Concave payoff patterns in equity fund holdings and

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

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

Examples of concave payout strategies ¯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 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

Hedge funds follow concave strategies R-rf = α + β (RS&P- rf) + γ (RS&Pr f) 2

Hedge funds follow concave strategies R-rf = α + β (RS&P- rf) + γ (RS&Pr f) 2 Concave strategies: tβ > 1. 96 & tγ < 1. 96

Hedge funds follow concave strategies R-rf = α + β (RS&P- rf) + γ (RS&PConcave Neutral Convex N r f) 2 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 Grand Total Source: TASS/Tremont 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 1099 429 60 11. 54% 86. 53% 1. 93% 3318

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 Ratio 6 0. 2157 13 0. 2000 20 0. 1968 25 0. 1988 37 0. 1578 38 0. 1955 Alpha FF Alpha 0. 4124 (5. 46) 0. 2706 (5. 65) 0. 3324 (6. 05) 0. 2883 (3. 85) 0. 1903 (3. 21) 0. 2323 (6. 52) 0. 4300 (6. 11) 0. 2908 (6. 15) 0. 3206 (6. 18) 0. 3208 (4. 11) 0. 2188 (3. 00) 0. 2295 (7. 40) Beta Skewness Kurtosis 1. 0761 -0. 7624 5. 8161 1. 0031 -0. 8107 5. 9314 1. 0059 -0. 5811 5. 3488 0. 8831 -0. 3509 4. 7580 0. 7214 -0. 2904 4. 6642 0. 9672 -0. 7011 5. 6731

Patterns of Returns Category Alpha Treynor Mazuy measure Modified Henriksson Merton measure 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 Number of observations

Patterns of Returns Largest 10 Institutional Manager Boutique firm Modified Henriksson Merton measure Category Alpha Treynor Mazuy measure 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 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 Number of observations

Patterns of Holdings Fund Investment Style Calls Puts Month end option positions Concavity decreasing Fund Number Strike 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. 957 0. 904 0. 952 0. 944 0. 985 0. 950 - 0. 674 - 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% Neutral 22 23 25 -0. 093 0. 567 0. 405 1. 038 0. 984 0. 854 -0. 093 - 0. 947 - Other 26 0. 079 1. 147 0. 965 Value 34 0. 050 0. 914 Passive/ Enhanced 39 40 -0. 013 -0. 026 0. 948 1. 036 GARP Growth -0. 017 -0. 041 100% 29% 59% 77% Concavity increasing 71% 41% 23% 100% Total 80 246 79 898 18 11 73% 100% 65% 87% 11 8 83 344 10% 100% 90% 208 10 1 94% 6% 35 57% 43% 23 0. 955 0. 959 9% 10% 91% 90% 340 613 Total 38% 62% 3027 35% 13%

Patterns of Holdings Calls Puts Month end option positions Fund Investment Style Fund Number Strike 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. 957 0. 904 0. 952 0. 944 0. 985 GARP 1 2 3 4 5 6 11 13 0. 950 - 0. 674 - -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% Growth 16 17 18 19 Neutral 22 23 25 -0. 093 0. 567 0. 405 1. 038 0. 984 0. 854 -0. 093 - 0. 947 - Other 26 0. 079 1. 147 0. 965 Value 34 0. 050 0. 914 Passive/ Enhanced 39 40 -0. 013 -0. 026 0. 948 1. 036 -0. 017 -0. 041 Concavity decreasing 100% 29% 59% 77% Concavity increasing 71% 41% 23% 100% Total 80 246 79 898 18 11 73% 100% 65% 87% 11 8 83 344 10% 100% 90% 208 10 1 94% 6% 35 57% 43% 23 0. 955 0. 959 9% 10% 91% 90% 340 613 Total 38% 62% 3027 35% 13%

Patterns of Holdings Calls Puts Month end option positions Fund Investment Style Fund Number Strike 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. 957 0. 904 0. 952 0. 944 0. 985 GARP 1 2 3 4 5 6 11 13 0. 950 - 0. 674 - -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% Growth 16 17 18 19 Neutral 22 23 25 -0. 093 0. 567 0. 405 1. 038 0. 984 0. 854 -0. 093 - 0. 947 - Other 26 0. 079 1. 147 0. 965 Value 34 0. 050 0. 914 Passive/ Enhanced 39 40 -0. 013 -0. 026 0. 948 1. 036 -0. 017 -0. 041 Concavity decreasing 100% 29% 59% 77% Concavity increasing 71% 41% 23% 100% Total 80 246 79 898 18 11 73% 100% 65% 87% 11 8 83 344 10% 100% 90% 208 10 1 94% 6% 35 57% 43% 23 0. 955 0. 959 9% 10% 91% 90% 340 613 Total 38% 62% 3027 35% 13%

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 Ratio 6 0. 2157 13 0. 2000 20 0. 1968 25 0. 1988 37 0. 1578 38 0. 1955 Alpha FF Alpha 0. 4124 (5. 46) 0. 2706 (5. 65) 0. 3324 (6. 05) 0. 2883 (3. 85) 0. 1903 (3. 21) 0. 2323 (6. 52) 0. 4300 (6. 11) 0. 2908 (6. 15) 0. 3206 (6. 18) 0. 3208 (4. 11) 0. 2188 (3. 00) 0. 2295 (7. 40) Beta Skewness Kurtosis 1. 0761 -0. 7624 5. 8161 1. 0031 -0. 8107 5. 9314 1. 0059 -0. 5811 5. 3488 0. 8831 -0. 3509 4. 7580 0. 7214 -0. 2904 4. 6642 0. 9672 -0. 7011 5. 6731

Some successful Australian funds Fund Sharpe Ratio 6 0. 2157 13 0. 2000 20 0. 1968 25 0. 1988 37 0. 1578 38 0. 1955 Alpha FF Alpha 0. 4124 (5. 46) 0. 2706 (5. 65) 0. 3324 (6. 05) 0. 2883 (3. 85) 0. 1903 (3. 21) 0. 2323 (6. 52) 0. 4300 (6. 11) 0. 2908 (6. 15) 0. 3206 (6. 18) 0. 3208 (4. 11) 0. 2188 (3. 00) 0. 2295 (7. 40) Beta Coefficie nt on trading Skewness on a loss 1. 0761 -0. 7624 1. 0031 -0. 8107 1. 0059 -0. 5811 0. 8831 -0. 3509 0. 7214 -0. 2904 0. 9672 -0. 7011 -0. 0804 (-3. 00) -0. 2272 (-5. 42) -0. 3343 (-6. 40) -0. 0973 (-4. 73) -0. 0253 (-3. 72) -0. 1104 (-5. 26)

Relationship between alpha and trading on a loss Alpha Coefficien t on trading on a loss Negative Zero Positive Total Negative 0 4 9 13 Zero 0 20 4 24 Positive 0 2 1 3 Total 0 26 14 40 Chi square = 10. 2451 (p-value 0. 006)

Sector Patterns Mining and minerals Industrial Change in value of position on position a loss on a gain GARP Largest Domestic Services Change in value of position on a loss Change in value of position on a gain Gain above high water mark -0. 2706 0. 0172 0. 0000 0. 1993 -0. 0172 0. 3859 -1. 0693 (-2. 56) (0. 05) (0. 17) (0. 58) (1. 46) (-2. 92) -0. 3615 -0. 1913 -0. 0001 0. 0048 -0. 0488 0. 2860 -0. 8497 (-3. 19) (-0. 74) (-0. 44) (0. 02) (1. 65) (-3. 33) -0. 2021 -0. 3987 -0. 0001 -0. 3439 -0. 0497 0. 1794 -0. 6017 (-3. 19) (-2. 43) (-0. 49) (-3. 82) (-2. 23) (-1. 28) (-3. 05) (-3. 87) (1. 59)

Seasonal patterns December. January GARP Largest Domestic February-May June-July August. November Change in value of position on a loss Change in value of position on a gain Gain above high water mark Change in value of position on a loss Change in value of position on a gain 0. 0001 0. 6250 -0. 0663 0. 1319 -0. 3226 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) -0. 0002 0. 5006 -0. 0773 0. 0426 -0. 1524 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) -0. 1259 0. 3522 -0. 0760 -0. 0954 -0. 0998 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 GARP Growth Neutral Other Value Passive/ Enhanced Passive Raw return 0. 28% (0. 81) -0. 07% (-0. 11) 1. 46% (1. 84) 2. 40% (1. 99) 1. 11% (2. 06) -1. 31% (-2. 40) Market Adjusted 0. 33% (0. 91) -0. 05% (-0. 07) 0. 83% (1. 53) 2. 48% (2. 11) 0. 92% (1. 64) -0. 80% (-3. 07)

Return to long buy/short sell (monthly) Raw return Market Adjuste d No 0. 86% (2. 49) 0. 65% (1. 99) Yes 0. 11% (0. 33) 0. 40% (1. 41) No 0. 42% (1. 27) 0. 40% (1. 35) Yes 1. 07% (2. 24) 0. 88% (1. 95) Category Largest 10 Institutional Manager Boutique firm

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