Ever heard of a Gaussian copula function?
It turns out to be quite an important thing. You see, it's a major piece of why the financial sector imploded.
To start with, the inventor of the formula, David X. Li, based his formula on a simplified model of the economic market and an implicit assumption that the market can price the risk of loan default correctly. By disregarding a lot of the small details, he came up with a single formula that offered a single, simple risk correlation number for almost any pool of securities. And thus was born the era of the CDO, the Collateralized Debt Obligation.
But the devil is in the details, and the CDO/CDS castle was built on the sand of the idea that correlations are stable, constant, and predictable. Despite repeated warnings that the copula was "not suitable for use in risk management or valuation", they kept using it anyway — because the piles of ultimately imaginary money meant more to them than warnings from naysayers.
Li himself was among those giving the warnings. But none of the fund managers and debt traders listened ... until the mortgage bubble burst, the correlations went negative, and suddenly the bottom fell out of all the CDO/CDS instruments.
"Li can't be blamed," says Gilkes of CreditSights. After all, he just invented the model. Instead, we should blame the bankers who misinterpreted it. And even then, the real danger was created not because any given trader adopted it but because every trader did. In financial markets, everybody doing the same thing is the classic recipe for a bubble and inevitable bust.
Nassim Nicholas Taleb, hedge fund manager and author of The Black Swan, is particularly harsh when it comes to the copula. "People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked," he says. "Co-association between securities is not measurable using correlation," because past history can never prepare you for that one day when everything goes south. "Anything that relies on correlation is charlatanism."
The writing's been on the wall for anyone to see for years, as in this article from September 2005:
"The most dangerous part," Mr. Li himself says of the model, "is when people believe everything coming out of it." Investors who put too much trust in it or don't understand all its subtleties may think they've eliminated their risks when they haven't.
Much of that money is riding on Mr. Li's idea, which he freely concedes has important flaws. For one, it merely relies on a snapshot of current credit curves, rather than taking into account the way they move. The result: Actual prices in the market often differ from what the model indicates they should be.
As with any model, forecasts investors make by using the model are only as good as the inputs. Someone asking the model to indicate how CDO prices will act in the future, for example, must first offer a guess about what will happen to the underlying credit curves - that is, to the market's perception of the riskiness of individual bonds over several years. Trouble awaits those who blindly trust the model's output instead of recognizing that they are making a bet based partly on what they told the model they think will happen. Mr. Li worries that "very few people understand the essence of the model."
The "incident" in May 2005 should have been a very clear warning that the investment structure was built on unstable ground. But traders and investors dismissed it as a fluke and went on just as they had been, assuming that it was a one-off event that would never happen again. The $275 billion of CDOs — "collateralized debt obligations" — on the market in 2000 grew to $4.7 trillion by 2006. Worse, the $920 billion in outstanding credit default swaps ballooned to $62 trillion by the end of 2007.
Then house prices stopped rising... and here we are.
