COMPARING THE SMALL-SAMPLE ESTIMATION ERROR OF CONCEPTUALLY DIFFERENT RISK MEASURES

Abstract

Motivated by the need to correctly rank risky alternatives in many investment, insurance and operations research applications, this paper uses a generalized location and scale framework from utility theory to propose a simple but powerful metric for comparing the estimation error of conceptually different risk measures. In an illustrative application, we obtain this metric — the probability that a risk measure ranks two assets falsely in finite samples — via Monte Carlo simulation for fourteen popular measures of risk and different distributional settings. Its results allow us to highlight interesting risk measure properties such as their relative quality under varying degrees of skewness and kurtosis. Because of the generality of our approach, the error probabilities derived for classic risk measures can serve as a benchmark for newly proposed measures seeking to replace the classic ones in decision making. It also supports the identification of the most suitable risk measures for a given distributional environment.