Reviewed by Robert F. MulliganTitle: "Chaos and Order in the Capital Markets: A New View of Cycles, Prices and Market Volatility" Second EditionAuthor: Edgar E. PetersLength: 288 pagesPrice: $65.00Reading time: 15 hoursReading rating: 3 (1=very hard, 10=very easy)Overall rating: 4 (1=average, 4=outstanding)

*Special to the Asheville
Citizen-Times*

When the first edition of "Chaos and Order in the Capital Markets" came out in 1991 it was hailed as the manifesto of a new breed of market analysts. Author Edgar E. Peters is a leading practitioner of innovative fractal market analysis based on the work of such legends of chaos theory as Ilya Prigogine and Benoit Mandelbrot. Peters puts this theory into practice at PanAgora Asset Management, a distinguished quant firm managing about $15 billion.

The first edition was so popular and influential, (and contained so many typographical errors in mathematical equations,) a second edition was clearly called for. Although much is retained from the first edition, the new edition is clearly a better book in every respect.

The book is organized in four parts, with the fourth being largely new to the second edition. Part One, The New Paradigm, motivates the need for fractal analysis in studying financial markets. Thorough discussions of shortcomings of the conventional Efficient Market Hypothesis and Capital Asset Pricing Model are presented.

Part Two, Fractal Structure in the Capital Markets, introduces one of the basic tools of fractal analysis - Mandelbrot's rescaled range or R/S analysis. Benoit Mandelbrot, famous for dazzling computer-generated pictures of the Mandelbrot set, is surely one of the most remarkable people of this or any other century. A true Renaissance man, he has enjoyed highly successful careers as an economist, physicist, mathematician, computer theoretician, and medical doctor! R/S analysis of a time series looks at the ratio of the range of the series (the difference between the largest and smallest values observed up to each point in time) "rescaled" by dividing the range by the standard deviation. Both the range and the standard deviation are recalculated for each observation in the series, including all earlier values, but not later ones. This section introduces the Hurst exponent, a measure of volatility which is lower and closer to 0.5 the riskier a financial asset.

Part Three, Nonlinear Dynamics, gives examples of calculating the fractal dimension of a series and estimating the Lyapunov exponent. This section also discusses various kinds of strange attractors financial asset behavior might mimic. Some of the insights fractal analysis might give to setting up a simulation or forecasting model are discussed. The fractal dimension of a variable indicates how many other variables should be included in a model, though unfortunately, it gives no indication of what those variables might be!

Part Four, Living with Complexity, is almost entirely new for this edition and includes particularly interesting discussions of new forecasting models and various approaches several leading financial management firms, including Peters' own PanAgora, have taken in including fractal analysis in their simulation and portfolio optimization practices.

This book is highly recommended for anyone desiring a basic knowledge of cutting-edge financial analysis. Though very clearly written considering the high theory content, readers must understand standard deviations and time series variables. Knowledge of least-squares regression, the Capital Asset Pricing Model, and the Efficient Market Hypothesis is helpful though not necessary.

*Robert F. Mulligan is visiting assistant professor of economics,
finance, and international business in the College of Business at Western
Carolina University. His research interests are monetary and international
economics and he is a fierce fan of Clarkson University and ECHL ice hockey.
For previously reviewed books, visit our web site at www.wcu.edu/cob/bookreviews/.*