From Intrinsic Value

Research on Safe Withdrawal Rates

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JWR1945
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From Intrinsic Value

Post by JWR1945 » Fri Aug 01, 2003 3:13 pm

From Intrinsic Value

Background

peteyperson has presented us with the concept of intrinsic value. Instead of working directly with prices as they happen to be, he would convert them back to more realistic values. He would scale according to P/E10 or something else that was suitable. He would manage his account on that basis, its intrinsic value.

I do not yet have anything to work with directly in terms of intrinsic value. But I can design a reliable withdrawal strategy based upon high valuations. I have been able to determine the primary mechanism for failure in such cases. The usefulness of my strategy (as originally defined) declines as I move toward lower valuations.

It has occurred to me that I can scale a portfolio from normal valuations to high valuations and then design from there. What I have not been able to do well has been the opposite kind of scaling: that is, modifying the design process to work with normal valuations.

The Starting Point

What I can do well is design a dividend strategy when valuations are high. The basic idea is to live off of the dividends and touch principal very lightly, if at all. If the dividend amount is steady and grows enough to match inflation, then the initial dividend yield is just under the safe withdrawal rate. If you restrict yourself to withdrawing one percent of capital or less in any single year, you can tolerate a fair amount of price variation with reasonable safety.

The key is to have a steady income stream from dividends and to sell very few shares of stocks. You must make a downward adjustment if the dividend amount drops abruptly in the first two or three years. Otherwise, you just take care not to sell too many shares when prices are unusually low.

At lower valuations this process does not work nearly as well. It is much too conservative. Stock prices are likely to rise. With rising prices, you only have to sell a few shares to raise your income. You can do so safely. You do not have to worry about selling heavily at low prices.

Scaling From Intrinsic Value

Conceptually, we divide your portfolio into two separate parts. We treat the dividend income the same as before. As long as the dividend amount is steady or rising, everything is fine. If dividends drop abruptly, of course, we have to adjust to the lower rates. It is easy to calculate the dividend amount. It is the dividend yield times the initial balance. That initial dividend yield is the first component in our withdrawal strategy.

We treat the price component in an amazingly simple manner. We estimate what price would support the dividend income stream if prices were to remain stable, similar to what happens at high valuations. For my first scale factor, I estimated this alternative price by scaling it to a P/E10 equal to 24, which was the second highest value of P/E10 before the bubble. The scaled, alternative price equals the product of (24 / [the actual P/E10] )*(the actual price). It turns out that I should have scaled it a little bit higher. I will talk about that some more, later.

I just treat prices and dividends as if they were independent. They aren't, of course. It just seems to work out reasonably well.

I calculate the withdrawal rate from selling stocks at higher prices as if the price rose steadily from its actual price to its alternative, scaled, higher price thirty years later. (I assumed a portfolio lifespan of thirty years.) The ratio of the final price to the initial price is (1 + the annualized price increase)^30 for 30 years. The formula to use with a calculator is, as follows:

The withdrawal rate from selling stocks = -1 + antilog ( [1/30]* [log (24 / [the actual P/E10] ). If the lifespan were 40 years, the [1/30] term would be replace with [1/40] and so forth.

It turns out that you can still sell some stocks safely without dipping too deeply into capital even at a P/E10 of 24. Something around 30 or 36 seems to fit the data a little bit better. In terms of the calculations, the net effect is to add a factor of {the thirtieth root of (30/24) or the thirtieth root of (36/24)} into the formula. Those roots are 1.0074 and 1.0136. The net effect is to add 0.74% or 1.36% to the calculated values. That is, a year's actual safe withdrawal rate is just a little bit higher than calculated initially.

I have included three tables ordered by valuations, from the lowest P/E10 level to the highest, from start years 1921-1980. I list the start year, the P/E10 level for January of that year, the dividend yield for January of that year, the estimate (using the dividend yield and scaling to a P/E10 level of 24) and that year's safe withdrawal rate assuming an 80% stock allocation. (I used FIRECalc. I selected 20% commercial paper. I used CPI for my inflation adjustment. I set expenses at 0.20%. I used a 30-year portfolio lifespan. My calculations were scaled according to an initial balance of $1000. Other inputs were left at their default settings.)

I have placed asterisks with those years followed by an abrupt dividend decrease. Those years behaved differently from others.

The estimate should be best at the highest valuations and it is. The appropriate adjustment for determining a year's safe withdrawal rate is to add about 1.0% to the estimate. That works very well at high valuations and reasonably well at lower valuations. The scatter decreases as P/E10 increases. That is as it should be.

Bubble Valuations

Do not use this formula blindly to extrapolate into bubble valuations. As long as stocks provide a steady income stream, you do not have to sell any shares. That is, the price adjustment should always be positive or zero, never negative. Scaling to a P/E10 of 43.7 in January 2000, would give a negative adjustment even if you never sold any shares. That is inappropriate. The correct adjustment becomes the dividend yield (1.17%) + the 1.0% that is used in general. The year 2000's safe withdrawal rate was 2.2%.

That having been said, it may have been optimistic. The real dividend amount in January 2000 was $16.50666 (from Professor Shiller's database) and it decreased to $15.022168 in June 2002, which was the last entry with a real dividend amount. That is a 9.88% drop in the dividend amount. (It had dropped as low as $14.623011 in June 2001.) The June 2002 real dividend amount is 1.05% of the January 2000 real price (index value). Thus, where our original calculation was for a 2.2% safe withdrawal rate in January 2000, it might have to be adjusted downward to 2.05% (in a calculation update resulting from subsequent events).

Conclusions

This simplistic scaling worked much better than I had expected. It extends our dividend design strategy down into the ranges of normal and even low valuations. However, it still works best at higher valuations.

Have fun.

John R.

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Post by JWR1945 » Fri Aug 01, 2003 3:20 pm

1921-1980 Estimated and Actual Safe Withdrawal Rates

The Twenty Years with the Lowest Valuations

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Year PE10 Dividend Yield Estimate SWR (80%)
1921 5.1 7.11% 12.40% 11.6%
1922 6.2 6.35% 10.96% 10.2%
1924 8.0 6.02% 9.74% 9.4%
1923 8.1 5.74% 9.42% 9.0%
1933 *** 8.7 6.98% 10.42% 8.4%
1980 8.8 5.18% 8.58% 10.4%
1975 8.9 4.99% 8.35% 8.2%
1978 9.2 5.22% 8.46% 9.2%
1979 9.2 5.12% 8.36% 9.6%
1932 *** 9.3 9.55% 12.76% 8.0%
1925 9.6 5.26% 8.37% 8.4%
1942 *** 10.1 7.87% 10.79% 9.0%
1943 10.1 5.90% 8.82% 9.2%
1949 10.2 6.18% 9.07% 11.0%
1948 10.4 5.69% 8.51% 10.8%
1950 10.7 6.84% 9.56% 10.2%
1944 11.0 5.19% 7.82% 8.6%
1976 11.1 3.80% 6.40% 7.2%
1926 11.3 4.82% 7.36% 7.6%
1935 11.4 4.85% 7.36% 7.6%

The Twenty Years with the Middle Valuations

Code: Select all

Year PE10 Dividend Yield Estimate SWR (80%)
1947 11.4 4.69% 7.20% 9.4%
1977 11.4 3.97% 6.48% 7.4%
1951 11.8 6.98% 9.37% 9.4%
1945 11.9 4.77% 7.13% 8.2%
1954 12.0 5.73% 8.06% 9.0%
1952 12.5 5.86% 8.05% 9.0%
1934 13.0 4.19% 6.25% 6.2%
1953 13.0 5.40% 7.46% 8.6%
1927 13.1 5.19% 7.22% 7.2%
1938 *** 13.5 7.02% 8.95% 6.6%
1974 13.5 3.53% 5.46% 5.8%
1958 13.7 4.33% 6.21% 7.0%
1941 *** 13.9 6.41% 8.24% 7.0%
1939 15.5 4.10% 5.56% 6.0%
1946 15.6 3.70% 5.14% 6.8%
1955 15.9 4.34% 5.72% 6.8%
1940 *** 16.3 5.06% 6.35% 6.0%
1971 16.4 3.35% 4.62% 6.8%
1931 *** 16.7 6.07% 7.28% 5.6%
1957 16.7 3.82% 5.03% 6.0%

The Twenty Years with the Highest Valuations

Code: Select all

Year PE10 Dividend Yield Estimate SWR (80%)
1936 17.0 3.50% 4.65% 5.4%
1970 17.0 3.50% 4.65% 4.8%
1972 17.2 2.98% 4.09% 4.8%
1959 17.9 3.15% 4.13% 5.4%
1956 18.2 3.78% 4.70% 5.8%
1960 18.3 3.21% 4.11% 5.2%
1961 18.4 3.26% 4.16% 5.2%
1973 18.7 2.67% 3.50% 4.6%
1928 18.8 4.43% 5.24% 5.8%
1963 19.2 3.28% 4.02% 5.0%
1967 20.4 3.41% 3.95% 4.4%
1962 21.1 2.93% 3.36% 4.8%
1969 21.1 3.01% 3.44% 4.2%
1968 21.6 3.08% 3.43% 4.2%
1937 *** 21.6 4.17% 4.52% 4.6%
1964 21.6 3.00% 3.35% 4.6%
1930 22.3 4.47% 4.71% 4.8%
1965 23.2 2.92% 3.03% 4.2%
1966 24.0 2.93% 2.93% 4.0%
1929 27.0 3.46% 3.07% 4.2%

JWR1945
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Post by JWR1945 » Mon Aug 25, 2003 10:40 am

I have now calculated the bias terms. You should add 0.773% to the previously calculated estimates to get Safe Withdrawal Rates. Another way of stating this is that the PE10 reference number in the formula should be 30 (actually 30.24) instead of 24. That is, when you see (24/[PE10]), replace it with (30/[PE10]).

I have separated the data according to valuations (as measured by P/E10). The correction for the twenty historical sequences with the most favorable valuations is 0.509%. The correction for the twenty historical sequences with middle level valuations is 0.915%. The correction for the twenty historical sequences with the least favorable valuations (i.e., highest prices) is 0.888%.

I now refer to the results for an 80% stock (and 20% commercial paper) portfolio from FIRECalc as Historical Database Rates. (Previously, I had erroneously called them Safe Withdrawal Rates. They have no predictive component. They are based entirely on historical data.)

When I made these calculations, I excluded years which were followed by sharp dividend cuts within two or three years. There are eight of them. I have marked them with asterisks.

Have fun.

John R.

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Post by JWR1945 » Mon Aug 25, 2003 10:52 am

PE10, SWR estimate, HDBR80 and Difference

Most favorable valuations/lowest values of PE10.

Code: Select all

Year  PE10  Yield  Estimate  HDBR80 Difference

1921    5.1   7.11%   12.40%   11.6%   -0.80%
1922    6.2   6.35%   10.96%   10.2%   -0.76%
1924    8.0   6.02%    9.74%    9.4%   -0.34%
1923    8.1   5.74%    9.42%    9.0%   -0.42%
1933*   8.7   6.98%   10.42%    8.4%   -2.02%
1980    8.8   5.18%    8.58%   10.4%   +1.82%
1975    8.9   4.99%    8.35%    8.2%   -0.15%
1978    9.2   5.22%    8.46%    9.2%   +0.74%
1979    9.2   5.12%    8.36%    9.6%   +1.24%
1932*   9.3   9.55%   12.76%    8.0%   -4.76%
1925    9.6   5.26%    8.37%    8.4%   +0.03%
1942*  10.1   7.87%   10.79%    9.0%   -1.79%
1943   10.1   5.90%    8.82%    9.2%   +0.38%
1949   10.2   6.18%    9.07%   11.0%   +1.93%
1948   10.4   5.69%    8.51%   10.8%   +2.29%
1950   10.7   6.84%    9.56%   10.2%   +0.64%
1944   11.0   5.19%    7.82%    8.6%   +0.78%
1976   11.1   3.80%    6.40%    7.2%   +0.80%
1926   11.3   4.82%    7.36%    7.6%   +0.24%
1935   11.4   4.85%    7.36%    7.6%   +0.24%



The sum of the differences is +0.09% (twenty terms).
The sum of the difference terms with asterisks is -8.57% (three terms).
The sum of the differences excluding those with asterisks is 8.66% (with 17 terms and an average of +0.509%).

Have fun.

John R.

JWR1945
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Post by JWR1945 » Mon Aug 25, 2003 10:57 am

PE10, SWR estimate, HDBR80 and Difference

Middle level valuations/middle values of PE10.

Code: Select all

Year  PE10  Yield  Estimate  HDBR80 Difference

1947   11.4   4.69%   7.20%   9.4%   +2.20%
1977   11.4   3.97%   6.48%   7.4%   +0.92%
1951   11.8   6.98%   9.37%   9.4%   +0.03%
1945   11.9   4.77%   7.13%   8.2%   +1.07%
1954   12.0   5.73%   8.06%   9.0%   +0.94%
1952   12.5   5.86%   8.05%   9.0%   +0.95%
1934   13.0   4.19%   6.25%   6.2%   -0.05%
1953   13.0   5.40%   7.46%   8.6%   +1.14%
1927   13.1   5.19%   7.22%   7.2%   -0.02%
1938*  13.5   7.02%   8.95%   6.6%   -2.35%
1974   13.5   3.53%   5.46%   5.8%   +0.34%
1958   13.7   4.33%   6.21%   7.0%   +0.79%
1941*  13.9   6.41%   8.24%   7.0%   -1.24%
1939   15.5   4.10%   5.56%   6.0%   +0.44%
1946   15.6   3.70%   5.14%   6.8%   +1.66%
1955   15.9   4.34%   5.72%   6.8%   +1.08%
1940*  16.3   5.06%   6.35%   6.0%   -0.35%
1971   16.4   3.35%   4.62%   6.8%   +2.18%
1931*  16.7   6.07%   7.28%   5.6%   -1.68%
1957   16.7   3.82%   5.03%   6.0%   +0.97%




The sum of the differences is +9.02% (twenty terms).
The sum of the difference terms with asterisks is -5.62% (four terms).
The sum of the differences excluding those with asterisks is 14.64% (with 16 terms and an average of +0.915%).

Have fun.

John R.

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Post by JWR1945 » Mon Aug 25, 2003 11:07 am

PE10, SWR estimate, HDBR80 and Difference

Least favorable valuations/highest values of PE10.

Code: Select all

Year  PE10  Yield  Estimate  HDBR80 Difference
1936   17.0   3.50%   4.65%   5.4%   +0.75%
1970   17.0   3.50%   4.65%   4.8%   +0.15%
1972   17.2   2.98%   4.09%   4.8%   +0.71%
1959   17.9   3.15%   4.13%   5.4%   +1.27%
1956   18.2   3.78%   4.70%   5.8%   +1.10%
1960   18.3   3.21%   4.11%   5.2%   +1.09%
1961   18.4   3.26%   4.16%   5.2%   +1.04%
1973   18.7   2.67%   3.50%   4.6%   +1.10%
1928   18.8   4.43%   5.24%   5.8%   +0.56%
1963   19.2   3.28%   4.02%   5.0%   +0.98%
1967   20.4   3.41%   3.95%   4.4%   +0.45%
1962   21.1   2.93%   3.36%   4.8%   +1.44%
1969   21.1   3.01%   3.44%   4.2%   +0.76%
1968   21.6   3.08%   3.43%   4.2%   +0.77%
1937*  21.6   4.17%   4.52%   4.6%   +0.08%
1964   21.6   3.00%   3.35%   4.6%   +1.25%
1930   22.3   4.47%   4.71%   4.8%   +0.09%
1965   23.2   2.92%   3.03%   4.2%   +1.17%
1966   24.0   2.93%   2.93%   4.0%   +1.07%
1929   27.0   3.46%   3.07%   4.2%   +1.13%




The sum of the differences is +16.96% (twenty terms).
The sum of the difference terms with asterisks is +0.08% (one term).
The sum of the differences excluding those with asterisks is 16.88% (with 19 terms and an average of +0.888%).

Combining all three tables
The overall sum of the differences is 0.09% + 9.02% + 16.96% = 26.07% (60 terms).
The overall sum of the difference terms with asterisks is -8.57% - 5.62% + 0.08% = -14.11% (8 terms).
The overall sum of the differences excluding those with asterisks is 26.07% - (-14.11%) = 40.18% (with 52 terms and an average of +0.773%).


Have fun.

John R.

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Post by JWR1945 » Mon Sep 01, 2003 6:04 am

The Time Sensitivity of Safe Withdrawal Rates

We have just seen that the scale factor term 24/PE10 should be 30/PE10 or, more precisely, 30.24/PE10.

Previously, the adjustment to the withdrawal rate from selling stocks was given by this formula = -1 + antilog ( [1/30]* [log (24 / [the actual P/E10] ), which equaled +0.74. If the lifespan were 40 years, the [1/30] term would be replace with [1/40] and so forth. In this latest form, our Safe Withdrawal Rate calculation becomes = -1 + antilog ( [1/30]* [log (30.24 / [the actual P/E10] ). Using this new scale factor, the adjustment for 30 years is 0.773%.

For PE10 = 24 and N = 30 years, the Historical Database Rate (HDBR) is close to 4%. That has been the traditional number cited for the Safe Withdrawal Rate. Now let us see what happens when we combine our new formula and PE10 = 24. Scaling for 40 years and for 50 years, our adjustments are +0.579% and +0.463%, respectively. Extending our portfolio lifespan from 30 years to 40 years reduces the Safe Withdrawal Rate by 0.194%. That is, 0.773 - 0.579 = 0.194. Extending the lifespan from 40 years to 50 years reduces the rate by another 0.116%. That is, 0.579 - 0.463 = 0.116.

These results are consistent with sensitivity studies that I have made previously. I used the FIRECalc and looked at Historical Database Rates at high levels of safety extending over 30, 40 and 50 years. Notice that there is a tremendous amount of sensitivity to small changes in the amounts that one withdraws.

Have fun.

John R.

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Post by JWR1945 » Sun Dec 07, 2003 3:06 pm

It is relatively straightforward (but time consuming) to calculate confidence limits for these tables. Here is how you do it for the third table, the one with the lowest withdrawal rates.

First, you should calculate Revised Estimates of the Safe Withdrawal Rates. To do this, you should calculate the average difference. It is 0.888% if you exclude data with asterisks. Add this to each number listed as an Estimate.

To calculate confidence limits, find the standard deviation of the Differences. To do this, you square each difference (nineteen terms when you exclude 1937) and add them up. I got 16.8960. Calculate the square of their average (or 0.888%^2) times the number of terms (nineteen) that you have added together. I got 14.9823. Subtract the two, divide by the number of degrees of freedom (in this case 18 ) and take the square root. I got 0.3261.

[The number of degrees of freedom equals the number of data points minus the number of intermediate terms that have to be calculated from the same data. In this case, the single intermediate calculation was finding the average of the differences (or 0.888%).]

Finally, apply the Student t test with the number of degrees of freedom (18 if you exclude the year 1937). I have done this. At a 95% confidence level, this adjustment works out to be plus and minus 0.68%. (If you include 1937, the confidence limits are plus and minus 0.57%. The number of degrees of freedom is 19. I recommend against including 1937 since it falls outside of the general applicability of the model. That historical sequence, starting in 1937, had an early dividend cut.)

If you would prefer to use the 90% confidence level, the adjustment would have been plus and minus 0.56% instead of 0.68% (or 0.47% instead of 0.57%). If you allowed yourself a very high degree of uncertainty, you could choose the 80% confidence level with its adjustment of plus and minus 0.43% instead of 0.68% (or 0.35% instead of 0.57%).

The uncertainty indicated by the data is plus and minus 0.6% to 0.7% at a high confidence level and 0.3% to 0.4% at a very low confidence level. My own preference is plus and minus 0.7%. I would not challenge anyone who chose 0.5% or 0.6%.

I do not want to claim too much reliability in these estimates. There are many standard qualifiers that always apply. This certainly gets you into the ballpark. These numbers (or calculations) are much better than many alternative methods might produce.

The reason that I stuck with a single table is that the best data are those closest to what you are interested in. This must be balanced against another issue. It is dangerous to rely too heavily on a very few data points.

Have fun.

John R.

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Post by Mike » Mon Dec 08, 2003 3:41 am

This morning's Journal listed the S&P dividend yield at 1.62%. Does this mean that the historical database suggests a withdrawal of 2.62% plus or minus .68%? IOW, a withdrawal range of 1.94% to 3.3%, using the 1.94% withdrawal rate for a S&P portfolio?

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Post by JWR1945 » Mon Dec 08, 2003 5:09 am

The tables were derived using this formula:
Estimate = initial dividend yield + (-1 + antilog ( [1/30]* [log (24 / [the initial value of P/E10] ).
Using only data from the third table:
Revised Estimate = Estimate + 0.888%.

Dr. Shiller's latest P/E10 value (for November 2003) is 25.898702.
The thirtieth root of (24 / [the initial value of P/E10] ) = the thirtieth root of (24 / 25.898702) = the thirtieth root of 0.9266874 = 0.9974653.
Estimate = initial dividend yield + (-1 + 0.9974653) = initial dividend yield - 0.0025347 = initial dividend yield - 0.25347%.
Revised Estimate = Estimate + 0.888% = initial dividend yield - 0. 25347% + 0.888% = initial dividend yield + 0.63%.

Using today's 1.62% dividend yield of the S&P500 and November's P/E10:
Revised Estimate = 1.62% + 0.63% = 2.25%.
The 95% confidence limits are plus and minus 0.68%.
The model calculates today's withdrawal rate as being above 1.57% and below 2.93%. The best estimate is 2.25%.

Most people would identify 1.57% as being the Safe Withdrawal Rate.

You should use the entire range of 1.57% (most pessimistic) to 2.93% (most optimistic) for planning purposes. Random and/or unknown factors will determine the actual withdrawal rate within that range that is safe today.

Have fun.

John R.

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Post by Mike » Mon Dec 08, 2003 8:51 am

Thanks John. I can see why you recommend TIPS for anyone who needs more than about 1.57% Combined with the switching calculator's results, there is a compelling case for switching to TIPS (for money in an IRA) if the S&P index is the only other option. Since the boomers, and the pension plans that serve them, are still in an accumulation phase, this strategy will likely result in underperfomance for a few years, but may save some people's retirement when reversion to the mean finally takes place. I am currently pondering how to incorporate other equity asset classes into the mix, as a risk reduction strategy for anyone who chooses to keep a portion of their portfolio in equities for the duration of the boomer accumulation phase.

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Post by ElSupremo » Mon Dec 08, 2003 11:00 am

Greetings Mike :)

I went ahead and removed your duplicate post. I hope that is ok with you and John. :oops:
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Post by Mike » Mon Dec 08, 2003 11:23 am

Thank you ES. I got a failure to deliver message when I hit the submit button, so I pushed the back button and tried again, not realizing that the first message had actually gone through. I looked for a delete button, but did not see one. I am just an amateur at this computing stuff. It is fortunate that you are looking out for us. :)

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Post by JWR1945 » Tue Dec 09, 2003 6:18 am

Mike wrote:I am currently pondering how to incorporate other equity asset classes into the mix, as a risk reduction strategy for anyone who chooses to keep a portion of their portfolio in equities for the duration of the boomer accumulation phase.

I recommend that you read BenSolar's posts along these lines. The Search function works very well (or well enough for me). BenSolar has gone through the steps that you are talking about. Although you may end up disagreeing on some points, I think that you will find his rationale to be excellent.

Have fun.

John R.

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Post by JWR1945 » Thu Dec 18, 2003 11:54 am

More about Confidence Limits

This thread (From Intrinsic Value) is based upon a theoretical model, albeit a very simple one. I have assumed that dividends provide a floor that matches inflation and that there is another increase that comes from price changes alone. This makes sense because the final balance is zero for the worst case condition. Instead of using a linear variation with P/E10, I used one based upon annualized price changes. The annualized return (actually, the annualized gain multiplier) is the Nth root of the final price divided by the initial price, where N is the number of years. That is what I did. I assumed that the effect of P/E10 would vary in accordance with the Nth root (in this case, N = 30 years). I used an empirical reference point, initially with P/E10 = 24, to set the price adjustment equal to zero under worst case conditions. Later, I changed that to P/E10 = 30. (In the discussion that follows, I refer to this step as making a Revised Estimate.)

(The annualized return is the number, which would produce the correct ratio of the final price to initial price if you had the same return each and every year. For example, if you got a ten percent return for one year, the ratio would be 1.10. If you got ten percent for two years in a row, the ratio would be (1.10)*(1.10) or (1.10)^2. If you got ten percent for three years in a row, the final balance would be (1.10)^3 times the initial balance. And so forth. After N years, the ratio would be (1.10)^N. The Nth root would be 1.10 for the annualized gain multiplier with an annualized percentage increase of 10%.)

My approach is non-standard in that I fit the data with a theoretical curve instead of a (mindlessly drawn) straight line.

Getting back to the tables, the column that I listed as the Estimate does not include the final adjustment. It is necessary to add the 0.888% (or 0.89% since we are using two decimal places). That results in a Revised Estimate. For 1929, the initial estimate was 3.07% but the revised estimate is 3.96% (or 3.07% + 0.89). Every estimate in the table should include this revision, that is, adding 0.89%. The confidence limits are placed around the revised estimates. For the 95% confidence limit (and excluding 1937, which is a special case), the adjustment is to add and subtract 0.68%. That means that we have a very high level of confidence (95%) that the (true) 1929 safe withdrawal rate was between 3.28% and 4.64%. Our calculations show that our best estimate (or guess, but based upon the historical data) of the (true) safe withdrawal rate is 3.96%.

Remembering that the 80% confidence limits were plus and minus 0.43%. It is reasonably likely (with an 80% confidence level) that the (true) safe withdrawal rate for 1929 was between 3.53% and 4.39%.

[Note: the uncertainty associated with the original 3.07% estimate is much larger than the 0.68% for the revised estimate. My calculations show that it is plus and minus 1.98% at the 95% confidence level.]

Political polls are quoted with even greater uncertainty. They quote the uncertainty as plus and minus one standard deviation, which corresponds to a 68% confidence level. [Do not confuse this 68% confidence level with the 0.68% associated with the 95% confidence level. Any similarity is coincidental.] That is, political polls should err by more than their quoted level of uncertainty about one-third of the time.

If our emphasis is on safety, we are likely to depend upon 3.3% to 3.5% in situations similar to 1929. If our emphasis is in establishing the likely range for planning under similar circumstances, we would allow for the possibility that we could be lucky. We could end up with safety at 4.6%. Or we could be unlucky. We might end up with safety only if we lower our withdrawal rate to 3.3%. Our range would be 3.3% to 4.6%. We might reasonably limit ourselves to looking at 3.5% to 4.4% in our initial planning.

As mentioned earlier on this thread, today's situation is not as bright as in 1929. Valuations are exceedingly high. The best estimate of the current Safe Withdrawal Rate is 2.25%. Random and/or unknown factors will determine the actual withdrawal rate within that range that is safe today. One should use the entire range of 1.57% (most pessimistic) to 2.93% (most optimistic) for planning purposes.

Have fun.

John R.

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Post by JWR1945 » Sat Jan 03, 2004 7:07 am

More about Confidence Limits from Intrinsic Value

This clarifies what I mean when I refer to the (original) estimate, the revised estimate and the Historical Database Rates (80% stocks).

The original estimate in the table is based (almost) entirely upon a theoretical model. That model estimates the (true) safe withdrawal rate to be equal to the initial dividend yield plus a price term that is determined entirely from the initial value of P/E10. The price term treats prices by making an annualized adjustment in P/E10. This is similar to what people do when adjusting their long-term estimates of stock returns for (P/E) multiple expansion or contraction. All of this is at the very beginning of a historical sequence. It is not necessary to adjust for prior history or later developments. The single exception is for dividend cuts in the first two or three years.

In this model I had one number that I had to guess. I assumed that the safe withdrawal rate was exactly equal to the initial dividend yield at some value of P/E10. My guess was that that value of P/E10 was equal to 24.0. My guess was based upon the peak values of P/E10 (around 24.0 to 27.0 looking at the years 1929 and 1966) before the bubble.

Notice that it is possible for the safe withdrawal rate to be less than the initial dividend yield. If prices decrease while dividend yields remain constant, dividend amounts decrease.

All of those numbers listed under Estimate are from that model. That model produced an estimate of 3.07% for the safe withdrawal rate in 1929. It is entirely independent of any of the historical data. It is entirely theoretical.

The table compares the Historical Database Rate (for an 80% stock and 20% commercial paper allocation or HDBR80) to this original Estimate. For 1929 the HDBR80 was 4.2%, which is 1.13% higher than what the model came up with.

My Revised Estimates uses the data to calibrate the price term. Instead of depending upon my original guess of 24.0 for the value at which the safe withdrawal rate equaled the initial dividend yield, I made use of the Historical Database Rates (HDBR80). That new value is a P/E10 of 30.24. Using this new number (of 30.24 instead of 24.0) requires us to add 0.89% (actually 0.888%) to every number listed under the estimate. The revised estimate for 1929 is 3.07% + 0.89% = 3.96%. (For 1929 the revised estimate is 0.24% less than the HDBR80 rate.)

Historical Database Rates are determined entirely from the investment returns associated with actual historical sequences. The portfolios are hypothetical but the returns are historical. HDBR80 is a high stock allocation portfolio. HDBR80 refers to a particular mixture of stocks and commercial paper (80% and 20% respectively). None of the Historical Database Rates are determined from theory. They are all based upon observations (i.e., measured returns). None of the Historical Database Rates can be determined in advance. They are all the results of past history.

I have estimated errors by comparing the revised estimates to the HDBR80 data. This comparison has produced confidence limits extending from minus 0.68% to plus 0.68% of the indicated value. The same confidence limits can be applied to both the revised estimates and the HDBR80 results. The precise interpretation differ in the two cases, but the confidence limits (of plus and minus 0.68%) themselves remain the same.

When applied to revised estimates of Safe Withdrawal Rates, they mean that the model calculates numbers that are within plus and minus 0.68% of the actual Safe Withdrawal Rates (95% of the time). That is, knowing the dividend yield and P/E10 at the very beginning of your retirement, you can accurately calculate the Safe Withdrawal Rate within 0.68%. That is, (the absolute value of) all of the sources of randomness taken together add up to less than 0.68% (at a 95% confidence level).

When we apply the 0.68% confidence levels to the Historical Database Rates (HDBR80), we mean that factors other than the initial dividend yield and the initial P/E10 have influenced the results. Those factors, taken together, have caused a variation of less than 0.68% (95% of the time). The measured HDBR80 rates differ from the deterministic part of Safe Withdrawal Rates because of (apparently) random factors that, when taken together, add up to (an absolute value of) less than 0.68% (95% of the time).

Standard qualifiers apply, of course, and looking forward we would not insist that the confidence level is exactly 95%. After all, there may be sources of error that we have not taken into account. Still, I will continue to assert that our level of confidence is very high.

Have fun.

John R.

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Post by JWR1945 » Fri Jan 09, 2004 5:20 am

More about Confidence Limits from Intrinsic Value (Continued)

These are the years that may have had a true Safe Withdrawal Rate of less than 4%, based upon the theoretical model (i.e., the revised estimate). That is, the lower confidence limit is less than 4.00%. The terms in parenthesis are the revised estimates themselves (add 0.888% or 0.89% to the estimates in the original table).

In 1929 the SWR may have been as low as 3.28% or as high as 4.64% (versus 3.96%).
In 1966 the SWR may have been as low as 3.14% or as high as 4.50% (versus 3.82%).
In 1965 the SWR may have been as low as 3.24% or as high as 4.60% (versus 3.92%).
In 1964 the SWR may have been as low as 3.56% or as high as 4.92% (versus 4.24%).
In 1968 the SWR may have been as low as 3.64% or as high as 5.00% (versus 4.32%).
In 1969 the SWR may have been as low as 3.65% or as high as 5.01% (versus 4.33%).
In 1962 the SWR may have been as low as 3.57% or as high as 4.93% (versus 4.25%).

These are the years in which the Historical Database Rates (HDBR80) may have exceeded 4.00% only because of unknown or random factors. The numbers in parentheses are values of HDBR80. In this list, by true rates I am referring to those than have been caused by (known) deterministic factors.

In 1929 the true rate may have been as low as 3.52% or as high as 4.88% (versus 4.2%).
In 1966 the true rate may have been as low as 3.32% or as high as 4.68% (versus 4.0%).
In 1965 the true rate may have been as low as 3.52% or as high as 4.88% (versus 4.2%).
In 1964 the true rate may have been as low as 3.92% or as high as 5.28% (versus 4.6%).
In 1937 the true rate may have been as low as 3.92% or as high as 5.28% (versus 4.6%).
In 1968 the true rate may have been as low as 3.52% or as high as 4.88% (versus 4.2%).
In 1969 the true rate may have been as low as 3.52% or as high as 4.88% (versus 4.2%).
In 1967 the true rate may have been as low as 3.72% or as high as 5.08% (versus 4.4%).
In 1973 the true rate may have been as low as 3.92% or as high as 5.28% (versus 4.6%).

Probability theory does not allow us to exclude any possibility. To reach a true 100% confidence level, it must be determined that a particular outcome is theoretically impossible. Because it is theoretically possible for stocks to fall substantially each and every year for 30 years, we can never claim 100% confidence for any withdrawal rate above zero.

The conventional methodology produces estimates of Safe Withdrawal Rates for the pre-bubble years. Most, if not all, advocates of the conventional methodology have failed to address the accuracy of their estimates. There are many different approaches as to how to make such estimates, most of which have serious technical problems. Instead of addressing the issue directly, many advocates have applied the tautology that their answer is correct unless the future is worse than the past. In this case the definition of worse than the past means only that their answer is wrong.

Using a theoretically meaningful approach, we have found that the conventional methodology has an accuracy of no better than plus and minus 0.3% (allowing for an estimation error of 20%). When we insist upon having a high level of confidence (i.e., the 95% confidence level, which means that the likelihood of an estimation error is 5%), the conventional methodology is found to have an accuracy of plus and minus 0.7%. These numbers (i.e., 0.3% and 0.7%) should be added and subtracted from all of the Safe Withdrawal Rate results produced by conventional methodology in the pre-bubble years. For example, a Safe Withdrawal Rate estimate of 4.0% really means that deterministic part of the rate is between 3.7% and 4.3% or, if we insist upon having a high level of confidence, between 3.3% and 4.7%. Random and/or unknown factors cause this uncertainty.

Have fun.

John R.

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Post by ataloss » Mon Jan 12, 2004 6:02 am

asdf
Last edited by ataloss on Thu Feb 03, 2005 1:03 pm, edited 1 time in total.
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Post by JWR1945 » Mon Jan 12, 2004 1:45 pm

The reference to post 15132 is this post on this thread:
http://nofeeboards.com/boards/viewtopic ... 132#p15132

We insist upon the precise use of words on this board so as to avoid confusion. The term Historical Database Rate refers to historical results that have no predictive element. The term Safe Withdrawal Rate is a mathematical calculation that makes a prediction. As with any analysis involving probability theory, the quality of a prediction is not measured directly in terms of an actual outcome.

BenSolar advocated using the term Historical Safe Withdrawal Rate (hSWR), but it was in a poisoned posting environment. The term Future Safe Withdrawal Rate (fSWR) corresponds to our present usage of the phrase Safe Withdrawal Rate.

Refer to this post for greater detail:
http://nofeeboards.com/boards/viewtopic ... 370#p16370

Advocates of the conventional methodology most certainly did assert that the lower bound of the Historical Database Rates was also a lower bound to Safe Withdrawal Rates. They most certainly did not include qualifiers associated with future market behavior. That only came later. Estimates that mentioned future market returns came from those who used Monte Carlo models.

The conventional methodology most certainly depended upon a tautology. It was a damaging tautology since it gave people the impression that it was not necessary to look further.

Only recently have advocates of the conventional methodology begun to back off as overwhelming evidence has shown that it fails. Only recently have people started to use the magic 4% number as a rule of thumb or a rough approximation.

We have shown, in fact, that the conventional methodology was not even within its range of applicability during and after the bubble. Valuations were higher than at anytime in the earlier record, including the previous peak in 1929. Dividend yields were lower than at anytime in the historical record. Close examination indicates that the historical sequences produced LUCKY results. Those historical sequences that had the smallest Historical Database Rates occurred in a non-typical fashion.

In contrast, we have searched out reliable, understandable cause and effect relationships. We depend upon the reliability of those relationships, not in numbers by themselves. We use numbers, of course, and they help. But we depend upon our understanding of the underlying relationships.

Mike summarized the cause and effect relationship very well in this post. http://nofeeboards.com/boards/viewtopic ... 6429#16429

It is not a tautology.

Have fun.

John R.

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Post by ataloss » Mon Jan 12, 2004 4:23 pm

asdf
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