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Backtesting Value-at-Risk: A Duration-Based Approach

Author

Listed:
  • Peter Christoffersen
  • Denis Pelletier
Abstract
Financial risk model evaluation or backtesting is a key part of the internal model's approach to market risk management as laid out by the Basle Commitee on Banking Supervision (1996). However, existing backtesting methods such as those developed in Christoffersen (1998), have relatively small power in realistic small sample settings. Methods suggested in Berkowitz (2001) fare better, but rely on information such as the shape of the left tail of the portfolio return distribution, which is often not available. By far the most common risk measure is Value-at-Risk (VaR), which is defined as a conditional quantile of the return distribution, and it says nothing about the shape of the tail to the left of the quantile. Our contribution is the exploration of a new tool for backtesting based on the duration of days between the violations of the VaR. The chief insight is that if the VaR model is correctly specified for coverage rate, p, then the conditional expected duration between violations should be a constant 1/p days. We suggest various ways of testing this null hypothesis and we conduct a Monte Carlo analysis which compares the new tests to those currently available. Our results show that in realistic situations, the duration based tests have better power properties than the previously suggested tests. The size of the tests is easily controlled using the Monte Carlo technique of Dufour (2000). L'évaluation des modèles de risque financier, ou test inversé, est une partie importante de l'approche avec modèle interne pour la gestion de risque tel qu'établie par le Comité de Basle pour la supervision bancaire (1996). Toutefois, les procédures existantes de tests inversés telles que celles développées dans Christoffersen (1998), ont une puissance relativement faible pour des tailles d'échantillon réalistes. Les méthodes suggérées dans Berkowitz (2001) performe mieux mais sont basées sur de l'information, telle que la forme de la queue gauche de la distribution des rendements du portefeuille, qui n'est pas toujours disponible. La mesure de risque de loin la plus courante est la Valeur-à-Risque (VaR), qui est définie comme un quantile de la distribution conditionnelle du rendement, et elle ne dit rien à-propos de la forme de la distribution à gauche du quantile. Notre contribution est l'exploration d'un nouvel outil pour les tests inversés basé sur la durée en jours entre les violations de la VaR. L'intuition est que si le modèle de VaR est correctement spécifié pour un taux de couverture p, alors la durée espérée conditionnelle entre les violations devrait être une constante 1/p jours. Nous proposons diverses façons de tester cette hypothèse nulle et nous effectuons une analyse Monte Carlo où l'on compare ces nouveaux tests à ceux présentement disponibles. Nos résultats montrent que pour des situations réalistes, les tests basés sur les durées ont de meilleures propriétés en termes de puissance que ceux précédemment proposés. La taille des tests est facilement contrôlée en utilisant la technique Monte Carlo de Dufour (2000).

Suggested Citation

  • Peter Christoffersen & Denis Pelletier, 2003. "Backtesting Value-at-Risk: A Duration-Based Approach," CIRANO Working Papers 2003s-05, CIRANO.
    • Handle: RePEc:cir:cirwor:2003s-05
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    References listed on IDEAS

    as
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