Chaotic Attractor in the Markets

One of the members of Long Term Capital Management, Myron Scholes (of Black-Scholes fame) was a student of Eugene Fama, author of the Efficient Markets Hypothesis in 1965. LTCM worked well for many years when the markets were steady and predictable, but failed when a number of 4 or 5 sigma events hit, destabilized their models and sent the whole thing to hell in a hand basket. In Scholes defense, the 4 sigma events should have happened only once in 5000 years, so he made a pretty good bet. That said, there were anomalies in their data which should not have occurred in the history of the universe if the Central Limit Theorem held. One might conclude then that the CLT does not hold and only the weak-EMH holds (if at all).

However, with a lot of non-linear dynamics and fractal math behind me, I can't help but see these kind of high-sigma events not so much as a refutation of the EMH (which it obviously is), but as evidence that there is a low-order chaotic attractor in the markets. With some knowledge of what that attractor looks like, one might be able to do a little better than the EMH in building a model that works in the stable times and squeaks loudly when it sees the influence of an attractor. It obviously wouldn't work *during* the phase change, but it would let you know quite a bit beforehand that the part of the phase space the market was entering was known to be chaotic. It also would not tell you if, during a particular week, the change was going to happen or it was going to miss, i.e. is it really unstable or merely soon-to-be unstable, but it would be better than what currently exists.

Fama's refutation of the critiques of the EMH is here and worth a read, in part because it's not persuasive. Basically he says that EMH is the best we have, so it must me right. I think it's only partly right and it's possible to do better.

I am also, BTW, certain someone else has looked for the attractor in the markets, but I want to see how far I get before going to look up the answer.