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

Challenge to active managment

Zero or negative alpha in fund returns

Can fund managers earn returns commensurate with fees they charge?

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)

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?

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)

Overview

Definition of concave payoff patterns

Detecting concave payoff strategies

Evidence from managed funds

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

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

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?

Sharpe Ratio of Benchmark

-200%

-150%

-100%

-50%

0%

50%

100%

-50% 0% 50% 100%

Benchmark

Sharpe ratio = .631

Maximum Sharpe Ratio

-200%

-150%

-100%

-50%

0%

50%

100%

-50% 0% 50% 100%

Benchmark

MaximumSharpe RatioStrategy

Sharpe ratio = .748

Concave trading strategies

-200%

-150%

-100%

-50%

0%

50%

100%

-50% 0% 50% 100%

Benchmark

Loss AverseTrading(Median)MaximumSharpe RatioStrategy

Examples of concave payout strategies

Long-term asset mix guidelines

Unhedged short volatilityWriting out of the money

calls and puts

Examples of concave payout strategies

Loss averse trading a.k.a. “Doubling”

Examples of concave payout strategies

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”

Forensic Finance

Implications of concave payoff strategies

Patterns of returns

Forensic Finance

Implications of Informationless investing

Patterns of returnsare returns concave to benchmark?

Forensic Finance

Implications of concave payoff strategies

Patterns of returnsare returns concave to benchmark?

Patterns of security holdings

Forensic Finance

Implications of concave payoff strategies

Patterns of returnsare returns concave to benchmark?

Patterns of security holdingsdo security holdings produce

concave payouts?

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

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?

Hedge funds follow concave strategies

R-rf = α + β (RS&P- rf) + γ (RS&P- rf)2

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

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

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

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)

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

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

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

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

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

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”)

Short Volatility Strategy

-200%

-150%

-100%

-50%

0%

50%

100%

-50% 0% 50% 100%Benchmark return

Port

folio

retu

rn

Sharpe ratio = .743

Short Volatility transactions

-8

-6

-4

-2

0

-50% 0% 50% 100%

Benchmark return

Tran

sact

ions/

ΔS

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)

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)

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)

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)

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)

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)

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)

National Australia Bank

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