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 Leeson Investment Managemen t Market (S&P 500) Benchmark Short-term Government Benchmark Average Return.0065.0050.0036 Std. Deviation.0106.0359.0015 Beta.06401.0.0 Alpha.0025 (1.92).0 Sharpe Ratio.2484.0318.0 Style: Index Arbitrage, 100% in cash at close of trading

4. Frequency distribution of monthly returns

5. Universe Comparisons 5% 10% 15% 20% 25% 30% 35% 40% Brownian Management S&P 500 One Quarter 1 Year3 Years5 Years Periods ending Dec 31 2002

6. Average Return Total Return comparison A B C D

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

8. Average Return Total Return comparison A B C D

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

10. r f = 1.08% σ S&P = 20.0% Average Return Standard Deviation R S&P = 13.68% Sharpe ratio comparison ^ A S&P 500 B C D Treasury Bills

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

12. r f = 1.08% σ S&P = 20.0% Average Return Standard Deviation R S&P = 13.68% Sharpe ratio comparison ^ A S&P 500 B C D Treasury Bills

13. 13 r f = 1.08% β S&P = 1.0 Average Return Beta R S&P = 13.68% Treynor Measure comparison A S&P 500 B C D Treasury Bills

14. 14 r f = 1.08% Average Return R S&P = 13.68% Treynor Measure comparison A S&P 500 B C D Treasury Bills Manager B worst Manager C best Treynor measure = Average return – r f Beta β S&P = 1.0 Beta

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

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 implies through 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 (no t 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 GSC1Event driven international GSC2Property/Fixed Income GSC3US Equity focus GSC4Non-directional/relative value GSC5Event driven domestic GSC6International focus GSC7Emerging markets GSC8Global macro

34. Regressing returns on classifications: Adjusted R 2 YearN GSC 8 classifications GSC 5 classification s TASS 17 classification s 19921490.38270.17130.4441 19932120.22240.1320.1186 19942880.16620.1040.0986 19954050.05760.05480.0446 19965240.15540.07690.1523 19976160.30660.18860.2538 19986680.28130.20190.1998 Average0.22460.13280.1874

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 Stock Value Profit to Covered Call Payoff to Covered Call

39. Unoptioned Portfolio Return Portfolio Return Expected Return

40. Optioned Return Portfolio Return Expected Return

41. Optioned Return (incl. premium) Portfolio Return Expected 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.  Unhedged short volatility  Writing out of the money calls and puts Examples of concave payout strategies

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

51.  Long-term asset mix guidelines  Unhedged short volatility  Writing out of the money calls and puts  Loss averse trading  a.k.a. “Doubling”

52. 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?

53. Manipulation proof measure  Criteria:  Ranks portfolios based on investor preferences  Cannot reward informationless trading  Should be scale invariant  Should be consistent with market equilibrium models 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.

54. Manipulation proof measure Certainty equivalent of portfolio return Number of observations Length of time between observations Chosen to make holding benchmark optimal for an uninformed investor

55. Implied risk aversion parameter What implied risk aversion parameter makes the market participant indifferent to holding the market portfolio?

56. Performance of beta ranked portfolios

57. Performance of vol ranked portfolios

58. Descriptive statistics of beta ranked portfolios Monthly returns: January 1980 - December 2011 lobetahibetamktbetalovolhivollobeta-hibetalovol-hivol Mean1.00%0.71%0.95%1.03%0.32%0.29%0.71% Std.Dev2.78%9.38%3.71%2.76%8.31%8.36%7.10% Skewness-1.741-0.253-1.146-1.207-0.2390.036-0.228 Kurtosis14.6194.1999.2087.9335.6014.5647.393 Beta0.3391.7910.6670.4641.450-1.449-0.983 Sharpe0.20800.03100.14150.2223-0.0123-0.01590.0411 Alpha0.391%-0.697%0.159%0.352%-0.903%0.667%0.833% t-value2.805-3.0221.3313.556-3.5222.3392.810 FF alpha0.322%-0.489%0.158%0.218%-0.776%0.391%0.574% t-value2.483-2.8661.6452.426-4.6281.5072.668 MPPM-.00205.00391-.00148-.00221.00453

59. Descriptive statistics of beta ranked portfolios Daily returns: January 1980 - December 2011 lobetahibetamktbetalovolhivollobeta-hibetalovol-hivol Mean0.05%0.03%0.04%0.05%0.01% 0.04% Std.Dev0.34%1.96%0.56%0.49%1.39%1.92%1.11% Skewness-2.926-0.133-1.829-1.171-0.597-0.1720.385 Kurtosis46.55710.47130.11637.26312.93110.88616.465 Beta0.0701.6150.4160.3781.033-1.545-0.655 Sharpe0.07640.00600.04110.0570-0.0085-0.00290.0182 Alpha0.024%-0.032%0.012%0.018%-0.040%0.037%0.038% t-value5.907-3.4232.9945.574-4.1803.5643.707 FF alpha0.025%-0.034%0.013%0.012%-0.041%0.039%0.034% t-value6.394-4.9844.0184.637-6.5274.5054.615 MPPM-.00009.00012-.00007-.00009.00013

60. Hedge funds follow concave strategies R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2

61. Hedge funds follow concave strategies R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2 Concave strategies: t β > 1.96 & t γ < - 1.96

62. Hedge funds follow concave strategies ConcaveNeutralConvexN Convertible Arbitrage Dedicated Short Bias Emerging Markets Equity Market Neutral Event Driven Fixed Income Arbitrage Fund of Funds Global Macro Long/Short Equity Hedge Managed Futures Other 5.38% 0.00% 21.89% 1.18% 27.03% 2.38% 16.38% 4.60% 11.19% 2.80% 5.00% 94.62% 100.00% 77.25% 97.06% 72.64% 95.24% 82.06% 91.38% 86.62% 94.17% 91.67% 0.00% 0.86% 1.76% 0.34% 2.38% 1.57% 4.02% 2.18% 3.03% 3.33% 130 27 233 170 296 126 574 174 1099 429 60 Grand Total11.54%86.53%1.93%3318 R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2 Source: TASS/Tremont

63. Standard deviation as a function of the number of funds in FoHFs Brown, Stephen J., Gregoriou, Greg N. and Pascalau, Razvan C., Diversification in Funds of Hedge Funds: Is it Possible to Overdiversify? Review of Asset Pricing Studies 2(1), 2012, pp.89-110 http://ssrn.com/abstract=1436468

64. Skewness as a function of the number of funds in FoHFs

65. Kurtosis as a function of the number of funds in FoHFs

66. Conclusion  Value of information interpretation of standard performance measures  New procedures for style analysis  Return based performance measures only tell part of the story