It's fascinating to read the post-mortem analysis of the economic meltdown, especially as it relates to the role quantitative analysts and their high-tech financial models played in pushing the industry off a cliff.

In a Wired article this week titled The Formula That Killed Wall Street, Felix Salmon writes about how a single formula, the Gaussian copula function, came to dominate financial risk modeling, and how it ultimately undermined the investment industry. The formula was the brainchild of David Li, a quantitative analyst (quant) who developed Gaussian copula to correlate risk in the now infamous collateralized debt obligations (CDOs) and credit default swaps (CDSs).

To distill the global financial collapse down to a single mathematical formula seems like a stretch, but Salmon makes a compelling case for how the Gaussian copula function insinuated itself into the ecosystem of professional financial analysts and investors:

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.

Then the model fell apart...

As it turns out, Gaussian copula, while elegant, was much too simplistic. For example, since the formula ignored the interrelationships of the individual loans that made up a CDO, as well as the historical data of housing assets, the risk correlation was all based on short-term behavior -- in this case, at a time when housing prices were rising dramatically. Investment bankers should have known that the risk was still out there. So, asks Salmon, why didn't the bankers question where the risk had gone?

They didn't know, or didn't ask. One reason was that the outputs came from "black box" computer models and were hard to subject to a commonsense smell test. Another was that the quants, who should have been more aware of the copula's weaknesses, weren't the ones making the big asset-allocation decisions. Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked.

Quantitative finance guru Paul Wilmott, who was cited in the Wired piece as one of the original critics of the copula model -- he's more of a Black-Scholes kind of guy -- thinks the industry's unexamined reliance on copula is just a symptom of a wider problem in the financial industry. In his blog this week, he laments about the cult-like tendencies that permeate the financial community:

Far more serious, because it extends to all of finance not just to a single model, is the poor education that people get in university financial engineering programs and also the blind-following-the-blind behavior that is so common throughout the industry.... It's getting quite tedious me telling people to get off their backsides and test the models for themselves.

The failure of the models is certain to have other repercussions, too. If we can believe a recent article in eFinancialCareers, the reputation of quants has taken a real beating:

What's a PhD with a bias towards quantitative finance to do? Banks have gone from screaming from the rooftops that they want quants, to whispering that they're only interested in a select handful of them. This leaves a lot of people on the sidelines.

Not only are fewer quantitative models being built, but firms are getting a lot more picky about their background. According to one recruiter, PhDs will still be needed to work on less lucrative algorithmic trading work, but funds are looking for "people experienced with dealing with noisy high frequency data sets, rather than the physicists and stochastic calculus experts previously sought after by banks."

In hindsight, it seems inevitable that financial risk models and the people designing them would have to take into account the larger social and economic context of the data. To me the whole episode should be viewed as a cautionary tale for all would-be model makers. Whether you're designing climate simulations, aircraft wings or designer drugs, it's always healthy questioning the applicability of the math. The fate of people's lives and livelihoods may hinge on such skepticism.