Bpp
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Hi John,
I did a little playing around with your HDBR data.
Putting your tables of PE10, HDBR50 and HDBR80 into gnuplot
and fitting straight lines to the scatter plots of 100/PE10 vs the two
HDBR series, I can basically reproduce your fitted slopes (to 3 decimal
places, actually, if I use 1923-1980).
One thing that really jumps out at me is that your cut-off at 1923 seems to
have a huge effect on the fit parameters. Using the data all the way back to 1871
gives an intercept (at 1/PE10 = 0, or infinite PE) of 3.77% for hdbr50, and 3.32% for hdbr80.
Using your 1923-1980 data only, these intercepts become 2.64% and 1.64%, respectively,
as you know. Just adding 1921 and 1922 back in raises the intercepts to roughly in between the 1923-on and the 1871-on data sets.
This is some pretty drastic sensitivity to the starting point...
How strong would your conclusions be if you used the whole 1871-on
dataset?
Bpp
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I have addressed the 1871-1920 data previously. The relationship between Historical Database Rates and P/E10 is different for that time period.
There are many possible reasons.
Data for 1921 and 1922 are outliers in the 1921-1980 data set. There is nothing magical about 1921-1980 versus 1923-1980 except that the first uses round numbers instead of appealing entirely to the data.
Data for 1921 and 1922 are consistent with the other data from a theoretical standpoint when one additional factor is considered. Those two years have the highest earnings yield in the whole data set. It may well be that, when P/E10 gets down to 5 or 6, stocks are such a screaming buy that valuations cannot stay that low for very long. [This is the strong form of mean reversion: prices are (loosely) related to earnings.] That caps the withdrawal rate albeit at a very high level.
My exclusion of 1871-1920 date is sometime criticized by those who use the Fama/French data. Don't fall for it. Their data begins in 1926.
Have fun.
John R.
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Hi John,
I'm not falling for anything. It is a serious, philosophical question. If there was a
secular change in the relation between HDBR and PE10 in the early 1920's, then
how do we know we are not on the cusp of something like that again? As you note,
1921 and 1922 were extrema of valuation. 2000 was another extremum, in the opposite
direction. If extrema in valuation signal such shifts (for example), then ... who knows?
(Maybe it will be even worse than even you expect?)
Bpp
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I have simply noted that there has been a qualitative change.
Two possible reasons include going off the gold standard and the rise of the Federal Reserve banking system. At the end of the 19th century, prices were declining becaused of increasing productivity as constrained by hard money. I do not expect that to reoccur.
Today, we have a fiat monetary system which favors inflation over prolonged periods of declining prices.
One of the side effects was that commercial paper was a great buy. Commercial paper alone would have supported withdrawal rates of 6% and more in real dollars.
There are those who challenge the credibility of any stock related data prior to 1926 or 1927.
We did not have good economic statistics before the Great Depression. Early estimates of inflation were difficult for economists to make and they can and have been challenged. Along with the Great Depression came the Federal Government's collection of economic statistics.
Consider these plausibility arguments to explain what is behind the relationship between earnings yield and Calculated Rates (and the Historical Database Rates). These are not proofs. They simply show plausibility.
It makes sense for the withdrawal rate to be related to earnings yield because earnings are what supports withdrawals.
It makes sense that the relationship between earnings yield and withdrawal rates should be linear, to a good first approximation, since that would be the result if there were no volatility.
It makes sense that there should be some randomness in the relationship since the sequence of returns (as opposed to the total return by itself) affects the safety of a withdrawal rate.
It makes sense that the relationship between earnings yield and withdrawal rates should be offset from zero since there is a return of capital. Even if a portfolio consisted only of cash (equivalents) matching inflation (with 0% real interest), the portfolio would survive 30 years with withdrawals of 3.33%.
As to whether something of significance has changed, I would need to know why it would make sense. Much to the contrary, what I have been reading is that we are in a typical post-bubble period which will end badly for many. And I can see lots of signs to make me believe that that is so.
I am very comfortable with the notion that the absolute levels of valuations have shifted somewhat. I am not comfortable with drastic changes that violate reasonableness. For example, John Bogle's version of the Gordon Model makes a lot of sense. Then toss in the possibility that productivity has increased permanently (as it did in the 19th century, first in the US and then in the UK). That still would not support today's valuations.
Have fun.
John R.
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I agree with your plausibility arguments on what the relationship between hdbr and pe should look like. I also think that you have identified some plausible explanations for why that relationship could have changed. However, the fact is that the historical data shows that sometimes the relationship does change without, apparently, prior warning. (I assume it would not have been obvious in 1923 that things had changed going forward.)
Much the same could have been said in, say, 1933, and yet that was, indeed, 10 years into a new regime -- and there would have been no way to prove that things had changed at that point, either.As to whether something of significance has changed, I would need to know why it would make sense. Much to the contrary, what I have been reading is that we are in a typical post-bubble period which will end badly for many. And I can see lots of signs to make me believe that that is so.
I guess my feeling is that if you just displayed the plot of 1/PE10 vs HDBR, and said "now doesn't this look suggestive?", then probably everyone would say, "yes, and darned scary, too." Where you get into trouble is in insisting that you have a degree of precision in your determinations that has yet to be justified in the minds of many.
[Snipped. --Bpp]
Bpp
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I strongly disagree with this suggestion. Our mathematical calculations should always be complete. Including the statistics is essential.I guess my feeling is that if you just displayed the plot of 1/PE10 vs HDBR, and said "now doesn't this look suggestive?", then probably everyone would say, "yes, and darned scary, too." Where you get into trouble is in insisting that you have a degree of precision in your determinations that has yet to be justified in the minds of many.
My impression is that you have not taken some of my comments seriously.
There really is a priority associated with the reliability of numbers: from mathematical certainty to underlying cause-and-effect relationships to numbers in a proper statistical context to numbers in isolation. These are not throwaway words. They are not meaningless boilerplate.
In addition, the logic behind statistics is far more important than the application of statistical tests.
When hocus separates the mathematical calculation from the actions that you take, those are not meaningless words. They are essential.
Your comments are focused on the interpretation. That is different from the calculation. It is wrong to restrict the mathematical calculations so as to force a particular interpretation. Rather, it is essential for the mathematical calculations to be complete so as not to limit information.
In terms of:
I think that it would have been quite the opposite. FDR was changing everything in the economy. The only question was what would happen as a result of his actions.Much the same could have been said in, say, 1933, and yet that was, indeed, 10 years into a new regime -- and there would have been no way to prove that things had changed at that point, either.
It is true that most people did not appreciate that it would change the relationship between stocks and bonds forever. [Inflation reduces the value of bonds.]
How about putting these messages together in a post? You certainly have my permission. The editing should not be difficult. I think that these discussions are of general interest.
Have fun.
John R.
P.S. I don't know how to post a graph. If it were left in Excel, it would be a memory hog.
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I strongly disagree with this suggestion. Our mathematical calculations should always be complete. Including the statistics is essential.
Of course, include the statistics.
I think we are in basic agreement. I think the interpretation of the logic behind the statistics is especially important if you want to project into the future.In addition, the logic behind statistics is far more important than the application of statistical tests.
I don't think I have suggested anything to the contrary.It is wrong to restrict the mathematical calculations so as to force a particular interpretation. Rather, it is essential for the mathematical calculations to be complete so as not to limit information.
Let's take it for the sake of argument that something really did fundamentally change around that time.I think that it would have been quite the opposite. FDR was changing everything in the economy. The only question was what would happen as a result of his actions.
It is true that most people did not appreciate that it would change the relationship between stocks and bonds forever. [Inflation reduces the value of bonds.]
My point was that retirements conducted after 1923 faced a different relationship between hdbr and pe10 than those conducted before that. Even if one had had a suspicion as early as 1923 that things were changing, there would have been no way to know that for sure, or even begin to calculate what the new relationship might be, until some time after 1953. If one had retired in 1950 using the relationship that was visible in the data up until that point, one would be using the wrong relationship. The confidence intervals derived from the data up to that point would have been inappropriate for basing decisions on from that point forward. And I don't see how one could have calculated new ones yet at that point.
This is a fundamental problem, and I don't see how it can be solved. One might feel comfortable ignoring it if the relationship had never changed. But given that it did change, and in a way that couldn't be quantified until much later, then one always has to keep in mind that it might happen again. Indeed, may already have happened again.
I hope you don't find this to be missing the point or not taking what you say seriously.
Well, maybe I will. Might not have the chance for it today, though.How about putting these messages together in a post? You certainly have my permission. The editing should not be difficult. I think that these discussions are of general interest.
I could make a jpeg from gnuplot, and try to find somewhere to put it.P.S. I don'tknow how to post a graph. If it were left in Excel, it would be a memory hog.
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Bpp