Value-at-risk backtesting: Beyond the empirical failure rate

Abstract

The quality of Value at Risk (VaR) forecasts is typically determined by the empirical assessment of the frequency of VaR misspecifications. Additionally, the risk of clustered VaR misspecification over time, especially in volatile market times, is usually assessed within a joint testing framework.In this paper, we exclusively focus on the identification of clustered VaR misspecficiations and discuss competing backtesting procedures with respect to their ability to detect inadequate VaR models that are characterized by risk clustering.We present a simulation analysis which comprises different VaR scenarios and we find that the quality of competing backtesting procedures depends on the underlying sample size. Moreover, if sample size is small, it is the parsimonious F-test which describes a sensible choice for applied VaR assessment.