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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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 10 (2007)
Issue (Month): 08 ()
Pages: 1339-1364

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Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:08:p:1339-1364

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Related research

Keywords: Sharpe ratio; jump-diffusion; two-fund separation; utility maximization; growth optimal portfolio; mutual fund;

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  1. John H. Cochrane & Jesús Saá-Requejo, 1998. "Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets," CRSP working papers 430, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  3. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
  4. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  5. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  6. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
  7. Nielsen, Lars Tyge & Vassalou, Maria, 2004. "Sharpe Ratios and Alphas in Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(01), pages 103-114, March.
  8. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation for Research in Economics, Yale University.
  10. Eckhard Platen, 2004. "Capital Asset Pricing for Markets with Intensity Based Jumps," Research Paper Series 143, Quantitative Finance Research Centre, University of Technology, Sydney.
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