Science News - November 5, 2011

Know the risk A change in stock price expected in 1 of 100 trading days has a similar size under a power law regime (red circles) and a Gaussian distribution (shaded circles). But for a 1-in- 10,000 event, the power law predicts a much bigger price change. SOURCE: J. FARMER AND J. GEANAKOPLOS/POWER LAWS IN ECONOMICS AND ELSEWHERE 2008

will mean incorporating more than just
power laws. Occasionally crashes are so
large that they are outliers even from
the power law distribution, says Didier
Sornette of ETH Zurich. Their special-
ness makes them predictable, says
Sornette, who calls the standout events
“dragon-kings.”
“Dragons are not like the ordinary ani-
mals you meet in the zoo,” Sornette says.
“They require new mechanisms, new
biology to explain them.” The “kings”
part of the name refers to the fortunes
of royal families, which after centuries
of concentrating wealth have so much
that they no longer even fit in Pareto’s
distribution of wealth.

BOT TOM: Z.-Q. JIANG ET AL/JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION 2010

“We believe that there are events that are in a class of their own,” Sornette says. “While the power law distribution is a good characterization of the distribution of returns, it actually misses the elephant in the room, the dragon-king.” Sornette and his colleagues argue that understanding dragon-kings may help economists spot markets teetering

toward crashes. Out-of-control growth can be one sign of an approaching dragon-king. When herding behavior among investors amps up, a stock’s or index’s growth rate can increase faster than exponentially, leading to more herding, Sornette says. This positive feedback among investors, the same sort of feedback that concentrates the wealth of kings, brings the system to a tipping point. About two-thirds of the time, a crash results, Sornette wrote in a 2009 paper online at arXiv.org.

Working out of the Financial Crisis Observatory at ETH Zurich, Sornette and his colleagues are now trying to use this aggressive growth as a signature to identify crashes before they happen (often encrypting the data so as not to influence the markets).

The researchers seem to be on to something. While other market watchers remained enthusiastic about the outlandish growth of the Shanghai Stock Exchange Composite Index into the summer of 2009, Sornette and his colleagues

2.0 E3 Event prediction A research team in Zurich was able to successfully predict two downturns in a Chinese market before they happened. Gray lines in the graph below show the expected range of dates predicted for the downturn; red lines show when the predictions were announced.

Shanghai Stock Exchange Composite Index

6.0 E3

4.0 E3

announced on July 10 that a downturn was coming. They predicted that the bubble burst would begin between July 17 and 27. It popped on July 29.

Though great strides are being made in understanding outliers, how to reconcile the newfound importance of seemingly freak events with traditional models based on stability and equilibrium isn’t yet clear.

Many economists agree that current models grossly oversimplify things: “Almost no economists think that the Gaussian is a very good approximation of reality,” Gabaix says.

But power law math is much messier than Gaussian math. Even figuring out where a power law distribution begins can be tough. Pareto’s classic case of income probably follows a power law only in its tail, for example, with the wealth of the majority of the population based on labor for pay.

To keep things simple, models leave out a lot, Gabaix says. The key, and a very difficult thing, is making sure that the most important ingredients are included. “Power laws,” he says, “are one of those intriguing facts that force people to write new theories that hopefully will explain them.” s