
There is an inverse correlation between the forward P/E of the S&P 500 and both the 10-year US Treasury bond yield and the comparable TIPS yield. The relationships seem to be fairly tight, but really only since 2014 or so.
The TIPS yield is available since 2003. The 10-year yield is available since 1953 and does show an inverse relationship with the forward P/E over most of that period, but rarely as tight as it has been in recent years.
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