Evaluating power of Value-at-Risk backtests

Abstract

Value-at-Risk (VaR) models provide quantile forecasts for future returns. If a loss is greater than or equal to the corresponding VaR forecast, we have a breach. A VaR model is usually validated by considering realized breach sequences. Several statistical tests exist for this purpose, called backtests. This paper presents an extensive study of the statistical power for the most recognized backtests. We simulate returns and estimate VaR forecasts, resulting in breach sequences not satisfying the null hypothesis of the backtests. We apply the backtests on the data, and assess their ability to reject misspecified models. The Geometric conditional coverage test by Berkowitz et al. (2011) performs best. A minimum amount of observations is needed to make inference with satisfying power. A sample size of 250 data points, which is the minimum requirement set by the Basel Committe on Banking Supervision (2011), is not sufficient. The common implementation of the Dynamic Quantile test, by Engle and Manganelli (2004), has a too high rejection rate for correctly specified VaR models.