In theory, there should be a good fit. If the PE ratio for a market - or for an individual stock - is low, that implies the market is cheap (price paid is low relative to earnings purchased). It follows that the market should perform well as investors hurry to buy those undervalued earnings. With the dividend yield, the relationship is the other way round - a high yield indicates good future performance because lots of income is on offer for the price paid.
These relationships - between market ratings and subsequent performance - must have been tested umpteen times, but I've never seen the proposition tested putting values for the PE ratio and the dividend yield into a basic regression equation.
The non-statistical will know a regression equation as a 'scattergram'. On a chart, we plot dots showing the relationship of one variable to another at regular intervals. When we have enough dots to make a decent sample, we draw a line that shows the best fit between all the dots. The predictive significance is in the direction that line slopes and how steep is its slope; the predictive power lies in how well the line fits those scattered dots.
The charts test the idea by juxtaposing the PE ratio and the dividend yield for London's All-Share index against the percentage change in the index's value 12 months after the observation. So, in the PE driver chart, that dot in the very top right-hand corner says that in April 2009 the market traded on a historic PE ratio of 7.7 times and that 12 months on - by April 2010 - it had risen 48 per cent. Make 75 identical observations once a quarter starting in April 1993 and we have a statistically significant sample.
Statistically significant, yes; nevertheless, the results show that the PE ratio - whose ubiquity implies it is truly important - has such weedy predictive power it's barely worth bothering with. Intuitively, that's obvious just from its chart. The dots are all over the place, so that the line of best fit - well, as we said - it's like Hardy on Laurel, which makes it all rather Laurel and Hardy.
We can use something called 'R squared' to quantify just how poor is that line of best fit. This apportions how much variability around the line is due to mean regression, which is statistically useful, and how much is due to unknown factors. If all observations in a series of data fell along the line of best fit, the regression equation would have perfect predictive power, the R squared value would be 1.0 - and that would not be a real-world finding. The higher the value of R squared between zero and 1.0, the better that the data fit the regression line and greater the predictive power of the relation between the variables. Yet with sophisticated systems - such as a stock market's drivers - R squared won't be higher than 0.5.
Even so, the R squared of 0.1 for the PE ratio is disappointing. To generalise, it says the PE ratio is responsible for just 10 per cent of a market's performance 12 months on and unknown factors drive the other 90 per cent. The dividend yield is more useful. Its R squared is 0.27, so it accounts for 27 per cent of a market's subsequent performance. It's also logical that dividend yields should be better predictors than PE ratios. Yields are based on cash - the money that companies distribute to shareholders - while PE ratios are based on earnings, an accounting device with limited relation to money.
And instinct says there won't be a factor that exerts more influence on a stock market than dividend yields, although others - especially interest rates and the oil price - may be big players. That contention is for another time. Meanwhile, don't think of this exercise as another nice mess I've gotten into. Think of it as a slimming exercise - watch yields; ignore PE ratios.
