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1、INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 7Optimal Risky Portfolios最优风险资产组合INVESTMENTS | BODIE, KANE, MARCUSThe Investment Decision投资决策Top-down process with 3 steps:自上而下1.Capital allocation between the risky portfo
2、lio and risk-free asset首先分配份额：安全、风险资产间2.Asset allocation across broad asset classes各类资产间的配置3.Security selection of individual assets within each asset class每类资产内部的证券选择2INVESTMENTS | BODIE, KANE, MARCUSDiversification 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
3、Firm-specific risk公司风险Diversifiable or nonsystematic可分散风险、非系统性风险3INVESTMENTS | BODIE, KANE, MARCUSFigure 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4INVESTMENTS | BODIE, KANE, MARCUSFigure 7.2 Portfolio Diversification组合分散化5INVESTMENTS | BODIE, KANE, MAR
4、CUSPortfolio Diversification: Intuition组合分散化: 直觉6INVESTMENTS | BODIE, KANE, MARCUSCovariance 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
5、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7INVESTMENTS | BODIE, KANE, MARCUSTwo-Security Portfolio: Return二资产组合收益情况8INVESTMENTS | BODIE, KANE, MARCUS = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security ETwo-Security Portfolio: Risk二资产组合风险情况
6、9INVESTMENTS | BODIE, KANE, MARCUSTwo-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10INVESTMENTS | BODIE, KANE, MARCUS D,E = Correlation coefficient of returns相关系数 Cov(rD,rE) = DE D E D = Standard deviation of returns for Security D标准差D E = Standard deviat
7、ion of returns for Security E标准差ECovariance协方差11INVESTMENTS | BODIE, KANE, MARCUSRange of values for 1,2+ 1.0 -1.0If = 1.0, the securities are perfectly positively correlated完全正相关If = - 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12INV
8、ESTMENTS | BODIE, KANE, MARCUSCorrelation 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13INVESTMENTS | BODIE, KANE, MARCUSTable 7.2 Computation of Portfolio Variance From the Covariance Matrix从协方差矩阵中算出组合方差14INVE
9、STMENTS | BODIE, KANE, MARCUSThree-Asset Portfolio三资产组合15INVESTMENTS | BODIE, KANE, MARCUSFigure 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16INVESTMENTS | BODIE, KANE, MARCUSFigure 7.4 Portfolio Standard Deviation as a Function of Investment Proportions组合标准差对
10、投资比例的函数17INVESTMENTS | BODIE, KANE, MARCUSThe 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
11、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018INVESTMENTS | BODIE, KANE, MARCUSFigure 7.5 Portfolio Expected Return as a
12、Function of Standard Deviation 组合期望收益对标准差的函数19INVESTMENTS | BODIE, KANE, MARCUSThe 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 possib
13、le.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20INVESTMENTS | BODIE, KANE, MARCUSFigure 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
14、资本配置线21INVESTMENTS | BODIE, KANE, MARCUSThe 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22INVESTMENTS | BODIE, KANE, MARCUSFigure 7.7 The Opportunity Set of the Debt and Equity Funds
15、 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23INVESTMENTS | BODIE, KANE, MARCUSFigure 7.8 Determination of the Optimal Overall Portfolio决定最优组合24INVESTMENTS | BODIE, KANE, MARCUSFigure 7.9 The Proportions of the Optimal Overall Portfolio最优组合的成分25INVESTMENTS | BODIE, K
16、ANE, MARCUSMarkowitz 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-r
17、eturn 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26INVESTMENTS | BODIE, KANE, MARCUSFigure 7.10 The Minimum-Variance Frontier of Risky Assets风险资产的最小方差边界27INVESTMENTS | BODIE, KANE, MARCUSMarkowitz 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 rat
18、io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28INVESTMENTS | BODIE, KANE, MARCUSFigure 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29INVESTMENTS | BODIE, KANE, MARCUSMarkowitz 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
19、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P30INVESTMENTS | BODIE, KANE, MARCUSCapital Allocation and the Separation Property资本配置与分离特性The separation property tells us that the portf
20、olio 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3
21、1INVESTMENTS | BODIE, KANE, MARCUSFigure 7.13 Capital Allocation Lines with Various Portfolios from the Efficient Set有限集组合和资本配置线32INVESTMENTS | BODIE, KANE, MARCUSThe 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
22、：33INVESTMENTS | BODIE, KANE, MARCUSThe 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34INVESTMENTS | BODIE, KANE, MARCUSTable 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35INVESTMENTS | BODIE,
23、KANE, MARCUSOptimal 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-var
24、iance 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36INVESTMENTS | BODIE, KANE, MARCUSRisk 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
25、.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
26、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37INVESTMENTS | BODIE, KANE, MARCUSRisk 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
27、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38INVESTMENTS | BODIE, KANE, MARCUSRisk
28、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39INVESTMENTS | BODIE, KANE, MARCUSInvestment for the Long Run长期投资Long Term StrategyInvest in the risky portfoli
29、o 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 StrategyInvest 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40
