A Monte Carlo evaluation of non-parametric estimators of expected shortfall

Abstract

Purpose Motivated by the growing importance of the expected shortfall in banking and finance, this study aims to compare the performance of popular non-parametric estimators of the expected shortfall (i.e. different variants of historical, outlier-adjusted and kernel methods) to each other, selected parametric benchmarks and estimates based on the idea of forecast combination. Design/methodology/approach Within a multidimensional simulation setup (spanned by different distributional settings, sample sizes and confidence levels), the authors rank the estimators based on classic error measures, as well as an innovative performance profile technique, which the authors adapt from the mathematical programming literature. Findings The rich set of results supports academics and practitioners in the search for an answer to the question of which estimators are preferable under which circumstances. This is because no estimator or combination of estimators ranks first in all considered settings. Originality/value To the best of their knowledge, the authors are the first to provide a structured simulation-based comparison of non-parametric expected shortfall estimators, study the effects of estimator averaging and apply the mentioned profiling technique in risk management.