From Earnings Yield

Research on Safe Withdrawal Rates

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Mike
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Post by Mike »

Thank you Keith. My y axis is 10 year return. I usually see log charts used with S&P over a period of decades, as it shows relative changes better than non log charts. It is probably not necessary here, since all returns are at the 10 year point. When I switched the charts between normal and log charts, the log was a bit easier for me to see the distribution pattern, but normal charting might be better for close examination. You have a nice web site by the way.
Shakespeare
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Post by Shakespeare »

Thanks for the kudos.

BTW, there's another little assumption in "normal" least squares: that the "y" axis errors associated with each point have normal distributions of the same width, independent of the "x" value. This can be pictured by drawing little bell curves on each data point. The axis of each curve is vertical, with the bell coming out of the page towards you, like |) . All the bells ("Gaussians") have the same width, independent of the "x" value. This means that percentage changes are considered independent of "x", rather than point changes.
JWR1945
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Post by JWR1945 »

Mike wrote:I generated a chart of P/E 10 versus nominal 10 year return.
Outstanding! Please continue your investigations along these lines. You are at the cutting edge of some important research. I will provide details in the not too distant future.

It is not necessary to use a logarithmic scale because Return0 has been annualized for you already. Return0 satisfies this equation: (1 + Return0)^N = [Balance after N years]/[Initial Balance], where Return0 is expressed as a decimal fraction instead of a percentage. That is, if Return0 = 8%, then (1 + Return0) = 1.08. A logarithmic scale would be appropriate if we were simply looking at the ratio on the right side of the equation, [Balance after N years]/[Initial Balance].

It makes sense to me that Return0 and the percentage earnings yield should be closely related, especially with time periods of 5 to 20 years. We should be able to see that in the values of R-squared. The relationship is likely to loosen considerably over longer periods.

I have made plots of Return0 versus the Percentage Earnings Yield for HDBR50 and HDBR80 portfolios (with 50% stock and 80% stock, respectively) at 5, 10, 15, 20, 25 and 30 years. For the most part, I have restricted myself to looking at the years 1923-1980.

I had previously made some graphs of (annualized, real) Return0 (with dividends reinvested and with 0.20% expenses) versus P/E10. That was before I realized the importance of using (percentage) earnings yield 100/[P/E10] instead of P/E10. You will find the graphs of Return0 versus Earning Yield 100/[P/E10] more meaningful and easier to understand.

The relationship between Return0 (the annualized real return of a portfolio with all dividends reinvested, no withdrawals and with an annual fee of 0.20% of the portfolio's current balance) and the percentage earnings yield 100/[E10/P] is strongest at 15 and 20 years with R-squared close to 60%. It is still useful at 10 years and 25 years, with R-squared values close to 40%. (At 10 years and 50% stocks, R-squared is 33%.) It is useful even at 5 years, with R-squared of 25% for 50% stocks and 35% for 80% stocks.

The initial percentage earnings yield 100/[E10/P] has almost no predictive power at 30 years. R-squared falls below 2% for both portfolios.

To understand this behavior, look at the equation for the annualized return once again. The purchase price has a great deal to do with the number of shares purchased initially. The rise in the portfolio's balance is seen in the ratio. If the initial price of one portfolio were one half that of another, yet the final balances ended up being the same, the ratio of the final balance to the initial balance of the first portfolio would be twice as large as for the second. But when you calculate the annualized return, taking the Nth root hides this fact.

For purposes of retirement planning, short time periods have the greatest influence on portfolio survival. A portfolio either grows enough to overcome the effects of withdrawals in the first decade (actually, eleven years is a better number) or it is likely to be in trouble. Looking at Return0 at 10 years, which is what you have done, is critically important.

You can easily plot curves for several data sets with Excel. You should separate them by using different colors and shapes for the data points and different colors and/or solid or dashed lines for the trendlines. It is best to place the values for the X-axis in one of the left-hand columns.

You might choose the order of your columns to be Year, P/E10, 100/[P/E10] and then (real, annualized) Return0 for 5, 10, 15, 20, 25 and 30 years. When you make your charts, you could choose P/E10 or 100/[P/E10] as the X-axis (by choosing which column that you highlight is farthest to the left) and selectively remove what you do not wish to plot. (If you are not careful, your plots are likely to become cluttered.)

Have fun.

John R.
Mike
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Post by Mike »

You will find the graphs of Return0 versus Earning Yield 100/[P/E10] more meaningful and easier to understand.
Ok. The modification was easy enough to make, and generates an interesting looking chart. Y=.1587+.1011 R^2=.3509
Mike
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Post by Mike »

An initial examination of the chart seems to indicate that there has not been a positive 10 year return on the S&P when the earnings 10 yield was below 5% since 1899.
JWR1945
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Post by JWR1945 »

Mike, I am not able to duplicate your results. Please supply me with the details of what you are doing.

Consider the years 1929 and 1930. Both had P/E10 level above 20 (and earnings yields below 5%), but they had positive real returns ten years later when there were no withdrawals but 0.20% in expenses (i.e., Return0 for HDBR50).

Have fun.

John R.
JWR1945
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Post by JWR1945 »

Mike, here is a heads-up on the research that I mentioned earlier.

Back at he beginning of the year I stated that my investigations into SWR (Safe Withdrawal Rate) Based Design had produced a useful tool as a byproduct. To get an idea of what it is, make XY Scatter plots with the 30-Year Historical Database Rates for 1921-1980 as the X-axis and Return0 at 5, 10, 15 and 20 years as the Y-axis. Have Excel plot linear (i.e., straight-line) trendlines and pay very close attention to R-squared.

You will find that knowing Return0 at intermediate time periods would have allowed you to estimate the 30-Year Historical Database Balance Rate accurately, especially at the 15-year point. (Fourteen years has the highest value of R-squared, 90%!) At later times, especially at the 25 and 30-year time periods, Return0 would have had less and less predictive power. That is because the most important years occur early and portfolio returns later on suppress their influence on Return0. [What you are interested in is predicting Historical Database Rates from Return0. The mathematics do not know whether you are using Return0 to estimate the Historical Database Rates or vice versa. You put the Historical Database Rates on the X-axis for convenience. This allows you to plot several lines (i.e., linear curves to fit the data) on the same graph.]

It turns out that knowing Return0 at the halfway point would have predicted the 10 and 20-Year Historical Database Rates as well. (I refer to these Historical Database Rates at these periods as WFAIL to avoid confusion. Almost all of the Historical Database Rates that I have previously listed have been for 30 years.)

We can use shorter-term estimates of Return0 to estimate longer-term Safe Withdrawal Rates (actually, to estimate Zero Balance Rates). We can also determine how much portfolio survival depends upon the sequence of returns and how much it depends upon the total return Return0. The accuracy of our calculations depends upon the accuracy of our estimate of Return0. There are many ways to estimate Return0. Using P/E10 or percentage earnings yield 100/[P/E10] is one of the best approaches. Careful application of the Gordon Equation is another.

This is how our current investigations fits into a larger problem. I reported the direct relationship between earnings yield and 30-Year Safe Withdrawal Rates at the beginning of this thread. As we extend our applications to SWR Based Design, we will want to break retirement planning into several segments and to monitor financial safety continually with time. These investigations and the new tool will combine to make that task easier.

Have fun.

John R.
Mike
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Post by Mike »

Return0 for HDBR50
I am using 100% equities, rather than 50%. I am also attempting to use nominal returns, rather than inflation adjusted ones at this point. I was trying to isolate the performance of the S&P in my initial examination. I remember seeing data for small caps and such in one of Gummy's calculators. I am having trouble unzipping it on my new computer, but if I can solve this problem, I may attempt to examine historical small cap performance also.
Mike
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Post by Mike »

Mike, here is a heads-up on the research that I mentioned earlier.
Thank you John. I will ponder this for a while.
JWR1945
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Post by JWR1945 »

Mike wrote:I am using 100% equities, rather than 50%. I am also attempting to use nominal returns, rather than inflation adjusted ones at this point.
I just brought up the unmodified Retire Early Safe Withdrawal Calculator (Version 1.61 from November 7, 2002). I used an initial balance of $1000, a withdrawal rate of 0.00% and 100% stocks.

The 10-year nominal returns for 1929 and 1930 are in cells T73 and T74, respectively. From cells BH186 and BI186, we see that P/E10 was 27.2 in 1929 and 22.3 in 1930. [The calculator shows rounded values. I have used truncated values many times in the past. You will often see that I have referred to the P/E10 of 1929 as 27.0, the truncated value, instead of 27.1, the rounded value.] That is, the earnings yield was below 5% in both 1929 and 1930.

With 0.20% expenses, cell T73 shows me a balance of $947 (nominal) after ten years. Cell T74 shows me a balance of $1067 (nominal) after ten years.

With 0.00% expenses, cell T73 shows me a balance of $966 (nominal) after ten years. Cell T74 shows me a balance of $1089 (nominal) after ten years.

This means that there was a loss (in nominal dollars) ten years after 1929, but a gain ten years after 1930.

Evidently, we have a difference in our inputs somewhere. Did you change any of the default settings? I am using the January data (cell B11 is set equal to 1). Otherwise, I do not see anything that theoretically would cause a difference.

Have fun.

John R.
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Post by JWR1945 »

Mike wrote:I am having trouble unzipping it on my new computer, but if I can solve this problem, I may attempt to examine historical small cap performance also.
Coffee Cup offers a free program for (zipping and) unzipping software. That is what I use.

Free ZIP wizard from Coffee Cup software:
http://www.coffeecup.com/freestuff/

I learned about it from Kim Komando's Tip of the Day (which is free):
http://www.komando.com/newsletter.asp

Have fun.

John R.
Mike
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Post by Mike »

I have pasted my data series here, in case my copy of the REHP got corrupted somehow in transmission:

Code: Select all

Date Yield 10 10 Year Return
1871 7.545045045 2.447087261
1872 6.893004115 1.87819069
1873 6.555772994 1.580635406
1874 7.188841202 1.566726209
1875 7.378854626 1.275657682
1876 7.511210762 1.476988862
1877 9.436619718 2.135730423
1878 10.30769231 2.253960882
1879 9.357541899 1.753100785
1880 6.555772994 0.879921751
1881 5.413026859 0.524314703
1882 6.378053715 0.695343367
1883 6.548677349 0.762545582
1884 6.928652063 0.679740614
1885 7.616252135 0.926836579
1886 5.990779901 0.630503051
1887 5.710297611 0.460685937
1888 6.510983616 0.53717761
1889 6.328198309 0.745387455
1890 5.807176654 0.997069246
1891 6.48130981 1.682407968
1892 5.258622083 1.453727891
1893 5.663590525 1.447026773
1894 6.353292887 1.699532685
1895 6.051640854 1.842505483
1896 6.032736708 2.566520739
1897 5.873190321 2.716478225
1898 5.195075063 1.485280942
1899 4.360565115 1.279388517
1900 5.354960129 1.463418068
1901 4.766766447 0.929350135
1902 4.476217472 0.803612095
1903 4.921712278 0.781640451
1904 6.304441248 0.873549684
1905 5.417161515 0.507938007
1906 4.967117123 0.475181123
1907 5.80756724 0.520427292
1908 8.401265527 0.86492329
1909 6.773040218 0.687088031
1910 6.873851403 0.632303081
1911 7.117835317 0.707201392
1912 7.249028153 0.854411838
1913 7.605668138 1.027405825
1914 8.593950537 0.993936825
1915 9.652664134 1.789292449
1916 7.972216066 1.599801226
1917 9.097226348 1.52542722
1918 15.05877584 2.240215024
1919 16.3975618 3.301090584
1920 16.69541681 2.497162444
1921 19.52292169 2.513260274
1922 15.9056166 1.346234697
1923 12.26361802 0.817675131
1924 12.38812064 1.079698244
1925 10.3171291 0.608033445
1926 8.817590877 0.773969844
1927 7.5838409 0.897792259
1928 5.317415523 0.296689942
1929 3.692325922 0.187084823
1930 4.482149422 0.272112909
1931 5.986060119 0.346342411
1932 10.7383629 0.92379678
1933 11.45731795 1.64147114
1934 7.677472554 0.906700292
1935 8.698747439 1.564531237
1936 5.852279164 1.154859052
1937 4.62561614 0.6563969
1938 7.401123624 1.801399687
1939 6.410406639 2.185573991
1940 6.105572551 2.187280859
1941 7.192093047 2.721647695
1942 9.899337172 2.344263822
1943 9.851698229 1.742666001
1944 9.047798172 1.824144154
1945 8.360880036 1.733239915
1946 6.400752451 1.78754817
1947 8.718930707 3.171878641
1948 9.59753444 2.014913823
1949 9.757729474 2.654874167
1950 9.306019162 2.168963427
1951 8.406356664 1.205849583
1952 7.98271917 0.920443806
1953 7.68593815 0.826052614
1954 8.331493077 1.151224651
1955 6.253603223 0.759215567
1956 5.466695817 0.710225854
1957 5.981655431 0.521720851
1958 7.252456497 0.691894568
1959 5.561630295 0.43725361
1960 5.453072631 0.406072689
1961 5.414062935 0.510716253
1962 4.717441439 0.494007306
1963 5.192315124 0.692754528
1964 4.623803595 0.416087106
1965 4.297501396 0.361501578
1966 4.156537982 0.512060914
1967 4.894225479 0.688579641
1968 4.648668532 0.45028325
1969 4.718100997 0.59182807
1970 5.851189713 0.874269633
1971 6.074672077 1.012586007
1972 5.792736984 0.875588453
1973 5.344012675 0.792909085
1974 7.390588676 1.592481972
1975 11.2095113 3.054914219
1976 8.940504318 2.257318391
1977 8.742816746 2.235145527
1978 10.82079839 2.988708957
1979 10.80189263 2.895974746
1980 11.29824242 2.409504668
1981 10.79983056 1.649935813
1982 13.53425389 2.778213646
1983 11.41971857 2.144114131
1984 10.10618385 1.413970621
1985 10.00299972 0.995916711
1986 8.536059348 1.172770012
1987 6.701421084 0.973913958
1988 7.195105593 1.184347326
1989 6.627781191 1.301359857
1990 5.865600668 1.165777365
1991 6.407824396 1.393540006
Mike
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Post by Mike »

Never mind. I see what I did wrong. All values in T are to be compared to an initial value of 1000, not the value 10 space up in T. All of the calculations have already been done for me. Thank you John.
JWR1945
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Post by JWR1945 »

Mike wrote:I remember seeing data for small caps and such in one of Gummy's calculators....I may attempt to examine historical small cap performance also.
That could be helpful. Gummy found that year-to-year nominal stock returns were almost independent, but real returns were not. He uses random nominal stock returns (with the actual probability distribution of stocks, which is not Gaussian) but he (randomly) picks actual historical sequences for inflation. I do not know whether this is true of all of his Monte Carlo simulators or just his most sophisticated one.

Gummy's Monte Carlo simulators do not include Mean Reversion, which is a unique feature of raddr's Monte Carlo simulator. The key is that raddr has actually defined reversion to the mean in a precise and usable manner. Much of the confusion about reversion to the mean has been from a lack of a good, working definition.

It is good to see you trying to extend the types of portfolios that we examine. We have limited ourselves to investigating the S&P500 plus a fixed income series (such as commercial paper, treasury notes and bonds, TIPS and ibonds) only because we are limited by our tools. The current choices are all that we have available to us. In terms of data availability, only Professor Robert Shiller's detailed data go back to 1871 and they are only for the equivalent of the S&P500.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

Mike wrote:Never mind. I see what I did wrong.
Thanks!

John R.

P.S. I did not assume that you were the one with the wrong numbers.
Mike
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Post by Mike »

As a suggestion for when you post data series, putting them in a post one column at a time would allow for rapid copying and pasting into Excel for those who want to run the numbers. IOW, one post for just column A, the next post would have column B, etc... The top post could have them all together the way you do now for reference on how they fit together. The extra pages should not add much time over what you do now, since you can just copy the column from Excel, and paste it onto the web.
JWR1945
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Post by JWR1945 »

I see what you mean. You cannot copy individual columns.

I am not sure that individual columns will transfer directly to Excel (or Word). If nothing else, they should be easier to cut and paste.

It would be much, much easier not to use tables with multiple columns. It takes a lot of work to get everything to line up. HINT: always take one column at a time, from left to right. Do not work row by row.

The hardest tables are those with more than four columns. They tend to wrap around and the Preview Display does not show it.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

If you will specify exactly what you want (e.g., 80% stocks from 1921-1980) along with its location/description/link, I will post individual columns for you. I still have the source material.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

Here are the annualized real returns Return0 for 50% stocks and 50% commercial paper (and 0.20% expenses) after 10 years. This covers the years 1871-1920 (50 years).

10.75
9.23
9.14
9.30
8.82
9.60
11.02
8.78
7.50
8.22
5.84
8.12
7.40
7.23
7.23
5.70
5.46
6.54
7.04
4.69
6.40
5.56
5.33
4.44
5.08
5.97
5.24
3.73
3.94
5.12
4.44
4.04
4.23
4.18
2.62
2.64
2.15
0.51
(1.61)
(1.95)
(2.76)
(1.45)
0.20
0.56
2.10
1.85
3.40
7.85
11.15
11.32

(more to follow)

John R.
Last edited by JWR1945 on Tue Apr 20, 2004 12:37 pm, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Here are the annualized real returns Return0 for 50% stocks and 50% commercial paper (and 0.20% expenses) after 10 years. This covers the years 1921-1980 (60 years).

11.19
8.23
7.31
9.45
7.31
8.60
8.97
5.22
3.63
4.12
3.81
3.24
2.70
1.33
2.68
1.99
(1.50)
(0.69)
(1.14)
(0.34)
1.01
3.10
3.67
2.96
4.46
4.34
6.87
7.15
8.60
7.95
7.36
7.73
6.84
7.78
6.40
5.56
4.94
6.17
4.78
3.72
3.53
3.08
4.03
1.86
(0.76)
(0.08 )
0.56
(0.77)
(0.87)
(0.33)
0.37
(0.56)
(0.05)
2.10
4.34
4.16
5.46
6.05
6.52
7.52

Have fun.

John R.
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