Fractal Market Analysis: Applying Chaos Theory to Investment and Economics.

Since its introduction in 1953 by Maurice Kendall, what came to be called the Efficient Market Hypothesis (EMH) assumed the mantle of religious orthodoxy -- anyone who suggested the markets might behave otherwise was often labeled a quack.

Yet the efficient marketeers could never explain

why markets make more large price changes relative to small ones than the efficient model predicts. The "fat tails" of the distribution of price changes cast a nettlesome shadow of doubt on the EMH, and also on the accuracy of popular options pricing models which assume log-normal distributions.

With efficient market doctrine in question, students have been seeking a better answer, and have embraced chaos theory as a likely candidate. Edgar E. Peters, an investment counselor with PanAgora Asset Management, is no mere academic -- with a $4.5 billion portfolio the author is grounded in market reality.

Fractal Market Analysis, the sequel to Chaos and Order in the Capital Markets, is an excellent technical elaboration of the concepts presented and answer to questions provoked in the first book. For readers tantalized by the charts of long-term memory effects in monthly S&P returns, and frustrated by the lack of sufficient explanation to duplicate them, this book should be an automatic buy.

A characteristic of "chaotic" systems is they exhibit a self-similarity over several dimensions, including space and time. Peters notes the "fat-tailed" profile of market price changes is self-similar over many time scales -- from 10-minute to monthly price changes. This "fractal" aspect of markets makes them candidates for chaotic systems analysis techniques. He applies a technique called rescaled-range (R/S) analysis used by a hydrologist to study non-periodic but cyclical flooding of the Nile River.

Peters includes an interesting chapter on historical and implied volatility. Where in other chapters Peters demonstrates that markets trend -- or are more persistent than a random model would assume -- here he shows that market volatility is more anti-persistent, and reverses direction more than a random model predicts -- a fact most volatility traders would intuitively confirm.

In addition to a step-by-step (albeit heavily mathematical) explanation of how he applies these techniques to market data, Peters provides an appendix of computer code in a language called GAUSS as an example of how to implement the techniques.

Whether or not chaos will put order into your trading regime remains an open question, but Peters guides you down some interesting pathways and opens your mind to new realms of market analysis.