Sunday, January 4, 2009

Lessons from the meltdown – the limits of modeling

I am amused to watch the debate over who was right and who was wrong in the meltdown. Of course the naysayers get their day, as if they were right all along. It is kind of like if you were to drive from San Francisco to New York and your travelling companion is convinced that you have to go south. You get on Interstate 80 and drive east. But shortly after you pass through Winnemucca in Nevada the highway swings south to Battle Mountain and for the better part of an hour you have to put up with “see I told you it was south”.

One of these annoying passengers is Nassim Nicholas Taleb who was profiled in an
article by Joe Nocera in the New York Times today. Taleb makes that case that all our modeling, most importantly Value at Risk (VaR) is a fraud. He makes the point that he has made a killing on the market down turn because he saw past this fraud and truly understood the market.

Like anyone who bet the markets would collapse, I have no doubt Taleb did well in the downturn. But his strategy is like a broken clock that is right twice a day. He even reinforces this point by pointing out that he has only made money three times in the last 25 years: Black Monday in ’87, the dot com crash in 2000, and in this recent market collapse.

Arguing who is right on a given day misses the point. There are very important lessons to be learned, not the least of which is that all models are limited and therefore in many circumstances they’re wrong.

I love this debate because it highlights the most crucial difference between mathematicians and engineers. I have a degree in Control Systems Engineering. Engineers are practical, we call it applied mathematics. Mathematicians and, their less academic colleague’s, economists, like to deal in concepts and principals. It is obvious to an engineer that any model, like VaR, is limited in its practical application.

First models work in narrow bands. Any financial model is an approximation of a very complex system. It is intuitively obvious that a simplifying model that ignores a good deal of the complexity will only work for a limited range of motion. Mathematically there is good reason for this: the behavior being modeled – price movements of complex derivative financial instruments – is nonlinear. But to create math to describe it you need to create a linear approximation.

It is easy to mathematically calculate the range for which any particular linear approximation is valid. Go beyond this range and the model tells you nothing valid. Think of a spring; you pull on it and it pulls back. But if you pull too hard that spring deforms and no longer pulls back. We call this saturation, and once you pass saturation the equation that once gave you the force of the pull very accurately is now completely worthless.

Second, models assume a continuous market. In engineering systems this is continuous feedback that stays in phase. In the markets this means that when you create a model of financial instruments which don’t all mature at the same time, you can create a hedge by executing the right trades at the right times for various instruments in a continuous market. If you have a discontinuity in pricing everything in the model goes haywire. If the market experiences a sudden jump or fall, or if you can’t execute a trade as it moves through a given price point, your model is invalid.

Third, models are only as good as the data you feed them. Here engineers agree with mathematicians – garbage in, garbage out. In the case of the mortgage backed securities and credit default swaps, historical data was used that was not valid for the underlying subprime mortgages contained in the instruments. And, the models proved invalid – garbage out.

Taleb does make one very interesting assertion that if true could be used to better understand the market. He contends that his “fat tail”, the dramatic market crashes that happen infrequently, out weigh the potential positive results you get cumulatively all the other times in the market. He is articulating a model that might prove true and can be used to modify VaR. That is if VaR is meant to be the potential assets at risk on any day 99% of the time. Taleb is saying the other 1% ruins your return.

So VaR normally looks like:

VaR = (.99 X ‘expected asset loss’)

Taleb’s VaR is:

T:VaR = (.99 X ‘expected asset loss’) + (.01 X ‘exceptional asset loss’)

He is basically saying that T:VaR is much bigger than VaR and thus overwhelms any potential profit in the market.

Maybe he is right. But I think it is worth testing the limits of his model. Historically the market goes up over time as value is created in the economy. I find it intuitively difficult to accept his assertion that crashes will always overwhelm any market gains. I think he is fundamentally misunderstanding the limits of his own model.

1 comment:

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