top of page


In this page, we discuss  a) what is econophysics and b) is it practical and most importantly  does it give better returns on investments than the existing methods ?


a) What is econophysics?

Around 1990, physicists working in statistical mechanics, in particular classical and quantum chaos, physical systems far from equilibrium such as turbulent systems, non-linear dynamics and so on realized that the field of economics, specifically financial market dynamics, had similar characteristics. Hence the methods developed for those physical systems could probably be applied to financial systems as well. In addition, around that time a vast amount of data started becoming available online so that these models could be tested. That was the start of the very active field of research econophysics. The term econophysics was coined by Prof. Eugene Stanley in 1994.

What does econophysics bring to the table that the existing financial models don't? To start with, many well-known financial models are based on the efficient market hypothesis according to which:

1) investors have all the information available to them and they independently make rational decisions using this information.

2) the market reacts to all the information available reaching equilibrium quickly.

3) in this equilibrium state the market essentially follows a random walk, which means, the  distributions of stock market returns are Gaussian (bell curve).

In such a system, extreme changes (crashes, bubbles) are very rare. 

 In reality however, the market is a complex system that is:

1) The result of decisions by interacting agents (e.g., herding behavior), traders who speculate

 and/or act impulsively on little news, etc.

2) This collective/chaotic behavior can lead to wild swings in the market, driving it away from equilibrium into the realm of non-linearity, resulting in a variety of interesting phenomena such as phase transition, critical phenomena such as bubbles, crashes and so on.

3) Lastly, a look at the distributions of market returns show that they are not Gaussian distributions

   at all. They have fat tails.

This is where econophysics comes in. As already mentioned above, there is considerable research

in statistical mechanics, particularly in the areas of chaotic, turbulent physical systems which exhibit characteristics similar to financial markets. Hence the methods developed there, may be applicable

to financial dynamics as well.


In the 1980s, Mandelbrot applied fractal theory to finance and showed that the dynamics of equity prices follow a power law behavior(show similar properties at differrent scales). See ref 1. below

under References. In the 1990s, Tsallis, a physicist, developed the so called 'q-statistics' (also called Tsallis statistics) particularly for non-extensive systems.   Here  it is assumed that the rate of change

of the probability distribution obeys a power law. (the parameter q represents the degree of non-extensivity and is related to the power law exponent) This method shows promise in addressing the issues connected with the  non-linear systems such as the present day stock markets. The Tsallis statistics, which is a generalization of normal statistics to non-extensive systems, was originally proposed to study classical and quantum chaos, physical systems far from equilibrium, and long

range interacting Hamiltonian systems.  However, in the last several years, there has been considerable interest in applying this method to analyze financial market dynamics as well   Several studies, including our own research, show that the real stock data characteristics are reasonably

well reproduced by Tsallis statistics.   For details see publications 3 and 4 in Research.

b) Is it practical/useful? 


We now come to the issue of  practicality. There are many good publications and books on econophysics describing in general terms, how  the methods can be applied to many fields in economics (eg. wealth distribution). But for  investment purposes, one needs to ask 'how practical

is it and do the methods perform better than the existing methods used by investors' ? These

questions are addressed in the next paragraph.

Long term investments involve constructing and managing portfolios that are expected to beat the markets in the long run.  This involves estimating the relative risk, i.e. the risk of individual equity relative to the market indices (S&P 500, Nasdaq etc. ---).  Ideally one wold like to use a risk range

that yields maximum return.  The commonly used risk measure is 'beta' defined in the Capital Asset Pricing Model (CAPM).  The CAPM, which is based on efficient market hypothesis (see emh for details)

was tested by Black, Jensen and Scholes in 1972. These tests and several other studies, including our own, show that the portfolios managed for very long periods (~16-18 years), in general, show the

behavior of increasing excess returns with increasing risk.  However, for shorter portfolio periods (~6-9 years), the risk return behavior is not always consistent. On the other hand, our studies show that the

risk-return patterns are very consistent when relative entropy estimated from Tsallis distributions,

(referred to as TRE) , is used as the risk measure. Further, over a period of 6-9 yrs,  the cumulative

returns from the portfolios constructed and managed using TRE way outperform those constructed using 'beta' as the risk measure. (See Portfolio Performane for details). This shows the practicality and

usefulness of Tsallis statistics, which was putforth to describe chaotic physical systems, in finance. 


To stress the practicality of q-statistics further,  we publish, every two weeks,  TRE risk tables for equities from several US and international indices.  A  tutorial on how one (even  individuals) can use these tables for investments is given in Portfolio Management,



  1.  Mandelbrot B B, 1997 Fractals and Scaling in Finance (New York; Springer)

  2. Tsallis C, 2000 Introduction to Nonextensive Statistical Mechanics (New York; Springer)

bottom of page