Summary
- We look at the relationship between 10y Treasury yields () and Shiller PE10 ratios () from 1971 to 2021.
- When these two measures are compared and correlated, without time lags, there seems to be no relationship.
- When we consider time lags, a relationship becomes apparent: periods of tightening, when yields go up, seem to be followed by contractions in Shiller PE10 ratios.
10y Treasury yields vs. Shiller PE10 ratios from 1971 to 2021
The graph below shows the relationship between 10y Treasury yields and Shiller PE10 ratios during the period going from 1971 to 2021. The low Shiller PE10 ratios shown at the bottom generally occur during market crashes. The R-squared for the relationship is shown next to the best-fitting inverted J curve.
As we can see, the 10y Treasury yield explains only 5.1 percent of the variance in the Shiller PE10 ratio, even after nonlinear function transformation (aka “warping”). The relationship is weaker if it is modeled as a linear association. This goes against the idea that there is a relationship between 10y Treasury yields and Shiller PE10 ratios.
Arguably the time period considered is too large to be representative of what might happen today. Notably, the S&P 500 has been much more strongly influenced by high growth companies since 2003, after the crash of the “tech bubble” and the emergence of a few large and very successful technology companies.
10y Treasury yields vs. Shiller PE10 ratios from 2003 to 2021
The graph below shows the relationship between 10y Treasury yields and Shiller PE10 ratios during the more recent period going from 2003 to 2021. Again, the low Shiller PE10 ratios at the bottom occur during the market crash of 2008 (those ratios did not drop as much during the COVID crash), and the R-squared for the relationship is shown next to the best-fitting J curve.
As we can see, the 10y Treasury yield explains 12.3 percent of the variance in the Shiller PE10 ratio, with nonlinear function transformation (aka “warping”). Still, this is a small number, which goes somewhat against the idea that there is a relationship between 10y Treasury yields and Shiller PE10 ratios.
However, closer inspection of the data suggests that market corrections and crashes, where typically Shiller PE10 ratios contract quickly, follow periods of tightening (top-right part of the graph). Also, PE10 expansion appears to occur after easing (top-left part of the graph).
Time series of 10y Treasury yields vs. Shiller PE10 ratios from 2003 to 2021
The graph below shows a time series with 10y Treasury yields in blue and Shiller PE10 ratios in orange, during the period going from 2003 to 2021. Since this is a time series graph, with time varying along the x axis, we can more easily spot lagged relationships.
Here we can see that periods of tightening (blue arrows up) appear to be followed by periods where the Shiller PE10 ratios drop (orange arrows down). This suggests that there is a relationship between 10y Treasury yields and Shiller PE10 ratios.
Conclusion
There seems to be a relationship between 10y Treasury yields and Shiller PE10 ratios. Periods of tightening, when yields go up, seem to be followed by drops in the Shiller PE10 ratios drop. And, given that yields rising precede PE10 ratios dropping, there is a predictive “flavor” to the relationship.
The problem is that as yields go up, so do PE10 ratios, until a point is reached where PE10 ratios drop precipitously. While it is not clear when the tipping point is reached, it seems to occur after a 1 to 2 percent point rise in yields.
