The Quant That Ate New York

One of the scariest things about the financial meltdown is how evaluating risk has changed dramatically. Federal regulators allowed banks to greatly increase their loan to asset ratios. And all sorts of higher mathematics equations popped up that seemed to justify trading in murky derivatives in ways not considered before.

Portfolio financial blogger Felix Salmon has an intriguing tale in Wired magazine about just one of these quantum humpers. He is David X. Li, a Chinese mathematician who studied in Canada and is former employee of JP Morgan Chase. While there, he came up with a mathematical breakthrough called the “Gaussian copula formula” that could model complicated risks in ways thought much easier and accurate than before.

Bear with me as I try to explain Salmon’s article since higher math has never been one of my high points. A basic problem with predicting risk is assessing correlations, such as who will default on a mortgage or a credit card relative to others.

As Salmon explains, consider a student in a grade school called Alice. Assume some probabilities relating to her and assume that the chances of such things happening as her parents getting divorced, or getting head lice or seeing someone slip on a banana peel are all 5 percent. If investors based their bets on this series, they’d be trading at about the same price.

But, Salmon points out, consider what happens if you add another girl named Britney who sits next to Alice. Chances remain the same 5 percent that either child’s parents will divorce. But if Britney gets head lice, the chances that Alice will, too, rise to 50 percent. If their teacher slips on a banana peel in class, chances are even higher than both girls will see it. Thus, when you add these different factors, prices would be set all over the place. The fact that there’s no historical data to base prices upon makes the exercise even harder.

Because of this problem, financial mathematicians had long relied upon historical data as away to set a default base for their calculations. Li’s accomplishment was that he came up with a way to way to model default correlation without having to look up historical default data. His idea: use market price data about then-new credit default swaps, which are insurance guarantees for various derivatives.

Investors can lend money in two ways, either directly or through credit default swaps they sell. They get money either way in interest payments or insurance payments. If they lose, they lose big. But one can sell an unlimited number of credit default swaps against reach borrower, unlike bonds which are limited in supply.

If the price of a CDS rises, then it is assumed that the default risk has risen. How much? You’d have to wait and collect historical data about actual defaults which are rare. Li’s solution to assess risk was to use historical prices in the CDS market. Using the schoolgirl examples, Salmon notes that it’s hard to build a historical model to predict Alice’s or Britney’s behavior but “anybody could see whether the price of credit default swaps on Britney tended to move in the same direction as that of Alice.” If they did, you had a strong correlation between the two girls’ default risk as priced by the market. Li insisted you could come up with a final correlation number that would sum up the risk.

When Li published his ideas, traders were electrified. They saw ways to sell all sorts of complex financial instruments in ways they couldn’t have before. Using Li’s theories, justification could be found to get past the risk problems and sell derivatives such as collateralized debt obligations for mortgages, loans, whatever. In 2001, a year after Li published his equation, the CDS market was about $920 billion. By 2008, it had soared to $62 trillion. The CDO market grew but not as dramatically.

Li didn’t quite anticipate what happened. He was just suggesting a theory. Traders were using it to justify all sorts of things he didn’t anticipate. And, one problem with Li’s copula was that tiny changes in assumptions meant very big changes in the correlation number. In some cases, traders got goofy, less volatile results, suggesting the risk was moving somewhere else, but where? No one knew. And, traders didn’t understand that the correlation number was a variable, not a constant.

As early as 2005, Li was complaining that people were misusing his model because they didn’t get it. Critics claim that Li’s copula never worked in the first place. Li has since moved back to China. We all know what happened to the markets.