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Sharpe Ratio Maximization And Expected Utility When Asset Prices Have Jumps

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  • MORTEN MOSEGAARD CHRISTENSEN

    (Danske Bank, Denmark)

  • ECKHARD PLATEN

    (University of Technology, Sydney, Australia)

Abstract

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. We show that in the presence of jumps, maximizing the Sharpe ratio is generally inconsistent with maximizing expected utility, in the sense that a utility maximizing individual will not choose a strategy which has a maximal Sharpe ratio. This result will hold unless markets are incomplete or jump risk has no risk premium. In case of an incomplete market we show that the optimal portfolio of a utility maximizing individual may "accidentally" have maximal Sharpe ratio. Furthermore, if there is no risk premium for jump risk, a utility maximizing investor may select a portfolio having a maximal Sharpe ratio, if jump risk can be hedged away. We note that uncritical use of the Sharpe ratio as a performance measure in a world where asset prices exhibit jumps may lead to unreasonable investments with positive probability of ruin.

Suggested Citation

  • Morten Mosegaard Christensen & Eckhard Platen, 2007. "Sharpe Ratio Maximization And Expected Utility When Asset Prices Have Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(08), pages 1339-1364.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:08:n:s0219024907004688
    DOI: 10.1142/S0219024907004688
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    3. Andrea Rigamonti & Alex Weissensteiner, 2020. "Asset allocation under predictability and parameter uncertainty using LASSO," Computational Management Science, Springer, vol. 17(2), pages 179-201, June.

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