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Sharpening Sharpe Ratios

Author

Listed:
  • William N. Goetzmann

    () (Yale School of Management, International Center for Finance)

  • Jonathan E. Ingersoll, Jr.

    () (Yale School of Management, International Center for Finance)

  • Matthew I. Spiegel

    () (Yale School of Management, International Center for Finance)

  • Ivo Welch

    () (Yale University - 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

Suggested Citation

  • William N. Goetzmann & Jonathan E. Ingersoll, Jr. & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," Yale School of Management Working Papers ysm29, Yale School of Management.
  • Handle: RePEc:ysm:somwrk:ysm29
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    References listed on IDEAS

    as
    1. 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-.
    2. Mark Mitchell, 2001. "Characteristics of Risk and Return in Risk Arbitrage," Journal of Finance, American Finance Association, vol. 56(6), pages 2135-2175, December.
    3. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119-119.
    4. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    5. Sharpe, W F, 1981. "Decentralized Investment Management," Journal of Finance, American Finance Association, vol. 36(2), pages 217-234, May.
    6. 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 233-251, April.
    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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    Cited by:

    1. Zakamouline, Valeri & Koekebakker, Steen, 2009. "Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1242-1254, July.
    2. Cvitanic, Jaksa & Lazrak, Ali & Wang, Tan, 2008. "Implications of the Sharpe ratio as a performance measure in multi-period settings," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1622-1649, May.
    3. Kabir, M. Humayun & Hassan, M. Kabir & Maroney, Neal, 2011. "International diversification with American Depository Receipts (ADRs)," Pacific-Basin Finance Journal, Elsevier, vol. 19(1), pages 98-114, January.
    4. Carolina Fugazza & Massimo Guidolin & Giovanna Nicodano, 2009. "Time and Risk Diversification in Real Estate Investments: Assessing the Ex Post Economic Value," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 37(3), pages 341-381.
    5. Francesco Franzoni & José M. Marin, 2005. "Portable Alphas from Pension Mispricing," Working Papers 227, Barcelona Graduate School of Economics.
    6. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
    7. Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
    8. Santa-Clara, Pedro & Saretto, Alessio, 2009. "Option strategies: Good deals and margin calls," Journal of Financial Markets, Elsevier, pages 391-417.
    9. Peter Temin & Hans-Joachim Voth, 2004. "Riding the South Sea Bubble," American Economic Review, American Economic Association, vol. 94(5), pages 1654-1668, December.
    10. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Robust evidence on the similarity of Sharpe ratio and drawdown-based hedge fund performance rankings," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 24(C), pages 153-165.
    11. Schuster, Martin & Auer, Benjamin R., 2012. "A note on empirical Sharpe ratio dynamics," Economics Letters, Elsevier, vol. 116(1), pages 124-128.
    12. Getmansky, Mila & Lo, Andrew W. & Makarov, Igor, 2004. "An econometric model of serial correlation and illiquidity in hedge fund returns," Journal of Financial Economics, Elsevier, vol. 74(3), pages 529-609, December.
    13. Abbas, Qaisar & Khan, Sabeen & Shah, Syed Zulfiqar Ali, 2013. "Volatility transmission in regional Asian stock markets," Emerging Markets Review, Elsevier, vol. 16(C), pages 66-77.
    14. Urcola, Hernan A. & Irwin, Scott H., 2006. "Has the Performance of the Hog Options Market Changed?," 2006 Annual meeting, July 23-26, Long Beach, CA 21479, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Auer, Benjamin R. & Schuhmacher, Frank, 2013. "Performance hypothesis testing with the Sharpe ratio: The case of hedge funds," Finance Research Letters, Elsevier, vol. 10(4), pages 196-208.
    16. Kent Smetters & Xingtan Zhang, 2013. "A Sharper Ratio: A General Measure for Correctly Ranking Non-Normal Investment Risks," NBER Working Papers 19500, National Bureau of Economic Research, Inc.
    17. repec:dau:papers:123456789/7739 is not listed on IDEAS
    18. repec:dau:papers:123456789/9298 is not listed on IDEAS
    19. El Kalak, Izidin & Azevedo, Alcino & Hudson, Robert, 2016. "Reviewing the hedge funds literature II: Hedge funds' returns and risk management characteristics," International Review of Financial Analysis, Elsevier, vol. 48(C), pages 55-66.
    20. André Lucas & Arjen Siegmann, 2008. "The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 35(1-2), pages 200-226.
    21. Marie Brière & Jean-David Fermanian & Hassan Malongo & Ombretta Signori, 2012. "Volatility Strategies for Global and Country Specific European Investors," Post-Print hal-01494509, HAL.
    22. Benjamin Auer, 2013. "The low return distortion of the Sharpe ratio," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(3), pages 299-306, September.
    23. Hentati-Kaffel, Rania, 2016. "Structured products under generalized kappa ratio," Economic Modelling, Elsevier, vol. 58(C), pages 599-614.

    More about this item

    Keywords

    Sharpe Ratio; Hedge Funds; Derivatives;

    JEL classification:

    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services

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