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Here's another study on CAPE that came out recently.
"Why the High Values for the CAPE Ratio in Recent Years Might Be Justified"
https://www.mdpi.com/1911-8074/16/9/410 The author says "Relying solely on historical CAPE averages to forecast equity returns may therefore prove unreliable. The findings in this paper indicate that investors should incorporate multiple factors, including required return and expected earnings growth, when forming capital allocation decisions across asset classes.
Rotating out of the equity market simply because the CAPE Ratio shows that the equity market is too expensive might not produce the desired outcome that investors hope for." 