Double or nothing: Patterns of equity fund holdings and transactions Stephen J. Brown NYU Stern School of Business David R. Gallagher University of NSW.

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

Performance measurement Leeson Investment Managemen t Market (S&P 500) Benchmark Short-term Government Benchmark Average Return.0065.0050.0036 Std. Deviation.0106.0359.0015 Beta.06401.0.0 Alpha.0025 (1.92).0 Sharpe Ratio.2484.0318.0 Style: Index Arbitrage, 100% in cash at close of trading

Frequency distribution of monthly returns

Percentage in cash (monthly)

Examples of riskless index arbitrage …

Percentage in cash (daily)

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 didn’t think I’d ever go through that kind of tension again. I’d 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

Sharpe ratio of doublers

Informationless investing

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

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

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

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

Examples of Informationless investing  Doubling  a.k.a. “Convergence trading”  Covered call writing  Unhedged short volatility  Writing out of the money calls and puts

Forensic Finance  Implications of Informationless investing  Patterns of returns  Patterns of security holdings  Patterns of trading

Sharpe Ratio of Benchmark Sharpe ratio =.631

Maximum Sharpe Ratio Sharpe ratio =.748

Short Volatility Strategy Sharpe ratio =.743

Doubling Sharpe ratio =.046

Doubling (no embezzlement) Sharpe ratio = 1.962

Concave trading strategies

Hedge funds follow concave strategies R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2

Hedge funds follow concave strategies R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2 Concave strategies: t β > 1.96 & t γ < - 1.96

Hedge funds follow concave strategies ConcaveNeutralConvexN 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% 0.86% 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 Total11.54%86.53%1.93%3318 R-r f = α + β (R S&P - r f ) + γ (R S&P - r f ) 2 Source: TASS/Tremont

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

Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBeta Skewnes s Kurtosi s Annual turnover 10.10170.08%0.10%0.90-0.52094.687820.69 (2.21)(2.58) 20.15000.16%0.17%1.110.08344.27770.79 (6.44)(5.88) 30.15590.19%0.20%1.080.73827.65401.18 (4.09)(4.36) 160.10790.09% 0.96-0.25584.17490.34 (2.66)(2.61) 270.09770.12%0.11%1.03-0.26673.43161.27 (2.42)(2.25) 360.18140.29%0.31%0.90-0.62485.12780.62 (3.02)(3.06)

Style and return patterns CategoryBeta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations GARP 0.96347 -0.01105 (-2.30) -0.08989 (-2.52) 2395 Growth 1.03670 -0.00708 (-1.53) -0.03762 (-1.15) 1899 Neutral 1.02830 -0.00110 (-0.29) -0.02092 (-0.71) 1313 Other 1.00670 -0.00196 (-0.53) 0.00676 (0.21) 640 Value 0.76691 -0.01215 (-1.93) -0.10350 (-2.24) 2250 Passive/ Enhanced 1.01440 0.00692 (1.51) 0.04593 (1.47) 859

Size and return patterns CategoryBeta 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 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 Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788

Incentives and return patterns CategoryBeta Treynor Mazuy measure Modified Henriksson Merton measure Number of observation s Annual Bonus No 0.9819 0.00013 (0.03) 0.01233 (0.35) 308 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 Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788

Patterns of derivative holdings Fund Investmen t Style CallsPutsMonth end option positions FundNumberStrikeNumberStrike Concavity decreasing Concavity increasingTotal 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% 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% 90% 208 10 1 Other250.0791.1470.1470.96594%6%35 Value330.0500.91457%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 Total38%62%3027

Doubling trades h 0 = S 0 – C 0 h 0 : Initial highwater mark S 0 : Initial stock position C 0 : Cost basis of initial position

Doubling trades h 0 = S 0 – C 0 S 1 = d S 0 C 1 = (1+r f ) C 0 Bad news!

Doubling trades h 0 = S 0 – C 0 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 Increase the equity position to cover the loss!

Doubling trades h 0 = S 0 – C 0 h 1 = u S 1 – (1+r f ) C 1 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 Good news!  1 is set to make up for past losses and re-establish security position

Doubling trades h 0 = S 0 – C 0 h 1 = u S 1 – (1+r f ) C 1 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 Good news!  1 is set to make up for past losses and re-establish security position  1 = + S 0 h 0 - u d S 0 + (1+r f ) 2 C 0 u – (1+r f )

Doubling trades h 0 = S 0 – C 0 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 S 2 = d S 1 C 2 = (1+r f ) C 1 Bad news again!

Doubling trades h 0 = S 0 – C 0 h 2 = u S 2 – (1+r f ) C 2 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 S 2 = d S 1 +  2 C 2 = (1+r f ) C 1 +  2 Good news finally!

Doubling trades h 0 = S 0 – C 0 h 2 = u S 2 – (1+r f ) C 2 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 S 2 = d S 1 +  2 C 2 = (1+r f ) C 1 +  2 Good news finally!  2 is set to make up for past losses and re-establish security position  2 = + S 0 h 1 - u d S 1 + (1+r f ) 2 C 1 u – (1+r f )

Doubling trades h 0 = S 0 – C 0 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 S 2 = d S 1 +  2 C 2 = (1+r f ) C 1 +  2 S 3 = d S 2 C 3 = (1+r f ) C 2 Bad news again!

Doubling trades h 0 = S 0 – C 0 S 1 = d S 0 +  1 C 1 = (1+r f ) C 0 +  1 S 2 = d S 1 +  2 C 2 = (1+r f ) C 1 +  2 Bad news again!

Observable implication of doubling  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i On a loss, trader will increase position size by otherwise, position is liquidated on a gain, for all trades  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i > 0 On a loss, trader will increase position size by otherwise, position is liquidated on a gain,

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i  i = 1 if highwatermark has been met otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i > 0 otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i V i = (1 -  i ) d S i-1, the value of security on a loss otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i < 0 otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i B i = (1 -  i ) (1 + r f ) C i-1, the cost basis of the security otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i > 0 otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i G i =  I (S i – C i – h i ), the measure of gain once highwatermark is reached otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i < 0 otherwise, position is liquidated on a gain, On a loss, trader will increase position size by

Observable implication of doubling  i = + S 0 h i-1 - u d S i-1 + (1+r f ) 2 C i-1 u – (1+r f )  i = a + b 1 (1 -  i ) h i-1 + b 2 V i + b 3 B i + b 4  i + b 5 G i < 0 > 0 ? On a loss, trader will increase position size by otherwise, position is liquidated on a gain,

Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBeta Skewnes s Kurtosi s Annual turnover 10.10170.08%0.10%0.90-0.52094.687820.69 (2.21)(2.58) 20.15000.16%0.17%1.110.08344.27770.79 (6.44)(5.88) 30.15590.19%0.20%1.080.73827.65401.18 (4.09)(4.36) 160.10790.09% 0.96-0.25584.17490.34 (2.66)(2.61) 270.09770.12%0.11%1.03-0.26673.43161.27 (2.42)(2.25) 360.18140.29%0.31%0.90-0.62485.12780.62 (3.02)(3.06)

Some successful Australian funds Fund Highwater mark on a loss Value of holdings on a loss Cost basis on a loss Value above highwater markRsq 10.0004-0.02660.0327-0.01190.0442 (0.21)(-2.39)(2.19)(-0.86) 20.0346-0.13010.0300-0.86140.3924 (2.97)(-6.45)(2.29)(-9.52) 30.0366-0.11250.0216-0.97710.6098 (2.58)(-6.02)(1.57)(-33.69) 160.6981-0.91350.0167-0.61330.1406 (0.69)(-2.06)(0.13)(-0.91) 27-0.0712-0.3305-0.1205-1.32770.3930 (-0.71)(-4.18)(-2.02)(-2.32) 36-0.0226-0.0973-0.0935-1.01660.3947 (-0.55)(-2.38)(-2.08)(-2.52)

Sharpe ratio and doubling

Do managers lack an equity stake?

Is fund owned by a bank or life insurance company?

Is fund one of 10 largest in Australia?

Is fund large (not a boutique manager)?

Style and return patterns CategoryBeta Treynor Mazuy measure Modified Henriksson Merton measure Number of observations GARP 0.96347 -0.01105 (-2.30) -0.08989 (-2.52) 2395 Growth 1.03670 -0.00708 (-1.53) -0.03762 (-1.15) 1899 Neutral 1.02830 -0.00110 (-0.29) -0.02092 (-0.71) 1313 Other 1.00670 -0.00196 (-0.53) 0.00676 (0.21) 640 Value 0.76691 -0.01215 (-1.93) -0.10350 (-2.24) 2250 Passive/ Enhanced 1.01440 0.00692 (1.51) 0.04593 (1.47) 859

Style and trading patterns Category Highwater mark on a loss Value of holdings on a loss Cost basis on a loss Value above highwater markRsq GARP0.0086-0.05840.0028-0.79570.4281 (2.45)(-7.93)(0.58)(-5.30) Growth0.03520.0291-0.0498-0.34290.1339 (1.04)(0.99)(-1.66)(-0.92) Neutral0.0005-0.02080.0035-0.21610.0341 (0.07)(-1.89)(0.35)(-3.69) Other0.0277-0.0242-0.0074-0.07120.0586 (1.84)(-1.75)(-0.60) Value-0.00060.0081-0.0104-0.11720.0113 (-0.07)(0.88)(-1.28)(-1.85) Passive/ Enhanced 0.0901-0.07690.0535-0.23070.0089 (2.06)(-1.54)(1.61)(-0.98)

Size and return patterns CategoryBeta 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 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 Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788

Size and trading patterns Category Highwater mark on a loss Value of holdings on a loss Cost Basis Value above highwater markRsq Largest 10 Institutional Manager No0.03840.0250-0.0443-0.43930.0630 (1.36)(0.92)(-1.62)(-1.26) Yes0.0077-0.01590.0011-0.76270.3017 (2.05)(-3.01)(0.24)(-4.82) Boutique firm No0.0015-0.0040-0.0093-0.75020.1607 (0.24)(-0.44)(-1.03)(-4.75) Yes0.0097-0.0270-0.0184-0.28470.0751 (0.66)(-1.42)(-1.07)(-4.23)

Incentives and return patterns CategoryBeta Treynor Mazuy measure Modified Henriksson Merton measure Number of observation s Annual Bonus No 0.9819 0.00013 (0.03) 0.01233 (0.35) 308 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 Yes 0.9556 -0.00452 (-1.25) -0.04184 (-1.49) 2788

Incentives and return patterns Categor y Highwate r mark on a loss Value of holdings on a loss Cost Basis Value above highwate rRsq Annual Bonus No0.0259-0.0233-0.00260.03880.0420 (1.52)(-1.55)(-0.20)(0.25) Yes0.0016-0.0040-0.0093-0.74930.1601 (0.25)(-0.45)(-1.04)(-4.74) Domestic owned No0.00250.0265-0.0395-0.07560.1229 (0.48)(1.24)(-1.57)(-0.95) Yes0.0148-0.02280.0069-0.90230.2063 (2.21)(-2.79)(0.99)(-12.68) Equity Ownership by senior staff No0.0015-0.0040-0.0093-0.75020.1607 (0.24)(-0.44)(-1.03)(-4.75) Yes0.0097-0.0270-0.0184-0.28470.0751 (0.66)(-1.42)(-1.07)(-4.23)

Mining and mineralsIndustrial Consumer & servicesBiotechnology Fund Value of Holdi ngs on a loss Cost Basis on a loss Value of Holdi ngs on a loss Cost Basis on a loss Value of Hold ings on a loss Cost Basis on a loss Value of Holdi ngs on a loss Cost Basis on a loss 1 0.0258 (0.13) -0.0224 (-0.16) 0.0610 (2.53) -0.0351 (-1.90) -0.0423 (-3.31) 0.0610 (3.46) -0.1002 (-1.14) 0.0447 (0.69) 2-0.0369 (-2.22) 0.0276 (2.00) -0.0524 (-2.76) 0.0175 (1.22) -0.0308 (-1.96) 0.0195 (1.48) -0.0786 (-4.65) 0.0300 (1.50) 3 -0.0400 (-2.16) 0.0222 (1.52) -0.0562 (-3.27) 0.0265 (1.95) -0.0292 (-1.59) -0.0078 (-0.34) -0.0611 (-2.32) 0.0741 (2.59) 16 -3.6349 (-3.42) 1.9348 (2.47) -1.2431 (-4.43) 0.2279 (3.84) -0.7807 (-2.87) 0.3892 (1.17) 27 0.2096 (1.51) -0.2619 (-2.48) -0.4150 (-1.85) 0.0802 (0.36) -0.3176 (-2.82) 0.1573 (1.65) 0.0127 (0.05) -0.8319 (-2.42) 36 -0.2141 (-2.42) 0.1423 (2.31) -0.1628 (-2.27) 0.1369 (2.03) -0.2033 (-3.13) 0.1777 (3.19) 0.4762 (0.51) -0.5258 (-0.54) Some successful Australian funds

National Australia Bank

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

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

Double or nothing: Patterns of equity fund holdings and transactions Stephen J. Brown NYU Stern School of Business David R. Gallagher University of NSW.

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Double or nothing: Patterns of equity fund holdings and transactions Stephen J. Brown NYU Stern School of Business David R. Gallagher University of NSW.

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