Fractal Market Analysis: Applying Chaos Theory to Investment and Economics (Wiley Finance) [Hardcover]

Edgar E. Peters wasn't satisfied with the Efficient Market Hypothesis (EMH). With the publication of his first book, Chaos and Order in Capital Markets, John Wiley & Sons, New York, 1991, he went public with his concerns about its underlying assumptions and with its empirical shortcomings. That book, a manifesto really, was followed last year by Fractal Market Analysis: Applying Chaos Theory to Investment & Economics (FMA). Where his first book broke ground, FMA has laid the foundation of a new conceptual infrastructure of capital markets.

Risk From The Past

Much of Peters argument is based on two things: one hundred three years of daily Dow Jones Industrial Average data, and Rescaled Range (R/S) analysis. He begins FMA by demonstrating that capital market returns in the United States are not a truly random walk. Instead, he contends they are a biased random walk and indicate a long memory process; they are persistent. Specifically. he characterizes their short term behavior (less than 1,200 days) as a stochastic nonlinear process and their long term behavior as a nonlinear dynamic, or chaotic, process. As a result, he enlarges the definition of risk to include a phenomenon he discovered about persistent processes: they are mirrored by antipersistent ones. If persistent processes are less random than random ones, antipersistent processes reverse themselves more often than random ones. An early insight due to this discovery is that risk in not merely the deviation from an expected value, viz., standard deviation, but the velocity of the second difference of price changes.

Peters offers the Stable-Levy, or fractal, frequency distribution as a more faithful representation of capital markets. When two key variables are fixed at certain levels, the normal distribution becomes a special case of fractal distributions. To hear that the random walk is a special case should be no more surprising than to hear that visible light is a special case of the electromagnetic spectrum. It is not so much a matter of losing something; instead, vast amounts of knowledge remain invisible as long as the old assumption remains intact and tools tuned to the different frequencies remain undeveloped. Instruments tuned to gamma, X-ray, infrared, and radio frequencies have shown astronomers far more about our universe than the special case of visible light ever could.

Both these facts, that finance time series are not random and that the Gaussian assumption is a special case of fractal distributions, suggest that:

1. major rethinking about risk and diversification is necessary,

2. new statistical tools need to be created, and

3. very exciting discoveries are in store for us.

Risk in the Present

While examining the same historic data at different time scales, Peters made another discovery. He found that the frequency distributions of investment horizons ranging from 1-day to 90-day intervals had the same shape. As a result, he concluded that capital markets do not have a characteristic time scale (an important attribute of fractal systems). Instead, he suggested that this phenomenon represented what he called "self-similar risk."

In Peters' view, investors don't struggle against each other trying to attain an above average rate of return (at the expense of the seller) as much as they sustain each other and diversify each other's risk by keeping the market liquid. As long as long-term investors remain long-term investors, they are willing to step in and buy securities that are unwanted by traders on shorter investment horizons.

Risk of the Future

In spite of the highest discipline, crashes happen. The EMH demurs. Crashes and stampedes are not efficient concepts. Copernicus had a similar problem. By placing the Sun at the center of the solar system, he was able to explain the wandering behavior of the planets-except for Mars.

The EMH finds itself in a similar predicament. As long as it clings to its simplifying assumptions like a jealous lover, it will never be able to explain why crashes and stampedes happen. The FMH, on the other hand, not explains why, it begins to construct a world view which explains how they happen, as well.

In the long term, Peters conjectures, capital markets behave like nonlinear dynamic systems. Their time series have all the requisite attributes; among them, sensitivity to initial conditions, and a fractal dimension. In addition, through the use of R/S analysis, Peters can identify the nonperiodic cycles, known in chaos theory as attractors, so characteristic of chaotic systems.

It may be this latter feature that will have the greatest impact on our understanding of risk and our techniques to minimize it. Though he does not explicitly suggest it in Fractal Market Analysis, he has speculated in earlier papers that sufficient understanding of the nonlinear dynamics of capital markets may provide a theoretic basis for market timing and tactical asset allocation.

Final Thoughts

I conclude this review with a few of my own comments about risk.

First, we risk making two types of errors when faced with a new and provocative world view. Type I: We too quickly appropriate a new idea or theory. Type II: We too quickly dismiss a new idea or theory. With Type I errors we agree without understanding; with Type II: we disagree without appreciating. The former is naive, the latter is insolent. With Type I errors we are not fully utilizing our critical faculties; with Type II errors we are forgetting our intuitive. Ignorance is non-market risk. We have an obligation to our clients to diversify it away, and the best way to do that is with an open and critical mind.

Finally, at the risk of overstating it, I would have to describe both of Peters' books as inspired. I say that because they not only informed me, they enlightened me. They changed the way I see the world, and they affected me at an emotional level. I have never before encountered a book at once so intellectually demanding and accessible. For me, the measure of a great book is taken in the number of times I return to it and the degree of new understanding each reading yields for me. In my library, Peters has few peers.

Readers interested in a more in-depth discussion of Fractal Market Analysis can find it on the World Wide Web at http://www.oara.org/mpc/fma/.

Michael P. Corning is the Quality Assurance Officer at Chuck Jones & Associates, Inc., Portland, Oregon. The opinions expressed in this review are his alone and not necessarily those of Chuck Jones & Associates, Inc.

This review was taken from a complete review first published in the Journal of Financial Planning, October, 1995.

The book also contains statements which are simply untrue. For example (p.19) The author claims that "Upon discovering this 'statistical memory' (inherent in a game of single-deck blackjack), casinos responded by using multiple decks, ... thus eliminating the memory". This is simply wrong, the statistical memory still exists in multiple-deck blackjack, and is exploited by blackjack players every day.

Even worse, the "Fractal Market Hypothesis" itself is stated in such a general and ill-defined manner that you may be left wondering what exactly the hypothesis is. There are certainly problems with the traditional efficient market hypothesis, but this is no excuse for mystical hand-waving about "fractals".

The useful information in the book could be written in a pamphlet of a few pages at most. Good luck.