The further to the left or the right you move, the more your lens on life distorts.

Tuesday, February 24, 2009

The Gaussian Copula Function

Have you ever heard of David X. Li? Probably not. Li is a mathematician who created something called Gaussian Copula Function—an elegant solution to a heretofore intractable problem that allowed banks, bond traders, insurance companies, hedge funds and others on Wall Street assess risk by examining the correlation of disparate, seemingly unrelated events that had little relation to the actual history of the entity under examination. In 2000, Li published a paper that—through misinterpretation by others, greed by many, and irresponsibility by most—would ultimately lead to the worst financial disaster of the last 100 years.

In an article that you should read in its entirety, Felix Salmon of Wired magazine describes the dangers of mathematical modeling when it loses sight of the realities of the real-world:
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.

His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored.

It was Li’s model, misused and misunderstood, that allowed credit rating agencies to look at toxic mortgage tranches and rate them AAA. Why? Because Li’s model never considered the realities of falling housing prices, the innate instability and unpredictability of mass markets, the irresponsibility of people who took loans they couldn’t afford, or the greed and stupidity of the Wall Street masters-of-the-universe who were making too much money to be bothered with questions about the reliability of the Gaussian Copula Function. Most of them probably never even heard of it—and they didn’t care.

The real world has a way of intervening, and it did in 2008. Salmon comments:
Then, the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.

Salmon titled his article “Recipe for Disaster: The Formula That Killed Wall Street.” But it did far more than that. Although Li himself is not to blame, the irresponsible fools who used it improperly destroyed small and large businesses, froze credit, caused 401Ks to evaporate, and did more damage our economy than can be imagined. The regulators and rating agencies shrug their collective shoulders and argue that they were just following the then-existing rules—process over common sense. The politicians who stood by—too ill-informed or stupid to properly understand and regulate the irresponsible fools—now pontificate on the need for fiduciary responsibility. And what about those of us who were responsible, who paid every debt, who never purchased more than we could afford? Why are we so quiet, so calm in the face of this travesty?

Maybe it’s because deep down we know that the people who lead us are less than we think they are. The people have a fiduciary responsibility to run financial houses, banks, and insurance companies in a responsible way are in it only for the year end bonuses. The people who regulate them are lazy or corrupt or both. And the people on “main street?” Most are solid citizens, but some are blatantly dishonest and greedy in their own way.

So we shrug our shoulders and lick our financial wounds and hope against hope that it’ll be different next time. It won’t.