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

Author

Listed:
  • Sander Barendse

    (University of Oxford)

  • Erik Kole

    (Erasmus University Rotterdam)

  • Dick van Dijk

    (Erasmus University Rotterdam)

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.

Suggested Citation

  • Sander Barendse & Erik Kole & Dick van Dijk, 2019. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Tinbergen Institute Discussion Papers 19-058/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:2019058
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    3. Simon Fritzsch & Maike Timphus & Gregor Weiss, 2021. "Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?," Papers 2109.10946, arXiv.org.

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    More about this item

    Keywords

    expected shortfall; backtesting; risk management; tail risk; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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