INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 8Index Models指数模型INVESTMENTS | BODIE, KANE, MARCUS8-2 Reduces the number of inputs for diversification减少分散化所需要的证券 数量 Easier for security analysts to specialize 使得证券分析更容易Advantages of the Single Index Model单指数模型的优势INVESTMENTS | BODIE, KANE, MARCUS8-3i = response of an individual securitys return to the common factor, m. Beta measures systematic risk.单 个证券对市场因子的反应，衡量的是系统风险m = a common macroeconomic factor that affects all security returns. The S&P 500 is often used as a proxy for m.共同的宏观市场因子，影响所有证券收益，标普 500指数通常可以作为它的的替代ei = firm-specific surprises单个证券的误差Single Factor Model单因子模型INVESTMENTS | BODIE, KANE, MARCUS8-4Single-Index Model单因子模型 Regression Equation: Expected return-beta relationship: 上式两端取期望INVESTMENTS | BODIE, KANE, MARCUS8-5 Single-Index Model单因子模型 Risk and covariance:风险与协方差 Variance = Systematic risk and Firm- specific risk:方差：系统风险与个体风险 Covariance = product of betas x market index risk:协方差意味着Beta与市场风险 的乘积INVESTMENTS | BODIE, KANE, MARCUS8-6 Single-Index Model单因子模型 Correlation = product of correlations with the market index相关系数是与市场相关系 数之间的乘积INVESTMENTS | BODIE, KANE, MARCUS8-7 Index Model and Diversification 指数模型与分散化 Variance of the equally weighted portfolio of firm-specific components: 等权重组合方差中非系统风险会减少1/n When n gets large, 2(ep) becomes negligible and firm specific risk is diversified away.当n趋于无穷时，非系统性风险会被分 散至零。INVESTMENTS | BODIE, KANE, MARCUS8-8 Figure 8.1 The Variance of an Equally Weighted Portfolio with Risk Coefficient p 等权重组合的方差与风险系数BetaINVESTMENTS | BODIE, KANE, MARCUS8-9 Figure 8.2 Excess Returns on HP and S&P 500惠普公司和标普500的超额收益INVESTMENTS | BODIE, KANE, MARCUS8-10 Figure 8.3 Scatter Diagram of HP, the S&P 500, and HPs Security Characteristic Line (SCL) 超额收益的散点图与惠普的证券特征线INVESTMENTS | BODIE, KANE, MARCUS8-11 Table 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-Packard Excel输出：HP证券特征线的回归统计INVESTMENTS | BODIE, KANE, MARCUS8-12Table 8.3 Interpretation 书上表8.3的解释 Correlation of HP with the S&P 500 is 0.7238.相关系数是 0.7238 The model explains about 52% of the variation in HP.解 释了52%的收益来源于市场 HPs alpha is 0.86% per month(10.32% annually) but it is not statistically significant. Alpha收益是10.32%每年，但 是统计不显著区别于零。 HPs beta is 2.0348, but the 95% confidence interval is 1.43 to 2.53. Beta收益是2.0348显著不为零，但是也有可 能是在143与2.53之间的其他数，可能性为95%INVESTMENTS | BODIE, KANE, MARCUS8-13 Figure 8.4 Excess Returns on Portfolio Assets组合资产的超额收益INVESTMENTS | BODIE, KANE, MARCUS8-14 Alpha and Security Analysis Alpha与证券分析1. Use macroeconomic analysis to estimate the risk premium and risk of the market index.运 用宏观分析估计市场指数的风险与溢价2. Use statistical analysis to estimate the beta coefficients of all securities and their residual variances, 2 (ei).运用统计分析估计单个证 券的Beta系数和个体风险方差INVESTMENTS | BODIE, KANE, MARCUS8-15 Alpha and Security AnalysisAlpha与证券分析3.Establish the expected return of each security absent any contribution from security analysis.建立 每只证券的期望收益，这时不需要任何证券分析，这 是贝塔溢价 4.Use security analysis to develop private forecasts of the expected returns for each security.使用证券分析 来建立每只证券期望收益的单独预测值，这是阿尔法 溢价 5.相同贝塔的证券很多，但是具有阿尔法溢价的少，因 此它是告诉我们证券高估低估的核心，阿尔法较大的 证券在组合中应该占据较大权重，阿尔法为负卖空INVESTMENTS | BODIE, KANE, MARCUS8-16 Single-Index Model Input List 单指数模型及其输入 Risk premium on the S&P 500 portfolio 标普500组合的风险溢价 Estimate of the SD of the S&P 500 portfolio标普500组合的标准差估计 n sets of estimates of Beta coefficient贝塔系数 Stock residual variances个股残差方 差 Alpha values证券的阿尔法值INVESTMENTS | BODIE, KANE, MARCUS8-17 Optimal Risky Portfolio of the Single-Index Model单指数模型的最优风险组合 Maximize the Sharpe ratio最大化夏普比 Expected return, SD, and Sharpe ratio:期望收益、标准差、夏普比INVESTMENTS | BODIE, KANE, MARCUS8-18 Combination of:两部分组成 Active portfolio denoted by A 积极组合A Market-index portfolio, the passive portfolio denoted by M 市场指数组合M，被动组合Optimal Risky Portfolio of the Single-Index Model单指数模型的最优风险组合INVESTMENTS | BODIE, KANE, MARCUS8-19Modification of active portfolio position:WhenOptimal Risky Portfolio of the Single-Index Model单指数模型的最优风险组合INVESTMENTS | BODIE, KANE, MARCUS8-20 The Information Ratio 信息比例 The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy):最优风险组合的夏普比将会超 过指数组合INVESTMENTS | BODIE, KANE, MARCUS8-21The Information Ratio 信息比例 The contribution of the active portfolio depends on the ratio of its alpha to its residual standard deviation.积极组合中证 券的权重取决于它的阿尔法比残差标准差 ，也叫信息比例。 The information ratio measures the extra return we can obtain from security analysis 信息比例衡量了额外收益的价值INVESTMENTS | BODIE, KANE, MARCUS8-22Figure 8.5 Efficient Frontiers with the Index Model and Full-Covariance Matrix 指数模型与全协方差模型的有效边界INVESTMENTS | BODIE, KANE, MARCUS8-23 Table 8.5 Portfolios from the Single-Index and Full- Covariance Models 指数模型和全方差模型组合的对比INVESTMENTS | BODIE, KANE, MARCUS8-24 Is the Index Model Inferi