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.

Evaluating value-at-risk models via quantile regression

This article is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christoffersen (1998) and Engle and Manganelli (2004) are based on such variables. In this article we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker and Xiao 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series. © 2011 American Statistical Association