Power-law tails provide an empirically adequate description of large positive and negative returns across a broad range of financial instruments and observation scales.

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Examine price records more closely, and you typically find a different kind of distribution than the bell curve: The tails do not become imperceptible but follow a "power law." These are common in nature. The area of a square plot of land grows by the power of two with its side. If the side doubles, the area quadruples; if the side triples, the area rises nine-fold. Another example: Gravity weakens by the inverse power of two with distance. If a spaceship doubles its distance from Earth, the gravitational pull on it falls to a fourth its original value. In economics, one classic power law was discovered by Italian economist Vilfredo Pareto a century ago. It describes the distribution of income in the upper reaches of society. That power law concentrates much more of a society's wealth among the very few; a bell curve would be more equitable, scattering incomes more evenly around an average. Now we reach one of my main findings. A power law also applies to positive or negative price movements of many financial instruments. It leaves room for many more big price swings than would the bell curve. And it fits the data for many price series. I provided the first evidence in a 1962 research report, sum-

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Now we reach one of my main findings, a power law that applies to positive or negative price movements of many financial instruments it leaves room for many more big price swings than would the bell curve and it fits the data for many price series. I provided the first evidence in a 1962 research report, summarized by a brief published paper. The report showed that in the distribution of cotton price movements over the past century, the tails followed a power law. There were far too many big price swings to fit a bell curve. The same report continued with wheat prices, many interest rates, and railroad stocks, in other words, all the data I could locate in dusty library corners. Since then, a similar pattern has been found in many other financial instruments. Economics is faddish, as in many scientific fields. So, in the dismal science, a consensus emerges about what is right and what is wrong, what research is worthy a doctoral thesis, and what is not.