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Efficient Diversification and Portfolio Risk

Learn about market risk, firm-specific risk, and the benefits of diversification in managing portfolio risk.

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Efficient Diversification and Portfolio Risk

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  1. CHAPTER 6 Efficient Diversification

  2. Diversification and Portfolio Risk • Market risk • Systematic or Nondiversifiable • Firm-specific risk • Diversifiable or nonsystematic

  3. Figure 6.1 Portfolio Risk as a Function of the Number of Stocks

  4. Two Asset Portfolio Return – Stock and Bond

  5. Covariance Cov(r1r2) = r1,2s1s2` r1,2 = Correlation coefficient of returns s1 = Standard deviation of returns for Security 1 s2 = Standard deviation of returns for Security 2

  6. Two Asset Portfolio St Dev – Stock and Bond

  7. Single Factor 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

  8. Single Index Model ( ) ( ) b a e r r r r - = + - + i f m f i i i Risk Prem Market Risk Prem or Index Risk Prem a = the stock’s expected return if the market’s excess return is zero i (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

  9. Let: Ri = (ri - rf) Risk premium format Rm = (rm - rf) Ri = ai + ßi(Rm)+ ei Risk Premium Format

  10. Measuring Components of Risk si2 = bi2sm2 + s2(ei) where; si2 = total variance bi2sm2 = systematic variance s2(ei) = unsystematic variance

  11. Examining Percentage of Variance Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = r2 ßi2 sm2 / s2 = r2 bi2sm2 / (bi2sm2 + s2(ei)) = r2 Note: ßi= r s / sm another way to calculate Beta

  12. Slope and Market Risk Premium M = Market portfolio rf = Risk free rate E(rM) - rf = Market risk premium E(rM) - rf = Market price of risk = Slope of the CAPM s M

  13. SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf]

  14. Table 7-2 Security Characteristic Line for GM: Summary Output

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