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Maximum Certain Equivalent Excess Returns and Equivalent Preference Criteria Part I - Theory

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  • Jacques Pézier

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    (ICMA Centre, University of Reading)

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    Abstract

    Generalizations of traditional preference criteria such as the Sharpe ratio, the information ratio and the Jensen alpha are obtained by maximizing a certain equivalent excess return (CER) under relevant investment conditions. They are increasing functions of CERs and therefore equivalent criteria. They are consistent with utility theory and are applicable to any investment choice. That is not the case for many other popular preference criteria (e.g., Omega index, Sortino ratio, expected shortfall and so-called 'coherent' preference criteria). Most are incompatible with expected utility maximization and therefore best avoided.

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    Bibliographic Info

    Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2008-05.

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    Length: 31 pages
    Date of creation: Aug 2007
    Date of revision: Dec 2008
    Handle: RePEc:rdg:icmadp:icma-dp2008-05

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    Related research

    Keywords: Certain equivalent excess return; risk adjusted performance measures; risk aversion; power utility functions; coherent risk measures; spectral indices; Sharpe ratio; generalized Sharpe ratio; information ratio; Treynor ratio; Jensen alpha; skewness; kurtosis; downside risk measures; expected shortfall; Sortino ratio; Omega ratio;

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    1. Fischer, T., 2003. "Risk capital allocation by coherent risk measures based on one-sided moments," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 135-146, February.
    2. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
    3. Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
    4. Dirk Tasche, 2002. "Expected Shortfall and Beyond," Papers cond-mat/0203558, arXiv.org, revised Oct 2002.
    5. Chris Brooks & Harry. M Kat, 2001. "The Statistical Properties of Hedge Fund Index Returns," ICMA Centre Discussion Papers in Finance icma-dp2001-09, Henley Business School, Reading University.
    6. Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
    7. Jensen, Michael C, 1969. "Risk, The Pricing of Capital Assets, and the Evaluation of Investment Portfolios," The Journal of Business, University of Chicago Press, vol. 42(2), pages 167-247, April.
    8. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119.
    9. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    10. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    11. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
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