Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting

TL;DR

This paper discusses the importance of elicitability in backtesting risk measures, proposing Diebold-Mariano tests for Expected Shortfall based on its joint elicitability with Value at Risk.

Contribution

It highlights the joint elicitability of Expected Shortfall and Value at Risk and introduces a method for backtesting ES using Diebold-Mariano tests.

Findings

Expected Shortfall is jointly elicitable with Value at Risk.

Diebold-Mariano tests can be applied for backtesting ES.

The approach improves risk measure validation.

Abstract

In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can be implemented for Expected Shortfall (ES), based on the recent result of Fissler and Ziegel (2015) that ES is jointly elicitable with Value at Risk.