Concave payoff patterns in equity fund holdings and transactions

1. Concave payoff patterns in equity fund holdings and transactions Stephen J. BrownNYU Stern School of Business David R. GallagherUniversity of NSW Onno SteenbeekErasmus University / ABP Investments Peter L. SwanUniversity 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. Examples of concave payout strategies • Unhedged short volatility • Writing out of the money calls and puts

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

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-rf =α + β (RS&P- rf) + γ(RS&P- rf)2

24. 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

25. Hedge funds follow concave strategies R-rf =α + β (RS&P- rf) + γ(RS&P- rf)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

28. Patterns of Returns

29. Patterns of Returns

30. Patterns of Holdings

31. Patterns of Holdings

32. Patterns of Holdings

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

37. Some successful Australian funds

38. Relationship between alpha and trading on a loss

39. Sector Patterns

40. Seasonal patterns

41. Return to long buy/short sell (monthly)

42. Return to long buy/short sell (monthly)

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