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Since the introduction of risk-based solvency regulation, pro-cyclicality hasbeen a subject of concerns from all market participants. Here, we lay down amethodology to evaluate the amount of pro-cyclicality in the way finnancialinstitutions measure risk, and identify factors explaining this pro-cyclicalbehavior. We introduce a new indicator based on the Sample Quantile Process(SQP, a dynamic generalization of Value-at-Risk), conditioned on realizedvolatility to quantify the pro-cyclicality, and evaluate its amount in themarkets, considering 11 stock indices as realizations of the SQP. Then wedetermine two main factors explaining the pro-cyclicality: the clustering andreturn-to-the-mean of volatility, as it could have been anticipated but notquantified before, and, more surprisingly, the very way risk is measured,independently of this return-to-the-mean effect.

Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source