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.

Time‐varying dynamics of expected shortfall in commodity futures markets

“…The popular alternatives to parametric distribution fitting are nonparametric estimation via historical simulation (see Mehlitz & Auer, 2020), quantile regression (see Taylor, 2008), and kernel techniques (see Scaillet, 2004). These methods do not assume that a theoretical distribution model holds but instead build on the nonsmoothed (historical simulation and quantile regression) or smoothed (kernel techniques) empirical distribution function.…”

A comparison of minimum variance and maximum Sharpe ratio portfolios for mainstream investors

“…As it is actuarial convention, all risk measures are defined to be positively valued. First, with the value-at-risk (VaR) and the conditional VaR (CVaR), estimated via historical simulation and set up with a regulatory confidence level of 97.5%, we capture the maximum loss not exceeded with probability 97.5% and the expected loss in the case of exceedance, respectively (see Mehlitz and Auer, 2020) [16]. Second, we compute lower partial moments (LPMs) with loss sensitivities of m 5 0, 1, 2 and target return c 5 0 (see Pedersen and Rudholm-Alfvin, 2003).…”