New backtests for unconditional coverage of expected shortfall

Robert Löser; Dominik Wied; Daniel Ziggel

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We present a new backtest for the unconditional coverage property of the ES with known finite-sample distribution and appealing size properties.
The test principle is extended to a multivariate test.
An application to bank returns reveals a better model fit in bullish compared to bearish markets.

Abstract

While value-at-risk has been the standard risk measure for a long time, expected shortfall (ES) has become more and more popular in recent times, as it provides important information about tail risk. We present a new backtest for the unconditional coverage property of the ES. The test is based on the so-called cumulative violation process, and its main advantage is that the distribution is known for finite out-of-sample size. This leads to better size and power properties compared with existing tests. Moreover, we extend the test principle to a multivariate test and analyze its behavior via simulations and an application to bank returns.

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