The Richter Scale of Finance

Romain/ juin 4, 2021/ Finance, Science/ 0 comments

In geology, Richter’s magnitude scale is a measure of the strength of earthquakes. Magnitudes are interesting metrics, as they exhibit nonlinear scale behavior. While magnitude 3 quakes would rarely cause damage, magnitude 9 events would lead to severe destruction around the epicenter. In other words, the energy released by an earthquake does not increase proportionally to its magnitude, but exponentially.

Besides, if we classify earthquakes by magnitudes, then the frequency of occurrence is distributed following something close to a power law (meaning that the log chart is a straight line). Thus, around magnitude 3 quakes may occur each year, while there is only one magnitude 9 disaster for decades.

How Nature Works

While this is not big news, it is worth noting that many others natural phenomena display similar behavior (e.g. floods, solar flares, species evolution). Danish physicist Per Bak put forward the concept of self-organized criticality to describe those complex systems [1]. Remarkably, all of them are subject to brutal organizational changes called “avalanches” and displaying power law distributions.

As already mentioned in previous posts, self-organized criticality may not be limited to physical and biological systems, and could actually be a main characteristic of humans-based frameworks such as an economy or financial markets, and probably also of the dynamics of so-called civilizations.

In finance, brilliant researchers like Mandelbrot [2] studied the behavior of asset prices, showing that returns display power-tailed distributions, meaning that the traditional Gaussian distribution should be used to model market dynamics and also that extreme drawdowns may occur more frequently than originally thought. Therefore, the question is are corrections a marker of markets avalanches?

As investors, we are naturally biased towards prices moves and numerous models were designed to anticipate those moves. However, from a pure fundamental perspective, it could be interesting to focus on another that other metric called volatility.

Market Volatility and Earthquakes

That is what I did in a recent paper published by the Hyperion International Journal of Econophysics and New Economy: “There might be a relation between price volatility and the degree of market interactions. A high degree of interactions between agents would imply a higher visibility on prices, and therefore lower fluctuations. Conversely, low visibility would be associated with higher price fluctuations.” [3]

In my opinion, markets naturally self-organize thanks to intersubjective narratives to offset entropic forces. When a dominant narrative vanishes, then visibility is reduced, and as a result the range of price fluctuations increases. In other words, instantaneous volatility spikes, which could be regarded as a form of energy dissipation.

Since instantaneous volatility is a complex concept, I suggest using the VIX index as a proxy for avalanches intensity. Remember that it represents the market’s expectations for volatility over the coming 30 days for the S&P 500. Somehow, an increase of the VIX value indicates that investors are anticipating higher stocks volatility and are willing to protect all or part of their net worth.

In my paper, I computed daily spikes ranging from January 2nd 1991 to October 1st 2019, in order to plot their frequency distribution. And it was interesting to note that those spikes are distributed following a form a power law, like the Gutenberg–Richter law for earthquakes.

This should not come a surprise, but it may confirm the idea that instantaneous volatility could be the real marker of avalanches intensity for self-organized critical markets, rather than price drawdowns. As in geology, it implies that the impact of a financial stress does not increase proportionally to the volatility spike, but exponentially. Moreover, extreme fluctuations regimes are technically possible, even if they will occur rarely (though more often than what a Gaussian law would suggest).

As a VIX compression pattern may end soon (see Sven Henrich’s charts on Northmantrader.com), and given the size of current financial mania, people should bear those results in mind, as the mother of all vol spikes may be around the corner.

[1] Bak, P. (1996) How Nature Works: The Science of Self-Organized Criticality. Copernicus.
[2] Mandelbrot, B., Hudson, R.L. (2004) The (Mis)Behavior of Markets. Basic Books.
[3] Bocher, R. (2020) Self-Organized Critical Markets: Implied Volatility and Avalanche Intensity. Hyperion International Journal of Econophysics & New Economy. 13(2): 45-50.

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