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.
His method 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.
Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li's formula hadn't expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system's foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.
Later in the article, Mr. Salmon documents that there were people who were warning about the use of the Gaussian copula function (including its creator, Mr. Li):
The damage was foreseeable and, in fact, foreseen. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable." Wilmott, a quantitative-finance consultant and lecturer, argued that no theory should be built on such unpredictable parameters. And he wasn't alone. During the boom years, everybody could reel off reasons why the Gaussian copula function wasn't perfect. Li's approach made no allowance for unpredictability: It assumed that correlation was a constant rather than something mercurial. Investment banks would regularly phone Stanford's Duffie and ask him to come in and talk to them about exactly what Li's copula was. Every time, he would warn them that it was not suitable for use in risk management or valuation.
In hindsight, ignoring those warnings looks foolhardy. But at the time, it was easy. Banks dismissed them, partly because the managers empowered to apply the brakes didn't understand the arguments between various arms of the quant universe. Besides, they were making too much money to stop.
In simpler terms, correlation is not causation, and as it applies to evaluating risk, unstable correlation is not an indicator of anything. Assuming that risk factors were a constant and could be used as a predictor of outcome is similar to saying that because one apple is ripe, all oranges are served sliced. What happens when an apple isn't ripe or when one rots?
Garbage in, garbage out is the fundamental rule when dealing with the reliability of formulas. The fact that the Finance world was using a formula they didn't understand, to simplify a universe that could not be simplified, should come as no surprise to anyone who tries to explain statistics/data to people who are in the middle of the IQ Bell Curve, especially when using it do to something it was never intended to do provides an incentive to do what people want to do anyway:
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.
One of the constant memes we hear (used by stupid people) is: real estate prices always go up. What is missing from that meme is the suffix: ... in the long term. Real estate prices fluctuate in the short-term and they don't necessarily rise in constant-dollars, but only in relation to inflation (giving the illusion of rising). The water in the bathtub rises for everything, making everything have a higher value, not in intrinsic, constant-dollar terms.
The March 2008 chart below details the long term trend of real estate prices (h/t Credit Bubble Stocks) from Robert Shiller (Long-Term Perspectives on the Current Boom in Home Prices):
For every dip in the above chart, real estate didn't rise. It contracted. The long term trend shows an increase in value, but only as inflation rose. If you have to sell during a down period, you will lose money when you sell (or people will default on their loans).
What is also misleading about charts like the above is that it averages the real estate market of entire nations, not individual markets. The majority of housing defaults in the U.S. are occurring in five markets.
This is especially relevant to the Gaussian copula function in that it gave a single evaluation number to a bundle of loans. That grab bag of loans could have been heavily loaded with loans in the markets where real estate was static or in decline.
It was on the average, national housing price index that the Gaussian copula function used as its correlation... which means it was always right, except when it was wrong, and the rating should have declined as house prices declined, just the opposite of constant-risk-evaluation that people thought it provided: A simplistic formula of no value whatsoever.
"Don't gamble; take all your savings and buy some good stock and hold it till it goes up, then sell it. If it don't go up, don't buy it."
-Will Rogers
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