The Economic Crisis and Fractals

This is cool (if you're a dork):

One of those long-time market watchers is fractal pioneer Benoit Mandelbrot. In 1999, Scientific American published an article by Mandelbrot that showed how fractal geometry can model market volatility, while revealing the intrinsic deficiencies of a cornerstone of finance called modern portfolio theory.

Mandelbrot, 83, contends that portfolio theory, which tries to maximize return for a given level of risk, treats extreme events (like, say, yesterday's market shockers) with “benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account.” The faulty assumption of modern portfolio theorists, in Mandelbrot’s view, is that price changes do not drift far from the mean when observing daily ups and downs—so extreme events are exceedingly rare. “Typhoons, in effect, are defined out of existence,” he wrote.

In place of modern portfolio theory’s reliance on the canonical Bell Curve, Mandelbrot drags in (surprise!) the fractal. A fractal is a geometric shape that can be divvied up into parts, each of which is a Mini-Me facsimile of the whole. If you look closely enough, you can see fractals everywhere. Besides monotonous screen savers, fractal patterns describe the distribution of galaxies and the shape of coastlines. Mandelbrot devised so-called multi-fractal generators that can use historical market data to simulate alternative scenarios of where stocks or other securities might be headed.

For fun, here's a pretty fractal.

Friday, September 19, 2008