John Tye's Reviews > The Misbehavior of Markets: A Fractal View of Financial Turbulence

The Misbehavior of Markets by Benoît B. Mandelbrot
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Aug 20, 11


Like most good books about the markets, Benoît Mandelbrot's The mis Behavior of Markets is not really about trading or making money (although, if it helps you better understand risk, it could save you money--which is essentially the same as making money). In fact, one could almost say the book is about fractal processes, using the markets as a case study. In this way, it is reminiscent of Nassim Nicholas Taleb's Fooled by Randomness, which uses the markets largely as a basis to investigate logical fallacies (and it is not particularly surprising to find blurbs of praise from Taleb on both the front and back covers).

The standard models of finance have been soundly thrashed, and yet they continue to be used because they are easy and convenient. As clever as they may have been, Markowitz and Sharpe and Black and Scholes, et al, were basically financial alchemists. Part of Mandelbrot's point is that their models are not merely inadequate, they so severely underestimate risk as to be catastrophically dangerous--worse than useless, and not improved by adding epicycles. Even if no one except perhaps some hermetic academics believe in the efficient-market hypothesis, typical analysis continues to rely on tools that make assumptions like normal distribution of returns and the applicability of continuous mathematics.

Mandelbrot's work in the area of finance remained, to the time of his death in October 2010, purely descriptive; he never created a model suitable for predicting market behavior. This is a limitation of this work, and one that Mandelbrot himself laments. He writes, "It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease. Financial markets are the machines in which much of human welfare is decided; yet we know more about how our car engines work than about how our global financial system functions.... So limited is our knowledge that we resort, not to science, but to shamans." This is a somewhat strange and emotional outburst, given how much simpler an engine is than a bunch of humans playing high-stakes guessing games. But it gives some indication of the difficulty involved.

One of Mandelbrot's more interesting propositions concerning the markets is that returns can show dependence without correlation, a seeming paradox. But as he explains it, "The key to this paradox lies in the distinction between size and direction of price changes. Suppose the direction is uncorrelated with the past: The fact that prices fell yesterday does not make them more likely to fall today. It remains possible for the absolute changes to be dependent: A 10 percent fall yesterday may well increase the odds of another 10 percent move today--but provide no advance way of telling whether it will be up or down. If so, the correlation vanishes, in spite of the strong dependence." Compellingly, he presents a multifractal model that combines Brownian price changes with fractal time, yielding clusters of volatility strikingly similar to real market behavior.

Clearly, this book is not the key to riches. That might be nice, but it would not be nearly as interesting. This book is more about how the same mathematics that applies to Nile flood levels or the measurement of coastlines can be used to describe the behavior of markets. Read it because you take pleasure in investigating recurring mathematical motifs in the world, not because you are on a single-minded quest to make money.
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