Efficient Diversification CHAPTER 6 Mc GrawHillIrwin 2007 The

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

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

Figure 6. 1 Portfolio Risk as a Function of the Number of Stocks Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

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

Covariance Cov(r 1 r 2) = r 1, 2 s 1 s 2` r 1, 2 = Correlation coefficient of returns s 1 = Standard deviation of returns for Security 1 s 2 = Standard deviation of returns for Security 2 Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

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

Single Factor Model ri = E(Ri) + ßi. F + 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&P 500 is the common factor Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Single Index Model (r - r )= a + b (r - r )+ e i f Risk Prem i i m f i Market Risk Prem or Index Risk Prem a i = the stock’s expected return if the market’s excess return is zero (rm - rf) = 0 ßi(rm - rf) = the component of return due to movements in the market index ei = firm specific component, not due to market movements Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Risk Premium Format Let: Ri = (ri - rf) R m = ( r m - r f) Risk premium format Ri = ai + ßi(Rm) + ei Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Measuring Components of Risk si 2 = bi 2 sm 2 + s 2(ei) where; si 2 = total variance bi 2 sm 2 = systematic variance s 2(ei) = unsystematic variance Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Examining Percentage of Variance Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = r 2 ß i 2 s m 2 / s 2 = r 2 bi 2 sm 2 / (bi 2 sm 2 + s 2(ei)) = r 2 Note: ß i= Beta Mc. Graw-Hill/Irwin r s / s m another way to calculate © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

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

SML Relationships b = [COV(ri, rm)] / sm 2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf] Mc. Graw-Hill/Irwin © 2004 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

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