Basic financial theory often measures shares' risk by their beta, defined as the extent to which they covary with the market. Using this measure often throws up a negative correlation between beta and alpha - the portion of a share's return that isn't due to its covariance with the market. For example, if we measure beta with respect to the All-Share index by looking at annual changes since January 2001, the correlation between beta and alpha for the 28 main FTSE sectors has been minus 0.28. Low-beta sectors such as beverages, food producers and tobacco have delivered good returns while high-beta sectors, most notably banks, have done badly.
This is remarkable. It tells us that there's no trade-off between risk and return. Quite the opposite. Safer stocks have actually done better than riskier ones.
Is this just a quirk of how we measure beta? To test this, I thought about tweaking the measure of beta.
When we consider the riskiness of an asset, what should matter is its contribution to our portfolio - whether it increases or decreases the variability of our total wealth. From this perspective, what matters is not so much a share's beta with respect to the All-Share index, but rather its beta with respect to a total portfolio that comprises assets such as bonds, housing and human capital, as well as shares.
So, let's measure beta not by a share's covariance with the All-Share index but by its covariance with a balanced portfolio. Of course, such portfolios can take countless forms. But let's consider a very simple one - one comprising 60 per cent UK equities and 40 per cent gilts.
Using annual returns since 2001, sectors' betas defined this way have varied from 0.46 for tobacco to 3.0 for IT.
Here, though, is a weird thing. If we plot these betas against alphas, we get a very strong negative correlation, as you can see in my chart below. Sectors that have been defensive with respect to a balanced portfolio such as tobacco and beverages have had high sector-specific returns. And sectors with high betas, such as IT and electronics, have had lower ones. This correlation is even more negative than it is in the case of conventional betas.
This isn't a quirk of my data period, and there's little sign of it disappearing. If we look only at the past five years, the negative correlation has been even stronger than that in my chart.
Stocks that have been risky at the margin (in the sense of adding to the risks of a balanced portfolio) have been overpriced. And stocks that have been relatively safe have been underpriced.
This mispricing has been so strong as to generate a negative correlation between sectors' overall price changes and beta. This is yet more evidence that there is in many ways no trade-off between risk and return, contrary to what conventional theory predicts.
I'm not sure this is because my measure of beta is flawed as a measure of risk. Of course, you can quibble with it. But is there really a plausible meaning of risk by which (say) banks have been safer stocks than (say) tobacco in recent years? I suspect not.
Instead, what we have is a fundamental puzzle. There might be three reasons for this.
>This is yet more evidence that there is in many ways no trade-off between risk and return, contrary to what conventional theory predicts
One has been pointed out by economists at AQR Capital Management. Many fund managers, they say, have to be fully invested in equities and cannot borrow very much, if anything. When they are bullish about equities generally - which is more often than not - they therefore express this bullishness not by running down cash or borrowing and holding more equities generally but rather by buying high-beta stocks. This causes such shares to be overpriced, on average.
A second reason has been suggested by Erik Eyster at the London School of Economics and Georg Weizsacker at Humboldt University in Berlin. Their experiments show that "people tend to ignore correlations". This causes them to underappreciate the virtues of shares with low beta that help to spread risk. Such stocks are therefore underpriced.
Thirdly, investors who appreciate this mispricing cannot eliminate it. Fund managers are reluctant to buy defensive stocks for fear that they might underperform a strongly rising market; because managers are judged on relative performance, this might cost them their jobs or bonuses. And it's expensive and risky to short-sell even relatively stable shares.
Textbook economics assumes that there are free and frictionless markets in which investors assess risk rationally, which leads to a trade-off between risk and return. The real world, however, is messier and so this trade-off hasn't been so evident.
The big question for investors is: will this remain the case? But then, it is uncertainty about this issue that has been yet another reason why defensives have been underpriced in the past.
