1. McGraw-Hill/Irwin Copyright © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. Efficient Diversification CHAPTER 6

2. 6-2 6.1 DIVERSIFICATION AND PORTFOLIO RISK

3. 6-3 Figure 6.2 Portfolio Risk as a Function of Number of Securities

4. 6-4 6.2 ASSET ALLOCATION WITH TWO RISKY ASSETS

5. 6-5 Covariance and Correlation Portfolio risk depends on the correlation or covariance between the returns of the assets in the portfolio

6. 6-6 Two Asset Portfolio Return

7. 6-7 Covariance and Correlation Coefficient Covariance: Correlation Coefficient:

8. 6-8 Correlation Coefficients: Possible Values If  = 1.0, the securities would be perfectly positively correlated If  = - 1.0, the securities would be perfectly negatively correlated Range of values for  S,B -1.0 <  < 1.0

9. 6-9 Two Asset Portfolio St Dev

10. 6-10 Three Rules of Two-Asset Portfolio Rate of return on the portfolio: Expected rate of return on the portfolio:

11. 6-11 Three Rules of Two-Asset Portfolio Variance of the rate of return on the portfolio:

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

13. 6-13 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 2 (.5) (.5) (12) (25) (0)] ½ [192.25] ½ = 13.87

14. 6-14 Investment Opportunity Set (Page 159)

15. 6-15 Figure 6.3 Investment Opportunity Set for Stocks and Bonds

16. 6-16 Figure 6.4 Investment Opportunity Set for Stocks and Bonds with Various Correlations

17. 6-17 6.3 THE OPTIMAL RISKY PORTFOLIO WITH A RISK-FREE ASSET

18. 6-18 Extending to Include Riskless Asset The optimal combination becomes linear A single combination of risky and riskless assets will dominate

19. 6-19 Figure 6.5 Opportunity Set Using Stocks and Bonds and Two Capital Allocation Lines

20. 6-20 Figure 6.6 Optimal Capital Allocation Line for Bonds, Stocks and T-Bills

21. 6-21 Dominant CAL with a Risk-Free Investment (F) CAL(FO) dominates other lines -- it has the best risk/return or the largest slope CAL(FO) dominates other lines -- it has the best risk/return or the largest slope

22. 6-22 Figure 6.7 The Complete Portfolio

23. 6-23 6.4 EFFICIENT DIVERSIFICATION WITH MANY RISKY ASSETS

24. 6-24 Figure 6.10 The Efficient Frontier of Risky Assets and Individual Assets

25. 6-25 6.5 A SINGLE-FACTOR ASSET MARKET

26. 6-26 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. 6-27 Figure 6.11 Scatter Diagram for Dell

28. 6-28 Figure 6.12 Various Scatter Diagrams

29. 6-29 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. 6-30 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

31. 6-31 Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk =  2 ß i 2  m 2 /  2 =  2 Examining Percentage of Variance

32. 6-32 Advantages of the Single Index Model Reduces the number of inputs for diversification Easier for security analysts to specialize