To see this, consider my table showing hypothetical returns on two imaginary stocks in 10 periods, with the same returns and volatility. Which is the defensive share, A or B?
Standard economics says it's B. It has a lower correlation with the market and a lower beta.
| How to define 'defensive' | |||
|---|---|---|---|
| Period | Market | Stock A | Stock B |
| 1 | 6 | 5 | 6 |
| 2 | 3 | -1 | 4 |
| 3 | 2 | 5 | 6 |
| 4 | 2 | -1 | 4 |
| 5 | 2 | -1 | -9 |
| 6 | 1 | 4 | 4 |
| 7 | -2 | 1 | -3 |
| 8 | -2 | 1 | -4 |
| 9 | -2 | 1 | -2 |
| 10 | -10 | -14 | -6 |
| Beta | 1.00 | 0.57 | |
| Correlation | 0.80 | 0.57 | |
| No of co-moves | 4 | 9 | |
But look at the number of times that the shares move in the same direction as the market. In nine periods out of 10, share B moves in the same direction as the market. But share A moves in a different direction more often than not. By this criterion, A is the defensive stock.
This difference exists because correlations and betas in effect give great weight to period 10, when there's a big fall in the market. Personally, I think this is reasonable: it's big falls that surely worry us.
And here's the thing. Michael Ungehauer and Martin Weber at the University of Mannheim show that people measure correlations not in the way economists do, but by simply counting the number of co-movements. They therefore infer that A is the defensive stock, not B.
Messrs Ungehauer and Weber established this experimentally, by showing subjects price moves such as those in my table and asking them to estimate correlations. They found that such estimates were formed by a simple count of co-moves in which big moves are underweighted. This is consistent with other research. Erik Eyster and Georg Weizsacker have shown that investors often neglect correlations when building their portfolios. And, in a different context, Benjamin Enke and Florian Zimmerman have shown that people ignore correlations between news stories and so overreact to unreliable signals. All this evidence suggests that people are bad at judging correlations.
You might object that what's true in the laboratory isn't true in the real world. However, Messrs Ungehauer and Weber then measured the riskiness of US shares in the same way that their lab subjects did - by simply counting the number of times they moved in the same direction as the market. They found that stocks that co-moved a lot have beaten the market on average since 1963 whereas high-beta stocks have not. This implies that in the real world it is frequency of co-movement that is regarded as risky and which thus attracts a risk premium, rather than beta.
This suggests that defensive stocks might outperform simply because investors don't regard them as defensive.
This, of course, is not the only explanation of the defensive anomaly. It's also possible that investors underweight the importance of monopoly power as a source of earnings growth and so neglect big defensive stocks. It's also the case that stocks investors like a lot will underperform if the market does very well. What we have here, though, is another explanation. Is it consistent with the idea that investors are rational? Well, that's another matter.
