Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error

Tinbergen Institute Discussion Paper 2019-058/III

75 Pages Posted: 22 Aug 2019 Last revised: 11 Mar 2021

See all articles by Sander Barendse

Sander Barendse

University of Amsterdam - Faculty of Economics and Business (FEB)

Erik Kole

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM; Tinbergen Institute

Dick J. C. van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM

Date Written: August 19, 2019

Abstract

We investigate the effect of estimation error on backtests of (multi-period) expected shortfall (ES) forecasts. These backtests are based on first order conditions of a recently introduced family of jointly consistent loss functions for Value-at-Risk (VaR) and ES. We provide explicit expressions for the additional terms in the asymptotic covariance matrix that result from estimation error, and propose robust tests that account for it. Monte Carlo experiments show that the tests that ignore these terms suffer from size distortions, which are more pronounced for higher ratios of out-of-sample to in-sample observations. Robust versions of the backtests perform well, although this also depends on the choice of conditioning variables. In an application to VaR and ES forecasts for daily FTSE 100 index returns as generated by AR-GARCH, AR-GJR-GARCH, and AR-HEAVY models, we find that estimation error substantially impacts the outcome of the backtests.

Keywords: expected shortfall, backtesting, risk management, tail risk, Value-at-Risk

JEL Classification: C12, C53, C58, G17

Suggested Citation

Barendse, Sander and Kole, Erik and van Dijk, Dick J.C., Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error (August 19, 2019). Tinbergen Institute Discussion Paper 2019-058/III, Available at SSRN: https://ssrn.com/abstract=3439309 or http://dx.doi.org/10.2139/ssrn.3439309

Sander Barendse (Contact Author)

University of Amsterdam - Faculty of Economics and Business (FEB) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Erik Kole

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 12 58 (Phone)

HOME PAGE: http://people.few.eur.nl/kole

ERIM

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

HOME PAGE: http://people.few.eur.nl/kole

Dick J.C. Van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute

P.O. Box 1738
3000 DR Rotterdam
Netherlands

ERIM ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1263 (Phone)
+31 10 4089162 (Fax)

HOME PAGE: http://people.few.eur.nl/djvandijk

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