Some misunderstandings in regards to the Chaos Theory

Chaos Theory, Nonlinear Dynamic as Neural Network technology has been definitely over-evaluated in dot com era of 90s years. This technology has been developed by very bright people (Benoit Mandelbrot, Doyne Farmer and others),  and their work gives a new breath to the stock market analysis.    

It became very popular, and this popularity played a bad joke with this greatest theory. IMHO people try to consider this theory as a myth, a kind of fairy tale. Therefore they use a lot expressions like "nonlinear system", "fractal nature of the market", etc. There is nothing bad in that. Probably, people need to have some myths. Scientific oriented traders look for their Holy Grail in Chaos Theory, while astrotraders look for their Grail in W.D. Gann works. However, Her Majesty Real Life gives us something totally different.

In this small article I will explore some statements of Chaos Theory and their applications.

Fractal Statistics: According to the classical statistics, the 20% or more drop of Dow Jones index can happen once in Eon; in spite of that, traders observed this drop in October, 1987. It was not a pleasant surprise for the scientists. Not pleasant - because a lot of economical/trading models are based on normal distribution, the most widely distribution in Nature. Trying to avoid it, scientists practically do it this way.

They calculate a histogram for daily gains (Dow Jones 1885-2008 yy):

This histogram differs from the normal distribution ("Gaussian bell"), we have a higher peak and - the more important thing - too many points in the "tails" of this distribution. Mandelbrot called them "heavy tails".  \

For traders these "heavy tails" play the role of  Pandora Box. They represent some price events that have not been taking into consideration yet. And this "not taken" territory is much more wider than we would expect (as our expectations are based on common sense, i.e. normal distribution).  Mandelbrot named this kind of distribution "wild randomness" in comparison with "mild randomness" we used to deal with.

The practical recommendation is: "The risk is higher than our common sense tells us". Say if your trading system provides 70 winning signals out of 100, the classical statistical analysis says that with the probability 99.5% this is not an occasional fact (Chi square=8). And with the probability 99.5%, this is 70% win/loss trading system. However, do not believe these digits!!!
Before using such a system in your trading, check it on 300 trades, better on 500 trades (I use 1000) if the price history allows to perform this analysis. This is especially important for developers of different mechanical trading systems.

I would rather believe 55% trading system described by Farmer http://www.cs.brown.edu/research/ai/dynamics/tutorial/Documents/CrackingWallStreet.html

You can read more about financial statistics in this book (it is a very good book, by the way):

"The (Mis)behavior of Markets" by Benoit Mandelbrot;

Fractals (R/S analysis): The typical understanding of the fractal nature of the stock market is something similar to this: "If we look at 5 min S&P price chart and compare it to the daily chart, we can see that both these charts look similar, though on different time scales". R/S analysis provides a research of the price history using different scales. This is how the results of R/S analysis look  (a red curve):

This diagram shows a totally different thing: the behavior of the stock market is different on different time scales. If it would be the same, we would get a straight red line. However, it is curved. It means that this financial instrument (FTSE in our example) follows different patterns in  different scales (time frames). 

Some information regarding R/S analysis can be found here: http://www.timingsolution.com/TS/Articles/Chaos/chaos_ts.htm . And I recommend this book:

"Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility" by Edgar E. Peters.

Regarding financial statistic this book is very well:

"The (Mis)behavior of Markets" of Benoit Mandelbrot;

December 10, 2009

Toronto, Canada

Sergey Tarasov./