合将是正相关证券组合将是正相关If If r r r r=1.0,the securities would be perfectly positively=1.0,the securities would be perfectly positively correlatedcorrelated如果如果如果如果 r r r r=-1.0,=-1.0,证券组合将是负相关证券组合将是负相关证券组合将是负相关证券组合将是负相关If If r r r r=-1.0,the securities would be perfectly negatively=-1.0,the securities would be perfectly negatively