Beware the Long Tail: Economic Models of Risk Don't Add Up, Cadre of Researchers Caution
When H. Eugene Stanley heard that Lehman Brothers had filed for bankruptcy, a small part of him was thrilled. Of course, the news was distressing.
The firm's seismic collapse had disastrous consequences, not only for the global economy but also for Stanley's daughter-in-law, who became instantly unemployed. But Lehman's downfall was exactly the kind of rare event that Stanley, a physicist at Boston University, had been expecting.
"Many economists will tell you that the chances of something really big and bad happening are really, really small," Stanley says. But when viewed through a different lens, he contends, catastrophic events--such as Lehman filing for bankruptcy in 2008--aren't exceptional but inevitable.
At the time of Lehman's collapse, Stanley had been exploring the notion that extreme economic events, the bubbles and crashes of financial markets, might be described by a mathematical law--a tidy law, like acceleration due to gravity. And he isn't the only outsider who has had an eye on the markets. Scientists from a range of fields have been poring over financial data, finding some curious patterns in the process.
These patterns suggest that standard economic models based on the notion of equilibrium--markets will fluctuate but then settle down like the surface of a still pond--may not capture the whole story. Freak events may be a normal part of long-term economic behavior. If that's true, then the mathematical methods guiding Wall Street's estimation of risk are seriously flawed, offering a dangerous false sense of security.
"You have to understand that the bad events can be really, really bad," says J. Doyne Farmer, who is trained in physics and does research spanning several disciplines at the Santa Fe Institute in New Mexico. "And there's a significant chance that over a five-year period we will get hit by a really big event. That's where the rubber really hits the road."
Discounting extreme events as improbable is a long-held tradition in economics, notes Stanley. Many mathematical models assume that financial data, such as changes in the price of a stock, fit what is known as a Gaussian, or normal, distribution--the good old bell curve. Most data cluster around an average. Move to either side of the average, and the data points become increasingly scarce, tapering off in a predictable way. A blizzard in July or the Dow Jones dropping 20 percent in one day are considered so rare that they might as well be impossible.
The Gaussian bell's roots in finance go back to work by French mathematician Louis Bachelier, who modeled changes in share prices in the early 1900s. Bachelier recognized that some of his model's assumptions were flawed, including the premise that the probability of extreme events is vanishingly small (he reportedly called such events "contaminators"). Yet these assumptions were preserved in later models, including the Black-Scholes formula, which underlies much of Wall Street's estimation of risk.
In some respects, the long reign of this Gaussian approach isn't that surprising. Many things measured in the real world fit the Gaussian mold, says Mark Newman of the Center for the Study of Complex Systems at the University of Michigan in Ann Arbor. Take the height of adult American males: It generally hovers around 6 feet, or about 180 centimeters. Plot the number of men with heights lower and higher, and the data points on either side taper off quickly. "You don't get a mile-high human" Newman says.
With truly Gaussian distributions, measurements that appear extraordinary, such as a person a mile tall, are probably flukes; perhaps the measurer didn't know how to use a ruler or made a mistake in writing down the number. Termed "outliers," these data points are often thrown out of the analysis.
But when it comes to financial data, a growing body of research suggests that outliers can be more like babies than bathwater. …