McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 10 Index Models.

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McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 10 Index Models

10-2 Reduces the number of inputs for diversification. Easier for security analysts to specialize. Advantages of the Single Index Model

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

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

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

10-6 Security Characteristic Line Excess Returns (i) SCL Excess returns on market index R i =  i + ß i R m + e i......

10-7 Jan. Feb.. Dec Mean Std Dev Excess Mkt. Ret. Excess GM Ret. Using the Text Example from Table 10-1

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

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

10-10  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

10-11 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

10-12 Index Model and Diversification

10-13 Risk Reduction with Diversification Number of Securities St. Deviation Market Risk Unique Risk  2 (e P )=  2 (e) / n P2M2P2M2

10-14 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.