In retrospect, I should have gone with the first idea I considered to try to make this report readable, i.e. "Alice in Wonderland" -- where nothing is as it appears. As opposed to getting cute in the in the title of Part II by changing 'r' to 'd' in 'Exploring'.

Maybe a little CAPE history would help -- just a little, don't get nervous:

(1) In his classic CAPE paper, "Stock Prices, Earnings, and Expected Dividends", Shiller commented on "the idea of smoothing out earnings over business cycles as intuitive and sensible", referring to the original suggestion of doing so (not implemented) by Graham and Dodd. Shiller implemented it and in that paper, now heavily referenced, showed that when used in the denominator of a P/E ratio "smoothed" earnings can lead to significantly accurate prediction of long term returns.

(2) In Shiller's 2001 follow-up paper "Valuation Ratios and the Long Run Stock Market Outlook: An Update" he wrote:
"We concluded in the 1998 version of this paper that the conventional valuation ratios, the dividend-price and price-smoothed-earnings ratios, have a special significance when compared with many other statistics that might be used to forecast stock prices. ... These valuation ratios deserve a special place among forecasting variables because we have such a long time series of data on these ratios, and because they relate stock prices to careful evaluations of the fundamental value of corporations. Earnings have been calculated and reported by US corporations for over a hundred years for the express purpose of allowing us to judge intrinsic value."

That's it for history, it's time for a picture!

Linked below is a graph of earnings, smoothed earnings, and the trend line of smoothed earnings over time from 1871 onward. I'm not sure I showed it before. There's considerable variation in the red smoothed earnings curve

dropbox.com: PDF document

My point is that the variations in the red curve, presumably reflecting
"careful evaluations of the fundamental value" that are "allowing us to judge intrinsic value"
is not necessarily why CAPE 'works' (in the sense of CAPE predicting long term returns). So CAPE 'working' is not a validation that determining fundamental value can help predict long term returns.

Why?

Because:

(1) FAPE1 replaced earnings, E, in the P/E ratio, with a straight line over time, i.e. all the "earnings ... reported by US corporations for over a hundred years for the express purpose of allowing us to judge intrinsic value" have been reduced to just two numbers, slope and intercept of the straight trend line (in log space).
FAPE1 is as accurate as CAPE, red squiggles don't seem to matter.

(2) FAPE2 replaced E in the denominator of P/E with a moving average of price so earnings doesn't enter at all.
FAPE2 is as accurate as CAPE.

CAPE works, I'm not claiming that it doesn't predict well in general. I hope I clearly showed in what periods it has predictive power and that periods it doesn't. But FAPE1 and FAPE2 show that CAPE 'working' for predicting long term return is not necessarily a validation that "careful evaluations of the fundamental value of corporations" is the reason that CAPE works. I'm also not claiming that that fundamental valuation doesn't work, I just don't think CAPE 'working' is a demonstration of fundamental valuation working.