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FINANCIAL PHYSICS

Recent studies in chaos theory and critical states have provided us with what may very well be a valuable insight into the cause (or causeless cause) of major market disruptions.

Imagine a flat surface where grains of sand are dropping, one after the other at a moderate pace. In time, a sand pile builds up, and slowly the sides of the sand pile get steeper.

This steepening continues until it reaches what is called a critical state. At the critical state, many grains rest on the verge of tumbling, and those grains link up into so-called fingers of instability of all possible lengths.

While many are short, others slice through the pile from one end to the other. So the chain reaction triggered by a single grain might lead to an avalanche of any size whatsoever, depending on whether that grain fell on a short, intermediate or long finger of instability.

In essence, the sand pile slowly evolves into self-organization, that is, the sand pile would eventually reach a point where it was predisposed to have an avalanche. These avalanches serve to relieve the strain and tension that have built up in the sand pile, enabling the system to return to stasis and further growth.

What makes one avalanche much larger than another has nothing to do with its original cause, and nothing to do with some special situation in the pile just before it starts. It only has to do with the perpetually unstable organization of the critical state, therein making it always possible for the next grain to be the trigger of an avalanche of indeterminate size.

A key point here is that large avalanches are part of the normal course of events, something that is to be expected, and something that does not need to have some significant cause. A cataclysmic avalanche can be started by a single grain of sand, the last straw that breaks the camel¡¯s back, so to speak. 

What does any of this have to do with the stock market?

Financial physics reminds us not only of the impossibility of forecasting the timing, but of the impossibility of forecasting the magnitude of the adjustment as well. What this implies is that any use of modeling as a forecasting tool for the correction is of questionable value. Modeling looks at what has been and projects what might be. The problem, according to critical theory, is that modeling does not consider what hasn't been when it creates its forecast.

For example, for over 100 years (from 1886 to 1988), the largest forest fire in Yellowstone National Park consumed approximately 25,000 acres. As such, the prevention model was built around a forest fire never consumes more than 25,000 acres. Then, along came the Shoshone Fire in 1988 which consumed 1,500,000 acres.

The same flawed modeling applies to the market as well. Prior to October 19, 1987, the largest single day percentage loss in the Dow Jones Industrial Average had been 6.5% on September 26, 1955. As such, trading strategies were built to reflect the market never loses more than 6.5% in a day. Then came October 19; the Dow fell 22.6%, blowing the model away and changing many lives forever.

Are we guilty of repeating the same mistake by believing the market can never lose more than 22.6% in a day? Who can say........but here's a clue.

Beginning in 1890, the U.S. Bureau of Land Management adopted a policy of zero-tolerance toward every forest fire that arose, regardless of its size. Each fire was to be extinguished as quickly as possible. In 1998, studies done by a team of geologists found that although the frequency of meaningful fires was reduced by this policy, there was a marked tendency toward catastrophic fires, fires that consumed entire forests. It was understood that this Yellowstone Effect was brought about because the forests were not allowed to relieve stress to the self organized system and thereafter return to balance. BLM readily admits that increasingly, over time, wildfires have become more severe and difficult to control.

The 2001-05 compound annual rate of growth for our stocks simulation is 42.2% whereas the S&P 500 had negative growth for the period. Through Sep 2006, performance was a gain of 13.3%. Learn more here.

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