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
“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
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
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
s For Sornette et al’s prediction papers:
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