Financial Analysis, Planning and Forecasting Theory and Application

1. Financial Analysis, Planning and ForecastingTheory and Application Chapter 7 Risk Estimation and Diversification By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University

2. Outline • 7.1 Introduction • 7.2 Risk classification • 7.3 Portfolio analysis and applications • 7.4 The market rate of return and market risk premium • 7.5 Determination of commercial lending rates • 7.6 The dominance principle and performance evaluation • 7.7 Summary • Appendix 7A. Estimation of market risk premium • Appendix 7B. Normal distribution and Value at Risk • Appendix 7C. Derivation of Minimum-Variance Portfolio • Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight

3. 7.1 Risk classification • Total risk=Business risk + Financial risk

4. 7.1 Risk classification 7.1A : Method (7.1) (7.2) (7.3) ROI: return on investment

5. 7.1 Risk classification 7.1B : Example Table 7-1

6. 7.2 Portfolio analysis and applications • Expected rate of return on a portfolio • Variance and standard deviations of a portfolio • The efficient portfolios • Corporate application of diversification

7. 7.3 Portfolio Analysis and Application (7.4) (7.5)

8. 7.3 Portfolio Analysis and Applications (7.6) (7.7)

9. 7.3 Portfolio analysis and applications Figure 7-2 Two Portfolios with same mean and different variance

10. 7.3 Portfolio analysis and applications (7.8) (7.9) (7.10) (7.11)

11. 7.3 Portfolio analysis and applications Figure 7-3 The Correlation Coefficients

12. 7.3 Portfolio analysis and applications Efficient Portfolios Under the mean-variance framework, a security or portfolio is efficient if E(A) > E(B) and var(A) = var(B) Or E(A) = E(B) and var(A) < var (B).

13. 7.3 Portfolio analysis and applications Figure 7-4 Efficient Frontier in Portfolio Analysis

14. 7.3 Portfolio analysis and applications Table 7-2 Variance-Covariance Matrix

15. 7.3 Portfolio analysis and applications

16. 7.4The market rate of return and market risk premium Table 7-3 Market Returns and T-bill Rates by Quarters

17. 7.4The market rate of return and market risk premium Table 7-3 Market Returns and T-bill Rates by Quarters (Cont’d)

18. 7.5 Determination of commercial lending rates Table 7.4

19. 7.5 Determination of commercial lending rates Table 7-5

20. 7.5 Determination of commercial lending rates

21. 7.6The dominance principle and performance evaluation Figure 7-5 Distribution of Leading Rate(R)

22. 7.6The dominance principle and performance evaluation Figure 7-6 The Dominance Principle in Portfolio Analysis

23. 7.6The dominance principle and performance evaluation The example of Sharpe Performance Measure Table 7-6

24. 7.7 Summary In Chapter 7, we defined the basic concepts of risk and risk measurement. Based on the relationship of risk and return, we demonstrated the efficient portfolio concept and its implementation, as well as the dominance principle and performance measures. Interest rates and market rates of return were used as measurements to show how the commercial lending rate and the market risk premium are calculated.

25. Appendix 7A. Estimation of market risk premium Table 7A-1 Summary Statistics of Annual Returns (1926-2006)

26. Appendix 7A. Estimation of market risk premium Exhibit 7A-1: Derived Series: Summary Statistics of Annual Component Returns (1926-2006)

27. Appendix 7A. Estimation of market risk premium Exhibit 7A-2: Simulated Total Return Distributions of Common Stock (1977-2000) by Geometric Average Annual Rates

28. Appendix 7B. Normal distribution and Value at Risk Figure 7B-1 Probability Density Function for a Normal Distribution, Showing the Probability That a Normal Random Variable Lies between a and b (Shaded Area)

29. Appendix 7B. Normal distribution and Value at Risk Figure 7B-2 Probability Density Function of Normal Random Variables with Equal Variances: Mean 2 is Greater Than 1. Figure 7B-3 Probability Density Functions of Normal Distributions with Equal Means and Different Variances

30. Appendix 7B. Normal distribution and Value at Risk Table 7B-1 Probability, P, That a Normal Random Variable with Mean and Standard Deviation σ lies between K – σ and K – σ. Mean =12. If the investor may believe there is a 50% chance that the actual return will be between 10.5% and 13.5%. K=(13.5-10.5)/2=1.5 and K/ σ=0.674 Then σ=1.5/0.674=2.2255, =4.95

31. Appendix 7B. Normal distribution and Value at Risk Figure 7B-5 For a Normal Random Variable with Mean 12, Standard Deviation 4.95, the Probability is .5 of a Value between 10.5 and 13.5

32. Appendix 7C. Derivation of Minimum-Variance Portfolio (7.C.2) By taking partial derivative of with respect to w1, we obtain

33. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight where = expected rates of return for portfolio P. = risk free rates of return = Sharpe performance measure as defined in equation (7.C.1) of Appendix C

34. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.1) (7.D.2) (7.D.3) (7.D.4)

35. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.5) (7.D.6) (7.D.7)

36. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.8) (7.D.9)

37. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.10) (7.D.11)

38. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.12)

39. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight Left hand side of equation (D12):

40. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight Right hand side of equation (D12)

41. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight (7.D.13) (7.D.14)

42. Appendix 7D. Sharpe Performance Approach to Derive Optimal Weight