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Quant who Killed Wall Street?

Wired article on David X. Li, aka the quant of the Gaussian copula (in)famy… finally getting a little sunshine, along with other underexposed incidents, tertiary bacchanalia and personas sub involvus like Blythe Masters (hyperbole alert: destroyer of worlds?).

But, whats with the head lice metaphors?

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let’s call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney’s parents get divorced, what are the chances that Alice’s parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

A copula is a multivariate joint distribution defined on the n-dimensional unit cube [0, 1]n such that every marginal distribution is uniform on the interval [0, 1]. (for a different take on the gaussian copula take a historical stroll over to quant dating site quantnet, where you can find discussions like these. Continuing the article,

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it’s a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

The exact science of relative value… hello? basic paradox. Avoid unless its fictional or hypothetical. You can laugh at metaphysics, until metaphysics laughs at you.

March 3, 2009
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