CAPE: A much stronger predictor of stock returns than many think

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CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Many, including myself, have been very skeptical of CAPE as a predictor of market returns. Part of this goes back to its creator, Robert Shiller, having admitted to just datamining the metric and having been generally very pessimistic about U.S. stock returns for the last three decades.

However, while I'm sure that someone has done the research already, I was not aware of any work that had examined how strongly correlated CAPE had been with forward stock returns since Shiller initially put forth the idea back in 1988. Therefore, I looked at the correlation between the starting CAPE value, as shown on Shiller's site, and the forward 10 years' real (i.e. inflation-adjusted) stock returns, as indicated by Portfolio Visualizer.

The results were shocking. The correlation between the starting CAPE and the forward 10 years' stock returns was -.9476. Remember that +1 and -1 mean that the linear correlation between the two variables is perfect. By squaring the correlation (i.e. r-square), we see that 90% of the variation in either of these variables is statistically accounted for by the other. As such, it seems that CAPE has indeed been an extremely powerful predictor of forward stock returns, so strong as to almost be deterministic.

Also, this analysis indicates that the relationship between CAPE and forward stock returns has been better explained via a regression formula (i.e. Y = a + bX) than the commonly used 1/CAPE. Using the above data (i.e. since 1989), the regression formula is as follows: .2111 + (-.00579*CAPE). With CAPE currently being 33.04, this means that forward U.S. stock returns are expected to be 2.00% real, not the 3.03% that 1/CAPE would predict.

I'm not saying that anyone should do anything differently based on this analysis. But it indicates that U.S. stock returns are, using the above data, very likely to be far lower than their historic average.
Last edited by willthrill81 on Mon Nov 30, 2020 8:27 pm, edited 1 time in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by scout1 »

This was already debunked in the below thread.

viewtopic.php?f=10&t=320775
Last edited by scout1 on Mon Nov 30, 2020 4:15 pm, edited 2 times in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Firemenot »

willthrill81 wrote: Mon Nov 30, 2020 2:53 pm Many, including myself, have been very skeptical of CAPE as a predictor of market returns. Part of this goes back to its creator, Robert Shiller, having admitted to just datamining the metric and having been generally very pessimistic about U.S. stock returns for the last three decades.

However, while I'm sure that someone has done the research already, I was not aware of any work that had examined how strongly correlated CAPE had been with forward stock returns since Shiller initially put forth the idea back in 1988. Therefore, I looked at the correlation between the starting CAPE value, as shown on Shiller's site, and the forward 10 years' real (i.e. inflation-adjusted) stock returns, as indicated by Portfolio Visualizer.

The results were shocking. The correlation between the starting CAPE and the forward 10 years' stock returns was -.9476%. Remember that +1 and -1 mean that the linear correlation between the two variables is perfect. By squaring the correlation (i.e. r-square), we see that 90% of the variation in either of these variables is statistically accounted for by the other. As such, it seems that CAPE has indeed been an extremely powerful predictor of forward stock returns, so strong as to almost be deterministic.

Also, this analysis indicates that the relationship between CAPE and forward stock returns has been better explained via a regression formula (i.e. Y = a + bX) than the commonly used 1/CAPE. Using the above data (i.e. since 1989), the regression formula is as follows: .2111 + (-.00579*CAPE). With CAPE currently being 33.04, this means that forward U.S. stock returns are expected to be 2.00% real, not the 3.03% that 1/CAPE would predict.

I'm not saying that anyone should do anything differently based on this analysis. But it indicates that U.S. stock returns are, using the above data, very likely to be far lower than their historic average.
That’s more math than I pretend to know or understand. Assuming you are correct that there’s a very high correlation in the past between CAPE and future past returns, will there be such a tight correlation in the future? Who knows? Also, for most of the past time interest rates were much higher, population growth was much higher, worker:retiree ratios were much higher, investment expenses were much higher, etc.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Firemenot wrote: Mon Nov 30, 2020 2:59 pmAlso, for most of the past time interest rates were much higher, population growth was much higher, worker:retiree ratios were much higher, investment expenses were much higher, etc.
"Most of the past" was not included in the analysis, only data since 1989. And the stock returns were actual returns of VTSMX.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by checkyourmath »

I think Robert Schiller received a Nobel Laureate, so I am a little surprised by the analysis. I think as long as someone uses dollar cost averaging with low cost index funds they are fine. Future returns might be negative but everything is fairly priced.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Forester »

Price has to matter it's just common sense. Hypothetically if you only ever DCA'd when CAPE was over 30, and never bought stocks the rest of the time, your returns would be risible. The truth of CAPE is masked by most people investing over a lifetime & US stocks are at a buoyant peak (maybe the peak continues a while).
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Northern Flicker »

A 10 year period with no deep bear market is not a very robust out-of-sample test.
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Re: CAPE: A much stronger predictor of stock returns than many think

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checkyourmath wrote: Mon Nov 30, 2020 3:07 pm I think Robert Schiller received a Nobel Laureate, so I am a little surprised by the analysis. I think as long as someone uses dollar cost averaging with low cost index funds they are fine. Future returns might be negative but everything is fairly priced.
I don't know why you think that I was bashing Shiller in the OP because I clearly wasn't. On the contrary, the metric he proposed has been very predictive of stock returns.

Neither DCAing nor 'everything being fairly priced' have been a guarantees that investors would get the returns they need when they need them.
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Re: CAPE: A much stronger predictor of stock returns than many think

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Northern Flicker wrote: Mon Nov 30, 2020 3:11 pm A 10 year period with no deep bear market is not a very robust out-of-sample test.
Whether the 10 year period in question 'happened' to have a 'deep bear market' is irrelevant for examining a metric specifically purported to predict the next 10 years' returns.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Forester »

I think Siegel or Bogle had a formula to allow for a little upward valuation drift over time. That's a minor mark against CAPE but this factor might feed on itself and allow market participants to permit themselves to bid up stocks.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by midareff »

I think the bigger danger (risk) to retirees is the possibility of future inflation, not substandard returns.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by checkyourmath »

Forester wrote: Mon Nov 30, 2020 3:10 pm Price has to matter it's just common sense. Hypothetically if you only ever DCA'd when CAPE was over 30, and never bought stocks the rest of the time, your returns would be risible. The truth of CAPE is masked by most people investing over a lifetime & US stocks are at a buoyant peak (maybe the peak continues a while).
Oh look it is Forester again being all pragmatic and logical. People are way too optimistic on here especially the 60 plus percent equities crowd.

2020-11-27 521,813 1,735,257 30.07

30 percent short interest index on VTI on Friday. I think this all seems to be very normal. I know there is a ton of smart people hiding in the weeds and reading this. I don't want to trade options but I am really curious about the volume numbers. I would love to overlap that data with CAPE info.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Firemenot »

My fear on all the CAPE talk on Bogleheads is it could cause new members to be afraid of investing in stock and not get started. Or be too conservative in their percentage equities for their age. CAPE doesn’t matter for people in it for the long-haul with DCA and decent savings rates.

And literally this same CAPE talk and pessimism has been endemic on Bogleheads for almost a decade.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

checkyourmath wrote: Mon Nov 30, 2020 3:23 pm
Forester wrote: Mon Nov 30, 2020 3:10 pm Price has to matter it's just common sense. Hypothetically if you only ever DCA'd when CAPE was over 30, and never bought stocks the rest of the time, your returns would be risible. The truth of CAPE is masked by most people investing over a lifetime & US stocks are at a buoyant peak (maybe the peak continues a while).
Oh look it is Forester again being all pragmatic and logical. People are way too optimistic on here especially the 60 plus percent equities crowd.
While it's clear that CAPE is predicting very low real returns for stocks, there aren't many places for investors to flee to. Bond yields are negative in real terms. Perhaps ex-U.S. stock will finally break out of its long slump.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Forester »

Global CAPE around 23 https://www.starcapital.de/en/research ... valuation/ An investor with a global portfolio and a Value tilt, in theory at least could expect reasonable middle-of-the-road future returns (this hypothetical investor however has had a lean time sonce early 2018).
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Barsoom »

willthrill81 wrote: Mon Nov 30, 2020 2:53 pm However, while I'm sure that someone has done the research already, I was not aware of any work that had examined how strongly correlated CAPE had been with forward stock returns since Shiller initially put forth the idea back in 1988.
I came across this article last year, actually a blurb in the middle of the article.

Another S&P 500 Warning Sign Appears, How To Deal With It, from Forbes October 31, 2019.

Excerpt:
Professor Robert Shiller of Yale: a man with a CAPE

Now, for that warning sign alluded to in the title of this article. Simply put, a signal flashed back at the end of last year. It involves the “Shiller CAPE Ratio.” The CAPE is a version of the oft-used price-earning (P/E) ratio developed by Yale Professor Bob Shiller, who is one of the most frequently cited market commentators around.

In reviewing the long-term history of the CAPE, I noticed a pattern. Major market declines in the past 50 years (those of more than 40%) have all occurred within a year or two of the 10-month moving average of the CAPE falling 10% from its high. In other words, a falling CAPE Ratio is part of every major bear market. Its a signal to pay attention. It is one of many I have cited over the past 2 years. As with any “moving average,” the idea is to filter out any temporarily wacky periods of time in market history. A moving average does that.
Go to the article in the link to see his supporting data and other conclusions. This topic is about 1/3 of the way down.

-B
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Forester wrote: Mon Nov 30, 2020 3:47 pm Global CAPE around 23 https://www.starcapital.de/en/research ... valuation/ An investor with a global portfolio and a Value tilt, in theory at least could expect reasonable middle-of-the-road future returns (this hypothetical investor however has had a lean time sonce early 2018).
Perhaps ex-U.S. SCV is set up to perform well in the next decade.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by absolute zero »

Forester wrote: Mon Nov 30, 2020 3:47 pm Global CAPE around 23 https://www.starcapital.de/en/research ... valuation/ An investor with a global portfolio and a Value tilt, in theory at least could expect reasonable middle-of-the-road future returns (this hypothetical investor however has had a lean time sonce early 2018).
Yep. For any US-only / cap-weighted investors that have questioned their own portfolio over the years, now may be the perfect time to add a value tilt and significantly increase international holdings. If they can stick with it.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by oldfort »

willthrill81 wrote: Mon Nov 30, 2020 2:53 pm
The results were shocking. The correlation between the starting CAPE and the forward 10 years' stock returns was -.9476%. Remember that +1 and -1 mean that the linear correlation between the two variables is perfect. By squaring the correlation (i.e. r-square), we see that 90% of the variation in either of these variables is statistically accounted for by the other. As such, it seems that CAPE has indeed been an extremely powerful predictor of forward stock returns, so strong as to almost be deterministic.
The correlation shouldn't be particularly shocking. Since you're starting at 1989, you have effectively three independent data points for 10-year returns.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by absolute zero »

Firemenot wrote: Mon Nov 30, 2020 3:29 pm My fear on all the CAPE talk on Bogleheads is it could cause new members to be afraid of investing in stock and not get started. Or be too conservative in their percentage equities for their age. CAPE doesn’t matter for people in it for the long-haul with DCA and decent savings rates.

And literally this same CAPE talk and pessimism has been endemic on Bogleheads for almost a decade.
Hopefully they look beyond the surface. For those that take the time to learn about CAPE ratios, the takeaway should not be "don't invest" but rather "diversify beyond US large cap stocks."
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by CalPoppy »

willthrill81 wrote: Mon Nov 30, 2020 2:53 pm The results were shocking. The correlation between the starting CAPE and the forward 10 years' stock returns was -.9476%. Remember that +1 and -1 mean that the linear correlation between the two variables is perfect. By squaring the correlation (i.e. r-square), we see that 90% of the variation in either of these variables is statistically accounted for by the other. As such, it seems that CAPE has indeed been an extremely powerful predictor of forward stock returns, so strong as to almost be deterministic.

Also, this analysis indicates that the relationship between CAPE and forward stock returns has been better explained via a regression formula (i.e. Y = a + bX) than the commonly used 1/CAPE. Using the above data (i.e. since 1989), the regression formula is as follows: .2111 + (-.00579*CAPE). With CAPE currently being 33.04, this means that forward U.S. stock returns are expected to be 2.00% real, not the 3.03% that 1/CAPE would predict.
ERN has a nice chart showing the correlation. See “Scatter Plot of Shiller CAPE (x-axis) vs. subsequent 10-year annualized real total return”
https://earlyretirementnow.com/2016/12/ ... valuation/
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Re: CAPE: A much stronger predictor of stock returns than many think

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oldfort wrote: Mon Nov 30, 2020 3:55 pm
willthrill81 wrote: Mon Nov 30, 2020 2:53 pm
The results were shocking. The correlation between the starting CAPE and the forward 10 years' stock returns was -.9476%. Remember that +1 and -1 mean that the linear correlation between the two variables is perfect. By squaring the correlation (i.e. r-square), we see that 90% of the variation in either of these variables is statistically accounted for by the other. As such, it seems that CAPE has indeed been an extremely powerful predictor of forward stock returns, so strong as to almost be deterministic.
The correlation shouldn't be particularly shocking. Since you're starting at 1989, you have effectively three independent data points for 10-year returns.
If we only examine 1990-1999, 2000-2009, and 2010-2019, the correlation increases to -.9997%.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

Well if we are going to look for data mined metrics, why not use butter prices in Bangladesh:

[https://www.forbes.com/sites/moneybuil ... says-buy/

Sure, it would seem butter prices in Bangladesh is unrelated to stock performance, but one might argue the profits of a company 10 years ago is equally irrelavlent to market direction 10 years from now.

Did you look at that thread pointed to above, particularly the analysis done be petulant about halfway down the page?
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Re: CAPE: A much stronger predictor of stock returns than many think

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willthrill81 wrote: Mon Nov 30, 2020 2:53 pm I'm not saying that anyone should do anything differently based on this analysis. But it indicates that U.S. stock returns are, using the above data, very likely to be far lower than their historic average.
Many times I’ve thought of using CAPE or Vanguard’s 10-year outlook in my ABW spreadsheet - but only for the next 10 years, and then using historical returns for year 11 onwards. Vanguard’s Personal Advisory Services does this, I believe.
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Re: CAPE: A much stronger predictor of stock returns than many think

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marcopolo wrote: Mon Nov 30, 2020 4:08 pm Well if we are going to look for data mined metrics, why not use butter prices in Bangladesh:

[https://www.forbes.com/sites/moneybuil ... says-buy/

Sure, it would seem butter prices in Bangladesh is unrelated to stock performance, but one might argue the profits of a company 10 years ago is equally irrelavlent to market direction 10 years from now.
Are you arguing that stock prices don't impact future returns?
marcopolo wrote: Mon Nov 30, 2020 4:08 pmDid you look at that thread pointed to above, particularly the analysis done be petulant about halfway down the page?
Yes, I've read it. And his/her point that the regression coefficients appear to have changed over time is a good one. Yet even s/he said "I'm sure that P/E matters." We just don't know exactly how much it matters.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by scout1 »

No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

willthrill81 wrote: Mon Nov 30, 2020 4:14 pm
marcopolo wrote: Mon Nov 30, 2020 4:08 pm Well if we are going to look for data mined metrics, why not use butter prices in Bangladesh:

[https://www.forbes.com/sites/moneybuil ... says-buy/

Sure, it would seem butter prices in Bangladesh is unrelated to stock performance, but one might argue the profits of a company 10 years ago is equally irrelavlent to market direction 10 years from now.
Are you arguing that stock prices don't impact future returns?
marcopolo wrote: Mon Nov 30, 2020 4:08 pmDid you look at that thread pointed to above, particularly the analysis done be petulant about halfway down the page?
Yes, I've read it. And his/her point that the regression coefficients appear to have changed over time is a good one. Yet even s/he said "I'm sure that P/E matters." We just don't know exactly how much it matters.
I am arguing that stock prices from 10 years don't have much impact on future returns today.
Yet, CAPE gives them equal weight as today's stock prices, why?

Why 10 years and not 7 or 12? Well, because as Shiller himself said at the time of the paper, they did a lot of data mining, and it is quite possible that it is just a result of that.

That is why the "good correlation" only shows up if you keep training the model on the data you are testing, less than reassuring to me.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
If there really were a metric that would give .99 correlation, you would think there would be a lot of investment managers that could have wildly successful results capitalizing on that, where are they all?
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Re: CAPE: A much stronger predictor of stock returns than many think

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Here is CAPE study done by an economist from the FED:

https://www.frbsf.org/economic-research ... acro-data/
A regression model that uses a small set of macroeconomic explanatory variables can help account for movements in the CAPE ratio over the past six decades. However, the model’s predicted CAPE ratios for the second and third quarters of 2020 are highly sensitive to the inclusion of a macroeconomic uncertainty index as an explanatory variable. Today’s investors appear to be reacting to macroeconomic uncertainty very differently than in the past. This result highlights the difficulty of judging whether the stock market is overvalued and makes it hard to predict how investors will react to a future episode of elevated uncertainty.
IMO, I think there's enough data to suggest that CAPE (valuation) affects forward looking returns. However, there's quite a bit of uncertainty around the coefficient so to predict the precise 10 year return won't be easy but does suggest that future return is more muted (pending macro economic uncertainty, trading/transaction barriers, interest rate and etc).

P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
Let’s be reasonable, shall we?

Not only is there a great deal of evidence that CAPE is highly predictive of future returns, it’d be entirely shocking if that weren’t the case.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
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Re: CAPE: A much stronger predictor of stock returns than many think

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jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did not do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
Last edited by willthrill81 on Thu Dec 03, 2020 12:42 pm, edited 1 time in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by oldfort »

willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
You're ignoring the number of data points. Select two data points and you're guaranteed to get a straight line, R^2 = 100%. Getting a high correlation with three data points isn't much more surprising. This isn't some election poll with 500-1000 independent data points.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

oldfort wrote: Mon Nov 30, 2020 4:48 pm
willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
You're ignoring the number of data points. Select two data points and you're guaranteed to get a straight line, R^2 = 100%. Getting a high correlation with three data points isn't much more surprising. This isn't some election poll with 500-1000 independent data points.
So you weren't happy with 30+ years of data, and you're not happy with three independent periods either.

What do you want?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Maker »

Obligatory post about average stock allocation, which IMO does not suffer from some of issues that characterize CAPE (not dependent on accounting standards, buyback influence etc etc) and has kept up since it's publication in 2013: https://financial-charts.effingapp.com/
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by jarjarM »

willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.
Will, I assume you mean did NOT. As a data scientist by trade, I do know how correlation is calculated and how it can be use. My point is actually related the limited sample size, if you have 2 points, the correlation will very likely be +1 or -1. I guess I'll have to see the correlation chart to understand how you come about with correlation of 0.99, that seems to be too high unless it's in a low sample size environment.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by oldfort »

willthrill81 wrote: Mon Nov 30, 2020 4:51 pm
oldfort wrote: Mon Nov 30, 2020 4:48 pm
willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
You're ignoring the number of data points. Select two data points and you're guaranteed to get a straight line, R^2 = 100%. Getting a high correlation with three data points isn't much more surprising. This isn't some election poll with 500-1000 independent data points.
So you weren't happy with 30+ years of data, and you're not happy with three independent periods either.

What do you want?
If you're a social scientist by trade, then let's call a sample size of 100 the minimum to have a statistically meaningful sample. So if I see a social science paper with a sample smaller than 100, it's suspect. 100 ten year samples = 1000 years of data.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
I've read all of that thread, and there actually weren't many different arguments against CAPE. Most of the arguments revolve around (1) the perennial 'overlapping periods' issue, (2) arguments about what the specific parameters of a 'CAPE model' should be, and (3) 'times have changed' so history basically doesn't mean anything. I agree that #1 is somewhat problematic, but we can still examine three independent 10 year periods since Shiller proposed CAPE, and I've already done that. I also agree that it definitely seems that the specific parameters of a regression model using CAPE and stock returns has changed, though it should be pointed out that CAPE has been much more strongly correlated with forward stock returns since Shiller proposed it than before. For those that believe in #3, all I can say is 'how do you determine how to invest?'.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

jarjarM wrote: Mon Nov 30, 2020 4:54 pm
willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.
Will, I assume you mean did NOT. As a data scientist by trade, I do know how correlation is calculated and how it can be use. My point is actually related the limited sample size, if you have 2 points, the correlation will very likely be +1 or -1. I guess I'll have to see the correlation chart to understand how you come about with correlation of 0.99, that seems to be too high unless it's in a low sample size environment.
Yes, I meant 'not'.

I agree that a sample size of three isn't even remotely close to being large enough to get statistically significant results. But I wasn't the one calling for it.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

oldfort wrote: Mon Nov 30, 2020 5:00 pm
willthrill81 wrote: Mon Nov 30, 2020 4:51 pm
oldfort wrote: Mon Nov 30, 2020 4:48 pm
willthrill81 wrote: Mon Nov 30, 2020 4:38 pm
jarjarM wrote: Mon Nov 30, 2020 4:26 pm P.S. As other suggested upthread, there is not out of sample verification for this so the high R square is expected. That's why the correlation for the 10 year individual sample set is 0.99, basically using the same data points to construct the model and its coefficients then testing it against the exact same data.
The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
You're ignoring the number of data points. Select two data points and you're guaranteed to get a straight line, R^2 = 100%. Getting a high correlation with three data points isn't much more surprising. This isn't some election poll with 500-1000 independent data points.
So you weren't happy with 30+ years of data, and you're not happy with three independent periods either.

What do you want?
If you're a social scientist by trade, then let's call a sample size of 100 the minimum to have a statistically meaningful sample. So if I see a social science paper with a sample smaller than 100, it's suspect. 100 ten year samples = 1000 years of data.
Most statisticians I know would say that 30 is a minimum sample size, assuming that the assumptions of regression are satisfied. But even then, that's 300 years of data. Are you suggesting that we wait until ~270 years before assessing whether CAPE is a meaningful predictor of market returns?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Firemenot »

willthrill81 wrote: Mon Nov 30, 2020 5:05 pm
scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
I've read all of that thread, and there actually weren't many different arguments against CAPE. Most of the arguments revolve around (1) the perennial 'overlapping periods' issue, (2) arguments about what the specific parameters of a 'CAPE model' should be, and (3) 'times have changed' so history basically doesn't mean anything. I agree that #1 is somewhat problematic, but we can still examine three independent 10 year periods since Shiller proposed CAPE, and I've already done that. I also agree that it definitely seems that the specific parameters of a regression model using CAPE and stock returns has changed, though it should be pointed out that CAPE has been much more strongly correlated with forward stock returns since Shiller proposed it than before. For those that believe in #3, all I can say is 'how do you determine how to invest?'.
Seems like #3 is getting at active management / market timing. Assuming you mean something different?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Maker wrote: Mon Nov 30, 2020 4:52 pm Obligatory post about average stock allocation, which IMO does not suffer from some of issues that characterize CAPE (not dependent on accounting standards, buyback influence etc etc) and has kept up since it's publication in 2013: https://financial-charts.effingapp.com/
Yes, that's been a solid indicator of future market returns as well, and it's calculated in a completely different way than CAPE. Interestingly, it's predicting 2.70% forward real returns over the next decade, close to what CAPE is predicting (whether 1/CAPE or a regression-fitted model since Shiller proposed CAPE).
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Firemenot wrote: Mon Nov 30, 2020 5:10 pm
willthrill81 wrote: Mon Nov 30, 2020 5:05 pm
scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
I've read all of that thread, and there actually weren't many different arguments against CAPE. Most of the arguments revolve around (1) the perennial 'overlapping periods' issue, (2) arguments about what the specific parameters of a 'CAPE model' should be, and (3) 'times have changed' so history basically doesn't mean anything. I agree that #1 is somewhat problematic, but we can still examine three independent 10 year periods since Shiller proposed CAPE, and I've already done that. I also agree that it definitely seems that the specific parameters of a regression model using CAPE and stock returns has changed, though it should be pointed out that CAPE has been much more strongly correlated with forward stock returns since Shiller proposed it than before. For those that believe in #3, all I can say is 'how do you determine how to invest?'.
Seems like #3 is getting at active management / market timing. Assuming you mean something different?
No, it's not an espousal of active management or market timing. If you don't think that history is usable in any way, then how do you determine your AA? How can you evaluate your risk tolerance since you too are always changing? How will you determine how much to withdraw in retirement?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Firemenot »

willthrill81 wrote: Mon Nov 30, 2020 5:12 pm
Firemenot wrote: Mon Nov 30, 2020 5:10 pm
willthrill81 wrote: Mon Nov 30, 2020 5:05 pm
scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
I've read all of that thread, and there actually weren't many different arguments against CAPE. Most of the arguments revolve around (1) the perennial 'overlapping periods' issue, (2) arguments about what the specific parameters of a 'CAPE model' should be, and (3) 'times have changed' so history basically doesn't mean anything. I agree that #1 is somewhat problematic, but we can still examine three independent 10 year periods since Shiller proposed CAPE, and I've already done that. I also agree that it definitely seems that the specific parameters of a regression model using CAPE and stock returns has changed, though it should be pointed out that CAPE has been much more strongly correlated with forward stock returns since Shiller proposed it than before. For those that believe in #3, all I can say is 'how do you determine how to invest?'.
Seems like #3 is getting at active management / market timing. Assuming you mean something different?
No, it's not an espousal of active management or market timing. If you don't think that history is usable in any way, then how do you determine your AA? How can you evaluate your risk tolerance since you too are always changing? How will you determine how much to withdraw in retirement?
I don’t think CAPE can actually help much in that regard — other than perhaps if someone wants to tilt towards foreign equities based on that. Doesn’t help much with bonds AA decision as their expected returns are so low anyhow. Biggest thing I suppose is err on the side of savings rate in case the CAPE doom and gloom is accurate.
Last edited by Firemenot on Mon Nov 30, 2020 5:33 pm, edited 1 time in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by oldfort »

willthrill81 wrote: Mon Nov 30, 2020 5:09 pm
oldfort wrote: Mon Nov 30, 2020 5:00 pm
willthrill81 wrote: Mon Nov 30, 2020 4:51 pm
oldfort wrote: Mon Nov 30, 2020 4:48 pm
willthrill81 wrote: Mon Nov 30, 2020 4:38 pm

The analysis I conducted did do what you claim in the last phrase whatsoever. That's not remotely close to how correlations or regression are calculated. The correlation between two sets of variables can range from -1 to +1 with 0 representing no correlation at all. As a social scientist by trade, I can tell you that correlations close to zero are quite common and that correlations close to -1 or +1 are quite rare outside of the physical sciences.

While you're correct that the specific parameters of the regression model are optimized for the data presented, which I've already said to be so, the point of the analysis in the OP was merely to illustrate that CAPE has been a very strong predictor of future market returns since Shiller proposed it. In other words, it is an out of sample test.
You're ignoring the number of data points. Select two data points and you're guaranteed to get a straight line, R^2 = 100%. Getting a high correlation with three data points isn't much more surprising. This isn't some election poll with 500-1000 independent data points.
So you weren't happy with 30+ years of data, and you're not happy with three independent periods either.

What do you want?
If you're a social scientist by trade, then let's call a sample size of 100 the minimum to have a statistically meaningful sample. So if I see a social science paper with a sample smaller than 100, it's suspect. 100 ten year samples = 1000 years of data.
Most statisticians I know would say that 30 is a minimum sample size, assuming that the assumptions of regression are satisfied. But even then, that's 300 years of data. Are you suggesting that we wait until ~270 years before assessing whether CAPE is a meaningful predictor of market returns?
Vanguard found a much lower R^2 ~ 0.43, from 1926-2012.

http://fairwaywealth.com/wp-content/upl ... 0-2014.pdf
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

Here is an actual academic paper: Forecasting the Equity Risk Premium: The Role of Technical Indicators

in-sample analysis for predicting equity risk premium, not statistically significant. EP is the earnings-price ratio.
Image

out-of-sample analysis, negative R^2 (= trash)
out-of-sample means they calculate the regression parameters and R^2 on a different test splits, which is only half out of sample.
Image

economical significance analysis 0.34% higher CER after transaction costs.
Image

Probably a much better idea to waste your time on some of the indicators that are statistically significant, such as TMS (term spread). Although to be fair, it's probably a much better idea to read "Life-Cycle Investing and Leverage: Buying Stock on Margin Can Reduce Retirement Risk" by Ayres and Nalebuff, and "A Five-Factor Asset Pricing Model" by Fama and French instead, but that's just me.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

willthrill81 wrote: Mon Nov 30, 2020 5:12 pm
Firemenot wrote: Mon Nov 30, 2020 5:10 pm
willthrill81 wrote: Mon Nov 30, 2020 5:05 pm
scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
I've read all of that thread, and there actually weren't many different arguments against CAPE. Most of the arguments revolve around (1) the perennial 'overlapping periods' issue, (2) arguments about what the specific parameters of a 'CAPE model' should be, and (3) 'times have changed' so history basically doesn't mean anything. I agree that #1 is somewhat problematic, but we can still examine three independent 10 year periods since Shiller proposed CAPE, and I've already done that. I also agree that it definitely seems that the specific parameters of a regression model using CAPE and stock returns has changed, though it should be pointed out that CAPE has been much more strongly correlated with forward stock returns since Shiller proposed it than before. For those that believe in #3, all I can say is 'how do you determine how to invest?'.
Seems like #3 is getting at active management / market timing. Assuming you mean something different?
No, it's not an espousal of active management or market timing. If you don't think that history is usable in any way, then how do you determine your AA? How can you evaluate your risk tolerance since you too are always changing? How will you determine how much to withdraw in retirement?
Surely there is middle ground between "history has no meaning"/"valuations don't matter" and "CAPE is 99% predictive of future returns!"?
Perhaps it might be true that very high PE ratios (valuations) are indicative of likely lower returns going forward than very low PEs (with many other factors being the same), without believing that they are tightly enough coupled (99%) to do anything really meaningful with that piece of information, than to perhaps save a bit more?
Once in a while you get shown the light, in the strangest of places if you look at it right.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

marcopolo wrote: Mon Nov 30, 2020 5:57 pm Surely there is middle ground between "history has no meaning"/"valuations don't matter" and "CAPE is 99% predictive of future returns!"?
Perhaps it might be true that very high PE ratios (valuations) are indicative of likely lower returns going forward than very low PEs (with many other factors being the same), without believing that they are tightly enough coupled (99%) to do anything really meaningful with that piece of information, than to perhaps save a bit more?
The "middle ground" is found by looking at a richer sample of data. The r2 over the past century (1926 to 2020) is a quite robust 0.53. That's highly predictive, as these things go, though it is less that 0.99.

Image

There are a couple of actionable steps I can imagine someone taking based on a realistic expectation that the next ten years may produce S&P 500 returns below those to which we've grown accustomed. Save a bit more (for people who are still working) is definitely one of them. Spend a bit less (for people who are already retired and count on portfolio withdrawals for income) is another. Make sure the portfolio is diversified away from the S&P 500 might be a third.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

vineviz wrote: Mon Nov 30, 2020 6:24 pm
marcopolo wrote: Mon Nov 30, 2020 5:57 pm Surely there is middle ground between "history has no meaning"/"valuations don't matter" and "CAPE is 99% predictive of future returns!"?
Perhaps it might be true that very high PE ratios (valuations) are indicative of likely lower returns going forward than very low PEs (with many other factors being the same), without believing that they are tightly enough coupled (99%) to do anything really meaningful with that piece of information, than to perhaps save a bit more?
The "middle ground" is found by looking at a richer sample of data. The r2 over the past century (1926 to 2020) is a quite robust 0.53. That's highly predictive, as these things go, though it is less that 0.99.

Image

There are a couple of actionable steps I can imagine someone taking based on a realistic expectation that the next ten years may produce S&P 500 returns below those to which we've grown accustomed. Save a bit more (for people who are still working) is definitely one of them. Spend a bit less (for people who are already retired and count on portfolio withdrawals for income) is another. Make sure the portfolio is diversified away from the S&P 500 might be a third.
That all seems perfectly reasonable. If that had been the premise of the OP, I doubt it would have garnered much commentary. "Meh, OK, expected lower returns".

It was the "look! It's 99% accurate" claim that triggers the BS detector.
Once in a while you get shown the light, in the strangest of places if you look at it right.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by bigskyguy »

vineviz wrote: Mon Nov 30, 2020 4:38 pm
scout1 wrote: Mon Nov 30, 2020 4:18 pm No Willthrill81, you need to thoroughly read the thread. Many posters throughout the thread go into detail about why this analysis, which has been done hundreds of times by many many people, is entirely wrong. Also, it should be suspicious to you that you're getting a correlation of -.99 in predicting the stock market.

viewtopic.php?f=10&t=320775
Let’s be reasonable, shall we?

Not only is there a great deal of evidence that CAPE is highly predictive of future returns, it’d be entirely shocking if that weren’t the case.
+1.

Rather than use the term "predict," it would likely temper the waves to utilize the term "probability." That is certainly the case when it comes to using statistical metrics in medicine, which is where I have spent my career. A correlation of this magnitude (>.95) certainly gets our attention. When it comes to my portfolio, this one certainly does.
Now that in no way means that I will act on this metric in isolation. The reality is that fixed income returns are also at extremes of a similar degree. My take is that the "probability" is that future returns for both fixed income and equity investments will be lower than the historical norms. That shouldn't surprise anyone.
Probabilities are not predictions.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by GAAP »

The degree to which CAPE is useful depends upon what you're using it for. If you want an accurate "prediction" of 10-years in the future, then you're not really thinking.

If you want an estimate of likely direction, so you can make an informed decision about actions in the next year or so, then CAPE can be useful. For example, if you're estimating returns for some annually-revisited TVM-based withdrawal method, then CAPE is quite reasonable. Look at the scatter-plot that vineviz posted above, and note that the derived trend with the 0.52 R2 value is actually the center-of-mass trend for that data. As such, at any given CAPE value, roughly half of the data points are above the line, and half are below. For a withdrawal calculation depending upon estimated returns, this means that only half of those points hurt you -- while the estimate is still better than a long-term average.
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