Tuesday, March 03, 2009

The Equation that Sunk the World's Economy

LinkThis reminds me of N-Rays and Flogiston...wacky ideas that were widely believed until they were proved to be mistakes... except this is just a mathematical function, an idea seized upon by financial managers who didn't understand it, but nontheless realized it could be a useful tool to help them make oodles of money. The function isn't a mistake. It's misapplication and misuse, however, have been catastrophic.

Ok, now that I think of it, it reminds me more of "The hunt for weapons of mass destruction in Iraq."

The article goes into great detail. This illustration is just the bare bones of it.


Here's what killed your 401(k) David X. Li's Gaussian copula function as first published in 2000. Investors exploited it as a quick—and fatally flawed—way to assess risk. A shorter version appears on this month's cover of Wired.


Specifically, this is a joint default probability—the likelihood that any two members of the pool (A and B) will both default. It's what investors are looking for, and the rest of the formula provides the answer.

Survival times

The amount of time between now and when A and B can be expected to default. Li took the idea from a concept in actuarial science that charts what happens to someone's life expectancy when their spouse dies.


A dangerously precise concept, since it leaves no room for error. Clean equations help both quants and their managers forget that the real world contains a surprising amount of uncertainty, fuzziness, and precariousness.


This couples (hence the Latinate term copula) the individual probabilities associated with A and B to come up with a single number. Errors here massively increase the risk of the whole equation blowing up.

Distribution functions

The probabilities of how long A and B are likely to survive. Since these are not certainties, they can be dangerous: Small miscalculations may leave you facing much more risk than the formula indicates.


The all-powerful correlation parameter, which reduces correlation to a single constant—something that should be highly improbable, if not impossible. This is the magic number that made Li's copula function irresistible.

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