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
• www.stern.nyu.edu/sbrown

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
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
8
Sharpe ratio of doublers
9
Informationless investing
10
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

11
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

12
We should care!

• Agency issues
• Fund flow, compensation based on historical
  performance
• Gruber (1996), Sirri and Tufano (1998), Del
  Guercio and Tkac (2002)
• Behavioral issues
• Strategy leads to certain ruin in the long term

13
Examples of Informationless investing

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

14
Forensic Finance

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

15
Sharpe Ratio of Benchmark
Sharpe ratio .631
16
Maximum Sharpe Ratio
Sharpe ratio .748
17
Short Volatility Strategy
Sharpe ratio .743
18
Doubling
Sharpe ratio .046
19
Doubling (no embezzlement)
Sharpe ratio 1.962
20
Concave trading strategies
21
Hedge funds follow concave strategies
R-rf a ß (RSP- rf) ? (RSP- rf)2
Concave strategies tß gt 1.96 t? lt -1.96
22
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
23
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

24
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)
16 0.1079 0.09 0.09 0.96 -0.2558 4.1749 0.34
(2.66) (2.61)
27 0.0977 0.12 0.11 1.03 -0.2667 3.4316 1.27
(2.42) (2.25)
36 0.1814 0.29 0.31 0.90 -0.6248 5.1278 0.62
(3.02) (3.06)
25
Style and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Modified Henriksson Merton measure Number of observations
GARP 0.96347 -0.01105 (-2.30) -0.08989 (-2.52) 2395 2395
Growth 1.03670 -0.00708 (-1.53) -0.03762 (-1.15) 1899 1899
Neutral 1.02830 -0.00110 (-0.29) -0.02092 (-0.71) 1313 1313
Other 1.00670 -0.00196 (-0.53) 0.00676 (0.21) 640 640
Value 0.76691 -0.01215 (-1.93) -0.10350 (-2.24) 2250 2250
Passive/ Enhanced 1.01440 0.00692 (1.51) 0.04593 (1.47) 859 859
26
Size and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
Largest 10 Institutional Manager No 0.9627 -0.00645 (-2.25) -0.05037 (-2.34) 6100
Largest 10 Institutional Manager Yes 0.8819 -0.01306 (-2.60) -0.10095 (-2.92) 2397
Boutique firm No 0.9322 -0.01029 (-3.12) -0.07616 (-3.23) 5709
Boutique firm Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788
27
Incentives and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
Annual Bonus No 0.9819 0.00013 (0.03) 0.01233 (0.35) 308
Annual Bonus Yes 0.9386 -0.00857 (-3.32) -0.06720 (-3.56) 8189
Domestic owned No 0.9739 -0.00990 (-2.80) -0.07282 (-2.79) 4262
Yes 0.9053 -0.00652 (-1.86) -0.05557 (-2.18) 4235
Equity Ownership by senior staff No 0.9322 -0.01029 (-3.12) -0.07616 (-3.23) 5709
Equity Ownership by senior staff Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788
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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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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 - ?i) hi-1 b2 Vi b3 Bi b4
?i 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 - ?i) hi-1 b2 Vi b3 Bi b4
?i b5 Gi
Vi (1 - ?i) d Si-1 , the value of security on a
loss
50
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 - ?i) hi-1 b2 Vi b3 Bi b4
?i b5 Gi
Bi (1 - ?i) (1 rf ) Ci-1 , the cost basis of
the security
51
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 - ?i) hi-1 b2 Vi b3 Bi b4
?i b5 Gi
Gi ?I (Si Ci hi) , the measure of gain once
highwatermark is reached
52
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 - ?i) hi-1 b2 Vi b3 Bi b4
?i b5 Gi
lt 0
lt 0
gt 0
gt 0
gt 0
?
53
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)
16 0.1079 0.09 0.09 0.96 -0.2558 4.1749 0.34
(2.66) (2.61)
27 0.0977 0.12 0.11 1.03 -0.2667 3.4316 1.27
(2.42) (2.25)
36 0.1814 0.29 0.31 0.90 -0.6248 5.1278 0.62
(3.02) (3.06)
54
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
1 0.0004 -0.0266 0.0327 -0.0119 0.0442
(0.21) (-2.39) (2.19) (-0.86)
2 0.0346 -0.1301 0.0300 -0.8614 0.3924
(2.97) (-6.45) (2.29) (-9.52)
3 0.0366 -0.1125 0.0216 -0.9771 0.6098
(2.58) (-6.02) (1.57) (-33.69)
16 0.6981 -0.9135 0.0167 -0.6133 0.1406
(0.69) (-2.06) (0.13) (-0.91)
27 -0.0712 -0.3305 -0.1205 -1.3277 0.3930
(-0.71) (-4.18) (-2.02) (-2.32)
36 -0.0226 -0.0973 -0.0935 -1.0166 0.3947
(-0.55) (-2.38) (-2.08) (-2.52)
55
Sharpe ratio and doubling
56
Do managers lack an equity stake?
57
Is fund owned by a bank or life insurance company?
58
Is fund one of 10 largest in Australia?
59
Is fund large (not a boutique manager)?
60
Style and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Modified Henriksson Merton measure Number of observations
GARP 0.96347 -0.01105 (-2.30) -0.08989 (-2.52) 2395 2395
Growth 1.03670 -0.00708 (-1.53) -0.03762 (-1.15) 1899 1899
Neutral 1.02830 -0.00110 (-0.29) -0.02092 (-0.71) 1313 1313
Other 1.00670 -0.00196 (-0.53) 0.00676 (0.21) 640 640
Value 0.76691 -0.01215 (-1.93) -0.10350 (-2.24) 2250 2250
Passive/ Enhanced 1.01440 0.00692 (1.51) 0.04593 (1.47) 859 859
61
Style and trading patterns
Category Highwater mark on a loss Value of holdings on a loss Cost basis on a loss Value above highwater mark Rsq
GARP 0.0086 -0.0584 0.0028 -0.7957 0.4281
(2.45) (-7.93) (0.58) (-5.30)
Growth 0.0352 0.0291 -0.0498 -0.3429 0.1339
(1.04) (0.99) (-1.66) (-0.92)
Neutral 0.0005 -0.0208 0.0035 -0.2161 0.0341
(0.07) (-1.89) (0.35) (-3.69)
Other 0.0277 -0.0242 -0.0074 -0.0712 0.0586
(1.84) (-1.75) (-0.60) (-0.60)
Value -0.0006 0.0081 -0.0104 -0.1172 0.0113
(-0.07) (0.88) (-1.28) (-1.85)
Passive/ Enhanced 0.0901 -0.0769 0.0535 -0.2307 0.0089
Passive/ Enhanced (2.06) (-1.54) (1.61) (-0.98)
62
Size and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
Largest 10 Institutional Manager No 0.9627 -0.00645 (-2.25) -0.05037 (-2.34) 6100
Largest 10 Institutional Manager Yes 0.8819 -0.01306 (-2.60) -0.10095 (-2.92) 2397
Boutique firm No 0.9322 -0.01029 (-3.12) -0.07616 (-3.23) 5709
Boutique firm Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788
63
Size and trading patterns
Category Highwater mark on a loss Value of holdings on a loss Cost Basis Value above highwatermark Rsq
Largest 10 Institutional Manager No 0.0384 0.0250 -0.0443 -0.4393 0.0630
Largest 10 Institutional Manager (1.36) (0.92) (-1.62) (-1.26)
Largest 10 Institutional Manager Yes 0.0077 -0.0159 0.0011 -0.7627 0.3017
Largest 10 Institutional Manager (2.05) (-3.01) (0.24) (-4.82)
Boutique firm No 0.0015 -0.0040 -0.0093 -0.7502 0.1607
Boutique firm (0.24) (-0.44) (-1.03) (-4.75)
Boutique firm Yes 0.0097 -0.0270 -0.0184 -0.2847 0.0751
Boutique firm (0.66) (-1.42) (-1.07) (-4.23)
64
Incentives and return patterns
Category Beta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations
Annual Bonus No 0.9819 0.00013 (0.03) 0.01233 (0.35) 308
Annual Bonus Yes 0.9386 -0.00857 (-3.32) -0.06720 (-3.56) 8189
Domestic owned No 0.9739 -0.00990 (-2.80) -0.07282 (-2.79) 4262
Yes 0.9053 -0.00652 (-1.86) -0.05557 (-2.18) 4235
Equity Ownership by senior staff No 0.9322 -0.01029 (-3.12) -0.07616 (-3.23) 5709
Equity Ownership by senior staff Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788
65
Incentives and return patterns
Category Highwater mark on a loss Value of holdings on a loss Cost Basis Value above highwater Rsq
Annual Bonus No 0.0259 -0.0233 -0.0026 0.0388 0.0420
Annual Bonus (1.52) (-1.55) (-0.20) (0.25)
Annual Bonus Yes 0.0016 -0.0040 -0.0093 -0.7493 0.1601
Annual Bonus (0.25) (-0.45) (-1.04) (-4.74)
Domestic owned No 0.0025 0.0265 -0.0395 -0.0756 0.1229
Domestic owned (0.48) (1.24) (-1.57) (-0.95)
Domestic owned Yes 0.0148 -0.0228 0.0069 -0.9023 0.2063
Domestic owned (2.21) (-2.79) (0.99) (-12.68)
Equity Ownership by senior staff No 0.0015 -0.0040 -0.0093 -0.7502 0.1607
Equity Ownership by senior staff (0.24) (-0.44) (-1.03) (-4.75)
Equity Ownership by senior staff Yes 0.0097 -0.0270 -0.0184 -0.2847 0.0751
Equity Ownership by senior staff (0.66) (-1.42) (-1.07) (-4.23)
66
National Australia Bank
67
Incentives are not everything!

• No evidence of doubling in asset allocation
• Large institutional funds are organized and
  compensated on a specialist team basis
• Behavioral explanations
• Prospect theory
• Narrow framing

68
Conclusion

• Informationless investing can be dangerous to
  your financial health
• Funds as a whole do not seem to use these
  techniques
• However, some of most successful funds have
  interesting trading patterns associated with
• Large, decentralized control
• Short term incentive compensation