DESIRABLE PROPERTIES OF AN IDEAL RISK MEASURE IN PORTFOLIO THEORY

Svetlozar Rachev, Sergio Ortobelli, Stoyan Stoyanov, Frank Fabozzi () and Almira Biglova
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Svetlozar Rachev: University of California, Santa Barbara and, University of Karlsruhe, Germany
Sergio Ortobelli: University of Bergamo, Italy
Stoyan Stoyanov: FinAnalytica Inc., USA
Almira Biglova: University of Karlsruhe, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 01, 19-54

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.

Keywords: Risk aversion; portfolio choice; investment risk; reward measure; diversification (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (32)

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DOI: 10.1142/S0219024908004713

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