Wall Street Became Over-Dependent on Numbers, Lost Touch With Reality

Fascination with the Gaussian copula led to economic doom.

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By Michael Barone, Thomas Jefferson Street blog

Several economic blogs have pointed me to this excellent article by Felix Salmon in Wired on the Gaussian copula devised by mathematician David X. Li in 2000. This was a mathematical formula to quantify risk that "was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored." It turns out that the formula underestimated the risk of many homeowners defaulting on mortgages at the same time. A method which was useful for insurance actuaries—for estimating the likelihood that a person whose spouse had died would die earlier than the actuarial tables would lead one to expect—turned out to be unreliable.

Li's formula was used to price collateral debt obligations (CDOs). I'll let Salmon tell how things played out:

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.

Oops. Salmon is careful to note that Li is not necessarily responsible for the misuse of his Gaussian copula. But he also notes that he's moved to Beijing.

I see a pattern here: the attempt to see quantitative patterns in human behavior can be misleading unless it is supplemented by acquaintance with the qualitative facts on the ground. Li's Gaussian copula was just irresistibly attractive to Wall Street bond traders, because it expressed in one easily comprehensible number the risk they thought they were taking. But a more accurate estimate of that risk could come from actually taking a look at the properties that were being mortgaged. In a previous blog post, I linked to Michael Lewis's marvelous Conde Nast Portfolio article on " The End of Wall Street." He recounts how a trader named Steve Eisman came to the conclusion around the beginning of 2007 that mortgage backed securities and CDOs based on them were hugely overvalued. He came to that conclusion in part because of his acquaintance with facts on the ground.

More generally, the subprime market tapped a tranche of the American public that did not typically have anything to do with Wall Street. Lenders were making loans to people who, based on their credit ratings, were less creditworthy than 71 percent of the population. Eisman knew some of these people. One day, his housekeeper, a South American woman, told him that she was planning to buy a townhouse in Queens. "The price was absurd, and they were giving her a low-down-payment option-ARM," says Eisman, who talked her into taking out a conventional fixed-rate mortgage. Next, the baby nurse he'd hired back in 1997 to take care of his newborn twin daughters phoned him. "She was this lovely woman from Jamaica," he says. "One day she calls me and says she and her sister own five townhouses in Queens. I said, 'How did that happen?'?" It happened because after they bought the first one and its value rose, the lenders came and suggested they refinance and take out $250,000, which they used to buy another one. Then the price of that one rose too, and they repeated the experiment. "By the time they were done," Eisman says, "they owned five of them, the market was falling, and they couldn't make any of the payments."

His head trader Danny Moses made similar observations.

Moses actually flew down to Miami and wandered around neighborhoods built with subprime loans to see how bad things were. "He'd call me and say, 'Oh my God, this is a calamity here,'?" recalls Eisman. All that was required for the BBB bonds to go to zero was for the default rate on the underlying loans to reach 14 percent. Eisman thought that, in certain sections of the country, it would go far, far higher.

I have been a consumer of political and demographic numbers from the time my parents bought the 1951 edition of the World Book Encyclopedia, which contained results from the 1950 Census. I was overjoyed; previously the reference books I had access to only contained results from the 1940 Census. Naturally I started typing lists showing how the populations of cities and states had changed in that 10-year interval. None of the other kids were interested in this stuff at all—I was seven at the time—but I committed the populations of the nation's largest cities in the 1950 Census down to the last digit to memory, and I still remember them today. That was the beginning of what has turned out to be a career, in political consulting and journalism, based in large part in knowing and analyzing the numbers.

But as I have grown older, I have come increasingly to believe that the numbers are just clues. Sometimes misleading clues. There's a reality on the ground that you're trying to understand, and the numbers help you make sense about it, help you develop theories of why things are happening or changing as they are. But you can become over-dependent on numbers, as Wall Street became over-dependent on David X. Li's Gaussian copula, and end up being really, really wrong about reality. And you have to constantly keep that in mind. That's why I made a point, after co-authoring the first edition of The Almanac of American Politics, of traveling to all 50 states and all 435 congressional districts—which I accomplished when I landed at Ted Stevens International Airport in Anchorage, Alaska, in February 1998. It's just one way of keeping in touch with the facts on the ground.

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