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HDBR versus SWR

 
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JWR1945
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Location: Crestview, Florida

PostPosted: Sun Jan 11, 2004 10:14 am    Post subject: HDBR versus SWR Reply with quote

The historical sequence method calculates the survivability of a hypothetical portfolio based upon the actual sequence of investment returns that took place in the past. Those are Historical Database Rates (HDBR). This is what FIRECalc generates. This is what the Retire Early Safe Withdrawal [Rate] Calculator generates, including all of my modified versions.

A Safe Withdrawal Rate (SWR) is the result of a mathematical calculation that predicts the survivability of a hypothetical portfolio. It is based entirely upon information up to and including a specified date and none thereafter. Since an SWR is a mathematical calculation, there is, at least notionally, such a thing as a single, correct solution (or a single, correct set of solutions). Since it is a prediction, that answer is described in terms of probability theory.

There are many ways to calculate an SWR. Some are better than others, as is the case with any prediction. Consider an example consisting of coin tosses. You might start out by assuming that the probability of heads is 50%. But it is highly unlikely that the true probability of heads is exactly 50%. If you were to flip the coin 10000 times, it is highly likely that you would have a better estimate. You could even show, at a high level of confidence, that the probability is not exactly 50%. You will never be able to calculate it exactly. But the idea that a single, true probability exists is meaningful and helpful.

It is meaningful to speak of a Safe Withdrawal Rate that applied to a year in the past. The calculation must be made only with information available up to that year and none thereafter. We can even talk in terms of a Safe Withdrawal Rate during a historical sequence. For example, we might talk about the Safe Withdrawal Rate in 1958 for the historical sequence that began in 1953. The calculation would use information up to 1958 including the actual sequence of returns from 1953-1958. That could include information related to reversion to the mean. [Reversion to the mean is based on the notion that stock returns are related to earnings and earnings growth (over several years). This means that prices are not entirely independent (over several years) but are somewhat predictable. raddr has provided a precise definition of reversion to the mean and he has proved that it exists.] The calculation would not use information after 1958. Nor should its value be judged strictly in terms of the particular sequence of returns that occurred after 1958.

The conventional methodology assumes that the lower bound of Historical Database Rates is also a lower bound of Safe Withdrawal Rates. We have proved conclusively that this is false. There have been numerous contributors using a variety of methods that have led to this conclusion.

The conventional methodology never even applied during the bubble. Market conditions put the conventional approach out of range. The future was worse than the past from the get go. In fact, raddr's sensitivity studies have raised serious doubts as to whether the conclusions from using the conventional methodology were ever true. It may well be that the historical sequences that we have experienced were lucky in that the lowest Historical Database Rates were not typical. That suggests that the Safe Withdrawal Rates (which are related to probabilities), when properly calculated, would have been lower than the actual outcomes.

It is critically important for the purposes of this board to understand that Historical Database Rates and Safe Withdrawal Rates are quite different. In addition, Safe Withdrawal Rates are not rules of thumb. Of course, different withdrawal strategies and different portfolio mixes can have different Safe Withdrawal Rates because the mathematical problem is specified differently in all of these cases.

Have fun.

John R.


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ataloss
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PostPosted: Sun Jan 11, 2004 4:27 pm    Post subject: Reply with quote

asdf?



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JWR1945
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PostPosted: Sun Jan 11, 2004 5:35 pm    Post subject: Reply with quote

Mike asked that question in the From Intrinsic Value thread on Dec 08, 2003. My most recent update is the post that follows his. It includes sufficient detail for you to update my calculations.
http://nofeeboards.com/boards/viewtopic.php?p=15021#15021

Have fun.

John R.


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wanderer
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PostPosted: Sun Jan 11, 2004 8:43 pm    Post subject: Reply with quote

Interesting. so SWR would still be abt 2%+- after 4 years in.

Not questioning your skills, JWR, but I wish I could figure out if that 'Student t' .68% adjustment made sense. Unfortunately, my knowledge of stats is sorely lacking.



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ataloss
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PostPosted: Mon Jan 12, 2004 1:54 am    Post subject: Reply with quote

asdf

t



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Ataloss


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Mike
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PostPosted: Mon Jan 12, 2004 6:46 am    Post subject: Reply with quote

Wanderer wrote:
Interesting. so SWR would still be abt 2%+- after 4 years in.

Mike opines:

Historically, a person could have lived exclusively on the dividends from the S&P, and gotten a more or less inflation adjusted income thereby. With dividends on the S&P below 1.6%, it does not seem remarkable to me that this is the only estimated 100% safe rate. Dividends have not risen much since Y2K, and they fell before they started rising again. I see this as the real reason that estimated 100% withdrawal rates have not moved up much despite the market's fall. Basically, the data seems to be saying that the only way to guarantee that a rare market disaster will not devastate your retirement is to live exclusively on the dividends. Even a 90% drop in the S&P price level (such as post 1929) will not deplete your portfolio if you don't touch your principal. Of course, things that have never happened before (such as a nuclear holocaust) would prevent a dividend only strategy from succeeding, but there is no way to estimate such things from the historical data base.


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JWR1945
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PostPosted: Mon Jan 12, 2004 12:31 pm    Post subject: Reply with quote

Blame Wanderer for this:

The Number of Degrees of Freedom

Determining an equivalent number of the degrees of freedom is difficult except for the simplest of problems. The terms in the Safe Withdrawal Rate calculation include Prices, Dividends and Earnings.

Dividend amounts are relatively stable. Earnings appear only as a ten-year average, the E10 part of P/E10. Gummy's investigations showed that nominal prices are almost completely independent, but that variations in inflation persist. That was why he decided to use actual sequences for inflation, but completely random numbers for prices.

Since prices appear as part of dividend yield and in P/E10 and since real prices are influenced by inflation, there is a reduction in the equivalent number of degrees of freedom. Since price fluctuations are larger than the fluctuations associated with inflation, the total effect on confidence limits is limited. I would place an upper bound on any adjustment to the confidence limits at a factor of two. Stated differently, I would not expect that the persistence in inflation is sufficient to reduce the equivalent number of totally independent samples by a factor as large as 4.

That places the 95% confidence limits at plus and minus something between 0.7% (actually, 0.68%) and 1.4%. Based on the relative sizes of price fluctuations and variations in inflation, I would expect an accurate revision to be closer to 0.7% than 1.4%.

Historical Database Rates have a measured persistence close to 7 years.

The error term consists of random effects and effects that are not explained by the model. It is the difference between the Safe Withdrawal Rate calculation and the Historical Database Rates. The size of this error falls dramatically when the model is used opposed to using just a mean and a variance (or standard deviation).

Have fun.

John R.


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JWR1945
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PostPosted: Mon Jan 12, 2004 12:35 pm    Post subject: Reply with quote

Mike has it exactly right.

We use numbers in our analyses, but we depend only upon the cause and effect relationships that we discover.

Have fun.

John R.


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JWR1945
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PostPosted: Fri Jan 23, 2004 6:57 pm    Post subject: Reply with quote

HDBR versus SWR: Validity

(I have recently reviewed some earlier discussions. I have just now realized their importance in terms of the conventional methodology.)

We are aware that market returns are highly volatile and that it is improper to exclude an unusually bad sequence of returns as being impossible. This means that no Safe Withdrawal Rate calculation should claim absolute safety as long as money is withdrawn. The probability of failure may be small, but it is never exactly equal to zero.

The conventional methodology takes a finite number of historical sequences (or samples) and defines the lowest Historical Database Rate as the worst case going forward. That is a single number. As has been pointed out by others, that number can only go down as the number of years in the Historical Database increases.

This is highly improper for specifying a statistical problem. The proper method is to identify a percentage of failures. For example, if one is interested in a 10% failure rate, then he will use one data point when he has ten samples, two when he has twenty samples, three when he has thirty samples and so forth.

Now let us think about whether the future is worse than the past. As the Historical Database increases from 10 sequences to 20 sequences and then to 30 sequences and so forth, the future is declared to be worse than the past every time that a single, smaller number (i.e., a lower Historical Database Rate) shows up. The statistical problem can be exactly the same as before. But because the single worst case data point is lower than before, it is declared that something has changed. In fact, nothing has changed. But advocates of the conventional methodology claim that things have changed.

Because the statistical problem is misstated, the conventional methodology is, in fact, an invalid methodology. Because of how it is set up, it will always conclude that the future is worse than the past given only that enough time is allowed to pass.

Have fun.

John R.


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ataloss
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PostPosted: Thu Jan 29, 2004 1:36 pm    Post subject: Reply with quote

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