Two of the biggest puzzles in equity investing are that volatility varies considerably and unpredictably; and that there seems to be no trade-off between it and returns on the aggregate market: Alan Moreira and Tyler Muir, and Andrew Lo, have shown that it actually pays to buy equities when volatility is low not high, which is the opposite of what you’d expect if there were a trade-off between risk and return. These two puzzles might be related.
The common theme is the concept of emergence. This is the idea that aggregate social behaviour is not simply individual behaviour writ large but rather emerges from interactions between people.
To see this, let’s consider a very simple case. Imagine there are three people on a demonstration: a troublemaker who wants a fight with the police; a peacemaker who will restrain one troublemaker but can do nothing if more than one person wants a fight; and an imitator who follows whoever is next to him.
Now, imagine these line up as: troublemaker; peacemaker; imitator. There’ll then be no violence. When the troublemaker kicks off, the peacemaker will restrain him and the imitator will help him do so.
But what if the line up as: troublemaker; imitator; peacemaker? Then the troublemaker starts a fight and the imitator will follow him. And the peacemaker can do nothing to stop them. There’ll be disorder.
Of course, you can easily extend this model to account for more complicated networks of people and for spectrums of behaviour. But this captures the essence. It’s a simplification of Mark Granovetter’s threshold model and of the complexity theories of Brian Arthur at the Santa Fe Institute.
The point here is that aggregate behaviour – whether we get a riot or not – is not explained by individuals’ dispositions. Our characters’ preferences are exactly the same in the first case as in the second, and yet in the first there is peace and in the second there is violence. Instead, outcomes depend upon interactions between people.
Simple as it seems, this model explains a lot. It helps explain why riots and revolutions can suddenly occur after years of stability: think of the collapse of communism in 1989 or the Arab spring in 2010-11. Tiny changes in interactions between people – a shift from troublemaker-peacemaker-imitator to troublemaker-imitator-peacemaker – can cause a big change in behaviour.
It can also explain why recessions are sudden and not predicted by mainstream economists. As MIT’s Daron Acemoglu has shown, these too arise from interlinkages. If a company is the hub of important relationships – say because it is a big debtor or because it supplies an important input (such as bank credit) – then the collapse of that company will cause significant distress for other companies. But if the company isn’t so central – if it’s a spoke in the network rather than a hub – it won’t. This is why the collapse of a bank can cause a recession but the collapse of a retailer doesn’t.
What’s this got to do with share prices?
Plenty. Let’s rename our characters. Let’s call the troublemaker a seller of shares, the peacemaker a value investor who buys on dips and the imitator a trend-follower. This might be because he follows the herd; or because he becomes a forced seller if prices drop; or because he uses some forms of portfolio insurance as in 1987.
Now, if these three line up as seller; value investor; trend-follower we’ll get price stability. The seller will tend to depress prices but he’ll quickly find the value investor who’ll buy on dips. The trend-follower will then have no trend to follow.
If, however, they line up as seller; trend-follower; value investor things are different. The trend follower reacts to the seller's selling by selling himself. Prices therefore fall. And the value investor’s stomach or pockets aren’t strong enough to stabilise them. We’ll then get a crash and increased volatility. (You can easily imagine a similar thing happening to cause bubbles if we replace our seller with a buyer.)
Now, here’s the thing. In my story nobody’s preferences have changed. Nobody’s become more or less risk-averse. The risk premium on equities, therefore, shouldn’t change. So there won’t be the positive relationship between risk and reward which mainstream theory wrongly predicts.
You might think this is simple stuff. Which it is, although modelling more complicated networks than the one I’ve described gets trickier. It is, however, very different from a lot of mainstream macroeconomics, which assumes there is a single 'representative agent' company and single such consumer. In stories of emergence, by contrast, it is differences between companies, and relationships between them, that generate recessions. Likewise, it is such relationships between traders that generate changes in share prices and volatility. As the cliché says, it takes differences of opinion to make a market.
What we have here is a story of how stock market crashes are like riots and revolutions. They are all surprises which follow periods of stability. And they occur because of small changes in the patterns of networks – changes which, at least with our current state of knowledge and technology, are unforeseeable. Perhaps, therefore, the unpredictability of so many events – such as revolutions, riots and stock market crashes – is due not to intellectual error but to the inherent impossibility of forecasting the small changes that can have dramatic effects.
Yes, volatility has been low for many months now. But we should not assume this will continue.
