Appetite For Destruction

This month’s Wired magazine has a cover story on David X. Li, the quant known for pioneering the Gaussian copula.  The Guassian copula was used (and still is) to price the collateralized mortgages that sent our financial system into the gutter.

Using Li’s theorem, the article describes how:

For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

But what bankers failed to realize was the domino effect that the giant swings in housing prices would have on the correlated, packaged mortgage instruments.  The article describes the basic statistical function by presenting the following, simplified scenario:

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let’s call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney’s parents get divorced, what are the chances that Alice’s parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

Li’s discoveries have been progressive for the financial industry as a whole, and he’s not to be solely blamed for the mess we’re in now.  Li was just the messenger, so why shoot him?  Li invented the models, but it was the bankers who (ab)used them.

Here’s the thing that bothers me as student.  My professors are still teaching theorems based on models that use the Gaussian copula, which would be fine, if they at least GAVE A DISCLAIMER that it’s not perfect.  The majority of students I speak to believe that the model is more of a “certainty” than a “speculative theory.”

And that’s where our financial system went wrong.

My professors response for the lack of “disclaimer,” as a result of my hostile questioning, was that “the model worked fine for 15 years.”

I told her that I agreed that it worked for 15 years, UNTIL IT FAILED.

If this isn’t a key part of any financial curriculum, I don’t know what is.

The bottom line is that financial models work, until they don’t.  Seems counter intuitive, right?

Exactly.

Related Essays

• Responsible Innovation
• Healthy Capital
• The City of Dreams

• « Social Leverage
• » A Wide-Net Strategy

blog comments powered by Disqus