Expected shortfall is jointly elicitable with value-at-risk: implications for backtesting

Elicitability is a critical issue in the current debate about the choice of a risk measure for regulatory purposes. In this article, Tobias Fissler, Johanna F. Ziegel and Tilmann Gneiting comment on the role of elicitability in backtesting problems. In particular, they introduce the notion of comparative backtests and show how they can be implemented for expected shortfall, based on the recent result of Fissler and Ziegel (2015) that expected shortfall is jointly elicitable with value-at-risk

There continues to be lively debate about the appropriate choice of quantitative risk measure for regulatory purposes and internal risk management. In this context, it has been shown by Weber (2006) and Gneiting (2011) that expected shortfall (ES) is not elicitable. Specifically, there is no strictly consistent scoring (or loss) function.

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