Empirical Financial Economics

1. Empirical Financial Economics 5. Current Approaches to Performance Measurement Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June 19-21 2006

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. 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

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

15. 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

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

17. 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

18. 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

19. 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)

20. 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)

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

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

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

24. 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

25. Eight style decomposition

26. Five style decomposition

27. Style classifications

28. Regressing returns on classifications: Adjusted R2

29. Variance explained by prior returns-based classifications

30. Variance explained by prior factor loadings

31. Percentage in cash (monthly)

32. Examples of riskless index arbitrage …

33. Percentage in cash (daily)

34. “Informationless” investing

35. 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

36. 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

37. We should care! • Delegated fund management • Fund flow, compensation based on historical performance • Limited incentive to monitor high Sharpe ratios • Behavioral issues • Prospect theory: lock in gains, gamble on loss • Are there incentives to control this behavior?

38. Sharpe Ratio of Benchmark Sharpe ratio = .631

39. Maximum Sharpe Ratio Sharpe ratio = .748

40. Concave trading strategies

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

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

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

44. Examples of concave payout strategies • Long-term asset mix guidelines • Unhedged short volatility • Writing out of the money calls and puts • Loss averse trading • a.k.a. “Doubling”

45. Forensic Finance • Implications of concave payoff strategies • Patterns of returns

46. Forensic Finance • Implications of Informationless investing • Patterns of returns • are returns concave to benchmark?

47. Forensic Finance • Implications of concave payoff strategies • Patterns of returns • are returns concave to benchmark? • Patterns of security holdings

48. Forensic Finance • Implications of concave payoff strategies • Patterns of returns • are returns concave to benchmark? • Patterns of security holdings • do security holdings produce concave payouts?

49. Forensic Finance • Implications of concave payoff strategies • Patterns of returns • are returns concave to benchmark? • Patterns of security holdings • do security holdings produce concave payouts? • Patterns of trading

50. Forensic Finance • Implications of concave payoff strategies • Patterns of returns • are returns concave to benchmark? • Patterns of security holdings • do security holdings produce concave payouts? • Patterns of trading • does pattern of trading lead to concave payouts?