Conventionally, we measure stock market 'value' by comparing prices with dividends or earnings. But comparing them to any stableish trend can also reveal mispricings.
To see this, I compared the All-share index with a simple time trend, which took the value of 100 in January 1985, 101 in February 1985 and so on: I then took the logarithm of this, to reflect the fact that the percentage change in the index should be the same now as it was years ago. As you would imagine, this time trend is strongly correlated with the All-Share index, simply because both tend to rise over time.
But here's the thing. I then asked: do deviations of the All-Share index from this trend predict future annual changes in the index?
They do. Since 1990 the correlation between deviations of the index from its trend and subsequent annual changes in the index has been 0.51, implying that such deviations can on their own explain over a quarter of the variation in annual changes in the index.
For example, the All-Share was overpriced relative to trend in 2000 and 2007 and it subsequently fell. And it was underpriced in 2003 and 2009, and shares subsequently rose.
What's more, since 1990 these deviations have done a slightly better job of predicting annual changes in the index than the dividend yield. Whereas it can explain 26.1 per cent of variations in subsequent annual returns, the dividend yield can explain only 21.3 per cent. And if we try to combine deviations from trend and the dividend yield, the yield become statistically insignificant. This means the dividend yield gives us no information about future returns that a simple time trend doesn't.
Time, then, matters more for subsequent returns than conventional valuations - or at least it has since 1990. This shouldn't be too surprising. When we say that the market is over- or under-valued, we're usually telling a story not about earnings or dividends or the market's intrinsic value - something which is unobservable anyway - but about prices. But such a story can be told simply by comparing prices to a time trend.
Herein lies a problem. Shares are now overpriced relative to this trend - by 15.9 per cent as of the end of last month. Granted, the overpricing is less than we saw in 2000 or 2007, when the market was 40 and 20 per cent overpriced respectively. But, even so, this is a bearish signal. If post-1990 relationships continue to hold, this overpricing points to the All-Share index falling by 1.9 per cent over the next 12 months. To put this more loosely (and accurately), there's a slightly more than 50:50 chance of the market falling.
Luckily, though, this is not the only indicator that predicts annual returns. So too does foreign buying of US equities. And this has recently been sending a buy signal. Duting 2013, foreigners were net sellers of $40.2bn of US shares. That suggests they have been unusually risk averse, and global equities often rise after sentiment has been so depressed. This points to UK equities doing well.
And unlike the dividend yield, this indicator does convey information about future returns which is not contained in simple deviations from trend. An equation which combines those deviations with foreign buying - based on post-1990 data - points to the All-Share rising by around 16 per cent in the next 12 months, with only a 10 per cent chance of prices falling. In this sense, the fact that prices are above trend mitigates the bullish signal sent by foreign selling of US shares, rather than sends an outright sell signal - for now, at any rate.
