12/13/20
A look at real total returns over various windows of time for the S&P 500 associated with various TRCAPE valuation levels.
12/02/20 Post - U.S. Stock Market Valuation Using P/E discussed some stock market valuation measures based on price-to-earnings ratios for the S&P 500 index. The best measures discussed were the Cyclically Adjusted Price to Earnings ratio (CAPE) and the Total Return Cyclically Adjusted Price to Earnings ratio (TRCAPE). The following chart from that post shows the TRCAPE as applied to the real (inflation adjusted) S&P 500:
Historically, when this TRCAPE valuation measure was high, the real total return of the S&P 500 tended to be lower in the future and when TRCAPE was low, the real total return tended to be higher in the future, as demonstrated in the following chart also from the mentioned post:
This begs the question, what did the future returns look like for various TRCAPE values and various time intervals, and have these return values been consistent enough to make return predictions about the future based on current TRCAPE values and past return behavior?
Using the TRCAPE data from the Real S&P 500 TRCAPE - Monthly chart above, this next chart looks at real total returns that were seen 5 years after the various TRCAPE values occurred. The x-axis represents TRCAPE values, and the y-axis represents real total return.
The previous chart shows a pretty wide variation in 5 year real total returns (y-axis). However, there are many interesting observations that can be made from this chart:
There are many instances of 5 year negative returns for all TRCAPE values.
As of the time of this post, there are no instances of 5 year positive total returns for TRCAPE values above 36.
Overall, there is a pretty wide variation in total returns, but there is much more variation for lower TRCAPE values and much less for higher TRCAPE values. For the TRCAPE values above 30, less variation may just be a natural result of there being very few times when the TRCAPE has been this high.
A definite downward trend is discernable as TRCAPE values increase. The gray trendline shows this.
The TRCAPE valuation measure would be most useful for predicting future stock market returns, if all of the data points were exactly on a trendline. The more dispersed the data points are from the trendline, the less useful TRCAPE is as a predictor. The R^2 value represents how good a fit there is between the data and trendline. A perfect fit would have an R^2 of 1. In this case, the R^2 is only 0.182.
The next chart shows the same total return vs. TRCAPE relationship for a 10 year time window.
The data in the 10 year chart looks similar to the data in the 5 year chart with a few interesting differences:
The downward total return trend for higher TRCAPE values is more pronounced. (The changing y-axis scale obscures this a bit.)
Overall, the typical total returns are a bit higher for this larger time window.
The variation in total return has narrowed a bit.
All of these differences are captured by differences in the 10 year trendline compared to the 5 year trendline. The slope of the trendline down and to the right is a bit steeper. The trendline is overall a bit higher. The trendline's higher R^2 value represents a better match between the trendline and the data points. This higher R^2 value also suggests that TRCAPE has been a better predictor for returns over the following 10 years than the following 5 years.
The next chart shows the same data for a 15 year time window.
The 15 year chart continues the pattern:
The downward total return trend for higher TRCAPE values is a bit more pronounced. (The changing y-axis scale obscures this a bit.)
Overall, the typical total returns are a bit higher for this larger time window.
The variation in total return has narrowed a bit.
Once again, all of these differences are captured by a trendline with a steeper slope, higher vertical offset, and higher R^2 value. This higher R^2 value suggests that TRCAPE has been an even better predictor for returns over the following 15 years.
It is also interesting to note that, for a 15 year window, while there are still some significant negative returns, the vast majority of the returns are positive.
The next chart shows the same data for a 20 year time window.
The 20 year chart continues the pattern for two of the trends:
The downward total return trend for higher TRCAPE values is a bit more pronounced. (The changing y-axis scale obscures this.)
Overall, the typical total returns are a bit higher for this larger time window.
The third trend, however reverses:
The variation in total return has widened a bit.
Once again, all of these differences are captured by a trendline with a steeper slope, that is offset a bit higher in the chart, and with a bit lower R^2 value. This lower R^2 value suggests that TRCAPE has been a slightly less good predictor of 20 year returns than 15.
There is also a new feature to note:
For a 20 year window, there have been no negative real total returns.
The next chart shows the same data for a 25 year time window.
The 25 year chart has these notable features:
The downward total return trend for higher TRCAPE values is about the same as on the 20 year chart. (The changing y-axis scale obscures this.)
Overall, the typical total returns are a bit higher for this larger time window.
The variation in total return has widened a bit.
No negative real total returns
All of these features are captured by a trendline with a similar slope, that is offset a bit higher in the chart, and with an lower R^2 value. This lower R^2 value suggests that TRCAPE has been a less good predictor of 25 year returns than 15 or 20.
The next chart shows the same data for a 30 year time window.
The 30 year chart has these notable features:
The downward total return trend for higher TRCAPE values is somewhat less than on the 25 year chart. (The changing y-axis scale obscures this.)
Overall, the typical total returns are a bit higher for this larger time window.
The variation in total return has widened a bit.
No negative real total returns
All of these features are captured by a trendline with a steeper downward to the right slope, that is offset a bit higher in the chart, and with an lower R^2 value. This lower R^2 value suggests that TRCAPE has been a less good predictor of 30 year returns than 15, 20, or 25.
The next chart shows all of the trendlines from the previous real total return vs. TRCAPE charts.
A few interesting observations can be made about the previous chart:
Despite the fact that the 20 year trendline goes negative at very high TRCAPE values, there are no negative total return data points for any windows of time 20 years or greater.
All of the trendlines slope down to the right demonstrating that historically higher TRCAPE values are associated with lower future returns and lower TRCAPE values are associated with higher future returns over all time windows considered.
The 15 year trendline has the best R^2 value and one of the steepest slopes, suggesting that historically, Real S&P 500 TRCAPE has been best at predicting returns ~15 years in the future.
Significant variation in returns suggests that TRCAPE has not been that good at predicting specific future return values.
The question posed at the beginning of this post was, "What did the future returns look like for various TRCAPE values and various time intervals, and have these return values been consistent enough to make return predictions about the future based on current TRCAPE values and past return behavior?" The charts presented showed what the returns looked like for various TRCAPE values at various time intervals. The data suggests that the prediction that can be made from TRCAPE values is that lower/higher TRCAPE values are a good predictor of higher/lower future returns over time windows ranging from 5 to 30 years. The data also suggests that the variation in returns is too high to make any good prediction about the specific size of these returns.