Is the Raddr Methodology Analytically Valid?

Research on Safe Withdrawal Rates

Moderator: hocus2004

JWR1945
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Post by JWR1945 »

Here are the actual 30-year annualized real returns of the S&P500 with all dividends reinvested using the calculator (and Professor Shiller's database). I have limited the final year to 1972 since the calculator uses dummy stock market returns after 2002.

Year, Percentage Earnings Yield, Final Balance If Starting With $100000, 30-Year Annualized Real Return.

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1871    7.52    1163913    8.53
1872    6.90    1192613    8.61
1873    6.54    1082699    8.26
1874    7.19     926920    7.70
1875    7.35    1046934    8.14
1876    7.52    1132204    8.43
1877    9.43    1258480    8.81
1878   10.31     869319    7.47
1879    9.35     895559    7.58
1880    6.54     769878    7.04
1881    5.41     602147    6.17
1882    6.37     673854    6.57
1883    6.54     636962    6.37
1884    6.94     577749    6.02
1885    7.63     547433    5.83
1886    5.99     522318    5.67
1887    5.71     452776    5.16
1888    6.49     336589    4.13
1889    6.33     307102    3.81
1890    5.81     277463    3.46
1891    6.49     267880    3.34
1892    5.26     261604    3.26
1893    5.65     341306    4.18
1894    6.37     365790    4.42
1895    6.06     424460    4.94
1896    6.02     493406    5.46
1897    5.88     528468    5.71
1898    5.21     623551    6.29
1899    4.37     726812    6.84
1900    5.35     750750    6.95
1901    4.76     522309    5.66
1902    4.48     308047    3.82
1903    4.93     320005    3.95
1904    6.29     543050    5.80
1905    5.41     384860    4.59
1906    4.98     478760    5.36
1907    5.81     639348    6.38
1908    8.40     567732    5.96
1909    6.76     498732    5.50
1910    6.90     497226    5.49
1911    7.14     434187    5.02
1912    7.25     344835    4.21
1913    7.63     381251    4.56
1914    8.62     484263    5.40
1915    9.62     596978    6.14
1916    8.00     637530    6.37
1917    9.09     498388    5.50
1918   15.15     658542    6.48
1919   16.39     724459    6.82
1920   16.67     852581    7.41

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1921   19.61   1175526    8.56
1922   15.87   1102033    8.33
1923   12.20    971242    7.87
1924   12.35    967719    7.86
1925   10.31   1123990    8.40
1926    8.85   1190605    8.61
1927    7.58   1085446    8.27
1928    5.32    726195    6.83
1929    3.69    674508    6.57
1930    4.48    782133    7.10
1931    5.99    953068    7.80
1932   10.75   1641908    9.78
1933   11.49   1541953    9.55
1934    7.69   1223922    8.71
1935    8.70   1556754    9.58
1936    5.85   1134187    8.43
1937    4.63    796936    7.16
1938    7.41   1255491    8.80
1939    6.41   1141326    8.45
1940    6.10    949370    7.79
1941    7.19   1060678    8.19
1942    9.90   1402584    9.20
1943    9.80   1437584    9.29
1944    9.01    934771    7.74
1945    8.33    580433    6.04
1946    6.41    556167    5.89
1947    8.70    778739    7.08
1948    9.62    717679    6.79
1949    9.80    700640    6.70
1950    9.35    600485    6.16
1951    8.40    545088    5.82
1952    8.00    410805    4.82
1953    7.69    447208    5.12
1954    8.33    504126    5.54
1955    6.25    360498    4.37
1956    5.46    341070    4.17
1957    5.99    422291    4.92
1958    7.25    435616    5.03
1959    5.56    357834    4.34
1960    5.46    391101    4.65
1961    5.41    352697    4.29
1962    4.72    381618    4.57
1963    5.18    412830    4.84
1964    4.63    378156    4.53
1965    4.29    325216    4.01
1966    4.15    389427    4.64
1967    4.90    527368    5.70
1968    4.65    592697    6.11
1969    4.72    722152    6.81
1970    5.85    935743    7.74
1971    6.06    848366    7.39
1972    5.78    658071    6.48
Have fun.

John R.
JWR1945
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Post by JWR1945 »

I have made graphs for 1923-1972 and 1871-1972 30-year returns versus the percentage earnings yield 100E10/P. I had Excel fit each graph with a straight line.

With 30-year periods and excluding all sequences with dummy data, results from 1923-1972 are available for making a curve fit if we stay within the modern era. The formula is y = 0.4159x+3.764 and the variation in the data is very close to and slightly greater than plus and minus 2%. R-squared is 0.3018. In terms of P/E10, the equation is y = [41.59 / (P/E10)]+3.764.

If we use 1871-1972 results, the formula is y = 0.2614x+4.4281 and the variation in the data is just a little bit less than plus and minus 3%. R-squared is only 0.2026. In terms of P/E10, the equation is y = [26.14 / (P/E10)]+4.4281.

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

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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 1923-1972 results to make the following table. The formula is y = [41.59 / (P/E10)]+3.764 and the confidence limits are plus and minus 2%. Today's S&P500 index level is close to the referenced level of 1134.11.

Year, 1923-1972 Calculated 30-Year Return, Upper Confidence Limit, Lower Confidence Limit

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1995    5.82   7.82   3.82
1996    5.44   7.44   3.44
1997    5.23   7.23   3.23
1998    5.03   7.03   3.03
1999    4.79   6.79   2.79
2000    4.72   6.72   2.72
2001    4.89   6.89   2.89
2002    5.14   7.14   3.14
2003    5.58   7.58   3.58
Today's Calculated 30-Year Return would be only slightly more than that of 1997. It would be less than that of 1996.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"I have made graphs for 1923-1972 and 1871-1972 30-year returns versus the percentage earnings yield 100E10/P."

Awesome! I have said it several times before, but it needs to be said again. You are an amazing resource for the entire Passion Saving/FIRE/Retire Early community, JWR1945.

Not all that you have put forward on this thread has entirely clicked with me yet. But it is beginning to click. I am well on the way to putting another piece of the big puzzle into place.

I believe that this thread is going to be a big help to me in taking our findings to the Big Bad World that exists outside the cozy confines of our little discussion board community. The SWR matter is strange in that the thing that makes the story unconvincing when people first hear it is not a lack of data supporting it--we have supportive data coming out of our ears. The part that is hard to believe is how something so obvious could have been missed by so many smart people for so many years. It appears to me that the point you kept driving at in this thread may go a long way towards explaining that riddle.

As I understand things today, it is only for about 20 years out into the future (perhaps less) that the starting-point valuation level has a big effect on the expected long-term return. That would explain why some very smart people generally follow a practice of not making a valuation adjustment when determining the long-term real return of investment in a stock index.

What they missed by doing that is the critical importance of the starting-point valuation level to the survival of retirement portfolios. It seems to me that what you are saying here is that there is some theoretical justification for not adjusting for valuation when determining the long-term return number but that for practical real-world reasons it is essential that retirees make such adjustments in assessing the long-term safety of their portfolios. I need to go back and read that "Illusion of Numbers" thread more carefully! There is a strange relationship between the theoretical and the practical here that tells a fascinating story about the risks of jumping to quick conclusions when putting together analytical frameworks for the examination of various possible investing strategies.

Your number for the most likely 30-year real-return starting from today's valuation level is about 5.3 percent and the range of possibilities goes from 3.3 to 7.3. Assume an investor who is 25 years old and who does not expect to retire for at least 30 years. Is it fair to say that, while this investor might obtain better results by keeping a good portion of his money out of stocks until prices return to more moderate levels, he would not be doing something all that terrible to put a good portion of it in stocks so long as he is absolutely certain that he possesses the inner strength to keep the same percentage in stocks through some severe price drops?
JWR1945
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Post by JWR1945 »

"I have made graphs for 1923-1972 and 1871-1972 30-year returns versus the percentage earnings yield 100E10/P."
This is not difficult for those who use windows and have Excel, which happens to exclude hocus2004.

First, you download my latest version of the (modified) Retire Early Safe Withdrawal Calculator, primarily to get its data analysis and data summary tables (in the region of A2600 and A2800 for nominal returns and A3200 and A3400 for real returns). Function key F5 can get you to these locations fast. The combination CTRL+Home gets you back to the starting location A1.

Then you set up the calculator. For this information, I set up the calculator with a starting balance of $100000, a 100% stock allocation, 0.000% for the initial withdrawal rate and expenses, 0% of capital gains removed and 100% of all dividends and interest reinvested. I chose to include adjustments to inflation in accordance with the CPI.

As a convenience, you copy whatever data interests you into a blank spreadsheet. For this kind of information, I copied the calendar year, values of 100E10/P from previous calculations (many older posts include this Percentage Earnings Yield information), the dollar balances (starting from $100000) from the A3200 area and the annualized real returns from the A3400 area. Since I was interested in data at year 30, I scrolled over until the year N was 30 (years into retirement for each sequence). Then I copied the columns of data corresponding to N = 30 and for calendar years 1871 through 1972.

From this new spreadsheet, I made my charts and curve fits. In Excel you highlight whatever you are interested in posting, then click Insert at the top (where you read File, Edit, etc.) and select Chart. I made scatter plots (which I have identified as my default selection). I highlighted the columns with 100E10/P, dollar balances at year 30 and annualized real returns at year 30. I did not highlight the calendar year. But having this available makes it easy to select portions such as 1923-1972 as well as using the entire period of 1871-1972. It is convenient to have 100E10/P to the left of the dollar balances and annualized real returns. The leftmost column becomes the default selection for the x-axis. (You can change this, but it is easier to have Excel select this for you.)

In making graphs (or charts) with scatter plots, you choose which data sets to use in the Data Series section. In addition, I always choose to include Major Gridlines and to put the legend at the bottom of a graph. I make separate charts instead of embedding the charts into a spreadsheet.

Once the initial work is done, you edit the spreadsheet. You right click whatever you wish to edit. If you put the mouse pointer on a data point and right click, you can Format the Data Series and you can also Add a Trendline. When you add a trendline, select whichever curve type that you want. The default is linear (i.e., a straight line) and that is what I almost always choose. Do NOT click OK. Click on the Tab. You will find three choices related to calculating equations. I almost always leave the first choice, which is to specify an intercept, blank. But I check the choices to have Excel write the equation on the chart and to include the value of R-squared.

Those are all of the critical steps for someone who has Excel but hasn't done anything like this before.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:As I understand things today, it is only for about 20 years out into the future (perhaps less) that the starting-point valuation level has a big effect on the expected long-term return. That would explain why some very smart people generally follow a practice of not making a valuation adjustment when determining the long-term real return of investment in a stock index.

What they missed by doing that is the critical importance of the starting-point valuation level to the survival of retirement portfolios. It seems to me that what you are saying here is that there is some theoretical justification for not adjusting for valuation when determining the long-term return number but that for practical real-world reasons it is essential that retirees make such adjustments in assessing the long-term safety of their portfolios.
Although I was aware of each point individually, I had not put them together in my mind prior to this thread.

The early years are critical to portfolio survival and Safe Withdrawal Rates. Safe Withdrawal Rate calculators, including Monte Carlo models, automatically emphasize the early years. The 10 to 15 (or 20) year returns are much more important in Safe Withdrawal Rate calculations than any long-term number.

Valuations have a big effect on investment returns from 10 to 20 years. This is why they are critically important when making Safe Withdrawal Rate calculations.

Valuations have only a small effect when describing long-term rates of return.

Because of the nature of Monte Carlo models (i.e., inner workings), they translate their inputs, which are supposed to be long-term returns, into intermediate-term returns.

[Errors caused by later years are very small. For example, reducing one's withdrawal rate by 0.1% or 0.2% (from 4.0%) usually adds a decade or more to portfolio survivability.]

Most, if not all, users of Monte Carlo models are unaware of these facts. They do not realize the significance that calculations have on the effective time frame of their inputs.

These points also apply to the Historical Sequence approach. The Historical Sequence approach already has valuations built in as part of the historical record. Users are not aware of what the historical valuations and returns actually were, nor their time frames. Users of Monte Carlo models have always been aware of investment returns. Monte Carlo models require inputs describing investment returns.

Have fun.

John R.
Last edited by JWR1945 on Fri Oct 08, 2004 4:42 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:Your number for the most likely 30-year real-return starting from today's valuation level is about 5.3 percent and the range of possibilities goes from 3.3 to 7.3. Assume an investor who is 25 years old and who does not expect to retire for at least 30 years. Is it fair to say that, while this investor might obtain better results by keeping a good portion of his money out of stocks until prices return to more moderate levels, he would not be doing something all that terrible to put a good portion of it in stocks so long as he is absolutely certain that he possesses the inner strength to keep the same percentage in stocks through some severe price drops?
Such an investor typically does not have his total investment at the start. Generally, he should use dollar cost averaging, which saves him 5% to 10% or more on his average cost per share purchased. In addition, it is best that he makes his mistakes as early as possible, while his holdings are small.

People do not understand their risk tolerance with stocks until they have lived through at least one major market decline. They have to see prices drop, feel the effect and later see prices climb back up, all in a way that is both erratic and dramatic. It is good for the new investor to learn about his actual risk tolerance as early as possible.

In addition, some investments do better than others when starting from high valuations. Value based selections in general and dividend based strategies in particular have less of a downside risk than growth strategies.

The single, most important consideration is avoiding a panic and selling out close to a bottom.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"Such an investor typically does not have his total investment at the start. "

OK. Forget about the 25-year-old. 25-year-olds have the world on a string anyway. They don't need our help.

Say that our investor has just turned 48, that he has saved a good bit, that he is fully aware of the risks of investing in stocks at today's valuation levels, and that he has family responsibilities. He would like to have some stocks in his portfolio for all of the obvious reasons and for some not-so-obvious ones as well (Believe it or not, I know a guy who fits the bill!)

Say that this individual would like to put 10 percent or 20 percent or perhaps even 30 percent of his portfolio in stocks. But he can't be taking wild risks because he depends on the income streams generated by his investments to provide for himself and his family. Say that he is confident that, even if stock prices were to fall 90 percent, he would not lower his stock allocation so long as stocks comprised only 20 percent of his portfolio and so long as he knew that the historical data supported his long-term return expectations.

Would you tell this poor befuddled soul that the historical data indicates that he can pretty much count on a 3.3 percent real return at the end of 30 years, that it is likely that he will get 5.3 percent, and that there is a long-shot chance that he might even get as much as 7.3 percent?

This guy is not a numbers guy. But he likes to have the numbers working on his behalf when its possible for him to arrange for that.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:Say that our investor has just turned 48, that he has saved a good bit, that he is fully aware of the risks of investing in stocks at today's valuation levels, and that he has family responsibilities. He would like to have some stocks in his portfolio for all of the obvious reasons and for some not-so-obvious ones as well (Believe it or not, I know a guy who fits the bill!)
So do I.
Say that this individual would like to put 10 percent or 20 percent or perhaps even 30 percent of his portfolio in stocks. But he can't be taking wild risks because he depends on the income streams generated by his investments to provide for himself and his family. Say that he is confident that, even if stock prices were to fall 90 percent, he would not lower his stock allocation so long as stocks comprised only 20 percent of his portfolio and so long as he knew that the historical data supported his long-term return expectations.

Would you tell this poor befuddled soul that the historical data indicates that he can pretty much count on a 3.3 percent real return at the end of 30 years, that it is likely that he will get 5.3 percent, and that there is a long-shot chance that he might even get as much as 7.3 percent?
He can do much better.

First, notice than this person's immediate concern is income streams. He can purchase reliable income streams offering more than 3.3% plus inflation. I would recommend a dividend-based strategy based upon books by Lowell Miller and David Dreman, specifically The Single Best Investment and Contrarian Investment Strategies: The Next Generation. Because of his situation, I would recommend that he seek a broad level of diversification. I would recommend trading infrequently to keep costs down. I would recommend that he start from a sufficiently high initial dividend yield. For example, if he were seeking to withdraw 4% plus inflation each year and if his stock initially yielded 4.5% and if his dividend amount stayed constant, it would take 4 years before inflation (at 3%) would catch up to him (i.e., to reduce the dividend amount to 4% in terms of real dollars). If the initial dividend yield were 5%, it would take 7.5 years to reduce the dividend payments to 4% plus inflation (based upon his initial investment).

It is not necessary for him to limit his selections to Dividend Achievers that increase dividends every year for 10 consecutive years. It is sufficient for his dividends to increase enough to catch up with inflation every 3 or 4 years provided that his initial dividend yield is adequate.

Starting at a reasonably high level of dividends with a reasonable expectation of dividend growth is sufficient.

In addition, it will take several years for this person to put together a diversified portfolio. There are always some stocks that are bargains relative to the rest of the market (although not necessarily on an absolute basis). Careful, patient stock selection limits his downside risk.

Technically, withdrawing dividends alters the long-term returns. But more importantly, it is reasonable to expect his income stream to grow more than 4% plus inflation and last in perpetuity (independent of capital gains after 30 years). There is considerable upside potential by year 30 in spite of today's valuations.
This guy is not a numbers guy. But he likes to have the numbers working on his behalf when its possible for him to arrange for that.
His most important numbers are captured by the Gordon Equation as applied to individual stocks:
The expected return equals the initial dividend yield + the dividend growth rate.

This equation works reasonably well provided that the initial dividend yield is sufficient and that the investor does not put too much emphasis on dividend growth rate estimates. Dividend growth can evaporate overnight. The initial dividend yield is very likely to provide a floor, especially if the company is sound financially. (Check for a good, investment grade bond rating). Finally, realize that the inputs to the equation become less and less reliable as time passes. He should review, but not necessarily change, his holdings within 7 to 10 years.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"He can do much better. First, notice than this person's immediate concern is income streams. He can purchase reliable income streams offering more than 3.3% plus inflation."

I understand. I'm not going to take all of my money and stick it in an S&P index fund because of the numbers that have been put forward in this thread. There are indeed other asset classes that are generally more attractive.

But it's possible that seeing these numbers could influence me to put a small percentage of my portfolio in an S&P index fund. As a general proposition, I like the idea of focusing on high-dividend stocks. I like that idea quite a bit. But I don't view the high-dividend-stock asset class as the one perfect asset class any more than I view the S&P-index-fund asset class as the one perfect asset class. My view is that all asset classes have their pros and cons and that you need to analyze as many as possible to make the best choice you are capable of making as to which ones to include in your portfolio and at what percentages.

There's a good chance that I won't be putting any money into an S&P index fund at today's valuations. But that does not mean that I do not benefit from knowing the number that is a reasonable 30-year return expectation for that asset class. That number informs me. It helps me compare the S&P class with other classes and determine which offers the superior value proposition. I could even use it in deciding what personal withdrawal rate (PWR) to apply for the portion of my portfolio directed to high-dividend stocks. The reasoning would be: (1) S&P stocks provide a minimum 30-year return of 3.3 at these valuation levels according to the historical data; (2) well-selected high-dividend stocks are likely to do better for the reasons cited on earlier threads; and therefore (3) I can safely use a take-out of 3.3 for the money invested in high-dividend stocks or perhaps a number a bit higher than that.

There are lots of ways to make use of the numbers developed from SWR analysis. My sense is that most people have never made use of more than a small fraction of the power of the tool. I think that is because the conventional methodology approach has until now been dominant. That methodology is rooted in nonsense assumptions, so obviously the numbers it generates are often nonsense numbers. People sense this even if they do not focus on it. The common response seems to be to limit one's use of the tool.

I propose something different. I propose not limiting one's use of SWR analysis, but enhancing SWR analysis so that it becomes a more legitmate way of assessing the size of income streams likely to be generated by various asset classes. When you build on a reasonably strong foundation, the end resullt is more stable and useful.

People have always used SWR numbers to form in their minds quick judgments as to what sorts of returns stocks will provide during the accumulation phase. It's not technically proper to do this because SWR analyses are set up to deal with the question of what is likely to happen during the distribution phase. Many people have a need for more quantifiable information re what is likely to happen in the accumulaton phase. So they jump on the SWR number, persumably making little adjustments in their heads to make the number sort of applicable to the assumulation phase. The problem with this reality, of course, is that the adjustments they make in their heads are not well-considered adjustments. The SWR numbers are wrong to begin with, and then they add on top of them adjustments that are also wrong, and they end up with doubly wrong numbers. You end up with someone like intercst saying that the "optimal" way to get to a safe retirement is with a 74 percent S&P allocation and lots of otherwise smart people shaking their heads and thinking "that sounds about right."

The question of whether to go with S&P stocks or with high-dividend stocks is a strategic question. I am generally in agreement with your view that high-dividend stocks offer a better deal today. But it is my sense that we are generally not ready yet to proceed too far with consideration of strategic questions. There are still a lot of factual questions that we have not answered; actually, there are a good number that we have hardly even addressed. Until we have all the facts on the table, it is not possible to make fully informed recommendations re stratagy.

I'm not saying that we should not discuss strategy at all. We all live in real time, and we need to make portfolio decisions in the world in which we live, so we are required by the fact that SWR analysis is not yet fully developed to make decisions without the benefit of SWR analysis. People would get bored if we never paid any mind to strategy. But I think that our most important work is developing and refining the SWR tool. The numbers put forward in this thread advance development of the SWR tool in important ways, in my view. I see this as a major step forward, although we obviously still need to refine our tentative findings.

We always knew that there was some relationship between SWRs and long-term returns. We also always knew that the relationship was not perfect. We didn't know the extent to which the two numbers differed, and, in my case, I did not possess a clear understanding of the reasons why they differed. With this thread we are making progress. I am now getting close to the point where I can explain better than I could before the reasons why they are different (I still have work to do here) and I can also give people a rough number to use as a 30-year return expectation for investments in an S&P index made during the accumulation phase. That's a very big deal indeed.

Again, that doesn't mean that I am recommending that people invest in an S&P index rather than in high-dividend stocks. My guess is that when we get to the end of this we will learn that it depends on the circumstances. Some people are probably better off going with an S&P index and some are probably better off going with high-dividend stocks. Some are probably better off going with a mix. I see it as the primary mission of this board to mine the data that provides us with the best information available to man as to which way people should go when faced with the various possible circumstances that can appear before them.

This is one of our best threads ever, JWR1945. Thanks once again for your willingness to hang in there so long. You're not just a Numbers Guy Extraordinaire. You are a PATIENT Numbers Guy Extraordinare. Even better than that, you are a Patient Numbers Guy Extraordinaire willing to work for the benefit of others for free. That's quite a combination.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:I understand. I'm not going to take all of my money and stick it in an S&P index fund because of the numbers that have been put forward in this thread. There are indeed other asset classes that are generally more attractive.

But it's possible that seeing these numbers could influence me to put a small percentage of my portfolio in an S&P index fund.
Here are the relevant 30-year numbers.
Year, 1923-1972 Calculated 30-Year Return, Upper Confidence Limit, Lower Confidence Limit

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1995    5.82   7.82   3.82
1996    5.44   7.44   3.44
1997    5.23   7.23   3.23
1998    5.03   7.03   3.03
1999    4.79   6.79   2.79
2000    4.72   6.72   2.72
2001    4.89   6.89   2.89
2002    5.14   7.14   3.14
2003    5.58   7.58   3.58
Today's Calculated 30-Year Return would be only slightly more than that of 1997. It would be less than that of 1996.
Here are the relevant 15-year numbers.
These are my calculated values of the 15-year returns. I have added 5% for a confidence limit on the high side. I have subtracted 5% for a confidence limit on the low side.

Year, Calculated 15-Year Return, Upper Confidence Limit, Lower Confidence Limit

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1995   3.21   8.21   (1.79)
1996   1.99   6.99   (3.01)
1997   1.30   6.30   (3.70)
1998   0.64   5.64   (4.36)
1999  (0.14)  4.86   (5.14)
2000  (0.38)  4.62   (5.38)
2001   0.19   5.19   (4.81)
2002   0.99   5.99   (4.01)
2003   2.43   7.43   (2.57)
Today's S&P500 index is close enough to 1134.41 to suggest that today's projections are similar to, but slightly higher than, those of 1997 and lower than those of 1996.

The 30-year numbers (i.e., annualized real return with all dividends reinvested) led hocus2004 to ponder:
Your number for the most likely 30-year real-return starting from today's valuation level is about 5.3 percent and the range of possibilities goes from 3.3 to 7.3. Assume an investor..who does not expect to retire for at least 30 years. Is it fair to say that, while this investor might obtain better results by keeping a good portion of his money out of stocks until prices return to more moderate levels, he would not be doing something all that terrible to put a good portion of it in stocks so long as he is absolutely certain that he possesses the inner strength to keep the same percentage in stocks through some severe price drops?
Looking at the 30-year results, the answer is yes. Today's situation is very similar to 1997 and slightly more favorable. This supports making plans based on a return of 5.3% plus and minus 2%.

Now consider a more realistic investor:
Say that this individual would like to put 10 percent or 20 percent or perhaps even 30 percent of his portfolio in stocks. But he can't be taking wild risks because he depends on the income streams generated by his investments to provide for himself and his family. Say that he is confident that, even if stock prices were to fall 90 percent, he would not lower his stock allocation so long as stocks comprised only 20 percent of his portfolio and so long as he knew that the historical data supported his long-term return expectations.[Emphasis added]
His dependence on income streams changes everything. We need to look at the 15-year numbers.

There is a tremendous amount of uncertainty at year 15. Using the 1997 results as representative of today's situation, this retiree is looking at a return with all dividends reinvested of 1.3% plus and minus 5% at the halfway point (i.e., year 15 while planning for 30 years). His actual return will be less because he is making withdrawals. He does not reinvest all of his dividends. His 15-year balance is less than 1.3% plus and minus 5%.

There is a good chance that he will have a loss at year 15 even if he makes no withdrawals. The downside risk, even if he reinvests all of his dividends, is (3.7%), that is, minus 3.7%. The upside potential at year 15 is 6.3%, but only if he makes no withdrawals.

Withdrawing a portion of the dividends to provide an income stream is similar to selling stock. Without withdrawals, reinvested dividends are deposits. With withdrawals, the failure to reinvest all of the dividends reduces the amount of these deposits. This is not exactly the same thing as selling shares. But it is similar.

I have determined the annualized real returns with and without reinvesting dividends at year 15. For 1929, the annualized real return with all dividends reinvested was 1.34%. With none of the dividends reinvested, the annualized real return was a loss, (3.38%) at year 15. For 1965, the annualized real return with all dividends reinvested was a small loss, (0.68%) at year 15. With none of the dividends reinvested, the annualized real return was (4.31%). For 1967, the annualized real return with all dividends reinvested was (0.86%). With none of the dividends reinvested, the annualized real return was (4.71%).

[Looking at the opposite extreme, for 1949 the annualized real returns were 13.77% and 9.43% with and without reinvested dividends. For 1985, the annualized real returns were 14.28% and 11.61%, respectively.]

Judging from these numbers, a failure to reinvest dividends reduces the annualized real return by (approximately) 3% at year 15. This changes our retiree's outlook at today's valuations to (1.7%) plus and minus 5% at year 15.
Would you tell this poor befuddled soul that the historical data indicates that he can pretty much count on a 3.3 percent real return at the end of 30 years, that it is likely that he will get 5.3 percent, and that there is a long-shot chance that he might even get as much as 7.3 percent?
No. Here are some numbers at year 30. [Actually, here are too many numbers.]

The annualized real returns for 1929 were 6.57% with dividends reinvested and 0.93% with dividends removed. For 1965, the annualized real returns were 4.01% with all dividends reinvested and 0.38% with no dividends reinvested. For 1967, the annualized real returns were 5.70% with all dividends reinvested and 2.12% with all dividends removed. There were no instances with a loss at year 30 with all dividends removed in the modern era (i.e., post 1921). There were several periods with losses prior to that. Losses at year 30 were never so bad as (2%).

For 1949, the annualized real returns were 6.70% with all dividends reinvested and 2.79% with no dividends reinvested. Data for 1985 does not extend to 30 years. For 1933, the annualized real returns were 9.78% with all dividends reinvested and 4.70% with all dividends removed. For 1943, the annualized real returns were 9.29% with all dividends reinvested and 5.26% with all dividends removed. [This was the highest return with all dividends removed.]

I would identify the range of annualized real returns in the (recent) historical record as 0% to 5% when dividends are removed (to supply an income stream). The corresponding range of returns with all dividends reinvested is 4% to 10%. I have not made projections for today's valuations with all dividends removed. Using the 1929, 1965 and 1967 returns as a rough guide, the range of annualized real returns would be 4% to 6% with all dividends reinvested and 0% to 2% with all dividends removed.

[We can compare these values of 4% to 6% with dividends reinvested in 1929, 1965 and 1967 with the (more accurate) projections of 3.3% plus and minus 2% in recent years. Projections using today's valuation are likely to be 2% less than the numbers that I have presented. With all dividends removed, the most likely real annualized return at year 30 would be a loss of (1%).]

Back to the original question:
Would you tell this poor befuddled soul that the historical data indicates that he can pretty much count on a 3.3 percent real return at the end of 30 years, that it is likely that he will get 5.3 percent, and that there is a long-shot chance that he might even get as much as 7.3 percent?
No. I would tell him that he should be prepared for a loss of buying power equal to (1%) plus and minus 2% if he uses all dividends for income. [ERROR: He should expect an annualized gain of 3.3% plus and minus 2% only if he reinvests all of the dividends.] CORRECTION: He should expect an annualized gain of 5.3% plus and minus 2% only if he reinvests all of the dividends.
This is one of our best threads ever, JWR1945. Thanks once again for your willingness to hang in there so long..You are a PATIENT Numbers Guy..
Thank you for your kind words. It is very easy to be patient when my calculations are likely to help real people. In addition, these exchanges are interesting. They have brought many things to my attention that I had not realized before.

Have fun.

John R.
Last edited by JWR1945 on Fri Oct 15, 2004 10:51 am, edited 1 time in total.
JWR1945
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Post by JWR1945 »

Year, 15-Year Annualized Real Returns with Dividends Reinvested, 15-Year Annualized Real Returns with Dividends Removed

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1871   10.40     4.10
1872   10.28     4.07
1873    9.32     3.21
1874    9.68     3.76
1875    9.66     3.97
1876    8.28     2.78
1877   10.96     5.77
1878    9.79     4.79
1879    7.63     2.55
1880    6.76     1.58
1881    4.99    (0.16)
1882    5.88     0.77
1883    6.54     1.55
1884    7.96     3.20
1885    7.17     2.78
1886    6.68     2.32
1887    6.97     2.61
1888    7.22     2.92
1889    5.77     1.39
1890    6.65     2.31
1891    8.57     4.29
1892    6.70     2.44
1893    5.21     0.72
1894    7.54     3.21
1895    7.32     3.07
1896    7.36     3.04
1897    7.26     2.88
1898    6.20     1.74
1899    4.12    (0.48)
1900    4.51    (0.28)
1901    4.66    (0.15)
1902    3.38    (1.51)
1903    1.13    (4.18)
1904    1.89    (3.46)
1905    0.37    (5.05)
1906   (1.64)   (7.29)
1907   (0.07)   (5.93)
1908    3.15    (2.64)
1909    1.39    (4.47)
1910    2.61    (3.34)
1911    3.60    (2.32)
1912    4.18    (1.75)
1913    6.39     0.44
1914    9.62     3.75
1915    9.45     3.66
1916    6.68     0.76
1917    4.26    (2.26)
1918    6.86     0.43
1919    9.86     3.51
1920    9.00     2.69

Code: Select all

1921   12.85     6.75
1922   13.25     7.33
1923    8.84     2.76
1924    9.78     3.80
1925    8.46     2.49
1926    6.45     0.38
1927    4.25    (1.96)
1928    2.77    (3.47)
1929    1.34    (4.93)
1930    2.93    (3.38)
1931    6.06    (0.10)
1932    6.75     1.33
1933    6.11     0.87
1934    3.87    (1.46)
1935    5.83     0.36
1936    4.43    (1.18)
1937    3.62    (2.06)
1938    6.91     1.42
1939    5.97     0.39
1940    8.34     2.77
1941   10.81     5.40
1942   12.45     7.34
1943   11.06     6.03
1944   12.07     7.15
1945   11.43     6.61
1946    9.58     4.81
1947   12.89     8.18
1948   13.09     8.54
1949   13.77     9.43
1950   13.47     9.39
1951   12.58     8.74
1952   10.83     7.14
1953   10.72     7.19
1954   11.00     7.66
1955    7.24     3.96
1956    5.63     2.39
1957    6.05     2.86
1958    7.56     4.49
1959    3.57     0.49
1960    0.90    (2.32)
1961    2.32    (0.93)
1962    1.57    (1.72)
1963    0.84    (2.59)
1964    0.08    (3.46)
1965   (0.68)   (4.31)
1966   (0.55)   (4.25)
1967   (0.86)   (4.71)
1968   (0.20)   (4.15)
1969    0.35    (3.68)
1970    1.57    (2.53)
1971    2.74    (1.41)
1972    3.80    (0.37)
1973    2.56    (1.65)
1974    5.12     0.89
1975    8.54     4.43
1976    6.30     2.21
1977    7.64     3.59
1978    9.00     5.12
1979    9.19     5.45
1980    8.92     5.31
1981   10.09     6.59
1982   12.69     9.44
1983   12.82     9.76
1984   13.69    10.80
1985   14.28    11.61
1986   12.25     9.76
1987    9.23     6.86
Have fun.

John R.
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Year, 30-Year Annualized Real Returns with Dividends Reinvested, 30-Year Annualized Real Returns with Dividends Removed

Code: Select all

1871   8.53     3.20
1872   8.61     3.34
1873   8.26     3.07
1874   7.70     2.57
1875   8.14     3.13
1876   8.43     3.53
1877   8.81     4.09
1878   7.47     2.73
1879   7.58     2.88
1880   7.04     2.32
1881   6.17     1.42
1882   6.57     1.82
1883   6.37     1.65
1884   6.02     1.34
1885   5.83     1.24
1886   5.67     1.08
1887   5.16     0.53
1888   4.13    (0.69)
1889   3.81    (1.06)
1890   3.46    (1.44)
1891   3.34    (1.67)
1892   3.26    (1.83)
1893   4.18    (0.97)
1894   4.42    (0.70)
1895   4.94    (0.19)
1896   5.46     0.33
1897   5.71     0.54
1898   6.29     1.09
1899   6.84     1.61
1900   6.95     1.67
1901   5.66     0.30
1902   3.82    (1.89)
1903   3.95    (1.90)
1904   5.80    (0.04)
1905   4.59    (1.26)
1906   5.36    (0.52)
1907   6.38     0.48
1908   5.96     0.02
1909   5.50    (0.42)
1910   5.49    (0.47)
1911   5.02    (0.98)
1912   4.21    (1.86)
1913   4.56    (1.53)
1914   5.40    (0.69)
1915   6.14     0.08
1916   6.37     0.33
1917   5.50    (0.48)
1918   6.48     0.65
1919   6.82     0.99
1920   7.41     1.51

Code: Select all

1921   8.56    2.71
1922   8.33    2.53
1923   7.87    2.09
1924   7.86    2.08
1925   8.40    2.63
1926   8.61    2.86
1927   8.27    2.58
1928   6.83    1.17
1929   6.57    0.93
1930   7.10    1.49
1931   7.80    2.33
1932   9.78    4.70
1933   9.55    4.64
1934   8.71    3.84
1935   9.58    4.78
1936   8.43    3.66
1937   7.16    2.43
1938   8.80    4.26
1939   8.45    3.96
1940   7.79    3.37
1941   8.19    3.89
1942   9.20    5.08
1943   9.29    5.26
1944   7.74    3.76
1945   6.04    2.05
1946   5.89    1.90
1947   7.08    3.11
1948   6.79    2.83
1949   6.70    2.79
1950   6.16    2.31
1951   5.82    2.04
1952   4.82    1.04
1953   5.12    1.36
1954   5.54    1.83
1955   4.37    0.66
1956   4.17    0.48
1957   4.92    1.23
1958   5.03    1.37
1959   4.34    0.69
1960   4.65    1.00
1961   4.29    0.63
1962   4.57    0.90
1963   4.84    1.19
1964   4.53    0.90
1965   4.01    0.38
1966   4.64    1.02
1967   5.70    2.12
1968   6.11    2.57
1969   6.81    3.31
1970   7.74    4.30
1971   7.39    4.03
1972   6.48    3.19
Have fun.

John R.
JWR1945
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Post by JWR1945 »

I am including this for completeness. Jump down to the last paragraph for a helpful rule of thumb.

I have plotted charts with the overall return with and without reinvesting dividends versus percentage earnings yield 100E10/P at years 15 and 30. They are calculated starting in 1923-1987 for the 15-year returns and in 1923-1975 for the 30-year returns.

These are the 15-year formulas:
y = 1.3492x-3.4612 with R-squared equal to 0.5693 with dividends reinvested and
y = 1.3407x-7.7509 with R-squared equal to 0.505 with all dividends removed.
The return in percent equals y. The percentage earnings yield 100E10/P equals x.

The slopes for the 15-year formulas are almost identical (1.3492 and 1.3407). They are exactly parallel on the graph with a fixed separation equal to the difference of their intercepts: (3.4612)-(7.7509) = +4.2897 or 4.3%.

To determine the return with all dividends removed, simply subtract 4.3% from the existing numbers (which assumed that all dividends were reinvested).

These are the 30-year formulas:
y = 0.4159x+3.764 with R-squared equal to 0.3018 with dividends reinvested and
y = 0.2902x+0.3906 with R-squared equal to 0.2252 with all dividends removed.
The return in percent equals y. The percentage earnings yield 100E10/P equals x.

In this case the lines that fit the data are similar but not quite parallel.

When P/E10 = 20, the percentage earnings yield 100E10/P equals 5.0%. The formulas tell us that the (calculated) return is 5.8435% with dividends reinvested. When P/E10 = 20, the percentage earnings yield 100E10/P is 5.0% and the (calculated) return is 1.8416% with dividends removed.

When P/E10 = 40, the percentage earnings yield 100E10/P equals 2.5%. The formulas tell us that the (calculated) return is 4.80375% with dividends reinvested. When P/E10 = 20, the percentage earnings yield 100E10/P is 5.0% and the (calculated) return is 1.1161% with dividends removed.

When P/E10 = 20, the difference between the (calculated) returns when dividends are reinvested and removed is 5.8435-1.8416 = 4.0019 or 4.0%.

When P/E10 = 40, the difference between the (calculated) returns when dividends are reinvested and removed is 4.80375-1.1161 = 3.68765 or 3.7%.

When valuations are high, calculate the return with all dividends removed by subtracting a number between 3.7% and 4.0% from the existing numbers (which assumes that all dividends are reinvested). When P/E10 is close to 20 (and 100E10/P is close to 5.0%), subtract the full 4.0%. As valuations increase and P/E10 moves closer to 40 (and 100E10/P moves closer to 2.5%), subtract less than 4.0%. When P/E10 equals 40, subtract 3.7%.

An alternative approach is simpler. Subtract 3.8% from the existing numbers (which are for high valuations and with all dividends reinvested). An error of 0.1% to 0.2% is not enough to be concerned about.

To a very good approximation, removing all dividends reduces the annualized real return by 4% as compared with having reinvested all of the dividends. The effect is a little bit larger at year 15. It is 4.3% instead of 4.0%. The effect is a little bit smaller at year 30, when it is 3.8% instead of 4.0%.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"His dependence on income streams changes everything. We need to look at the 15-year numbers. "

We are using different understandings of the concept of "income streams," JWR1945. When I say that I would consider putting 20 percent of my portfolio in S&P stocks presuming that the income stream is large enough, I don't mean to suggest that I would need that asset class by itself to generate the amount needed to cover that income stream on an annual basis (only that it would do so on a long-term basis).

Say that my stock investment is worth $200,000 in today's dollars, that it is 20 percent of my portfolio, and that I am counting on an inflation-adjusted income stream of 4 percent from it ($8,000 per year). You are of course correct that, if I were taking the $8,000 only from money invested in stocks, I would either need to sell chares or not reinvest dividends. That's not my intent. My intent would be generally not to sell the stock and generally to reinvest the dividends. The exception would be, if stock prices went up enough that I were overinvested in stocks on a percentage basis. In that event, I might sell something to bring the percentages to where I wanted them. I would not be planning to sell shares as a regular course of business, however.

Money is generally fungible. So there is no need to collect the income stream one is counting on from stocks from the stocks themselves. Today, I count on income streams from my TIPS and ibonds, but I have never sold any TIPs or ibonds. I allow CDs to expire, and cover my costs of living from those. My CDs were intended to serve as my fluid asset class.

I very much agree with your statement that the thing to avoid is selling stocks when prices are low. It was concern over doing that that got me interested in SWR analysis in the first place. I see SWR analysis as a means of translating the irregular returns obtained from stocks into terms that are more comparable to the regular returns received from an asset class like CDs.

If stocks paid an even 7 percent each year, I don't see that there would be any need for SWR analysis. The SWR would be 7 percent. You would just take out what you earned that year. It's because you receive the long-term 7 percent return in such an irregular fashion that you need to employ SWR analysis to make the number comparable to the return you would get from a less volatile asset class.

If I knew that I was "guaranteed" a 3.3 percent return from an S&P stock investment, I would assume in my planning at least a 3.3 percent return (probably something a little more than that). But I would not actually take the 3.3 percent amount from the stock investment each year. I would generally take it from an investment class that I consider more fluid (like CDs). That would allow the stock investment to build up over time in the way that it needs to to actually generate the 3.3 percent long-term return.

This is one of the reasons why I am skeptical of recommendations that people invest 74 percent in stocks, by the way. If you have that percentage of your assets in stocks, you are required to pull money from stocks to cover living expenses, and that kills you if you do it when prices are down. If you have only 20 percent in stocks (or anything up to 50 percent,) you can set things up so that you have the flexibility needed to cover your living expenses from an investment class that is less volatile and for which there is less of a penalty for making withdrawals to cover living expenses. I believe that a mix of volatile and non-volatile asset classes generally makes the most sense.

What I mean when I say that I will be counting on an income stream from a stock investment is that I want to know that in 30 years it will be sure to generate x level of return. I am generally assuming reinvestment of dividends when I say something like that. It might be that in real life I would take out some of the dividends at some point,. However, if I did that, I would of course be aware that it would effect the long-term return that I would obtain from that investment. For purposes of the question above, I intended an assumption that dividends would be reinvested. So I believe that the 3.3, 5.3, and 7.3 percent long-term returns apply.

Does all of that make a reasonable amount of sense?
JWR1945
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Post by JWR1945 »

hocus2004 asks "Does all of that make a reasonable amount of sense?" The answer is yes. But in the process of coming to this conclusion, our investigation reveals a subtle point regarding rebalancing.
hocus2004 wrote:Your number for the most likely 30-year real-return starting from today's valuation level is about 5.3 percent and the range of possibilities goes from 3.3 to 7.3. Assume an investor..who does not expect to retire for at least 30 years. Is it fair to say that, while this investor might obtain better results by keeping a good portion of his money out of stocks until prices return to more moderate levels, he would not be doing something all that terrible to put a good portion of it in stocks so long as he is absolutely certain that he possesses the inner strength to keep the same percentage in stocks through some severe price drops?
I answered:
Looking at the 30-year results, the answer is yes. Today's situation is very similar to 1997 and slightly more favorable. This supports making plans based on a return of 5.3% plus and minus 2%.
hocus2004 wrote:Would you tell this poor befuddled soul that the historical data indicates that he can pretty much count on a 3.3 percent real return at the end of 30 years, that it is likely that he will get 5.3 percent, and that there is a long-shot chance that he might even get as much as 7.3 percent?
This was my response:
No. I would tell him that he should be prepared for a loss of buying power equal to (1%) plus and minus 2% if he uses all dividends for income. [ERROR: He should expect an annualized gain of 3.3% plus and minus 2% only if he reinvests all of the dividends. CORRECTION: He should expect an annualized gain of 5.3% plus and minus 2% only if he reinvests all of the dividends.[Emphasis added.]
hocus2004 wrote:What I mean when I say that I will be counting on an income stream from a stock investment is that I want to know that in 30 years it will be sure to generate x level of return. I am generally assuming reinvestment of dividends when I say something like that..For purposes of the question above, I intended an assumption that dividends would be reinvested. So I believe that the 3.3, 5.3, and 7.3 percent long-term returns apply.
This is correct. You have met the conditions that led me originally to use the words only if.

Here is another way of looking at this: Your portfolio is similar to holding stocks and bonds without rebalancing. It is not quite the same because you are not making any early withdrawals from stocks.

You are taking advantage of the one really attractive feature that refusing to rebalance offers. By not rebalancing, you are leaving your portfolio's upside potential in place. I looked at this recently and found that rebalancing had very little to offer in many circumstances. It improved Safe Withdrawal Rates less than 0.1% while eliminating almost all of the upside.

Rebalancing can be a good idea when investments offer similar returns but have little correlation otherwise. Rebalancing is not always a good idea. It fails if one or more of the investments have substantially poorer returns than the rest of the portfolio.

Usually, investigations of rebalancing assume that the basic time period is one year. That is nowhere close to your time period. Your time period with stocks could be as long as 30 years and it is likely to be no less than 10 years. All of the mathematics in favor of rebalancing breaks down. Important assumptions are not satisfied. The mathematical theorems do not apply. They are of little help in evaluating your situation.

Have fun.

John R.
JWR1945
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Post by JWR1945 »

hocus2004 is concerned about a 30 year time frame. This perspective and its importance is entirely consistent with some of John Bogle's comments written in Common Sense on Mutual Funds.

John Bogle mentions the importance of long-term return and the relative unimportance of risk (as measure by volatility) on page 150 in a box A Ratio Too Acute about the Sharpe Ratio. John Bogle states flatly:
Here is the reality of investing as I see it: An extra percentage point of standard deviation is meaningless, but an extra percentage point of return is priceless. Large differences in risk are extremely important - there is a difference between a stock portfolio and a bond portfolio - but the expedient of weighting risk and return equally, in a simple formula, leaves much to be desired.
He repeats this idea on pages 301-302.
As I noted in Chapter 6, however, counting one unit of risk as the equivalent of one unit of return seems simplistic, for at the margin it hardly seems rational to weight a meaningless difference of one percentage point of volatility equally with a priceless difference of one percentage point of long-term reward.
Have fun.

John R.
hocus2004
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Post by hocus2004 »

"It was Ben Solar who pointed out that the Gordon Equation calculates a long-term return, not an intermediate return. When we see it applied, however, it is for the intermediate term. "

I presume this was in a thread from when the SWR discussions were being held at the FIRE board. Do you know the rough time-period or are you able to provide a rough approximation of the thread title? Please don't go to any great trouble over this. I want to track down the thread and there were a lot of SWR threads, so any clues you can provide might help.
JWR1945
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Post by JWR1945 »

hocus2004 wrote:"It was Ben Solar who pointed out that the Gordon Equation calculates a long-term return, not an intermediate return. When we see it applied, however, it is for the intermediate term. "

I presume this was in a thread from when the SWR discussions were being held at the FIRE board. Do you know the rough time-period or are you able to provide a rough approximation of the thread title?
The source was this board!

Read everything on my first thread about John Bogle's book Common Sense on Mutual Funds:
From Chapter 1 dated Tuesday, May 11, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2474

I mentioned the idea of sticking two time periods together but keeping the final answer (i.e., long-term stock market return) fixed. If the first part is unusually bullish, the second part needs to be subdued in order for the final price to remain the same.

I used John Bogle's most recent period (which covered 15 years) for the first part and his 50-year long-term return as the final answer and calculated what this suggests about the remaining 35 years (mostly in the future).

You can see the back-and-forth of the discussion first hand and close up.

This was when I first became aware of the inconsistency of how the Gordon Model is used (for the intermediate-term) and its time period assumed in the mathematics (which is the very long-term).

Only recently have I been able to resolve the issue. The application of the Gordon Model is inconsistent with the stock market's 7% long-term real return, which is what John Bogle and others point out. It turns out that (1) the mathematical assumptions of the Gordon Model break down after a few years (i.e., a decade or so at best) so that it no longer applies and (2) its applications such as Monte Carlo models heavily weight the earlier years, which means that later years do not influence the results very much.

[When I say recently, I am referring to this thread. You are watching research as it happens.]

Have fun.

John R.
JWR1945
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Post by JWR1945 »

I have thought about this matter further. I am staying with my original estimates. If one were to invest in S&P500 index at today's valuations, reinvest all dividends and otherwise leave the account untouched for 30 years [in a tax deferred account], he can reasonably expect to get of real return of 5.3% plus and minus 2%.

These numbers were determined by including the effect of valuations in the calculation. This narrows down degree of uncertainty substantially. A sensitivity study using a similar procedure, when applied to Safe Withdrawal Rate calculations, showed that it quickly snapped down to provide stable and accurate projections (with errors typical of those for any extrapolation).

These numbers are consistent with breaking investment periods into two parts. The first part starts with the returns from 1982-1997 as reported by John Bogle. The second part is determined by assuming that the (50-year) long-term return of the stock market starting from 1982 remains unchanged.

I did not use the more general rules of thumb that the aftermath of a bubble takes longer if the bubble takes longer and that prices fall further to the extent that they rose higher during the bubble. We have very limited information about what happens after a bubble in the US stock market. We are almost entirely restricted to the aftermath of 1929. It is likely that other bubbles and stock markets outside of the United States provide helpful information, but there is a question as to the degree of applicability.

The three procedures are reasonably consistent. My procedure is likely to be more accurate because it incorporates valuations directly. In addition, my procedure produces confidence limits, which adds to our understanding.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

"I did not use the more general rules of thumb that the aftermath of a bubble takes longer if the bubble takes longer and that prices fall further to the extent that they rose higher during the bubble."

This language concerns me.

I do not understand the ins and outs of how you are doing these calculations. When I have some time, I am going to go back through this thread carefully and also go through related threads that were referenced in it. I need to possess a clearer understanding of what is going on here.

If what you are tentatively putting forward stands up to scrutiny, I think it is a big deal. It seems to me possible that it will. My reluctance to accept these findings 100 percent is that the extent of the Selling Stock Penalty that you are finding seems to me to be extremely high.

You are saying that investors who follows the rules necessary for your calcculations to apply (no sales of stock, reinvestment of dividends) are virtually guaranteed a 3.3 percent return over 30 years. That's not all so bad for a guaranteed return, in my view. You wouldn't have to take much risk to get that number up to 4 percent. So you are saying that a 4 percent personal withdrawal rate (PWR) for the portion of one's portfolio invested in S&P stocks is not out of line even at today's valuation levels. To make this happen, the investor would need to lower his percentage allocation in stocks to a point where he: (1) would not be seriously tempted to lower his stock allocation when prices fell; and (2) would be able to cover living expenses from the non-stock portion of his portfolio. But I think it is remarkable, given what we have found on the SWR side, that following these rules an investor could get 3.3 virtually guaranteed and up to 4 percent without a whole lot of risk from a S&P investment.

Your SWR number, in contrast, is very low. Your SWR for S&P stocks at today's valuations is about 2.5 percent. TIPs paying a zero percent return would provide a SWR of 3.3 percent (because the portfolio is diminished over time). So the SWR calculations for the 80 percent S&P investment are showing a result worse than what you would get from TIPS paying a zero percent real return. That's pretty darn bad.

As I understand things, the factor causing the difference is the Stock Selling Penalty. When you calculate the SWR number, you are assuming that the investor may need to sell shares in a downturn to cover living expenses. It's the selling of those shares that causes the problems down the road, is it not?

I do not say that this all is not so. It makes a certain amount of sense. There obviously should be a significant negative impact from selling shares. I am just surprised by the size of the Stock Selling Penalty. That's why I think this thread is a big deal. If this holds up, it helps us provide advice as to how to structure a portfolio for early retirement. The sensible advice would be that it is absolutely imperative to avoid the Stock Selling Penalty. Where I see this going is that people will be told that there is almost no circumstance where it makes sense to go with a portfolio of 74 percent S&P stocks at a time of high valuation. The Stock Selling Penalty is just too high to justify such an allocation, except in extremely unusual circumstances. This advice is directly contrary to the advice that has been put forward from authors of conventional SWR studies, that a 74 percent S&P allocation is "optimal."

The language quoted above concerns me. Again, the technical aspects of the calculations are over my head, so I cannot comment on them. But intuitively it seems to me that, when you are starting from a valuation level higher than what has been experienced before, you need an adjustment for valuation larger than what has applied before. I understand that we do not have direct experience with what happens from these valuation levels--that's the biggest reason why we needed to reject the conventional methodology and come up with one that makes more sense in this sort of valuation environment. But we need to have valuation's effects reflected in the calculations. It may be that they are reflected. I really do not know at this point. All that I am trying to say here is that the language quoted above concerns me a little, given how large the difference is between the SWR number you are coming up with for an S&P investment and the 30-year real return number you are coming up with for an S&P investment (where the necessary rules noted elsewhere apply--no stock sales and reinvested of dividends).

Again, I will try to take a more in-depth look at this thread and related materials when some time opens up for me. No matter how it turns out, we are exploring important stuff in this thread and that is how we learn together. I am confident that this thread is going to generate singificant insights that will help aspiring early retirees of the future achieve their life goals.
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