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Sharpening Sharpe Ratios

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Author Info

  • William N. Goetzmann

    ()
    (Yale University, School of Management)

  • Jonathan E. Ingersoll Jr.

    ()
    (School of Management)

  • Matthew I. Spiegel

    ()
    (School of Management)

  • Ivo Welch

    ()
    (International Center for Finance)

Abstract

It is now well known that the Sharpe ratio and other related reward-to-risk measures may be manipulated with option-like strategies. In this paper we derive the general conditions for achieving the maximum expected Sharpe ratio. We derive static rules for achieving the maximum Sharpe ratio with two or more options, as well as a continuum of derivative contracts. The optimal strategy has a truncated right tail and a fat left tail. We also derive dynamic rules for increasing the Sharpe ratio. Our results have implications for performance measurement in any setting in which managers may use derivative contracts. In a performance measurement setting, we suggest that the distribution of high Sharpe ratio managers should be compared with that of the optimal Sharpe ratio strategy. This has particular application in the hedge fund industry where use of derivatives is unconstrained and manager compensation itself induces a non-linear payoff. The shape of the optimal Sharpe ratio leads to further conjectures. Expected returns being held constant, high Sharpe ratio strategies are, by definition, strategies that generate regular modest profits punctuated by occasional crashes. Our evidence suggests that the "peso problem" may be ubiquitous in any investment management industry that rewards high Sharpe ratio managers.

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Bibliographic Info

Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm273.

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Date of creation: 22 Mar 2002
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Handle: RePEc:ysm:somwrk:ysm273

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Web page: http://icf.som.yale.edu/
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Keywords: Sharpe Ratio; Hedge Funds; Derivatives;

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  1. Stephen Brown & William Goetzmann & James Park, 1998. "Hedge Funds and the Asian Currency Crisis of 1997," Yale School of Management Working Papers ysm84, Yale School of Management, revised 01 Apr 2008.
  2. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-51, April.
  3. Judith A. Chevalier & Glenn D. Ellison, 1995. "Risk Taking by Mutual Funds as a Response to Incentives," NBER Working Papers 5234, National Bureau of Economic Research, Inc.
  4. Mark Mitchell, 2001. "Characteristics of Risk and Return in Risk Arbitrage," Journal of Finance, American Finance Association, vol. 56(6), pages 2135-2175, December.
  5. Sharpe, W F, 1981. "Decentralized Investment Management," Journal of Finance, American Finance Association, vol. 36(2), pages 217-34, May.
  6. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
  7. Brown, Keith C & Harlow, W V & Starks, Laura T, 1996. " Of Tournaments and Temptations: An Analysis of Managerial Incentives in the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 51(1), pages 85-110, March.
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