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

Sander Barendse, Erik Kole () and Dick van Dijk
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Sander Barendse: University of Oxford

No 19-058/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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 (search for similar items in EconPapers)
JEL-codes: C12 C53 C58 G17 (search for similar items in EconPapers)
Date: 2019-08-19
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error* (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:2019058

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