Abstract : In this study we empirically explore the capacity of historical VaR to correctly predict the future risk of a financial institution. We observe that rolling samples are better able to capture the dynamics of future risks. We thus introduce another risk measure, the Sample Quantile Process, which is a generalization of the VaR calculated on a rolling sample, and study its behavior as a predictor by varying its parameters.
Moreover, we study the behavior of the future risk as a function of past volatility. We show that if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in period of high volatility, the risk measure overestimates the risk, confirming that the current way financial institutions measure their risk is highly procyclical.