The solution was a formula using a technique called a Gaussian copula function. All of Wall Street rejoiced because suddenly it was easy to calculate risk without waiting for historic data:
The effect on the securitization market was electric. Armed with Li's formula, Wall Street's quants saw a new world of possibilities. And the first thing they did was start creating a huge number of brand-new triple-A securities. Using Li's copula approach meant that ratings agencies like Moody's—or anybody wanting to model the risk of a tranche—no longer needed to puzzle over the underlying securities. All they needed was that correlation number, and out would come a rating telling them how safe or risky the tranche was.And then, eventually, the market imploded. But when you look at the approach the mathematician took - examining the historic prices of credit default swaps - you start to see just how stupidly so many in finance acted:
The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.The article focuses on how you cannot count on the correlation of financial securities, because risks that seem out of sync one day can suddenly all manifest at the same time.
I'll put it a little differently than stated in the article becuase I think there's an even more fundamental point that financiers missed. Like any market, CDO purchases largely move on emotion - it's one of those indisputably human activities. When people think they are safe, they will do the most astoundingly stupid things because they simply don't perceive danger.
CDO prices are an accurate historic measurement of what people thought risk was, not of the actual inherent risk of the underlying investment on which the CDO was taken. So all of these investment decisions were made based on looking at people's perception of risk, whether right or wrong, and not the actual risk. No wonder everything blew up. It was like betting on the results of a card game when you weren't one of the players, didn't know their history of success, and couldn't see any of the cards. Here's the scary part: the people who didn't notice the difference are the ones still in charge.