When math goes bad

After the sub-prime mortgage meltdown and subsequent collapse of the financial system, a lot of people wondered how the credit ratings agencies got things so horribly wrong.  After Wall Street firms scraped some toxic waste from the bottom of the barrel and packaged it  as a new investment product, the rating agencies still gave it a AAA rating. It’s as good as a Treasury Bill!

Clearly there was a conflict of interest, and a lot of pressure to rate their favored client’s products favorably. But they were also using some really bad math from the Quants in the back room. Formulas that the traders really didn’t understand. Hey, but it’s all good, as long as everyone’s still making money, right?

The Wired magazine article: Recipe for Disaster: The Formula That Killed Wall Street shows what how things went horribly wrong. They tracked down the source of those optimistic ratings to one formula, developed by David X. Li at JP Morgan Chase. In 2000, he published the formula in a paper: “On Default Correlation: A Copula Function Approach.”

Li’s formula tried to compute the joint probability that any two instruments will both default.  And it did not require any historical data – just the spot prices of credit default swaps. That speed and simplicity meant that soon everyone was using the formula.

For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

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.

As a result, just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked. The consequent pools were often known as collateralized debt obligations, or CDOs. You could tranche that pool and create a triple-A security even if none of the components were themselves triple-A. You could even take lower-rated tranches of other CDOs, put them in a pool, and tranche them—an instrument known as a CDO-squared, which at that point was so far removed from any actual underlying bond or loan or mortgage that no one really had a clue what it included. But it didn’t matter. All you needed was Li’s copula function.

Of course, the formula had serious problems, as other mathematicians soon pointed out. But they were largely ignored by Wall Street firms, until things came crashing down in 2008.

In a final bit of irony, last year Li moved to China, where he heads a department of the China International Capital Corporation. He’s in charge of risk assessment for Chinese investments.

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