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

TL;DR

This paper develops a methodology to quantify and analyze the sources of pro-cyclicality in risk measurement practices, focusing on the impact of volatility clustering and measurement methods.

Contribution

It introduces a new indicator based on Sample Quantile Process to measure pro-cyclicality and identifies key factors influencing it, including measurement approach and volatility behavior.

Findings

Pro-cyclicality varies across different stock indices.

Volatility clustering significantly contributes to pro-cyclicality.

Measurement methods independently affect pro-cyclicality.

Abstract

Since the introduction of risk-based solvency regulation, pro-cyclicality has been a subject of concerns from all market participants. Here, we lay down a methodology to evaluate the amount of pro-cyclicality in the way finnancial institutions measure risk, and identify factors explaining this pro-cyclical behavior. We introduce a new indicator based on the Sample Quantile Process (SQP, a dynamic generalization of Value-at-Risk), conditioned on realized volatility to quantify the pro-cyclicality, and evaluate its amount in the markets, considering 11 stock indices as realizations of the SQP. Then we determine two main factors explaining the pro-cyclicality: the clustering and return-to-the-mean of volatility, as it could have been anticipated but not quantified before, and, more surprisingly, the very way risk is measured, independently of this return-to-the-mean effect.