Clients often ask us to what extent our expected returns should adjust to changing market conditions. For an investment grade bond, this is relatively easy - you will earn the credit spread less any defaults. So it’s quite straightforward and objective. For equities, it is much harder to say whether the market is over or under-valued. There are lots of measures that appear to work historically, but interpreting the evidence is fraught with subtleties. One commonly used metric is the Shiller P/E ratio- but does the evidence hold up?

## Shiller P/E Ratio

**Click to tweet >>**The Shiller P/E ratio differs from the normal P/E ratio in that it uses the average earnings over the last few years. @Redington

The Shiller P/E ratio differs from the normal P/E ratio in that it uses the average earnings over the last few years. Typically people use the last 10 years, although here we used the average of the last 5 years’ earnings to make slightly more use of the data set. This is not material and the takeaway point is the same.

This ratio is often used to tilt expected return assumptions for equities, and it’s easy to see why; over the long-term, the correlation between the Shiller P/E ratio and subsequent 10 year returns is around -45%. We show a graph of the results below, colour-coding each decade to make it more readable.

## What does this mean?

This is certainly not just luck; something else must explain it.

**Click to tweet >>**The obvious conclusion is the Shiller P/E can predict equity returns. But is that the most logical take-away point from the data? @Redington

The obvious conclusion is that the Shiller P/E can predict equity returns. But is that the most logical take-away point from the data? The results pass a simple significance test. But we should think about what results we would expect under different assumptions.

## What if there were no links?

To make sense of any results, it’s worth asking what the results would look like if various hypotheses were true. If the ratio had no predictive power, we might expect zero correlation with successive returns. As it turns out, this is not true.

To explore this, we ran some simulations. We assumed equity prices and earnings were log-normally distributed on a monthly basis. This meant returns and earnings from any two months were independent. We did this to ensure that any technical analysis, including P/E ratios, would have no predictive power

We kept the mean growth the same for equities and earnings. We did this because without a broadly equal assumption there can be no sense of when the ratio is high or low.

We then ran 10,000 simulated periods of 150 years.

## Results

With no predictive power, the average correlation was -35%, with a standard deviation of 20%. This means that the seemingly high historical correlation could just be noise. It is about what we’d expect if the P/E ratio had no predictive power. Even though the historical correlation is high, it is not high enough to suggest that the ratio has predictive power.

## What’s going on?

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 average of the last 10 years’ earnings does not change much over a short horizon, while the price can change dramatically, so most change is coming from the price. This means any justification of the P/E ratio comes down to a justification of mean reversion, or some sort of fundamental value. There must be some “pull to par”, whereby prices bounce around but return to a fundamental, “true” level, which 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 P/E 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 realised (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.

Realised 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. Better methods would be time-weighted volatilities or autocorrelations.

## Takeaways

We haven’t disproved the efficacy of the Shiller P/E ratio, and it may still work; it certainly makes economic sense.

What we have done is show that the historical correlation with index returns is not evidence of its predictive power. Based on this, we don’t incorporate it into our expected return assumptions. More broadly, data often includes subtle effects like mean reversion and survivorship bias. This means you need to be careful interpreting any data, and the intuitive tools may not be the best.