The crash of Wall Street had been aggravated by people looking for rationales to confirm their beliefs. And there was no better source of inspiration than one modeled after a seemingly impervious mathematical formula.
An article from Wired.com on “Recipe for Disaster: The Formula That Killed Wall Street” by Felix Salmon, gives a splendid narrative.
Some excerpts (all bold highlights mine),
``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….
``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.
``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.
``In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years' worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.
``As Li himself said of his own model: "The most dangerous part is when people believe everything coming out of it."
Some observations:
One. This is another example of people how people (including the majority of experts and professionals) fall prey to cognitive biases, such as the confirmation bias, in order to buttress their beliefs.
Two. This also shows of people’s penchant to trustingly espouse mathematical models to address the concerns of social structures especially in markets.
The illustrious Friedrich A. Hayek (1899–1992) in his Nobel Prize speech The Pretence of Knowledge warned of this, ``A theory of essentially complex phenomena must refer to a large number of particular facts; and to derive a prediction from it, or to test it, we have to ascertain all these particular facts. Once we succeeded in this there should be no particular difficulty about deriving testable predictions — with the help of modern computers it should be easy enough to insert these data into the appropriate blanks of the theoretical formulae and to derive a prediction. The real difficulty, to the solution of which science has little to contribute, and which is sometimes indeed insoluble, consists in the ascertainment of the particular facts.”
For pundits, math models elicit intellectual attraction of a system that can be deliberately controlled. However, the sad reality is that they hardly capture all variables required out of the complexity of the environment. And over reliance thereof may lead to disastrous consequences, similar to the LTCM fiasco.
And this applies not only to Wall Street but to the general economics or even to the environment.
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