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CHAPTER 6

CHAPTER 6. Efficient Diversification. 6.1 DIVERSIFICATION AND PORTFOLIO RISK. Figure 6.2 Portfolio Risk as a Function of Number of Securities. 6.2 ASSET ALLOCATION WITH TWO RISKY ASSETS. Covariance and Correlation.

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CHAPTER 6

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  1. CHAPTER 6 Efficient Diversification

  2. 6.1 DIVERSIFICATION AND PORTFOLIO RISK

  3. Figure 6.2 Portfolio Risk as a Function of Number of Securities

  4. 6.2 ASSET ALLOCATION WITH TWO RISKY ASSETS

  5. Covariance and Correlation • Portfolio risk depends on the correlation or covariance between the returns of the assets in the portfolio

  6. Two Asset Portfolio Return

  7. Covariance and Correlation Coefficient • Covariance: • Correlation Coefficient:

  8. Correlation Coefficients: Possible Values Range of values for rS,B -1.0 <r < 1.0 If r = 1.0, the securities would be perfectly positively correlated If r = - 1.0, the securities would be perfectly negatively correlated

  9. Two Asset Portfolio St Dev

  10. Three Rules of Two-Asset Portfolio • Rate of return on the portfolio: • Expected rate of return on the portfolio:

  11. Three Rules of Two-Asset Portfolio • Variance of the rate of return on the portfolio:

  12. Numerical Text Example: Bond and Stock (Page 158) Returns Bond = 6% Stock = 10% Standard Deviation Bond = 12% Stock = 25% Weights Bond = .5 Stock = .5 Correlation Coefficient (Bonds and Stock) = 0

  13. Numerical Text Example: Bond and Stock Returns (Page 158) Return = 8% .5(6) + .5 (10) Standard Deviation = 13.87% [(.5)2 (12)2 + (.5)2 (25)2 + … 2 (.5) (.5) (12) (25) (0)] ½ [192.25] ½ = 13.87

  14. Investment Opportunity Set (Page 159)

  15. Figure 6.3 Investment Opportunity Set for Stocks and Bonds

  16. Figure 6.4 Investment Opportunity Set for Stocks and Bonds with Various Correlations

  17. 6.3 THE OPTIMAL RISKY PORTFOLIO WITH A RISK-FREE ASSET

  18. Extending to Include Riskless Asset • The optimal combination becomes linear • A single combination of risky and riskless assets will dominate

  19. Figure 6.5 Opportunity Set Using Stocks and Bonds and Two Capital Allocation Lines

  20. Figure 6.6 Optimal Capital Allocation Line for Bonds, Stocks and T-Bills

  21. Dominant CAL with a Risk-Free Investment (F) • CAL(FO) dominates other lines -- it has the best risk/return or the largest slope

  22. Figure 6.7 The Complete Portfolio

  23. 6.4 EFFICIENT DIVERSIFICATION WITH MANY RISKY ASSETS

  24. Figure 6.10 The Efficient Frontier of Risky Assets and Individual Assets

  25. 6.5 A SINGLE-FACTOR ASSET MARKET

  26. Specification of a Single-Index Model of Security Returns • Use the S&P 500 as a market proxy • Excess return can now be stated as:

  27. Figure 6.11 Scatter Diagram for Dell

  28. Figure 6.12 Various Scatter Diagrams

  29. Components of Risk • 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 Risk + Unsystematic Risk

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

  31. Examining Percentage of Variance Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = r2 ßi2 sm2 / s2 = r2

  32. Advantages of the Single Index Model • Reduces the number of inputs for diversification • Easier for security analysts to specialize

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