Recipe for Disaster: The Formula That Killed Wall Street:
In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn’t understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.
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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. They could, however, understand something as simple as a single correlation number. That was the problem.
Pr[TA < 1, TB < 1] = Φ2(Φ-1(FA(1)),Φ-1(FB(1),γ)), the Gaussian copula. I’m waiting for the book to come out titled “The World Is Not Normal.” Here’s a PDF of the paper referenced in the article, a quick skim doesn’t suggest that it’s really that opaque a piece of financial mathematics. The problem seems to be the same as with Value at Risk which was profiled in The New York Times Magazine. Long Term Capital Management was claiming regular occurrences of “10 sigma events” when it was going through its meltdown in 1998. Risk has a tail as long and vicious as a Diplodocus.
Update: See comments at Marginal Revolution.
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