1. Asset Management Lecture Three

2. Outline for today Index model Index model Single-factor index model Single-factor index model Alpha and security analysis Alpha and security analysis

3. Drawbacks of Markowitz The model requires a huge number of estimates The model requires a huge number of estimates E.g. 50 stocks E.g. 50 stocks 50 estimates of E(r) 50 estimates of E(r) 50 estimates of var(r) 50 estimates of var(r) 1225 estimates of cov(ri, rj) 1225 estimates of cov(ri, rj) The model does not provide guideline to the forecasting of E(r)-rf The model does not provide guideline to the forecasting of E(r)-rf

4. Assumption: a broad market index like the S&P 500 is the common factor. ß i = index of a securities’ particular return to the factor ß i = index of a securities’ particular return to the factor m = Unanticipated movement in common factor that drives security returns m = Unanticipated movement in common factor that drives security returns e i = firm-specific surprise e i = firm-specific surprise Single Factor Model

5. Single-Index Model Regression Equation: Regression Equation: Expected return-beta relationship: Expected return-beta relationship: Systematic risk premium Non-market premium

6. Single-Index Model Continued Risk and covariance: Risk and covariance: Total risk = Systematic risk + Firm-specific risk: Total risk = Systematic risk + Firm-specific risk: Covariance = product of betas x market index risk: Covariance = product of betas x market index risk: Correlation = product of correlations with the market index Correlation = product of correlations with the market index

7. Index Model and Diversification Portfolio’s variance: Portfolio’s variance: Variance of the equally weighted portfolio of firm-specific components: Variance of the equally weighted portfolio of firm-specific components: When n gets large, becomes negligible When n gets large, becomes negligible

8. Figure 8.1 The Variance of an Equally Weighted Portfolio with Risk Coefficient β p in the Single-Factor Economy

9. Example: HP and the S&P 500

11. Table 8.1 Excel Output: Regression Statistics for the SCL of Hewlett-Packard

12. Figure 8.4 Excess Returns on Portfolio Assets

13. Alpha and Security Analysis Macroeconomic analysis is used to estimate the risk premium and risk of the market index 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, σ 2 ( e i ) Statistical analysis is used to estimate the beta coefficients of all securities and their residual variances, σ 2 ( e i ) Developed from security analysis Developed from security analysis

14. Alpha and Security Analysis The market-driven expected return is conditional on information common to all securities 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 Security-specific expected return forecasts are derived from various security-valuation models The alpha value distills the incremental risk premium attributable to private information The alpha value distills the incremental risk premium attributable to private information Helps determine whether security is a good or bad buy Helps determine whether security is a good or bad buy