# Correlation analysis of cyclically adjusted valuation measures and subsequent returns

**Data based investing**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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Typically CAPE, also known as P/E10, is calculated by using a 10-year formation period. The maximum time period for both the formation period and measurement period we’ll use is 30, which means that the performance of for example P/E1-P/E30 will be tested by looking forward 1-30 years.

For CAPB, longer measurement periods of about twenty years seem to work the best. The r-squared is much larger than with CAPE or CAPD. Even the worst formation periods seem to work better in explaining future returns than the CAPE with the best formation period. This is consistent with Keimling’s research (pdf, page 16), which suggests that normal P/B is almost as strong in predicting future returns as CAPE. The plot above shows that the cyclically-adjusted P/B is even stronger than CAPE in predicting future returns.

The reason why the r-squared of the CAPE is lower than what is often quoted is because of the long time period of the data. As you can see from the plot below, the rolling 10-year correlation of CAPE and subsequent returns has been rising over time.

Another way of viewing these correlations is bringing them into Excel and color coding them. Notice that we are now using simple correlations instead of the r-squared. The x-axis tells the formation period of the valuation measure, and y-axis tells the measurement period i.e. how long into the future the valuation measure is used to predict.

The 10-year CAPE has surprisingly high explanatory power even for forecasting 1-year periods. The explanatory power starts declining noticeably from P/E8 to the left and P/E14 to the right.

For CAPD, the correlations are weaker, but the shape is about the same.

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