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Double or nothing: Patterns of equity fund holdings and transactions

Double or nothing: Patterns of 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 www.stern.nyu.edu/~sbrown. Performance measurement.

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Double or nothing: Patterns of equity fund holdings and transactions

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  1. Double or nothing: Patterns of 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 www.stern.nyu.edu/~sbrown

  2. Performance measurement Style: Index Arbitrage, 100% in cash at close of trading

  3. Frequency distribution of monthly returns

  4. Percentage in cash (monthly)

  5. Examples of riskless index arbitrage …

  6. Percentage in cash (daily)

  7. Apologia of Nick Leeson “I felt no elation at this success. I was determined to win back the losses. And as the spring wore on, I traded harder and harder, risking more and more. I was well down, but increasingly sure that my doubling up and doubling up would pay off ... I redoubled my exposure. The risk was that the market could crumble down, but on this occasion it carried on upwards ... As the market soared in July [1993] my position translated from a £6 million loss back into glorious profit. I was so happy that night I didn’t think I’d ever go through that kind of tension again. I’d pulled back a large position simply by holding my nerve ... but first thing on Monday morning I found that I had to use the 88888 account again ... it became an addiction” Nick Leeson Rogue Trader pp.63-64

  8. Sharpe ratio of doublers

  9. Informationless investing

  10. Informationless investing • Zero net investment overlay strategy (Weisman 2002) • Uses only public information • Designed to yield Sharpe ratio greater than benchmark • Why should we care? • Sharpe ratio obviously inappropriate here

  11. Informationless investing • Zero net investment overlay strategy (Weisman 2002) • Uses only public information • Designed to yield Sharpe ratio greater than benchmark • Why should we care? • Sharpe ratio obviously inappropriate here • But is metric of choice of hedge funds and derivatives traders

  12. We should care! • Agency issues • Fund flow, compensation based on historical performance • Gruber (1996), Sirri and Tufano (1998), Del Guercio and Tkac (2002) • Behavioral issues • Strategy leads to certain ruin in the long term

  13. Examples of Informationless investing • Doubling • a.k.a. “Convergence trading” • Covered call writing • Unhedged short volatility • Writing out of the money calls and puts

  14. Forensic Finance • Implications of Informationless investing • Patterns of returns • Patterns of security holdings • Patterns of trading

  15. Sharpe Ratio of Benchmark Sharpe ratio = .631

  16. Maximum Sharpe Ratio Sharpe ratio = .748

  17. Short Volatility Strategy Sharpe ratio = .743

  18. Doubling Sharpe ratio = .046

  19. Doubling (no embezzlement) Sharpe ratio = 1.962

  20. Concave trading strategies

  21. 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

  22. Hedge funds follow concave strategies R-rf =α + β (RS&P- rf) + γ(RS&P- rf)2 Source: TASS/Tremont

  23. 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

  24. Some successful Australian funds

  25. Style and return patterns

  26. Size and return patterns

  27. Incentives and return patterns

  28. Patterns of derivative holdings

  29. Patterns of derivative holdings

  30. Patterns of derivative holdings

  31. Doubling trades h0 = S0 – C0 h0 : Initial highwater mark S0 : Initial stock position C0 : Cost basis of initial position

  32. Doubling trades h0 = S0 – C0 Bad news! S1 = d S0 C1 = (1+rf ) C0

  33. Doubling trades h0 = S0 – C0 Increase the equity position to cover the loss! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1

  34. Doubling trades h0 = S0 – C0 h1 = u S1 – (1+rf) C1 Good news! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 1 is set to make up for past losses and re-establish security position

  35. Doubling trades h0 = S0 – C0 h1 = u S1 – (1+rf) C1 Good news! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 1 is set to make up for past losses and re-establish security position h0 - u d S0 + (1+rf)2 C0 1 = + S0 u– (1+rf)

  36. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 C2 = (1+rf ) C1

  37. Doubling trades h0 = S0 – C0 h2 = u S2 – (1+rf) C2 S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 Good news finally!

  38. Doubling trades h0 = S0 – C0 h2 = u S2 – (1+rf) C2 S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 2 is set to make up for past losses and re-establish security position Good news finally! h1 - u d S1+ (1+rf)2 C1 2 = + S0 u– (1+rf)

  39. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  40. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  41. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  42. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  43. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  44. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  45. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  46. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2 S3 = d S2 C3 = (1+rf ) C2

  47. Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 + 2 C2 = (1+rf ) C1 + 2

  48. Observable implication of doubling On a loss, trader will increase position size by hi-1 - u d Si-1+ (1+rf)2 Ci-1 i = + S0 u– (1+rf) otherwise, position is liquidated on a gain, i = a + b1 (1 - i) hi-1 + b2 Vi + b3 Bi + b4i + b5 Gi for all trades

  49. Observable implication of doubling On a loss, trader will increase position size by hi-1 - u d Si-1+ (1+rf)2 Ci-1 i = + S0 u– (1+rf) otherwise, position is liquidated on a gain, i = a + b1 (1 - i) hi-1 + b2 Vi + b3 Bi + b4i + b5 Gi Vi = (1 - i) d Si-1 , the value of security on a loss

  50. Observable implication of doubling On a loss, trader will increase position size by hi-1 - u d Si-1+ (1+rf)2 Ci-1 i = + S0 u– (1+rf) otherwise, position is liquidated on a gain, i = a + b1 (1 - i) hi-1 + b2 Vi + b3 Bi + b4i + b5 Gi Bi = (1 - i) (1 + rf ) Ci-1, the cost basis of the security

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