Nested L-statistics and their use in comparing the riskiness of portfolios

Abstract

Inspired by the problem of testing hypotheses about the equality of several risk measure values, we find that the ‘nested L-statistic’—a notion introduced herein—is natural and particularly convenient. Indeed, the test statistic that we explore in this paper is a nested L-statistic. We discuss large-sample properties of the statistic, investigate its performance using a simulation study, and consider an example involving the comparison of risk measure values where the risks of interest are those associated with tornado damage in different time periods and different regions.