The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-1 Single Index and Multifactor Models Chapter 10
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-2 Reduces the number of inputs for diversification Easier for security analysts to specialize Advantages of the Single Index Model
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-3 r i = E(R i ) + ß i F + e ß i = index of a securities’ particular return to the factor F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns Assumption: a broad market index like the S&P500 is the common factor Single Factor Model
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-4 (r i - r f ) = i + ß i (r m - r f ) + e i Risk Prem Market Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero ß i (r m - r f ) = the component of return due to movements in the market index (r m - r f ) = 0 e i = firm specific component, not due to market movements Single Index Model
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-5 Let: R i = (r i - r f ) R m = (r m - r f ) Risk premium format R i = i + ß i (R m ) + e i Risk Premium Format
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-6 Security Characteristic Line Excess Returns (i) SCL Excess returns on market index R i = i + ß i R m + e i
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-7 Jan. Feb.. Dec Mean Std Dev Excess Mkt. Ret. Excess GM Ret. Using the Text Example from Table 10-1
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-8 Estimated coefficient Std error of estimate Variance of residuals = Std dev of residuals = R-SQR = ß ß (1.547) (0.309) r GM - r f = + ß(r m - r f ) Regression Results
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 10-9 Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic Components of Risk
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill i 2 = i 2 m 2 + 2 (e i ) where; i 2 = total variance i 2 m 2 = systematic variance 2 (e i ) = unsystematic variance Measuring Components of Risk
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = 2 ß i 2 m 2 / 2 = 2 i 2 m 2 / i 2 m 2 + 2 (e i ) = 2 Examining Percentage of Variance
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Index Model and Diversification
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Risk Reduction with Diversification Number of Securities St. Deviation Market Risk Unique Risk 2 (e P )= 2 (e) / n P2M2P2M2
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Industry Prediction of Beta Merrill Lynch Example - Use returns not risk premiums has a different interpretation = + r f (1- ) Forecasting beta as a function of past beta Forecasting beta as a function of firm size, growth, leverage etc.
The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Multifactor Models Use factors in addition to market return - Examples include industrial production, expected inflation etc. - Estimate a beta for each factor using multiple regression Fama and French - Returns a function of size and book-to-market value as well as market returns