Naïve delusion of fat tails
by Raphael Douady, 2014
Fat tailed models have been introduced in risk management to overcome the insufficiencies of the long-lasted “normal model”, based on Gaussian distributions. But risk management is not simply risk measurement. The principle of fat tails is to enhance the probability of large events (5 to 10 standard deviations) from truly negligible to one or a few percents, in order to enter into VaR calculations.
However, this approach, based on stretching the shape of distributions in order to force them to incorporate observed occurrences that don’t fit into the “normal” model, miss the essential of risk estimation, and therefore of its management: the actual behaviour of markets during a crisis is far different from what can be observed in business as usual situations. Like a crowd in panic rushing through the door when the alarm rings has nothing to do with the same crowd, calmly exiting the room at the end of the show. Yet, the panic behaviour can be anticipated, not by “stretching” the normal one, but by observing the same or other crowds under panic.
When financial markets enter a crisis, a certain number of well known features are observed: different asset classes, which usually are uncorrelated, become correlated, alternative investments, which have been precisely chosen for delivering alpha without beta, suddenly exhibit beta and no alpha at all, etc. Fat tail models, which are mostly calibrated on business-as-usual periods, completely miss these particular features. So-called “robust calibration” is even more of a flawed patch to the problem, as it minimizes the weight of large events in the calibration, when one should, on the contrary, increase it.
The only possible approach to anticipate crises (even small ones) and provide meaningful hedging or risk mitigation recommendations is to use models in which, in order to simulate extreme events, the calibration specifically focuses on the most agitated periods and, more particularly, on those extreme correlations one can observe during these periods. This is the case of nonlinear models used in FOFiX and of the StressVaR as a risk measure.
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