Is the Raddr Methodology Analytically Valid?

Research on Safe Withdrawal Rates

Moderator: hocus2004

JWR1945
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Post by JWR1945 »

hocus2004
In the statement I quote at the top of this post, you indicate that the Gordon Equation's prediction of a 3 percent long-term real return is wrong. Is the correct expectation 7 percent or something between 3 percent and 7 percent?
Five hundred years from now, the answer will be much closer to 7% than to 3%. One hundred years from now, the answer will be closer to 7% than to 3%. Fifty years from now, the answer is likely to be closer to 7% than to 3%. Ten years from now, the answer is much more likely to be 3% than 7%.

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Post by JWR1945 »

hocus2004
Are you saying that the long-term return will be 7 percent from any possible starting point? If that is what you are saying, that's probably the part that I am having a hard time understanding. It's hard for me to understand why that would be so. Shouldn't the long-term return vary according to the valuation level that applies at the starting point?
The long-term return does vary with the starting point.

The ratio of the [final balance/initial balance] varies with the starting point (and with the end point as well).

As the number of years of compounding N increases, the effect of a slight change in the annualized total return r becomes magnified. For example, if we change r from 6.0% to 6.5% over 50 years, (1+r)^50 changes from 18.42 to 23.31, which is an increase of 23.31/18.42 = 1.265. If we change r from 6.0% to 6.5% over 100 years, (1+r)^50 changes from 339.30 to 543.20, which is an increase of 543.20/339.30 = 1.601.

This tells us that a price difference of 26.5% causes a 0.5% change in r when the long-term is 50-years. When the long-term is 100 years, a 0.5% change in r corresponds to a price difference of 60.1%.
Shouldn't the long-term return vary according to the valuation level that applies at the starting point?
Yes. It only seems not to vary much when we look at the percentage return r instead of looking at the ratio of the [final balance/initial balance]. The ratio of the [final balance/initial balance] includes the purchase price directly. The effects caused by the annualized return r is magnified greatly because of years of compounding.
Are you saying that the long-term return will be 7 percent from any possible starting point?
The long-term return will be 7% (or whatever the true long-term return happens to be) plus and minus some percentage that varies with valuations. This plus and minus percentage becomes smaller when the total number of years of compounding becomes very large.

Another way of looking at it is this: There are limits as to how much prices are likely to vary from one year to the next. A reasonable number might be a factor of 3 or 4. It takes only a very small change in the total return r to absorb such a factor if the number of years of compounding is very large: 50 years or, if necessary, even longer.

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John R.
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Post by Mike »

Five hundred years from now...
Equity returns for the 19th and 20th centuries had the tail wind of a rapidly rising population. It is not physically possible for that rate of population increase to continue for 500 more years. Population growth plus productivity growth is what translates into economic growth.
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Post by JWR1945 »

From an earlier post of mine on this thread:
http://nofeeboards.com/boards/viewtopic ... 038#p24038
This is complicated a little bit because the 6.5% to 7.0% long-term return assumes that all dividends are reinvested. Fortunately, I can use my calculators to generate this data easily.
The two middle values of annualized returns in my table are 6.32% and 6.42%. The median long-term annualized real return in what I have presented is actually 6.38% and not between 6.5% and 7.0%, as has been commonly reported by others.

John Bogle's procedure has been to identify specific pairs of dates and report the average single-year (i.e., annual) return for each pair, not the annualized long-term return. Obviously, his selection of dates affects his reported numbers. His choices for Table 1.2 on page 11 of Common Sense on Mutual Funds were 1802-1870, 1871-1925 and 1926 -1997. [Gummy has a formula that relates averaged annual returns and annualized returns. The annualized return is lower whenever there is any randomness.]

Mike is right to caution us about projections into the future. (And I am reluctant to believe any projection that is 500 years into the future, including my own.) Notionally, what I have in mind are prices varying around a very long-term trendline (with a semi-logarithmic graph of dollars versus dates similar to Figure 1.2 on page 7 of John Bogle's Common Sense on Mutual Funds). My remarks about 7% versus 3% were based upon a statistical description of what might happen. I would keep the statistical properties of differences between the trendline and actual prices (in percent, not dollars) the same as in the historical record. Otherwise, I would allow report prices randomly. Under those conditions and assuming that the long-term trendline is 7%, my remarks would be accurate.

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Post by JWR1945 »

hocus2004 wrote:I am thrown by your statement that "Any study that uses historical sequences has this (7%) return embedded in it." This seems to suggest that the 7 percent expected return applies regardless of the starting-point valuation level. But then you say that "the false notion that one's purchase price does not matter in the long-run...." which suggests to me that the same return assumption should not always be embedded in an analysis.
Refer to Figure 1.2 on page 7 of John Bogle's Common Sense on Mutual Funds or to page 11 of Jeremy Siegel's Stocks for the Long Run (2nd edition, 1998), which is the original source.

The plot shows the total real return of various investments (including stocks, bonds, bills, gold and the dollar) starting from a $10000 initial investment. Imagine drawing a straight line on that graph that approximates the stock return. [A computer can do this for you. Or you can use a straight edge (such as a ruler) and your eyeball to come up with something surprisingly good and useful.] Actual stock prices would be higher at times and lower at other times, but the straight line would give you a good description of how well stocks have done overall. It would seldom be exactly right. But it would almost always be approximately right.

The 7% real return (or, according to my own calculations, the 6.38% return) corresponds to this straight line. Actual prices are (almost) always different, but usually very close. The straight line is derived the historical data. It is in this sense that the 7% (or the 6.38%) real return is embedded in the historical record.

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Post by hocus2004 »

"The long-term return will be 7% (or whatever the true long-term return happens to be) plus and minus some percentage that varies with valuations."

I believe that this is the point that is driving Bernstein's criticism of the conventional methodology on grounds that it inappropriately contains an embedded long-term (in this case meaning 30 years) real return expectation of 7 percent. This criticism does not apply to the JWR1945 methodology, in my view. Your methodlogy shows the Unsafe Withdrawal Rate (the annual take-out number with only a 5 percent chance of working out) to be about 5.7 percent at today's valuations. It seems to me that your expected real return must be lower than 7 percent for that to be the Unsafe Withdrawal Rate (especially since the Unsafe Withdrawal Rate calculation assumes that the portfolio is depleted over the course of the 30 years).

Both Bernstein and I accept that 7 percent (or perhaps 6.4 percent) is the long-term return number you obtain if you look at high valuation, moderate valuaton, and low valuation start-years all mixed together. His criticism of the conventional methodology (as I understand it) is that to mix all the years together generates a "highly misleading" expectation as to what the 30-year real return is likely to be from a retirement beginning at a time of high valuation. It is by mixing all the valuation possibilities together in determining what long-term return to expect that the conventional methodology imappropriately "embeds" the 7 percent number.

Say that you had lived your entire life in China and, were moving to New York City, and wanted to have a picnic on the day you arrived to celebrate your arrival. You go to your local library and ask whether there is likely to be good picnic weather in New York City when you arrive there on February 1. The librarian pulls out an almanac, determines that the average daily high temperature in New York City is 68 degrees and says "Yes, it sounds like the picnic idea is a good one."

Looking at the average temperature in New York City to determine the temperature likely to apply on February 1 is as silly as looking at the average long-term return expectation to determine what return expectation is reasonable for the 30-year time-period following from a retirement date starting at a time of high valuation. To get a sense of what temperature to expect on February 1, you need to look at average winter temperatures, not average temperatures for all the seasons combined. To get a ballpark number for the 30-year return you can expect from a stock portfolio, you need to look at the historical data for valuation levels similar to the one that prevails at the time of the retirement, not a mix of data from low, moderate, and high valuation levels.

I appreciate your point that over very long time-periods the 7 percent (or 6.4 percent) number will gradually come closer to the mark. It seems to me that that is because the effect of the initial error of using a blended-valuation-level return expectation is diluted as over time the mix of valuation levels experienced by your portfolio becomes ever more varied. It still seems to me, however, that using the 7 percent number (or 6.4 percent number) for retirements beginning at low and high valuation levels is inappropriate. I can not come up with any justification for using the number obtained from looking at a blend of starting-point valuation levels when it is known that a more accurate returns expectation can be obtained by using a number determined by referencing only data from valuation levels similar to the one that applies at the time the retirement begins.

My focus is on the practical implications of the work we are doing. I think that Bernstein's criticism of the conventional methodology's embedded 7 percent return expectation does a good job of pointing middle-class investors to the core flaw of that methodology. The REHP numbers would be reasonable if it were reasonable to expect a 7 percent long-term return in 30 years from all possible valuation levels. It is not. That's why the conventional methodology generates numbers that are "highly misleading" (Bernstein's phrase).

I'm not trying to argue that the Bernstein methodology is perfect or superior to the JWR1945 methodology. My view is that it is on the right side of the reasonable/unreasonable divide because it at least makes an adjustment for changes in valuation levels. The conventional methodology is on the wrong side of the reasonable/unreasonable divide because it makes no adjustment whatsoever. The assumption that starting on the day of my retirement changes in valuation levels will for the first time in history begin having zero effect on the return I will obtain 30 years out is about as far-fetched a possibility as can be imagined by the mind of man. It is irresponsible in the extreme that this assumption is being used to generate take-out numbers that are advertised as being "100 percent safe."

I know that you agree with me on the core criticism of the conventional methodology, JWR1945. My sense is that you are focusing on a flaw in the Bernstein methodology that probably really is present. I am just trying to restate things in layman's language so that no one listening in will get the idea that perhaps the conventional methodology is not so far off the mark as Bernstein maintains. The conventional methodology is truly dangerous. The historical data shows that it is not realistic to expect a 7 percent real return for a 30-year time-period beginning at the valuation levels that apply today. There is no informed analyst who takes issue with these core points (at least not in my understanding of things).

If I said something that is flat-out wrong, please correct me, JWR1945.
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Post by JWR1945 »

hocus2004 wrote:Both Bernstein and I accept that 7 percent (or perhaps 6.4 percent) is the long-term return number you obtain if you look at high valuation, moderate valuation, and low valuation start-years all mixed together. His criticism of the conventional methodology (as I understand it) is that to mix all the years together generates a "highly misleading" expectation as to what the 30-year real return is likely to be from a retirement beginning at a time of high valuation. It is by mixing all the valuation possibilities together in determining what long-term return to expect that the conventional methodology inappropriately "embeds" the 7 percent number.
This is accurate and well said.

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John R.
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Post by JWR1945 »

hocus2004 wrote:I appreciate your point that over very long time-periods the 7 percent (or 6.4 percent) number will gradually come closer to the mark. It seems to me that that is because the effect of the initial error of using a blended-valuation-level return expectation is diluted as over time the mix of valuation levels experienced by your portfolio becomes ever more varied. It still seems to me, however, that using the 7 percent number (or 6.4 percent number) for retirements beginning at low and high valuation levels is inappropriate. I can not come up with any justification for using the number obtained from looking at a blend of starting-point valuation levels when it is known that a more accurate returns expectation can be obtained by using a number determined by referencing only data from valuation levels similar to the one that applies at the time the retirement begins.
This is not it.

Safe Withdrawal Rates are influenced much more during the first 10 to 15 years than at any time later. That is, the long-term return doesn't matter nearly as much as the 10 to 15 year return. At the same time, valuations influence the 10 to 15 year returns much, much more than they do long-term (50-year or more) returns.

For those looking at the mathematics, you should need to focus on the ratio of the [final balance/initial balance] at 10 to 15 years, not at 50 years or more. For a specified final balance, low prices initially make this ratio larger and high prices make it lower. For a given variation in the initial prices (e.g., a factor of 3 or 4), the effect on r in the equation (1+r)^N = (the factor of 3 or 4) = [final balance/initial balance] is larger when N is 10 to 15 than when N is 50 or even bigger. [The Nth root of (3 or 4) is closer to 1 when N is 50 than when N is 10 or 15.]

Even though the effect of valuations decreases as the number of years increase when calculating the long-term annualized return of the market, the effect of valuations on Safe Withdrawal Rates begins to hold steady by 10 to 15 years. [Another way of stating this is that it takes only a very small change in the withdrawal rate to extend a portfolio's lifetime from 30 to 50 or more years.]

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Post by JWR1945 »

These tables show a tremendous amount of variation in the 15-year real rates of return. Sequences that have dummy data have been excluded.

These numbers are for the S&P500 index with all dividends reinvested.

Year, Percentage Earnings Yield, Final Balances starting from $100000, Annualized Real Rates of Return at Year 15

Code: Select all

1871     7.52    441102    10.40
1872     6.90    433873    10.28
1873     6.54    380685     9.32
1874     7.19    399762     9.68
1875     7.35    398617     9.66
1876     7.52    329896     8.28
1877     9.43    475828    10.96
1878    10.31    405743     9.79
1879     9.35    301143     7.63
1880     6.54    266914     6.76
1881     5.41    207489     4.99
1882     6.37    235537     5.88
1883     6.54    258537     6.54
1884     6.94    315362     7.96
1885     7.63    282362     7.17
1886     5.99    263865     6.68
1887     5.71    274876     6.97
1888     6.49    284409     7.22
1889     6.33    231868     5.77
1890     5.81    262642     6.65
1891     6.49    343200     8.57
1892     5.26    264482     6.70
1893     5.65    214254     5.21
1894     6.37    297386     7.54
1895     6.06    288436     7.32
1896     6.02    290206     7.36
1897     5.88    286092     7.26
1898     5.21    246372     6.20
1899     4.37    183202     4.12
1900     5.35    193876     4.51
1901     4.76    197949     4.66
1902     4.48    164720     3.38
1903     4.93    118347     1.13
1904     6.29    132447     1.89
1905     5.41    105643     0.37
1906     4.98     78054    (1.64)
1907     5.81     98912    (0.07)
1908     8.40    159300     3.15
1909     6.76    123001     1.39
1910     6.90    147159     2.61
1911     7.14    170019     3.60
1912     7.25    184719     4.18
1913     7.63    253093     6.39
1914     8.62    396727     9.62
1915     9.62    387231     9.45
1916     8.00    263860     6.68
1917     9.09    187012     4.26
1918    15.15    270395     6.86
1919    16.39    410013     9.86
1920    16.67    364301     9.00

Code: Select all

1921    19.61    613373    12.85
1922    15.87    646382    13.25
1923    12.20    356392     8.84
1924    12.35    405468     9.78
1925    10.31    337884     8.46
1926     8.85    255376     6.45
1927     7.58    186681     4.25
1928     5.32    150637     2.77
1929     3.69    122064     1.34
1930     4.48    154166     2.93
1931     5.99    241616     6.06
1932    10.75    266500     6.75
1933    11.49    243548     6.11
1934     7.69    176691     3.87
1935     8.70    234032     5.83
1936     5.85    191649     4.43
1937     4.63    170492     3.62
1938     7.41    272521     6.91
1939     6.41    238667     5.97
1940     6.10    332656     8.34
1941     7.19    466216    10.81
1942     9.90    581446    12.45
1943     9.80    482084    11.06
1944     9.01    552584    12.07
1945     8.33    507332    11.43
1946     6.41    394455     9.58
1947     8.70    616100    12.89
1948     9.62    633121    13.09
1949     9.80    692689    13.77
1950     9.35    665189    13.47
1951     8.40    591803    12.58
1952     8.00    467432    10.83
1953     7.69    460696    10.72
1954     8.33    478209    11.00
1955     6.25    285391     7.24
1956     5.46    227508     5.63
1957     5.99    241224     6.05
1958     7.25    298202     7.56
1959     5.56    169164     3.57
1960     5.46    114409     0.90
1961     5.41    140996     2.32
1962     4.72    126398     1.57
1963     5.18    113356     0.84
1964     4.63    101148     0.08
1965     4.29     90273    (0.68)
1966     4.15     92106    (0.55)
1967     4.90     87886    (0.86)
1968     4.65     97072    (0.20)
1969     4.72    105420     0.35
1970     5.85    126317     1.57
1971     6.06    149916     2.74
1972     5.78    175062     3.80
1973     5.35    146081     2.56
1974     7.41    211532     5.12
1975    11.24    341845     8.54
1976     8.93    250147     6.30
1977     8.77    301917     7.64
1978    10.87    364190     9.00
1979    10.75    373865     9.19
1980    11.24    360259     8.92
1981    10.80    422802    10.09
1982    13.53    600062    12.69
1983    11.42    610573    12.82
1984    10.11    685026    13.69
1985    10.00    740788    14.28
1986     8.54    565895    12.25
1987     6.70    375907     9.23
These tables show the narrow range of variation in the 50-year real rates of return. Sequences that have dummy data have been excluded.

These numbers are for the S&P500 index with all dividends reinvested.

Year, Percentage Earnings Yield, Final Balances starting from $100000, Annualized Real Rates of Return at Year 50

Code: Select all

1871     7.52    1398519    5.42
1872     6.90    1515075    5.59
1873     6.54    1791451    5.94
1874     7.19    1780685    5.93
1875     7.35    1980833    6.15
1876     7.52    2137094    6.32
1877     9.43    2791395    6.88
1878    10.31    3308257    7.25
1879     9.35    3784620    7.54
1880     6.54    2857353    6.93
1881     5.41    1840233    6.00
1882     6.37    1345962    5.34
1883     6.54    1305115    5.27
1884     6.94    1885857    6.05
1885     7.63    1709699    5.84
1886     5.99    1944707    6.12
1887     5.71    2257151    6.43
1888     6.49    1677134    5.80
1889     6.33    1806104    5.96
1890     5.81    1679033    5.80
1891     6.49    1654346    5.77
1892     5.26    1095142    4.90
1893     5.65    1228227    5.14
1894     6.37    1534044    5.61
1895     6.06    1650368    5.77
1896     6.02    2142909    6.32
1897     5.88    1522899    5.60
1898     5.21    1229449    5.15
1899     4.37    1056611    4.83
1900     5.35    1417061    5.45
1901     4.76    1412473    5.44
1902     4.48    1400004    5.42
1903     4.93    1607032    5.71
1904     6.29    1859062    6.02
1905     5.41    2126625    6.31
1906     4.98    2247329    6.42
1907     5.81    2407594    6.57
1908     8.40    2763587    6.86
1909     6.76    2850459    6.93
1910     6.90    2902838    6.97
1911     7.14    2912688    6.98
1912     7.25    3279564    7.23
1913     7.63    3159410    7.15
1914     8.62    3995060    7.65
1915     9.62    4861929    8.08
1916     8.00    4222831    7.77
1917     9.09    3972838    7.64
1918    15.15    6255777    8.62
1919    16.39    6712274    8.78
1920    16.67    5744992    8.44

Code: Select all

1921    19.61    6550430    8.72
1922    15.87    5871586    8.49
1923    12.20    5173310    8.21
1924    12.35    3920231    7.61
1925    10.31    2256815    6.43
1926     8.85    2415487    6.58
1927     7.58    2244111    6.42
1928     5.32    1415040    5.44
1929     3.69    1018564    4.75
1930     4.48    1133432    4.98
1931     5.99    1474075    5.53
1932    10.75    1867018    6.03
1933    11.49    2245833    6.42
1934     7.69    1725810    5.86
1935     8.70    1992009    6.17
1936     5.85    1601005    5.70
1937     4.63    1590222    5.69
1938     7.41    2120477    6.30
1939     6.41    2045172    6.22
1940     6.10    2283274    6.46
1941     7.19    2366025    6.53
1942     9.90    3629384    7.45
1943     9.80    3421105    7.32
1944     9.01    3119705    7.12
1945     8.33    2648633    6.77
1946     6.41    2579465    6.72
1947     8.70    4203849    7.76
1948     9.62    5630286    8.40
1949     9.80    6690902    8.77
1950     9.35    6305366    8.64
1951     8.40    4727385    8.02
1952     8.00    3506174    7.37
Graphs of the 15 and 50-Year Real Returns versus Percentage Earnings Yield (100E10/P) show well behaved data with the annualized real returns rising with earnings yield. The cluster of data points about a linear curve fit is tighter for the 50-year returns than for the 15-year returns. R-squared is 41% with the 15-year returns. R-squared is 61% with the 50-year returns.

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Post by JWR1945 »

Here are some references that show how tightly Safe Withdrawal Rates are related to stock market returns at 10 to 15 years in contrast to returns at 30 years.

A New Tool: Overview dated Wednesday, Apr 28, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2426
A New Tool dated Wednesday, Apr 28, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2427

The New Tool shows the relationship between 30-year Historical Surviving Withdrawal Rates and Annualized Real Returns as measured at different times during those 30 years.

With 50% stocks and 50% commercial paper, R-squared is 0.7381 at year 10, peaks at 0.9027 at year 14 and is still very high (0.8964) at year 15. At year 30 it is 0.0004.

With 80% stocks and 20% commercial paper, R-squared is 0.7478 at year 10, peaks at 0.9045 at year 14 and is still very high (0.891) at year 15. At year 30 it is 0.0318.

This means that Safe Withdrawal Rates are tightly related to the stock market's annualized real returns in years 10 to 15. They are almost totally independent of the stock market's return at 30 years. In all cases the stock market's return is closely related to earnings yield. Better prices (i.e., higher earnings yield as measured by 100E10/P) result in better returns.

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John R.
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Post by hocus2004 »

"This means that Safe Withdrawal Rates are tightly related to the stock market's annualized real returns in years 10 to 15. They are almost totally independent of the stock market's return at 30 years. In all cases the stock market's return is closely related to earnings yield. Better prices (i.e., higher earnings yield as measured by 100E10/P) result in better returns."￾

This is clearly an important point. I am probably saying something that suggests that I am taking issue with you on this. It's not my intention to do that. There is one point on which my understanding is rock solid (that the conventional SWR methodology is analytically invalid for purposes of determining SWRs). On many other points (such as the one you make in the words above) my understanding is foggy at best. I defer to others on that sort of stuff. I might ask questions on it from time to time in an aim to enhance my understanding. But I do not possess the skills needed to challenge anyone on these sorts of points, so I don't want anyone to think that is what I am doing.

It would help me if you could explain more fully the practical implications of what you are saying above. Say that there are two investors, Investor A and Investor B. Both are 40 years old on the day they hand in their resignations. Investor A uses a conventional SWR methodology study to inform his investment decisions. Investor B uses the Data-Based SWR Tool. I presume that you agree with me that Investor A possesses an edge at the start because the methodology he uses is analytically valid while the methodology used by Investor B is not. Does that edge diminish over time or is it a permanent edge? My understanding is that it is a permanent edge. My sense is that this is so basic a question that it is almost insulting to ask it. But I do not mean to be insulting. I am asking because it is very important for me to be clear in my thinking on this question and I also think that others listening in need to be clear on this point.

Assuming that the edge possessed at the start by Investor A is permanent, is that only because the two investors are at the stage of the investment cycle where they are making withdrawals from their portfolios? Or would Investor A possess an edge (and would it be temporary or permanant) even if the two investors were in the stage where they were accumulating capital over time?

I am not trying in any way to suggest that the technical points that you are making are not important. My sense is that they are very important. My concern is that we have an unusual debate going on here in that you and me and some others have accepted the basics of what the historical data really says and in some cases have moved on to exploration of more sophisticated points, while others are trapped in conventional methodology thinking (there's probably a third group that finds itself somewhere mid-way between these two positions). I don't want to do anything to discourage anyone from using this board to explore sophisticated points of SWR analysis. To the contrary. But I believe that learning is achieved through a building block process, and that it is the fundamentals that are most important. So I very much want to know as soon as possible if I have gotten on the wrong track on some fundamental point. I am probably going to be one of the last in the community to come to terms with some of the sophisticated stuff. But I have been the leader on getting the fundamentals right (probably because my lack of ability to understand sophisticated numbers stuff is so great that I am incapable of turning my attention to anything other than the fundamantals). I see my role as serving as a guide to those trying to come to terms with the fundamentals. So I tend to inject my comments when I see any possibility of misunderstanding developing on some fundamental question.

The thing that I want to be absolutely clear about is that it is never appropriate to use a mix of long-term returns from times of low valuation, moderate valuation, and high valuation to assess one's prospects for a particular long-term return on an investment decision taking place at some one particular point in time (at which one particular valuation level applies and not a mix of all the possibilities). This point is of such supreme significance that I am coming to the conclusion that we need to come up with some new terminology to distinguish the 7 percent (or 6.4 percent) long-term real return number referred to by Bernstein as being improperly embedded in the conventional methodology studies and the far lower (for recent years) long-term real return number that I see as being embedded in the JWR1945 methodology. Perhaps we should call the 7 percent (or 6.4 percent) number the "Unadjusted Long-Term Return"Â￾ or the "Mixed-Valuation Long-Term Return"Â￾ or something like that. People need to understand that it is a mistake to take the average daily high temperature over the course of a year in New York City to determine whether it is a good idea to plan a picnic in Central Park on February 1. The average daily high number is NOT a good rule of thumb for assessing what sort of temperature you are likely to get on February 1. It is a "highly misleading " (Bernstein's phrase) way of trying to get a handle on the question.

I think that it would help if we knew the 30-year real return assumptions "embedded"Â￾ in the JWR methodology. Would you be able to take the Calculated Rates, Safe Withdrawal Rates, and Unsafe Withdrawal Rates reported in the "Calculated Rates of the Last Decade"Â￾ thread, and say what annualized real return would apply to produce those numbers. It seems to me that knowing those numbers would help make clear to people the significance of the change we are proposing in urging that the conventional SWR methodology be replaced with the data-based methodology. The reality is that, when you purchase a stock index at a time of high valuation, you are acquiring an asset of less intrinsic value that the investor who purchases a stock index at a time of low valuation or moderate valuation. Seeing in dollar terms how great the difference in value propositions can be might help people come to understand better the potential of the data-based SWR tool to help aspiring early retirees achieve their goals many years sooner than would otherwise be possible.
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Post by hocus2004 »

"I presume that you agree with me that Investor A possesses an edge at the start because the methodology he uses is analytically valid while the methodology used by Investor B is not. "

This is another case in which I failed to read a post over enough times before hitting the "Submit" button. My actual presumption is just the opposite of what is stated in the words above. I presume that Investor B (the one using the data-based methodology) possesses the edge.
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Post by JWR1945 »

hocus2004 wrote:This point is of such supreme significance that I am coming to the conclusion that we need to come up with some new terminology to distinguish the 7 percent (or 6.4 percent) long-term real return number referred to by Bernstein as being improperly embedded in the conventional methodology studies and the far lower (for recent years) long-term real return number that I see as being embedded in the JWR1945 methodology.
This is the key point: When it comes to Safe Withdrawal Rates, the long-term return does not matter very much. The intermediate-term return does.

[Ignoring some mathematical details, primarily related to the choice of definitions:] The long-term return matters only because the average of intermediate-term returns equals the long-term return.

Consider 1929 and 1949. The year 1929 had an earnings yield of 3.69%. Its 50-year return was 4.75% and its 15-year return was 1.34%. The year 1949 had an earnings yield of 9.80%. Its 50-year return was 8.77% and its 15-year return was 13.77%.

If we were to focus on the long-term, we would look at 50-year returns and see that different valuations had a noticeable, but small, effect: 4.75% for 1929 and 8.77% for 1949. When we focus on the intermediate-term, we look at the 15-year return. Valuations had a profound effect: 1.34% for 1929 and 13.77% for 1949.

Valuations have a large influence on intermediate-term returns. They also have a big influence on Safe Withdrawal Rates.

Now let us see what William Bernstein is talking about. When he mentions the 7% return that is embedded in the historical record, his point [poorly stated and possibly not discerned consciously] is that the conventional methodology fails to distinguish among intermediate-term returns. The average of intermediate returns is 7%. This corresponds to medium levels of valuations. It does not separate those sequences with low intermediate-term returns, which correspond to high valuations. Nor does it separate those sequences with high intermediate-term returns, which correspond to low valuations.

William Bernstein realizes that using a 7% return is overly optimistic at today's valuations. The long-term return will remain very close to 7% in the long-term regardless of today's valuations. William Bernstein prefers to use 3% to 4% as his input to his Monte Carlo models. Those numbers are intermediate-term numbers.

William Bernstein may not be fully aware of some of the implications of what he is doing. If you were to press the issue, I suspect that he would have to take a little time for him to untangle the contradiction in using 3% to 4% as determined by the Gordon Model while simultaneously mentioning that 7% is the long-term return of the market. The Gordon Model calculates a result for the very long-term. As a practical matter, its applicability is limited to the intermediate-term. The assumptions behind the mathematics to apply fall apart after a few years.

Have fun.

John R.
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Post by JWR1945 »

hocus2004 wrote:It would help me if you could explain more fully the practical implications of what you are saying above. Say that there are two investors, Investor A and Investor B. Both are 40 years old on the day they hand in their resignations. Investor B uses a conventional SWR methodology study to inform his investment decisions. Investor A uses the Data-Based SWR Tool. I presume that you agree with me that Investor A possesses an edge at the start because the methodology he uses is analytically valid while the methodology used by Investor B is not. Does that edge diminish over time or is it a permanent edge? My understanding is that it is a permanent edge. [The identities of Investors A and B have been corrected.]
Investor A always possesses more accurate information than Investor B.

Investor A has more accurate information when he determines how much money he needs for retirement. I assert that this is always worth knowing. If Investor B underestimates his needs, his retirement is in danger. If Investor B overestimates what is required, he may give up and conclude that he will never be able to retire.

In a sense, the advantage of accurate information can diminish. If the market produces fabulous returns in the early years, a retiree's portfolio may grow so dramatically that the retiree will have enough in spite of himself.

Even then, people tend to adjust their standard of living in accordance with the money available instead of matching their needs.

Have fun.

John R.
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Post by JWR1945 »

Summary:

Safe Withdrawal Rates depend upon intermediate-term returns. The likelihood of success or failure is usually known by the eleventh year. Typically, a portfolio has grown sufficiently that safety is no longer in doubt or it is already in trouble.

The long-term return of the market is important primarily because it is the average of intermediate-term returns.

Valuations have a profound effect in the intermediate-term.

The conventional methodology treats all intermediate-term returns equally. In effect, it assumes that valuations are always typical, never high and never low.

When we apply valuations in our calculations, we limit ourselves to those intermediate-term conditions that apply to our problem. We are able to separate the effects of high, medium and low valuations. This gives us much greater accuracy and precision.

When William Bernstein and others use the Gordon Equation to provide inputs to a Monte Carlo model, they are actually estimating the intermediate return of the market, not the long-term return. This is because their Monte Carlo models are calculating Safe Withdrawal Rates and such calculations depend much more on the first few years than on later years. [The Gordon Equation (theoretically) calculates a long-term return.]

Monte Carlo models, in effect, convert any long-term input into an intermediate-term number.

This is the source of confusion. Theoretically, Monte Carlo models have an error built in. They never see the later adjustments as stock market returns gradually revert back to 7%. This is not a practical problem. Returns that happen later on have only a small effect on Safe Withdrawal Rates.

Have fun.

John R.
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Post by JWR1945 »


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Post by hocus2004 »

"I think that the 15-year real returns are more important. I have outlined the reason just prior to this post. Intermediate-term returns determine Safe Withdrawal Rates, not long-term returns."

That's very helpful. JWR1945. Thanks.

I still would like to know the 30-year numbers. I presume that they are higher than the 15-year numbers. I believe that it would be helpful to compare the 15-year numbers with the 30-year numbers, and also to consider the relationship between the 30-year return numbers and the 30-year SWR numbers.

This has turned out to be a most illuminating thread (at least for me and I hope for a few others). I much appreciate your continued participation. My wife gets mad at me when I ask too many follow-up questions. So I try to keep that under control a bit. But once a journalist....
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Post by JWR1945 »

hocus2004
I still would like to know the 30-year numbers. I presume that they are higher than the 15-year numbers. I believe that it would be helpful to compare the 15-year numbers with the 30-year numbers, and also to consider the relationship between the 30-year return numbers and the 30-year SWR numbers.
I already have the answers for 50-year returns. I do not have them yet for 30-year returns.

I had already made graphs for 1923-1952 and 1871-1952 50-year returns versus the percentage earnings yield 100E10/P. I had Excel fit each graph with a straight line.

With 50-year periods and excluding all sequences with dummy data, only 1923-1952 results are available for making a curve fit if we stay within the modern era. The formula is y = 0.3228x+4.0934, the variation in the data looks like plus and minus 1% and R-squared is 0.4719, which is good. In terms of P/E10, the equation is y = [32.28 / (P/E10)]+4.0934.

If we use 1871-1952 results, the formula is y = 0.2788x+4.3637, the variation in the data is a little bit less than plus and minus 2% and R-squared is 0.6094, which is surprisingly good. In terms of P/E10, the equation is y = [27.88 / (P/E10)]+4.3637.

Once again, I looked up the values of P/E10 from the post Calculated Rates of the Last Decade dated Wednesday, Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657

Code: Select all

1995    20.219819
1996    24.763281
1997    28.333753
1998    32.860928
1999    40.578255
2000    43.774387
2001    36.98056
2002    30.277409
2003    22.894158
The last entry in Professor Shiller's list is for November 2003. The S&P500 index was at 1054.87 and P/E10 was 25.898702. [To help with scaling: today's the S&P500 index started at 1134.41. If ten-year earnings were the same as in November 2003, today's P/E10 would be 25.898702*(1134.41/1054.87) = 27.851533.]
I used the 1871-1952 results in the following table. The formula is y = [27.88 / (P/E10)]+4.3637 and the confidence limits are plus and minus 2%.

Year, 1871-1952 Calculated 50-Year Return, Lower Confidence Limit, Upper Confidence Limit

Code: Select all

1995    5.74   3.74   7.74
1996    5.49   3.49   7.49
1997    5.35   3.35   7.35
1998    5.21   3.21   7.21
1999    5.05   3.05   7.05
2000    5.00   3.00   7.00
2001    5.12   3.12   7.12
2002    5.28   3.28   7.28
2003    5.58   3.58   7.58
Today's value would be only slightly more than that of 1997. It would be less than that of 1996.

I prefer to use the 1871-1952 data set because of the number of data points. It is necessary to verify that the numbers from the earlier era are still representative in the modern era. [There is an addition issue about the amount of scatter. I am satisfied to use the wider range of variation associated with the 1871-1952 data.]

Here are 50-Year Calculated Returns based on 1923-1952. I have excluded the confidence limits from this table because of the limited number of data points. The formula is y = [32.28 / (P/E10)]+4.0934 [and the confidence limits are at least plus and minus 1% but no wider than plus and minus 2%].

Year, 1923-1952 Calculated 50-Year Return

Code: Select all

1995    5.69
1996    5.40
1997    5.23
1998    5.08
1999    4.89
2000    4.83
2001    4.97
2002    5.16
2003    5.50
Once again, today's value would be only slightly more than that of 1997. It would be less than that of 1996.

The two sets of calculated returns are similar. The calculated returns based on 1923-1952 data vary from 4.83% in 2000 to 5.69% in 1995. The calculated returns based on 1871-1952 data vary from 5.00% in 2000 to 5.74% in 1995.

Have fun.

John R.
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Post by JWR1945 »

I wrote this in an earlier post:
With 50% stocks and 50% commercial paper, R-squared is 0.7381 at year 10, peaks at 0.9027 at year 14 and is still very high (0.8964) at year 15. At year 30 it is 0.0004.

With 80% stocks and 20% commercial paper, R-squared is 0.7478 at year 10, peaks at 0.9045 at year 14 and is still very high (0.891) at year 15. At year 30 it is 0.0318.[Emphasis added.]
Small values of R-squared indicates that there is very little influence. In this instance, the relationship is between 30-year Historical Surviving Withdrawal Rates and the annualized (real, total) return. These exceedingly small numbers (0.0318 or 3.18% and 0.0004 or 0.04%) tell us that the annualized total return has almost no influence at all on Historical Surviving Withdrawal Rates.

The effects of valuations are almost totally extinguished when using 30-year returns.

The effect returns on Historical Surviving Withdrawal Rates are strongest at 14 years. They are consistently strong between 10 to 20 years. The effect of valuations on returns are strong during these years. Valuations cause 15-year returns to vary from 1.5% (roughly) to 15% (roughly).

Have fun.

John R.
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Post by JWR1945 »

This has turned out to be a most illuminating thread (at least for me and I hope for a few others). I much appreciate your continued participation. My wife gets mad at me when I ask too many follow-up questions. So I try to keep that under control a bit. But once a journalist....
I have mentioned the value of our interaction many times. These exchanges illustrate what I mean. It would be interesting to know whether others agree with my assessment that they are quite valuable.

Have fun.

John R.
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