PE10 predicitive power

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richard
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PE10 predicitive power

Post by richard »

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drjdpowell
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Post by drjdpowell »

Problem is, these plots aren't very statistically significant. They look like they are, because they use overlapping or "rolling" periods, but the actual statistical significance is low due to the low amount of independent data on 10 and 20-year periods.

-- James
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Post by bhmlurker »

Between PE10 of 12.5 and 22.5, there does not appear to be a significant shift in 10-yr annual return. The mean seems to be centered around 6-7.5% annual return and the correlation probably isn't so high if data outside the 12.5-22.5 range were excluded.

There does appear to be a better correlation between PE10 and 20-yr annual return. The current PE10 of 18 would place the mean 20-yr annual return at 6%

It would be interesting to see if the variation of annual return between time periods of similar/identical PE10 is a function of LT interest rate. PE10 of 10 might be attractive when LT interest rate is <5%, but perhaps not so much when it's > 10%.
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richard
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Post by richard »

James, true, and that's the problem with so many studies of past data.

My favorite is using the 100 or so years of data we have to predict the next 40 or 50 years. 2 or 3 data points are not enough.

Delong (author of the charts) has said prior similar results are on the edge of statistical significance.
Last edited by richard on Thu Oct 08, 2009 1:05 pm, edited 1 time in total.
Rodc
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Post by Rodc »

What is MSL?

All past discussions of the validity of using combinations of 6 points to make hundreds of points need to be remembered.

(120 year/20 years = six real independent data points, adjust as required for other periods, I did not see explicitly how many years were used).

If I take X1, X2,..., X6 and then form lots of points like

y1 = X1, Y2 = .95X1+.05X2, Y3 = .90X1+.10X2, etc I get lots of points. Does Y2 tell us anything significantly different from Y1? Y2 and Y3 vs Y1?

No.

But I can make lots of dots and plot them it and LOOKS impressive.

Now, maybe the conclusions still hold, I don't know. But be careful not to simply take pretty pictures at face value.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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richard
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Post by richard »

Rodc wrote:But be careful not to simply take pretty pictures at face value.
What a cynical attitude. Next you'll be saying we can't believe everything we see on TV. :D

I tend to think there is a weak relation here, suggested by the charts as clouds rather than straight lines. Low statistical significance does not mean wrong.

It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal). Problems include that E is based on the past, not the future, that other effects (including changing p/e ratio) can swamp any predictive power, and that all else is so rarely equal.

Campbell has a defense of low statistical significance in this context, but I can't immediately find it.
Last edited by richard on Thu Oct 08, 2009 1:17 pm, edited 1 time in total.
peter71
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Post by peter71 »

Rodc wrote:What is MSL?

All past discussions of the validity of using combinations of 6 points to make hundreds of points need to be remembered.

(120 year/20 years = six real independent data points, adjust as required for other periods, I did not see explicitly how many years were used).

If I take X1, X2,..., X6 and then form lots of points like

y1 = X1, Y2 = .95X1+.05X2, Y3 = .90X1+.10X2, etc I get lots of points. Does Y2 tell us anything significantly different from Y1? Y2 and Y3 vs Y1?

No.

But I can make lots of dots and plot them it and LOOKS impressive.

Now, maybe the conclusions still hold, I don't know. But be careful not to simply take pretty pictures at face value.
Hi Rod,

I was wondering about MSL too . . . I believe it's 138 years of data so I suspect we're getting closer to the point where, say, a one-tailed test of independent five or seven year periods might give a significant result, but even then I think it'll come back to how people feel about the theory.

To the person who asked about interest rates, Delong actually mentions that they're low and suggests that as a result stocks are still a buy at P/E 10 of 18 as of 10/6 (now up to 19).

All best,
Pete
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Post by Rodc »

richard wrote:
Rodc wrote:But be careful not to simply take pretty pictures at face value.
What a cynical attitude. Next you'll be saying we can't believe everything we see on TV. :D

I tend to think there is a weak relation here, suggested by the charts as clouds rather than straight lines. Low statistical significance does not mean wrong.

It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal). Problems include that E is based on the past, not the future, that other effects (including changing p/e ratio) can swamp any predictive power, and that all else is so rarely equal.

Campbell has a defense of low statistical significance in this context, but I can't immediately find it.
agreed
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Post by Rodc »

peter71 wrote:
Rodc wrote:What is MSL?

All past discussions of the validity of using combinations of 6 points to make hundreds of points need to be remembered.

(120 year/20 years = six real independent data points, adjust as required for other periods, I did not see explicitly how many years were used).

If I take X1, X2,..., X6 and then form lots of points like

y1 = X1, Y2 = .95X1+.05X2, Y3 = .90X1+.10X2, etc I get lots of points. Does Y2 tell us anything significantly different from Y1? Y2 and Y3 vs Y1?

No.

But I can make lots of dots and plot them it and LOOKS impressive.

Now, maybe the conclusions still hold, I don't know. But be careful not to simply take pretty pictures at face value.
Hi Rod,

I was wondering about MSL too . . . I believe it's 138 years of data so I suspect we're getting closer to the point where, say, a one-tailed test of independent five or seven year periods might give a significant result, but even then I think it'll come back to how people feel about the theory.

To the person who asked about interest rates, Delong actually mentions that they're low and suggests that as a result stocks are still a buy at P/E 10 of 18 as of 10/6 (now up to 19).

All best,
Pete
Hi Pete,

I tend to think that the first step is to plot out a time history of those points and for example take a look at the time periods in that second graph where something interesting happens, like say where P/E10 (which despite the label on the x-axis I presume is what the x-axis really is) is greater than about 35 or maybe 30. That may be a SINGLE event, the great tech bubble - so in effect one data point repeated multiple times.

Or on the flip side, maybe only a few events where P/E10 was down in single digits. Do those events also have some particular cause?

The date are few enough that one can get to an actual cause and effect type understanding of the extreme events that drive any correlation between P/E10 and 20 year returns.

Statistics are best used when things are so complicated, or your understanding of the "physics" of a process so limited that you can't really get to a cause and effect level of understanding.

If I had more time and interest that is how I would proceed.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
peter71
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Post by peter71 »

richard wrote:
Rodc wrote:But be careful not to simply take pretty pictures at face value.
What a cynical attitude. Next you'll be saying we can't believe everything we see on TV. :D

I tend to think there is a weak relation here, suggested by the charts as clouds rather than straight lines. Low statistical significance does not mean wrong.

It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal). Problems include that E is based on the past, not the future, that other effects (including changing p/e ratio) can swamp any predictive power, and that all else is so rarely equal.

Campbell has a defense of low statistical significance in this context, but I can't immediately find it.
The concern about non-independent periods really goes to the exaggerated density of the cloud rather than to its shape . . . with 138 data points this is definitely a slopey enough cloud to be statistically significant, but with only 13.8 or 6.9 data points it's not even that close. The problem is basically just that a lot of weird things can happen with only 6.9 coin flips, and fairly weird things can happen with considerable frequency even with 14 coin flips . . .

On the shape of the cloud issue, on the other hand, the thing doesn't have to be anywhere near a line to be economically significant . . . basically, the regressions are saying that for every 1-point increase in P/E you lose about 50 basis points of annual return (a little less than that in the ten-year model and a little more than that in the twenty-year model). So even if the model exaggerates the relationship by a factor of two due to random sampling error or bias or whatever, the annual difference between a P/E 10 of 15 and a P/E 10 of 25 would be equivalent to the difference between buying a low cost VG fund and paying an advisor 1% of AUM to put you in the highest of high fee funds with a 1.75% ER . . .

All best,
Pete
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Post by Rodc »

One thing I do not understand: if both graphs are P/E10 vs some return value, why do they not both have the same x-axis?

Why do we see points with P/E10 greater than 35 in the second and none in the first?

ADDED: probably due to the fact that since the Great Tech bubble is less than 20 years old, those data do not appear in the analysis.

When they do appear, the relationship will likely strengthen (unless this down turn really drags on for years).
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
peter71
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Post by peter71 »

Rodc wrote:
peter71 wrote:
Rodc wrote:What is MSL?

All past discussions of the validity of using combinations of 6 points to make hundreds of points need to be remembered.

(120 year/20 years = six real independent data points, adjust as required for other periods, I did not see explicitly how many years were used).

If I take X1, X2,..., X6 and then form lots of points like

y1 = X1, Y2 = .95X1+.05X2, Y3 = .90X1+.10X2, etc I get lots of points. Does Y2 tell us anything significantly different from Y1? Y2 and Y3 vs Y1?

No.

But I can make lots of dots and plot them it and LOOKS impressive.

Now, maybe the conclusions still hold, I don't know. But be careful not to simply take pretty pictures at face value.
Hi Rod,

I was wondering about MSL too . . . I believe it's 138 years of data so I suspect we're getting closer to the point where, say, a one-tailed test of independent five or seven year periods might give a significant result, but even then I think it'll come back to how people feel about the theory.

To the person who asked about interest rates, Delong actually mentions that they're low and suggests that as a result stocks are still a buy at P/E 10 of 18 as of 10/6 (now up to 19).

All best,
Pete
Hi Pete,

I tend to think that the first step is to plot out a time history of those points and for example take a look at the time periods in that second graph where something interesting happens, like say where P/E10 (which despite the label on the x-axis I presume is what the x-axis really is) is greater than about 35 or maybe 30. That may be a SINGLE event, the great tech bubble - so in effect one data point repeated multiple times.

Or on the flip side, maybe only a few events where P/E10 was down in single digits. Do those events also have some particular cause?

The date are few enough that one can get to an actual cause and effect type understanding of the extreme events that drive any correlation between P/E10 and 20 year returns.

Statistics are best used when things are so complicated, or your understanding of the "physics" of a process so limited that you can't really get to a cause and effect level of understanding.

If I had more time and interest that is how I would proceed.
Hi Rod,

I agree that the "sales and bubbles happen" theory was developed on same tech bubble data that's now being used to test that theory, but I suspect that Shiller would offer a similar critique of Fama's (1992?) articulation of EMH . . . so a priori I'm just not sure which of the two theories -- "valuations matter" vs. EMH -- I think is more compelling.

All best,
Pete
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Post by tadamsmar »

richard wrote:It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal).
Why?

If that is true, then shareholders should demand that all stocks they own split till they only cost a penny, thereby optimizing this "low price = high return" effect you speak of.
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Post by diasurfer »

Rodc wrote:One thing I do not understand: if both graphs are P/E10 vs some return value, why do they not both have the same x-axis?

Why do we see points with P/E10 greater than 35 in the second and none in the first?

ADDED: probably due to the fact that since the Great Tech bubble is less than 20 years old, those data do not appear in the analysis.

When they do appear, the relationship will likely strengthen (unless this down turn really drags on for years).
Isn't it just the difference between a 10 year average and a 20 year? More smoothing with the longer average. If there were a plot using 5 year averages, I suspect there would be even more extreme values.
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Post by Rodc »

diasurfer wrote:
Rodc wrote:One thing I do not understand: if both graphs are P/E10 vs some return value, why do they not both have the same x-axis?

Why do we see points with P/E10 greater than 35 in the second and none in the first?

ADDED: probably due to the fact that since the Great Tech bubble is less than 20 years old, those data do not appear in the analysis.

When they do appear, the relationship will likely strengthen (unless this down turn really drags on for years).
Isn't it just the difference between a 10 year average and a 20 year? More smoothing with the longer average. If there were a plot using 5 year averages, I suspect there would be even more extreme values.
Isn't that a comment on the y-axis?

Both graphs seem to have the same x-axis.

But I think I answered the question above. While we have P/E10 numbers for the tech bubble, we only have the 10 year results for what followed, but not the 20 year results. So, the tech bubble data show up in the 10 year graph, but not on the 20 year graph.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Post by schwarm »

tadamsmar wrote:
richard wrote:It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal).
Why?

If that is true, then shareholders should demand that all stocks they own split till they only cost a penny, thereby optimizing this "low price = high return" effect you speak of.
I think that would cut into earnings per share too and have no effect.
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Post by diasurfer »

Rodc wrote:
diasurfer wrote:
Rodc wrote:One thing I do not understand: if both graphs are P/E10 vs some return value, why do they not both have the same x-axis?

Why do we see points with P/E10 greater than 35 in the second and none in the first?

ADDED: probably due to the fact that since the Great Tech bubble is less than 20 years old, those data do not appear in the analysis.

When they do appear, the relationship will likely strengthen (unless this down turn really drags on for years).
Isn't it just the difference between a 10 year average and a 20 year? More smoothing with the longer average. If there were a plot using 5 year averages, I suspect there would be even more extreme values.
Isn't that a comment on the y-axis?

Both graphs seem to have the same x-axis.

But I think I answered the question above. While we have P/E10 numbers for the tech bubble, we only have the 10 year results for what followed, but not the 20 year results. So, the tech bubble data show up in the 10 year graph, but not on the 20 year graph.
Well you're probably right but it seems like my comment would apply to both the x-axis and the y-axis. Imagine a plot of one-year returns vs one-year P/E. Both axes would have more extreme values.
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Post by Rodc »

diasurfer wrote:
Rodc wrote:
diasurfer wrote:
Rodc wrote:One thing I do not understand: if both graphs are P/E10 vs some return value, why do they not both have the same x-axis?

Why do we see points with P/E10 greater than 35 in the second and none in the first?

ADDED: probably due to the fact that since the Great Tech bubble is less than 20 years old, those data do not appear in the analysis.

When they do appear, the relationship will likely strengthen (unless this down turn really drags on for years).
Isn't it just the difference between a 10 year average and a 20 year? More smoothing with the longer average. If there were a plot using 5 year averages, I suspect there would be even more extreme values.
Isn't that a comment on the y-axis?

Both graphs seem to have the same x-axis.

But I think I answered the question above. While we have P/E10 numbers for the tech bubble, we only have the 10 year results for what followed, but not the 20 year results. So, the tech bubble data show up in the 10 year graph, but not on the 20 year graph.
Well you're probably right but it seems like my comment would apply to both the x-axis and the y-axis. Imagine a plot of one-year returns vs one-year P/E. Both axes would have more extreme values.
Certainly true. But that would apply if for example he was plotting P/E10 vs 10-year return in one graph, and P/E20 vs 20-year return in the other.

But from the text I think he is using P/E10 in both graphs.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Post by diasurfer »

doh!
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Post by richard »

tadamsmar wrote:
richard wrote:It makes sense that buying stocks at a lower prices will result in higher returns (all else being equal).
Why?

If that is true, then shareholders should demand that all stocks they own split till they only cost a penny, thereby optimizing this "low price = high return" effect you speak of.
Lower price means lower p/e in this context.

It may be clearer if you think of bonds. Lower price (higher yield) means higher returns (holding credit quality, maturity, etc. constant).
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Post by richard »

peter71 wrote:I agree that the "sales and bubbles happen" theory was developed on same tech bubble data that's now being used to test that theory, but I suspect that Shiller would offer a similar critique of Fama's (1992?) articulation of EMH . . . so a priori I'm just not sure which of the two theories -- "valuations matter" vs. EMH -- I think is more compelling.
Why do you regard the two as inconsistent?

p/e tends to be lower at times of higher risk. Higher expected return at times of higher risk is something EMH would endorse. No one should be saying "valuations matter" means you are guaranteed a high return if you buy when valuations are low.
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Post by Rodc »

diasurfer wrote:doh!
We've all been there... :)
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Post by stratton »

Single predictors are worthless. They work except when they don't. This is analgous to people using the backtest spreadsheet only looking at volatiltity as risk without looking at draw down and other measures of "risk" such as examining individual assets under a variety of market conditions.

There is NO single easy indicator.

Paul
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Post by peter71 »

richard wrote:
peter71 wrote:I agree that the "sales and bubbles happen" theory was developed on same tech bubble data that's now being used to test that theory, but I suspect that Shiller would offer a similar critique of Fama's (1992?) articulation of EMH . . . so a priori I'm just not sure which of the two theories -- "valuations matter" vs. EMH -- I think is more compelling.
Why do you regard the two as inconsistent?

p/e tends to be lower at times of higher risk. Higher expected return at times of higher risk is something EMH would endorse. No one should be saying "valuations matter" means you are guaranteed a high return if you buy when valuations are low.
If they're consistent then there should be a more or less monotonic relationship between P/E 10 and whatever reasonable risk metric you want to suggest e.g., as P/E 10 goes up, SD or left tail risk or whatever goes down, but although I haven't looked I don't think that's the case. It seems to me that a more plausible possibility is that there's a non-monotonic relationship between extremely high OR low P/E and various risk metrics, but inasmuch as these different extreme values of P/E would be associated with radically different expected returns for Fama et al. I don't think that'd be consistent . . . but have you seen something that suggests that SD or tail risk is really low when P/E 10 is high?

All best,
Pete
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Post by peter71 »

stratton wrote:Single predictors are worthless. They work except when they don't. This is analgous to people using the backtest spreadsheet only looking at volatiltity as risk without looking at draw down and other measures of "risk" such as examining individual assets under a variety of market conditions.

There is NO single easy indicator.

Paul
I'd replace "worthless" with "always incomplete," though in the case of P/E 10 the directly countervailing effects of momentum complicate things further than is typical. More generally, however, smoking is a good example of a single predictor of lung cancer that remains robust even though it fails to "work" in the vast majority of cases -- i.e., in that the vast majority of smokers never get lung cancer.

All best,
Pete
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Post by richard »

peter71 wrote:If they're consistent then there should be a more or less monotonic relationship between P/E 10 and whatever reasonable risk metric you want to suggest e.g., as P/E 10 goes up, SD or left tail risk or whatever goes down, but although I haven't looked I don't think that's the case. It seems to me that a more plausible possibility is that there's a non-monotonic relationship between extremely high OR low P/E and various risk metrics, but inasmuch as these different extreme values of P/E would be associated with radically different expected returns for Fama et al. I don't think that'd be consistent . . . but have you seen something that suggests that SD or tail risk is really low when P/E 10 is high?
You seem to be looking for more precision than likely exists in this area, especially due to the inadequacy of existing risk quantifications.

The intuition is that people pay higher multiples when they perceive risk as low and lower multiples when they perceive risk as high.

As mentioned above, bond pricing provides a good metaphor. See Bill Bernstein's discussion of the pricing of the Venetian Prestiti in http://www.efficientfrontier.com/files/TIM.pdf. It clearly doesn't have the exactness you are looking for, but is a good illustration of the thought and is likely as good as it gets in this area.
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Post by peter71 »

richard wrote:
peter71 wrote:If they're consistent then there should be a more or less monotonic relationship between P/E 10 and whatever reasonable risk metric you want to suggest e.g., as P/E 10 goes up, SD or left tail risk or whatever goes down, but although I haven't looked I don't think that's the case. It seems to me that a more plausible possibility is that there's a non-monotonic relationship between extremely high OR low P/E and various risk metrics, but inasmuch as these different extreme values of P/E would be associated with radically different expected returns for Fama et al. I don't think that'd be consistent . . . but have you seen something that suggests that SD or tail risk is really low when P/E 10 is high?
You seem to be looking for more precision than likely exists in this area, especially due to the inadequacy of existing risk quantifications.

The intuition is that people pay higher multiples when they perceive risk as low and lower multiples when they perceive risk as high.

As mentioned above, bond pricing provides a good metaphor. See Bill Bernstein's discussion of the pricing of the Venetian Prestiti in http://www.efficientfrontier.com/files/TIM.pdf. It clearly doesn't have the exactness you are looking for, but is a good illustration of the thought and is likely as good as it gets in this area.
I'm certainly not denying that higher-risk bonds pay investors a premium but the question is how well the basic risk-return logic applies to P/E 10. So all we'd really need to look into it is some periodic data on risk (which could be derived from periodic returns data) and some periodic data on P/E 10 (available on Shiller's site). Given that, I think we could test for three different possibilities in addition to the null hypothesis that risk and P/E 10 are unrelated:

1) As valuations go up, SD and/or drawdown risk goes up too . . .

This is kind of the Shiller CW right?

2) As valuations go up, SD and/or drawdown risk goes down because expectied returns go down.

I think this what you're saying -- kind of like Larry's valuations matter modification of Fama -- might lead you to buy more stocks when valuations are high.

3) Extreme valuations (high or low) are associated with high SD and high drawdown risk.

This is kind of a compromise between 1 and 2 (though it calls the direction of the causal flow into question) and I think it's a real possibility.

Again, though, to me the "pure" Fama/Malkiel position is just the null hypothesis. i.e., valuations are related neither to risk nor to return.

All best,
Pete
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Post by SP-diceman »

peter71 wrote:
with 138 data points this is definitely a slopey enough cloud to be statistically significant, but with only 13.8 or 6.9 data points it's not even that close. The problem is basically just that a lot of weird things can happen with only 6.9 coin flips, and fairly weird things can happen with considerable frequency even with 14 coin flips . . .
First let me say I'm not a statistician.
That being said. Isn't the fact that there are few
data points simply because its the ruler you chose to
measure with?

I can make millions of years one event.
(dinosaurs ruled the earth then dinosaurs were extinct)

When the SP500 has a return for the year, that's one event.
However, is it really one thing?
How did the earnings and sales of the 500 companies
progress per day?
How many 100's of thousands of shares traded to create the
final result?
Did company X have a better July than company Y?
Did company J have a good holiday season?

What if company Z had 10% earnings growth in one quarter.
What if the earnings were changed to a daily slope and
daily sales and earnings were measured against it?
Would that be enough data?
(assuming it was carried out on all companies for all years)

I thought the whole idea of the charts was to eliminate
the massive crushing amount of statistics that go into every
single trading day in the markets.


Thanks
SP-diceman
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Post by peter71 »

Hi SP,

The issue is that while you can indeed cut the data into as tiny of slices as you like, e.g., "what does P/E 10 say about returns over the next 10 minutes" once you get down to about a year and 138 observations you no longer get a "slopey cloud" so much as just a "random cloud" . . . one of the Bob's has some good files on this (albeit not yet updated thru 2008). Hmm, tried to search on "Bob's files" and a few other things but no luck. I'm sure someone knows the charts I mean . . .

All best,
Pete

P.S. On the second issue you raise about looking at each company individually -- I guess at one level that's covered by the research on value companies and at another level it would just seem like double counting in terms of Shiller's research in that macro events make the periodic movements of different companies less than totally independent too.
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Post by bob90245 »

peter71 wrote:. . . one of the Bob's has some good files on this (albeit not yet updated thru 2008). Hmm, tried to search on "Bob's files" and a few other things but no luck. I'm sure someone knows the charts I mean . . .
I try to keep those files and charts concealed. :lol: But for you, I'll make an exception. :wink:

http://bobsfiles.home.att.net/OddsAndEnds.html
Ignore the market noise. Keep to your rebalancing schedule whether that is semi-annual, annual or trigger bands.
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Post by dave.d »

Just for the record (i.e., so I can find this thread a year and a half from now using Google), DeLong's post linked in the OP refers to these as Campbell-Shiller regressions.
Value-based allocation.
grayfox
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Post by grayfox »

On the subject of the predictive power of P/E10, it seems that it is based on a belief that P/E10 is mean reverting. So I decided to look at what mean P/E10 is supposed to be mean reverting to, and how quickly this mean reversion occurs.

I made a plot of P/E10 and the AVERAGE(P/E10), which is just the average of all the P/E10's up to any point in time. In theory, this is supposed to be the best estimate of the mean of P/E10. The latest value is about 16.37.

Image

The average started back in Jan-1881 at a value of 18.47 when there was just one sample of P/E10. Rather quickly it went down to about 15 around 1885. Then it bumped up to over 17 in the early 20th century. The average got back down to 15 by the 1920s and seemed to be homing in on somewhere between 14 and 15 until 1997. But since 1997, the average has been drifting upwards to where it is now at 16.37.

I don't see a whole bunch of mean reversion going on. I also don't see the average converging to any particular value. You can say the average has stayed within a range from about 14 1/4 to 17 1/2, after the initial startup transient.

If there is a rubber band attached to the mean, it must be a pretty weak rubber band. P/E10 was above it's mean from Nov-1988 until Oct-2008, which is 20 years.

You could spend a big chunk of your life waiting for mean reversion to happen. It's not anywhere near as exciting as watching paint dry. It's more like watching trees grow. A retired guy may run out of time before mean reversion finally shows up.

And to me it looks like the rubber band broke sometime around 1997.
Last edited by grayfox on Wed May 26, 2010 1:54 am, edited 1 time in total.
peter71
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Post by peter71 »

grayfox wrote:On the subject of the predictive power of P/E10, it seems that it is based on a belief that P/E10 is mean reverting. So I decided to look at what mean P/E10 is supposed to be mean reverting to, and how quickly this mean reversion occurs.

I made a plot of P/E10 and the AVERAGE(P/E10), which is just the average of all the P/E10's up to any point in time. In theory, this is supposed to be the best estimate of the mean of P/E10. The latest value is about 16.37.

Image

The average started back in Jan-1881 at a value of 18.47 when there was just one sample of P/E10. Rather quickly it went down to about 15 around 1885. Then it bumped up to over 17 in the early 20th century. The average got back down to 15 by the 1920s and seemed to be homing in on somewhere between 14 and 15 until 1997. But since 1997, the average has been drifting upwards to where it is now at 16.37.

I don't see a whole bunch of mean reversion going on. I also don't see the average converging to any particular value. You can say the average has stayed within a range from about 14 1/4 to 17 1/2, after the initial startup transient.

If there is a rubber band attached to the mean, it must be a pretty weak rubber band. P/E10 was above it's mean from Nov-1988 until Oct-2008, which is 20 years. You could spend a big chunk of your working life waiting for mean reversion to happen. It's not anywhere near as exciting as watching paint dry. It's more like watching trees grow.

And to me it looks like the rubber band broke sometime around 1997.
As a general rule it's not the case that x needs to be mean-reverting to predict y -- e.g., height might predict basketball ability whether or not height is mean-reverting.

With P/E 10 predicting returns it's a little tricker, because returns aren't entirely separable from prices and the model certainly does imply that price bubbles happen, but to me the model is interesting because of what it says about how unit changes in x (valuations) affect y (returns), not because of what it may or may not imply about the central tendency of x (or even y) over time . . .

All best,
Pete
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Post by grayfox »

Right. I think the best use of P/E10 is to come up with a number for the expected 20-year return. Then you can see how it compares against alternatives like 20-year TIPS. Used in that sense I think valuations matter. In other words, what is the offer TODAY.

As far as expecting to see P/E10's back below 10 someday because it must eventually mean revert, I don't think it's so useful. I could name people that ran out of time waiting for favorable valuations.
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Post by peter71 »

grayfox wrote:.
As far as expecting to see P/E10's back below 10 someday because it must eventually mean revert, I don't think it's so useful. I could name people that ran out of time waiting for favorable valuations.
I agree with this, though personally I think there may be an element of "markets can become rational before you can confidently exploit their irrationality" involved too. I also agree that the alternatives or opportunity costs to owning stocks (e.g., premium over TIPS now) are always important, but I can't say I don't keep the "range of averages" for earnings yields and bond yields in the back of my mind, particularly at moments like the present one when prospects for both stocks and bonds seem, broadly speaking, "below average."

All best,
Pete
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Post by grayfox »

Here is something I am thinking.

The time frame for all this mean reversion stuff seems to be like 20 years. Suppose valuations aren't so favorable, say above 20 like in 1966. So you decide to wait for more favorable valuations before investing, say below 10.
This finally happens around 1973, 7 years later.
Then you buy in at PE=10.
Then PE stays between 5 and 10 until 1985, 12 years.
Finally by about 1995 PE is back up over 20, another 10 years.
It peaks in 2000, 5 years later
So the whole cycle takes 30 or 40 years.

Who has that much time? Maybe someone 25 or 30 years old. Someone retired definitely can't be investing on a 40-year schedule. They need something that is shorter term. Well, momentum is a short-term phenomenon. So perhaps someone in withdrawal phase should should be looking at momentum investing, i.e. 200-day moving average. Leave the value investing and mean reversion to the early accumulators.
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Post by cjking »

The charts measure the result of predicting the wrong thing, returns to a single end-date. They should measure the result of predicting average returns, for example the returns of an investor who sold 1/10 or 1/20 of his initial portfolio over 10 or 20 years.

Suppose the stock market went up at exactly 10% a year, on average, but on any given year-end someone flipped a coin and the resulting year-end balance was 50% or 200% of the trend value. In these circumstances I would say the average return was highly predictable, but someone in these forums would (incorrectly) dispute this by posting data/charts based on a single end-date, where the temporary 50% discount/100% premium dominated the figures. They are literally being "fooled by randomness" into not seeing the predictive power that is there. When you average, the overvaluation of one end-date is offset by the undervalution at another.

Of course, what you predict is a matter of user-choice. I just get annoyed with people saying PE10 has no predictive power. The statement is meaningless unless you also specify what it is you are trying to predict. PE10 is a very good predictor of the future trend, it is nowhere near as good a predictor of of the level of the stock-market on a particular date.
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Post by richard »

cjking wrote:Of course, what you predict is a matter of user-choice. I just get annoyed with people saying PE10 has no predictive power. The statement is meaningless unless you also specify what it is you are trying to predict. PE10 is a very good predictor of the future trend, it is nowhere near as good a predictor of of the level of the stock-market on a particular date.
The usual claim is that measuring from date A to date B, where B is X years from A, returns will be higher the lower the p/e. This makes sense, if for no other reason than that sales must be on specific dates.

"a very good predictor of the future trend" is a vague statement. Please state it more precisely, both what you mean by "very good predictor" and "predictor of future trend.

As to very good predictor, whatever the definition, there aren't enough independent data points to be statistically significant for 10 and 20 year periods.
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Post by richard »

grayfox wrote:Right. I think the best use of P/E10 is to come up with a number for the expected 20-year return. Then you can see how it compares against alternatives like 20-year TIPS. Used in that sense I think valuations matter. In other words, what is the offer TODAY.

As far as expecting to see P/E10's back below 10 someday because it must eventually mean revert, I don't think it's so useful. I could name people that ran out of time waiting for favorable valuations.
Makes sense, although I wonder how PE10 compares to the Gordon dividend model

People used to use stock yields versus bond yields as a predictor. Using this signal in the late 1950s and waiting for mean reversions did not turn out well

Image

Image

http://www.marketoracle.co.uk/Article7124.html
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Post by cjking »

richard wrote:The usual claim is that measuring from date A to date B, where B is X years from A, returns will be higher the lower the p/e. This makes sense, if for no other reason than that sales must be on specific dates.
I agree that's what's usually discussed, I'm saying that it shouldn't be, and that PE10 is being unfairly dismissed because of this semi-straw man. I say "semi" because it does have some predictive power in this case
"a very good predictor of the future trend" is a vague statement. Please state it more precisely, both what you mean by "very good predictor" and "predictor of future trend.
I'll sidestep the first part by asking you to substitute "much better" for "very good."

With regard to the second, the standard definition I've posted in many previous threads on this subject is Andrew Smither's "hindsight value": the average annual return experienced by a cohort of 40 investors with holding periods from 1 to 40 years.

Note that you do not have to have a 40 year holding period to use hindsight value, as some seem to assume. Whatever your holding period, it tells you something about the value of shares on the day you buy.

You need to understand that the shorter your holding period and the fewer end-dates your sales are average across, the greater the likelihood that your experience will be away from the trend. i.e. undestand the limitations.

Anyone who buys shares is buying variability. No matter how great the variability, it can still be helpful to know where the approximate centre of the distribution is. For example, when the centre translated to a yield of 2% and TIPS were yielding more that that, one might have chosen not to buy shares, and indeed to sell any one owned.


As to very good predictor, whatever the definition, there aren't enough independent data points to be statistically significant for 10 and 20 year periods.
So there's not enough evidence to disprove that PE10 works? Then why not use it? It makes sense, and using it in any vaguely sensible way cannot reduce risk-adjusted expected returns.

Presumably the lack of independent data points means we can say nothing about the returns on stocks over 10 or 20 year periods. Perhaps we should all get out of equities until someone can prove they are likely to return more than bonds over those timeframes. (I think I'm saying you are requiring an inconsistent level of proof for PE10.)
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Post by richard »

cjking wrote:
richard wrote:"a very good predictor of the future trend" is a vague statement. Please state it more precisely, both what you mean by "very good predictor" and "predictor of future trend.
I'll sidestep the first part by asking you to substitute "much better" for "very good."

With regard to the second, the standard definition I've posted in many previous threads on this subject is Andrew Smither's "hindsight value": the average annual return experienced by a cohort of 40 investors with holding periods from 1 to 40 years.
Much better than what?

Average over 1-40 year periods seems odd, but everyone's entitled to their own metrics. Presumably PE10 did well on this test?
cjking wrote:So there's not enough evidence to disprove that PE10 works? Then why not use it? It makes sense, and using it in any vaguely sensible way cannot reduce risk-adjusted expected returns.
Why not?

The trouble with intuitively appealing metrics is that there are so many. Choosing is a problem.

In the absence of useful numbers, I believe the right thing to do is hold a diversified portfolio. Corporate bonds are less risky than stocks because they're higher in the capital structure than stocks - they get paid off first. US government bonds are safer than corporates because they are backed by the full faith & credit of the government and are denominated in US dollars, and I spend in US dollars, so no meaningful default risk. TIPS are the safest, because they are adjusted for inflation, thereby protecting against inflation, at least to the extent CPI measures inflation.
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Post by cjking »

richard wrote:Much better than what?
PE10 is a much better predictor of the average of returns to different dates than of returns to a single date.
The trouble with intuitively appealing metrics is that there are so many. Choosing is a problem.
In fairness, one should start with what it is one wants to predict, which may well be returns over a 10 or 20 year fixed period. However usually it isn't, people usually just want some feel for whether stocks are a good bet at current prices, and that is exactly what "hindsight value" measures.
cjking wrote:So there's not enough evidence to disprove that PE10 works? Then why not use it? It makes sense, and using it in any vaguely sensible way cannot reduce risk-adjusted expected returns.
Why not?
I regard all Boglehead allocations between 100:0 and 0:100 as equivalent, in the sense that though a member of the set may be inappropriate for a particular investor, none is what I would categorise as dangerous. Each will, with average luck, get the returns it is entitled to. (There are other allocations, such as leveraged ones, or ones that use narrow asset classes, which would not make it into this equivalence class I'm defining.) Therefore varying a Boglehead allocation in any way, say with PE10, will still result in an allocation in the same equivalence class of acceptable portfolios.

A particular individual can constrain the equivalence class to only those portfolios appropriate for him.

Another way to put it, is that you can design your algorithm for turning PE10 into an asset allocation so that all possible outcomes are within the range of acceptability for you.
In the absence of useful numbers, I believe the right thing to do is hold a diversified portfolio. Corporate bonds are less risky than stocks because they're higher in the capital structure than stocks - they get paid off first. US government bonds are safer than corporates because they are backed by the full faith & credit of the government and are denominated in US dollars, and I spend in US dollars, so no meaningful default risk. TIPS are the safest, because they are adjusted for inflation, thereby protecting against inflation, at least to the extent CPI measures inflation.
If you had a sufficiently large pot to put a portion of money into rental properties, would you take no account of the average rental yield over the past ten years in your decision on how much money to allocate?

If buying a private business, would you take no account of the profits it had made in the last ten years, in deciding between that business and alternative investments?

If no to both, why would you buy the stock index without regard to the earnings yield at the price you are paying?

The answer to the last question, I guess, is that the higher volatility of stocks overrides the underlying fundamentals to such an extent that investors give up in disgust. They shouldn't. Variability may mean that your individual experience could be anything, but the fundamentals tell you where the probabilities lie, and sometimes that makes a difference.

Also, investors believe stock market efficiency in very liquid markets means the price is always right. I believe in stock market unpredictability, except on average over the long term, but that unpredictability is not entirely the result of a rational market that immediately prices in new information, some of it is somtimes due to unpredictable (chaotic?) investor behaviour, therefore the price can be very wrong, at times.
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Post by Drain »

I never like these analyses that look at returns over fixed periods--e.g., 10-year returns, 20-year returns. They don't reflect the way I'd actually invest if I were to develop a system around PE10. I wouldn't buy in at, say, PE10=12, and then wait 10 years before doing anything else. Furthermore, as has been noted, there aren't enough independent data points from which to draw reliable statistical conclusions.

I'm not sure I've thought this through well enough, but here it is, anyway. What I'd propose is a regression of average annualized returns on PE10, without reference to time periods. (You do need to use time to calculate the average annualized returns, of course.) I'll try to explain via examples.

Let's say the current PE10 is around 20--that is, rounded to the nearest tenth, it's on the interval [19.5, 20.4). I want to know the annualized return while the PE10 remains on that interval. The moment the PE10 hits either 19.4 or 20.5, the collection process for that data point ends. If, say, the PE10 goes to 19.4, then I calculate the annualized return until the PE10 either goes back to 19.5 or drops to 18.4. This process might result in data that looked something like the following:

20 -18.2%
19 -5.1%
18 7.0%
19 -20.5%
18 -3.2%
etc.

A data set like that would reflect a sequence of events in which the PE10 started at 20. The market dropped (or earnings increased), bringing PE10 to 19. The market dropped again to 18, at which point it rallied back to 19, only to drop again.

Like I said, you then regress the returns on PE10. This would give a relationship that would estimate the expected return and the variance for a given PE10, which, I believe, is what we're really interested in.
Darin
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Post by jeffyscott »

grayfox wrote:Right. I think the best use of P/E10 is to come up with a number for the expected 20-year return. Then you can see how it compares against alternatives like 20-year TIPS. Used in that sense I think valuations matter. In other words, what is the offer TODAY.
Yes, use P/E10 or something to give some indication of the level of prices and expected returns and compare that to other places you can put your money. Seems sensible to me.
The time frame for all this mean reversion stuff seems to be like 20 years. Suppose valuations aren't so favorable, say above 20 like in 1966. So you decide to wait for more favorable valuations before investing, say below 10...


Rather than going all in or all out, based on crossing various bright lines, why not just vary the stock allocation based on valuations or based on valuations compared to alternatives. Own more stocks when they appear to offer more attractive future returns and less when they don't. If you want to use P/E10 and some arbitrary rule, it could be something like percent in stock = (X)(1/PE10)... say you choose X=800, so then at P/E10 = 20, you have 40% in stock and at P/E10 = 10 you have 80%. Not saying this is a good rule or anything, just illustrating the idea of varying allocation based on valuations for those that want a defined way to do this.

Similarly there is someone here running a portfolio comparison where one of the portfolios is based on GMO's assessments of relative valuations and he has a specific defined rule for how the allocations will vary.
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Post by chuck-lyn »

grayfox wrote:Here is something I am thinking.

Who has that much time? Maybe someone 25 or 30 years old. Someone retired definitely can't be investing on a 40-year schedule. They need something that is shorter term. Well, momentum is a short-term phenomenon. So perhaps someone in withdrawal phase should should be looking at momentum investing, i.e. 200-day moving average. Leave the value investing and mean reversion to the early accumulators.
As a 76 year old retired since 1989, I think this makes sense. My approach is to adopt a 25% stock/bond AA and use momentum techniques on the 25% stock part. I am using the rule suggested by another poster that that you be "in the market" when the 10 day EMA
is above either the 50 day or 200 day and "out" otherwise.

I am "out" as of 5/24/2010.

I know this is very un Boggleheadish but it makes me feel good. :lol:

Cheers,

charlie
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Post by chuck-lyn »

grayfox wrote:Here is something I am thinking.

Who has that much time? Maybe someone 25 or 30 years old. Someone retired definitely can't be investing on a 40-year schedule. They need something that is shorter term. Well, momentum is a short-term phenomenon. So perhaps someone in withdrawal phase should should be looking at momentum investing, i.e. 200-day moving average. Leave the value investing and mean reversion to the early accumulators.
As a 76 year old retired since 1989, I think this makes sense. My approach is to adopt a 25% stock/bond AA and use momentum techniques on the 25% stock part. I am using the rule suggested by another poster that that you be "in the market" when the 10 day EMA
is above either the 50 day or 200 day and "out" otherwise.

I am "out" as of 5/24/2010.

I know this is very un Boggleheadish but it makes me feel good. :lol:

Cheers,

charlie
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efficient market hypothesis

Post by Duno »

I'm a beginner with all this stuff but how does the efficient market hypothesis relate to what this thread is discussing? It just seems that P/E ratios and the like apply to individual stock picking and that trying to apply it to the entire market is like trying to squeeze juice out of prune. By looking at the P/E of the S&P 500 or other large indexes, is that a good way to find out useful information that the markets haven't already price in?

Warren Buffet thinks that 95% of all common investors should invest a broad based index fund. Are the other 5% using methods that is being discussed in this thread? I've only been passively investing since 2000. But if what you guys are talking about works, I sure want to learn it!
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Post by richard »

cjking wrote:I regard all Boglehead allocations between 100:0 and 0:100 as equivalent, in the sense that though a member of the set may be inappropriate for a particular investor, none is what I would categorise as dangerous. Each will, with average luck, get the returns it is entitled to. (There are other allocations, such as leveraged ones, or ones that use narrow asset classes, which would not make it into this equivalence class I'm defining.) Therefore varying a Boglehead allocation in any way, say with PE10, will still result in an allocation in the same equivalence class of acceptable portfolios.
In an efficient market, the risk-adjusted returns for all diversified portfolios should be the same for the "representative" investor.

However, switching allocations can incur transactions costs - direct costs, taxes, etc. That would seem to be the downside. Of course, rebalancing can also have this problem, depending on how implemented.
cjking wrote:If you had a sufficiently large pot to put a portion of money into rental properties, would you take no account of the average rental yield over the past ten years in your decision on how much money to allocate?
What you want to know is the average yield over the next ten years.

Using the past may be a good way to estimate this. Or not.

It's possible the market is better at predicting future earnings than you are and has taken this into account in pricing the investment.
cjking wrote:Also, investors believe stock market efficiency in very liquid markets means the price is always right. I believe in stock market unpredictability, except on average over the long term, but that unpredictability is not entirely the result of a rational market that immediately prices in new information, some of it is somtimes due to unpredictable (chaotic?) investor behaviour, therefore the price can be very wrong, at times.
If you can identify wrong pricing, then it is likely you can make above average returns, either through extra dividends (if the error is to price too low) or if and when the market returns to its senses.
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Re: efficient market hypothesis

Post by richard »

Duno wrote:Warren Buffet thinks that 95% of all common investors should invest a broad based index fund. Are the other 5% using methods that is being discussed in this thread? I've only been passively investing since 2000. But if what you guys are talking about works, I sure want to learn it!
It is not known whether using simple valuation metrics such as PE10 work. As discussed, there just isn't enough data to tell.

It has intuitive appeal, but lots of ideas have intuitive appeal.

If it were a reliable method, you'd think more people would use it, and that there would be track records of mutual fund managers with truly superior performance. Not a lot of evidence of that.

The other 5% are most likely using much more sophisticated methods.
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Post by dbr »

The issue has nothing to do with what to invest in but rather when.

Historical data in which there is a weak relationship and lots of noise is not suggestive of an effective method for building an investment strategy.

I think this is the point that developed in the first few posts on this thread.

It is possible that there is guidance when at extreme low and high values of the valuation.

The possibility of markets running to extremes is a fact of life however one wants to view efficient hypotheses.

Boglehead advice tends to run in the vein of not trying to react to market trends and levels as these are more likely to mislead than to lead.
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