Empirical Financial Economics

1. Empirical Financial Economics Current Approaches to Performance Measurement

2. Overview of lecture • Standard approaches • Theoretical foundation • Practical implementation • Relation to style analysis • Gaming performance metrics

3. Performance measurement Style: Index Arbitrage, 100% in cash at close of trading

4. Frequency distribution of monthly returns

5. Universe Comparisons 40% Brownian Management 35% S&P 500 30% 25% 20% 15% 10% 5% 1 Year 3 Years 5 Years One Quarter Periods ending Dec 31 2002

6. Total Return comparison Average Return A B C D

7. Total Return comparison Average Return A Manager A best RS&P = 13.68% S&P 500 B C Manager D worst D rf = 1.08% Treasury Bills

8. Total Return comparison Average Return A B C D

9. Sharpe ratio comparison Average Return A B C D Standard Deviation

10. Sharpe ratio comparison Average Return A RS&P = 13.68% S&P 500 B C D rf = 1.08% Treasury Bills Standard Deviation ^ σS&P = 20.0%

11. Sharpe ratio comparison Average Return A RS&P = 13.68% S&P 500 B C Manager C worst Sharpe ratio = D Manager D best Average return – rf Standard Deviation rf = 1.08% Treasury Bills Standard Deviation ^ σS&P = 20.0%

12. Sharpe ratio comparison Average Return A RS&P = 13.68% S&P 500 B C D rf = 1.08% Treasury Bills Standard Deviation ^ σS&P = 20.0%

13. Treynor Measure comparison A Average Return RS&P = 13.68% S&P 500 B C D rf = 1.08% Treasury Bills Beta βS&P = 1.0

14. Treynor Measure comparison A Average Return RS&P = 13.68% S&P 500 B Manager B worst C Manager C best Treynor measure = D Average return – rfBeta rf = 1.08% Treasury Bills Beta βS&P = 1.0

15. Jensen’s Alpha comparison Average Return A RS&P = 13.68% S&P 500 B Manager B worst C Manager C best Jensen’s alpha = D Average return – {rf + β (RS&P - rf )} rf = 1.08% Treasury Bills Beta βS&P = 1.0

16. Intertemporal equilibrium model • Multiperiod problem: • First order conditions: • Stochastic discount factor interpretation: • “stochastic discount factor”, “pricing kernel”

17. Value of Private Information • Investor has access to information • Value of is given by where and are returns on optimal portfolios given and • Under CAPM (Chen & Knez 1996) • Jensen’s alpha measures value of private information • Other pricing kernels:

18. The geometry of mean variance Note: returns are in excess of the risk free rate

19. Informed portfolio strategy • Excess return on informed strategy where is the return on an optimal orthogonal portfolio (MacKinlay 1995) • Sharpe ratio squared of informed strategy • Assumes well diversified portfolios

20. Informed portfolio strategy • Excess return on informed strategy where is the return on an optimal orthogonal portfolio (MacKinlay 1995) • Sharpe ratio squared of informed strategy • Assumes well diversified portfolios Used in tests of mean variance efficiency of benchmark

21. Practical issues • Sharpe ratio sensitive to diversification, but invariant to leverage • Risk premium and standard deviation proportionate to fraction of investment financed by borrowing • Jensen’s alpha invariant to diversification, but sensitive to leverage • In a complete market impliesthrough borrowing (Goetzmann et al 2002)

22. Changes in Information Set • How do we measure alpha when information set is not constant? • Rolling regression, use subperiods to estimate (not subscript) – Sharpe (1992) • Use macroeconomic variable controls – Ferson and Schadt(1996) • Use GSC procedure – Brown and Goetzmann (1997)

23. Style management is crucial … Economist, July 16, 1995 But who determines styles?

24. Characteristics-based Styles • Traditional approach … • are changing characteristics (PER, Price/Book) • are returns to characteristics • Style benchmarks are given by

25. Returns-based Styles • Sharpe (1992) approach … • are a dynamic portfolio strategy • are benchmark portfolio returns • Style benchmarks are given by

26. Returns-based Styles • GSC (1997) approach … • vary through time but are fixed for style • Allocate funds to styles directly using • Style benchmarks are given by

27. Basis Assets • GSC (1997) approach … • vary through time but fixed for risk class • Allocate equities to risk classes directly using • Style benchmarks are given by Brown, Stephen J. and William N. Goetzmann, 1997 Mutual Fund Styles. Journal of Financial Economics 43:3, 373-399.

28. Switching Regression • Quandt (1958) • If regimes not observed

29. K means procedure • Hartigan (1975) • If regimes not observed, use iterative algorithm to determine regime membership

30. Switching Regression • Quandt and Ramsey (1978) • Method of moments ...

31. Eight style decomposition

32. Five style decomposition

33. Style classifications

34. Regressing returns on classifications: Adjusted R2

35. “Informationless” investing

36. Analytic Optioned Our fund purchases a stock and simultaneously sells a call option against the stock. By doing this, the fund receives both dividend income from the stock and a cash premium from the sale of the option. This strategy is designed for the longer term investor who wants to reduce risk. It is particularly suited for pension plans IRAs and Keoghs. Our defensive buy/write strategy is designed to put greater emphasis on risk reduction by focusing on “in-the-money” call options. The results speak for themselves. Over a twelve year period, of 153 institutional portfolios in the Frank Russell Co. universe, no other portfolio had a higher return with less risk than our All Buy/Write Accounts Index. In the terminology of modern portfolio theory, our clients’ portfolios dominated the market averages.

37. Modern Portfolio Theory

38. Covered Call Strategy Value Stock Profit to Covered Call Payoff to Covered Call

39. Unoptioned Portfolio Return Expected Return Portfolio Return

40. Optioned Return Expected Return Portfolio Return

41. Optioned Return (incl. premium) Expected Return Portfolio Return

42. Concave payout strategies • Zero net investment overlay strategy (Weisman 2002) • Uses only public information • Designed to yield Sharpe ratio greater than benchmark • Using strategies that are concave to benchmark

43. Concave payout strategies • Zero net investment overlay strategy (Weisman 2002) • Uses only public information • Designed to yield Sharpe ratio greater than benchmark • Using strategies that are concave to benchmark • Why should we care? • Sharpe ratio obviously inappropriate here • But is metric of choice of hedge funds and derivatives traders Goetzmann, William N., Ingersoll, Jonathan E., Spiegel, Matthew I. and Welch, Ivo, 2007 Portfolio Performance Manipulation and Manipulation-proof Performance Measures, Review of Financial Studies 20(5) 1503-1546.

44. Sharpe Ratio of Benchmark Sharpe ratio = .631

45. Maximum Sharpe Ratio Sharpe ratio = .748

46. Short Volatility Strategy Sharpe ratio = .743

47. Concave trading strategies

48. Examples of concave payout strategies • Long-term asset mix guidelines

49. Examples of concave payout strategies • Unhedged short volatility • Writing out of the money calls and puts

50. Examples of concave payout strategies • Loss averse trading • a.k.a. “Doubling”