The Impact of the Choice of Risk and Dispersion Measure on Procyclicality

TL;DR

This paper investigates how the choice of risk and dispersion measures, along with model assumptions, influences the procyclicality of risk estimation, showing that procyclicality persists across different configurations.

Contribution

It systematically analyzes the impact of various risk measures, volatility estimators, and models on procyclicality, highlighting its persistent nature regardless of choices.

Findings

Procyclicality strength varies with risk measure, volatility estimator, and model.

Procyclicality is always present, regardless of the specific measures or models used.

Different combinations influence the degree but not the existence of procyclicality.

Abstract

Procyclicality of historical risk measure estimation means that one tends to over-estimate future risk when present realized volatility is high and vice versa under-estimate future risk when the realized volatility is low. Out of it different questions arise, relevant for applications and theory: What are the factors which affect the degree of procyclicality? More specifically, how does the choice of risk measure affect this? How does this behaviour vary with the choice of realized volatility estimator? How do different underlying model assumptions influence the pro-cyclical effect? In this paper we consider three different well-known risk measures (Value-at-Risk, Expected Shortfall, Expectile), the r-th absolute centred sample moment, for any integer $r>0$, as realized volatility estimator (this includes the sample variance and the sample mean absolute deviation around the sample mean) and two models (either an iid model or an augmented GARCH($p$,$q$) model). We show that the strength of procyclicality depends on these three factors, the choice of risk measure, the realized volatility estimator and the model considered. But, no matter the choices, the procyclicality will always be present.