Chap007最优风险资产组合.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,INVESTMENTS,|,BODIE,KANE,MARCUS,7-,*,CHAPTER 7,Optimal Risky Portfolios,最优风险资产组合,7-,2,The Investment Decision,投资决策,Top-down process with 3 steps:,自上而下,Capital allocation,between the risky portfolio and risk-free asset,首先分配份额：安全、风险资产间,Asset allocation,across broad asset classes,各类资产间的配置,Security selection,of individual assets within each asset class,每类资产内部的证券选择,7-,3,Diversification and Portfolio Risk,分散化与组合风险,Market risk,市场风险,Systematic or nondiversifiable,系统风险也是不可分散风险,Firm-specific risk,公司风险,Diversifiable or nonsystematic,可分散风险、非系统性风险,7-,4,Figure 7.1 Portfolio Risk as a Function of the Number of Stocks in the Portfolio,组合风险作为组合内股票数量的函数,7-,5,Figure 7.2 Portfolio Diversification,组合分散化,7-,6,Portfolio Diversification:Intuition,组合分散化,:,直觉,7-,7,Covariance and Correlation,协方差与相关系数,Portfolio risk depends on the correlation between the returns of the assets in the portfolio,组合风险依赖于组合资产回报之间的相关系数,Covariance and the correlation coefficient provide a measure of the way returns of two assets vary,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,7-,8,Two-Security Portfolio:Return,二资产组合,收益情况,7-,9,=,Variance of Security D,=,Variance of Security E,=,Covariance of returns for,Security D and Security E,Two-Security Portfolio:Risk,二资产组合,风险情况,7-,10,Two-Security Portfolio:Risk,风险情况,Another way to express variance of the portfolio:,表达组合方差的另一种办法,7-,11,D,E,=,Correlation coefficient of,returns,相关系数,Cov(r,D,r,E,)=,DE,D,E,D,=,Standard deviation of,returns for Security D,标准差,D,E,=,Standard deviation of,returns for Security E,标准差,E,Covariance,协方差,7-,12,Range of values for,1,2,+1.0,r,-1.0,If,r,=1.0,the securities are perfectly positively correlated,完全正相关,If,r,=,-1.0,the securities are perfectly negatively correlated,完全负相关,Correlation Coefficients:Possible Values,相关系数的可能值,7-,13,Correlation Coefficients,相关系数,When,DE,=1,there is no diversification,如果相关系数为,1,就没有风险分散效果,When,DE,=-1,a perfect hedge is possible,如果相关系数为,-1,，可以做出完全对冲效果,7-,14,Table 7.2 Computation of Portfolio Variance From the Covariance Matrix,从协方差矩阵中算出组合方差,7-,15,Three-Asset Portfolio,三资产组合,7-,16,Figure 7.3 Portfolio Expected Return as a Function of Investment Proportions,组合期望收益对投资比例的函数,7-,17,Figure 7.4 Portfolio Standard Deviation as a Function of Investment Proportions,组合标准差对投资比例的函数,7-,18,The Minimum Variance Portfolio,最小方差投资组合,The minimum variance portfolio is the portfolio composed of the risky assets that has the smallest standard deviation,the portfolio with least risk.,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,When correlation is less than+1,the portfolio standard deviation may be smaller than that of either of the individual component assets.,相关系数小于,1,时会有分散化效果,When correlation is-1,the standard deviation of the minimum variance portfolio is zero.,相关系数等于,-1,时最小方差组合标准差为,0,7-,19,Figure 7.5 Portfolio Expected Return as a Function of Standard Deviation,组合期望收益对标准差的函数,7-,20,The amount of possible risk reduction through diversification depends on the correlation.,可能降低的风险取决于相关系数,The risk reduction potential increases as the correlation approaches-1.,为,-1,时最低,If,r,=+1.0,no risk reduction is possible.,没分散,If,r,=0,P,may be less than the standard deviation of either component asset.,可能比任何一种资产都低,If,r,=-1.0,a riskless hedge is possible完全消除风险,Correlation Effects,相关系数效应,7-,21,Figure 7.6 The Opportunity Set of the Debt and Equity Funds and Two Feasible CALs,债券和股权基金的投资可行集,与两条资本配置线,7-,22,The Sharpe Ratio,夏普比,Maximize the slope of the CAL for any possible portfolio,P.,最大化,CAL,的斜率,The objective function is the slope:,The slope is also the Sharpe ratio.,斜率就是夏普比,7-,23,Figure 7.7 The Opportunity Set of the Debt and Equity Funds with the Optimal CAL and the Optimal Risky Portfolio,债券与股权的投资可行集,-,最优,CAL,与最优风险组合,7-,24,Figure 7.8 Determination of the Optimal Overall Portfolio,决定最优组合,7-,25,Figure 7.9 The Proportions of the Optimal Overall Portfolio,最优组合的成分,7-,26,Markowitz Portfolio Selection Model,马克维茨资产组合选择模型,Security Selection,证券选择,The first step is to determine the risk-return opportunities available.,第一步是决定风险收益的投资机会,All portfolios that lie on the minimum-variance frontier from the global minimum-variance portfolio and upward provide the best risk-return combinations,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,7-,27,Figure 7.10 The Minimum-Variance Frontier of Risky Assets,风险资产的最小方差边界,7-,28,Markowitz Portfolio Selection Model,马克维茨资产组合选择模型,We now search for the CAL with the highest reward-to-variability ratio,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,7-,29,Figure 7.11 The Efficient Frontier of Risky Assets with the Optimal CAL,风险资产有效边界和最优资本配置线,7-,30,Markowitz Portfolio Selection Model,马克维茨资产组合选择模型,Everyone invests in P,regardless of their degree of risk aversion.,每一个人都将投资于组合,P,无论他的风险偏好,More risk averse investors put more in the risk-free asset.,风险厌恶者更多份额投向无风险资产,Less risk averse investors put more in P.,不那么厌恶风险的投资者就多投资于,P,7-,31,Capital Allocation and the Separation Property,资本配置与分离特性,The separation property tells us that the portfolio choice problem may be separated into two independent tasks,分离特性告诉我们组合决策问题可以分为两个独立的步骤,Determination of the optimal risky portfolio is purely technical.,决定最优风险组合这是纯技术性的工作,Allocation of the complete portfolio to T-bills versus the risky portfolio depends on personal preference.,根据风险偏好在短期国库券和最优风险组合之间配比,7-,32,Figure 7.13 Capital Allocation Lines with Various Portfolios from the Efficient Set,有限集组合和资本配置线,7-,33,The Power of Diversification,分散化的威力,Remember:,If we define the average variance and average covariance of the securities as:,如果我们定义平均方差与协方差为：,7-,34,The Power of Diversification,分散化的威力,We can then express portfolio variance as:,可以将组合的方差表达为,7-,35,Table 7.4 Risk Reduction of Equally Weighted Portfolios in Correlated and Uncorrelated Universes,相关性和无相关性的证券等权重构造组合的风险降低,7-,36,Optimal Portfolios and Nonnormal Returns,最优组合与非正态收益,Fat-tailed distributions can result in extreme values of VaR and ES and encourage smaller allocations to the risky portfolio.,肥尾分布可以导致,VaR,和,ES,的极值，会导致风险组合的更小份额,If other portfolios provide sufficiently better VaR and ES values than the mean-variance efficient portfolio,we may prefer these when faced with fat-tailed distributions.,如果其他组合比均值方差有效组合提供更好的,VaR,和,ES/,期望收益的话，我们在肥尾分布下可能更倾向于这一组合,7-,37,Risk Pooling and the Insurance Principle,风险汇聚和保险原则,Risk pooling:,merging uncorrelated,risky projects as a means to reduce risk.,风险汇聚，汇聚大量不相关的风险项目做完降低风险的手段,increases the,scale,of the risky investment by adding,additional,uncorrelated assets.,通过增加不相干资产的办法增加风险投资的规模,The,insurance principle,:risk increases less than proportionally to the number of policies insured when the policies are uncorrelated,保险原则，风险增加比率低于不相关保单的增长速度，组合获利,/,风险组合比例上升了，但是总体风险还是增长了,Sharpe ratio increases,或者说是夏普比增长了，但是风险也是,7-,38,Risk Sharing,风险共享,As risky assets are added to the portfolio,a portion of the pool is sold to maintain a risky portfolio of,fixed size.,当风险资产被增加到组合中，资产池的一部分被出售以保持风险资产的固定规模,Risk sharing combined with risk pooling is the key,to the insurance,industry.,风险共享和风险汇聚联合起来解释了保险行业的关键,True diversification means spreading a portfolio of,fixed size across many assets,not merely adding more risky bets to an ever-growing risky portfolio.,真正的分散意味着固定规模的组合包含很多资产，而不是向风险组合中增加越来越多的资产使之变得越来越大,739,Risk Sharing,风险共享,想象一个投资机会（或者说一个不需要本金的赌局），,500,万美元，扔硬币决定，正面没钱反面送给你,500,万美元，期望收益,250,万元，波动性很大也就是很刺激；,想象开,500,个这样的赌局，每个下注,1,万，期望也是,250,万元，但是波动性就较小，也没有那么刺激；,再想象开,500,万个这样的赌局，每个下注,1,元，期望收益也是,250,万元，几乎就没有波动性，送给你,250,万元毫不意外,7-,40,Investment for the Long Run,长期投资,Long Term Strategy,Invest in the risky portfolio for 2 years.,投资风险组合两年,Long-term strategy is riskier.,长期策略风险大,Risk can be reduced by selling some of the risky assets in year 2.,在第二年卖出部分风险资产可以降低风险,“Time diversification”is not true diversification.,时间分散不是真正的分散,Short Term Strategy,Invest in the risky portfolio for 1 year and in the risk-free asset for the second year.,投资风险组合,1,年，第二年投资无风险组合,将投资期延长会提升夏普比率，同时也会增加风险,