Empirical Financial Economics

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Empirical Financial Economics

• 5. Current Approaches to Performance Measurement

Stephen Brown NYU Stern School of Business UNSW
PhD Seminar, June 19-21 2006
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Overview of lecture

• Standard approaches
• Theoretical foundation
• Practical implementation
• Relation to style analysis
• Gaming performance metrics

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Performance measurement
Leeson Investment Management Market (SP 500) Benchmark Short-term Government Benchmark
Average Return .0065 .0050 .0036
Std. Deviation .0106 .0359 .0015
Beta .0640 1.0 .0
Alpha .0025 (1.92) .0 .0
Sharpe Ratio .2484 .0318 .0
Style Index Arbitrage, 100 in cash at close of
trading
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Frequency distribution of monthly returns
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Universe Comparisons
40
Brownian Management
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SP 500
30
25
20
15
10
5
1 Year
3 Years
5 Years
One Quarter
Periods ending Dec 31 2002
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Total Return comparison
Average Return
A
B
C
D
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Total Return comparison
Average Return
A
Manager A best
RSP 13.68
SP 500
B
C
Manager D worst
D
rf 1.08
Treasury Bills
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Total Return comparison
Average Return
A
B
C
D
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Sharpe ratio comparison
Average Return
A
B
C
D
Standard Deviation
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Sharpe ratio comparison
Average Return
A
RSP 13.68
SP 500
B
C
D
rf 1.08
Treasury Bills
Standard Deviation

sSP 20.0
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Sharpe ratio comparison
Average Return
A
RSP 13.68
SP 500
B
C
Manager C worst
Sharpe ratio
D
Manager D best
Average return rf Standard Deviation
rf 1.08
Treasury Bills
Standard Deviation

sSP 20.0
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Sharpe ratio comparison
Average Return
A
RSP 13.68
SP 500
B
C
D
rf 1.08
Treasury Bills
Standard Deviation

sSP 20.0
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Jensens Alpha comparison
Average Return
A
RSP 13.68
SP 500
B
Manager B worst
C
Manager C best
Jensens alpha
D
Average return rf ß (RSP - rf )

rf 1.08
Treasury Bills
Beta
ßSP 1.0
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Intertemporal equilibrium model

• Multiperiod problem
• First order conditions
• Stochastic discount factor interpretation
• stochastic discount factor, pricing
  kernel

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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)
• Jensens alpha measures value of private
  information

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

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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

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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
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Practical issues

• Sharpe ratio sensitive to diversification, but
  invariant to leverage
• Risk premium and standard deviation proportionate
  to fraction of investment financed by borrowing
• Jensens alpha invariant to diversification, but
  sensitive to leverage
• In a complete market implies
  through borrowing (Goetzmann et al 2002)

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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)

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Style management is crucial
Economist, July 16, 1995
But who determines styles?
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Characteristics-based Styles

• Traditional approach
• are changing characteristics (PER,
  Price/Book)
• are returns to characteristics
• Style benchmarks are given by

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Returns-based Styles

• Sharpe (1992) approach
• are a dynamic portfolio strategy
• are benchmark portfolio returns
• Style benchmarks are given by

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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

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Eight style decomposition
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Five style decomposition
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Style classifications
GSC1 Event driven international
GSC2 Property/Fixed Income
GSC3 US Equity focus
GSC4 Non-directional/relative value
GSC5 Event driven domestic
GSC6 International focus
GSC7 Emerging markets
GSC8 Global macro
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Regressing returns on classifications Adjusted R2
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Variance explained by prior returns-based
classifications
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Variance explained by prior factor loadings
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Percentage in cash (monthly)
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Examples of riskless index arbitrage
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Percentage in cash (daily)
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Informationless investing
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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

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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

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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?

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Sharpe Ratio of Benchmark
Sharpe ratio .631
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Maximum Sharpe Ratio
Sharpe ratio .748
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Concave trading strategies
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Examples of concave payout strategies

• Long-term asset mix guidelines

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Examples of concave payout strategies

• Unhedged short volatility
• Writing out of the money calls and puts

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Examples of concave payout strategies

• Loss averse trading
• a.k.a. Doubling

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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

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Forensic Finance

• Implications of concave payoff strategies
• Patterns of returns

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Forensic Finance

• Implications of Informationless investing
• Patterns of returns
• are returns concave to benchmark?

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Forensic Finance

• Implications of concave payoff strategies
• Patterns of returns
• are returns concave to benchmark?
• Patterns of security holdings

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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?

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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

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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?

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Conclusion

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