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Earlier I posted a guide to exploring the bright lights and dark alleyways of CAPEtown. The board post is
https://www.shrewdm.com/MB?pid=592241089
and includes the dropbox link to Part I:
https://www.dropbox.com/scl/fi/45ye2kdeeliso6y3kd4...

Here's the promised Part II, a guide to exploding CAPEtown. It turned out differently than I thought!
https://www.dropbox.com/scl/fi/jde95ejz56v1keirgq4...

Tedthedog

For me, a wonderful explanation of CAPE and alternatives.

If you wouldn't mind, a few questions.

For FAPE2, when calculating the twenty year average, did you use daily closings or some other method? Was the pricing adjusted for dividends? Did you look at using actual prices and not real prices? Did you look at other averages (e.g. EMA) for calculating the denominator? Did you look at other time periods than 20 years? Did you look at other correlations other than 10 years forward return?

Thanks for sharing your work.

Aussi

All data for this post is from Shiller's website (link in the post). I used this data because it's a canonical data set used in many other analyses. His price data is monthly, all prices are 'real' i.e. inflation adjusted, dividends are not included, however his return data does include dividends i.e. it's 'total return'. It was his choice to use ten years for forward returns.

I hope I was clear that the FAPE1 and FAPE2 "alternatives" are in fact straw men that I set up as experiments, fully expecting to knock them down.
But to my dismay, they didn't fall down!

FAPE1 substitutes for the earnings data, i.e. the E in CAPE, the values from the trend line of earnings over time. The trend line is completeley smooth, it has no features or wiggles of any sort. But FAPE1 still looks like CAPE (the graph) and feels like CAPE (the accuracy).

FAPE2 doesn't use earnings at all. But it still looks like CAPE (the graph) and feels like CAPE (the accuracy). To answer a question, I first tried 10 years for the average in FAPE2 but doubled it to 20 years because 20 worked better, that's the only tuning. IMO, FAPE2 is both amusing and somewhat alarming, but a bit of a trick. It's FAPE1 that I find more disconcerting: a simple change to CAPE i.e. remove all details about earnings other than "earnings go up" and it still works.

In some initial investigations I tried the 'Hull average', because it's supposed to have less lag than the SMA that Shiller used. But "solving lag" turned out not to be the point at all. In fact, you can make lag worse by artificially lagging Shiller's earning data by years, and not affect the outcome of CAPE very much.

That point is that CAPE is surprisingly and distressingly insensitive to details of earnings: you can make the earnings totally smooth as in FAPE1, you can even totally eliminate use of earnings as in FAPE2, and it'll still look like CAPE (the graph) and have the feel of CAPE (similar accuracy).

I had thought, as many others do (lots of papers are written on CAPE), that it's the interplay of details of E and P in Shiller's CAPE that makes CAPE predictive and that CAPE is a shining example that "valuation matters".
But you can quash, and even kill (eliminate) the details of E, and "CAPE" (i.e. the FAPE1 and FAPE2 versions of CAPE) still work.
To be clear, I'm not saying that valuation doesn't matter (I believe that it does). I'm saying that CAPE doesn't show that valuation matters.

Tedthedog,

I really enjoyed Part I of your analysis and I really enjoyed following as you dug into this. I don't quite understand what you hoped to conclude though from your analysis in part II.

I didn't see any of the experiments you did as an invalidation of CAPE. In the FAPE I experiments, if I understood it correctly, you took the straight line best fit to the 10 year smoothed earnings used in CAPE. That straight line looks pretty close to the smoothed earnings, since smoothing earnings takes out a lot of the volatility to begin with. So no surprise, it works pretty well and behaves similarly to what CAPE would do in terms of correlating to future returns. I wasn't sure what kind of explosion that implied about CAPE. Its what you would expect, no? Certainly doesn't seem contrary to what CAPE theory suggests. It maybe even supports it - e.g., using smoothed earnings help with longer term expected return?

For the FAPE 2 experiment, you used smoothed market prices as the denominator. Random in the short term but less random over time. Aggregate prices over time at least have some correlations to aggregate earnings, even if that doesn't work for individual stocks. So the stock prices over time, if smoothed, should also be correlated to CAPE earnings, but probably less so and with a different multiple. If I understand your analysis correctly, that is also what you found.

I get that multiple things that have smoothed linear trajectory that goes up over time could seem like they have the predictive power of CAPE ... as long as they look similar to CAPE. But how does that blow up CAPE, which has a theoretical grounding for the why?

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.

I didn't see any of the experiments you did as an invalidation of CAPE.
I'd like to be as clear as possible, I'm not claiming to have invalidated CAPE.
CAPE "works" in the sense that there's good prediction accuracy of long-terms returns (but the predictive accuracy depends on what period of time you're looking at, as I showed).

What is invalidated, at least in my mind, is the logic chain:
(1) because CAPE "works" (good accuracy), and
(2) because CAPE is a valuation measure
then "CAPE working" is a long sought demonstration that "valuation works".
I'm sure I'm not the only one who had subscribed to that logic chain, given the huge number of publications on CAPE, and on what its value might imply for the economy.

> smoothing earnings takes out a lot of the volatility to begin with
Shiller set out to smooth earnings, not eliminate earnings.
But I took out in FAPE1 all the volatility, every single wiggle of earnings, so that there's basically no information left about earnings other than two numbers, slope and intercept (you can even change those two numbers by a large amount), and FAPE1 still achieves basically the accuracy of CAPE.
FAPE2 doesn't even use earnings at all, yet it still looks like (graph) and feels like (accuracy) CAPE.

To my mind, a valuation measure that walks up to you and says
"I'll compare price to earnings for you and predict the future"
but the predictions don't really depend much on earnings (if at all on earnings, at least explicitly), isn't doing much valuation. That's disappointing!

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

https://www.dropbox.com/scl/fi/dx8ci8celj3bsag7qxh...

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.

I think the idea of FAPE1 working is somewhat flawed as you can only draw the straight line retrospectively so it includes a crystal ball element.

FAPE2 is interesting. I think there is some validity to it working. If you accept that prices are pulled slowly or even weakly (mean reverting) to some "typical" multiple of earnings, it follows that for a large index, the moving average of price will align to some extent with certain multiple of value (earnings). So it is not so surprising that this works.

StevnFool

Totally agree with the crystal ball comment, I've been working on a "walk forward" analysis where you compute the trend line up to "now" to predict returns in the future of "now". Will report on that, and other stuff, when I get time.

I have a love/hate relationship with FAPE2. I did not want to see it 'work' (predict future returns as well as CAPE), but given that it does work it's interesting to understand why.

Hi,

Pardon my ignorance, What is FAPE2?

Thank you,

Elizabeth

It's described in Part I, the link is at the top of this thread.
Instead of CAPE, which is Price/Earnings (smoothed earnings), FAPE2 was created as a straw man that is price over smoothed price.
But the straw man didn't fall down, it turned out to be just as accurate as CAPE.

Excellent study with a creative presentation that prompted me to think of CAPE differently. CAPE can be deconstructed (exploded) into a detrending step and a valuation step. Detrending is needed because prices have trended higher over the years, and so something is needed to allow comparison between different time periods. Valuation is what we are evaluating: is the valuation predictive of future returns.

Another possible strawman is to use a random price series. Standard deviation of monthly returns has been stable around 3.5% (except for the 1930s). Maybe generate a random price series using monthly change: average 0.0, standard deviation 3.5%.

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