The equation that blew up the market

From the Mises blog, as also O&M, comes this WIRED story of a mathematical model based on an equation that obliterated the derivatives market-

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.

David X. Li, it’s safe to say, won’t be getting that Nobel anytime soon. One result of the collapse has been the end of financial economics as something to be celebrated rather than feared. And Li’s Gaussian copula formula will go down in history as instrumental in causing the unfathomable losses that brought the world financial system to its knees.

The important part-

Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

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 bankers, investors, rating agencies, all of them simply ignored the model’s limitations, and Li’s warning – “The most dangerous part is when people believe everything coming out of it.” If I were ultra-religious, I would probably condemn Li and Co. for their hubris, playing God [with the market] etc etc. But even avowed deists like Bush and Obama suffer from a “God Complex” when it comes to markets; they feel, thanks to Keynes and his acolytes (found a new one today, in the Times of India), that the market is something that can be predicted, and centrally planned and controlled. As I have repeated again and again, it cannot be done because omniscience is not one of man’s abilities.

Philosophically speaking, everything in the universe works on the basis of the law of causality – effects always follow the cause. It follows then, that you can predict the consequences of a particular action given sufficient information. However, the more complex the phenomena and the more the variables involved, the less likely that you can predict anything at all. The problem with predicting anything as regards the universe, or the markets, is not uncertainty – it is lack of sufficient knowledge. If you try to do it – predict – regardless, you are indulging in scientism, and Hayek called it the pretense of knowledge. The actions of the bankers earlier, and governments now, flow from either their failure to understand the complexity of the phenomenon known as the market, or their belief in some twisted kind of determinism. Either way they will fall flat on their faces.

All this reminds me of Hans Bethe and his “Three Lectures” on Quantum Mechanics. In the third lecture, he says-

The inventors of quantum mechanics including the best ones like Bohr and Heisenberg and Schrodinger did a very bad service to people by putting that uncertainty principle so high in their discussion. Only the orbits of electrons and atoms cannot be described. But quantum mechanics makes exact predictions for all observable quantities; for instance for the wavelength of spectral lines. It is completely misleading to say quantum mechanics makes things uncertain. In particular, if there were no quantum theory then atoms could not exist because what you have is a nucleus – positive charge – and electrons around it. If you didn’t have quantum theory, the electrons would fall into the nucleus in quite a short time – a second or less – and you couldn’t have any atoms, you couldn’t have any chemistry, you couldn’t exist without quantum mechanics. So the idea that quantum theory makes things uncertain is totally wrong. And of course once the physicists stated it [the uncertainty principle], the philosophers were delighted and said well, everything is uncertain. That is not at all correct.

But, at least in the atomic domain, determinism does not hold. Laplace stated determinism two hundred years ago. He said: If I knew the position and the velocity of every particle in the universe at this moment, I could predict the future, exactly, and I could also predict the past, exactly, and everything is well determined. The premise of Laplace’s statement is wrong in the atomic domain.

The problem today is that people like Bethe’s philosophers and Laplace are running the world – into the ground.

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