Double or nothing: Patterns of equity fund holdings and transactions

1
Double or nothing Patterns of equity fund
holdings and transactions

• Stephen J. Brown NYU Stern School of Business
• David R. Gallagher University of NSW
• Onno Steenbeek Erasmus University / ABP
  Investments
• Peter L. Swan University of NSW
• Frontiers of Finance 2005, Bonaire

2
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
3
Frequency distribution of monthly returns
4
Percentage in cash (monthly)
5
Examples of riskless index arbitrage
6
Percentage in cash (daily)
7
Sharpe ratio of doublers
8
Informationless investing
9
Apologia of Nick Leeson
I felt no elation at this success. I was
determined to win back the losses. And as the
spring wore on, I traded harder and harder,
risking more and more. I was well down, but
increasingly sure that my doubling up and
doubling up would pay off ... I redoubled my
exposure. The risk was that the market could
crumble down, but on this occasion it carried on
upwards ... As the market soared in July 1993
my position translated from a 6 million loss
back into glorious profit. I was so happy that
night I didnt think Id ever go through that
kind of tension again. Id pulled back a large
position simply by holding my nerve ... but first
thing on Monday morning I found that I had to use
the 88888 account again ... it became an
addiction Nick Leeson Rogue Trader pp.63-64
10
Infinitely many ways to lose money!

• Manager trades SP contracts
• µ 12.5, s 20, r 5 per annum
• Fired on a string of 12 losses (a drawdown of
  13.5 times initial capital)
• Probability of 12 losses .024
• Trading 8 times a day for a year
• Only 70 probability of surviving year!

11
Infinitely many ways to lose money!
12
Informationless investing

• Zero net investment overlay strategy (Weisman
  2002)
• Uses only public information
• Designed to yield Sharpe ratio greater than
  benchmark

13
Informationless investing

• Zero net investment overlay strategy (Weisman
  2002)
• Uses only public information
• Designed to yield Sharpe ratio greater than
  benchmark
• Why should we care?
• Sharpe ratio obviously inappropriate here

14
Informationless investing

• Zero net investment overlay strategy (Weisman
  2002)
• Uses only public information
• Designed to yield Sharpe ratio greater than
  benchmark
• Why should we care?
• Sharpe ratio obviously inappropriate here
• But is metric of choice of hedge funds and
  derivatives traders

15
We should care!

• Behavioral issues
• Prospect theory lock in gains, gamble on loss
• Are there incentives to control this behavior?
• Delegated fund management
• Fund flow, compensation based on historical
  performance
• Limited incentive to monitor high Sharpe ratios

16
Examples of Informationless investing

• Doubling
• a.k.a. Convergence trading
• Covered call writing
• Unhedged short volatility
• Writing out of the money calls and puts

17
Forensic Finance

• Implications of Informationless investing
• Patterns of returns
• Patterns of security holdings
• Patterns of trading

18
Sharpe Ratio of Benchmark
Sharpe ratio .631
19
Maximum Sharpe Ratio
Sharpe ratio .748
20
Concave trading strategies
21
Hedge funds follow concave strategies
R-rf a ß (RSP- rf) ? (RSP- rf)2
22
Hedge funds follow concave strategies
R-rf a ß (RSP- rf) ? (RSP- rf)2
Concave strategies tß gt 1.96 t? lt -1.96
23
Hedge funds follow concave strategies
R-rf a ß (RSP- rf) ? (RSP- rf)2
Concave Neutral Convex N
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 0.00 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 Total 11.54 86.53 1.93 3318
Source TASS/Tremont
24
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

25
Some successful Australian funds
Fund Sharpe Ratio Alpha FF Alpha Beta Skewness Kurtosis Annual turnover
1 0.1017 0.08 0.10 0.90 -0.5209 4.6878 20.69
(2.21) (2.58)
2 0.1500 0.16 0.17 1.11 0.0834 4.2777 0.79
(6.44) (5.88)
3 0.1559 0.19 0.20 1.08 0.7382 7.6540 1.18
(4.09) (4.36)
15 0.1079 0.09 0.09 0.96 -0.2558 4.1749 0.34
(2.66) (2.61)
26 0.0977 0.12 0.11 1.03 -0.2667 3.4316 1.27
(2.42) (2.25)
35 0.1814 0.29 0.31 0.90 -0.6248 5.1278 0.62
(3.02) (3.06)
26
Style and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
GARP 0.9608 -0.0111 (-2.25) -0.0895 (-2.47) 2372
Growth 1.0367 -0.0071 (-1.53) -0.0376 (-1.15) 1899
Neutral 1.0284 -0.0011 (-0.29) -0.0210 (-0.72) 1313
Other 1.0067 -0.0020 (-0.53) 0.0068 (0.21) 640
Value 0.7690 -0.0126 (-2.01) -0.1082 (-2.36) 2250
Passive/ Enhanced 1.0146 0.0069 (1.50) 0.0457 (1.46) 859
27
Size and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
Largest 10 Institutional Manager No 0.9644 -0.0058 (-2.12) -0.04580 (-2.25) 6467
Largest 10 Institutional Manager Yes 0.9059 -0.0100 (-2.25) -0.0779 (-2.56) 2866
Boutique firm No 0.9430 -0.0082 (-2.78) -0.0613 (-2.91) 6567
Boutique firm Yes 0.9543 -0.0045 (-1.23) -0.0428 (-1.53) 2766
28
Patterns of derivative holdings
Fund Investment Style Calls Calls Puts Puts Month end option positions Month end option positions Month end option positions
Fund Investment Style Fund Number Strike Number Strike Concavity decreasing Concavity increasing Total
GARP 1 2 3 4 5 6 11 13 0.726 -0.061 0.099 0.041 -0.650 0.222 0.811 0.054 1.017 1.050 1.017 1.023 1.062 1.076 0.002 1.076 0.395 -0.122 0.021 0.008 -1.346 0.950 - 0.957 0.904 0.952 0.944 0.985 0.674 - 100 29 59 77 100 100 100 71 41 23 100 80 246 79 898 18 11 8 11
Growth 15 16 17 18 -0.033 -0.039 -0.367 -0.059 1.056 1.060 1.067 1.023 - - 0.107 0.108 - - 0.951 0.913 27 35 13 73 100 65 87 11 8 83 344
Neutral 21 22 24 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - - 0.947 - - 10 100 100 90 208 10 1
Other 25 0.079 1.147 0.147 0.965 94 6 35
Value 33 0.050 0.914 57 43 23
Passive/ Enhanced 38 39 -0.013 -0.026 0.948 1.036 -0.017 -0.041 0.955 0.959 9 10 91 90 340 613
Total 38 62 3027
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Patterns of derivative holdings
Fund Investment Style Calls Calls Puts Puts Month end option positions Month end option positions Month end option positions
Fund Investment Style Fund Number Strike Number Strike Concavity decreasing Concavity increasing Total
GARP 1 2 3 4 5 6 11 13 0.726 -0.061 0.099 0.041 -0.650 0.222 0.811 0.054 1.017 1.050 1.017 1.023 1.062 1.076 0.002 1.076 0.395 -0.122 0.021 0.008 -1.346 0.950 - 0.957 0.904 0.952 0.944 0.985 0.674 - 100 29 59 77 100 100 100 71 41 23 100 80 246 79 898 18 11 8 11
Growth 15 16 17 18 -0.033 -0.039 -0.367 -0.059 1.056 1.060 1.067 1.023 - - 0.107 0.108 - - 0.951 0.913 27 35 13 73 100 65 87 11 8 83 344
Neutral 21 22 24 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - - 0.947 - - 10 100 100 90 208 10 1
Other 25 0.079 1.147 0.147 0.965 94 6 35
Value 33 0.050 0.914 57 43 23
Passive/ Enhanced 38 39 -0.013 -0.026 0.948 1.036 -0.017 -0.041 0.955 0.959 9 10 91 90 340 613
Total 38 62 3027
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Patterns of derivative holdings
Fund Investment Style Calls Calls Puts Puts Month end option positions Month end option positions Month end option positions
Fund Investment Style Fund Number Strike Number Strike Concavity decreasing Concavity increasing Total
GARP 1 2 3 4 5 6 11 13 0.726 -0.061 0.099 0.041 -0.650 0.222 0.811 0.054 1.017 1.050 1.017 1.023 1.062 1.076 0.002 1.076 0.395 -0.122 0.021 0.008 -1.346 0.950 - 0.957 0.904 0.952 0.944 0.985 0.674 - 100 29 59 77 100 100 100 71 41 23 100 80 246 79 898 18 11 8 11
Growth 15 16 17 18 -0.033 -0.039 -0.367 -0.059 1.056 1.060 1.067 1.023 - - 0.107 0.108 - - 0.951 0.913 27 35 13 73 100 65 87 11 8 83 344
Neutral 21 22 24 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - - 0.947 - - 10 100 100 90 208 10 1
Other 25 0.079 1.147 0.147 0.965 94 6 35
Value 33 0.050 0.914 57 43 23
Passive/ Enhanced 38 39 -0.013 -0.026 0.948 1.036 -0.017 -0.041 0.955 0.959 9 10 91 90 340 613
Total 38 62 3027
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Doubling trades
h0 S0 C0
h0 Initial highwater mark
S0 Initial stock position
C0 Cost basis of initial position
32
Doubling trades
h0 S0 C0
Bad news!
S1 d S0
C1 (1rf ) C0
33
Doubling trades
h0 S0 C0
Increase the equity position to cover the loss!
S1 d S0 ?1
C1 (1rf ) C0 ?1
34
Doubling trades
h0 S0 C0
h1 u S1 (1rf) C1
Good news!
S1 d S0 ?1
C1 (1rf ) C0 ?1
?1 is set to make up for past losses and
re-establish security position
35
Doubling trades
h0 S0 C0
h1 u S1 (1rf) C1
Good news!
S1 d S0 ?1
C1 (1rf ) C0 ?1
?1 is set to make up for past losses and
re-establish security position
h0 - u d S0 (1rf)2 C0
?1 S0
u (1rf)
36
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1
C2 (1rf ) C1
37
Doubling trades
h0 S0 C0
h2 u S2 (1rf) C2
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
Good news finally!
38
Doubling trades
h0 S0 C0
h2 u S2 (1rf) C2
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
?2 is set to make up for past losses and
re-establish security position
Good news finally!
h1 - u d S1 (1rf)2 C1
?2 S0
u (1rf)
39
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
40
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
41
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
42
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
43
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
44
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
45
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
46
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 ?1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
S3 d S2
C3 (1rf ) C2
47
Doubling trades
h0 S0 C0
Bad news again!
S1 d S0 1
C1 (1rf ) C0 ?1
S2 d S1 ?2
C2 (1rf ) C1 ?2
48
Observable implication of doubling
On a loss, trader will increase position size by
hi-1 - u d Si-1 (1rf)2 Ci-1
?i S0
u (1rf)
otherwise, position is liquidated on a gain,
?i a b1 (1 - di) hi-1 b2 Vi b3 Bi b4
di b5 Gi
for all trades
49
Observable implication of doubling
On a loss, trader will increase position size by
hi-1 - u d Si-1 (1rf)2 Ci-1
?i S0
u (1rf)
otherwise, position is liquidated on a gain,
?i a b1 (1 - di) hi-1 b2 Vi b3 Bi b4
di b5 Gi
lt 0
lt 0
gt 0
gt 0
gt 0
?
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Some successful Australian funds
Fund Sharpe Ratio Alpha FF Alpha Beta Skewness Kurtosis Annual turnover
1 0.1017 0.08 0.10 0.90 -0.5209 4.6878 20.69
(2.21) (2.58)
2 0.1500 0.16 0.17 1.11 0.0834 4.2777 0.79
(6.44) (5.88)
3 0.1559 0.19 0.20 1.08 0.7382 7.6540 1.18
(4.09) (4.36)
15 0.1079 0.09 0.09 0.96 -0.2558 4.1749 0.34
(2.66) (2.61)
26 0.0977 0.12 0.11 1.03 -0.2667 3.4316 1.27
(2.42) (2.25)
35 0.1814 0.29 0.31 0.90 -0.6248 5.1278 0.62
(3.02) (3.06)
51
Some successful Australian funds
Fund Highwater mark on a loss Value of holdings on a loss Cost basis on a loss Value above highwater mark Rsq Gain from long buy short sell (one month)
1 0.0004 -0.0373 0.056 -0.018 0.067 -0.58
(0.24) (-2.82) (3.74) (-1.04)
2 0.0167 -0.1673 0.014 -0.881 0.421 0.50
(1.56) (-7.69) (1.19) (-11.55)
3 -0.0023 -0.1704 -0.005 -0.982 0.642 -0.27
(-0.19) (-8.22) (-0.39) (-39.16)
15 1.1659 -0.9163 0.080 -0.170 0.185 -1.30
(1.17) (-2.16) (0.57) (-0.22)
26 -0.3633 -0.1626 -0.253 -1.133 0.448 4.49
(-3.57) (-1.83) (-3.79) (-2.00)
35 -0.0184 -0.1297 -0.081 -1.010 0.420 2.63
(-0.45) (-3.30) (-1.80) (-2.48)
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Sharpe ratio and doubling
53
Sector Patterns
High Water Mark on a loss Mining and minerals Mining and minerals Industrial Industrial Services Services Health and Biotechnology Health and Biotechnology Gain above high water mark
High Water Mark on a loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Gain above high water mark
GARP 0.010 -0.029 0.009 -0.044 0.003 -0.021 -0.004 -0.064 0.031 -0.791
(2.97) (-2.56) (1.71) (-3.62) (0.55) (-1.88) (-0.41) (-4.50) (2.22) (-5.14)
Largest 0.012 -0.027 0.013 -0.039 0.006 -0.015 -0.004 -0.065 0.039 -0.764
(3.20) (-3.07) (2.19) (-4.48) (1.14) (-2.19) (-0.62) (-5.66) (3.37) (-4.76)
Domestic 0.022 -0.044 0.022 -0.056 0.016 -0.027 0.000 -0.078 0.047 -0.898
(3.18) (-4.23) (2.58) (-5.45) (2.07) (-3.18) (0.00) (-6.40) (3.74) (-11.99)
54
Seasonal patterns
High Water Mark on a loss February - April February - April May - July May - July August October August October November January November January Gain above high water mark
High Water Mark on a loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Value of Holdings on Loss Cost Basis on Loss Gain above high water mark
GARP 0.009 -0.021 0.008 -0.040 0.010 -0.018 -0.003 -0.025 0.005 -0.791
(2.77) (-1.34) (0.57) (-3.53) (1.19) (-1.64) (-0.51) (-2.43) (1.04) (-5.14)
Largest 0.012 -0.023 0.002 -0.030 0.014 -0.018 0.000 -0.012 0.001 -0.764
(2.98) (-2.38) (0.24) (-3.68) (1.65) (-2.63) (0.07) (-1.43) (0.21) (-4.76)
Domestic 0.021 -0.037 0.008 -0.044 0.022 -0.031 0.007 -0.026 0.009 -0.897
(3.05) (-3.39) (0.74) (-4.22) (2.01) (-3.62) (0.96) (-2.46) (1.05) (-11.94)
55
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
Passive/ Enhanced Passive (-2.40) (-3.07)
56
Return to long buy/short sell (monthly)
Category Raw return Market Adjusted
Largest 10 Institutional Manager No 0.86 0.65
Largest 10 Institutional Manager (2.49) (1.99)
Largest 10 Institutional Manager Yes 0.11 0.40
Largest 10 Institutional Manager (0.33) (1.41)
Boutique firm No 0.42 0.40
Boutique firm (1.27) (1.35)
Boutique firm Yes 1.07 0.88
Boutique firm (2.24) (1.95)
57
National Australia Bank
58
A clear and present danger?

• No evidence of informationless investing at fund
  level
• Behavioral theories
• Prospect theory
• Lock in gains, gambling on losses
• Narrow Framing
• Consider only one gamble at a time
• Window dressing
• Doubling at end of fiscal year

59
Conclusion

• Behavioral patterns of trading are common
• Concave trading patterns create adverse
  incentives
• Narrow framing limits negative consequences