Does the Shiller PE predict returns?

1. The data- PE ratios against next 10 years’ returns- History

The Shiller data provides the backbone of much of the analysis I do. One common conclusion from it is that the "Shiller PE", or "PE-10" (the price-earnings ratio, but using the average of the last 10 years' earnings) can be used to predict future returns. But does it work?

At first glance, it's pretty convincing. The correlation between PE-5 (price/average of last 5 years’ earnings) and the next 10 years’ excess returns is -44% (we used PE-5 to get more out of the data set, but the results are similar). This is certainly not just luck, and something else must explain it.

We show the full data set, and colour code each decade separately (see Figure 1). As this is relatively hard to read, we split out a few decades, chosen to roughly span the data set (see Figure 2). The decades are then coloured by the starting date; so, for example, the data point for 1985 refers to the PE-5 ratio at 1985 and the returns from 1985 to 1995

Figure 1 – 10Y Equity Excess Returns against PE-5 ratios. Source: Redington, Shiller

Figure 2 – 10Y Equity Excess Returns against PE-5 ratios, sampled data set. Source: Redington, Shiller

There is a clear general trend that lower PE-5 ratios are followed by higher returns. However, the quantification of this relationship seems very inconsistent. A PE-5 ratio of 20 in the 1980s seems to mean something very different from the same ratio in the 1920s. This is a bit of a red flag for whether it is a genuine predictor or just a function of the way it's calculated

2.  What would happen if the PE ratio had no predictive power?

Idea

?

The data is subtle, and not immediately easy to understand. One approach to help make sense of it is to ask the contrapositive; that is, what would we expect to happen if the PE-10 had no predictive power?

Crucially, assuming no relationship should not lead us to expect a correlation of 0%

Approach

We simulated 100 years of monthly equity returns, using some simple assumptions. We assumed equity prices and earnings were lognormally distributed on a monthly basis, so any two months were independent. This means that any technical analysis would have no predictive power

We also kept the mean growth the same for equities and earnings. A broadly equivalent assumption is needed for the PE ratio to be useful at all- otherwise there can be no sense of when the ratio is high or low

We also switched from PE-5 to PE-10 as we were no longer constrained by data. This is pretty immaterial

We then ran 1000 simulations of the next 100 years

Findings

With no predictive power, the PE-10 still showed a correlation of, on average, -39% with the next 10 years’ returns.

Moreover, the standard deviation was 23%. This model easily explains enough of the history that the correlation observed is no longer significant.

Explanation

It is perhaps counter-intuitive that something built to have no predictive power should show a meaningful correlation with "future" returns. The explanation is that it is not predicting the future, it is predicting the past

The P/E ratio (and especially the PE-10) is dominated by the price. The average earnings of the last 10 years does not change much over a short horizon (and correlations are based on short-term changes), so any change is coming from the price. Dividing by the earnings largely serves to remove the upward trend so the prices are more comparable through time.

Any justification of the P/E ratio is really a justification of mean reversion, or some sort of fundamental value. There must be some active "pull to par", whereby prices bounce around but are drawn back to a fundamental level that is a function of earnings. This is a sensible idea and may well be true- the point is it is the ideological backbone of the PE argument.

One problem with using correlation to measure this is that any historical time series either stops or mean reverts. Whether there’s anything fundamental going on or not, once the returns are realized (and only then), there will be peaks and troughs. Once the data is there, it will go up from its lowest point, and down from its highest. Realized returns have to do this, by definition. Future returns do not. This means correlation is a poor measuring tool for this type of subtle effect.

 3.  So Does Mean Reversion Happen?

We have shown that what seemed like very strong evidence is actually rather weak evidence for the predictive power of the PE-10. While we should not accept it as effective without sufficiently strong evidence, we have also not shown that it fails. What we have done is shown that its predictive power, if present, is substantially less than it might appear.