Chaos, Finance and Non-linear Behaviour

With all the noise around cause and remedies for the financial woes we are currently experience something has been niggling at the back of my mind. It was only after watching the BBC documentary "High Anxieties: The Mathematics of Chaos" on Chaos math and reading some posts on nodes that it twigged.

The idea that the financial system is fundamentally chaotic (in mathematical terms) has been around for a while so that isn’t new. A system being chaotic is not a problem in itself, it just is. The problem lies in the transition from linear to non-linear response in chaotic system. Here we had a situation that seemed to be out of portion to reasonable rules of thumb for the system response. The size of the sub-prime looses shouldn’t have been enough to trigger the meltdown.

Unless of course the system was optimised and being highly driven. The past 20 to 30 years has seen the financial system optimised for making money. Without getting into the whys, wherefores and who did it, the optimisation process pushed the financial system to the edge of instability. Optimisation moves a system closer and closer to instability, which is how you get “optimised performance.” This works fine when a system is steady-state without unexpected shocks. The downside is it takes very little amount of non-steady state change to force the system into instability.

In chaotic system instability creates non-linear response that is unpredictable. That is what we are facing. A relatively small shock has sent the system into non-linear response. The system was pushed to the edge of non-linearity by two forces: growth in connections between nodes and the hard driving of the system.
The interconnection of nodes grew exponentially via the creation of various 2nd and higher order derivatives. The intent was to “spread risk”. Instead it amplified the risk across the system which would in turn amplify driving forces. The second part was the cheap credit. This acted to effectively increase the energy sloshing around the system, driving it hard.

To stop future financial crises, we need to de-optimise the system. We need to make the system robust. Regulatory changes such as tying capital ratio to the incentive system of executives, whether a good idea or not, will do little in an optimised chaotic system as even a small shock can have massive consequences. Instead we need regulations that look at limiting interconnectedness of the various nodes in the system and work to dampen movement of a shock through the system.

Put another way, we want to shift the system into an area that has the broadest linear response to shocks as possible. Some possible ideas are banning all 2nd and higher order derivatives or counter cyclical capital ratios. There will be great resistance to making the financial system fundamentally robust as it will limit the money making ability of financial institutions.