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Concave payoff patterns in equity fund holdings and transactions Stephen J. Brown NYU Stern School of Business David R. Gallagher University of NSW Onno.

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Presentation on theme: "Concave payoff patterns in equity fund holdings and transactions Stephen J. Brown NYU Stern School of Business David R. Gallagher University of NSW Onno."— Presentation transcript:

1 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

2 Challenge to active managment  Zero or negative alpha in fund returns  Can fund managers earn returns commensurate with fees they charge?

3 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)

4 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?

5 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)

6 Overview  Definition of concave payoff patterns  Detecting concave payoff strategies  Evidence from managed funds

7 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

8 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

9 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?

10 Sharpe Ratio of Benchmark Sharpe ratio =.631

11 Maximum Sharpe Ratio Sharpe ratio =.748

12 Concave trading strategies

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

14  Unhedged short volatility  Writing out of the money calls and puts Examples of concave payout strategies

15  Loss averse trading  a.k.a. “Doubling” Examples of concave payout strategies

16 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”

17 Forensic Finance  Implications of concave payoff strategies  Patterns of returns

18 Forensic Finance  Implications of Informationless investing  Patterns of returns  are returns concave to benchmark?

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

20 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?

21 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

22 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?

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

24 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

25 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

26 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

27 Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBetaSkewnessKurtosis 60.21570.41240.43001.0761-0.76245.8161 (5.46)(6.11) 130.20000.27060.29081.0031-0.81075.9314 (5.65)(6.15) 200.19680.33240.32061.0059-0.58115.3488 (6.05)(6.18) 250.19880.28830.32080.8831-0.35094.7580 (3.85)(4.11) 370.15780.19030.21880.7214-0.29044.6642 (3.21)(3.00) 380.19550.23230.22950.9672-0.70115.6731 (6.52)(7.40)

28 Patterns of Returns CategoryAlpha Treynor Mazuy measure Modified Henriksson Merton measure Number of observations GARP 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/ Enhanced 0.05205 (0.52) -0.02119 (-1.69) -0.24707 (-1.44) 253

29 Patterns of Returns CategoryAlpha Treynor Mazuy measure Modified Henriksson Merton measure Number of observations Largest 10 Institutional 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

30 Patterns of Holdings Fund Investment Style CallsPutsMonth end option positions FundNumberStrikeNumberStrike Concavity decreasing Concavity increasingTotal GARP 1 2 3 4 5 6 11 14 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 16 17 18 19 -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 22 23 25 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - 0.947 - 10% 100% 90% 208 10 1 Other260.0791.1470.1470.96594%6%35 Value340.0500.91457%43%23 Passive/ Enhanced 39 40 -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

31 Patterns of Holdings Fund Investment 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 16 17 18 19 -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 22 23 25 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - 0.947 - 10% 100% 90% 208 10 1 Other260.0791.1470.1470.96594%6%35 Value340.0500.91457%43%23 Passive/ Enhanced 39 40 -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

32 Patterns of Holdings Fund Investment 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 16 17 18 19 -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 22 23 25 -0.093 0.567 0.405 1.038 0.984 0.854 -0.093 - 0.947 - 10% 100% 90% 208 10 1 Other260.0791.1470.1470.96594%6%35 Value340.0500.91457%43%23 Passive/ Enhanced 39 40 -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

33 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”)

34 Short Volatility Strategy Sharpe ratio =.743

35 Short Volatility transactions

36 Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBetaSkewnessKurtosis 60.21570.41240.43001.0761-0.76245.8161 (5.46)(6.11) 130.20000.27060.29081.0031-0.81075.9314 (5.65)(6.15) 200.19680.33240.32061.0059-0.58115.3488 (6.05)(6.18) 250.19880.28830.32080.8831-0.35094.7580 (3.85)(4.11) 370.15780.19030.21880.7214-0.29044.6642 (3.21)(3.00) 380.19550.23230.22950.9672-0.70115.6731 (6.52)(7.40)

37 Some successful Australian funds Fund Sharpe RatioAlpha FF AlphaBetaSkewness Coefficie nt on trading on a loss 60.21570.41240.43001.0761-0.7624-0.0804 (5.46)(6.11)(-3.00) 130.20000.27060.29081.0031-0.8107-0.2272 (5.65)(6.15)(-5.42) 200.19680.33240.32061.0059-0.5811-0.3343 (6.05)(6.18)(-6.40) 250.19880.28830.32080.8831-0.3509-0.0973 (3.85)(4.11)(-4.73) 370.15780.19030.21880.7214-0.2904-0.0253 (3.21)(3.00)(-3.72) 380.19550.23230.22950.9672-0.7011-0.1104 (6.52)(7.40) (-5.26)

38 Relationship between alpha and trading on a loss Alpha NegativeZeroPositiveTotal Coefficien t on trading on a loss Negative04913 Zero020424 Positive0213 Total0261440 Chi square = 10.2451 (p-value 0.006)

39 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 -0.27060.01720.00000.1993-0.01720.3859-1.0693 (-2.56)(0.05)(0.17)(0.58)(-1.28) (1.46)(-2.92) Largest -0.3615-0.1913-0.00010.0048-0.04880.2860-0.8497 (-3.19)(-0.74)(-0.44)(0.02)(-3.05) (1.65)(-3.33) Domestic -0.2021-0.3987-0.0001-0.3439-0.04970.1794-0.6017 (-3.19)(-2.43)(-0.49)(-2.23)(-3.87)(1.59)(-3.82)

40 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 0.00010.6250-0.06630.1319-0.32260.2283-0.03950.2623-1.1372 (1.33)(2.39)(-1.87)(0.38)(-2.44)(0.77)(-1.52)(0.88)(-3.34) Largest -0.00020.5006-0.07730.0426-0.15240.0962-0.06750.1610-1.0076 (-0.54)(3.22)(-1.49)(0.21)(-2.02)(0.64)(-2.90)(0.79)(-4.76) Domestic -0.12590.3522-0.0760-0.0954-0.09980.0302-0.0007-0.1494-0.7966 (-4.55)(3.25)(-2.38)(-0.70)(-2.19)(0.27)(-0.84)(-1.17)(-6.00)

41 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)

42 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)

43 National Australia Bank

44 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

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