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|Publications|APS News|

December 2008 (Volume 17, Number 11)|

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Econophysics and the Current Economic Turmoil
By H. Eugene Stanley
Almost every physicist by now has heard of thefast-growing subdiscipline of “econophysics”, a fieldcharacterized by collaborations between physicists
and economists and focused on asking if new insights
or even laws could emerge if the concepts andapproaches of statistical physics were brought tobear on questions that originate in economics. And
almost everyone, physicist or nonphysicist, has by
now heard that the economies of every country–large
or small, Eastern or Western–are witnessing truly
huge fluctuations. So it is natural to ask“Does econophysics have anything to say about thecurrent financial/economic turmoil?’’
The answer to this question is a resounding “Yes!”
since econophysics is statistical physics applied tothe economy, and fluctuations are the substance ofstatistical physics. In economics, the probability
density function (pdf) of price changes has beenstudied for over 100 years, ever since the PhD thesisof Bachelier in 1900 analyzed real data–without
benefit of computers. Then, to understand thepattern he witnessed, he introduced a model whichtoday we call the drunkard’s walk. This is the model
immortalized to the general public in the aphorism“random walk down Wall Street.’’H. Eugene Stanley

Approximately 50 years ago, as more data became
available, it became clear that the drunkard’s walk fails to describe all the data. The term “fat tail”
was used to describe the mathematical counterpart of this statement, that the pdf of price changes
contains many more events in the tail than predicted by the Gaussian pdf characterizing thedrunkard’s walk. Nonetheless, more than 99 percent of the then available data were reasonably
approximated by a Gaussian, so a terminology grew up where events corresponding to these fat tails
became known as “rare events,” or sometimes “tsunamis.” Since there was no theory for them, someargued, and since they are indeed very rare, we can as well ignore them. The word “outlier” issometimes used to describe a data point that does not conform to the widely used Gaussian
distribution of price fluctuations.
Then along came the physicists, starting about 15 years ago when the neologism “econophysics” wascoined by this author to describe efforts to apply physics approaches to this and other questions ofinterest in economics. This field can trace its roots to Newton and Copernicus, two physicists who
worked extensively on economics problems, and to a number of others over the centuries whoapplied to economics the fundamental approach of physics. First, to be eternally skeptical of
everything–especially in this case of the practice of calling something that does not agree with atheory an “outlier” or “tsunami.” And, perhaps most importantly, to collect as many data as possible
before making any theory to interpret them.
Unlike traditional topics in physics, where collecting data often requires imagination and sometimes
years of painstaking labor, in the case of price changes every transaction of every stock is recorded
and stored. Apparently all the data were not analyzed, so two Boston University graduate students,
Parameswaran Gopikrishnan and Vasiliki Plerou (now happily married!), set about to acquire andanalyze the data on every transaction...such a voluminous data set that their University computer
system had to acquire a significant addition to its storage capacity.
When they analyzed these data–200 million of them–in exactly the same fashion that Bachelier had

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analyzed data almost a century earlier, they made a startling discovery. The pdf of price changes was
not Gaussian plus outliers, as previously believed. Rather, all the data–including data previously
termed outliers–conformed to a single pdf encompassing both everyday fluctuations and “once in acentury” fluctuations. Instead of a Gaussian or some correction to a Gaussian, they found a powerlaw pdf with exponent -4, a sufficiently large exponent that the difference from a Gaussian is nothuge; however, the probability of a “once in a century” event of, say, 100 standard deviations isexp(-10,000) for the Gaussian, but simply 10-8 for an inverse quartic law. If one analyzes a data set
containing 200 million data in two years, this means there are only two such events–in two years!
Now which is better, the concept of “everyday fluctuations” which can be modeled with a drunkard’s
walk, complemented by a few “once in a century” outliers? Or a single empirical law with no outliers
but for which a complete theory does not exist despite promising progress by Xavier Gabaix of NYU’s
Stern School of Management and his collaborators? Here we come to one of the most salient
differences between traditional economics and the econophysicists: economists are hesitant to put
much stock in laws that have no coherent and complete theory supporting them, while physicists
cannot afford this reluctance. There are so many phenomena we do not understand. Indeed, many
physics “laws” have proved useful long before any theoretical underpinning was developed . . .
Newton’s laws and Coulomb’s law to name but two.
And all of us are loathe to accept even a well-documented empirical law that seems to go against ourown everyday experience. For stock price fluctuations, we all experience calm periods of everyday
fluctuations, punctuated by highly volatile periods that seem to cluster. So we would expect the pdf
of stock price fluctuations to be bimodal, with a broad maximum centered around, say, 1-3 standard
deviations and then a narrow peak centered around, say, 50 standard deviations. And it is easy toshow that if we do not have access to “all the data” but instead sample only a small fraction of the200 million data recently analyzed, then this everyday experience is perfectly correct, since the rare
events are indeed rare and we barely recall those that are “large but not that large”.
The same is true for earthquakes: our everyday experience teaches us that small quakes are goingon all the time but are barely noticeable except by those who work at seismic detection stations. And
every so often occurs a “once in a century” truly horrific event, such as the famous San Francisco
earthquake. Yet when seismic stations analyze all the data, they find not the bimodal distribution ofeveryday experience but rather a power law, the Gutenberg-Richter law, describing the number ofearthquakes of a given magnitude.
There is another problem with accepting an empirical law that quantifies the probability toexperience a financial shock of a given size. Many scientists, especially economists, feel that it isbetter to really understand a law before proposing it. However imagine what must have happened
when earthquake specialists uncovered the Gutenberg-Richter law describing the number ofearthquakes of a given magnitude. San Francisco last experienced a truly huge earthquake in 1906.
Do we ignore the Gutenberg-Richter law that informs us the precise probability of another San
Francisco earthquake of comparable magnitude because we do not understand it? Or do we design
San Francisco buildings so that they withstand once-in-a-century earthquakes?
Similarly, do we ignore the inverse quartic law that fits all the data including once-in-a-century
events? Or do we design a financial system that has safeguards to minimize the damage when one ofthese rare events actually occurs?
We cannot predict the future but we all know what already happened. Governments worldwide madeno contingency plans, and when the current crisis finally appeared to not “just go away,” meetings ofexperts were called and policies hastily crafted. We cannot know at this stage if these policies are thebest possible or not, but the speed with which they were crafted seems incommensurate with the factthat we physicists knew for 10 years the probability of shocks of this magnitude, just as we know the
probability of an earthquake of a given magnitude. California buildings are required by government
to be reinforced, but financial systems are not. Indeed, the haste with which current policies wereadopted clearly has the potential for making a bad situation worse than it would be if more careful
policies were proposed, back-tested on real economic data, refined, and discussed at all levels frommany points of view, by individuals from the Paul Krugmans to the Alan Greenspans.
I now briefly address a second question, a question raised frequently by the news media: “There haveeven been accusations that physicists are to blame for what’s been going on, because they haveallegedly invented the complex financial instruments that nobody else understands but that are now
doing us in.”
It is indeed true that physicists have been among those who invented complex financial instruments.
But so what? Physicists also invented many other things that others have used for destructive
purposes. Bernoulli invented the principles underlying flight yet it is not customary to blame
physicists for flight accidents caused by the failure of these principles (in, e.g., turbulent airconditions). Nor is it customary to blame physicists for the nuclear disaster at Chernobyl despite theacknowledged role that physicists have played since Frisch and Meitner first proposed the idea of
nuclear fission. It is natural to want someone to blame for major disasters...whether the disaster iscompletely natural like Hurricane Katrina or man-made like the current economic crisis. Just as thefundamental flaw that made Hurricane Katrina the disaster it was involved not preparing for theunlikely event of a direct hit of a major storm, so also the fundamental flaw that causes much of
today’s economic problems is not preparing for the unlikely event of a very large economicfluctuation.
In any case, the probability of a disastrous economic fluctuation seems to be fairly independent of

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time period, since Plerou and Gopikrishnan found that the same inverse quartic law holds for different
time periods in history, dating back as far as the 1929 crash...long before physicists were as popular
as they are now on Wall Street. So if it is the physicists who are to blame, how do we explain the factthat large and not-so-large crashes have been appearing with frequencies that are approximately
time-independent?
But if one wants a scapegoat then you can look no further than the author of this article. The inverse
quartic law is a quantitative, not a qualitative, law: it tells the exact probability of a crash of a given
size. So before the inverse quartic law, one knew only the qualitative statement that rare events dooccur, but not the exact probability of a rare event, making it easier to ignore since indeed the eventsare very rare. Why didn’t we write letters to those with the power to plan exactly what to do when the“once in a century” bad news indeed occurs?
Physicists do not generally stop at extracting empirical laws from data. Additionally, they try tounderstand the laws. What can a physicist offer as a first step to begin to understand the fact that
there appears to be scale-free phenomena at work in stock price fluctuations? I can offer a tentative
picture–based largely on analogy with another scale-free phenomenon, a system near its critical point(now called a “tipping point” due to the popular book of this title by Malcolm Gladwell). Indeed,physicists often like to argue by analogy, on the “parsimony principle” (often credited to Feynman)that there are not that many fundamentally different phenomena.
Large strides were made in understanding the scale-free phenomena occurring in systems near their“tipping points” by the recognition of the fundamental role played by two variables: the interactions
among the units comprising the systems, and the interaction of the units with an external force field.
In economics, if the units are firms, the first is called the “herd effect” (if one unit changes, otherunits influenced by that unit are more likely to change), and the second is called the “news effect”(all units respond to external news). The complexity of this picture is that the units do not simply
interact with equal strength with a small number of other units, but rather have interactions of bothsign (“ferromagnetic” and “antiferromagnetic”) with other units...much as in an Edwards-Anderson
spin glass except that the distribution of interactions is not known and will certainly even vary overtime. Similarly, the interactions with “news” can take on a huge range of strengths–some news isvery good, good, bad, or very bad–and news affects different firms differently...much as in a random
field Ising model.
Of course this model is not exactly solvable, which makes it not very attractive to economists who
generally prefer models that are amenable to solution. Nonetheless, it is attractive to physicists
because we have developed a fairly deep understanding about phase transitions in idealized models,
not only “pure” nearest-neighbor Ising models in a uniform external field, but also complex spinglasses and complex random field Ising models. Certainly we know enough to understand why the“globalization” of recent years might serve to introduce more “ferromagnetic” bonds, and hence toincrease the magnitude of the sort of “spin flips” that occur in big clusters near the critical point. AndAlbert-László Barabasi has taught us that the networks formed by agreements among leaders of
economic institutions serve to establish still more long-range ferromagnetic interactions, again withthe result that cluster flips could be more dramatic.
Many physicists have viewed the film by Fumiko Yonezawa of her simulations below the critical pointof Ising models with nearest neighbor interactions bathed in a uniform magnetic field. One can neverforget how all the spins are flipping nonstop but suddenly a huge cluster of spins which were mostly“up” suddenly flip and become mostly “down”. The effect of additional long-range ferromagnetic
interactions would be to increase the magnitude of these dramatic flips.
In short, this physicist’s intuition is that an overconnected system is WORSE, not BETTER, in ametastable condition, for encouraging large fluctuations. So if this argument has any validity, thenthe fluctuations are larger, not because of physicists making up new instruments, but rather becauseof the links between corporations, and the links between countries.
H. Eugene Stanley is University Professor and Director of the Center for Polymer Studies at Boston
University.

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