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Understanding Efficient Diversification and Portfolio Risk

Learn about the concepts of market risk, systematic risk, and firm-specific risk, and how diversification can help reduce portfolio risk. Explore the relationship between returns and factors like correlation coefficient and standard deviation. Gain insights into measuring risk components and the use of CAPM and SML in evaluating securities.

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Understanding 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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