Wall Street's Infatuation With Gauss
02/25/2009
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Felix Salmon has a readable article in Wired called "Recipe for Disaster: The Formula that Killed Wall Street" on David X. Li's wildly popular 2000 financial economics innovation, the Gaussian cupola function, which was used to price mortgage-backed securities by estimating the correlation in Time to Default among different mortgages.

Li has an actuarial degree (among others), and that appears to be his downfall: he assumed mortgage defaults were like deaths to a life insurance actuary: largely random events that could be modeled.

Steve Hsu's website Information Processing has a 2005 WSJ article on Li's Gaussian Cupola:

In 1997, nobody knew how to calculate default correlations with any precision. Mr. Li's solution drew inspiration from a concept in actuarial science known as the "broken heart": People tend to die faster after the death of a beloved spouse. Some of his colleagues from academia were working on a way to predict this death correlation, something quite useful to companies that sell life insurance and joint annuities.

"Suddenly I thought that the problem I was trying to solve was exactly like the problem these guys were trying to solve," says Mr. Li. "Default is like the death of a company, so we should model this the same way we model human life."

His colleagues' work gave him the idea of using copulas: mathematical functions the colleagues had begun applying to actuarial science. Copulas help predict the likelihood of various events occurring when those events depend to some extent on one another. Among the best copulas for bond pools turned out to be one named after Carl Friedrich Gauss, a 19th-century German statistician [among much else].

Uh-oh.

The Gaussian distribution (a.k.a., normal distribution or bell curve) assumes randomness: Flip a coin ten times. How many heads did you get? Four. Write it down and do it again. Seven. Do it again. Five. As you keep running repeating this flip-a-coin-ten-times experiment, the plot of the number of heads you get each time will slowly turn into a bell curve with a mean/median of five.

But the Housing Bubble didn't consist of random events that everybody was trying their best to avoid. Instead, human beings were responding to incentives. The closest actuarial analogy might be the big insurance payouts that fire insurance companies got stuck with in the South Bronx in the 1970s when decayed businesses that were now worth less than their fire insurance payouts developed an extraordinary tendency to burst into flames in the middle of the night.