Concave payoff patterns in equity fund holdings and transactions
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Transcript of Concave payoff patterns in equity fund holdings and transactions
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Concave payoff patterns in equity fund holdings and transactions
Stephen J. Brown NYU Stern School of Business
David R. Gallagher University of NSWOnno Steenbeek Erasmus University / ABP
InvestmentsPeter L. Swan University of NSW
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Challenge to active managment
Zero or negative alpha in fund returns
Can fund managers earn returns commensurate with fees they charge?
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Challenge to active managment
Zero or negative alpha in fund returns
Can fund managers earn returns commensurate with fees they charge?
Recent evidence shows active trading does generate positive returns (Wermers 2000)
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Challenge to active managment
Zero or negative alpha in fund returns
Can fund managers earn returns commensurate with fees they charge?
Recent evidence shows active trading does generate positive returns (Wermers 2000)
Negative quadratic term in market model
Can fund managers time the market?
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Challenge to active managment
Zero or negative alpha in fund returns
Can fund managers earn returns commensurate with fees they charge?
Recent evidence shows active trading does generate positive returns (Wermers 2000)
Negative quadratic term in market model
Can fund managers time the market?Recent evidence shows hedge fund managers
use concave payout overlay strategies (Agarwall & Naik 2004)
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Overview
Definition of concave payoff patterns
Detecting concave payoff strategies
Evidence from managed funds
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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
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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
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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?
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Sharpe Ratio of Benchmark
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
Sharpe ratio = .631
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Maximum Sharpe Ratio
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
MaximumSharpe RatioStrategy
Sharpe ratio = .748
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Concave trading strategies
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%
Benchmark
Loss AverseTrading(Median)MaximumSharpe RatioStrategy
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Examples of concave payout strategies
Long-term asset mix guidelines
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Unhedged short volatilityWriting out of the money
calls and puts
Examples of concave payout strategies
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Loss averse trading a.k.a. “Doubling”
Examples of concave payout strategies
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Examples of informationless investing
Long-term asset mix guidelines
Unhedged short volatilityWriting 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 returnsare returns concave to benchmark?
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Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdings
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Forensic Finance
Implications of concave payoff strategies
Patterns of returnsare returns concave to benchmark?
Patterns of security holdingsdo security holdings produce
concave payouts?
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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
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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?
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Hedge funds follow concave strategies
R-rf = α + β (RS&P- rf) + γ (RS&P- rf)2
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Hedge funds follow concave strategies
R-rf = α + β (RS&P- rf) + γ (RS&P- rf)2
Concave strategies: tβ > 1.96 & tγ < -1.96
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Hedge funds follow concave strategies
Concave NeutralConve
x NConvertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven Fixed Income
Arbitrage Fund of Funds Global Macro Long/Short Equity
HedgeManaged 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%0.00%0.86%1.76%0.34%2.38%1.57%4.02%2.18%3.03%3.33%
13027
233170296126574174109942960
Grand Total 11.54% 86.53% 1.93% 3318
R-rf = α + β (RS&P- rf) + γ (RS&P- rf)2
Source: TASS/Tremont
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Portfolio Analytics Database
36 Australian institutional equity funds managers
Data on Portfolio holdings Daily returns Aggregate returns Fund size
59 funds (no more than 4 per manager) 51 active 3 enhanced index funds 4 passive 1 international
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Some successful Australian funds
FundSharpe Ratio Alpha
FF Alpha Beta
Skewness
Kurtosis
6 0.21570.412
40.430
01.076
1 -0.7624 5.8161(5.46) (6.11)
13 0.20000.270
60.290
81.003
1 -0.8107 5.9314(5.65) (6.15)
20 0.19680.332
40.320
61.005
9 -0.5811 5.3488(6.05) (6.18)
25 0.19880.288
30.320
80.883
1 -0.3509 4.7580(3.85) (4.11)
37 0.15780.190
30.218
80.721
4 -0.2904 4.6642(3.21) (3.00)
38 0.19550.232
30.229
50.967
2 -0.7011 5.6731(6.52) (7.40)
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Patterns of Returns
Category Alpha
Treynor Mazuy
measure
Modified Henriksson
Merton measure
Number of observation
sGARP
0.11795(3.49)
-0.01287(-2.79)
-0.14274(-2.41)
1164
Growth
0.05089(1.01)
-0.00842(-1.30)
-0.07343(-0.93)
469
Neutral
0.16678(2.16)
-0.01233(-1.47)
-0.18396(-1.79)
187
Other
0.12765(2.46)
-0.01682(-2.82)
-0.2128(-2.60)
397
Value
0.11968(2.15)
-0.01775(-2.02)
-0.19097(-1.85)
772
Passive/ Enhance
d
0.05205(0.52)
-0.02119(-1.69)
-0.24707(-1.44)
253
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Patterns of Returns
Category Alpha
Treynor Mazuy
measure
Modified Henriksson Merton measure
Number of observatio
ns
Largest 10 Institution
al Manager
No
0.08313
(2.73)
-0.01637(-4.11)
-0.18654(-3.58)
1952
Yes
0.14964
(4.39)
-0.01184(-2.15)
-0.12781(-2.02)
1290
Boutique firm
No
0.11326
(4.43)
-0.01487(-3.98)
-0.17119(-3.82)
2821
Yes
0.07198
(1.85)
-0.00936(-2.05)
-0.08085(-1.22)
421
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Patterns of Holdings
Fund Investment
Style
Calls Puts Month end option positions
Fund Number Strike Number StrikeConcavity decreasing
Concavity increasing Total
GARP 1234561114
0.726-0.0610.0990.041-0.6500.2220.8110.054
1.0171.0501.0171.0231.0621.0760.0021.076
0.395-0.1220.0210.008-1.346
0.950
-
0.9570.9040.9520.9440.985
0.674
-
100%29%59%77%
100%100%100%
71%41%23%
100%
8024679
8981811811
Growth 16171819
-0.033-0.039-0.367-0.059
1.0561.0601.0671.023
--
0.1070.108
--
0.9510.913
27%
35%13%
73%100%65%87%
11883
344
Neutral 222325
-0.0930.5670.405
1.0380.9840.854
-0.093--
0.947--
10%100%100%
90%
208101
Other 26 0.079 1.147 0.147 0.965 94% 6% 35
Value 34 0.050 0.914 57% 43% 23
Passive/ Enhanced
3940
-0.013-0.026
0.9481.036
-0.017-0.041
0.9550.959
9%10%
91%90%
340613
Total 38% 62% 3027
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Patterns of Holdings
Fund Investment
Style
Calls Puts Month end option positions
Fund Number Strike Number StrikeConcavity decreasing
Concavity increasing Total
GARP
1234561113
0.726-0.0610.0990.041-0.6500.2220.8110.054
1.0171.0501.0171.0231.0621.0760.0021.076
0.395-0.1220.0210.008-1.346
0.950
-
0.9570.9040.9520.9440.985
0.674
-
100%29%59%77%
100%100%100%
71%41%23%
100%
8024679
8981811811
Growth
16171819
-0.033-0.039-0.367-0.059
1.0561.0601.0671.023
--
0.1070.108
--
0.9510.913
27%
35%13%
73%100%65%87%
11883
344
Neutral
222325
-0.0930.5670.405
1.0380.9840.854
-0.093--
0.947--
10%100%100%
90%
208101
Other 26 0.079 1.147 0.147 0.965 94% 6% 35
Value 34 0.050 0.914 57% 43% 23
Passive/ Enhanced
3940
-0.013-0.026
0.9481.036
-0.017-0.041
0.9550.959
9%10%
91%90%
340613
Total 38% 62% 3027
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Patterns of Holdings
Fund Investment
Style
Calls Puts Month end option positions
Fund Number Strike Number StrikeConcavity decreasing
Concavity increasing Total
GARP
1234561113
0.726-0.0610.0990.041-0.6500.2220.8110.054
1.0171.0501.0171.0231.0621.0760.0021.076
0.395-0.1220.0210.008-1.346
0.950
-
0.9570.9040.9520.9440.985
0.674
-
100%29%59%77%
100%100%100%
71%41%23%
100%
8024679
8981811811
Growth
16171819
-0.033-0.039-0.367-0.059
1.0561.0601.0671.023
--
0.1070.108
--
0.9510.913
27%
35%13%
73%100%65%87%
11883
344
Neutral
222325
-0.0930.5670.405
1.0380.9840.854
-0.093--
0.947--
10%100%100%
90%
208101
Other 26 0.079 1.147 0.147 0.965 94% 6% 35
Value 34 0.050 0.914 57% 43% 23
Passive/ Enhanced
3940
-0.013-0.026
0.9481.036
-0.017-0.041
0.9550.959
9%10%
91%90%
340613
Total 38% 62% 3027
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Patterns of Trading
Buying on a loss and selling on a gain leads to concave payouts
Short Volatility replication
Loss averse trading (a.k.a. “Doubling”)
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Short Volatility Strategy
-200%
-150%
-100%
-50%
0%
50%
100%
-50% 0% 50% 100%Benchmark return
Port
folio
retu
rn
Sharpe ratio = .743
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Short Volatility transactions
-8
-6
-4
-2
0
-50% 0% 50% 100%
Benchmark return
Tran
sact
ions/
ΔS
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Some successful Australian funds
FundSharpe Ratio Alpha
FF Alpha Beta
Skewness
Kurtosis
6 0.21570.412
40.430
01.076
1 -0.7624 5.8161(5.46) (6.11)
13 0.20000.270
60.290
81.003
1 -0.8107 5.9314(5.65) (6.15)
20 0.19680.332
40.320
61.005
9 -0.5811 5.3488(6.05) (6.18)
25 0.19880.288
30.320
80.883
1 -0.3509 4.7580(3.85) (4.11)
37 0.15780.190
30.218
80.721
4 -0.2904 4.6642(3.21) (3.00)
38 0.19550.232
30.229
50.967
2 -0.7011 5.6731(6.52) (7.40)
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Some successful Australian funds
FundSharpe Ratio Alpha
FF Alpha Beta
Skewness
Coefficient on trading
on a loss
6 0.21570.412
40.430
01.076
1 -0.7624 -0.0804(5.46) (6.11) (-3.00)
13 0.20000.270
60.290
81.003
1 -0.8107 -0.2272(5.65) (6.15) (-5.42)
20 0.19680.332
40.320
61.005
9 -0.5811 -0.3343(6.05) (6.18) (-6.40)
25 0.19880.288
30.320
80.883
1 -0.3509 -0.0973(3.85) (4.11) (-4.73)
37 0.15780.190
30.218
80.721
4 -0.2904 -0.0253(3.21) (3.00) (-3.72)
38 0.19550.232
30.229
50.967
2 -0.7011 -0.1104(6.52) (7.40) (-5.26)
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Relationship between alpha and trading on a loss
AlphaNegativ
e Zero Positive Total
Coefficient on
trading on a loss
Negative 0 4 9 13Zero 0 20 4 24
Positive 0 2 1 3Total 0 26 14 40
Chi square = 10.2451 (p-value 0.006)
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Sector Patterns
Mining and minerals Industrial Services
Gain above high
water mark
Change in value of position on a loss
Change in value
of position on a gain
Change in value of position on a loss
Change in value
of position
on a gain
Change in value
of position on a loss
Change in value
of position
on a gain
GARP -0.2706 0.0172 0.0000 0.1993 -0.0172 0.3859 -1.0693(-2.56) (0.05) (0.17) (0.58) (-1.28) (1.46) (-2.92)
Largest -0.3615-
0.1913 -0.0001 0.0048-
0.0488 0.2860 -0.8497(-3.19) (-0.74) (-0.44) (0.02) (-3.05) (1.65) (-3.33)
Domestic -0.2021
-0.3987 -0.0001
-0.3439
-0.0497 0.1794 -0.6017
(-3.19) (-2.43) (-0.49) (-2.23) (-3.87) (1.59) (-3.82)
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Seasonal patterns
December-January February-May June-July
August-November
Gain above high
water mark
Change in value of position on a loss
Change in value
of position
on a gain
Change in value
of position on a loss
Change in value
of position
on a gain
Change in value
of position
on a loss
Change in value
of position
on a gain
Change in value
of position on a loss
Change in value
of position
on a gain
GARP 0.0001 0.6250 -0.0663 0.1319
-0.322
6 0.2283 -0.0395 0.2623-
1.1372
(1.33) (2.39) (-1.87) (0.38)(-
2.44) (0.77) (-1.52) (0.88) (-3.34)
Largest -0.0002 0.5006 -0.0773 0.0426
-0.152
4 0.0962-
0.0675 0.1610-
1.0076
(-0.54) (3.22) (-1.49) (0.21)(-
2.02) (0.64) (-2.90) (0.79) (-4.76)
Domestic -0.1259 0.3522-
0.0760-
0.0954
-0.099
8 0.0302 -0.0007 -0.1494-
0.7966
(-4.55) (3.25) (-2.38) (-0.70)(-
2.19) (0.27) (-0.84) (-1.17) (-6.00)
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Return to long buy/short sell (monthly)
Category Raw return
Market Adjusted
GARP 0.28% 0.33%(0.81) (0.91)
Growth -0.07% -0.05%(-0.11) (-0.07)
Neutral 1.46% 0.83%(1.84) (1.53)
Other 2.40% 2.48%(1.99) (2.11)
Value 1.11% 0.92%(2.06) (1.64)
Passive/ Enhanced
Passive
-1.31% -0.80%(-2.40) (-3.07)
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Return to long buy/short sell (monthly)
CategoryRaw
return
Market Adjust
edLargest 10 Institution
al Manager
No 0.86% 0.65%(2.49) (1.99)
Yes 0.11% 0.40%(0.33) (1.41)
Boutique firm
No 0.42% 0.40%(1.27) (1.35)
Yes 1.07% 0.88%(2.24) (1.95)
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National Australia Bank
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A clear and present danger?
Evidence of concave payout pattern in managed fundsEvidence in returnsEvidence in security holdingsEvidence in pattern of transactions
Consistent withAdverse incentive storyBehavioral theories of trading
Effect limited to large, diversified funds