Many of you regard Bitcoin, and the 1,500 other crypto-currencies, as a speculative fad. I’m tempted to agree. But what if we’re wrong? Let’s suppose Bitcoin is now fairly priced: it has halved in price since December. What sort of returns might we reasonably expect on it?
Economic theory gives us a simple way of answering this. And this method works. It more or less fits the long-run returns on housing and gold, and the returns on equities in the last 20 years (although not before then). It says that average annual returns on any asset should be the product of four things:
- Its volatility. High risk requires high expected returns.
- The correlation between the asset’s returns and our financial circumstances. An asset that does badly when our other finances are doing badly is especially risky and so requires high expected returns. By contrast, an asset that holds up well when the rest of our finances are struggling offers us insurance which we should be willing to pay for in the form of low returns.
- The likelihood of bad times. The more fragile our financial situation, the less able we are to bear risk and so the higher returns have to be to induce us to do so.
- Our risk aversion. The less we like risk, the higher must be expected returns if we are take it on.
All this is common sense. Let’s now try to quantify it: my numbers will necessarily be rough but they’ll show the general point.
First, the volatility of Bitcoin. Since the start of 2012, the annualised volatility of monthly returns has been 186 per cent.
I don’t know what to make of this: it implies a very high chance of investors losing everything. But can we make such an inference given that the volatility has been upwards?
On the other hand, though, price risk isn’t the only danger for Bitcoin investors. Benjamin Edelman at Harvard Business School points out that there’s also counterparty risk: crypto-currency exchanges have sometimes closed with the loss of investors’ money.
Let’s, then, use the 186 per cent.
Our second variable is the correlation between Bitcoin and our general financial circumstances. Given that Bitcoin has only been actively traded for a short while, we don’t have much data here. But the fact that it did well last year when shares rose but has fallen this year when shares also fell suggests it is correlated with equities, which we know have been cyclical; they do badly in recessions. Let’s call the correlation 0.5.
Our third variable is the likelihood of bad times. We can measure this by the standard deviation of real consumer spending growth: spending only falls in bad times. This has been 2.3 percentage points since 1955. But of course individuals face more risk than this. So let’s multiply this by 3.
Finally, we need a measure of risk aversion, where one indicates risk neutrality and higher numbers greater risk aversion. Let’s call this 3.
Multiplying these numbers together gives us 19.3 per cent: 1.86 x 0.5 x 0.069 x 3. That’s a high annual average return. This doesn’t mean Bitcoin should rise by so much for many years, however. As (or if) it matures, its volatility should fall which should drag down expected returns.
This might, however, err on the high side even if we assume Bitcoin is now fairly priced. It could be that it has some insurance value. Some of Bitcoin’s advocates regard it as protection against the loss of value of conventional currency: defences of Bitcoin sometimes become diatribes against 'fiat money'. You can’t, however, have it both ways. You cannot claim that Bitcoin is a form of insurance and that it offers high returns. People pay for insurance, which means low returns. You can only square this circle by arguing that Bitcoin is underpriced. Given the lack of obvious valuation metrics, however, I find this tricky.
What’s more, my calculation implies that Bitcoin offers only moderate risk-adjusted returns. It implies a Sharpe ratio (return divided by standard deviation) of only around 0.1. That’s probably around the same as housing and equities.
There are only two ways to get a high expected Sharpe ratio on Bitcoin relative to other assets. One would be if it is currently underpriced. The other would be for it to be likely to do worse than other assets in bad times and so require high expected returns as compensation for risk.
The point of all this is not to provide precise numbers, but to suggest a way of organising our thoughts. All this suggests that you don’t need to believe that Bitcoin is in a bubble to be wary of it. Standard financial theory (which is really just common sense in this case) says it needn’t offer high expected risk-adjusted returns. The question, then, is: what’s wrong with this common sense? I’m not sure there is much.
