Concave payoff patterns in 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

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 information  Designed to yield Sharpe ratio greater than benchmark  Using strategies that are concave to benchmark

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

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

Sharpe Ratio of Benchmark Sharpe ratio =.631

Maximum Sharpe Ratio Sharpe ratio =.748

Concave trading strategies

Examples of concave payout strategies  Long-term asset mix guidelines

 Unhedged short volatility  Writing 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 volatility  Writing 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 returns  are returns concave to benchmark?

Forensic Finance  Implications of concave payoff strategies  Patterns of returns  are returns concave to benchmark?  Patterns of security holdings

Forensic Finance  Implications of concave payoff strategies  Patterns of returns  are returns concave to benchmark?  Patterns of security holdings  do security holdings produce concave payouts?

Forensic Finance  Implications of concave payoff strategies  Patterns of returns  are returns concave to benchmark?  Patterns of security holdings  do security holdings produce concave payouts?  Patterns of trading

Forensic Finance  Implications of concave payoff strategies  Patterns of returns  are returns concave to benchmark?  Patterns of security holdings  do security holdings produce concave payouts?  Patterns of trading  does pattern of trading lead to concave payouts?

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 <

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% % 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% 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 AlphaBetaSkewnessKurtosis (5.46)(6.11) (5.65)(6.15) (6.05)(6.18) (3.85)(4.11) (3.21)(3.00) (6.52)(7.40)

Patterns of Returns CategoryAlpha Treynor Mazuy measure Modified Henriksson Merton measure Number of observations GARP (3.49) (-2.79) (-2.41) 1164 Growth (1.01) (-1.30) (-0.93) 469 Neutral (2.16) (-1.47) (-1.79) 187 Other (2.46) (-2.82) (-2.60) 397 Value (2.15) (-2.02) (-1.85) 772 Passive/ Enhanced (0.52) (-1.69) (-1.44) 253

Patterns of Returns CategoryAlpha Treynor Mazuy measure Modified Henriksson Merton measure Number of observations Largest 10 Institutional Manager No (2.73) (-4.11) (-3.58) 1952 Yes (4.39) (-2.15) (-2.02) 1290 Boutique firm No (4.43) (-3.98) (-3.82) 2821 Yes (1.85) (-2.05) (-1.22) 421

Patterns of Holdings Fund Investment Style CallsPutsMonth end option positions FundNumberStrikeNumberStrike Concavity decreasing Concavity increasingTotal GARP % 29% 59% 77% 100% 71% 41% 23% 100% Growth % 35% 13% 73% 100% 65% 87% Neutral % 100% 90% Other %6%35 Value %43%23 Passive/ Enhanced % 10% 91% 90% Total38%62%3027

Patterns of Holdings Fund Investment Style CallsPutsMonth end option positions FundNumberStrikeNumberStrike Concavity decreasing Concavity increasingTotal GARP % 29% 59% 77% 100% 71% 41% 23% 100% Growth % 35% 13% 73% 100% 65% 87% Neutral % 100% 90% Other %6%35 Value %43%23 Passive/ Enhanced % 10% 91% 90% Total38%62%3027

Patterns of Holdings Fund Investment Style CallsPutsMonth end option positions FundNumberStrikeNumberStrike Concavity decreasing Concavity increasingTotal GARP % 29% 59% 77% 100% 71% 41% 23% 100% Growth % 35% 13% 73% 100% 65% 87% Neutral % 100% 90% Other %6%35 Value %43%23 Passive/ Enhanced % 10% 91% 90% Total38%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 Sharpe ratio =.743

Short Volatility transactions

Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBetaSkewnessKurtosis (5.46)(6.11) (5.65)(6.15) (6.05)(6.18) (3.85)(4.11) (3.21)(3.00) (6.52)(7.40)

Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBetaSkewness Coefficie nt on trading on a loss (5.46)(6.11)(-3.00) (5.65)(6.15)(-5.42) (6.05)(6.18)(-6.40) (3.85)(4.11)(-4.73) (3.21)(3.00)(-3.72) (6.52)(7.40) (-5.26)

Relationship between alpha and trading on a loss Alpha NegativeZeroPositiveTotal Coefficien t on trading on a loss Negative04913 Zero Positive0213 Total Chi square = (p-value 0.006)

Sector Patterns Mining and mineralsIndustrial 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 (-2.56)(0.05)(0.17)(0.58)(-1.28) (1.46)(-2.92) Largest (-3.19)(-0.74)(-0.44)(0.02)(-3.05) (1.65)(-3.33) Domestic (-3.19)(-2.43)(-0.49)(-2.23)(-3.87)(1.59)(-3.82)

Seasonal patterns December- JanuaryFebruary-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 (1.33)(2.39)(-1.87)(0.38)(-2.44)(0.77)(-1.52)(0.88)(-3.34) Largest (-0.54)(3.22)(-1.49)(0.21)(-2.02)(0.64)(-2.90)(0.79)(-4.76) Domestic (-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) CategoryRaw return Market Adjusted GARP0.28%0.33% (0.81)(0.91) Growth-0.07%-0.05% (-0.11)(-0.07) Neutral1.46%0.83% (1.84)(1.53) Other2.40%2.48% (1.99)(2.11) Value1.11%0.92% (2.06)(1.64) Passive/ Enhanced Passive -1.31%-0.80% (-2.40)(-3.07)

Return to long buy/short sell (monthly) Category Raw return Market Adjuste d Largest 10 Institutional Manager No0.86%0.65% (2.49)(1.99) Yes0.11%0.40% (0.33)(1.41) Boutique firm No0.42%0.40% (1.27)(1.35) Yes1.07%0.88% (2.24)(1.95)

National Australia Bank

A clear and present danger?  Evidence of concave payout pattern in managed funds  Evidence in returns  Evidence in security holdings  Evidence in pattern of transactions  Consistent with  Adverse incentive story  Behavioral theories of trading  Effect limited to large, diversified funds