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

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

Post by Uncorrelated »

JackoC wrote: Tue Dec 08, 2020 9:37 am
Uncorrelated wrote: Mon Dec 07, 2020 4:14 pm
JackoC wrote: Mon Dec 07, 2020 2:32 pm
Uncorrelated wrote: Mon Dec 07, 2020 11:18 am
alex_686 wrote: Mon Dec 07, 2020 10:35 am
...
To repeat..

We must have some market expectation about the equity market.
I have seen no evidence that 1/CAPE or CAPE linear regression outperforms a constant allocation. I have seen some evidence (from papers) that a constant allocation is extremely hard to beat, and that a simple regression on P/E ratio's does not beat a constant allocation by anything that can be considered significant. The expected gains of "optimally" using CAPE in your investment strategy have not been examined yet by any source linked to in this thread. You seem to believe the opposite, could you link to a few papers that investigate the certainty equivalent gains for using a CAPE timing strategy?
You are interested in 'optimal allocation' and perhaps a 'CAPE timing strategy'. Fine, and perhaps even some 'pro CAPE' posters are also. But the post you just responded to is not talking about that as I read it. I've definitely not been talking about that.

Starting from zero in a financial plan I need some indicator of expected return, even if it's going to be quasi-fixed (age dependent) % stock/bond. People who say they don't need this are confusing themselves IMO, I see no way around it. Dealing in 'actual' past returns inevitably means assuming implicitly that the expected return now is the average of past returns. Because in fact you must assume something, even be it a range, but any range has a midpoint, which is basically (not necessarily mathematically exactly) what the expected return is.

The earnings yield is a fundamental estimator of expected return per the derivation linked above, standard.
https://docfinder.is.bnpparibas-ip.com/ ... 07E654E5AE

To reject the 'paper airplane' of 1/CAPE=real expected return for basic planning, not dynamic asset allocation, purposes I believe you must explain why it's systematically biased in one direction or another (how the real world violates the assumptions of the derivation in a way which makes 1/CAPE systematically under/overstate expected return), and show why another estimate is better*.

'Active long vol' or factors can only refer to a strategy neither is itself an estimate of expected return, whereas bond yield can be a measure of expected return but not a strategy. The term 'CAPE' used loosely might refer to either an estimate of expected return or a strategy to use a regression of past CAPE v past subsequent return to vary allocation attempting to raise risk v return performance. So it's perhaps in part a semantic problem, but seems you also would rather talk about 'optimal allocation' only partly depending whether other people are talking about it. :happy
1. I believe there is enough evidence to think that the 1/CAPE is colossally wrong. This can be easily observed by performing a regression of 1/CAPE and observing that the intercept is not 0. An more neutral question is: if we want to determine μ, does CAPE contain any signal of economical significance? If the conclusion is that the signal is too weak or not economically significant, the natural choice is to fall back on a constant estimate for μ, which is what I suggested as the default option. Dynamically adjusting μ over time based on CAPE *is* an attempt to raise risk/return and should be met with the same skepticism as all other forms of market timing.

2. My experience tells me it's fairly hard to beat a constant allocation, even if there is some signal in the indicator. For example, VIX is an ok-ish estimator of future volatility (R^2 of 30% on a monthly timescale, IIRC). But actually trading on that in the optimal way (or at least, the way that theory suggests is optimal) results in a lower certainty equivalent return than a simple constant allocation. Therefore, if 1/CAPE has a nonzero amount of signal, it doesn't imply that it will be better than a constant estimate.
1. Again you speak strictly in terms of a regression analysis of past CAPE v subsequent past return. You do not address the fundamental derivation whereby earnings yield=expected return, at all. And then you assume the allocation would be changed according to CAPE which I very specifically said am I not proposing. It really seems you have a certain hammer, and see all counter arguments as nails, so to speak. :happy

The reason the regression analysis is not the only or even necessarily central issue actually a reason you've pointed out yourself. The regression is heavily influenced by change in CAPE over what's actually a pretty small sample. It is not a good evaluation of whether there are flaws in the fundamental derivation which says earnings yield=expected return. The argument against that must be made in terms of that derivation and its assumptions: which ones result in the measure being systematically biased up or down? Which is the question at hand in my contention that the 'paper airplane' of 1/CAPE is the best easy estimate of expected return *for planning purposes*. To address my point, I believe you must drop regressions and t-statistics and tell me the flaws in the derivation which make some other easy estimate of expected return a better one.

Again, current risk free rate + historical average ERP is not as bad as just assuming past return period as the best indicator of future return. But it has the obvious mismatch that it assumes we have 100% ability to derive the expected return of the 'rfa' from current market prices, but 0% ability to derive the expected equity return from current market prices, rather instead have to take an average of the difference in past realized equity and bond return over a past period part or all of which may bear little fundamental resemblance to now. When we just rejected that same method for the rfa itself...and for good reason.

2. Again a strange response to my post I think clearly saying 'let's assume a quasi fixed (perhaps age, but not market dependent) % stock/bond, more than once.
A fundamental derivation is only useful to the extent it can be tested. For example, CAPM (capital asset pricing model) is a very fundamental and theoretical model that follows from very simple assumptions, but it's not a very good one because economics have difficulty showing market beta is related to return, which is a result of CAPM.

Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.

If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).

I understand you want a quasi fixed stock/bond allocation, but that is simply not where CAPE will lead you. CAPE will lead you either to an asset allocation that changes as often as monthly, or to a contradiction of the bellman equation. You don't seem to want the former and the latter is clearly very, very bad.
JackoC
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by JackoC »

Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm
JackoC wrote: Tue Dec 08, 2020 9:37 am
Uncorrelated wrote: Mon Dec 07, 2020 4:14 pm
JackoC wrote: Mon Dec 07, 2020 2:32 pm
Uncorrelated wrote: Mon Dec 07, 2020 11:18 am
I have seen no evidence that 1/CAPE or CAPE linear regression outperforms a constant allocation. I have seen some evidence (from papers) that a constant allocation is extremely hard to beat, and that a simple regression on P/E ratio's does not beat a constant allocation by anything that can be considered significant. The expected gains of "optimally" using CAPE in your investment strategy have not been examined yet by any source linked to in this thread. You seem to believe the opposite, could you link to a few papers that investigate the certainty equivalent gains for using a CAPE timing strategy?
You are interested in 'optimal allocation' and perhaps a 'CAPE timing strategy'. Fine, and perhaps even some 'pro CAPE' posters are also. But the post you just responded to is not talking about that as I read it. I've definitely not been talking about that.

Starting from zero in a financial plan I need some indicator of expected return, even if it's going to be quasi-fixed (age dependent) % stock/bond. People who say they don't need this are confusing themselves IMO, I see no way around it. Dealing in 'actual' past returns inevitably means assuming implicitly that the expected return now is the average of past returns. Because in fact you must assume something, even be it a range, but any range has a midpoint, which is basically (not necessarily mathematically exactly) what the expected return is.

The earnings yield is a fundamental estimator of expected return per the derivation linked above, standard.
https://docfinder.is.bnpparibas-ip.com/ ... 07E654E5AE

To reject the 'paper airplane' of 1/CAPE=real expected return for basic planning, not dynamic asset allocation, purposes I believe you must explain why it's systematically biased in one direction or another (how the real world violates the assumptions of the derivation in a way which makes 1/CAPE systematically under/overstate expected return), and show why another estimate is better*.

'Active long vol' or factors can only refer to a strategy neither is itself an estimate of expected return, whereas bond yield can be a measure of expected return but not a strategy. The term 'CAPE' used loosely might refer to either an estimate of expected return or a strategy to use a regression of past CAPE v past subsequent return to vary allocation attempting to raise risk v return performance. So it's perhaps in part a semantic problem, but seems you also would rather talk about 'optimal allocation' only partly depending whether other people are talking about it. :happy
1. I believe there is enough evidence to think that the 1/CAPE is colossally wrong. This can be easily observed by performing a regression of 1/CAPE and observing that the intercept is not 0. An more neutral question is: if we want to determine μ, does CAPE contain any signal of economical significance? If the conclusion is that the signal is too weak or not economically significant, the natural choice is to fall back on a constant estimate for μ, which is what I suggested as the default option. Dynamically adjusting μ over time based on CAPE *is* an attempt to raise risk/return and should be met with the same skepticism as all other forms of market timing.

2. My experience tells me it's fairly hard to beat a constant allocation, even if there is some signal in the indicator. For example, VIX is an ok-ish estimator of future volatility (R^2 of 30% on a monthly timescale, IIRC). But actually trading on that in the optimal way (or at least, the way that theory suggests is optimal) results in a lower certainty equivalent return than a simple constant allocation. Therefore, if 1/CAPE has a nonzero amount of signal, it doesn't imply that it will be better than a constant estimate.
1. Again you speak strictly in terms of a regression analysis of past CAPE v subsequent past return. You do not address the fundamental derivation whereby earnings yield=expected return, at all. And then you assume the allocation would be changed according to CAPE which I very specifically said am I not proposing. It really seems you have a certain hammer, and see all counter arguments as nails, so to speak. :happy

The reason the regression analysis is not the only or even necessarily central issue actually a reason you've pointed out yourself. The regression is heavily influenced by change in CAPE over what's actually a pretty small sample. It is not a good evaluation of whether there are flaws in the fundamental derivation which says earnings yield=expected return. The argument against that must be made in terms of that derivation and its assumptions: which ones result in the measure being systematically biased up or down? Which is the question at hand in my contention that the 'paper airplane' of 1/CAPE is the best easy estimate of expected return *for planning purposes*. To address my point, I believe you must drop regressions and t-statistics and tell me the flaws in the derivation which make some other easy estimate of expected return a better one.

Again, current risk free rate + historical average ERP is not as bad as just assuming past return period as the best indicator of future return. But it has the obvious mismatch that it assumes we have 100% ability to derive the expected return of the 'rfa' from current market prices, but 0% ability to derive the expected equity return from current market prices, rather instead have to take an average of the difference in past realized equity and bond return over a past period part or all of which may bear little fundamental resemblance to now. When we just rejected that same method for the rfa itself...and for good reason.

2. Again a strange response to my post I think clearly saying 'let's assume a quasi fixed (perhaps age, but not market dependent) % stock/bond, more than once.
1. A fundamental derivation is only useful to the extent it can be tested. For example, CAPM (capital asset pricing model) is a very fundamental and theoretical model that follows from very simple assumptions, but it's not a very good one because economics have difficulty showing market beta is related to return, which is a result of CAPM.

2. Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.

3. If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).

I understand you want a quasi fixed stock/bond allocation, but that is simply not where CAPE will lead you. CAPE will lead you either to an asset allocation that changes as often as monthly, or to a contradiction of the bellman equation. You don't seem to want the former and the latter is clearly very, very bad.
1. I'm still bemused by your posts and really whole thread, that there would be so little discussion of the derivation and what's wrong with it. You'd almost think maybe people aren't even familiar with it. :happy

2. No actually, if there's a fundamental reason it would indicate expected return and you can't establish why it's a systematic over or under estimate then you haven't refuted it. Maybe here you are falling into the same trap less sophisticated posters do confusing realized and expected return. I believe any reasonably easy to derive indicator is a poor estimator for *realized* return unless there's overwhelming proof. But if you can't show in which direction a fundamental indictor of *expected* return is systematically biased, then it's useful.

3. That's bootstrap logic, *assuming* the CAPE has an impact on your asset allocation. How about assuming instead the practical reality for 99%+ of investors: they don't recognize a direct deterministic relationship between their estimate of equity v bond expected return and their asset allocation, they might be perfectly happy to make that allocation constant % of at least non-market dependent. You yourself said constant % is 'hard to beat'. But they still need an estimate of the expected equity return (to estimate how much to save, for one little thing). But they'd throw out an indicator of expected return with more actual market information (1/CAPE) over one with less relevant information (what the ERP averaged in various different economic, political etc contexts in the past of various relevance to now) just because there's an old paper saying they'd 'have to' vary allocation monthly if their estimate of the ERP changes. That's seriously your argument? :happy
abc132
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

I see there are no takers.

1. Start with an earnings of 10, and use an earnings annual percentage growth rate (mean=5, standard deviation=6).
2. Pick a random price multiple for each year of 8+RAND(25), which is anywhere from 8 to 33. (price will jump around dramatically each year)
3. Calculate 60 years worth of earnings growth, and use that years multiple to find the price. (price=earnings*multiple)
4. Calculate CAPE10 for years 11-50.
5. Calculate the average annual growth rate for each 10 year period (years 21-60) --> this is a forward prediction
6. Plot 10 year forward average annual growth rate vs CAPE10 from ten years earlier.
7. Fit a linear trend line and display the R^2 value

What you will find is that the R^2 of 0.5 is purely an artifact of not having samples with lower or higher CAPE ratios. Purely random P/E ratios each year will produce an R^2 of 0.5 - a chart almost identical to Shillers.


Image
Figure: Avg annual 10 year price growth rate vs CAPE 10 for purely random PE multiples each year

WHY? The highest CAPE10 ratio in any data set can not have gain from upwards movement in CAPE10, and will therefore have lower returns. This is an artifact of not having data with higher CAPE10 ratios, rather than a prediction of 0 returns. This is exactly what we saw play out - when CAPE10 ratios went higher than ever before they produced higher returns than predicted and the new maximum once again predicts 0 returns.

Any set of random data will predict lower returns (0% real) at the highest PE ratios (at wherever maximum PE we choose), and the R^2 of 0.5 is a direct result of not having data for higher PE ratios - and is not a real prediction of 0 real returns. 0 real returns should actually happen at the limit of whatever CAPE10 ratio we will ever tolerate - likely much higher than present and closer to 80 given the Japan example.

If people are willing to tolerate the current CAPE10 ratios moving forward, we should have AVERAGE stock returns. Or better said CAPE10 only predicts such low returns if we are not willing to tolerate such a high CAPE10 ratio moving forward.

Changing the random data set to allow higher PE's shifts the curve exactly as should be suspected - just like the past vs present CAPE10 curves. The new CAPE10 equation is a predictable result of having data with higher CAPE10 ratios - both in that it changed and in how it changed.

CONCLUSION: Purely random data will predict an R^2 of 0.5 for any rangebound set of PE multiples, and the model curve fit will always under predict growth rates at high PE multiples specifically because the model lacks data above that multiple.
Last edited by abc132 on Tue Dec 08, 2020 3:09 pm, edited 6 times in total.
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Uncorrelated
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

JackoC wrote: Tue Dec 08, 2020 2:18 pm
Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm
JackoC wrote: Tue Dec 08, 2020 9:37 am
Uncorrelated wrote: Mon Dec 07, 2020 4:14 pm
JackoC wrote: Mon Dec 07, 2020 2:32 pm
You are interested in 'optimal allocation' and perhaps a 'CAPE timing strategy'. Fine, and perhaps even some 'pro CAPE' posters are also. But the post you just responded to is not talking about that as I read it. I've definitely not been talking about that.

Starting from zero in a financial plan I need some indicator of expected return, even if it's going to be quasi-fixed (age dependent) % stock/bond. People who say they don't need this are confusing themselves IMO, I see no way around it. Dealing in 'actual' past returns inevitably means assuming implicitly that the expected return now is the average of past returns. Because in fact you must assume something, even be it a range, but any range has a midpoint, which is basically (not necessarily mathematically exactly) what the expected return is.

The earnings yield is a fundamental estimator of expected return per the derivation linked above, standard.
https://docfinder.is.bnpparibas-ip.com/ ... 07E654E5AE

To reject the 'paper airplane' of 1/CAPE=real expected return for basic planning, not dynamic asset allocation, purposes I believe you must explain why it's systematically biased in one direction or another (how the real world violates the assumptions of the derivation in a way which makes 1/CAPE systematically under/overstate expected return), and show why another estimate is better*.

'Active long vol' or factors can only refer to a strategy neither is itself an estimate of expected return, whereas bond yield can be a measure of expected return but not a strategy. The term 'CAPE' used loosely might refer to either an estimate of expected return or a strategy to use a regression of past CAPE v past subsequent return to vary allocation attempting to raise risk v return performance. So it's perhaps in part a semantic problem, but seems you also would rather talk about 'optimal allocation' only partly depending whether other people are talking about it. :happy
1. I believe there is enough evidence to think that the 1/CAPE is colossally wrong. This can be easily observed by performing a regression of 1/CAPE and observing that the intercept is not 0. An more neutral question is: if we want to determine μ, does CAPE contain any signal of economical significance? If the conclusion is that the signal is too weak or not economically significant, the natural choice is to fall back on a constant estimate for μ, which is what I suggested as the default option. Dynamically adjusting μ over time based on CAPE *is* an attempt to raise risk/return and should be met with the same skepticism as all other forms of market timing.

2. My experience tells me it's fairly hard to beat a constant allocation, even if there is some signal in the indicator. For example, VIX is an ok-ish estimator of future volatility (R^2 of 30% on a monthly timescale, IIRC). But actually trading on that in the optimal way (or at least, the way that theory suggests is optimal) results in a lower certainty equivalent return than a simple constant allocation. Therefore, if 1/CAPE has a nonzero amount of signal, it doesn't imply that it will be better than a constant estimate.
1. Again you speak strictly in terms of a regression analysis of past CAPE v subsequent past return. You do not address the fundamental derivation whereby earnings yield=expected return, at all. And then you assume the allocation would be changed according to CAPE which I very specifically said am I not proposing. It really seems you have a certain hammer, and see all counter arguments as nails, so to speak. :happy

The reason the regression analysis is not the only or even necessarily central issue actually a reason you've pointed out yourself. The regression is heavily influenced by change in CAPE over what's actually a pretty small sample. It is not a good evaluation of whether there are flaws in the fundamental derivation which says earnings yield=expected return. The argument against that must be made in terms of that derivation and its assumptions: which ones result in the measure being systematically biased up or down? Which is the question at hand in my contention that the 'paper airplane' of 1/CAPE is the best easy estimate of expected return *for planning purposes*. To address my point, I believe you must drop regressions and t-statistics and tell me the flaws in the derivation which make some other easy estimate of expected return a better one.

Again, current risk free rate + historical average ERP is not as bad as just assuming past return period as the best indicator of future return. But it has the obvious mismatch that it assumes we have 100% ability to derive the expected return of the 'rfa' from current market prices, but 0% ability to derive the expected equity return from current market prices, rather instead have to take an average of the difference in past realized equity and bond return over a past period part or all of which may bear little fundamental resemblance to now. When we just rejected that same method for the rfa itself...and for good reason.

2. Again a strange response to my post I think clearly saying 'let's assume a quasi fixed (perhaps age, but not market dependent) % stock/bond, more than once.
1. A fundamental derivation is only useful to the extent it can be tested. For example, CAPM (capital asset pricing model) is a very fundamental and theoretical model that follows from very simple assumptions, but it's not a very good one because economics have difficulty showing market beta is related to return, which is a result of CAPM.

2. Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.

3. If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).

I understand you want a quasi fixed stock/bond allocation, but that is simply not where CAPE will lead you. CAPE will lead you either to an asset allocation that changes as often as monthly, or to a contradiction of the bellman equation. You don't seem to want the former and the latter is clearly very, very bad.
1. I'm still bemused by your posts and really whole thread, that there would be so little discussion of the derivation and what's wrong with it. You'd almost think maybe people aren't even familiar with it. :happy

2. No actually, if there's a fundamental reason it would indicate expected return and you can't establish why it's a systematic over or under estimate then you haven't refuted it. Maybe here you are falling into the same trap less sophisticated posters do confusing realized and expected return. I believe any reasonably easy to derive indicator is a poor estimator for *realized* return unless there's overwhelming proof. But if you can't show in which direction a fundamental indictor of *expected* return is systematically biased, then it's useful.

3. That's bootstrap logic, *assuming* the CAPE has an impact on your asset allocation. How about assuming instead the practical reality for 99%+ of investors: they don't recognize a direct deterministic relationship between their estimate of equity v bond expected return and their asset allocation, they might be perfectly happy to make that allocation constant % of at least non-market dependent. You yourself said constant % is 'hard to beat'. But they still need an estimate of the expected equity return (to estimate how much to save, for one little thing). But they'd throw out an indicator of expected return with more actual market information (1/CAPE) over one with less relevant information (what the ERP averaged in various different economic, political etc contexts in the past of various relevance to now) just because there's an old paper saying they'd 'have to' vary allocation monthly if their estimate of the ERP changes. That's seriously your argument? :happy
1. I really don't care about the derivation. My argument never was that CAPE doesn't predict future returns, my argument was that the statistical evidence put forth by others was too weak and/or wrong.

2. A dice roll is not a biased estimator of a function that returns a random number between 3 and 4. But it is an useless estimator. If an indicator has good t-stats and a solid theoretical foundation, it doesn't mean that translates into economically significant results. I gave an example involving VIX earlier.

3. When I mean constant allocation, I mean rf + ERP style estimation plus merton's portfolio problem. This is hard to beat. A constant allocation based on CAPE isn't hard to beat: it is trivial to find a better allocation by just fixing the ways in which the strategy violates bellman's principle of optimality.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.

If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).
If CAPE based models for expected returns are wrong then your proposal (rf + ERP) is even MORE wrong.

Not only is there no theoretical argument for a constant ERP (an argument that CAPE actually does have, BTW) but empirically uses a constant ERP has performed much worse than CAPE has.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Ocean77 »

alex_686 wrote: Tue Dec 08, 2020 9:39 am Earnings increase solely due to accounting changes.
Which would lower the CAPE, all else being equal. As the earnings are in the denominator of the CAPE ratio. So this would not explain why the CAPE got so high? Or to put it differently, if accounting had not changed, then the current CAPE would be even higher than it already is.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by GAAP »

willthrill81 wrote: Tue Dec 08, 2020 9:46 am I agree that accounting changes are likely responsible for some of the post 1988 shift. But I can't help but think that declining interest rates are partly responsible as well since declining real rates boosts the prices of real assets. But how much of the change is due to one or the other is unknown to me.
Interest rates, combined with a much tamer inflationary/deflationary environment

I would add to that the much larger presence of retail investors -- via IRAs and 401(k)s initially, then with a greater after-tax presence over time.

Combine the above with computerized tools that make it practical to trade frequently, using options, leverage, etc. -- and without the need to call a broker.

It probably really is a different environment now.
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

vineviz wrote: Tue Dec 08, 2020 3:01 pm
Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm Even if 1/CAPE doesn't systematically over or under-estimate the expected return, it doesn't mean it's a good estimate. That is something to be determined with empirical research. All models are wrong, but some are useful. I believe it's up to you to show this model is useful, or more useful than others.

If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).
If CAPE based models for expected returns are wrong then your proposal (rf + ERP) is even MORE wrong.
Citation needed.

Not only is there no theoretical argument for a constant ERP (an argument that CAPE actually does have, BTW) but empirically uses a constant ERP has performed much worse than CAPE has.
Citation needed (2x).


It certainly isn't hard to find papers that regard a constant equity risk premium as a very high bar to beat. i.e.:
This popular benchmark forecast (e.g., Goyal and Welch 2003, 2008, Campbell and Thompson 2008, Ferreira and Santa-Clara 2011) assumes a constant expected equity risk premium (r t+1 = α + ε t+1 ). Goyal and Welch (2003, 2008) show that (26) is a very stringent out-of-sample benchmark: predictive regression forecasts based on individual macroeconomic variables typically fail to outperform the historical average.
Forecasting the Equity Risk Premium: The Role of Technical Indicators

Must've been the 10th time I cited this paper this week.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

Ocean77 wrote: Tue Dec 08, 2020 3:13 pm
alex_686 wrote: Tue Dec 08, 2020 9:39 am Earnings increase solely due to accounting changes.
Which would lower the CAPE, all else being equal. As the earnings are in the denominator of the CAPE ratio. So this would not explain why the CAPE got so high? Or to put it differently, if accounting had not changed, then the current CAPE would be even higher than it already is.

I think this is backwards. My understanding is accoiunting changes have tightened the rules around what companies can call earnings such that earnings are now lower than what they would have been under the old rules. Thus elevating CAPE to some degree.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

willthrill81 wrote: Sat Dec 05, 2020 2:38 pm Conclusions that say that a readily visible relationship does not exist are wrong.
Can you explain why picking completely random PE multiples produces this readily visible relationship?

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

Post by inbox788 »

abc132 wrote: Tue Dec 08, 2020 3:55 pm
willthrill81 wrote: Sat Dec 05, 2020 2:38 pm Conclusions that say that a readily visible relationship does not exist are wrong.
Can you explain why picking completely random PE multiples produces this readily visible relationship?

Image
The visible relationship I'm seeing is that it's V shaped, bottoming out at 40, so if the CAPE goes higher than 40, it predicts INCREASING returns. We need more data points at 60, 70 and 80 to see if the trend continues.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

Uncorrelated wrote: Tue Dec 08, 2020 3:29 pm
vineviz wrote: Tue Dec 08, 2020 3:01 pm If CAPE based models for expected returns are wrong then your proposal (rf + ERP) is even MORE wrong.
Citation needed.
It's plainly evident if you do a side-by-side comparison of the two approaches. Here's an example comparing the forward realized return to predictions from the two models from 1951 to 2010. The CAPE model is slightly different from the one I used earlier (it treats expected inflation, real risk-free yield, and Shiller's ECY as separate variables), and for each year t the regression uses parameter estimates from 1928 through year t-1. Likewise the Constant ERP model updates annually, with the prediction being equal to the yield on the risk-free asset plus the average realized equity premium from 1928 through year t-1.

Image

The CAPE-based model is a better fit in every way: higher R-squared, slope closer to 1, intercept closer to 0.
Uncorrelated wrote: Tue Dec 08, 2020 3:29 pm
Not only is there no theoretical argument for a constant ERP (an argument that CAPE actually does have, BTW) but empirically uses a constant ERP has performed much worse than CAPE has.
Citation needed (2x).
No citation needed on this one: nothing in MPT or the EFH leads to a prediction of a constant ERP. The only way that would be indicated would be that equity RISK is constant, but clearly it's not: economic growth isn't constant, the savings rate isn't constant, tax-treatment isn't constant, the market portfolios allocation between debt and equity isn't constant, etc.

Imagine we wake up tomorrow and find that the capital gains tax rate is now 60% for all investors: do you think that would no impact on the price of stocks? Or if the tax rate on Treasury instruments went to zero?

An efficient market is SUPPOSED to adjust equity prices based on new information, but a constant ERP would mean that equity prices NEVER change based on new information EXCEPT for changes in the yield on the risk-free asset. Do you really think that sounds right?

No, it doesn't. The expected ERP changes based on changes in expectations about things like taxation, monetary policy, fiscal policy, economic growth, exchange rates, and more. If the market is theoretically adjusting the demanded ERP based on changes in expected risk (which it must do to ensure that it is optimizing it's risk-adjusted return), then we certainly can't say that the ERP is theoretically constant.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

inbox788 wrote: Tue Dec 08, 2020 4:34 pm
abc132 wrote: Tue Dec 08, 2020 3:55 pm
willthrill81 wrote: Sat Dec 05, 2020 2:38 pm Conclusions that say that a readily visible relationship does not exist are wrong.
Can you explain why picking completely random PE multiples produces this readily visible relationship?

Image
The visible relationship I'm seeing is that it's V shaped, bottoming out at 40, so if the CAPE goes higher than 40, it predicts INCREASING returns. We need more data points at 60, 70 and 80 to see if the trend continues.
Inbox,

This is random data I created other than PE is bound between PE of 8 and 33, and the high performance there that makes it look like a V is just a result of that particular data run. Here is another run:

Image
Figure: Average annual 10 year future returns vs CAPE10 using random, ranged bound PE multiples. (Run #2)

Earnings started at 10, and grew with a mean of 5% and 6% standard deviation, so generally up but with some down years. 95% of years the growth would be between -7% and 17% if my understanding of 2 standard deviations is correct.

My price each year was the earnings multiplied by a random real number between 8 and 33 - so the P/E ratio was random other than being range bound. There is almost no relationship between one year and the next other than the limits to PE.

When random numbers produce the same graph and R^2 value as Shiller's Cape10, I think you can probably conclude that much of the prediction equation is simply due to being range bound.

I'm open to comments and criticism.

I get R^2 between 0.4 and 0.6 if I do a bunch of runs. This is 158 years worth of fake data - I was very roughly approximating the graph Vineviz showed earlier, so this is my yearly data, as calculations are only computed once a year.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

Image
Figure: Run #3 with PE going from 5 to 55

Lo and behold, look what random PE data does when we extend the allowed PE multiples to go from (5 to 55) instead of (8 to 33) --> the predicted CAPE10 value for zero real returns moves to the right.

Look at how random data (PE 8 to 33) predicted 0 real returns at CAPE10 of 35, and look at how it now moves to 50 with (PE 5 to 55).

It's exactly what happened when we got more historical data for higher CAPE10 multiples.

Random data without relationship from one year to the next should produce this result.

It's looking like "the data mining artifact" Shiller suggested is just having range bound data.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by marcopolo »

abc132 wrote: Tue Dec 08, 2020 6:21 pm Image
Figure: Run #3 with PE going from 5 to 55

Lo and behold, look what random PE data does when we extend the allowed PE multiples to go from (5 to 55) instead of (8 to 33) --> the predicted CAPE10 value for zero real returns moves to the right.

Look at how random data (PE 8 to 33) predicted 0 real returns at CAPE10 of 35, and look at how it now moves to 50 with (PE 5 to 55).

It's exactly what happened when we got more historical data for higher CAPE10 multiples.

Random data without relationship from one year to the next should produce this result.

It's looking like "the data mining artifact" Shiller suggested is just having range bound data.

To his credit Shiller did say that it was quite possible his results were due to data mining and that they did not check for statistical significance. I guess the Nobel committee probably does not have any statisticians on it.

Edit: That was jsut a joke, no need to start a long conversation defending his Nobel Prize accomplishments.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by GoneOnTilt »

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.
A practical question: If CAPE is highly predictive of future returns, what does one do about it?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by GAAP »

bck63 wrote: Tue Dec 08, 2020 7:12 pm A practical question: If CAPE is highly predictive of future returns, what does one do about it?
Adjust your plans accordingly -- whether savings rate or withdrawal rate or years to hit a target or whatever. That could be part of a regularly-scheduled effort to keep your plans on track.

This is not the same thing as saying "change your AA", "save more", "save less", etc. Use it to inform your decisions -- whether or not that means to act on anything.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

marcopolo wrote: Tue Dec 08, 2020 6:59 pm
To his credit Shiller did say that it was quite possible his results were due to data mining and that they did not check for statistical significance. I guess the Nobel committee probably does not have any statisticians on it.

Edit: That was just a joke, no need to start a long conversation defending his Nobel Prize accomplishments.
Haha, no worries here.

If anyone reading this goes from trend searching to thinking about the why of that trend, my time will have been well spent. I am curious why nobody has examined why that R^2 of 0.5 exists.

The actionable is to think about whether we will support such high CAPE10 values moving forward. The answer will tell you whether or not to expect a better chance of low, average, or above average returns in the next 10 years.

One could make an argument that low bond rates, and fed support could make it go higher. I'm not making that argument, but it shows where the lower expected returns crowd could be wrong.

Bogle showed us overvaluation can persist for decades, which along with CAPE10 saying the past predicts the future - these should have been the clues that something was amiss.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

abc132 wrote: Tue Dec 08, 2020 6:21 pm Random data without relationship from one year to the next should produce this result.

It's looking like "the data mining artifact" Shiller suggested is just having range bound data.
Okay, I replicated your methodology.

However, your methodology has not created "random data without relationship from one year to the next". Instead, it has somewhat reasonably simulated the actual fundamental workings of the stock market.

You've created an EPS time series that behaves very similarly to the actual EPS time series we observe in real life, random walk with drift (aka Geometric Brownian motion).

You've also created (likely by accident) a PE time series that behaves similarly to the actual CAPE time series in one very important way. You've modeled each year's PE ratio as a completely random (though range-bound) variable BUT you're measuring the geometric total return over 10-year intervals. It's true that in the real-life the annual CAPE ratio is positively autocorrelated, however that autocorrelation decays fairly robustly over the course of approximately 10 years. In other words, the real-life correlation between CAPE10 in year t with CAPE10 in year t+10 is so low (depending on which periods you lag, somewhere around 0.1) that your random PE series exhibits essentially the same behavior.

In short, the combination of a Brownian EPS series and random PE series produces an economically legitimate ACTUAL relationship: higher average returns when the earnings stream is purchased at a low price than when the same stream is purchased at a high price.

Even though the future PE ratio is not predictable in your simulation, the EPS stream having a positive drift means that future prices (and therefore future returns) ARE predictable. As you'd expect.

It's not the range-bound nature of the PE ratio which creates the predictability in your model, it's the (realistic) predictability of the EPS series that does it. Change the EPS time series to purely random series and the predictability goes away.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

vineviz wrote: Tue Dec 08, 2020 8:44 pm
abc132 wrote: Tue Dec 08, 2020 6:21 pm Random data without relationship from one year to the next should produce this result.

It's looking like "the data mining artifact" Shiller suggested is just having range bound data.
Okay, I replicated your methodology.

However, your methodology has not created "random data without relationship from one year to the next". Instead, it has somewhat reasonably simulated the actual fundamental workings of the stock market.

You've created an EPS time series that behaves very similarly to the actual EPS time series we observe in real life, random walk with drift (aka Geometric Brownian motion).

You've also created (likely by accident) a PE time series that behaves similarly to the actual CAPE time series in one very important way. You've modeled each year's PE ratio as a completely random (though range-bound) variable BUT you're measuring the geometric total return over 10-year intervals. It's true that in the real-life the annual CAPE ratio is positively autocorrelated, however that autocorrelation decays fairly robustly over the course of approximately 10 years. In other words, the real-life correlation between CAPE10 in year t with CAPE10 in year t+10 is so low (depending on which periods you lag, somewhere around 0.1) that your random PE series exhibits essentially the same behavior.

In short, the combination of a Brownian EPS series and random PE series produces an economically legitimate ACTUAL relationship: higher average returns when the earnings stream is purchased at a low price than when the same stream is purchased at a high price.

Even though the future PE ratio is not predictable in your simulation, the EPS stream having a positive drift means that future prices (and therefore future returns) ARE predictable. As you'd expect.

It's not the range-bound nature of the PE ratio which creates the predictability in your model, it's the (realistic) predictability of the EPS series that does it. Change the EPS time series to purely random series and the predictability goes away.
Thanks for confirming the results.

Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

vineviz wrote: Tue Dec 08, 2020 8:44 pm
abc132 wrote: Tue Dec 08, 2020 6:21 pm Random data without relationship from one year to the next should produce this result.

It's looking like "the data mining artifact" Shiller suggested is just having range bound data.
Okay, I replicated your methodology.

However, your methodology has not created "random data without relationship from one year to the next". Instead, it has somewhat reasonably simulated the actual fundamental workings of the stock market.

You've created an EPS time series that behaves very similarly to the actual EPS time series we observe in real life, random walk with drift (aka Geometric Brownian motion).

You've also created (likely by accident) a PE time series that behaves similarly to the actual CAPE time series in one very important way. You've modeled each year's PE ratio as a completely random (though range-bound) variable BUT you're measuring the geometric total return over 10-year intervals. It's true that in the real-life the annual CAPE ratio is positively autocorrelated, however that autocorrelation decays fairly robustly over the course of approximately 10 years. In other words, the real-life correlation between CAPE10 in year t with CAPE10 in year t+10 is so low (depending on which periods you lag, somewhere around 0.1) that your random PE series exhibits essentially the same behavior.

In short, the combination of a Brownian EPS series and random PE series produces an economically legitimate ACTUAL relationship: higher average returns when the earnings stream is purchased at a low price than when the same stream is purchased at a high price.

Even though the future PE ratio is not predictable in your simulation, the EPS stream having a positive drift means that future prices (and therefore future returns) ARE predictable. As you'd expect.

It's not the range-bound nature of the PE ratio which creates the predictability in your model, it's the (realistic) predictability of the EPS series that does it. Change the EPS time series to purely random series and the predictability goes away.
Further, it's a very safe bet that if either your independent or dependent variable is truly random, then, by definition, you shouldn't be consistently finding a statistically significant relationship between the two. If you are, something is clearly wrong.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

willthrill81 wrote: Tue Dec 08, 2020 10:17 pm
Further, it's a very safe bet that if either your independent or dependent variable is truly random, then, by definition, you shouldn't be consistently finding a statistically significant relationship between the two. If you are, something is clearly wrong.
That's correct.

My thesis is that it is only the top bound on CAPE10 that makes it non random.

As Vineviz pointed out, when we make that choice truly random (non range bound) the correlation is zero.

I'm not sure why Vineviz thought the mean being positive mattered, so I'll wait for a confirmation of my results and a revision of that statement. Making the mean=0 just puts the 0 real returns at the midpoint of the observed CAPE10 ratios.
Last edited by abc132 on Tue Dec 08, 2020 10:53 pm, edited 1 time in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

abc132 wrote: Tue Dec 08, 2020 10:12 pm
Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

vineviz wrote: Tue Dec 08, 2020 10:53 pm
abc132 wrote: Tue Dec 08, 2020 10:12 pm
Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
I tried earnings starting at 10 and going up by 0.1 each year and got the same result.

Also completely random number between 0 and 10, although the R^2 is reduced a bit. (around 0.3) This produces more of an exponential decay than linear curve.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

abc132 wrote: Tue Dec 08, 2020 10:57 pm
vineviz wrote: Tue Dec 08, 2020 10:53 pm
abc132 wrote: Tue Dec 08, 2020 10:12 pm
Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
I tried earnings starting at 10 and going up by 0.1 each year and got the same result.
Yep, still a random walk. Try it using the same kind of formula you used with the PE ratio, eg 5+RAND(15).
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by alex_686 »

So, I am going to squish 3 posts into 1.
Uncorrelated wrote: Mon Dec 07, 2020 11:18 am I have seen no evidence that 1/CAPE or CAPE linear regression outperforms a constant allocation. I have seen some evidence (from papers) that a constant allocation is extremely hard to beat, and that a simple regression on P/E ratio's does not beat a constant allocation by anything that can be considered significant. The expected gains of "optimally" using CAPE in your investment strategy have not been examined yet by any source linked to in this thread. You seem to believe the opposite, could you link to a few papers that investigate the certainty equivalent gains for using a CAPE timing strategy?
and
Uncorrelated wrote: Mon Dec 07, 2020 3:05 pm This is technically true but also highlights one more problem with this discussion: it gives the impression that predicting market returns is a desirable goal.

Your goal is to obtain financial security, or something similar. Forecasting future market returns is only useful to the extent this will help you obtain your financial goals. If CAPE market timing gives 0.2% higher certainty equivalent return and factor investing gives 1% higher certainty equivalent return, then it is obvious CAPE market timing is a waste of your time. I tested/invented quite a few market timing strategies but was never able to find anything that works better than a single factor investing portfolio. From what I have seen here, CAPE does not come close to obtaining that goal even in the best case scenario. That is before factoring in the much higher statistical significance factor investing has.

I see only two paths forward. Path 1, use ridiculously high standards of proof and reject all forms of market timing. This brings you to an estimate of the equity risk premium equal to the historical average. Path 2, pick your cutoff for statistical significance around the 5% significance threshold, and come to the conclusion that there are better investment strategies than something involving CAPE.
So, let us go back to first principles.

1). How much do you think that you need to save from current consumption to meet your future goals. I think this is the most important.
2). You state that a constant asset allocation beats CAPE 10. Ok. How does one come up with a constant asset allocation?

Upthread you mentioned historical returns. The problem here is that historical returns are worse than CAPE 10. Specifically, the mean is time varying. Pick one time period and you get one return, pick another period and you get a statically different mean return. Decompose the returns and you will find the same thing. Earnings Yield, Earnings Growth, Dividend Yield, Equity Risk Premium, Real Interest Rate, Volatility, Correlation between Assets, etc.
Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).
I think that this is a important difference between us. First, PE ratios can't be used by themselves as a overvalued / undervalued signal. Economic structures evolve, so the inputs evolve, so the correct PE ratio is time varying. It does not revert to the mean.

We may be closer to optimizing expected utility. However, if I am reading the Bellman equation correctly, it is assuming a constant discount factor, or B. We don't have this. I am also trying to wrap my head around the payoff, F(x,a). The function will change unknowable over time.

Anyways, ERP's mean is also time varying. I have not heard a suggestion before that it was.

So, back to how we estimate future equity return and ERP. Their means time vary. I think this is the value we want. The value that we are going to use to calculate our savings rate and asset allocation. CAPE's solution is crude. Assume that the past 10 years of earnings is reflective of the future. Grand sweep of history. It has its strengths and weaknesses. For something better I will point you to Jump Diffusion models and the Hurst exponent.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

vineviz wrote: Tue Dec 08, 2020 11:01 pm
abc132 wrote: Tue Dec 08, 2020 10:57 pm
vineviz wrote: Tue Dec 08, 2020 10:53 pm
abc132 wrote: Tue Dec 08, 2020 10:12 pm
Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
I tried earnings starting at 10 and going up by 0.1 each year and got the same result.
Yep, still a random walk. Try it using the same kind of formula you used with the PE ratio, eg 5+RAND(15).
I got the same result with static earnings of 5 + rand(10) R^2=0.45

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

Post by vineviz »

abc132 wrote: Tue Dec 08, 2020 11:03 pm
vineviz wrote: Tue Dec 08, 2020 11:01 pm
abc132 wrote: Tue Dec 08, 2020 10:57 pm
vineviz wrote: Tue Dec 08, 2020 10:53 pm
abc132 wrote: Tue Dec 08, 2020 10:12 pm
Did you actually try mean=0 standard deviation=6?

Because I get the same relationship without a positive drift.
Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
I tried earnings starting at 10 and going up by 0.1 each year and got the same result.
Yep, still a random walk. Try it using the same kind of formula you used with the PE ratio, eg 5+RAND(15).
I got the same result with 5 + rand(10) R^2=0.5

Image
Are you doing this in Excel? If you want to PM me a link to your spreadsheet I can see if I can figure out why mine and yours don’t agree.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

vineviz wrote: Tue Dec 08, 2020 11:06 pm
abc132 wrote: Tue Dec 08, 2020 11:03 pm
vineviz wrote: Tue Dec 08, 2020 11:01 pm
abc132 wrote: Tue Dec 08, 2020 10:57 pm
vineviz wrote: Tue Dec 08, 2020 10:53 pm

Yep you get the same result even with a zero drift, or a negative drift. I probably should have used better language: it’s the random walk (ie Brownian movement) that triggers the result. The sign of the drift (negative, zero, or positive) only affects the regression parameters, not the r-squared value.

If you replace the geometric progression for EPS with a random number from something like a continuous uniform distribution (as the PE ratio was modeled) the slope and r-squared should both collapse to zero. That’s true whether the EPS value, PE ratio, or both are bounded or unbounded.
I tried earnings starting at 10 and going up by 0.1 each year and got the same result.
Yep, still a random walk. Try it using the same kind of formula you used with the PE ratio, eg 5+RAND(15).
I got the same result with 5 + rand(10) R^2=0.5

Image
Are you doing this in Excel? If you want to PM me a link to your spreadsheet I can see if I can figure out why mine and yours don’t agree.
You can tell by the high quality graphing software :happy

Yes, let me clean it up to just the relevant sheet and I'll PM it.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

vineviz wrote: Tue Dec 08, 2020 5:33 pm
Uncorrelated wrote: Tue Dec 08, 2020 3:29 pm
vineviz wrote: Tue Dec 08, 2020 3:01 pm If CAPE based models for expected returns are wrong then your proposal (rf + ERP) is even MORE wrong.
Citation needed.
It's plainly evident if you do a side-by-side comparison of the two approaches. Here's an example comparing the forward realized return to predictions from the two models from 1951 to 2010. The CAPE model is slightly different from the one I used earlier (it treats expected inflation, real risk-free yield, and Shiller's ECY as separate variables), and for each year t the regression uses parameter estimates from 1928 through year t-1. Likewise the Constant ERP model updates annually, with the prediction being equal to the yield on the risk-free asset plus the average realized equity premium from 1928 through year t-1.

Image

The CAPE-based model is a better fit in every way: higher R-squared, slope closer to 1, intercept closer to 0.
This methodology is so wrong that I don't even know where to begin.

Papers, please.
Uncorrelated wrote: Tue Dec 08, 2020 3:29 pm
Not only is there no theoretical argument for a constant ERP (an argument that CAPE actually does have, BTW) but empirically uses a constant ERP has performed much worse than CAPE has.
Citation needed (2x).
No citation needed on this one: nothing in MPT or the EFH leads to a prediction of a constant ERP. The only way that would be indicated would be that equity RISK is constant, but clearly it's not: economic growth isn't constant, the savings rate isn't constant, tax-treatment isn't constant, the market portfolios allocation between debt and equity isn't constant, etc.
...and that leads to a predictable ERP according to which papers....? The paper "Forecasting the Equity Risk Premium: The Role of Technical Indicators" (here is it again!) had severe difficulties proving technical indicators predict ERP.

Yes some variables are predictive, but only bond related variables appear to be economically significant. Not because they have long-range predictive power, but because they appear to be excellent proxies for recessions.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

alex_686 wrote: Tue Dec 08, 2020 11:02 pm So, let us go back to first principles.

1). How much do you think that you need to save from current consumption to meet your future goals. I think this is the most important.
2). You state that a constant asset allocation beats CAPE 10. Ok. How does one come up with a constant asset allocation?

Upthread you mentioned historical returns. The problem here is that historical returns are worse than CAPE 10. Specifically, the mean is time varying. Pick one time period and you get one return, pick another period and you get a statically different mean return. Decompose the returns and you will find the same thing. Earnings Yield, Earnings Growth, Dividend Yield, Equity Risk Premium, Real Interest Rate, Volatility, Correlation between Assets, etc.

Uncorrelated wrote: Tue Dec 08, 2020 1:52 pm If you accept that CAPE is useful for planning purposes, then you must also accept it can be used for market timing. Intuitively, if CAPE10 has impact on your asset allocation, then it must be true that next month's CAPE10 figure contains more information than the last. Changing your asset allocation as soon as next months CAPE10 figure comes in must result in higher expected utility. If you don't do this, you'll end a path dependent asset allocation, which is always suboptimal (wikipedia has some more info, but it's quite hard to read if this is outside your area of expertise...). rf + ERP doesn't have this problem, the ERP is assumed to be constant, and if the rf changes or is mis-estimated then it does not affect the asset allocation at all. (see the solution to merton's portfolio problem).
I think that this is a important difference between us. First, PE ratios can't be used by themselves as a overvalued / undervalued signal. Economic structures evolve, so the inputs evolve, so the correct PE ratio is time varying. It does not revert to the mean.

We may be closer to optimizing expected utility. However, if I am reading the Bellman equation correctly, it is assuming a constant discount factor, or B. We don't have this. I am also trying to wrap my head around the payoff, F(x,a). The function will change unknowable over time.

Anyways, ERP's mean is also time varying. I have not heard a suggestion before that it was.

So, back to how we estimate future equity return and ERP. Their means time vary. I think this is the value we want. The value that we are going to use to calculate our savings rate and asset allocation. CAPE's solution is crude. Assume that the past 10 years of earnings is reflective of the future. Grand sweep of history. It has its strengths and weaknesses. For something better I will point you to Jump Diffusion models and the Hurst exponent.
When I say constant allocation, I mean a constant ERP and Merton's portfolio problem. Merton's portfolio model simply means performing expected utility maximization with these assumptions and a CRRA utility function. The bellman equation is one way of finding the optimal solution. This equation is convenient because it outlines clear conditions for optimality, one of which (path independence) is violated extremely frequently. As far as I'm aware of, the rf + ERP + merton model is the only one in which the optimal solution is a constant allocation to equities.

Merton's portfolio problem does not depend on anything mean reverting. It depends on you having self-consistent risk preferences. If the market model is jump diffusion instead of lognormal, it still follows from Merton's portfolio model that the optimal allocation is constant although the allocation is slightly lower.

I'm not against the idea that equity returns are predictable (if sufficient evidence is provided), but the idea of using a slow-moving asset allocation with a prediction based on fast-moving variables is a clear violation of path independence. If equity returns are predictable, then the asset allocation should change as fast as the underlying variables. I have seen the suggestion that CAPE is useful to perform long-term planning, but that is just not plausible as P/E changes fast and long-term planning suggests an asset allocation that changes slowly.

The discount rate is your own personal discount rate and does not depend on the market, the intuitive idea is that you're better of obtaining a reward now than at some point infinitely far in the future. Without this property you can end up with A.I. that takes infinitely long to make a move.

I'm not an expert on savings rate calculations, but as far as I know the risk-free rate is more important for your savings rate than the ERP. The risk-free rate can be estimated by looking at bond yields.

The 95% confidence interval of the ERP over the last 100 years is somewhere between 2% and 10%, I don't think it's true that different periods give a statistically different mean. Source for 95% CI. If I remember correctly (own calculations), the difference between the USA and the worst performing nation in the last 100 years isn't even statistically significant. This makes it quite problematic to prove one model is better than any other.


I would like to have a source that says historical returns are worse than CAPE. The paper "Forecasting the Equity Risk Premium: The Role of Technical Indicators" does not explicitly test CAPE, but does state that the 12-month moving average of P/E has an out-of-sample R^2 that is negative. As far as I'm concerned is provides quite strong evidence that a constant ERP is better than one based on P/E ratio's or CAPE.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
"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

Post by tadamsmar »

When I see a discussion about an investing strategy I usually try to debunk it by finding the ETFs that utilize it. But looks like Barclay's Shiller CAPE EFT has a scary good 5 year performance:

https://www.google.com/finance/quote/.I ... RCA%3ACAPE

(click 5Y after opening the link)

Anyway, the funds I find that use CAPE all seem to be (basically) stock picker models. They don't seem to be any timing model EFTs for getting in and out of the broad market.

I guess value investing or slice and dice would capture some of this CAPE stock picker effect, not sure.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by inbox788 »

abc132 wrote: Tue Dec 08, 2020 5:46 pmI get R^2 between 0.4 and 0.6 if I do a bunch of runs. This is 158 years worth of fake data - I was very roughly approximating the graph Vineviz showed earlier, so this is my yearly data, as calculations are only computed once a year.
Thanks for taking the time to respond to my half in jest observation of the data set. My understanding of CAPE is very basic, and the statistics even less. Anyway, I question whether high CAPE is sustainable, let alone predictive. I found this article helpful, and interesting that they model a logarithmic fit, which reduces the extremely high CAPE effect.

The Shiller PE (CAPE) Ratio: Current Market Valuations
https://www.lynalden.com/shiller-pe-cape-ratio/
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

Vineviz,

Did you get my PM?

I'm interested in your response.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by GoneOnTilt »

GAAP wrote: Tue Dec 08, 2020 7:16 pm
bck63 wrote: Tue Dec 08, 2020 7:12 pm A practical question: If CAPE is highly predictive of future returns, what does one do about it?
Adjust your plans accordingly -- whether savings rate or withdrawal rate or years to hit a target or whatever. That could be part of a regularly-scheduled effort to keep your plans on track.

This is not the same thing as saying "change your AA", "save more", "save less", etc. Use it to inform your decisions -- whether or not that means to act on anything.
Thank you.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

vineviz wrote: Wed Dec 09, 2020 7:08 am
Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

willthrill81 wrote: Thu Dec 10, 2020 10:36 am
vineviz wrote: Wed Dec 09, 2020 7:08 am
Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
Vineviz hasn't commented yet, other than in being busy with some other things right now and not having looked at my formulas.

So far nothing has been shown to be wrong, and at last communication we already agreed with all graphs except for the random price one.

It should take less than 30 minutes to repeat the analysis if you are curious - the more the merrier.

Once the difference in last graph is confirmed we can talk about the why.

Establishing the things we agree on is the basis for discussion, and you are welcome to join us.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

willthrill81 wrote: Thu Dec 10, 2020 10:36 am
vineviz wrote: Wed Dec 09, 2020 7:08 am
Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
I'm sorry, I don't think explaining how to properly test a hypothesis for the third time in this thread is worth my time.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Uncorrelated wrote: Thu Dec 10, 2020 12:05 pm
willthrill81 wrote: Thu Dec 10, 2020 10:36 am
vineviz wrote: Wed Dec 09, 2020 7:08 am
Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
I'm sorry, I don't think explaining how to properly test a hypothesis for the third time in this thread is worth my time.
That's obviously your prerogative, but simply saying that something is 'so wrong' but that it's not 'worth your time' to specifically address why doesn't move the ball down the field at all.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

willthrill81 wrote: Thu Dec 10, 2020 2:56 pm
Uncorrelated wrote: Thu Dec 10, 2020 12:05 pm
willthrill81 wrote: Thu Dec 10, 2020 10:36 am
vineviz wrote: Wed Dec 09, 2020 7:08 am
Uncorrelated wrote: Wed Dec 09, 2020 1:43 am
This methodology is so wrong that I don't even know where to begin.
It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
I'm sorry, I don't think explaining how to properly test a hypothesis for the third time in this thread is worth my time.
That's obviously your prerogative, but simply saying that something is 'so wrong' but that it's not 'worth your time' to specifically address why doesn't move the ball down the field at all.
Me and other have mentioned multiple times that in-sample R^2 is not a correct measurement for this application. I linked several times to a paper that contains almost the exact regression we want, with a negative out-of-sample R^2 and statistically insignificant t-statistic. Others have linked to a paper that shows averaging numbers over long time horizons increases R^2 without an increase in statistical significance.

I made multiple calls for papers that support the other side of the argument, but got no response.

Meanwhile, people are still trying pass of in-sample R^2 and highly questionable data science practices as evidence. It's hard to keep the ball rolling if methodological criticism and requests to provide additional evidence are consistently ignored.


If you are sincerely interested in additional evidence, look here:
Image
A Comprehensive Look at The Empirical Performance of Equity Premium Prediction, table 3. http://www.hec.unil.ch/agoyal/docs/Pred ... ty_RFS.pdf.

Results indicate that trading on CAPE10 would not have resulted in superior forecasting performance than a simple mean. Exactly the opposite conclusion of vineviz analysis that I rejected based on methodological concerns.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by willthrill81 »

Uncorrelated wrote: Thu Dec 10, 2020 6:30 pm
willthrill81 wrote: Thu Dec 10, 2020 2:56 pm
Uncorrelated wrote: Thu Dec 10, 2020 12:05 pm
willthrill81 wrote: Thu Dec 10, 2020 10:36 am
vineviz wrote: Wed Dec 09, 2020 7:08 am

It’s not even a little bit wrong. Begin with telling me one thing about it that you don’t understand and I’ll try to explain it to you.
I would really like to hear what's supposedly wrong with your analysis.
I'm sorry, I don't think explaining how to properly test a hypothesis for the third time in this thread is worth my time.
That's obviously your prerogative, but simply saying that something is 'so wrong' but that it's not 'worth your time' to specifically address why doesn't move the ball down the field at all.
Me and other have mentioned multiple times that in-sample R^2 is not a correct measurement for this application. I linked several times to a paper that contains almost the exact regression we want, with a negative out-of-sample R^2 and statistically insignificant t-statistic. Others have linked to a paper that shows averaging numbers over long time horizons increases R^2 without an increase in statistical significance.
The 1989-2010 data set I provided in the OP was out of Shiller's sample, showed a higher r-square than did Shiller's data, and was most definitely statistically significant, both with and without inflation and bond yields also in the regression model. Yes, the statistics (i.e. intercept and slope) were different, but only in magnitude, not general direction.

If you're trying to argue that there's an intervening variable(s) with some type of moderating and/or mediating effect, then by all means reveal it.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

Anything yet Vineviz?

I'm now thinking maybe the 10 year average for earnings may be what makes the process seem to move in a predictable direction (have an R^2 value).

With both random PE ratios and a random prices, the result still has a preferential direction because the average of 10 random earnings numbers is mean reverting.

If true, maybe using 10 year average PE moving towards the mean should created an R^2 value - even when price and earnings are totally random.

Comments??? Thoughts??? This one is pretty rough/early in thought process, but probabilistically should the 10 year average E move towards the center of the available values, and thus creating a P/E (CAPE10) that has a negative slope with R^2 around 0.5 - even for completely random data?

EDIT: Taking 10 random numbers and averaging confirms the averaging produces the R^2 10 year forward prediction from random data.
Last edited by abc132 on Thu Dec 10, 2020 9:37 pm, edited 1 time in total.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

willthrill81 wrote: Thu Dec 10, 2020 6:37 pm
If you're trying to argue that there's an intervening variable(s) with some type of moderating and/or mediating effect, then by all means reveal it.
Your answer is above - 10 year averaging of earnings produces a preferential direction from random data.

Even for random data, low 10 year average earnings value will probabilistically move toward the average 10 year earnings value.
Even for random data, high 10 year average earnings value will probabilistically move toward the average 10 year earnings value.

Completely random price and earnings data will produce an R^2 of around 0.5 and negative slope because of 10 year averaging.

Nobel prizes can be sent to abc132. :happy
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

Random data will produce a negative slope based on the min CAPE10 and max CAPE10 value with an R^2 of around 0.5

This graph will be symmetrical with respect to the CAPE10 ratios available, but it is adjusted upwards by the mean annual gain in price.

Putting in mean=0 gives an x intercept at the average CAPE10 value.


This should all match up nicely with the two sets of historical data shown earlier in the thread - extending the high end of cape10 ratios changed the slope almost exactly as would be expected from completely random data.


I suspect that the trend fit should be of the form 1/x, and that if this is true the R^2 from a linear fit to random data will improve as the CAPE10 ratio rises - no proof just preliminary intuition.


It appears that the 10 year average within a bound range of CAPE10 ratios produces the statistical significance - even when price and earnings are completely random.


Actionable: CAPE10 ratios only predict lower future returns if the chance of CAPE10 going down is greater than it going up, and the CAPE10 curve fit (R^2) is severely biased by the 10 year averaging - so much so that the dire predictions of annual returns at current CAPE10 are not much meaningful than CAPE10 dropping from say 20 to 15. Take a look at the (stock% vs 10 year future returns) graph linked earlier in this thread and think about if further stock purchases can push CAPE10 higher.

Or just be a Boglehead, and take what the market gives. It's worked great so far!
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by dont_know_mind »

Thank you everyone for the very interesting discussion and thoughts on CAPE.

Here are my thoughts, which could be very wrong:
1. I think paying any attention to CAPE as a valuation measure has been negative for me since I started investing (1999). I am a value investor and I have to say I fell into the CAPE narrative rather unthinkingly. I am much more skeptical about it, although I am still a value investor.
2. The data does appear to indicate a change in relationship since 1988 and a tendency towards higher valuations.
3. Interest rates alone cannot account for this as other low interest rate periods did not accompany valuation increases like this e.g 3 month treasury bills were below 0.5% from 1942-1946.
4. The main contender I can see is the Fed or central bank put, which started with Greenspan after the 1987 stockmarket crash:
https://en.wikipedia.org/wiki/Greenspan_put
An unkind interpretation is that the central bankers are a bunch of serial bubble blowers (whatever a bubble is). A less severe interpretation is that they save the system from systemic risk and this has the side-effect of sometimes increasing accepted valuations.
5. There are only a limited number of datapoints that I can see: 1987 (black friday), 1997 (LTCM), 2001 (WTC), 2008 (GFC) and 2020 (Covid).
6. Rather than CAPE, I surmised and I am sure many other market participants have come to this conclusion (and it could be an incorrect or correct interpretation) that when the Fed says they are intervening significantly (especially if they say they are going "all in"), that the equity holders are unlikely to be allowed to be wiped out. This takes care of the left side tail risks.
7. On a completely theoretical level, I think it is intuitive to try to look at all the data from when stockmarket information was recorded properly to intuit some universal truth, but this may be pointless. When you think about it, we are modeling human, social behavior and this is likely to vary depending on societal factors. It seems to me obvious that changes in the nature of interventions by the Central Bank may have a large effect on equity risk premiums and valuations. On a very basic level, there are 3 levels of assets : 1. the equity holders, 2. corporate bondholders 3. The government and central bank. If equity holders are wiped out, the equity ownership is taken over by the bondholders. If 3 underwrite 1 and reduce the risk of systemic equity wipeout then this has a potentially large effect on the investing ecosystem.
8. Test as a market timing mechanism, when the Fed says it is going "all in", increase equity allocation. As a very rough proxy for this you could use a SP500 decline of 30%. If you backtest moving your 70:30 allocation to 100:0 or 150:-50, then I suspect this will beat the performance of any CAPE based strategy. As someone previously mentioned any CAPE based stategy gets pole axed if valuations increase to over the previous maximium and you have to set a median value estimate which may well be increasing over time with the fed put (until it doesn't or said put fails).

Basically it boils down to JBTFD. Which is very contrary to rational valuation based thinking, but it is rational if you think of it in terms of a central bank put. We don't know whether this put will be applied in the future and whether it will hold though.

Something else that may have affected valuations may be increased retirement savings and movement of savings from government to private (defined benefit vs defined contribution) over the last 30 years. This may have structurally reduced interest rates.

If interest rates don't have to mean revert then why does CAPE ?

To all those who believe in CAPE being good predictor of future returns - good luck!
You may find that the central banks not only take away your lunch (deprive you of low CAPE periods) but give you a massive prolonged wedgie (in terms of higher CAPEs than you currently imagine possible).
Last edited by dont_know_mind on Fri Dec 11, 2020 4:46 am, edited 1 time in total.
My ramblings are probably rubbish, biased by my position and talking my own book. No-one should invest based on my views. Some days I wonder whether I've had some skill or just been a lucky gambler.
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by Uncorrelated »

willthrill81 wrote: Thu Dec 10, 2020 6:37 pm
Uncorrelated wrote: Thu Dec 10, 2020 6:30 pm
willthrill81 wrote: Thu Dec 10, 2020 2:56 pm
Uncorrelated wrote: Thu Dec 10, 2020 12:05 pm
willthrill81 wrote: Thu Dec 10, 2020 10:36 am

I would really like to hear what's supposedly wrong with your analysis.
I'm sorry, I don't think explaining how to properly test a hypothesis for the third time in this thread is worth my time.
That's obviously your prerogative, but simply saying that something is 'so wrong' but that it's not 'worth your time' to specifically address why doesn't move the ball down the field at all.
Me and other have mentioned multiple times that in-sample R^2 is not a correct measurement for this application. I linked several times to a paper that contains almost the exact regression we want, with a negative out-of-sample R^2 and statistically insignificant t-statistic. Others have linked to a paper that shows averaging numbers over long time horizons increases R^2 without an increase in statistical significance.
The 1989-2010 data set I provided in the OP was out of Shiller's sample, showed a higher r-square than did Shiller's data, and was most definitely statistically significant, both with and without inflation and bond yields also in the regression model. Yes, the statistics (i.e. intercept and slope) were different, but only in magnitude, not general direction.

If you're trying to argue that there's an intervening variable(s) with some type of moderating and/or mediating effect, then by all means reveal it.
So If I understand it correctly, you believe that the results from Goyal and Welch (linked in my previous post) are wrong? They find the exact opposite conclusion than you do with your regression of three independent data points.

There are a million things that can go wrong, you didn't give nearly enough information to be able to spot them. If you want us to actually be able to point out what the errors are, consider describing your methodology in great accuracy and showing on every step that the assumptions of the methodology are satisfied. For example, "UNCLOAKING CAPE: A NEW LOOK AT AN OLD VALUATION RATIO" claims regressions with CAPE violate OLS assumptions because price appears on both sides of the equation, which adjustments have you made to counter this effect?
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by vineviz »

abc132 wrote: Thu Dec 10, 2020 10:49 pm
It appears that the 10 year average within a bound range of CAPE10 ratios produces the statistical significance - even when price and earnings are completely random.
I think it might be helpful to step back to a more fundamental level than I took in my prior post.

If we model a world in which the price and earnings are completely random, then we would - as you say -would expect to observe that PE predicts future returns. This should be true for the reason you identified earlier: mean reversion. And - broadly speaking - as earnings become "less random" the tighter the relationship between current PE and future returns will be. This, again, is a fundamental economic relationship and not a statistical anomaly or artifact.

I suspect that this is the effect to which you are referring when you use the phrase "range bound", but I prefer to focus on the fact that in real life the level of earnings isn't very random at all. Next year's earnings have someone like a 0.93 correlation with this year's earnings, which is a very high level of correlation.

There are real, fundamental economic forces that dampen the volatility of EPS. And although the trend towards which CAPE will trend can change over time, for instance due to trends in the real rate of return of the risk-free rate, there are real, fundamental economic forces (e.g. GDP growth, inflation) that work to keep the CAPE within a plausible range of values.

So I don't think the ability of a tool like CAPE to predict future returns should be viewed as either surprising or anomalous. It'd be weird if it didn't, actually.
"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

Post by abc132 »

vineviz wrote: Fri Dec 11, 2020 8:57 am
abc132 wrote: Thu Dec 10, 2020 10:49 pm
It appears that the 10 year average within a bound range of CAPE10 ratios produces the statistical significance - even when price and earnings are completely random.
I think it might be helpful to step back to a more fundamental level than I took in my prior post.

If we model a world in which the price and earnings are completely random, then we would - as you say -would expect to observe that PE predicts future returns. This should be true for the reason you identified earlier: mean reversion. And - broadly speaking - as earnings become "less random" the tighter the relationship between current PE and future returns will be. This, again, is a fundamental economic relationship and not a statistical anomaly or artifact.

I suspect that this is the effect to which you are referring when you use the phrase "range bound", but I prefer to focus on the fact that in real life the level of earnings isn't very random at all. Next year's earnings have someone like a 0.93 correlation with this year's earnings, which is a very high level of correlation.

There are real, fundamental economic forces that dampen the volatility of EPS. And although the trend towards which CAPE will trend can change over time, for instance due to trends in the real rate of return of the risk-free rate, there are real, fundamental economic forces (e.g. GDP growth, inflation) that work to keep the CAPE within a plausible range of values.

So I don't think the ability of a tool like CAPE to predict future returns should be viewed as either surprising or anomalous. It'd be weird if it didn't, actually.
Thanks for your correspondence. For those reading, we now agree on all my past charts as being technically correct, although we are still debating what they mean.

We already tried several different highly correlated earnings correlations (mean, standard deviation) in a at least somewhat sensible manner - and none of them improved the R^2 value over random data. Increasing the earnings correlation does not showing any change in the predicted R^2.

You can see in the PM that I sent you that I also put a correlation on price that could be changed from 0 to 1. A coefficient of 1 is completely random, and you can put in something line 0.15 or 0 if you want more price correlation. Having constant price doesn't change the answer. The analysis shows that it doesn't matter how closely price is correlated when determining the R^2 value.

The key conclusion is that an R^2 of around 0.42 is achieved for large data sets purely due to the earnings averaging. With the amount of yearly data we have (say 100 points), my tests show it's not uncommon to get an R^2 of up to 0.6. Shiller likely calculated CAPE7,8,9,10 with a similar change in forward years and CAPE10 happened to have the best R^2 due to small sample size. They aren't meaningfully different from each other (CAPE8 vs CAPE9 vs CAPE10) for large data sets.

Repeating the experiment with 7,8,9,10 year averages and 7,8,9,10 year forward predictions - none of them are meaningfully different. If there really was a 10 year forward signal, they should be different from each other (for large data sets) and they should be meaningfully different from completely random data.

Things I believe we agree on:
- To the extent that people believe in CAPE10, or not paying too high of PE, or PE/G there should be some price reversion effect.

Things we may agree on
- R^2 as being used in CAPE10 calculations should not be the measure to determine significance. Random data getting R^2 of 0.42 demonstrates this effect.

Things we may disagree on
- There has not been shown to be anything special about a 10 year period for that reversion to happen. Evidence is in Bogles book when he mentions that overvaluation can happen for periods much longer than 10 years, and in people trying to use CAPE10 as a forward predictor without much success.

- I can respect all your thought processes without needing there to be a 10 year forward signal, as long as the time period for that reversion is much more varied than 10 years. We don't know what the mean should be, and it could be 2 months, 5 years, 30 years, or longer than our investing horizon before that reversion happens - making it largely unactionable.
Last edited by abc132 on Fri Dec 11, 2020 12:46 pm, edited 1 time in total.
abc132
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Re: CAPE: A much stronger predictor of stock returns than many think

Post by abc132 »

dont_know_mind wrote: Fri Dec 11, 2020 4:33 am Thank you everyone for the very interesting discussion and thoughts on CAPE.

....

To all those who believe in CAPE being good predictor of future returns - good luck!
You may find that the central banks not only take away your lunch (deprive you of low CAPE periods) but give you a massive prolonged wedgie (in terms of higher CAPEs than you currently imagine possible).
Your first hand experience is very interesting. Thanks for sharing.

Would this discussion have made a difference in your past approach, had you read it years ago?
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