Risk Latte - Is UBS A Victim of Chaos Theory?

Is UBS A Victim of Chaos Theory?

Rahul Bhattacharya
May 31, 2005

Well, we are tired of collecting theme articles about goof ups and crises at UBS, the venerable investment bank. To us it is becoming boring and it seems UBS is becoming very predictable in its actions.

It came to our attention today – though belatedly – that UBS has once again managed to goof up in Japan. Apparently, the Tokyo branch of the bank has lost a computer disk thought to be containing sensitive customer information and as expected FSA, the Japanese regulator has launched an enquiry into it.

Our reaction was: No, not again!

So, this morning, our one of our resident quants, the junior most member of our team, who knows practically nothing about the sins and virtues of investment bankers suggested that perhaps this is all simply a mathematical phenomenon. His argument is that what if all these things happening in this reputable and incredibly large and diversified bank is the symptom of a chaotic system dynamics.

Our CEO and two other senior members promptly excused themselves from the room, possibly so that they don’t betray the expression of pain and total incomprehension on their faces.

I am a content editor, and I have no choice but to burden myself with all the esoteric and complex mysteries of life. So I listened on.

Chaos theory is the study of complex non-linear dynamical system. That is a mouthful of math jargons. Well, UBS like any other large financial system is complex, non-linear and a dynamic system. A little more math will tell us that chaos theory is the study of “forever” changing complex systems, such as weather patterns, animal population in a game reserve, and of course, financial systems, based on the mathematical concepts of recursion, whether in a form of a recursive process or a set of differential equations modelling a physical or an economic system.

I have to take my quants word for granted when he tells me that the behaviour of a large bank can be modeled based on a system of non-linear differential equations. Well, this is a good time to leave this page, if you are having any thoughts about it.

We have all watched Jurassic Park. What starts out as nice little excursion in a game reserve turns out to be a humongous nightmare for the tourists. Initially small things start to go wrong; incidental and marginal changes that no one thinks are material. A short circuit, untimely rain and thunder, a malfunction in the monitoring system, and suddenly they all start to add up and result into totally unexpected events, major events, that disrupts the whole party and plunges the tourists into a hell hole. Well, that is chaos for you.

Actually, a moot point about chaos theory is order. "Chaos" in the chaos theory is not disorder but rather order. Chaos theory actually outlines the order that is inherent in every complex, non-linear system, be it biological, social or economic. But this order is a-periodic order that is never in steady state. This is the reason why most people think chaotic systems are actually moving towards disorder.

Chaotic systems are ordered - they always follow a path but they never settled down to a single point, as happens in a steady state system, and since they never repeat the same thing, they aren't periodic either. Capital Asset Pricing Model (CAPM), the foundation of portfolio theory is an equilibrium model and so is Black-Sholes option pricing models.

If we make small changes in the initial conditions then either of the above will not blow up or result in something totally unpredictable. Once again, please note that "unpredictable" doesn't mean disorder, it simply means that we see something that we haven't seen before, or thought we will ever see.

Our reaction was: No, not again!

This is the essence of chaos. A small change in initial conditions in the system results in unpredictable behaviour and we see something that we never expected to see. The system does not settle down at a point and nor does it repeat the past. It is orderly but frightening at the same time.

So maybe it is that some initial conditions in the functioning of the system called UBS got modified a bit. Just a tiny bit and no one noticed. Maybe a little bit of complacency, a little bit of extra arrogance, small holes in risk reports, a quant tinkering with a pricing model, a bit of an extra client pressure and just a wee bit of extra greed, a minor altercation between a male and a female employee and so on, and all these seemingly minor and inconsequential incidents may have added up to result in a tornado. A massive and ugly court case, large derivatives losses, getting banned from securities trading in a major emerging market and of course the loss of a compute disk containing sensitive client information.

Maybe, UBS is so large and complex and so non-linear in its operation that an infinitesimally small change inside its hallowed walls can give rise to large behavioural anomalies.

And yes, non-linear systems could be really messy sometimes. Take a piece of paper out of your writing pad and it feels smooth. Draw a straight line and it remains a straight line. The two dimensional paper is a linear system. Now crumple the paper in your palm. It feels messy. And the straight line that you drew on it no longer appears straight.

Almost all financial and natural misfortunes are the result of extreme non-linearity in the system. A recipe for chaos!

Any comments and queries can be sent through our web-based form.

More on Quantitative Finance >>

back to top


More from Articles

Quantitative Finance