double or nothing: patterns of equity fund holdings and transactions

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 Investmen

tManagem

Market (S&P 500)

Benchmar

Short-term

Government

Benchmark

Average Return

.0065 .0050 .0036

Std. Deviation

.0106 .0359 .0015

Beta .0640 1.0 .0

Alpha .0025(1.92)

Sharpe Ratio

.2484 .0318 .0

Style: Index Arbitrage, 100% in cash at close of trading

Frequency distribution of monthly returns

Percentage in cash (monthly)

31-Dec-1989 15-May-1991 26-Sep-1992 8-Feb-1994

Examples of riskless index arbitrage …

Percentage in cash (daily)

31-Dec-1989 15-May-1991 26-Sep-1992 8-Feb-1994

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

All Doublers

Doublers who have notyet embezzled

Sharpe Ratio ofMarket

Informationless investing

Zero net investment overlay strategy (Weisman 2002)

Uses only public informationDesigned 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 informationDesigned to yield Sharpe ratio greater than benchmark

Why should we care?

Sharpe ratio obviously inappropriate hereBut is metric of choice of hedge funds and derivatives

traders

We should care!

Agency issuesFund flow, compensation based on

historical performanceGruber (1996), Sirri and Tufano

(1998), Del Guercio and Tkac (2002)

Behavioral issuesStrategy leads to certain ruin in the

long term

Examples of Informationless investing

Doubling a.k.a. “Convergence trading”

Covered call writing

Unhedged short volatilityWriting 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

-50% 0% 50% 100%

Benchmark

Sharpe ratio = .631

Maximum Sharpe Ratio

-50% 0% 50% 100%

Benchmark

MaximumSharpe RatioStrategy

Sharpe ratio = .748

Short Volatility Strategy

-50% 0% 50% 100%

Benchmark

Shortvolatility

Sharpe ratio = .743

Doubling

-50% 0% 50% 100%

Benchmark

Doubling(upper 5%)

Doubling(median)

Doubling(lower 5%)

Sharpe ratio = .046

Doubling (no embezzlement)

-50% 0% 50% 100%

Benchmark

Doubling(upper 5%)

Doubling(median)

Doubling(lower 5%)

Sharpe ratio = 1.962

Concave trading strategies

-50% 0% 50% 100%

Benchmark

Doubling(median)

MaximumSharpe RatioStrategy

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

Hedge funds follow concave strategies

ConcaveNeutra

lConve

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

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%

13027233170296126574174

109942960

Grand Total 11.54% 86.53% 1.93% 3318

R-rf = α + β (RS&P- rf) + γ (RS&P- rf)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

Sharpe

Ratio AlphaFF

AlphaBet

aSkewne

ssKurtos

Annual turnov

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)

Style and return patterns

Category Beta

Treynor Mazuy

measure

Modified Henriksson

Merton measure

Number of observatio

0.96347

-0.01105(-2.30)

-0.08989(-2.52)

Growth

1.03670

-0.00708(-1.53)

-0.03762(-1.15)

Neutral

1.02830

-0.00110(-0.29)

-0.02092(-0.71)

1.00670

-0.00196(-0.53)

0.00676(0.21)

0.76691

-0.01215(-1.93)

-0.10350(-2.24)

Passive/Enhanced

1.01440

0.00692(1.51)

0.04593(1.47)

Size and return patterns

Category Beta

Treynor Mazuy

measure

Modified Henriksson Merton measure

Number of observation

Largest 10 Institution

al Manager

0.9627

-0.00645(-2.25)

-0.05037(-2.34)

0.8819

-0.01306(-2.60)

-0.10095(-2.92)

Boutique firm

0.9322

-0.01029(-3.12)

-0.07616(-3.23)

0.9556

-0.00452(-1.25)

-0.04184(-1.49)

Incentives and return patterns

Category Beta

Treynor Mazuy

measure

Modified Henriksson

Merton measure

Number of

observations

Annual Bonus

0.9819

0.00013(0.03)

0.01233(0.35)

0.9386

-0.00857(-3.32)

-0.06720(-3.56)

Domestic owned

0.9739

-0.00990(-2.80)

-0.07282(-2.79)

0.9053

-0.00652(-1.86)

-0.05557(-2.18)

Equity Ownershi

p by senior staff

0.9322

-0.01029(-3.12)

-0.07616(-3.23)

0.9556

-0.00452(-1.25)

-0.04184(-1.49)

Patterns of derivative holdings

Fund Investm

ent Style

Calls Puts Month end option positions

Number Strike Number Strike

Concavity decreasing

Concavity increasing Total

GARP 123456

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

0.9570.9040.9520.9440.985

100%29%59%77%

100%100%100%

71%41%23%

8024679

89818118

Growth 15161718

-0.033-0.039-0.367-0.059

1.0561.0601.0671.023

0.1070.108

0.9510.913

35%13%

73%100%65%87%

Neutral 212224

-0.0930.5670.405

1.0380.9840.854

-0.093 0.947 10%100%100%

208101

Other 25 0.079 1.147 0.147 0.965 94% 6% 35

Value 33 0.050 0.914 57% 43% 23

Passive/ Enhanced

-0.013-0.026

0.9481.036

-0.017-0.041

0.9550.959

91%90%

340613

Total 38% 62% 3027

Fund Investm

ent Style

GARP 123456

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

0.9570.9040.9520.9440.985

100%29%59%77%

100%100%100%

71%41%23%

8024679

89818118

Growth 15161718

-0.033-0.039-0.367-0.059

1.0561.0601.0671.023

0.1070.108

0.9510.913

35%13%

73%100%65%87%

Neutral 212224

-0.0930.5670.405

1.0380.9840.854

-0.093 0.947 10%100%100%

208101

Other 25 0.079 1.147 0.147 0.965 94% 6% 35

Value 33 0.050 0.914 57% 43% 23

Passive/ Enhanced

-0.013-0.026

0.9481.036

-0.017-0.041

0.9550.959

91%90%

340613

Total 38% 62% 3027

Fund Investm

ent Style

GARP 123456

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

0.9570.9040.9520.9440.985

100%29%59%77%

100%100%100%

71%41%23%

8024679

89818118

Growth 15161718

-0.033-0.039-0.367-0.059

1.0561.0601.0671.023

0.1070.108

0.9510.913

35%13%

73%100%65%87%

Neutral 212224

-0.0930.5670.405

1.0380.9840.854

-0.093 0.947 10%100%100%

208101

Other 25 0.079 1.147 0.147 0.965 94% 6% 35

Value 33 0.050 0.914 57% 43% 23

Passive/ Enhanced

-0.013-0.026

0.9481.036

-0.017-0.041

0.9550.959

91%90%

340613

Total 38% 62% 3027

Doubling trades

h0 = S0 – C0

h0 : Initial highwater mark

S0 : Initial stock position

C0 : Cost basis of initial position

Doubling trades

h0 = S0 – C0

S1 = d S0

C1 = (1+rf ) C0

Bad news!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

Increase the equity position to cover the loss!

Doubling trades

h0 = S0 – C0 h1 = u S1 – (1+rf) C1

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

Good news!

1 is set to make up for past losses and re-establish security position

Doubling trades

h0 = S0 – C0 h1 = u S1 – (1+rf) C1

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

Good news!

1 = + S0 h0 - u d S0 + (1+rf)2 C0

u – (1+rf)

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1

C2 = (1+rf ) C1

Bad news again!

Doubling trades

h0 = S0 – C0 h2 = u S2 – (1+rf) C2

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

Good news finally!

Doubling trades

h0 = S0 – C0 h2 = u S2 – (1+rf) C2

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

Good news finally!

2 = + S0 h1 - u d S1+ (1+rf)2 C1

u – (1+rf)

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

S3 = d S2

C3 = (1+rf ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

S3 = d S2

C3 = (1+rf ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

S3 = d S

3 = (1+rf ) C

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2S

3 = d S2

C3 = (1+r

f ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2S3 =

f ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

f ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

f ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

f ) C2

Bad news again!

Doubling trades

h0 = S0 – C0

S1 = d S0 + 1

C1 = (1+rf ) C0 + 1

S2 = d S1 + 2

C2 = (1+rf ) C1 + 2

Bad news again!

Observable implication of doubling

i = a + b1 (1 - i) hi-1 + b2 Vi + b3 Bi + b4 i + b5 Gi

On a loss, trader will increase position size by

otherwise, position is liquidated on a gain,

for all trades