Title: Pro-Cyclicality Beyond Business Cycles: The Case of Traditional Risk Measurements

Abstract: There is an accepted idea that risk measurements are pro-cyclical: in times of crisis, they overestimate the future risk, while they underestimate it in quiet times. We lay down a simple and efficient methodology to evaluate the amount of pro-cyclicality in the way financial institutions measure risk. To do so, we introduce a new indicator based on the Sample Quantile Process (a dynamic extension of Value-at-Risk), conditioned on realized volatility. Using this framework, we prove that pro-cyclicality is inherent in risk measure estimates based on historical data. We identify two main factors explaining this pro-cyclical behavior: the clustering and return-to-the-mean of volatility, as it could have been anticipated but not yet quantified, and, more surprisingly, the very way risk is measured, even in a world with constant volatility, though the empirical magnitude of the mean-reversion is greater than what would be observed in that special case. We develop CLTs and FCLT’s for functionals of quantile and dispersion estimators to support theoretically those empirical findings. This is a joint work with Dr. Marcel Bräutigam and Dr. Michel Dacorogna.