In theory, there’s a good reason to expect high returns on cryptocurrencies such as Bitcoin. In practice, though, this reason might not work – which tells all investors something about our attitudes to risk.
Of course, Bitcoin should offer high returns to compensate for its riskiness. This risk, however, isn’t simply its high volatility and tendency to fall when shares do, as happened last March. It’s something else too – the danger of non-ergodicity.
To see this, we must know what ergodicity is. A process is ergodic if its probability doesn’t change over time. A roulette wheel, for example, is ergodic: the chances of it rolling the number 16 are 36-1 (or 37-1 if you’re in the US). And this chance is the same today as it was 50 years’ ago or in 50 years’ time. An ergodic process, then, is one where past probabilities are a guide to the future.
But are asset prices ergodic? Here, we must distinguish two types of non-ergodicity, one common, one which is rarer but nastier.
The common type is that volatilities and average returns vary over shortish periods. Bull markets see good returns and typically lower volatility, while bear markets see low returns and high volatility. If you use bull market probabilities as a guide, a bear market will look non-ergodic as those past probabilities are no help in predicting future returns.
The more serious type of non-ergodicity occurs when even long-term history is no help in predicting the future.
Some important things are obviously non-ergodic: we can’t predict how our lives will turn out by looking at our past – a fact which, as the NIESR’s Roger Farmer says, might help explain wealth inequality.
We know that sometimes stock markets are non-ergodic. Imagine you were investing in Russian equities in 1916. Looking at past returns, you’d infer that the market offered reasonable chances of making money: you had 50 years of albeit volatile returns to reassure you of this. Within a few months, though, the Bolsheviks wiped you out. You suffered from non-ergodicity: the market’s past movements were no guide to future ones, as they told you nothing about the chances of revolution.
This is not an isolated example. Will Goetzmann and Philippe Jorion have shown that around a third of the national stock markets that existed in the 1920s were subsequently closed by war or revolution with investors losing almost everything.
This isn’t to say that non-ergodicity is everywhere. Even large falls in prices are consistent with returns being ergodic. For example, last March the All-Share index lost 15.4 per cent. Price movements in the previous 30 years suggested that this was the sort of move that we should expect one month every 24 years. That’s consistent with equities being ergodic. Yes, returns are not normally distributed, because extreme returns are more likely than a bell-curve predicts. But this isn’t the same as non-ergodicity.
Which brings us to why we should in principle expect big returns on cryptocurrencies. These are new assets (at least relative to bonds, equities, cash or gold) so we cannot be at all confident that the past distribution of returns is a guide to the future. In this sense, cryptocurrencies carry greater risk of non-ergodicity than mainstream assets. More cautious investors should therefore be avoiding them on this count, which means they should offer high returns to the braver investor as compensation for this risk.
Two facts bolster this suspicion. One is that ever since the work of Daniel Ellsberg in the 1950s economists have known that people hate risks that they think are unquantifiable. That’s why political uncertainty depresses shares so much and why investors own lots of shares in their own country or industry. The danger that the past might be no guide to the future is an uncertainty just like political uncertainty. So it should cause assets to be underpriced and so offer a risk premium.
Secondly, Tilburg University’s Ben Jacobsen has shown that one reason why equities have offered good long-run returns is that investors need compensation for disaster risk – the sort of thing that past probabilities do not prepare us for. If ergodicity risk is priced into shares, shouldn’t it also be priced into assets where it is potentially a bigger problem?
Not necessarily. We’ve two big pieces of evidence which tell us that new assets – which should in principle carry ergodicity risk – actually underperform and so do not carry an ergodicity risk premium.
One comes from the financial crisis. This showed us that returns on mortgage derivatives in the mid-2000s were in fact insufficient to compensate for their non-ergodicity – the fact that their risks and returns before 2007 were no guide to their subsequent future risks.
The other evidence comes from newly floated shares. Because these have little history they should in principle carry lots of ergodicity risk and so should do well to compensate for that risk. But they don’t. As the University of Florida’s Jay Ritter has documented, they on average consistently underperform the market in the three years after flotation.
Newish assets, then, do not always offer a risk premium.
I suspect there’s a reason for this. Newness isn’t only a source of risk. It’s also a source of hope. We can tell ourselves stories of how a new company will win a big market or how cryptocurrencies will displace 'fiat money'*. This is why bubbles occur in new assets: you can persuade yourself and others that a new company will grow a lot far easier than that, say, Unilever will.
This is not to say that Bitcoin is in a bubble now (though I don’t own any). It is rather to point out an oddity about asset pricing generally – that some risks are not always priced into assets: speculative and high-beta stocks, for example, do not on average outperform. Higher risk doesn’t always mean higher returns.
*Talk of fiat money is very often a sign of a crank.
