投资学英文课件：Chap008 Index Models

1、Investments, 8th editionBodie, Kane and MarcusMcGraw-Hill/IrwinCopyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved.8-2 Reduces the number of inputs for diversification Easier for security analysts to specializeAdvantages of the Single Index Model8-3 i = index of a securities partic

2、ular return to the factor m = Unanticipated movement related to security returns ei = Assumption: a broad market index like the S&P 500 is the common factor.Single Factor Model( )iiiirE rme8-4Single-Index Model Regression Equation: Expected return-beta relationship:( )( )( )titMiR tRte t()()iiiM

3、E RE R8-5Single-Index Model Continued Risk and covariance: Total risk = Systematic risk + Firm-specific risk: Covariance = product of betas x market index risk: Correlation = product of correlations with the market index2222( )iiMie 2( ,)ijijMCov r r 222( ,)( ,)( ,)ijMiMjMijiMjMijiMjMCorr r rCorr r

4、rxCorr r r 8-6Index Model and Diversification Portfolios variance: Variance of the equally weighted portfolio of firm-specific components: When n gets large, becomes negligible 2222111()( )( )nPiieeenn2222()PPMPe 2( )Pe8-7Figure 8.1 The Variance of an Equally Weighted Portfolio with Risk Coefficient

5、 p in the Single-Factor Economy8-8Figure 8.2 Excess Returns on HP and S&P 500 April 2001 March 20068-9Figure 8.3 Scatter Diagram of HP, the S&P 500, and the Security Characteristic Line (SCL) for HP8-10Table 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-Packard8-11Figure 8.4

6、 Excess Returns on Portfolio Assets8-12Alpha and Security Analysis Macroeconomic analysis is used to estimate the risk premium and risk of the market index Statistical analysis is used to estimate the beta coefficients of all securities and their residual variances, 2 ( e i ) Developed from security

7、 analysis8-13Alpha and Security Analysis Continued The market-driven expected return is conditional on information common to all securities Security-specific expected return forecasts are derived from various security-valuation models The alpha value distills the incremental risk premium attributabl

8、e to private information Helps determine whether security is a good or bad buy8-14Single-Index Model Input List Risk premium on the S&P 500 portfolio Estimate of the SD of the S&P 500 portfolio n sets of estimates ofBeta coefficientStock residual variancesAlpha values8-15Optimal Risky Portfo

9、lio of the Single-Index Model Maximize the Sharpe ratioExpected return, SD, and Sharpe ratio:1111122111222222211()()()()( )()nnPPMPiiMiiiinnPPMPMiiiiiiPPPE RE RwE RwewweE RS 8-16Optimal Risky Portfolio of the Single-Index Model Continued Combination of:Active portfolio denoted by AMarket-index portf

10、olio, the (n+1)th asset which we call the passive portfolio and denote by MModification of active portfolio position:When 0*01 (1)AAAAwww*01,AAAww8-17The Information Ratio The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy):222()APMAess8-18Figure 8.5 Efficient Frontiers with the Index Model and Full-Covariance Matrix8-19Table 8.2 Comparison of Portfolios from the Single-Index and