投资学：Chap008.ppt

1、INVESTMENTS | BODIE, KANE, MARCUS Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin CHAPTER 8 Index Models INVESTMENTS | BODIE, KANE, MARCUS Reduces the number of inputs for diversification Easier for security analysts to specialize Advantages of the Single Inde

2、x Model INVESTMENTS | BODIE, KANE, MARCUS i = response of an individual securitys return to the common factor, m. Beta measures systematic risk. m = a common macroeconomic factor that affects all security returns. The S&P 500 is often used as a proxy for m. ei = firm-specific surprises Single Factor

3、 Model ( ) iiii rE rme INVESTMENTS | BODIE, KANE, MARCUS Single-Index Model Regression Equation: Expected return-beta relationship: tetRtR iMiii Miii RERE INVESTMENTS | BODIE, KANE, MARCUS Single-Index Model Risk and covariance: Variance = Systematic risk and Firm- specific risk: Covariance = produc

4、t of betas x market index risk: 2222 ( ) iiMi e 2 ( ,) ijijM Cov r r INVESTMENTS | BODIE, KANE, MARCUS Single-Index Model Correlation = product of correlations with the market index 222 ( ,)( ,)( ,) ijMiMjM ijiMjM ijiMjM Corr r rCorr r rxCorr r r INVESTMENTS | BODIE, KANE, MARCUS Index Model and Div

5、ersification Variance of the equally weighted portfolio of firm-specific components: When n gets large, 2(ep) becomes negligible and firm specific risk is diversified away. 2 2 22 1 11 ()( )( ) n Pi i eee nn INVESTMENTS | BODIE, KANE, MARCUS Figure 8.1 The Variance of an Equally Weighted Portfolio w

6、ith Risk Coefficient p INVESTMENTS | BODIE, KANE, MARCUS Figure 8.2 Excess Returns on HP and S&P 500 INVESTMENTS | BODIE, KANE, MARCUS Figure 8.3 Scatter Diagram of HP, the S&P 500, and HPs Security Characteristic Line (SCL) tetRtR HPPSHPHPHP 500& INVESTMENTS | BODIE, KANE, MARCUS Table 8.1 Excel Ou

7、tput: Regression Statistics for the SCL of Hewlett-Packard INVESTMENTS | BODIE, KANE, MARCUS Table 8.1 Interpretation Correlation of HP with the S&P 500 is 0.7238. The model explains about 52% of the variation in HP. HPs alpha is 0.86% per month(10.32% annually) but it is not statistically significa

8、nt. HPs beta is 2.0348, but the 95% confidence interval is 1.43 to 2.53. INVESTMENTS | BODIE, KANE, MARCUS Figure 8.4 Excess Returns on Portfolio Assets INVESTMENTS | BODIE, KANE, MARCUS Alpha and Security Analysis 1. Use macroeconomic analysis to estimate the risk premium and risk of the market ind

9、ex. 2. Use statistical analysis to estimate the beta coefficients of all securities and their residual variances, 2 (ei). INVESTMENTS | BODIE, KANE, MARCUS Alpha and Security Analysis 3. Establish the expected return of each security absent any contribution from security analysis. 4. Use security an

10、alysis to develop private forecasts of the expected returns for each security. INVESTMENTS | BODIE, KANE, MARCUS Single-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 of Beta coefficient Stock residual variances Alpha valu

11、es INVESTMENTS | BODIE, KANE, MARCUS Optimal Risky Portfolio of the Single-Index Model Maximize the Sharpe ratio Expected return, SD, and Sharpe ratio: 11 11 1 2 21 11 222222 2 11 ()()() ()( ) () nn PPMPiiMii ii nn PPMPMiiii ii P P P E RE RwE Rw ewwe E R S INVESTMENTS | BODIE, KANE, MARCUS Optimal R

12、isky Portfolio of the Single-Index Model Combination of: Active portfolio denoted by A Market-index portfolio, the passive portfolio denoted by M INVESTMENTS | BODIE, KANE, MARCUS Optimal Risky Portfolio of the Single-Index Model Modification of active portfolio position: When 0 * 0 1 (1) A A AA w w

13、 w *0 1, AAA ww INVESTMENTS | BODIE, KANE, MARCUS The Information Ratio The Sharpe ratio of an optimally constructed risky portfolio will exceed that of the index portfolio (the passive strategy): 2 22 () A PM A e ss INVESTMENTS | BODIE, KANE, MARCUS The Information Ratio The contribution of the act

14、ive portfolio depends on the ratio of its alpha to its residual standard deviation. The information ratio measures the extra return we can obtain from security analysis. INVESTMENTS | BODIE, KANE, MARCUS Figure 8.5 Efficient Frontiers with the Index Model and Full-Covariance Matrix INVESTMENTS | BOD

15、IE, KANE, MARCUS Table 8.2 Portfolios from the Single-Index and Full-Covariance Models INVESTMENTS | BODIE, KANE, MARCUS Is the Index Model Inferior to the Full-Covariance Model? Full Markowitz model may be better in principle, but Using the full-covariance matrix invokes estimation risk of thousand

16、s of terms. Cumulative errors may result in a portfolio that is actually inferior to that derived from the single-index model. The single-index model is practical and decentralizes macro and security analysis. INVESTMENTS | BODIE, KANE, MARCUS Beta Book: Industry Version of the Index Model Use 60 mo

17、st recent months of price data Use S&P 500 as proxy for M Compute total returns that ignore dividends Estimate index model without excess returns: * ebrar m INVESTMENTS | BODIE, KANE, MARCUS Beta Book: Industry Version of the Index Model The average beta over all securities is 1. Thus, our best forecast of the beta would be that it is 1. Also, firms may become more “typical” as they age, causing their betas to approach 1. Adjust beta because: INVESTMENTS | BODIE, KANE, MARCUS Table 8.4 Industry Betas and Adjustment Factors