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

by Benoît B. Mandelbrot

The old financial orthodoxy was founded on two critical assumptions in Bachelier’s key model: Price changes are statistically independent, and they are normally distributed. The facts, as I vehemently argued in the 1960s and many economists now acknowledge, show otherwise. First, price changes are not independent of each other. Research over the past few decades, by me and then by others, shows that many financial price series have a “memory,” of sorts. Today does, in fact, influence tomorrow. If prices take a big leap up or down now, there is a measurably greater likelihood that they will move just as violently the next day.

Second, contrary to orthodoxy, price changes are very far from following the bell curve.

Warren E. Buffett, the famously successful investor and industrialist, jested that he would like to fund university chairs in the Efficient Market Hypothesis, so that the professors would train even more misguided financiers whose money he could win. He called the orthodox theory “foolish” and plain wrong.

Patterns are the fool’s gold of financial markets. The power of chance suffices to create spurious patterns and pseudo-cycles that, for all the world, appear predictable and bankable. But a financial market is especially prone to such statistical mirages. My mathematical models can generate charts that—purely by the operation of random processes—appear to trend and cycle. They would fool any professional “chartist.” Likewise, bubbles and crashes are inherent to markets. They are the inevitable consequence of the human need to find patterns in the patternless.

Anticipation is a feature unique to economics. It is psychology, individual and mass—even harder to fathom than the paradoxes of quantum mechanics. Anticipation is the stuff of dreams and vapors.