Backtesting expected shortfall: a simple recipe?

Abstract

We propose a new backtesting framework for expected shortfall (ES) that can be used by regulators. Instead of looking at estimated capital reserve and realized cashflow separately, one can bind them into a secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of ES 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 realizations for the secured position that adds up to a negative total. Surprisingly, this simple quantity can be used to construct an efficient backtesting framework for unconditional coverage of ES 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.