Backtesting Expected Shortfall: A Simple Recipe?

18 Pages Posted: 11 Sep 2017 Last revised: 10 Aug 2018

See all articles by Felix Moldenhauer

Felix Moldenhauer

Independent

Marcin Pitera

Jagiellonian University in Krakow

Multiple version iconThere are 2 versions of this paper

Date Written: August 10, 2018

Abstract

We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of Expected Shortfall 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 realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient backtesting framework for unconditional coverage of Expected Shortfall 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.

Keywords: value-at-risk, expected shortfall, backtesting, backtest, risk bias, risk estimation, risk conservativeness, internal model-based approach, unconditional coverage test, funda- mental review of the trading book

JEL Classification: C19, C50, D81, G17, G28

Suggested Citation

Moldenhauer, Felix and Pitera, Marcin, Backtesting Expected Shortfall: A Simple Recipe? (August 10, 2018). Available at SSRN: https://ssrn.com/abstract=3033862 or http://dx.doi.org/10.2139/ssrn.3033862

Felix Moldenhauer

Independent ( email )

Marcin Pitera (Contact Author)

Jagiellonian University in Krakow ( email )

ul. Gołębia 24
Kraków, 31-007
Poland

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