Evaluating Value-at-Risk Models via Quantile Regressions

We propose an alternative backtest to evaluate the performance of Value-at-Risk (VaR) models. The presented methodology allows us to directly test the performance of many competing VaR models, as well as identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Quantile regressions provide us an appropriate environment to investigate VaR models, since they can naturally be viewed as a conditional quantile function of a given return series. A Monte Carlo simulation is presented, revealing that our proposed test might exhibit more power in comparison to other backtests presented in the literature. Finally, an empirical exercise is conducted for daily S&P500 return series in order to explore the practical relevance of our methodology by evaluating five competing VaRs through four different backtests.