优化风险投资组合课件

1、CHAPTER 7Optimal Risky Portfolios优化风险投资组合Diversification and Portfolio Risk分散化和投资组合风险Market risk 市场风险Systematic or nondiversifiable 系统风险或不可分散风险Firm-specific risk 公司特有风险Diversifiable or nonsystematic 可分散风险或非系统风险GM and Toyota Share Prices通用和丰田股票价格Figure 7.1 Portfolio Risk as a Function of the Number o

2、f Stocks in the Portfolio投资组合风险是投资组合中股票数量的函数Two-Security Portfolio: Return两大风险资产的投资组合:收益Two-Security Portfolio: Risk两大风险资产投资组合:风险 = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security ECovariance 协方差Cov(rD,rE) = DEDED,E = Correlation coefficient of ret

3、urns 收益相关系数 D = Standard deviation of returns for Security D 风险资产D的收益标准差E = Standard deviation of returns for Security E 风险资产E的收益标准差Range of values for 1,2 + 1.0 r -1.0If r= 1.0, the securities would be perfectly positively correlated If r= - 1.0, the securities would be perfectly negatively correla

4、tedCorrelation Coefficients: Possible Values相关系数: 估计值Table 7.1 Descriptive Statistics for Two Mutual Funds两种共同资产的描述性统计Table 7.3 Expected Return and Standard Deviation with Various Correlation Coefficients不同相关系数下的期望收益和标准差Figure 7.4 Portfolio Standard Deviation as a Function of Investment Proportions投

5、资组合标准差是投资比率的函数Figure 7.5 Portfolio Expected Return as a function of Standard Deviation 投资组合期望收益是标准差的函数The relationship depends on correlation coefficient. 关系取决于相关系数-1.0 +1.0The smaller the correlation, the greater the risk reduction potential. 系数越小,风险分散化效果越好If r = +1.0, no risk reduction is possible

6、. 相关系数等于+1, 则无分散风险的效果Correlation Effects相关效应 Figure 7.6 The Opportunity Set of the Debt and Equity Funds and Two Feasible CALs债务与股权基金可行集和两条可行的资本配置线The Sharpe Ratio夏普比率Maximize the slope of the CAL for any possible portfolio, p 在任何可能的投资组合中使资本配置线的斜率最大化The objective function is the slope: 目标函数是斜率Figure

7、 7.8 Determination of the Optimal Overall Portfolio最优全部投资组合的决策Figure 7.9 The Proportions of the Optimal Overall Portfolio最优全部投资组合的比例Figure 7.10 The Minimum-Variance Frontier of Risky Assets风险资产的最小方差边界Markowitz Portfolio Selection Model Continued续:马科维茨投资组合选择模型We now search for the CAL with the highes

8、t reward-to-variability ratio 我们现在找到最大斜率的资本配置线Markowitz Portfolio Selection Model Continued续前Now the individual chooses the appropriate mix between the optimal risky portfolio P and T-bills as in Figure 7.8 现在从最优风险投资组合P和短期国库券中选择合适的组合, 如图7.8Figure 7.12 The Efficient Portfolio Set有效投资组合集Capital Alloca

9、tion and the Separation Property资本配置与资产分割The separation property tells us that the portfolio choice problem may be separated into two independent tasks 资产分割告诉我们投资组合选择问题可分解为两个相互独立的工作Determination of the optimal risky portfolio is purely technical 最优风险投资组合的决策完全是技术性的Allocation of the complete portfolio to T-bills versus the risky portfolio depends on personal preference 根据个人的偏好决定资本在国库券和风险投资组合中的大分配The Power of Diversification分散化的力量Remember:If we define the average variance and average covariance of the securities as: We can