During the last five years, mining stocks have had the highest sensitivity of any FTSE sector to monthly changes in the All-Share index, with a beta of 1.62. They have also had the worst returns of any sector, losing an average of 1.9 per cent per month - a fact that remains true even if we control for miners' sensitivity to returns on the general market.
This is part of a pattern. Across the 28 main FTSE sectors in the last five years there has been a significant negative correlation (of minus 0.51) between beta and alpha, or market-adjusted returns. For example, the five lowest-beta sectors (general retailers, healthcare, utilities, food producers and non-life insurers) have had an average monthly alpha of 0.82 in the last five years. This means that if the market had been flat, they would have risen by over 10 per cent per year. By contrast, the five highest beta sectors had a slightly negative alpha, as bad returns on miners and banks offset good ones on IT hardware.
This is no mere quirk of the last five years. Since 1987 there has also been a negative correlation (of minus 0.43) between sectors' alpha and beta.
Nor is it just a UK phenomenon. Lasse Heje Pedersen and Andrea Frazzini of AQR Capital Management have studied international stock markets, bonds and commodities and found a similar pattern in all of them. "High beta is associated with low alpha," they conclude. This, of course, is just another way of saying that defensive stocks usually do better than they should.
They believe there's a simple reason for this. To see it, imagine you are bullish of equities. What do you do? Textbook theory says you should reduce your holdings of safe assets and increase your holdings of the market generally, perhaps even borrowing to finance buying of the general market if you are willing to take on risk.
Many investors, however, cannot or will not do this. Unit trust managers are expected to be more or less fully invested and many other institutional investors can't or don't change their asset allocation very much or are unable to borrow. All this means they can't express their bullishness by buying the general market. Instead, they do so by being overweight in high beta shares in the hope that these will outperform if the market rises. In effect, they use high-beta stocks rather than borrowing to get a geared position on the market.
This, though, means that high beta stocks will be overpriced. And because most investors are bullish most of the time, it means they will be overpriced on average over the long run - although not always. The upshot is that high beta stocks will, on average, underperform and a strategy of betting against beta will make profits, as Messrs Pedersen and Frazzini show.
Now, this doesn't mean you should necessarily avoid high beta sectors such as miners. If markets bounce back strongly - say because they see signs of a recovery in China - their betas might generate sufficiently high returns to offset their usually low alphas. And absolute returns matter: as the old saying goes, you can't eat risk-adjusted returns.
What it does mean, though, is that you should be very sceptical of the idea that high beta stocks - miners, financials, whatever - are fundamentally underpriced. Of course, some might be sometimes. But both history and theory tell us that it is defensive stocks rather than high-beta ones that are more likely to be underpriced.