Monday, August 16, 2010

Physics Envy in Finance

This represents my personal opinion, not the views of the SEC or its staff.

If all you have is a hammer...


I read a New York Times article a while ago on econophysics – the use of the tools of physics in economics – that featured the application of seismology to solve the problems of market crises. I can see the twists of logic that led to this approach: during an earthquake things shake around and fall, and during a market crisis things shake around and fall. Seismology predicts the former, so why not the latter?

This type of logical leap too far is nothing new. I remember the popularity of Kalman filters and the application of the principles of torque to measure the strength of market turns (I’m not kidding) in the seventies. Later came the emergence of chaos theory to model market dynamics and catastrophe theory to model market breaks, the logic being that markets look chaotic, and that market breaks are, well, breaks.

None of these work, and as I will get to in a bit, there is a reason they don’t work. But the use of physics in finance and economics persists, thus the fledgling discipline of econophysics. The reason it persists is first of all, there are not many jobs for physicist in physics, and most of finance is child’s play once you have gone through the rigors of a physics degree, so a lot of physicists end up in finance. Another reason is that most of those in finance really do have physics envy. They want to have the solid structure, the clean answers, and the sexy mathematical models of physics.
So if you are a physicist by training, what is more natural than to take to your new home with your physics hammer, especially if everyone wants you to look at everything as if it is a nail.

Boards don’t hit back
Andrew Lo and Mark Meuller have has a recent paper that addresses the issue of physics envy. They focus on the applicability of the tools of physics as the type of uncertainty becomes more profound, pointing out that while physics can generate useful models if there is well-parameterized uncertainty, where we know the distribution of the randomness, it becomes less useful if the uncertainty is fuzzy and ill-defined, what is called Knightian uncertainty.

I think it is useful to go one step further, and ask where this fuzzy, ill-defined uncertainty comes from. It is not all inevitable, it is not just that this is the way the world works. It is also the creation of those in the market, created because that is how those in the market make their money. That is, the markets are difficult to model, whether with the methods of physics or anything else, because those in the market make their money by having it difficult to model, or, more generally, difficult for others to anticipate and do as well.

In the Bruce Lee movie, Enter the Dragon, Lee faces his arch enemy in a fight. To intimidate Lee, his opponent holds up a board, and splits it in two with his fist. Lee watches passively and says, “Boards don’t hit back”. That gets to the reason physics does not work in finance: markets do hit back.
The markets are not physical systems guided by timeless and universal laws. They are systems based on creating an informational advantage, on gaming, on action and strategic reaction, in a space without well structured rules or defined possibilities. There is feedback to undo whatever is put in place, to neutralize whatever information comes in.

The natural reply of the physicist to this observation is, “Not to worry. I will build a physics-based model that includes feedback. I do that all the time”. The problem is that the feedback in the markets is designed specifically not to fit into a model, to be obscure, stealthy, coming from a direction where no one is looking. That is, the Knightian uncertainty is endogenous. You can’t build in a feedback or reactive model, because you don’t know what to model. And if you do know – by the time you know – the odds are the market has changed. That is the whole point of what makes a trader successful – he can see things in ways most others do not, anticipate in ways others cannot, and then change his behavior when he starts to see others catching on.

For example, I have seen this issue repeatedly in risk management, and it is one reason any risk management model will not cover all the risks. Once the risk model is specified, the traders will try to find a way around it. Are you measuring DV01 risk? Well, fine, then I will do DV01-neutral yield curve trades. Now are you measuring yield curve risk? Fine, then I will do DV01 and yield curve neutral butterfly trades. One of the problems with VaR – and for that matter with any complex model – is that it opens up all the more dimensions for such gaming, and for gaming in a way that is harder to detect. Maybe this can be put into a model, but if it can, it won’t look like how things are modeled in physics.

So it is not by chance that there are so many people trying to add complexity to the markets. Whatever rules are put in place, whatever metrics are devised, traders will try to find ways around them. In an engineering system, if you find a poorly designed valve in a nuclear power plant and replace it with a new and better deigned one, the new valve doesn’t try to figure out ways to make you think it is closed when it is really open. But traders will do that.

Lo and Mueller conclude their paper by considering that “the study of economics may be closer to disciplines such as evolutionary biology, ecology, and meteorology”. And indeed, an increasingly popular alternative to borrowing from the tools of physics is to push finance into a biological model. The argument is that in the biological sphere, there is the interaction and feedback that physics lacks. Evolution is the result of this dynamic, of one species changing over time to best another species, just as one trader will change strategies to best another trader. But this model also does not fit. Evolution is not a conscious process. It is a winnowing out of the poorly designed and emergence of the better designed on the basis of the process of natural selection. In contrast, in finance the process is conscious and intelligent.

A better analogy than physics or biology is a military one. The point is that there is a strategy of intelligent reaction to any action, an arms race to leapfrog one another in information gathering and technology, to know what others are doing, and to react in a way that they will not anticipate. This is the point where I could pull out quotes from The Art War about seeing into the mind of the enemy, attacking when your opponent believes you will retreat, and the like. That is not physics.