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6 Billion Years is About Half the Age of the Universe

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Statisticians talk about rare events in terms of tails...

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What if something that was expected to happen once every 6.6 billion years just happened? Would you be stunned? Entertained? Perplexed? Would it cause you to purchase a lottery ticket in the hopes that rare events happen in clusters ("in threes" seems to be a heuristic my mom always believed)?

Statisticians talk about rare events in terms of tails – they look at the distribution of events around a mean derived from the historical record or from theory – and place each event within that distribution. Far to the left or right of the average (or mean) event and you get that slightly illicit term: fat tails.

Here is a distribution of the Shanghai Index daily returns since its 2002 inception. The red line to the left is last night's return data point. And that red line represents a 1 in 6.6 billion year event.

A 1 in 6.6 billion year event? Yeah, you can consider that a fat, nay obese, tail. A tail choking on trans fats, white flour, and refined sugars.

In a Buzz entitled Shanghai Monkey, I wrote that my firm's complexity models had come to the conclusion that the Shanghai index was showing approximately 70% of the critical instability of the Nasdaq 100 in the lead up to the NDX's 2000 peak. The macroeconomic implications of the conclusion – that the Shanghai index was set to fall significantly – remain the same (read: dire) as they did then. So again, watching this index for its implication on the mercantilist relationships between China and the US remains very important.

But more to the larger point is this: last night's Shanghai index decline brings into full relief one of the central tenets of my firm's theory of markets as complex adaptive systems: that the statistical signature of actual market returns is nowhere close to the theoretical market return distribution that efficient market theorists cling to. And that this gap between the efficient market hypothesis theory and the actual market statistical fingerprint must be addressed both theoretically and mathematically. Complexity, I believe, hits both of those birds with one stone.
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