The (Mis)Behavior of Markets

by Benoît B. Mandelbrot

First, independence: Each change in price—whether a five-cent uptick or a $26 collapse—appears independently from the last, and price changes last week or last year do not influence those today. That means any information that could be used to predict tomorrow’s price is contained in today’s price, so there is no need to study the historical charts. A second assumption: statistical stationarity of the price changes. That means the process generating price changes, whatever it may be, stays the same over time. If you assume coin tosses decide prices, the coin does not get switched or weighted in the middle of the game. All that changes are the number of heads or tails as the coin is tossed; not the coin itself. And a third assumption: the normal distribution. Price changes follow the proportions of the bell curve—most changes are small, an extremely few are large, in predictable and rapidly declining frequency. Reality: Life is more complex. This third set of assumptions is the one most clearly contradicted by the facts. Because it underpins almost every tool of modern finance, it gets special attention in the following chapter-in-a-chapter. Pictorial Essay: Images of the Abnormal PICTURES