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Sharpening Sharpe Ratios

  • William Goetzmann
  • Jonathan Ingersoll
  • Matthew I. Spiegel
  • Ivo Welch

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 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 punctunated 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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File URL: http://www.nber.org/papers/w9116.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9116.

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Date of creation: Aug 2002
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Handle: RePEc:nbr:nberwo:9116
Note: AP
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  1. 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.
  2. 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.
  3. Mark Mitchell, 2001. "Characteristics of Risk and Return in Risk Arbitrage," Journal of Finance, American Finance Association, vol. 56(6), pages 2135-2175, December.
  4. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
  5. Stephen J. Brown & William N. Goetzmann & James M. Park, 1998. "Hedge Funds and the Asian Currency Crisis of 1997," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-014, New York University, Leonard N. Stern School of Business-.
  6. Sharpe, W F, 1981. "Decentralized Investment Management," Journal of Finance, American Finance Association, vol. 36(2), pages 217-34, May.
  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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