The other observation is that the smoothing is part of why CAPE isn't a good market timing signal. Its not really a representation of the now (the price part is, but the earning are not). So it's terrible at being a short term signal. But if you believe that the direction of market valuations in the short term are difficult to predict anyways, that might not be much of a detriment. CAPE isn't the tool for that.

But is it good indicator of longer term returns? Its gotta be informative about that, even if its not deterministic. How informative for any given time horizon is probably the question that is worth analyzing. I am just not sure the FAPE analysis sheds any light there. And in that sense, I don't know if its a relevant analysis for understanding if CAPE is useful.