How
Variable Are The Variable Withdrawal Rates?
............. 
This article was posted on May 1, 2000. How
Variable Are The Variable Withdrawal Rates? And
how much is that in dollars? by Dory36, who prefers
to remain reasonably anonymous prior to retirement, but can be reached on The
Retire Early forum on The Motley Fool (http://boards.fool.com/Messages.asp?id=1380025000000000). Credits: Bob
Herlien introduced these possibilities in several articles on these pages. The
spreadsheet below was built by modifying his calculator in “Safe Retirement
Withdrawals with Cash Buffers” (see cashwith.html).
In addition to added information, which will be obvious to anyone comparing Bob’s
sheet and the one below, this one uses a different algorithm for calculating
withdrawals and for rebalancing. IntroductionWhat
happens to your safe withdrawal rate and your annual withdrawals if you vary
your withdrawals as the market varies?
After all, we might be willing to really tighten our belts for a year or
two in a 30 year payout period in order to achieve a much higher withdrawal in
other years. It
seems obvious that if we tweak the withdrawal rate to the point where it just
barely accomplishes our goal – say, a 100% safe withdrawal rate over 30 years –
then every penny of the growth in good years is being used to cover those
really bad years. But what if we were willing to decrease our withdrawals in
those bad years? Well, obviously there is more money available than there was
in the “just barely” case. Now, what if you take some of the growth money out
after the good years? What would be the effect on the withdrawals overall? And
just how many bad years might there be? Bob
Herlien’s work explored the impact on safe rates of one particular approach to
varying the withdrawals. I took a slightly different approach, and also looked
more closely at just what those withdrawals might be – and what the odds were
of getting lots of leans years in a row. MethodologyI
took Bob’s spreadsheet (1.5rah) as a starting point. His algorithm for
calculating when and how much to vary the withdrawals did not lend itself to my
purposes, so I used a different, very simple, approach: If the past year’s growth in the portfolio is less than the entered minimum withdrawal, use the minimum. If the past year’s growth is greater than the maximum withdrawal, use the maximum. Otherwise, withdraw the amount of the past year’s growth in the portfolio. The
specified initial withdrawal rate is only used for the first year, in the
variable withdrawal model. After the first year, it is ignored. To
allow use of this spreadsheet in exploring fixed withdrawals, or cash buffered
withdrawals, these features were left intact. The rebalancing algorithm for
cash buffered withdrawals was modified slightly from the starting spreadsheet,
to allow the cash buffer to diminish over multiple years if the portfolio is
repeatedly down from the previous years.
(The impact of using a cash buffer was not thoroughly explored with
variable withdrawals. There was a slight, 12%, improvement in the
survivability percentages for a given fixed withdrawal rate, as Bob previously
reported.) Let
me define a term, to avoid confusion. In this spreadsheet, and all of the other
safe withdrawal rate calculators I’ve seen, we look at what would happen over a
long period of time if we started with a certain portfolio value, and withdrew
according to a certain strategy. We then examine the outcome of following that
same approach beginning with every year for which we have data. In the
discussions that follow, I’m using the term cycle to refer to a
single starting year and all subsequent years within the selected payout
period. Finally,
it was necessary to report yearly withdrawals in inflationadjusted dollars so
that reasonable conclusions could be reached. Therefore, the yearly withdrawals
are all reported in constant dollars, as of the starting year of the cycle. In
other words, all 50 calculated withdrawals following a hypothetical retirement
in 1942 are reported in 1942 dollars, and all 50 following a 1943 retirement
are in 1943 dollars. Using the SpreadsheetData
entry is only needed in the few cells at the upper left part of the spreadsheet
that are in blue, bold typeface. The
initial withdrawal rate is used only for the first year, in the variable
scenario. (It is used for every year in the fixed withdrawal scenario.) How
much can you really take? If you scroll down to row 31, you will
see some tabular data on annual withdrawals.
There
are three columns, and two rows. The
two rows allow us to look at all of the available cycles or just at those
cycles since 1948. An
average is calculated for each cycle using every year in that cycle (of 10, 20,
30, 40, or 50 years). The
big picture: The first column reports the average of all of
these cycle averages, or in row two,
all the averages since 1948. This shows the overall, inflation adjusted,
withdrawal rate for the selected strategy, after averaging every available
cycle. I’m
a pessimist. How bad can it get? Unfortunately, choosing the wrong year to
retire can be a problem. That’s why we do all this safe withdrawal rate stuff.
The second column shows how bad it would be for you if you selected the worst
possible year to retire, and followed the strategy you’ve selected above. Important: the “Worst Cycle” figure shown is the average of all of the years in the worst cycle, not the worst year within the cycle. Every year in which the growth in the portfolio is less than the minimum will result in a minimum withdrawal. Since there were losing years frequently in the past 128 years, we can be certain that every cycle, even the best, will have a number of years in which we have to get by on the minimum we selected. I’m
an eternal optimist! How good can it be? The third column
shows the results of picking the best possible year to retire and follow the
strategy you’ve selected. But
how often will a cycle be really bad, and how often will it be really good? Scrolling on down to row 36, you’ll see a
breakdown of all the cycles into four categories. These are also shown in the
adjoining pie chart. Since my idea of what is a really bad year might differ from yours, I’ve calculated some breakpoints to define the good, the bad, and the ugly. Although
the initial withdrawal rate (call it “R”) is used only for the first year, it
is also used as a dividing point for the breakdown of how many cycles fall into
what category. The
spreadsheet calculates a figure (call it “D”) of half of the difference between
R and your specified minimum. Cycles
that are really bad are arbitrarily defined as those whose averages are between
the minimum and the minimum + D. Those I’d view as fairly bad have an average
withdrawal between the minimum + D and R. Fairly good cycles have average
withdrawals between R and R + D. Cycles with averages higher than that are
really good. To illustrate, if you select an initial withdrawal rate (R) of 4%, and a minimum of 2%, then the spreadsheet will categorize all cycles as really bad (23%), fairly bad (34%), fairly good (45%), and really good (>5%). (There is room for improvement in this breakdown; to use your own figures, change the formula or values at BD1:BG1 on the Annual Withdrawals worksheet.) OK,
but let me see some yearbyyear actual results.
You can look at the results sprinkled all through the Safe Rate Calculator,
starting at cell C159 and the following cells for 1871 and onward, then 16 rows
down and one cell to the right to start for 1872 and onward, and so forth. Or,
take a look at the Annual Withdrawals worksheet. Each withdrawal is shown, in
constant dollars, for each year. (Note that if you select a 10 year payout,
only 10 years of data are shown. So select 50 years if you want to look through
these numbers.) Some ResultsThe
value in all of this will really come when you play around with the
spreadsheet, trying out your own assumptions. But I have done some preliminary
investigation. As
you would expect, the more willing you are to constrain yourself, the better
the overall return. Risk (of occasional
lower withdrawals) gets rewarded (with higher average withdrawals). Settings for the table below: Minimum withdrawals were adjusted by 0.5%, and maximum withdrawals were adjusted in 0.25% increments as needed to achieve a 100% safe withdrawal rate for a 30 year payout period. Stocks were set to 85% of the portfolio, and the first year withdrawal was 3.5% of the portfolio value. Rebalancing was annual. As you can see below, the highest average cycle figure was obtained with a strategy of taking only 1% in years when there was 1% or less growth in the portfolio from the previous year. You could take all of the growth every other year, and still achieve a 100% safe rate for a 30 year payout period. (But note the 49% survival rate for a 50 year payout period.) Assuming a random start year, you could expect 7.5% for the entire cycle (8.4%, looking at cycles since 1948). If you picked the worst year to retire, you’d be looking at an average of under 3.4% for the next 30 years, but if you picked the right year, then you could see a 15.5% annual withdrawal! As the minimum increases, the maximum decreases rapidly to maintain a 100% safe 30 year payout. The 50 year survivability also improves rapidly as that maximum falls. As expected, the rising minimum and decreasing maximum converge at the fixed safe rate.
So what? How does this help me?Let’s assume you have concluded that you want to retire, and would like to be able to expect around $40,000 a year in withdrawals. With the fixed 100% safe rate of about 3.8%, you will need to accumulate a portfolio of $1.05 million. If your retirement plans include a lot of discretionary spending, such as travel, and you can get by on $14,000 if absolutely necessary, but wouldn’t be willing to risk a yeartoyear average that was below $25,000, you could retire when your portfolio reaches about $700,000, and still have reason to expect an annual withdrawal of over $46,000 – a 16% improvement over what you would have received on a fixed withdrawal strategy. And the odds aren’t bad. Out of 118 periods available, you’d have averaged between $25,000 and $29,750 in only eight cycles. The other 110 would have you taking an average of over $29,750. If you look beyond the first page of the spreadsheet, you can see that 86 of those 110 cycles would have permitted average withdrawals of over $40,000. If you look at each of the 3309 different annual withdrawals in all of the available 30 year cycles, you’d find that about 30% of the possible years were in the gloomy $14,000 to $17,500 range, but 47% were over $45,000. Here’s where these figures come from, and an example of how to use the spreadsheet. 1. Enter your starting portfolio size, or leave it at $1,000 to work with percentages, which I have done for this example. 2. Enter the payout period. I’ve used “3”, for 30 years, for this example. 3. Enter the allocation to stocks. I’ve used 85%. 4. Enter the type of nonstock investment. I used “1” for commercial paper, because the data is more accurate for that series, according to the original source of these spreadsheets. 5. Enter your initial withdrawal rate. I’ve used 3.5%. (Remember, though, that in the variable withdrawal model on this spreadsheet, this figure only enters calculations to indicate the first year’s withdrawal.) 6. Enter “1” to indicate a variable withdrawal model. 7. Enter investment expenses. I’ve used 0.02%. 8. How will you rebalance your portfolio? I used “1” for annual rebalancing here., as I found by trial and error that the survivability goes from 100% with annual rebalancing (“1”) to 99% with no rebalancing, and under 92% for rebalancing when the portfolio is up for the year (“2), but there is a negligible change in the average withdrawal rate with these changes. 9. I’m using “1” for “PPI” inflation index. 10. Skip the maximum withdrawal rate for a moment, and look at the minimum withdrawal rate. To fit my hypothetical circumstances, I used 2% as the minimum I absolutely had to have, in any year. 11. Returning to the maximum withdrawal rate, you’ll have to do some experimenting. The higher the withdrawal maximum, the less growth you are preserving to handle bad years. Consequently, a toohigh maximum will cause your survivability to decrease. So I tried various numbers until I found 11.25% as the highest figure that would still leave me with a 100% safe 30 year payout period. 12. To look at the average of all the cycles, see cell B33. The next columns show worst and best cycles. (Remember, though – these are the best and worst cycles. A cycle averaging 4% might have many years with 2%, and several with 10%, depending on your settings.) 13. To see how many cycles averaged withdrawals with different breakpoints, see cells D36D39. If you followed my example, the breakpoints are 2.00 to 2.75%, 2.75 – 3.50%, 3.50 – 4.25%, and over 4.25%. My results are 0, 0, 8, and 110. 14. To look at how individual cycles performed, select the “Annual Withdrawal” tab. There, you can see the annual inflation adjusted withdrawals for each cycle. Note that if you have selected a 30 year payout period, there will be blanks where the withdrawals would appear in later years. Conclusion This new spreadsheet validates everything we’ve seen in the safe withdrawal rate research. But it shows that your longterm average withdrawal rate is likely to be higher than the fixed safe withdrawal rate if you can accept a reduced withdrawal rate following poor market years. The corollary is that you can achieve a significant decrease in the portfolio size that will likely be needed to support a given withdrawal amount over the long term, if you can accept occasional shortfalls in the funds available to withdraw. Note the use of the word “likely.”

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