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Implications of the Sharpe ratio as a performance measure in multi-period settings

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  • Cvitanic, Jaksa
  • Lazrak, Ali
  • Wang, Tan

Abstract

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic market. We demonstrate that the manager's focus on the short horizon is detrimental to the long-horizon investor. When the returns are iid, the performance loss is significant, even when horizons are not very different. When the returns are mean reverting, the performance loss is exacerbated. We show that the manager's strategy tends to increase (decrease) the risk in the latter part of the optimization period after a bad (good) performance in the earlier part of the period, in agreement with empirical observations.

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  • 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.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:5:p:1622-1649
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    Cited by:

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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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, December.
    7. Anthony Tay, 2008. "Time-Varying Incentives in the Mutual Fund Industry," Finance Working Papers 22484, East Asian Bureau of Economic Research.
    8. Olivier, Jacques & Tay, Anthony, 2008. "Time-Varying Incentives in the Mutual Fund Industry," CEPR Discussion Papers 6893, C.E.P.R. Discussion Papers.
    9. 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.
    10. 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.
    11. 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.

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