Desirable Properties of an Ideal Risk Measure in Portfolio Theory

International Journal of Theoretical and Applied Finance, Vol. 11, No. 1, pp. 19-54 , 2008

Posted: 25 Apr 2010

See all articles by Svetlozar Rachev

Svetlozar Rachev

Texas Tech University

Sergio Ortobelli Lozza

University of Bergamo - Mathematics, Statistics, Computer Science and Applications (MSIA)

Stoyan Stoyanov

affiliation not provided to SSRN

Frank J. Fabozzi

EDHEC Business School

Date Written: February 1, 2008

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

Suggested Citation

Rachev, Svetlozar and Ortobelli Lozza, Sergio and Stoyanov, Stoyan and Fabozzi, Frank J., Desirable Properties of an Ideal Risk Measure in Portfolio Theory (February 1, 2008). International Journal of Theoretical and Applied Finance, Vol. 11, No. 1, pp. 19-54 , 2008, Available at SSRN: https://ssrn.com/abstract=1515581

Svetlozar Rachev (Contact Author)

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Sergio Ortobelli Lozza

University of Bergamo - Mathematics, Statistics, Computer Science and Applications (MSIA) ( email )

Via Salvecchio, 19
Bergamo, 24129
Italy

Stoyan Stoyanov

affiliation not provided to SSRN ( email )

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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