Comment: Stop Looking for Reason at the Edge of Chaos

Is it time to buy gold or flee to cash? With all of the hyperbole in the market on Friday following the 500 point fall in the Dow Jones Industrial Average on Thursday, and heavy selling in Asia and Europe Friday, the answer might be bottled water, tinned food and shovels.

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In between talking up the most recent crisis, market watchers are puzzling over a good reason as to why it happened.

Some analysts and commentators  speak of a "perfect storm"—a devastating combination of economic, political and market factors.

But fundamentally, what changed? The persistent economic and financial stresses in developed markets seem to have moved on incrementally, if at all, in the past couple of days, after the relief of the successful conclusion of the U.S. debt talks.

There was no sudden revelation to alter sentiment. What did we know on Thursday that we didn’t know on Wednesday? The answer: very little.

European banks were hoarding cash ahead of the European Central Bank (ECB) meetings on Thursday, but whether that really should be seen as a lead indicator for a market slump, or an indication of anything except vague doubt over what president Jean-Claude Trichet might say as he winds down his tenure, is far from certain.

The ECB's press conference Thursday saw Trichet give some support to the markets by indicating that the bank would provide a degree of bridging liquidity ahead of the creation of the European Financial Stability Facility (EFSF).

Some in the markets might believe these measures, and the EFSF's ultimate levels of capitalization, were insufficient. However, given that European crisis resolution is and has been a piecemeal approach, with policymakers staggering from proximate step to proximate step while commentators shout "crisis," the notion that a not-quite-perfect promise from the ECB could spook a market already desensitized to the likelihood of Greek default is mildly absurd.

The increasing primacy and muscle of Germany in euro zone decision making, the partial fiscal integration promised by the EFSF and the acknowledgement - many months late - by the Italian prime minister that his country has to deal with market pressures all hint at an eventual resolution to some of the longer term problems of currency union.

A better-than-expected U.S. nonfarm payrolls report provided some salve for the markets, but the Bank of Japan's intervention on Wednesday could have led to margin selling. But surely neither of these factors should really be large enough to spark this kind of sell-off.

London had two bright, hot days on Tuesday and Wednesday, but heavy rain broke the spell on Thursday. Could that have done it?

The answer, sadly, is yes to all.

For this analysis, we can look back to a 1994 monograph with the Amazon-friendly title of "Nonlinear Dynamics and Predictability of Geophysical Phenomena." More specifically, one paper within that: "Self-Organized Criticality: Consequences for Statistics and Predictability of Earthquakes," written by the physicists Kim Christensen—who among his other accolades used to lecture me in my university days—Per Bak and Zeev Olami.

Bak, along with Chao Tang and Kurt Weisenfeld, evolved an experiment that has considerable rhetorical and mathematical significance.

By piling sand grains, one on top of the other and continually dropping more, they found that at a certain level of complexity—when the system had enough "degrees of freedom"—every further grain of sand led to an avalanche on the side of the pile. The number of dislodged grains could be as small as one, or it could be the total collapse of the pile. The point: The stimulus was the same, but the response could vary wildly, a phenomenon known as "scale invariance."

This point of complexity is sometimes referred to as "the edge of chaos," and the Bak-Tang-Weisenfeld sand pile is a common entry point into chaos theory for students.

"Nonlinear Dynamics and Predictability of Geophysical Phenomena" takes the sand pile a step forward and notes that on the same principle, looking at the distribution of tiny seismic events, the probability distribution of larger seismic events can be derived and the likelihood across a given time period demonstrated.

Markets, like meteorology and seismology, are fractal in nature. The mathematician Benoit Mandelbrot observed that in the 1960s.

What does this mean? It means that you can infer that from every small avalanche in the markets the likelihood—even inevitability—of a big collapse. We could even derive what it would look like. And the trigger of that collapse would be no different in scale than the day to day that shifts markets up and down.

The problem is never the events, it is the structure of the system. Fixating on the panic around those events is missing the point.

Looking to ascribe a causal link to all of these factors simply does not give any salve to the fact that the market was at the edge of chaos, and looking for something "big enough" to push it over that edge is a futile exercise.

More importantly: If there are no fundamental reasons for the scale of the sell-off, perhaps there isn't a new crisis after all.