What is EconoPhysics?

Abstract

I present some ideas of how EconoPhysics has come to life in the past few years, what it deals with, the main topics of discussion in this community, and perhaps what can it offer in the future. One can see that the tools of Statistical Physics can indeed be utilized properly to understand better the behavior of the markets by constructing mathematical functions which use empirical/historical values. As the volume of such historical data explodes in recent years in an all-electronic world, it has become more and more necessary to use such new tools, thus entering a new era in the financial world, where computers play a very important role in decision making.

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Journal of Engineering Science and Technology Review 4 (3) (2011) 207 – 208
Special Issue on Econophysics
Note
What is EconoPhysics?
P. Argyrakis*
Dep. of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece.
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Abstract
I present some ideas of how EconoPhysics has come to life in the past few years, what it deals with, the main topics of
discussion in this community, and perhaps what can it offer in the future. One can see that the tools of Statistical Physics
can indeed be utilized properly to understand better the behavior of the markets by constructing mathematical functions
which use empirical/historical values. As the volume of such historical data explodes in recent years in an all-electronic
world, it has become more and more necessary to use such new tools, thus entering a new era in the financial world,
where computers play a very important role in decision making.
Keywords: EconoPhysics, probability distribution functions, correlation functions.
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1. EconoPhysics
During the past twenty or so years [1-5] there has been an
emergence of new approaches in mostly all sciences which
are based on the idea that practically all entities considered,
whether they are molecules, human relations, or prices of
goods, exist through some sort of interaction between the
multitude of their elements, which strongly affects their
overall behavior. Thus, a new picture based on graph theory
has spawned new ways to visualize nature, by casting these
elements as network nodes and their interactions as the links
(bonds) that connect these nodes. It is really amazing how in
such a short period of time a huge variety of applications
found their way in such pictures, and new ways were
generated to visualize old problems, thus improving their
understanding and/or offering explanations that were not
conceivable earlier. Economics is a science which was not
left out of this approach. It is a science that is trying to
assign the proper value to every item that people deal with in
our world. Of course, one can easily see that it is not related
at all to the quantities that we commonly meet in Physics or
the other Natural Sciences, i.e. the physical laws in nature.
Thus, one may naively ask what is the common element
between the two, how can they possibly be related, and what
has prevented it all along. This is a good question. The
answer is simple, it is that the values assigned to all goods of
the Economy are characterized by fluctuations. But
fluctuations constitute an inherent characteristic of all
natural measurements. It is a subject that is studied in
Statistical Physics in great detail. Thus, this common
characteristic constitutes the bridge between these two
disparate fields, which seemingly are concerned with so
different ideas. One would then hope to apply well known
methods from Statistical Physics to real-world data coming
from the economy, calculate equivalent quantities that one
has in Physics, but now using data such as prices of some
common instrument, instead of using data arising from
physical measurements. One would ask at first if this is
possible, and the quick answer is that indeed it is possible, as
it has been shown in a large number of cases recently.
What has additionally promoted such an approach is the
huge volumes of economic data that in the past few years
have been continuously generating. Of course, the reason for
this is the transition to all-electronic markets, making
possible to keep records of transactions at extremely small
time increments, of the order of msec, something unheard of
just a few years ago. This has necessitated on one hand the
use of powerful computers, and on the other hand the use of
powerful statistical methods in order to produce meaningful
pictures of the financial markets in a very short period of
time, and all this must be realized, of course, in real time.
The huge increase of the volume of currency trading, and the
introduction of derivatives in the 70s have all helped such
trends and necessitated new approaches for the financial
markets.
A first impetus to the statistical analysis of financial
markets was shown by the unexpected observation in the
behavior of the distribution of the price fluctuations of some
instrument. It can safely be assumed as a starting point that
price fluctuations occur at all scales and very importantly
they are random, i.e. prices in any time increment are not
correlated. This was proposed over 100 years ago as an
empirical result and it was commonly accepted. If this is true
one would expect intuitively to have a Gaussian or Normal
distribution for the changes of the price of a stock. Recent
results in the last two decades showed that this is not so.
While the line shape around the maximum value of the
distribution of price changes seems to be correct, the shape
at the two extremes (the two tails) do not obey a Gaussian at
all, but rather they agree with a Levy distribution, which
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* E-mail address: panos@physics.auth.gr
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P. Argyrakis /Journal of Engineering Science and Technology Review 4 (3) (2011) 207-208
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falls much more sharply at the ends (rather than having long
tails that go asymptotically to zero as in the Gaussian).
As mentioned earlier, in financial markets one is not
interested only in the price itself, but also in the fluctuations
of this price, which is usually called the volatility in the
price. At periods of extreme volatility it is when huge market
gyrations occur, such as market crashes, i.e. very sharp
changes in a very short period of time, such as the one on
October 1987 when the main market indices in USA fell by
over 20% in one day. Conceivably, the same could happen
in large upswing changes, for symmetry reasons, even
though historically this is not true. Such changes belong to
the tails of the distributions, which as mentioned above are
far from Gaussian. Actually, if they were Gaussian, then the
1987 market crash would have a probability of 10-135 to
happen, the inverse of which is larger than the size of the
universe. Thus, it is now clear that the behaviors of the tails
of such distributions are far from random, even though the
prices themselves could be taken to be random. The
interplay of these two quantities (i.e. the price of an
instrument and the volatility of this price) is still a very
active field of research, where no definite answers have
emerged.
Such sharp changes as described above belong to the
class of the so-called "rare events", which are events that
happen very rarely in the world, but when they happen they
have a very large impact on people. Such events could be,
for example, a very large earthquake, a powerful tsunami, a
catastrophic nuclear accident, or a huge swing in the
financial markets discussed above. Such events may occur
only once or twice within a lifetime, or let us say that they
have a frequency (roughly) of the order of a century. The
question then is if they can be predicted or if any
information about them can be obtained ahead of time, as for
example, if they have any precursors. Actually, this is the
holy grail of the markets, for obvious reasons. I will give
some simple arguments which I believe show that this is not
possible to do. One wants to believe that we all live in a
world of efficient markets. This hypothesis states that no
matter how complex markets are, valuations are made in a
rational way, which means that they are based on the supply-
demand ratio. It also states that all players have all the
available information in all parts of the world, so that if
some form of arbitrage may temporarily take place, soon it
will be smoothened out exactly by the same forces that have
generated it and by the same mechanism. Equivalently, it is
palatable to assume that if any such precursor would emerge,
then the market forces would immediately take effect,
making this precursor useless. Who would buy a stock if it is
known that tomorrow it will be half price and the day after
quarter-price? If such a real precursor would exist, then this
would in effect shut down the market. For a market to
operate smoothly, it is by definition required to have both
buyers and sellers. When one of the two ceases to exist, then
the market simply cannot operate at all. The market is not an
infinite bath of financial instruments which are traded
between a customer and the market. The market is simply a
mechanism of matching buyers and sellers, therefore, if a
catastrophic change takes place, then the balance between
buyers and sellers is strongly disturbed, making trading
impossible. With these thoughts, one can see that (almost by
definition) such indications as predicting bubble bursts,
finding precursors, etc. do not make any sense in a normal
market. But just like with all other human behavior in
history claims to the opposite abound and will do so in the
future, because it is part of human nature.
Another property of interest is the correlation between
two or more financial instruments. By this term it is simply
meant how does the change in one instrument depend on the
change in another. For example, if we have two stocks, how
does the rise or fall of one compare to the behavior of the
other in the same time period. It is well known that in daily
fluctuations typically most stocks move in unison, this is
true at least for the large valuation stocks, such as the ones
contained in the DJ Industrials. Also, the same may be true
for stocks that belong to some particular sector, such as for
example, oil industry, or banking, etc. One wants to know
more in detail the quantitative behavior of these stocks.
Thus, it is possible to calculate the so called correlation
coefficient, which answers this question. The correlation
coefficient is a function similar to the correlation function,
which gives, for example, the relative positions or velocities
of particles in a physical system.
Finally, an area where methods from Physics can
contribute is the estimation of risk and the creation of an
optimal portfolio. These ideas have come to the forefront
more so in recent years because of the increase of derivative
trading. As we know derivatives carry a much larger risk
than stocks themselves. Because they involve in addition to
the valuation of the underlying instrument, the parameter of
time and volatility, estimating their fair value is not an easy
task. Probability theory used in physical processes can aid
significantly at this point, for which there is still no general
consensus. Important seminal results as the Black-Scholes
theory for option pricing do not agree with empirical, real
prices even today.
Summarizing, Physics can contribute to Economics by
lending the mathematical tools that have been developed
over the years for the study of atoms and molecules. These
mainly include probability distribution functions and
correlation functions. Large volumes of historical data exist
today that include among others, prices of stocks,
derivatives, such as options, commodities, currency pairs,
index of inflation, income distribution, import-export of
goods between countries, etc. to name only a few. Such
functions as the ones mentioned above may give a better
understanding of the mechanism that governs their behavior.
It is not expected that EconoPhysics will revolutionize
Economics or be able to predict trends in the Economy. But
experience has shown that interdisciplinary approaches are
always useful for the advancement of knowledge.
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References
1. R. N. Mantegna and H. E. Stanley, “An Introduction to
Econophysics: Correlations and Complexity in Finance”,
Cambridge University Press, (2000).
2. J. L. McCauley, “Dynamics of Markets: Econophysics and
Finance”, Cambridge University Press, (2004).
3. J. P. Bouchaud and M. Potters, “Theory of Financial Risks: From
Statistical Physics to Risk Management”, Cambridge University
Press, (2000).
4. D. Sornette, “Why Stock Markets Crash: Critical Events in
Complex Financial Systems”, Princeton University Press, (2003).
5. B. Mandelbrot and R. L. Hudson, “The (Mis)Behavior of Markets:
A Fractal View of Risk, Ruin and Reward”, Basic Books, (2004).