Black swans are difficult to predict but we still need maths in finance

James Owen Weatherall
SINCE the 2008 crash, we’ve heard steady criticism of the role of physicists in finance. The terms quants, derivatives and models have all taken on nasty connotations. But if you think about mathematical modelling in the right way, this criticism is wrongheaded.

One of the most prominent critiques is an argument from psychology. It suggests that ideas from physics are doomed to fail in finance because they treat markets as if they’re composed of quarks or pulleys. Physics is fine for space travel but, as Newton said, it cannot predict the madness of men. This draws on ideas from behavioural economics, which tries to understand markets by drawing on psychology. As markets are about the foibles of humans, they cannot be reduced to formulas.

There is nothing wrong with behavioural economics. But a criticism of mathematical modelling based on it trades on a misunderstanding. Using physics as a springboard for new ideas in finance does not involve describing people as if they were quarks. Some physicists made progress by drawing on statistics to identify new ways of thinking about risk. Others used their expertise at extracting information from noisy sources to identify patterns that could be useful for trading. Still others combined observations about markets with theories learned in physics to come up with expressions that describe how observable features of markets (like stock prices) relate to opaque features (like oncoming crashes).

None of this involves assuming that investors are a bunch of quarks. A careful study of human behaviour, in fact, is not inconsistent with using mathematical models to study markets. You should expect psychology and human behaviour to be symbiotic with mathematical approaches to economics.

A second criticism has found its biggest champion in Nassim Taleb. His influential book The Black Swan argues that markets are far too wild to be tamed by physicists. A black swan is an event that is so unprecedented it is impossible to predict. Black swans, Taleb argues, are what matter, yet they are precisely what our best mathematical models are unable to anticipate.

This is a problem for financial modelling, Taleb says. He argues that physics lives in a world called “Mediocristan,” whereas finance lives in “Extremistan.” The difference is that randomness in Mediocristan is well-behaved and can be described by normal distributions. In Extremistan, normal distributions are misleading. Applying ideas from physics to finance is a fool’s errand.

On one level, Taleb is right. We’ll can never predict everything that can happen. But recognising this is part of thinking like a physicist. It amounts to resisting complacency in model-building. But it shouldn’t stop us from figuring out how to predict as many kinds of would-be black swans as possible.

Taleb believes that black swans show that mathematical modelling is fundamentally unreliable. It seems to me you can argue that a model is flawed, albeit usually in ways that a responsible builder would recognise from the start. But arguing that model-building as a whole is doomed is different.

The process of building models is the basic methodology underlying all science and engineering. It’s the best basic tool we have for understanding the world. We use models to build bridges and to design airplanes. What does it mean to say that, since the methodology behind these models cannot be used to predict everything that could ever happen, it should be abandoned? If Taleb is right, you should never drive over a bridge. At any moment an unprecedented earthquake could occur that the bridge builders’ models didn’t account for and the bridge could collapse. You should never build a skyscraper because it might be hit by a meteor. Don’t fly in an aeroplane, lest a black swan collide with its engines.

Taleb would have it that finance is different to engineering – that its extreme events are more unpredictable or more dangerous. But it’s hard to see why. Catastrophic events usually come without warning. This is true in all walks of life. And yet, it doesn’t follow that we shouldn’t do our best to understand what risks we can.

It’s important to distinguish between the impossible and the merely very difficult. There’s little doubt that mastering financial risk is extremely difficult – much more difficult than solving problems in physics. But the process is the best way we have for addressing our biggest challenges.

James Owen Weatherall is assistant professor of logic and philosophy of science at University of California, Irvine, and author of The Physics of Finance (Short Books).