To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it's harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation's macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?

Enter Li, a star mathematician who grew up in rural China in the 1960s. He excelled in school and eventually got a master's degree in economics from Nankai University before leaving the country to get an MBA from Laval University in Quebec. That was followed by two more degrees: a master's in actuarial science and a PhD in statistics, both from Ontario's University of Waterloo. In 1997 he landed at Canadian Imperial Bank of Commerce, where his financial career began in earnest; he later moved to Barclays Capital and by 2004 was charged with rebuilding its quantitative analytics team.

Li's trajectory is typical of the quant era, which began in the mid-1980s. Academia could never compete with the enormous salaries that banks and hedge funds were offering. At the same time, legions of math and physics PhDs were required to create, price, and arbitrage Wall Street's ever more complex investment structures.

In 2000, while working at JPMorgan Chase, Li published a paper in The Journal of Fixed Income titled "On Default Correlation: A Copula Function Approach." (In statistics, a copula is used to couple the behavior of two or more variables.) Using some relatively simple math—by Wall Street standards, anyway—Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

If you're an investor, you have a choice these days: You can either lend directly to borrowers or sell investors credit default swaps, insurance against those same borrowers defaulting. Either way, you get a regular income stream—interest payments or insurance payments—and either way, if the borrower defaults, you lose a lot of money. The returns on both strategies are nearly identical, but because an unlimited number of credit default swaps can be sold against each borrower, the supply of swaps isn't constrained the way the supply of bonds is, so the CDS market managed to grow extremely rapidly. Though credit default swaps were relatively new when Li's paper came out, they soon became a bigger and more liquid market than the bonds on which they were based.

When the price of a credit default swap goes up, that indicates that default risk has risen. Li's breakthrough was that instead of waiting to assemble enough historical data about actual defaults, which are rare in the real world, he used historical prices from the CDS market. 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 on Alice. If it did, then there was a strong correlation between Alice's and Britney's default risks, as priced by the market. Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn't just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything.