Baa bonds versus S&P

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Mike
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Baa bonds versus S&P

Post by Mike »

Ken Fisher has remarked on the relationship between Baa bond yield and S&P 10 year returns. It occurred to me that Baa bonds are less likely to be affected by boomer savings, since they are not generally offered in 401k plans. The St. Louis fed has a chart of 45 years of Baa bonds in case anyone else finds this of interest:

http://research.stlouisfed.org/fred2/series/WBAA/47/Max

http://www.forbes.com/forbes/2004/0412/226.html
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BenSolar
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Post by BenSolar »

Mike wrote:Ken Fisher has remarked on the relationship between Baa bond yield and S&P 10 year returns.
I'm not impressed by Fishers analysis:
Fisher wrote:There is no right way to make long-term market forecasts, as opposed to guesses. Those who say they "know" where stocks will be in 2014 are telling you more about what they don't know than what they do.

Future stock prices are determined by shifts in supply and demand for equities. ...

In 78% of all ten-year periods since 1925, average stock returns have beaten the beginning Baa yield. The only times this wasn't true were long ago. ...

So, after a three-year bear market starting in 2000, I'm more than 75% confident stocks will beat the current 6.2% Baa yield over the next decade.
:? He makes no mention of the good research showing the predictive power of the better valuation measures. Which are surely better than his simple comparison to Baa bond yields.
It occurred to me that Baa bonds are less likely to be affected by boomer savings, since they are not generally offered in 401k plans.
Implying comparitively lower demand for them over the next decade or so, dropping prices and raising yields. The huge US debt and loose money policies also imply rising yields as inflation cycles back up. So if we decide TSM is not a great bet right now because of valuation, we don't want to put a big chunk there. But typical bonds don't look so good either for the above mentioned reason(s). Looks to me like the current strategy is to seek out a portfolio that lets one ride out the next decade or so while interest rates rise - giving more competition to stocks for investment dollars, dropping stocks to a more reasonable valuation, until we find ourselves back in the land of high returns. :D

My portfolio is heavy in real estate and fixed value/return accounts because I believe. 8) I do still have significant exposure to US large cap stocks, though. I'm not as brave as raddr, but if I had better options in my 401k I would contemplate dumping the S&P 500.
"Do not spoil what you have by desiring what you have not; remember that what you now have was once among the things only hoped for." - Epicurus
JWR1945
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Post by JWR1945 »

For Mike:

Thanks for including the link to the St. Louis Federal Reserve Bank. It is critically important for understanding Ken Fisher's arguments.

I find his arguments to be somewhat less than compelling. It sounds as if he has found a correlation of dubious value and little more.

The one argument that does make sense has to do with supply and demand. You have already focused our attention on demographics. Ken Fisher's remarks about total market capitalization as opposed to the S&P500 index (or some other measure of overall stock market behavior) are well worth noting. We should not expect to be able to capture the entire increase in total market capitalization. Nor should we feel condemned to suffer the full effects of any decrease.

Thanks again and have fun.

John R.
Mike
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Post by Mike »

But typical bonds don't look so good either for the above mentioned reason(s).
I agree. I was not suggesting that Baa long bonds are a good deal now. There are better values elsewhere. I was simply wondering if the correlation that Fisher saw in past data may no longer hold as closely due to equity valuations being stretched more than Baa bonds by boomer 401k savings.
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Post by Mike »

My portfolio is heavy in real estate...
Rental real estate is an excellent investment for those with the temperament and savvy to pick and manage rentals. I know people who have done quite well with these. I don't own any myself, because I don't have the temperament to do so. However, for those who do, it can be an excellent investment.
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Post by Mike »

Nor should we feel condemned to suffer the full effects of any decrease.
I agree.
...a correlation of dubious value...
There are better measures and correlations. This is just one more piece of the puzzle to me. I like to consider all data.
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Post by BenSolar »

Mike wrote:Rental real estate is an excellent investment for those with the temperament and savvy to pick and manage rentals. I know people who have done quite well with these. I don't own any myself, because I don't have the temperament to do so. However, for those who do, it can be an excellent investment.
It does bring a certain excitement to life every so often. :shock:
"Do not spoil what you have by desiring what you have not; remember that what you now have was once among the things only hoped for." - Epicurus
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Post by JWR1945 »

...a correlation of dubious value...
Mike wrote:There are better measures and correlations. This is just one more piece of the puzzle to me. I like to consider all data.
You have made an excellent point. It behooves me to respond fully.

I will start by looking at the statistical calculations first. Ken Fisher has rightfully identified his numbers as a guess. But he has presented a plausibility argument involving statistics.

Ken Fisher has converted his data into a binary form, which allows us to use binomial statistics. There is no concern about the underlying probability distribution (except for variations with time). Presenting data in this form strengthens some assertions and weakens others. When statistical significance is claimed, it is likely to hold up to intense scrutiny. In terms of the using the relationship itself, it is weaker than using a scatter plot and making curve fits. (Excel can make the fit for you and give the square of the correlation coefficient as well.)

Here is how I approach the statistics at the start. These are imprecise but useful approximations, the kind of hand calculations that I would use in the preliminary stages of designing a test.

The probability that Ken Fisher mentions is 75%. [He refers to data that show 78%. Ken Fisher rounds it to 75%.] The Gaussian (i.e., normal) distribution approximates the binomial distribution with the mean equal to the percentage p, which is 75% in this case, and with a variance equal to p*(1-p)/N, where N is the number of (independent) data points.

[When setting up the null hypothesis, the assumed distribution has a true probability of 50% and independent data points. When the null hypothesis is rejected, the reason can be that the data points are dependent. Rejecting the null hypothesis does not guarantee that the relationship that you are hoping to discover actually exists. One has to be careful about that kind of detail in his interpretation of the data.]

The product p*(1-p) = 0.75*(1-0.75) = (3/4)*(1/4) = 3/[4^2]. If N = 49, then it equals 7^2. If N = 81, then it equals 9^2. [Ken Fisher data sequences start in 1925 and continue up to the present. Each sequence lasts ten years. This means that N = 70.] When we look at the standard deviation, we will be looking at the square root of the variance (making no adjustments in the number of degrees of freedom at this stage). Taking the square root of p*(1-p)/N, we get [(the square root of 3)/4]/[the square root of N] = [the square root of 3]/[4*(something in the neighborhood of 7 to 9)]. When we make confidence limits, we will want to look at something around 2 standard deviations (for a confidence level of 95%) or, possibly, something as low as 1.5 (for a confidence level close to but less than 90%). Looking at 2 standard deviations, we get 2*[the square root of 3]/[4*(something in the neighborhood of 7 to 9)] = [the square root of 3]/[2*{something in the neighborhood of 7 to 9)]. For those of us who remember, the square root of three is 1.732 (to three decimal points). If we were to divide it by 8 (which is in the neighborhood of 7 to 9), we would get something just above 0.2. If we divide by 2, we end up with something close to 0.1 or 10%. That means that the confidence limits will be reasonably close to plus and minus 10%. Since the measured probability is 75%, the confidence interval ranges from 65% to 85% (approximately and conservatively). [Actually, the probability is 78%, not 75%, and the confidence interval is from 68% to 88%.] We would declare statistical significance, provided that other factors did not dominate.

The other factors are known collectively as the logic behind the statistics. They are not often mentioned although they should be. They are far more important than a statistical test by itself.

I have already mentioned one of these other factors. It has to do with the strength of the relationship that we are trying to show (or to discover). Converting the data to binary form was a tradeoff, but I will not dwell on that point. What I will focus on is the embarrassing question: How did Ken Fisher come up with his relationship in the first place?

I strongly suspect that he engaged in screening. He applied the same kind of question to several dozen possible choices and found the one that suited him best. If so, he was virtually guaranteed to find something that would show statistical significance.

In view of the strength of the relationship (which rejects an assumed probability of 50% by 4 standard deviations), we might look more closely into things such as how it varies with time. Since we already know that there exist long-term effects in the stock market, such as multiple expansion and compression, it is likely that we are not looking at independent data points or anything close to independent data points.

Looking at the St. Louis Federal Reserve Bank data, we see that bond yields varied slowly. Once again, we have reason to be concerned about the independence of data points (and their effective number of degrees of freedom).

Now for a very nasty, but very relevant question: Did Ken Fisher have an answer in mind and did that factor into his screening (assuming that he engaged in screening)? My guess is that he did. It was not necessarily 7%. But it would be something not too far from the 6% (nominal) that Warren Buffett has mentioned and within the ranges of others.

Notice that Ken Fisher's 7% is nominal growth, not real growth. It is distinctly below the long-term 10% to 11% nominal growth frequently cited for the stock market. He also has some slop in the sense that he will be able to claim success if his 7% nominal growth occurs around 8 to 12 years. I do not fault him for that. In fact, I make use of that kind of slop myself when monitoring portfolio performance (in terms of safe withdrawal rates).

What is missing is a search for underlying cause and effect relationships. Ken Fisher's remarks about supply and demand are definitely on point, but they are not tied to Baa bond yields per se. Ken Fisher's presentation about Baa bond yields resembles those of the widely accepted, frequently mentioned but thoroughly and convincingly discredited (by BenSolar and Asness) Federal Reserve indicator. I would be much more impressed if Ken Fisher were to show that initial Baa bond yields and ten-year stock market returns were closely related quantitatively (that is, with similar percentages) instead of qualitatively (i.e., better or worse). He mentioned in passing that they sometimes differ by a small amount and at other times by a large amount.

Ken Fisher was accurate in presenting his number as a guess. I doubt that his plausibility argument came from the data presented. I suspect that the data were selected because they were convenient.

IMHO, it is best to focus on the relationship between stocks and bonds (in this case with Baa bonds). They are in competition. I am not convinced that looking at the initial yield of bonds is sufficient. Should the stock market fail to perform, bonds will look more attractive, which will drive their yields down (and prices up). This is likely to be balanced by an increase of bond yields as a result of Federal Reserve tightening in the future and/or an increase in inflation. [Most people expect bond yields to rise in the future. They disagree as to when they will rise and by how much.] The relative attractiveness of bonds depends upon how well their yields hold up.

Have fun.

John R.
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Post by Mike »

I would be much more impressed if Ken Fisher were to show that initial Baa bond yields and ten-year stock market returns were closely related quantitatively (that is, with similar percentages) instead of qualitatively (i.e., better or worse).
Equity valuation varies far more quickly than Baa bond yield, making initial Baa yield an unlikely indicator of probable equity returns. Ken seems to be trying to use this metric as some sort of ball park floor, below which equity returns seldom venture. I question this relationship in an era of unprecedented valuation. Many models break down at extremes. For example, the Gordon equation predicts positive returns for any possible valuation level. If the S&P yield were to fall to .000001%, the model would predict a positive return of a few per cent based upon dividend growth alone. Jack Bogle tried to account for this by incorporating an adjustment for valuations above or below the historic norm. Current dividend yield, plus the dividend growth rate, plus or minus the tenth root of the ratio of current valuation to the historic norm (for 10 year return estimates). His model corresponds better to what your modifications of the REHP calculator show. Equity valuations do matter.

As far as cause an effect, I don't see Baa yield causing equity returns. IMO, corporate profit plus profit growth causes equity return in the long run. A rapidly growing population, combined with increasing productivity is what has made the market return well the last 2 centuries (high growth). In the short run, initial equity valuations can get extended beyond what can be supported by our economy's long term growth rate. The inevitable reversion to the mean can deliver negative returns in the short run (10 years). Fluctuations in productivity growth or population can affect the growth rate up or down for decades at a time, adding yet another factor into the equation, but a factor not yet quantified.
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Post by JWR1945 »

I like your comments, Mike. They are well thought out and helpful.

I will add that I like the way that Jack Bogle adjusts for valuations, although alternative endpoints can also make sense. That is, you might want to use a final valuation other than the historical norm. You might be able to capture some of the long-term variation above and below those norms in a very rough manner. If nothing less, you should be able to identify the likely range of outcomes.
Current dividend yield, plus the dividend growth rate, plus or minus the tenth root of the ratio of current valuation to the historic norm (for 10 year return estimates). His model corresponds better to what your modifications of the REHP calculator show. Equity valuations do matter.
In terms of my own investigations, I have not made estimates of market returns using the Retire Early Safe Withdrawal Calculator, nor can I (even with my modifications). I have only made estimates of the variation of Safe Withdrawal Rates. That is not the same as the market return.

I have presented calculations of historical returns with and without dividend reinvestments. I do that by setting withdrawals equal to zero and looking at a portfolio's balance, looking at the real return and the nominal return separately. I read them off of some special data reduction tables that I have included among my modifications.

[I take the Nth root of (the balance N years after the start) divided by (the initial balance). I make two sets of tables, one without inflation adjustments and one with inflation adjustments.]

Have fun.

John R.
Mike
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Post by Mike »

Thank you for your kind words. I enjoy talking with smart people who also treat other people well.
I have not made estimates of market returns using the Retire Early Safe Withdrawal Calculator, nor can I...
There is a section devoted to portfolio returns, but it does not specifically cross reference with initial P/E ratios. By setting the withdrawal rate to 0, and stocks to 100%, the range of 10 year returns is negative .54% to 18.58%. The 30 year range of returns is 5.13% to 13.02%. This shows that vast differences were returned at various historical starting points. The terminal portfolio value section shows gains with 0% withdrawals when a switching model is used, hinting that initial P/E may have been a factor in the past with regard to subsequent market returns. That is all that I have been able to determine so far.
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Post by JWR1945 »

I have listed the order of P/E10 and several other indicators on this thread:
http://nofeeboards.com/boards/viewtopic.php?t=1305

In addition, with my newest modifications, I can make tables of annualized returns with the calculators very easily. This can include dividend reinvestments other than 0% and 100%. It can include (the equivalent of) annualized returns as withdrawals are made. The most difficult part is posting the tables at this site.

I hope that this helps.

Have fun.

John R.
Mike
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Post by Mike »

Thank you John.

Mike
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