Wednesday, March 04, 2009

how the Gaussian Copula Function is to Mr. Li as the Cow is to Mrs. O'Leary

OK, I was reading some papers yesterday on the financial markets and came across the story of the day. This is so cool that I can’t believe it has not been picked up by Fox News (or maybe it has; I guess I should start watching Fox News).

It appears that much of the fault in the financial (particularly the bond markets) may be traced to the misuse of the so called Gaussian Copula Function. I just have to say, that is the coolest name for a harbinger of doom that I have ever heard! It’s so cool, I don’t even want to refer to it as the GCF – I just like typing it too much. It sounds like something from the new Star Trek series.

Gaussian = Distribution of events in a bell shaped curve.

Copula = General way of formulating a multi-variate distribution in such a way that general types of dependences can be represented.

Gaussian + Copula + Function = An untested theory allowing the conversion of power from dilithium crystals to be use to power a seized Romulan warship. i.e. “Captain, I can try to pass the power from our dilithium crystals through a Gaussian Copula Function to get enough power to make warp speed; but it’s never been done before!”

In reality, it’s a mathematical model that attempts to make sense of many disparate factors and calculate uncertainty so a decision can be made on risk (and therefore maximize return) – i.e. if the Gaussian Copula Function produces a number below the risk adjusted rate of return, take the investment; if it’s above, pass on the investment. OK, I’m neither a bond trader nor a mathematician, so I don’t know if I have the details right in the above; but that’s part of the intrigue.

Many bond traders and their managers are not mathematicians either. So it turns out that a really smart guy; let’s call him Mr. Li (mostly because that’s his name), came up with this formula. Like many theories, it does not work in all cases. But the bond guys ignored that fact; or they liked saying the name so much they couldn’t stop themselves from using it (it’s like the name Boutros Boutros Ghali, it’s so much fun to say that news guys were creating stories just to say his name). Turns out, the bond guys didn’t understand the formula or the application either, and so they made complex bets that had their basis in equal parts science, fantasy, and luck.

Even Mr. Li said of the formula “The most dangerous part is when people believe everything coming out of it”. Ain’t that the truth?

I challenge each of you to casually throw into party talk the phrase “Gaussian Copula Function” at least 3 times per week. I’d like to see if it will catch on.

Email from the BHOTW, the man whose keen eye brought you the cheddar menace.


I, Rodius said...

And the "Copula" makes it sound vaguely sexual. It's the phrase that has everything!

The way your friend writes emails, he should definitely be blogging. Or at least Tweeting.

Anonymous said...

Interesting- I read a very similar piece on a major error in the way the huge banking institutions were viewing their loan risk: they assumed that the risk of any given loan failing was independent of all of their other loans. But in fact the Nationwide interest rates, economic conditions, and expiring balloon mortgages were the dominant poles that affected them all simultaneously. It's one thing to have 1% of loans fail every year for ten years, and quite another to have 10% of loans fail in one year.

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