# Derivatives and Airplanes

Newsweek

has an

about the guts of our financial crisis and a school for the quants who would fix it. I recommend it, even though its brilliant lede is built upon a false metaphor:

This is brilliant because it casts the financial bust in concrete terms. Everyone can relate to being in a plane that's crashing. It's wrong, though, because it supposes there is a mathematical formula for predicting mortgage defaults, and claims that the quantitative analysts who devised the contracts that failed merely disregarded the formula. That's not how it happened.

A better way to envision the disaster using airplanes is to recall the Sopwith Camel, the WWI-era biplane fighter. As with all early aircraft designs, the Camel was developed by trial and error, and was absurdly dangerous compared to a modern plane. In the hands of an experienced pilot it was deadly maneuverable. But novices crashed Camels with regularity, owing to a design in which the engine itself rotated with the propeller. The spinning engine block created massive gyroscopic torque, so the plane tended to dive to the right, particularly when taking off. A slight error in fuel metering, a moment of distraction, and the plane would pitch forward and corkscrew to the ground, immolating its pilot in a cloud of fire.

The quants who formulated collateralized debt obligations and the other derivatives that just crashed and burned are akin to the "aeronautical engineers" who designed and built the early aircraft while not knowing much about flying and while discounting angular momentum. The

Newsweek

piece profiles Paul Wilmott, an Oxford mathematician with a bit of humility about the forces his formulas would try to tame.

Guided by Wilmott, the piece overcomes its initial error further in, where we learn that there was a guy who invented a formula--a false formula--that made predicting default rates seem easy:

This was the fatal shortcut. Or, at least, it was one of the fatal shortcuts. Li's paper,

presented a formula based on a theory that, given past results, the future fate of various bundles of debts could be predicted. A few observers understood what he was doing and realized it was bogus. Li himself understood the limits of his method, and apparently did not endorse its use for pricing trillions of dollars of securities without any secondary checks and balances. But most of the finance industry thought of the copula function as a key invention. It allowed the industry to mechanize and streamline the process of creating and selling the derivatives that fueled the boom and inflated the bubble. And here Newsweek gets it right too, comparing the world of finance to an industrial factory, where once a process is standardized, everyone in the business has to adopt the standard and increase production even as profit margins fall:

Overproduction always leads to bad things; the overproduction of debt isn't unique. The old way of analyzing risk required work, skill, and time--like building a biplane in your garage. To tweak

Newsweek's

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metaphor, Li's formula (and other financial "innovations" of the 1980s, 1890s, and 2000s) made possible mass-produced aircraft. But it made the planes without testing them in the real world, because there were no regulators looking over their shoulders. It was like building millions of Sopwith Camels and selling them to student pilots.