Evaluating Risk

Wired magazine had a really interesting article on Feb. 23, which I just saw today, called Recipe for Disaster: The Formula That Killed Wall Street. It's the story of how a Chinese mathematician (or quant) called David Li developed a formula for modeling risk, which was so brilliantly simple that it came to be used all over the financial industry - until the assumptions it was based on fell apart. For the mathematically inclined, the formula (called a Gaussian copula function) is reproduced and analyzed (at a very high level).

The article describes the curious reactions in the financial industry to Mr. Li's formula. The principal response seems to have been, "This is so easy, it must be right." Here's a quote from Wired:

At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

Why was it so simple and beautiful? For one thing, it didn't bother to use real data on mortgage defaults behind the securities to make the estimation; that would have taken too much time to gather. It used the historical prices of credit default swaps on the mortgage-backed securities as the measure of risk, assuming that the financial markets had priced those risks correctly. Of course, all those prices were based on a world in which housing prices went ever onward and upward. Unfortunately, the people who used it to make investment decisions weren't mathematically adept enough to understand the distinction between correlation and causation.

The whole episode reminds me of a famous quote from Lewis Carroll's The Hunting of the Snark:

He had bought a large map representing the sea,
Without the least vestige of land:
And the crew were much pleased when they found it to be
A map they could all understand.