Desirable Properties of an Ideal Risk Measure in Portfolio Theory

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 to understand how to classify an investor’s risk. The risk is an asymmetric, relative, heteroskedastic, multidimensional concept that has to take into account asymptotic behavior of returns, inter-temporal dependence, risk-time aggregation, further sources of risk, 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 the risk we propose and analyze the relationship between distributional modeling and risk measures. Similarly 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. Then we emphasize the parallels between risk measures and probability metrics underlying the computational advantage and disadvantage of different approaches.