McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Efficient Diversification CHAPTER 6

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Diversification and Portfolio Risk Market risk Systematic or Nondiversifiable Firm-specific risk Diversifiable or nonsystematic

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Figure 6.1 Portfolio Risk as a Function of the Number of Stocks

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Two Asset Portfolio Return – Stock and Bond

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Covariance  1,2 = Correlation coefficient of returns  1,2 = Correlation coefficient of returns Cov(r 1 r 2 ) =    1  2`  1 = Standard deviation of returns for Security 1  2 = Standard deviation of returns for Security 2  1 = Standard deviation of returns for Security 1  2 = Standard deviation of returns for Security 2

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Two Asset Portfolio St Dev – Stock and Bond

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Single Factor Model 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Single Index Model Risk Prem Market Risk Prem or Index Risk Prem or Index Risk Prem i = the stock’s expected return if the market’s excess return is zero market’s excess return is zero ß i (r m - r f ) = the component of return due to movements in the market index movements in the market index (r m - r f ) = 0 e i = firm specific component, not due to market movements movements   e rrrr i fm i i fi   

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Let: R i = (r i - r f ) R m = (r m - r f ) R m = (r m - r f ) Risk premium format R i =  i + ß i (R m ) + e i Risk Premium Format

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Measuring Components of Risk  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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 Note: ß i =  /  m another way to calculate Beta Examining Percentage of Variance

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. M=Market portfolio r f =Risk free rate E(r M ) - r f =Market risk premium E(r M ) - r f =Market price of risk =Slope of the CAPM Slope and Market Risk Premium M 

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. SML Relationships  = [COV(r i,r m )] /  m 2 Slope SML =E(r m ) - r f =market risk premium SML = r f +  [E(r m ) - r f ]

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Table 7-2 Security Characteristic Line for GM: Summary Output