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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 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
Performance measurement Style: Index Arbitrage, 100% in cash at close of trading
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
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
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
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
Examples of Informationless investing • Doubling • a.k.a. “Convergence trading” • Covered call writing • Unhedged short volatility • Writing out of the money calls and puts
Forensic Finance • Implications of Informationless investing • Patterns of returns • Patterns of security holdings • Patterns of trading
Sharpe Ratio of Benchmark Sharpe ratio = .631
Maximum Sharpe Ratio Sharpe ratio = .748
Short Volatility Strategy Sharpe ratio = .743
Doubling Sharpe ratio = .046
Doubling (no embezzlement) Sharpe ratio = 1.962
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
Hedge funds follow concave strategies R-rf =α + β (RS&P- rf) + γ(RS&P- rf)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
Doubling trades h0 = S0 – C0 h0 : Initial highwater mark S0 : Initial stock position C0 : Cost basis of initial position
Doubling trades h0 = S0 – C0 Bad news! S1 = d S0 C1 = (1+rf ) C0
Doubling trades h0 = S0 – C0 Increase the equity position to cover the loss! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1
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
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)
Doubling trades h0 = S0 – C0 Bad news again! S1 = d S0 + 1 C1 = (1+rf ) C0 + 1 S2 = d S1 C2 = (1+rf ) C1
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!
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)
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
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
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
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
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
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
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
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
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
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 + b4i + b5 Gi for all trades
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 + b4i + b5 Gi Vi = (1 - i) d Si-1 , the value of security on a loss
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 + b4i + b5 Gi Bi = (1 - i) (1 + rf ) Ci-1, the cost basis of the security