Part of the problem in explaining the genesis of the financial crisis is that much of it was just so danged complicated. I’m not excusing the press here, I’m just saying YOU try to tell the uninitiated how collateralized-debt obligations worked, how they were created, how they were rated, and who bought them, in twenty inches—thirty if you’re lucky.
That’s partially why a loopy Howard Beale wannabe can become a fifteen-minute sensation: Greedy neighbors buying houses they can’t afford and defaulting on them, dragging down the poor bankers who lent to them and forcing taxpayers to prop the banks up is easy to understand. It’s soundbite- and slogan-ready in the Age of a Hundred and Forty Characters. Why those poor banks were so eager to lend and what their agents did to shovel product out the door is a more convoluted story, one more prone to glaze the eyes than fire the subcortex.
So it was nice to see a major magazine—Wired—put a story about a math formula that helped create the crisis on its cover. It’s even better that that story is well done, clearly explaining something called a Gaussian copula function in a way that even this Math for Non-Majors guy can understand.
The author, Felix Salmon, writes a blog for Portfolio called Market Movers—one of my regular reads. There, he has a knack for delving into the more complex issues that often fly over the heads of other reporters—or under their radar.
With the Wired cover, he tells how an obscure mathematician named David X. Li wrote a paper in 2000 that effectively “solved” the issue of how to measure risk, allowing the securitization market for mortgages to explode.
Here’s why Wall Street needed Li’s elegant formula:
…bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quantitative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoever—in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.
But gauging correlation in mortgages is very difficult:
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?
Salmon explains that Li’s insight was essentially to measure correlation based on the prices of credit-default swaps, which presumably rose and fell according to the underlying risk of what they insured.
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.
Salmon makes a compelling case that Li’s formula had a large role in enabling the securitization boom, and thus the housing boom, by putting a relatively easy to understand number on risk. But it had a major flaw:
Li’s copula function was used to price hundreds of billions of dollars’ worth of CDOs filled with mortgages. And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.
Bankers securitizing mortgages knew that their models were highly sensitive to house-price appreciation. If it ever turned negative on a national scale, a lot of bonds that had been rated triple-A, or risk-free, by copula-powered computer models would blow up. But no one was willing to stop the creation of CDOs, and the big investment banks happily kept on building more, drawing their correlation data from a period when real estate only went up.
Salmon doesn’t blame Li, who warned that his formula was being misunderstood and misused. But he does quote Nassim Nicholas Taleb, who says the whole thing was fundamentally flawed:
“People got very excited about the Gaussian copula because of its mathematical elegance, but the thing never worked… Anything that relies on correlation is charlatanism.”