Wednesday, March 3, 2010

Revisiting Mandelbrot

I’ve just finished re-reading one of the best books written about market prices and financial theory. The book is THE (MIS)BEHAVIOR of MARKETS by Benoit Mandelbrot and Richard L. Hudson. Mr. Mandelbrot is truly a remarkable man. Most people know him as the founder of fractal geometry and perhaps by the famous fractal image of The Mandelbrot Set. His work has been applied in a variety of sciences and disciplines ranging from astronomy, physics, biology, linguistics, mathematics, turbulence theory and many others. What many people do not associate with him, however, is the study of market prices and market structure theory. This book describes all his ideas of how markets (mis)behave and calls for new theories and ways of thinking about market prices for the future.

Mr. Mandelbrot’s ideas shake the foundations of some of the standard theories of finance we were taught in school; such as random walk, normal bell curve distributions, the Black-Scholes option pricing model, and CAPM. The following paragraph seems to best summarize all his ideas:

“the market has the turbulent parts that scale up to echo the whole. It has a multifractal spectrum that characterizes the scaling. It has a long term dependence so that an event here and now affects every other event elsewhere and in the distant future. It shows turbulence in a wild kind of variation far outside the normal expectations of the bell curve; in a concentration of changes here and there; in a discontinuity in the system jumping from one value to another; and in one set of mathematical rules that can, in large measure, describe it all.”

After reading this book I cannot help feeling how I used to feel when I listened to all my professors in business school. I never agreed with what they were teaching us. I think the current financial crises can, in some way, be attributed to those who did buy into those ideas. It is clear to me that Mr. Mandelbrot’s ideas will need to be considered as the basis for new theories in finance and financial markets as we move forward.

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