Chapter 10 - Arbitrage pricing theory and multifactor models of risk and return. We begin by showing how the decomposition of risk into market versus firm-specific influences that we introduced in earlier cha pters can be extended to deal with the multifaceted nature of systematic risk. Multifactor models of security returns can be used to measure and manage exposure to each of many economy-wide factors such as business-cycle risk, interest or inflation rate risk, energy price risk, and so on. | Chapter 10 Index Models Reduces the number of inputs for diversification. Easier for security analysts to specialize. Advantages of the Single Index Model ri = E(Ri) + ßiF + e ßi = 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 (ri - rf) = i + ßi(rm - rf) + ei a Risk Prem Market Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero ßi(rm - rf) = the component of return due to movements in the market index (rm - rf) = 0 ei = firm specific component, not due to market movements a Single Index Model Let: Ri = (ri - rf) Rm = (rm - rf) Risk premium format Ri = i + ßi(Rm) + ei Risk Premium Format Security Characteristic Line Excess Returns (i) SCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excess returns on market index Ri = i + ßiRm + ei . . . Jan. Feb. . . Dec Mean Std Dev . . .93 . . Excess Mkt. Ret. Excess GM Ret. Using the Text Example from Table 10-1 Estimated coefficient Std error of estimate Variance of residuals = Std dev of residuals = R-SQR = ß () () rGM - rf = + ß(rm - rf) Regression Results 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 i2 = i2 m2 + 2(ei) where; i2 = total variance i2 m2 = systematic variance 2(ei) = unsystematic variance Measuring Components of Risk Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = 2 ßi2 m2 / 2 = 2 i2 m2 / i2 m2 + 2(ei) = 2 Examining Percentage of Variance Index Model and Diversification Risk Reduction with Diversification Number of Securities St. Deviation Market Risk Unique Risk s2(eP)=s2(e) / n bP2sM2 Industry Prediction of Beta Merrill Lynch Example Use returns not risk premiums a has a different interpretation a = a + rf (1-b) Forecasting beta as a function of past beta Forecasting beta as a function of firm size, growth, leverage etc. | Chapter 10 Index Models Reduces the number of inputs for diversification. Easier for security analysts to specialize. Advantages of the Single Index Model ri = E(Ri) + ßiF + e ßi = 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 (ri - rf) = i + ßi(rm - rf) + ei a Risk Prem Market Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero ßi(rm - rf) = the component of return due to movements in the market index (rm - rf) = 0 ei = firm specific component, not due to market movements a Single Index Model Let: Ri = (ri - rf) Rm = (rm - rf) Risk premium format Ri = i + ßi(Rm) + ei Risk Premium Format Security Characteristic Line Excess Returns (i) SCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
