The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward

By Benoit Mandelbrot and Richard L. Hudson
Perseus, 2004
328 pages, $27.50

The Sterling Professor of Mathematical Sciences at Yale University, Benoit Mandelbrot, is a mathematical genius who has transformed our understanding of nature with his work on fractal geometry. Now, together with Richard L. Hudson, former managing editor of the Wall Street Journal’s European edition, he turns his powerful analytical skills on markets and how they behave, or rather, don’t behave. In The (Mis)behavior of Markets, the two men challenge the fundamental assumptions that underpin modern financial theory. Their objective is bold; they want to change the way people think and to reform practice.

Modern financial theory, Professor Mandelbrot and Mr. Hudson contend, seriously underestimates risk. To support their case, they use evidence both from Professor Mandelbrot’s studies of long-term prices for commodities like cotton and from recent volatile episodes in financial markets. Among the most notorious of recent examples is the 1998 failure of Long-Term Capital Management LP, which, after several years of stellar returns, collapsed when Russia defaulted on its bonds and the fund was unable to liquidate its positions.

According to modern finance theory, which looks at risk through the lens of the normal, or bell curve, distribution, the probability of an event like Russia defaulting on its debt was infinitesimal. Yet it happened. Professor Mandelbrot and Mr. Hudson argue that the reason such events occur more frequently than theory predicts is that the assumptions of modern finance theory are not borne out in the real world of financial markets.

The mathematics supporting the authors’ conclusions are arcane and the statistical evidence is complex, but they have done a fine job of making their arguments and evidence accessible to the lay reader. Risk management has been a hot topic in both the corporate and financial worlds recently, and, for many practitioners, modern financial theory has been an article of faith on which their risk management strategies have been built. It is a disturbing (and heretical) thought that the elegant mathematics of risk and the precision of risk measurement might be dangerous illusions.

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