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Desirable Properties Of An Ideal Risk Measure In Portfolio Theory

Author

Listed:
  • SVETLOZAR RACHEV

    (University of California, Santa Barbara and, University of Karlsruhe, Germany)

  • SERGIO ORTOBELLI

    (University of Bergamo, Italy)

  • STOYAN STOYANOV

    (FinAnalytica Inc., USA)

  • FRANK J. FABOZZI

    (School of Management, Yale University, 135 Prospect Street, New Haven, CT 06520-8200, USA)

  • ALMIRA BIGLOVA

    (University of Karlsruhe, Germany)

Abstract

This paper examines the properties that a risk measure should satisfy in order to characterize an investor's preferences. In particular, we propose some intuitive and realistic examples that describe several desirable features of an ideal risk measure. This analysis is the first step in understanding how to classify an investor's risk. Risk is an asymmetric, relative, heteroskedastic, multidimensional concept that has to take into account asymptotic behavior of returns, inter-temporal dependence, risk-time aggregation, and the impact of several economic phenomena that could influence an investor's preferences. In order to consider the financial impact of the several aspects of risk, we propose and analyze the relationship between distributional modeling and risk measures. Similar to the notion of ideal probability metric to a given approximation problem, we are in the search for an ideal risk measure or ideal performance ratio for a portfolio selection problem. We then emphasize the parallels between risk measures and probability metrics, underlying the computational advantage and disadvantage of different approaches.

Suggested Citation

  • Svetlozar Rachev & Sergio Ortobelli & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2008. "Desirable Properties Of An Ideal Risk Measure In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 19-54.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:01:n:s0219024908004713
    DOI: 10.1142/S0219024908004713
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