Portfolio optimization with warren and bill

1. Stodder, Efficient Frontier Portfolio Optimization MethodologyHow to Find that Efficient Frontier! Theoretical & “Real Life” Examples

2. Concept of Beta

4. Security Market Line Equation Required Return=Risk Free + Risk Premium on Stock iRate on Stock i Required Return=Risk Free + βi(Market Risk) on Stock iRate Premium Ri= Rrf+ βi(Rm - Rrf)

5. Beta of the Market = 1 βi= (Ri– Rrf)/(Rm - Rrf) So if Ri = Rm, βi = βm then βm = (Rm– Rrf)/(Rm - Rrf) = 1

6. The Efficient Frontier Non-Diversifiable Risk

7. How do We Find the Efficient Frontier? Basic Strategy: Find the Standard Deviation(σi) and Mean Return(μi) of every stock Stock i. For any given rate of return, find the minimal standard deviation portfolio that can achieve that return.

8. At what point do we have least risk?

9. WHY DIVERSIFY?

10. Use More Than One Basket for Your Eggs The Axiom The Concept of Risk Aversion Revisited Preliminary Steps in Forming a Portfolio The Reduced Security Universe Security Statistics Interpreting the Statistics The Role of Uncorrelated Securities The Variance of a Linear Combination Diversification and Utility The Concept of Dominance

11. The Efficient Frontier Optimum Diversification of Risky Assets The Minimum Variance Portfolio The Effect of a Risk free Rate The Efficient Frontier with Borrowing Different Borrowing and Lending Rates Naive Diversification The Single Index Model

13. Failure to diversify may violate the terms of a fiduciary trust.

15. Preliminary Steps in Forming a Portfolio Insert Figure 16-1 here.

16. Preliminary Steps in Forming a Portfolio Insert Figure 16-2 here.

17. Preliminary Steps in Forming a Portfolio Interpret the statistics. 1. Do the values seem reasonable? 2. Is any unusual price behavior expected to recur? 3. Are any of the results unsustainable? 4. Low correlations: Fact or fantasy?

23. The Efficient Frontier : The Effect of a Riskfree Rate In capital market theory, point M is called the market portfolio. The straight portion of the line is tangent to the risky securities efficient frontier at point M and is called the capital market line. Since buying a Treasury bill amounts to lending money to the U.S. Treasury, a portfolio partially invested in the riskfree rate is often called a lending portfolio.

25. The Efficient Frontier : Naive Diversification The remaining risk, when no further diversification occurs, is pure market risk. Market risk is also called systematic risk and is measured by beta. A security with average market risk has a beta equal to 1.0. Riskier securities have a beta greater than one, and vice versa.

26. The Efficient Frontier : The Single Index Model A pairwise comparison of the thousands of stocks in existence would be an unwieldy task. To get around this problem, the single index model compares all securities to a benchmark measure. The single index model relates security returns to their betas, thereby measuring how each security varies with the overall market.

28. The Efficient Frontier : The Single Index Model Insert Figure 16-12 here.

30. The Axiom

31. The Concept of Risk Aversion Revisited

32. Preliminary Steps in Forming a Portfolio

33. The Reduced Security Universe

34. Security Statistics

35. Interpreting the Statistics

36. The Role of Uncorrelated Securities

37. The Variance of a Linear Combination

38. Diversification and Utility

40. Optimum Diversification of Risky Assets

41. The Minimum Variance Portfolio

42. The Effect of a Riskfree Rate

43. The Efficient Frontier with Borrowing

44. Different Borrowing and Lending Rates

45. Naive Diversification

47. Four factors that make the market move:

48. The economy

49. Fed policy

50. Valuation

52. Appendix: Arbitrage Pricing Theory