Why maths can tell us little about financial markets

Why are the financial markets so hard to predict? In the past weeks we’ve seen bond yields rocketing, stock markets teetering and men in suits panicking. It’s odd, really, that with all the computer programmes and maths geniuses who work in finance that they just don’t have a clue what is going to happen next.

In fact, all this maths is part of the problem. There’s no doubt that numbers can help to clarify things, and calculations like the Black-Scholes-Merton model for pricing options has been a force for good in the world, but it’s a strange modern disease to think that maths is always helpful.

The history of philosophy shows that mathematisation is a dead end. In the early 20th century the logical positivists tried to use mathematical logic to solve philosophical problems. They soon realised that they just couldn’t make sense of ethics, religion, art or any of the others things that matter to people. They concluded that all those things were literal nonsense. Everybody else decided that logical positivism was hokum.

Perhaps Nietzsche’s greatest insight was that whenever human beings talk about anything, the language they use is a complicated mess of assumptions, suppositions, traditions, theories and personal experience, most of which is invisible to the speaker. All our language is - to use Nietzsche’s phrase - human, all too human. To a large extent language creates reality. That is very true indeed of economic language.

Recently, I read a commentary by an economist who said that the laws of economics are like the laws of physics, meaning (I think) that they are always the same, everywhere. That would have had Nietzsche snorting through his moustache.

There is what sociologists call a “generic resemblance” between much of modern finance theory and mathematical physics; they look the same in some respects. But there is a crucial difference: theorising about financial markets becomes a part of those markets. If you start telling people how markets work, they will use that information and the market changes. “The market” is constantly mutating, it isn’t a stable thing that you can sit back and observe, but a kaleidoscope that is changed by your attempts to make sense of it.

Economics is what sociologists call a “social kind” and not a “natural kind” discourse. The Black-Scholes-Merton equation is in fact similar to the theory of Brownian motion, but the crucial difference is that using Black-Scholes-Merton equation changes the way the markets work, while talking about Brownian motion doesn’t make one iota of difference to the way particles move.

Financial markets are chock-full of feedback loops and self-fulfilling prophesies – interestingly, that term was invented by a sociologist called Robert K Merton who studied financial markets, and who used a bank run as the paradigm example. It’s a truism for sociologists that all stable social institutions rely on self-validating assumptions, and especially when it comes to finance: that money will be exchangeable for goods and services, that insurers will pay up, that Italian government bonds are safe.

When those assumptions evaporate, the boffins might as well go home. Trying to predict what will happen next in this human, all too human turmoil is a mug’s game. Expect more pinstriped panic, and frowning at computers.