Ecology and Topology in the Financial World

by Yaniv Altshuler

“‘Tipping points’, ‘thresholds and breakpoints’, ‘regime shifts’ — all are terms that describe the flip of a complex dynamical system from one state to another. Catastrophic changes in the overall state of a system can ultimately derive from how it is organized — from feedback mechanisms within it, and from linkages that are latent and often unrecognized. The change may be initiated by some obvious external event, such as a war, but is more usually triggered by a seemingly minor happenstance or even an unsubstantial rumor. Once set in motion, however, such changes can become explosive and afterwards will typically exhibit some form of hysteresis, such that recovery is much slower than the collapse.”

These are the opening lines of the stimulating paper “Ecology for Bankers” (May et. Al, Nature, 2008), that attempts to explore the roots of the 2008 economic crisis, and try to understand how (if at all possible) it could have been avoided.

Are economical and financial systems prone to develop time and time again self consuming collective behaviors? Is the appearance of toxic patterns in financial communities an inherent part of their being, or is it linked with a specific feature of their internal structure (and can therefore be avoided, or at least predicted ahead of time) ?

An answer to these questions would be of an obvious importance not only to the more traditional financial structures, but also to the emerging field of social trading. In fact as the number of individuals interacting in social trading networks is significantly higher than the number of institutes that act as payers in conventional financial market (banks, money managers, etc.), we can conjecture that it is expected to react even more radically to triggers as the ones described above.

The novelty of May et. al’s paper lays in the innovative way the dynamics of the financial crisis was analyzed, combining network analysis with environmental science. This somewhat strange mixture of methods (stemmed from the authors’ own diverse background) aspired to look at the underlying social network behind America’s financial institutes, and investigate the stability of this network using ecologic systems as analogues. This “stability” was measure as the “risk” that is encapsulated in the system. The main claim of the paper was that performing risk analysis for individual players is inherently (and significantly) less accurate than a “holistic” risk analysis that would take into account interactions between players, then in turn may imply positive correlation between them, rendering conventional risk-analysis techniques impractical – by voiding the basic assumption that all players can be modeled by uncorrelated variables.

In order to understand this notion, let us first observe the behavior of two uncorrelated variables, X and Y, representing the projected price of two assets :

 

We can easily see that when we have some information about variable X, it do us little good when trying to forecast the behavior of variable Y (and vice versa). This also means that we can apply independently analysis techniques on both variables – techniques that in turn might required some information about the behavior of the other variable (information about X, for the purpose of analyzing Y, for example).

However, this is not the case when the two variables are correlated (for example, where X represents the expected price of gold, and Y represents the expected price of a “short” option on gold, in which case there would be a very strong negative correlation between the two).


In this case, using analysis techniques that does not take into account the correlation between the two variables may lead to highly inaccurate predictions.

So, how should be analyze the markets, and how does it have to do with ecology ? On this, next time.