The Misbehavior of Markets: A Fractal View of Financial Turbulence

The Misbehavior of Markets: A Fractal View of Financial Turbulence

Benoit Mandelbrot, Richard L. Hudson

Language: English

Pages: 368

ISBN: 0465043577

Format: PDF / Kindle (mobi) / ePub


Mathematical superstar and inventor of fractal geometry, Benoit Mandelbrot, has spent the past forty years studying the underlying mathematics of space and natural patterns. What many of his followers don't realize is that he has also been watching patterns of market change. In The (Mis)Behavior of Markets, Mandelbrot joins with science journalist and former Wall Street Journal editor Richard L. Hudson to reveal what a fractal view of the world of finance looks like. The result is a revolutionary reevaluation of the standard tools and models of modern financial theory. Markets, we learn, are far riskier than we have wanted to believe. From the gyrations of IBM's stock price and the Dow, to cotton trading, and the dollar-Euro exchange rate--Mandelbrot shows that the world of finance can be understood in more accurate, and volatile, terms than the tired theories of yesteryear.The ability to simplify the complex has made Mandelbrot one of the century's most influential mathematicians. With The (Mis)Behavior of Markets, he puts the tools of higher mathematics into the hands of every person involved with markets, from financial analysts to economists to 401(k) holders. Markets will never be seen as "safe bets" again.

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name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.” Before Poincaré on that day in 1900 was one of his doctoral students, Louis Bachelier.1 Jobs for Ph.D.’s were scarce; and so the award of a doctorate in France was a formal, trying process. The young mathematician’s schooling had been mediocre, at best. Now he had to pass two final tests before Poincaré and the doctoral “jury.” The lesser one was an oral

“Bachelier was blackballed,” as Lévy ruefully recalled years later, in correspondence with me. By then, Lévy regretted the incident. He had read only the passage highlighted by Gevrey rather than the entire treatise; and in the full context of Bachelier’s work the error appears benign. Lévy later apologized to Bachelier that “an impression, produced by a single initial error, should have kept me from going on with my reading of a work in which there were so many interesting ideas.” Apologies

earlier. Something unusual develops as you use ever-smaller rulers: The length you measure is growing faster than the rulers are shrinking. And that phenomenon is measured by a quantity called fractal dimension. Begin simply. For a straight line, the fractal dimension is 1. And one dimension is exactly what we expect a straight line to have. But the British coastline, it turns out, has a fractal dimension of about 1.25. Does that make sense? Certainly. A rugged coast is more intricate than a

same direction; in other words, price changes can run in long streaks of positive values—or, conversely, negative. Here, H = 0.9. The top chart shows the opposite phenomenon: once pointed one way, the motion will tend to reverse and head the other way. Here, H = 0.1. It is a peculiar property of most long-memory processes that seeming patterns arise and fall, appear and disappear. They could vanish at any instant. They have no real permanence. They cannot be predicted. Look again at the

size or direction. The changes can be persistent, meaning that they reinforce each other; a trend once started tends to keep going. Or they can be anti-persistent, meaning they contradict each other; a trend once begun is likely to reverse itself. The persistent variety, especially those with an H exponent near 0.75, are especially curious, and these are the type common to many financial and economic data series. In our research in the late 1960s, Wallis and I generated such records by the purest

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