Let's take an obvious measure of expected returns, the dividend yield on the All-Share index. A high yield should be a sign of high expected returns. There should therefore be a positive correlation between the dividend yield and measures of risk such as the Vix index.
But is there? Since 1989, the correlation between the yield and the Vix index (in end-month data) has been zero. This, however, disguises a lot of variation. During the tech bubble, and early stages of the bursting of that bubble, the correlation was negative, as low yields were accompanied by highish volatility. Over most of the rest of the period, though, the correlation has been positive, albeit variable.
There's another oddity: expected returns are more persistent than risk. For example, the correlation between the dividend yield in one month and that six months later has been 0.84 since 1989. But the sale correlation for the Vix index has been only 0.46. This tells us that risk fades away faster than expected returns, which undermines the claim that there's a close relationship between the two.
You might object that the Vix is a bad measure of risk. Sure enough, there is an alternative measure which seems better related to expected returns - the index of policy uncertainty compiled by economists at Stanford University. Since it began in 1997 it has been well correlated with the dividend yield, with a correlation coefficient of 0.51. And it is about as persistent as the yield. If we measure risk in this way, therefore, there does seem to be a positive relationship between risk and return.
There are, however, two oddities here.
One is that political uncertainty is only a subset of the overall uncertainties investors face. Why, then, should it be more related to expected returns than what is usually considered a wider measure of risk such as the Vix?
Secondly, even policy uncertainty has only a slight relationship to subsequent short-term returns on the All-Share index. Since January 1997 its correlation with returns in the subsequent month has been only 0.09.
Perhaps, though, there's a solution here. It's that the dividend yield only really predicts longer-term returns. Since 1989 the correlation between it and subsequent monthly returns on the All-Share index has been a measly 0.12. But the correlation with three-year returns has been a hefty 0.71. And the correlation between the political uncertainty index and subsequent three-year returns has been a respectable 0.39. The correlation between the Vix and longer-term returns, however, is negative.
This raises an intriguing possibility. Perhaps high risk does mean high expected returns, but only for some types of risk and only for longer-term returns.
This isn't merely good news for conventional economic theory. It's also good for investors. With policy uncertainty unusually high right now, this points to decent equity returns over the longer-term.