by Nick Chater, Adam Sanborn, Zhu Jianqiao and Jake Spicer

Financial markets are, of course, notable for their unpredictability. They undergo periods of relative calm, but also periods of dramatic seesawing (a phenomenon known as volatility clustering) and booms, and especially busts, are far more likely than the ‘random walk’ model would predict.

These characteristics of financial markets - unpredictability, fat tails and volatility clustering - are just some of a long list of empirically observed patterns that finance theorists hope to explain. Our research project for Rebuilding Macroeconomics considers these patterns from a rather unusual point of view: rooted not in finance theory and economics, but in experimental psychology and the natural sciences.

Famously, some of the unpredictability of financial markets seems inevitable. If everyone could know that the market was about to go steadily upwards, people would rush to buy, to make a predictable profit. So the market would jump up in a flash, rather than creeping steadily and predictably upwards. The same applies on the downside – if we could reliably see losses on the horizon, we’d all sell and the losses would arrive today.

There are, though, also lots of other patterns in markets, so-called “stylised facts” that finance scholars and traders consistently observe. One of the most notable, and important, is the existence of “fat tails” in the distributions of returns. “Fat compared to what?” you may ask. Well, if the stock were a pure random walk, bobbling up and down, moment-by-moment, with no further constraints, then a big loss or a big gain on the market should be pretty rare.

Indeed, we can work out just how rare, by considering the chance of a series of a certain run of all or mostly upward steps; or downward steps, occurring by chance. The ‘normal’ bell-shaped distribution that results makes extreme up-turns or down-turns rather unlikely. The tails of this distribution are reassuringly thin – extreme market shocks should be rare. But the truth is very different. Stock booms, and especially busts, are far more likely than the ‘random walk’ model would predict. The observed tails in markets are actually alarmingly fat. Extreme market events, including crashes, happen ominously often.

Not only that, the market doesn’t bobble steadily up and down, with price movements being roughly the same size from one day, week, or month to the next. Rather, price changes tend to clump together---there are periods of relative calm, but also periods of dramatic see-sawing, or volatility clustering.

In our project we started by asking how far the “stylized facts” in financial data are actually specific to finance at all. As psychologists, we knew from previous research that time-series generated by single individuals in experimental conditions can have some rich and interesting statistical properties.

So we started out by collecting some new data from what is almost the simplest (and most boring!) experiment imaginable. The hapless participant is exposed to a regular sound (e.g., once every second) and then has to tap in ‘time’ with that pulse as accurately as possible, continuing when the pulse is removed. A thousand taps or so later, the experiment is over, and the participant can escape. Hardly an exciting activity – and clearly very different from trading on the stock market.

But it might be ‘telling’ if it turned out that noisy ‘brains’ automatically generate patterns that are not so different from noisy markets.

Indeed, when we compiled the list successive times between taps, treated these ‘as if’ they were stock prices, and carried out the standard analyses from finance, we found that many of the stylized facts about markets turn out to be stylized facts about tapping! Taps are unpredictable; their distributions have fat tails (extremely slow or fast taps are surprisingly common); and they, too, show volatility clustering (periods where tapping is regular, and periods where taps are highly irregular). Indeed, many of the patterns in our simple tapping task turn out to be eerily similar to market behaviour.

What is going on? One possibility is that noisy brains show characteristic patterns, almost whatever the task; and noisy investors (who possess, after all, those noisy brains) merely amplify these effects when they are linked together in a market.

We explored this approach by applying a simple psychological model of sequential behaviour that had previously developed for entirely different purposes. This model, using a sampling method borrowed from computational statistics (the grandly titled “Metropolis-coupled Markov Chain Monte Carlo” algorithm) turns out to generate data that also match many of the ‘stylized facts’ both of the tapping data and financial time series.

Now we can build a simple model of the market (by having many simulated noisy brains, now noisy traders, guessing the future stock price, rather than tapping) and adding in so-called ‘rational traders’ (who could be funds or algorithms) who might exploit any patterns created by the noise traders. Using a classic behavioural finance model developed by our collaborator at Harvard University, Andrei Shleifer, we generated price series from this mix of simulated noise traders and rational traders. Indeed, the price series generated by our simulations also show the very same characteristic stylized patterns – the properties of individual noisy brains may, then, percolate up to explain market behaviour.

There is, though, also an alternative possibility. Perhaps a wide range of complex systems, including brains, markets and perhaps many others, automatically generate these patterns, for some deeper reasons arising from the theory of complexity. Our colleagues on other parts of the Rebuilding Macroeconomics project, Jean-Pierre Bouchaud and Doyne Farmer, have pointed out some fascinating indications from past work in physics, which suggests this may be right. So we’re now looking for data on broader types of time-series, including those generated by atmospheric turbulence, heart-beats, and more, that may throw light on the link between noisy brains and noisy markets.