Backtesting Expected Shortfall: a simple recipe?

TL;DR

This paper introduces a straightforward and efficient backtesting framework for Expected Shortfall, leveraging the concept of secured positions and monotonicity, suitable for regulatory use and extending existing Value-at-R risk methods.

Contribution

It proposes a novel backtesting approach for Expected Shortfall based on secured positions and a simple test statistic, enhancing regulatory risk assessment tools.

Findings

The test statistic effectively assesses unconditional coverage of Expected Shortfall.

The framework is computationally simple and grounded in duality principles.

It extends the regulatory traffic-light approach for Value-at-Risk to Expected Shortfall.

Abstract

We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of Expected Shortfall with respect to its target confidence level we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient backtesting framework for unconditional coverage of Expected Shortfall in a natural extension of the regulatory traffic-light approach for Value-at-Risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures.