Evaluating the Precision of Estimators of Quantile-Based Risk Measures

TL;DR

This paper evaluates the accuracy of estimators for quantile-based risk measures, proposing a Monte Carlo approach for better precision estimation and analyzing the reliability of asymptotic normality assumptions in practical sample sizes.

Contribution

It introduces a Monte Carlo method to estimate the precision of risk measure estimators and analyzes their distribution and reliability in typical sample sizes.

Findings

Monte Carlo method improves precision estimation accuracy

Asymptotic normality may be unreliable with common sample sizes

Risk estimator precision depends on the underlying loss distribution

Abstract

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions.