Formula From Hell
05.08.09, 12:01 AM ET
Every crisis has its evildoers. And the list associated with the current financial crisis is long, ranging from the famous Alan Greenspan to the merely infamous Richard Fuld.
But now the list has gown again with the addition of something called the Gaussian copula. At first, this evildoer excited scorn only on finance blogs, but lately it's making appearances in the mainstream financial media.
So what, exactly, is this evildoer?
The short answer: It's the formula used to figure out the risk in a pool of debts, like a mortgage-backed security. Or, to put the matter in the negative: It puts a number value on the danger that the mortgages could default at the same time. (Gaussian refers to a normal distribution, or bell curve, and copula refers to the behavior of more than one variable.)
The Gaussian copula function is a standard statistical technique. But in 2000, a numbers guy at JPMorgan Chase tricked it out as a quick and dirty way to quantify risk in very complex financial instruments. And, since the blame game is more delicious when personalized, that man was David X. Li, who came to the U.S. from China after earning a Ph.D in statistics in Canada.
Mr. Li's copula function rummages around in a lot of individual debt securities and then pops out one number that gives the probability of the securities all going bad at once. If the default correlation among the securities is low (meaning they aren't dependent, or related, to one another) then a low number pops out which means, presumably, the pool carries a low risk.
Sounds good, eh? But, even better, Mr. Li discovered a clever way to come up with the default correlation. The usual practice to determine default probability was to engage in a mind-numbing gathering of historical data on actual defaults. But Mr. Li cut that corner by using prices for credit default swaps as a proxy for the actual data.
At any rate, Mr. Li's copula was a moment waiting to happen. It was embraced ardently by investors, banks and ratings agencies like
And Mr. Li's copula was as fertile as it was popular. It ballooned a family of credit instruments like collaterized debt obligations and collaterized loan obligations which, in turn, gave birth to really fancy derivatives like collaterized debt obligations squared--or CDOs that invested in other CDOs.
So, eventually, several trillion dollars were invested in these things. And why not? The risks were known and therefore under control.
Well, as we now know, the risks weren't known and were, in fact, totally out of control. As soon as prices in the housing market started to swoon and defaults began to pile up, default correlations shot for the moon. What were once low numbers became fatally high, triggering a chain reaction in exploded paper. It was clear by 2008 that Mr. Li's copula was a joke. Hence the torrent of abuse and its status as evildoer.
Some criticisms of the copula are misguided, however. Please take, for example, the claim that the fault lay in the substitution of swap prices for actual data. The entire historical record for credit default swaps only goes back to the 1990s. And, sure, since that was a decade of rising home prices and low defaults, swap prices were uniformly and misleadingly low. But even if actual mortgage defaults had been used, it's not clear the result would have been different.
The post-war housing market was a steady grower--the only busts were occasional regional ones. Thus, in the absence of a boom-bust cycle, determining whether or not defaults were correlated would have been a mug's game in any case.
Another criticism--and one that Mr. Li acknowledged--was the assumption that correlations were constant, not changeable. This is, of course, a hilariously and obviously silly assumption. In the financial world, relationships between, and among, assets are extremely fluid. Abiding by one number is akin to spotting a fish in a swiftly moving stream and going back an hour later to catch it.
There were, in fact, many doubts about the value of the copula. But they were mostly ignored because it provided a handy bridge to connect bankers with a big pot of capital yearning to be invested in the oxymoron high-return, low-risk credit instruments. As Lisa Hess, a New York money manager, says: "The problem with copula investing was a lack of common sense, not the lack of statistical integrity."
Two weeks ago, Allison Schrager, who blogs for The Economist, bravely offered a defense of the copula. Essentially, the argument described it as imperfect but useful: A statistical convenience that reduced a complex relationship into something approximate, yet could provide guidance about risk and return under certain circumstances.
Even this rather mild and intelligent defense provoked a storm of comments--less than half of which were supportive. (Apparently once something appears on the list of evildoers, people don't tolerate much ambiguity.)
As for Mr. Li, he left Wall Street two years ago. In fact, he left the country. He's now back in China working for the China International Capital Corporation Limited. But he's still in business, so to speak. The CICC, according to its Web site, is a full-service investment bank.
Susan Lee has written several books on economics, including a college text. She is an economics commentator for NPR's "Marketplace" and a weekly columnist for Forbes.com."