Variable Withdrawals in Retirement    (Updated 9/11/11)

Introduction

Academic studies have examined historical data and concluded that the “safe” initial withdrawal rate from a balanced portfolio has been 4%. ( See note 1 ) In other words, a retiree who started with a $1,000,000 portfolio and took out $40,000 in the first year and increased that withdrawal each subsequent year by the prior year’s inflation rate, after 30 years, the portfolio would have had at least $1 left.

There are two drawbacks with this procedure. The first is that poor returns early in retirement can put stress on the portfolio and increase the chance of early depletion. So while there have been a few test cases in the past where a retirement portfolio survived 30 years despite poor returns in the early years, the experience was not very pleasant. Therefore, some retirees may elect to reduce their withdrawals following a year of poor returns if only to ensure some peace of mind.

The second drawback is that the 4% initial withdrawal rate is really a “worse case scenario”. Therefore, it is likely that a higher initial withdrawal rate can be deemed “safe”. ( See note 2 ) But of course, there is no way to know what that higher initial withdrawal rate will be.

As a result, several authors have proposed variable withdrawal strategies in order to maximize withdrawals while at the same time incorporating some provision to reduce withdrawals when warranted. I will summarize their strategies in this article. I will include links to the author’s articles. Plus, I will provide Excel spreadsheets so that their strategies can be examined using historical data.

~~~

Table of Contents

Strategy	Author
Floor and Ceiling	William Bengen
Sensible Withdrawals	Peter Ponzo (Gummy)
Decision Rules with Guardrails	Jonathan Guyton
Rational Investing	Bob Clyatt
Endowment Formula	Robert Carlson
Five Year Plan	Ben Stein & Phil DeMuth
Flexible Withdrawal Rate	Paul Merriman
Maximize Withdrawals	Cut-Throat & LBill
Withdraw Maximum Gains	Cut-Throat
Prosperous Spending Model	William Bengen

Floor and Ceiling
Author	William Bengen
Link	Conserving Client Portfolios During Retirement, Part IV (pdf)
Spreadsheet	withdrawBengen.xls
Description The withdrawal amount is calculated as a percentage of the portfolio’s total value. The withdrawal amount is allowed to rise or fall with the performance of the portfolio. However, the withdrawal will neither fall below a “floor” nor rise above a “ceiling”. Both the “floor” and “ceiling” are adjusted upwards for inflation. As an example, the initial floor can be set at 3.6% and rise with inflation. And the initial ceiling can be set at 5% and rise with inflation. The withdrawal amount can be set initially at a fixed percentage like 4%. On a $1,000,000 portfolio, the withdrawal will not fall below an inflation-adjusted amount of $36,000. Nor will the withdrawal rise above an inflation-adjusted amount of $50,000.
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Sensible Withdrawals
Author	Peter Ponzo (Gummy)
Link	Sensible Withdrawals
Spreadsheet	withdrawGummy.xls
Description Like Bengen’s “Floor and Ceiling” method, the initial floor can be set at a low level and rise with inflation. However, if after withdrawing the “floor” amount, and the portfolio’s total value has still risen by the rate of inflation, then an extra amount is withdrawn. The extra amount can be a small percentage of those gains. Or it can be a large percentage of that gain. The extra amount withdrawn can be capped at a maximum amount that is also inflation-adjusted. As an example, let’s say the initial floor is set at 3%. And let’s further say that the extra withdrawal amount will be 50% of the gain after taking the “floor” withdrawal. If we start with a $1,000,000 portfolio and the portfolio gains 10% in the first year and inflation was 4%, we first take $31,200 ($1,000,000 x 0.03 x 1.04). The portfolio then has $1,068,800 ($1,100,000 - $31,200). The resultant portfolio has risen by at least the inflation rate ($1,040,000). So we can calculate the “extras” available ($1,068,800 - $1,040,000 = $28,800). So an additional amount is taken -- in this case, 50% or $14,400 ($28,800 x 0.50). So at the end of the first year, $45,600 was withdrawn ($31,200 + $14,400).
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the end of each year. Bottom chart shows portfolio value at the end of each year immediately following that year’s withdrawal.

Decision Rules with Guardrails
Author	Jonathan Guyton
Link	Decision Rules and Maximum Initial Withdrawal Rates (pdf)
Spreadsheet	withdrawGuyton.xls
Description Guyton’s decision rules to determine each year’s withdrawals are complex. Therefore, I have paraphrased his instructions here. Enhanced Withdrawal Rule Withdrawals increase with inflation. But if inflation exceeds 6%, the increase is capped at 6%. However, there is no increase following a year where the portfolio’s total return is negative and when that year’s withdrawal rate (based on the portfolio’s current total value) would be greater than the initial withdrawal rate. In other words, under those conditions, the withdrawal amount would be frozen. Capital Preservation Rule When a current year’s withdrawal rate (based on the portfolio’s total value) has risen more than 20 percent above the initial withdrawal rate, the amount withdrawn is reduced by 10 percent. This decreased withdrawal becomes the basis for determining the following year’s withdrawal amount. This rule expires 15 years before the maximum age to which the retiree wishes to plan. For example, a retiree assuming she would not live beyond age 100 would discontinue the capital preservation rule after age 85. Prosperity Rule When a current year’s withdrawal rate (based on the portfolio’s total value) has fallen more than 20 percent below the initial withdrawal rate, the Prosperity Rule takes effect. Under these conditions, the inflation adjustment cap of 6% is removed. And the amount withdrawn is increased by 10 percent. This increased withdrawal becomes the basis for determining the following year’s withdrawal amount. To summarize: Condition Action The year's total return is negative and the current withdrawal rate is greater than the initial withdrawal rate Freeze withdrawal The current withdrawal rate is 20% greater than the initial withdrawal rate Cut withdrawal by 10% The current withdrawal rate is 20% smaller than the initial withdrawal rate Increase withdrawal by 10% All other conditions Increase withdrawal with inflation rate (up to 6%)
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Rational Investing
Author	Bob Clyatt
Link	Retire Early Book Review: Work Less, Live More
Spreadsheet	withdrawClyatt.xls
Description In this method, the withdrawal amount is calculated by multiplying the portfolio’s total value by a fixed percentage. So the amount withdrawn will rise and fall with the performance of the portfolio. However, when the portfolio shows a loss for the year, a “95% rule” is put into effect. So even if the total portfolio value has fallen by more than 5%, the amount taken will be 95% of the previous year’s withdrawal.
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Endowment Formula
Author	Robert Carlson
Link	How Much To Spend Safely in Retirement
Spreadsheet	withdrawCarlson.xls
Description In this method, the withdrawal amount is divided into two parts. In the first part, spending will increase with inflation. The second part takes a fixed percentage from the total portfolio value. In this way, Carlson uses both the “Fixed Dollar” method (rising with inflation) and the “Fixed Percentage” method of withdrawals. Carlson takes 70% from the Fixed Dollar amount and 30% from the Fixed Percentage amount. Here is an example. Let’s start with a $1,000,000 portfolio. Let’s say the portfolio rises to $1,100,000 at the end of the first year and inflation was 3%. Initially, we took out $40,000 at the start of the year. We will also use 4% for the "Fixed Percentage" calculation. There are many steps. So, I will break each step down. Step 1 Take last year’s spending of $40,000 and increase it with inflation. This gives us $41,200. ($40,000 x 1.03) Step 2 Multiply step 1 by 70%. This gives us $28,840. ($41,200 x 0.70) Step 3 Multiply $1,100,000 times 4%. This produces $44,000. ($1,100,000 x 0.04) Step 4 Multiply step 3 by 30%. This gives us $13,200. ($44,000 x 0.30) Step 5 Add the two parts (step 2 plus step 4) to obtain the withdrawal amount of $42,040. ($28,840 + $13,200) Let’s continue this example for another year. This time, the portfolio falls to $900,000. And we’ll say that inflation was again 3%. Step 1 Take last year’s spending of $42,040 and increase it with inflation. This gives us $43,301. ($42,040 x 1.03) Step 2 Multiply step 1 by 70%. This gives us $30,310. ($43,301 x 0.70) Step 3 Multiply $900,000 times 4%. This produces $36,000. ($900,000 x 0.04) Step 4 Multiply step 3 by 30%. This gives us $10,800. ($36,000 x 0.30) Step 5 Add the two parts (step 2 plus step 4) to obtain the withdrawal amount of $41,110. ($30,310 + $10,800)
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Five Year Plan
Authors	Ben Stein & Phil DeMuth
Link	Yes, You Can Still Retire Comfortably!
Spreadsheet	withdrawStein.xls
Description In this method, the retirement is broken into five-year periods. Independently separate withdrawal rates can be assigned to each five-year period. In the first year of each period, the withdrawal amount is calculated by multiplying the total amount remaining in the portfolio by the withdrawal rate assigned to that five-year period. Then in years two through five of each five-year period, the withdrawal amount is increased by the previous year’s inflation rate. However, in the event that the returns during first five years are poor, whereby the total portfolio declines by 10% or more, the withdrawal amount gets reset. The new withdrawal amount is obtained by multiplying the value of the now-reduced portfolio by 4%. The withdrawal amount is then increased by the previous year’s inflation rate for the remainder of the first five-year period. There is no “4% reset” in subsequent five-year periods. Furthermore, there is no withdrawal rate reset for the final five-year period. Instead, Stein and DeMuth suggest the following: “When you only have ten years left, we strongly suggest that you switch to the 100 percent safe-withdrawal rate going forward, which is 8.6%. Then continue to adjust for inflation every year thereafter.” Through Monte Carlo Simulation, Stein and DeMuth created a table of withdrawal rates. The authors designate success rates in three tiers: “100% Safe”, “99% Safe” and “95% Safe”. I have also added withdrawal rates that had 100% success according to the historical data for a portfolio consisting of 50% stocks (S&P 500) and 50% bonds (5-year Treasuries). (Historical data obtained from my Maximum Withdrawal Rate Spreadsheet.) Number of Years Remaining Stein & DeMuth Monte Carlo Simulation Historical 100% Safe 100% Safe 99% Safe 95% Safe 30 3.5% 5.3% 6.2% 4.0% 25 3.7% 5.6% 6.6% 4.3% 20 4.1% 6.4% 7.5% 4.9% 15 5.6% 7.9% 8.9% 6.0% 10 8.6% 10.9% 12.2% 8.1%
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Flexible Withdrawal Rate
Author	Paul Merriman
Link	Live It Up Without Outliving Your Money!: Getting the Most From Your Investments in Retirement
Spreadsheet	withdrawMerriman.xls
Description In this method, the withdrawal amount is calculated as a percentage of the portfolio’s total value. The withdrawal amount is allowed to rise or fall with the performance of the portfolio. If the portfolio’s total value rises, the withdrawal rate is allowed to increase. For example, if the portfolio starts at $1,000,000, the withdrawal rate might be 4.0%. This will result in a withdrawal amount of $40,000. Then if the portfolio rises to $1,250,000, the withdrawal rate might rise to 4.25%. This will result in a withdrawal amount of $53,125. Merriman offers two sets of withdrawal rate thresholds. One set starts at 4% and rises to 6%. The other set starts at 5% and rises to 6%. The two sets of withdrawal rate thresholds are summarized in this chart: - < $1.25M < $1.5M < $1.75M < $2.0M > $2.0M Set 1 4.0% 4.5% 5.0% 5.5% 6.0% Set 2 5.0% 5.25% 5.5% 5.75% 6.0% I also added a feature not mentioned by Merriman. But I thought it might be useful. Like Bengen’s “Floor and Ceiling” method, I added a “floor” to the annual withdrawal. As an example, the initial floor can be set at 3.6% and rise with inflation. In this way, the withdrawal amount will never fall to unacceptably low levels even during stretches of poor portfolio performance.
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Maximize Withdrawals
Authors	Cut-Throat & LBill
Link	Simple method of SWR without leaving a Big Pile at the End
Spreadsheet	withdrawMax.xls
Description In the method proposed by Cut-Throat on the Bogleheads Investment Forum, the withdrawal amount is calculated as a percentage of the portfolio’s total value. The withdrawal amount is allowed to rise or fall with the performance of the portfolio. Like Stein & DeMuth’s “Five Year Plan”, the withdrawal rate is increased based on the number of years remaining. However, rather than update the withdrawal rate once every five years, the withdrawal rate is updated each year. I determine the “Safe” Withdrawal Rate (SWR) for every stock/bond mix (S&P 500 and Five-Year Treasuries) and number of years remaining from my Maximum Withdrawal Rate Spreadsheet (xls). This SWR data is contained in a detailed Lookup Table and summarized in this chart: One option for this method is to use or not use a buffer. A standard practice is to plan a 30-year retirement. Based on historical data for a 50/50 stock/bond mix, a 4.0% initial withdrawal rate was “safe” for a 30-year “Length of Plan”. However to add a margin of safety, one can add a 5-year buffer. This will make the “Length of Plan” 35 years. From the Lookup Table, a 3.8% initial withdrawal would be used. Later on that Bogleheads thread, LBill offered a related method that would be more certain to not leave a big pile at the end. Rather than allow the withdrawal amount to fall in response to a portfolio decline, the withdrawal amount either stays level in real terms (inflation-adjusted) or rises when the portfolio rises. In the spreadsheet, a “Maximize” checkbox toggles between these two versions. When checked, LBill’s method is followed. When the “Maximize” checkbox is unchecked, Cut-Throat’s method is followed. The chart below is an example of LBill’s Maximized method.
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Withdraw Maximum Gains
Author	Cut-Throat
Link	Simple, But Aggressive SWR for Not leaving a Big Pile
Spreadsheet	withdrawMaxGains.xls
Description Like Gummy’s “Sensible Withdrawals” method, a withdrawal rate is initially set (the “floor” amount) and rises with inflation. However in this method, the floor amount is calculated from historical data which is contained in a detailed Lookup Table. Using data from my Maximum Withdrawal Rate Spreadsheet (xls), these are the “Safe” Withdrawal Rates (SWR) for every stock/bond mix (S&P 500 and Five-Year Treasuries) and number of years remaining. Also like Gummy’s method, if after withdrawing the “floor” amount, the portfolio’s total value is above a certain amount, then an extra amount is withdrawn. Otherwise, the withdrawal reverts to the “floor” amount which is a continuation of the inflation-adjusted initial withdrawal. And like Cut-Throat’s other method described in the previous section, there is the option to use a buffer or not use a buffer. So if a margin of safety is desired, one can add a 5-year buffer. This will make the “Length of Plan” 35 years rather than 30 years (no buffer). The following example illustrates the procedure using the 1955-1984 period, a 50/50 stock/bond mix (S&P 500 and Five-Year Treasures) and no buffer. The top chart shows each year’s withdrawals. Withdrawals are taken at the end of each year. Bottom chart shows portfolio value at the end of each year immediately following that year’s withdrawal. The portfolio starts at $1,000,000 with $500,000 in stocks and $500,000 in bonds. At the end of 1955, the value of the portfolio grew to $1,154,702. From the lookup table, a 50/50 stock/bond mix supported a 4.14% inflation-adjusted inititial withdrawal rate for 30 years. Since there was 0.4% inflation in 1955, the inflation-adjusted withdrawal would be $41,567 ($41,400 x 1.004). Next, we want to determine the maximum withdrawal that the portfolio will allow and not run out of money at the end of the 30-year period. This is done in two steps. First, the “supportable portfolio” is calculated by dividing the “default” inflation-adjusted withdrawal of $41,567 by the current year SWR of 4.14%. The “supportable portfolio” is $1,004,031 ($41,567 / 4.14%). In the second step, we calculate the maximum withdrawal. This is simply the difference between the current portfolio value and the “supportable portfolio”. In this case, the maximum withdrawal will be $1,154,702 minus $1,004,031. So we withdraw $150,671 at the end of the first year. With the first year completed, I can describe how to determine the second year’s withdrawal that will be taken at the end of 1956. First, we calculate the “supportable portfolio”. To do this, we first calculate the “default” inflation-adjusted withdrawal. The inflation rate for 1956 was 3.0%. So we multiply $41,567 by 1.03 which comes to $42,813. Then, we look up the SWR that supported a 50/50 stock/bond mix for 29 years. This was 4.19%. The “supportable portfolio” is $1,021,788 ($42,813 / 4.19%). In the second step, we calculate the maximum withdrawal. At the end of 1956, the portfolio grew to $1,034,848. If we subtract $1,021,788 from $1,034,848, the difference is only $13,060 which is less than the “default” inflation-adjusted withdrawal of $42,813. In this year, there are no extra gains. So we simply take the default withdrawal of $42,813.
Another Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the end of each year. Bottom chart shows portfolio value at the end of each year immediately following that year’s withdrawal.

Prosperous Spending Model
Author	William Bengen
Link	Prosperous Spending Model in Retirement
Spreadsheet	withdrawProsperous.xls
Description This method assumes that spending varies as one ages. For example, in the first ten years, the retiree might spend more pursuing hobbies, travel and entertainment. Then in the second ten years, spending declines as activity slows down. In the final ten years, activity may slow down even further. However, spending might not decline as much if more money is spent on rising health care expenses. The withdrawal amount for the first year is calculated using an initial withdrawal rate that is higher than the standard 4%. The withdrawal amount might rise in the first ten years along with a rise in inflation In the second ten years, the withdrawal amount may grow slower than inflation. For example, we might assume spending grows by inflation less 3%. Similarly, we might assume spending grows by inflation less 1% in the final ten years of retirement.
Chart Example Top chart shows each year’s withdrawals. Withdrawals are taken at the beginning of each year. Bottom chart shows portfolio value at the beginning of each year immediately following that year’s withdrawal.

Note 1

The following articles are historical studies that have examined “safe” withdrawal rates. Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable The Retirement Calculator from Hell Determining Withdrawal Rates Using Historical Data (pdf) Asset Allocation for a Lifetime (pdf) Conserving Client Portfolios During Retirement, Part III (pdf) The following calculators will demonstrate “safe” withdrawal rates using historical data. FIRECalc Max Rate Withdrawal Spreadsheet (xls) Return to the Top

More Links Withdrawal Strategies: Articles and More