DESIRABLE PROPERTIES OF AN IDEAL RISK MEASURE IN PORTFOLIO THEORY

TLDR

Risk is a multidimensional, asymmetric, heteroskedastic concept that depends on return asymptotics, inter‑temporal dependence, risk‑time aggregation, and economic factors, and the search for an ideal risk measure parallels the quest for an ideal probability metric in portfolio selection. The paper investigates the properties a risk measure must satisfy to capture investor preferences, proposes intuitive examples of desirable features, and examines the link between distributional modeling and risk measures. The authors illustrate desirable features through concrete examples, analyze how distributional modeling informs risk measures, and highlight parallels with probability metrics, noting computational advantages and disadvantages of each approach. The study establishes a foundational step toward classifying investor risk.

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.