# Understanding Procyclicality

« The major mistake made in 2010 was imposing austerity at the worst moment ». Gilles Moëc (Chief Economist at AXA), Le Monde, January 21st, 2020

Procyclicality (i.e.the tendency of risk measurements to overestimate future risk in times of crisis, while underestimating it in normal times) is a major problem that all financial institutions must manage: insurance companies, banks, regulatory bodies… As a result, they are required to provide substantial capital in the aftermath of a financial crisis, but far less capital prior to such crises. Hence Gilles Moëc’s warning.

In a recent paper that is published online by Mathematical Finance, our PRS colleague Michel Dacorogna and co-authors Marie Kratz and Marcel Bräutigam from the ESSEC Business School, tackle this question from another angle, namely that of the procyclicality of the risk measure estimation, and examine the two following issues: How can we quantify procyclicality? How can we explain it?

In this study, taking a statistical point of view, they examine the possibility that the way of estimating capital requirements using risk measures (such as VaR and ES) is a possible source of procyclicality. Starting from this very concrete question, they study it both empirically and theoretically, going back and forth between these two approaches, in order to mathematically validate (or disqualify) the empirical facts they discovered.

They developed a methodology to quantify the procyclicality, using a new indicator called the “look-forward ratio” that compares (a posteriori) the estimated capital requirements with the actual capital that would have been required if we knew the future. The practical advantage of this method of backtesting the accuracy of risk predictions is that it measures unambiguously the degree of under- or over-estimation of the risk-adjusted capital. If the predicted risk is close to the actual risk one year later, the ratio will be around 1. Otherwise, it will be either less than 1 (if the prediction was too conservative) or greater than 1 (if the risk was underestimated).

This indicator is then analyzed conditioned to the current market situation. To determine the state of the market, they use the volatility, as the realized volatility is high in times of crisis and low otherwise. This allows to identify two main factors that explain procyclicality: (i) the clustering and mean reversion effect of volatility, caused by fluctuations in the macroeconomic cycle (as expected) and highlighted by GARCH models and, more surprisingly, (ii) the very way in which risk is measured, even in the case of independent variables, i.e., independent of market cycles!

The graph below illustrates clearly their finding by plotting the average behavior of the capital requirement (in terms of the look-forward ratio based around 1) as a function of the state of the market (in terms of its volatility in ascending order from 1 to 10 on the basis of 11 stock market indices of the major economies).

We can clearly observe and quantify the effect of procyclicality in this graph. Indeed, for low volatilities, i.e., in "normal" times, we observe a look-forward ratio greater than 1. This indicates an underestimation of capital (shown in orange), which can be over 40% for very low volatility. In contrast, in times of crisis, which come with high volatilities, the capital required from institutions is overestimated (look-forward ratio less than 1). The excess (represented by the striped pattern) can be as high as about 30% of the capital required – and all this while companies and institutions have to face up to the crisis...

Details on this research is available at this web address: http://doi.org/10.1111/mafi.12369

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