The Black Swan: The Impact of the Highly Improbable

The only comment I found unacceptable was, “You are right; we need you to remind us of the weakness of these methods, but you cannot throw the baby out with the bath water,” meaning that I needed to accept their reductive Gaussian distribution while also accepting that large deviations could occur—they didn’t realize the incompatibility of the two approaches. It was as if one could be half dead. Not one of these users of portfolio theory in twenty years of debates, explained how they could accept the Gaussian framework as well as large deviations. Not one.

Confirmation

Along the way I saw enough of the confirmation error to make Karl Popper stand up with rage. People would find data in which there were no jumps or extreme events, and show me a “proof” that one could use the Gaussian. This was exactly like my example of the “proof” that O. J. Simpson is not a killer in Chapter 5. The entire statistical business confused absence of proof with proof of absence. Furthermore, people did not understand the elementary asymmetry involved: you need one single observation to reject the Gaussian, but millions of observations will not fully confirm the validity of its application. Why? Because the Gaussian bell curve disallows large deviations, but tools of Extremistan, the alternative, do not disallow long quiet stretches.

I did not know that Mandelbrot’s work mattered outside aesthetics and geometry. Unlike him, I was not ostracized: I got a lot of approval from practitioners and decision makers, though not from their research staffs.

But suddenly I got the most unexpected vindication.

IT WAS JUST A BLACK SWAN

Robert Merton, Jr., and Myron Scholes were founding partners in the large speculative trading firm called Long-Term Capital Management, or LTCM, which I mentioned in Chapter 4. It was a collection of people with top-notch résumés, from the highest ranks of academia. They were considered geniuses. The ideas of portfolio theory inspired their risk management of possible outcomes—thanks to their sophisticated “calculations.” They managed to enlarge the ludic fallacy to industrial proportions.

Then, during the summer of 1998, a combination of large events, triggered by a Russian financial crisis, took place that lay outside their models. It was a Black Swan. LTCM went bust and almost took down the entire financial system with it, as the exposures were massive. Since their models ruled out the possibility of large deviations, they allowed themselves to take a monstrous amount of risk. The ideas of Merton and Scholes, as well as those of Modern Portfolio Theory, were starting to go bust. The magnitude of the losses was spectacular, too spectacular to allow us to ignore the intellectual comedy. Many friends and I thought that the portfolio theorists would suffer the fate of tobacco companies: they were endangering people’s savings and would soon be brought to account for the consequences of their Gaussian-inspired methods.

None of that happened.

Instead, MBAs in business schools went on learning portfolio theory. And the option formula went on bearing the name Black-Scholes-Merton, instead of reverting to its true owners, Louis Bachelier, Ed Thorp, and others.

How to “Prove” Things

Merton the younger is a representative of the school of neoclassical economics, which, as we have seen with LTCM, represents most powerfully the dangers of Platonified knowledge.[62] Looking at his methodology, I see the following pattern. He starts with rigidly Platonic assumptions, completely unrealistic—such as the Gaussian probabilities, along with many more equally disturbing ones. Then he generates “theorems” and “proofs” from these. The math is tight and elegant. The theorems are compatible with other theorems from Modern Portfolio Theory, themselves compatible with still other theorems, building a grand theory of how people consume, save, face uncertainty, spend, and project the future. He assumes that we know the likelihood of events. The beastly word equilibrium is always present. But the whole edifice is like a game that is entirely closed, like Monopoly with all of its rules.

A scholar who applies such methodology resembles Locke’s definition of a madman: someone “reasoning correctly from erroneous premises.”

Now, elegant mathematics has this property: it is perfectly right, not 99 percent so. This property appeals to mechanistic minds who do not want to deal with ambiguities. Unfortunately you have to cheat somewhere to make the world fit perfect mathematics; and you have to fudge your assumptions somewhere. We have seen with the Hardy quote that professional “pure” mathematicians, however, are as honest as they come.

So where matters get confusing is when someone like Merton tries to be mathematical and airtight rather than focus on fitness to reality.