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Implications of Sharpe Ratio as a Performance Measure in Multi-Period Settings

Author

Listed:
  • Ali Lazrak

    (Sauder - Sauder School of Business [British Columbia] - UBC - University of British Columbia [Canada])

  • Jaksa Cvitanic

    (Division of the humanities and social sciences - CALTECH - California Institute of Technology)

  • Tan Wang

    (Division of finance; China Academy of Financial Research (CAFR) - UBC - University of British Columbia [Canada])

Abstract

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager's focus on the short horizon performance is detrimental to the investor's long horizon performance. Numerical experiments illustrate that when returns are iid, the performance loss is significant, even when the investor's investment horizon is not much longer than the manager's. When expected returns are mean reverting, the performance loss is exacerbated. Second, we show that Sharpe ratio maximization strategies tend to increase (decrease) the risk in the later part of the optimization period after a bad (good) performance in the earlier part of the optimization period. As illustrated by a simulation exercise, this prediction is in agreement with empirical observations, and it presents a rational expectations alternative to the prevalent tournament theory explanation.

Suggested Citation

  • Ali Lazrak & Jaksa Cvitanic & Tan Wang, 2008. "Implications of Sharpe Ratio as a Performance Measure in Multi-Period Settings," Post-Print hal-00485697, HAL.
    • Handle: RePEc:hal:journl:hal-00485697
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    Cited by:

    1. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Continuous time mean-variance-utility portfolio problem and its equilibrium strategy," Papers 2005.06782, arXiv.org, revised Nov 2020.
    2. Francis In & Sangbae Kim, 2012. "An Introduction to Wavelet Theory in Finance:A Wavelet Multiscale Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8431, September.
    3. Olivier, Jacques & Tay, Anthony, 2008. "Time-Varying Incentives in the Mutual Fund Industry," CEPR Discussion Papers 6893, C.E.P.R. Discussion Papers.
    4. Lu, Jin-Ray & Li, Xiu-Yan, 2021. "Identifying the fair value of Sharpe ratio by an option valuation approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 63-70.
    5. Rossello, Damiano, 2015. "Ranking of investment funds: Acceptability versus robustness," European Journal of Operational Research, Elsevier, vol. 245(3), pages 828-836.
    6. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    7. Xiangyu Cui & Jianjun Gao & Yun Shi, 2021. "Multi-period mean–variance portfolio optimization with management fees," Operational Research, Springer, vol. 21(2), pages 1333-1354, June.
    8. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    9. Anthony Tay, 2008. "Time-Varying Incentives in the Mutual Fund Industry," Finance Working Papers 22484, East Asian Bureau of Economic Research.
    10. Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
    11. Ben-Zhang Yang & Xin-Jiang He & Song-Ping Zhu, 2020. "Mean-variance-utility portfolio selection with time and state dependent risk aversion," Papers 2007.06510, arXiv.org, revised Aug 2020.

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