With US share prices near record highs, the obvious question is: is the market overpriced? In truth, it's not obvious.
The strongest evidence that it is comes from the cyclically-adjusted price-earnings ratio, or CAPE, as measured by Yale University's RobertShiller. The is the ratio of the S&P 500 to earnings per share averaged over the past 10 years. The point of such averaging is to smooth out cyclical ups and downs in earnings, and thus remove the tendency for valuations to look high in recessions when earnings are depressed, but low in booms when earnings are high.
This ratio is now 29.8. This is far above the long-run average, which has been 16.7 since data began in 1881. It is also higher than at any time except for 1929 and the late 1990s - and on both those occasions, prices subsequently collapsed.
If this message seems clear, it shouldn't be.
One problem is that the CAPE has been well above its long-term average since at least 2011 but prices have continued to rise since then. The investor who got out of equities three or four years ago because the CAPE was high would have missed out on some big profits.
Also, there are two reasons why the CAPE should be high now.
One, says Tom Porcelli at RBC Capital Markets, is that it looks high in part simply because earnings collapsed in the slump of 2009. It makes no sense to sell shares today because of what happened eight years ago. Unless we get a massive recession, the CAPE should fall over the next few years simply because the low earnings of 2009 will drop out of the denominator and be replaced by higher ones.
Secondly, real bond yields are now probably well below their long-term average. I say 'probably' because inflation-proofed bonds were only issued quite recently so we don't have a long history of their yields. It's likely, though, that real yields, at 0.6 per cent for 10-year maturities, are some two percentage points below their post-1881 average. This should mean a higher than average CAPE simply because future earnings are discounted less heavily. This is one reason why the CAPE has been high for a long time: since 2001, it has averaged 24.4, which isn't far from its current level.
In light of all this, one fact should become less surprising; the CAPE is only moderately good at predicting future returns.
Let's consider five-yearly changes in the S&P 500, adjusted for inflation; five years should be a long enough period to overcome the tendency for expensive markets to become even more expensive in the short term. The correlation between such changes and the CAPE five years previously has been 0.3 since 1881. Yes, this is statistically significant. But it means that the CAPE can explain less than 10 per cent of the variation in subsequent five-yearly returns.
This relationship currently points to the S&P falling by 9.6 per cent in real terms over the next five years. But the margin of error in the relationship is so big as to suggest there's a roughly 40 per cent chance of the market rising, and a 25 per cent chance of it rising by 20 per cent or more.
Yes, the CAPE is sending us a sell signal. But it's quite a weak one.
If you want to be pessimistic, I'd adopt a different line. I'd argue that low bond yields aren't a justification for high equity prices. This is because yields are low because some investors believe that equities face big long-term risks - whether it be of incumbent companies being rendered unprofitable by new technologies; of a shift from profits to wages; of continued or deeper secular stagnation; or of a cyclical downturn that cannot or will not be fully offset by monetary or fiscal policy. High valuations might be a sign that some equity investors at least are not taking these dangers sufficiently seriously.
Of course, these risks might not materialise. And they do seem low for the near term. In the longer term, however - the sort of horizon over which valuations might send a useful signal - we cannot discount them. It's reasonable to feel uneasy about the combination of such dangers plus high valuations, even if high valuations in themselves can be explained away.