# Forecast Encompassing Tests for the Expected Shortfall

## TL;DR

This paper develops new statistical tests to evaluate the accuracy of Expected Shortfall forecasts, a key risk measure in banking regulation, using robust theory and simulation studies.

## Contribution

It introduces novel forecast encompassing tests for Expected Shortfall, incorporating joint loss functions and robust asymptotic theory, with applications to financial asset forecasting.

## Key findings

- Tests perform well in finite samples
- Forecast combination methods improve risk prediction
- Applicable to various financial assets

## Abstract

We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for the international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we investigate the finite sample properties of the tests in an extensive simulation study. We use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets.