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

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

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

Frequency distribution of monthly returns

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

Average Return Total Return comparison A B C D

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

Average Return Total Return comparison A B C D

Average Return Standard Deviation Sharpe ratio comparison A B C D

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

Eight style decomposition

Five style decomposition

Style classifications GSC1Event driven international GSC2Property/Fixed Income GSC3US Equity focus GSC4Non-directional/relative value GSC5Event driven domestic GSC6International focus GSC7Emerging markets GSC8Global macro

Regressing returns on classifications: Adjusted R 2

Variance explained by prior returns-based classifications

Variance explained by prior factor loadings

Percentage in cash (monthly)

Examples of riskless index arbitrage …

Percentage in cash (daily)

“Informationless” investing

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

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

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?

Sharpe Ratio of Benchmark Sharpe ratio =.631

Maximum Sharpe Ratio Sharpe ratio =.748

Concave trading strategies

Examples of concave payout strategies  Long-term asset mix guidelines

 Unhedged short volatility  Writing out of the money calls and puts Examples of concave payout strategies

 Loss averse trading  a.k.a. “Doubling” 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”

Forensic Finance  Implications of concave payoff strategies  Patterns of returns

Forensic Finance  Implications of Informationless investing  Patterns of returns  are returns concave to benchmark?

Forensic Finance  Implications of concave payoff strategies  Patterns of returns  are returns concave to benchmark?  Patterns of security holdings

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?

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

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?

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