In this study we consider the risk estimation as a stochastic process based on the Sample Quantile Process (SQP) - which is a generalization of the Value-at-Risk calculated on a rolling sample. Using SQP's, we are able to show and quantify the pro-cyclicality of the current way financial institutions measure their risk. Analysing 11 stock indices, we show that, if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in periods of high volatility, the risk measure overestimates the risk. Moreover, using a simple GARCH(1,1) model, we conclude that this pro-cyclical effect is related to the clustering of volatility. We argue that this has important consequences for the regulation in times of crisis.
BRÄUTIGAM, M., DACOROGNA, M. and KRATZ, M. (2018). Predicting Risk with Risk Measures: An Empirical Study. ESSEC Business School.