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Empirical Financial Economics
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Transcript of Empirical Financial Economics
Empirical Financial Economics
5. Current Approaches to Performance Measurement
Stephen Brown NYU Stern School of Business
UNSW PhD Seminar, June 19-21 2006
Overview of lecture
Standard approachesTheoretical foundationPractical implementationRelation to style analysisGaming performance metrics
Performance measurement
Leeson InvestmentManagement
Market (S&P 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
Frequency distribution of monthly returns
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5
10
15
20
25
30
35
-1.00
%
-0.50%
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%
0.50
%1.0
0%1.5
0%
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%
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%
3.00
%
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%
4.00
%
4.50
%
5.00
%
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%
6.00
%
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%
Universe Comparisons
5%
10%
15%
20%
25%
30%
35%
40%
Brownian ManagementS&P 500
One Quarter
1 Year 3 Years 5 Years
Periods ending Dec 31 2002
Average Return
Total Return comparison
A
BCD
rf = 1.08%
Average Return
RS&P = 13.68%
Total Return comparison
AS&P 500
BCD
Treasury Bills
Manager A best
Manager D worst
Average Return
Total Return comparison
A
BCD
Average Return
Standard Deviation
Sharpe ratio comparison
A
BC
D
rf = 1.08%
σS&P = 20.0%
Average Return
Standard Deviation
RS&P = 13.68%
Sharpe ratio comparison
^
AS&P 500
BC
D
Treasury Bills
rf = 1.08%
σS&P = 20.0%
Average Return
Standard Deviation
RS&P = 13.68%
Sharpe ratio comparison
^
AS&P 500
BC
D
Treasury Bills
Manager D bestManager C worstSharpe ratio =
Average return – rf
Standard Deviation
rf = 1.08%
σS&P = 20.0%
Average Return
Standard Deviation
RS&P = 13.68%
Sharpe ratio comparison
^
AS&P 500
BC
D
Treasury Bills
rf = 1.08%
Average Return
RS&P = 13.68%
Jensen’s Alpha comparison
AS&P 500
BCD
Treasury Bills
Manager B worstJensen’s alpha = Average return
–
{rf + β (RS&P - rf )}
βS&P = 1.0Beta
Manager C best
Intertemporal equilibrium model
Multiperiod problem:
First order conditions:
Stochastic discount factor interpretation:
“stochastic discount factor”, “pricing kernel”
0
Max ( )jt t j
j
E U c
,( ) (1 ) ( )jt t i t j t jU c E r U c
, , ,
( )1 (1 ) ,
( )t jj
t i t j t j t jt
U cE r m m
U c
,t jm
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
1 0I I
1 0I I 1 0[( ) ]t tE R R m 1R 0R1I 0I
1 0 1 1 1[( ) ] ( )t t t ft t mt ftE R R m r r
The geometry of mean variance
a
b
a
b
E
2 1a
1 1
2
1/1/
0
bx b
22
2
2a bE cE
ac b
Note: returns are in excess of the risk free rate
fr
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
1 0f fR r R r
2 1 1 2 2 21 0 0 0 0( ) ( )f fr r
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
1 0f fR r R r
2 1 1 2 2 21 0 0 0 0( ) ( )f fr r
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)
2 0
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)
1 1 1 ( )t t ft t mt ftr r 1tI
1 1 1( )f m ftr r
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
jt Jt Jt t jtr I j J
jt Jt jtr j J
JttI
Jt
Returns-based Styles
Sharpe (1992) approach …
are a dynamic portfolio strategy are benchmark portfolio returns Style benchmarks are given by
jt Jt Jt t jtr I j J
jt Jt jtr j J
JttI
Jt
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
jt Jt Jt t jtr I j J
jt Jt jtr j J
,jT Jt
Jt
J
Jt
Eight style decomposition
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20%
40%
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100%
GSC1 GSC2 GSC3 GSC4 GSC5 GSC6 GSC7 GSC8Other Pure PropertyPure Emerging Market Pure Leveraged CurrencyGlobal Macro Non Directional/Relative ValueEvent Driven Non-US Equity HedgeUS Equity Hedge
Five style decomposition
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20%
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60%
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100%
GSC1 GSC2 GSC3 GSC4 GSC5Other Pure PropertyPure Emerging Market Pure Leveraged CurrencyGlobal Macro Non Directional/Relative ValueEvent Driven Non-US Equity HedgeUS Equity Hedge
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
Regressing returns on classifications: Adjusted R2
Year N GSC 8
classifications GSC 5
classificationsTASS 17
classifications1992 149 0.3827 0.1713 0.44411993 212 0.2224 0.1320 0.11861994 288 0.1662 0.1040 0.09861995 405 0.0576 0.0548 0.04461996 524 0.1554 0.0769 0.15231997 616 0.3066 0.1886 0.25381998 668 0.2813 0.2019 0.1998
Average 0.2246 0.1328 0.1874
Variance explained by prior returns-based classifications
Year N8 GSC
Classifications8 Principal
Components 8 Benchmarks(predetermined)
1992 198 0.3622 0.0572 0.17691993 276 0.1779 0.0351 0.17481994 348 0.1590 0.0761 0.04811995 455 0.0611 0.0799 0.08621996 557 0.1543 0.0286 0.06911997 649 0.2969 0.0211 0.06421998 687 0.2824 0.2862 0.2030
Average 0.2134 0.0835 0.1175
Variance explained by prior factor loadings
Year N8 GSC
Classifications8 Principal
Components 8 Benchmarks
(predetermined)1992 198 0.2742 0.1607 0.25521993 276 0.2170 0.0928 0.09321994 348 0.1760 0.1577 0.07001995 455 0.0670 0.0783 0.08291996 557 0.1444 0.0888 0.03491997 649 0.3135 0.3069 0.08991998 687 0.2752 0.3744 0.3765
Average 0.2096 0.1799 0.1432
Percentage in cash (monthly)
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20%
40%
60%
80%
100%
120%
31-Dec-1989 15-May-1991 26-Sep-1992 8-Feb-1994
Examples of riskless index arbitrage …
Percentage in cash (daily)
-600%
-500%
-400%
-300%
-200%
-100%
0%
100%
200%
31-Dec-1989 15-May-1991 26-Sep-1992 8-Feb-1994
“Informationless” investing
Concave payout strategies
Zero net investment overlay strategy (Weisman 2002)
Uses only public informationDesigned to yield Sharpe ratio greater than benchmarkUsing strategies that are concave to benchmark
Concave payout strategies
Zero net investment overlay strategy (Weisman 2002)
Uses only public informationDesigned to yield Sharpe ratio greater than
benchmarkUsing strategies that are concave to benchmark
Why should we care?
Sharpe ratio obviously inappropriate hereBut is metric of choice of hedge funds and
derivatives traders
We should care!
Delegated fund managementFund flow, compensation based on
historical performanceLimited incentive to monitor high
Sharpe ratiosBehavioral issues
Prospect theory: lock in gains, gamble on loss
Are there incentives to control this behavior?
Sharpe Ratio of Benchmark
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
Sharpe ratio = .631
Maximum Sharpe Ratio
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
MaximumSharpe RatioStrategy
Sharpe ratio = .748
Concave trading strategies
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
Loss AverseTrading(Median)MaximumSharpe RatioStrategy
Examples of concave payout strategies
Long-term asset mix guidelines
Unhedged short volatilityWriting out of the money
calls and puts
Examples of concave payout strategies
Loss averse trading a.k.a. “Doubling”
Examples of concave payout strategies
Examples of concave payout strategies
Long-term asset mix guidelines
Unhedged short volatilityWriting 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 returnsare returns concave to benchmark?
Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdings
Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdingsdo security holdings produce
concave payouts?
Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdingsdo security holdings produce concave
payouts?
Patterns of trading
Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdingsdo security holdings produce concave
payouts?
Patterns of tradingdoes 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