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Re: Bengen's 4% Distribution Method


@Mustang wrote:

@PatMorgan wrote:

Taking an initial withdrawal of 4%, with later withdrawals adjusted for inflation, lasted longer when starting for 1968 than it would have for some other starting years.  The number of years depend on details of how the calculation is done.  My calculation adjust for inflation using the average CPI-U over 12 month periods, rather than the change for a month, such as December, from a year ago.  I spent during each month of the year and not only during one month.


I used the inflation Year to Year inflation numbers from the link below.  How is that wrong?  Why would average be better than year to year?


As I wrote: "I spent during each month of the year and not only during one month."  Using the average of the CPI-U over 12 months is a better measure of spending that was done during those months than the CPI-U of only one month of the year.

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Re: Bengen's 4% Distribution Method


@Saratoga wrote:

Mustang,

Thanks.   Just to be sure, would you state once more your method of 5 year review you used in the test?


In Bengen's method the initial investment is multiplied times a rate to get the initial withdrawal.  Subsequent withdrawals are increased for inflation. That rate is different depending upon the length of the retirement period.  The shorter the period the bigger the initial rate that was 100% successful in his tests.  Bengen (and others) have listed the various rates usually in five year increments.

I had a crazy idea that for a five year review to just act as if it was your first year of retirement with a shorter period.  That meant you would multiply the balance after each five year increment times the new higher rate and then increase for inflation.  I had to estimate a rate for a couple of reviews.  In 1968 it fixed the problem of outliving the portfolio but it robbed too much from mid-year retirement for my comfort.  I listed those rates in the other post.

It’s a good year vs. bad year method.  For the 1968 retirement period it robbed a lot mid-years.  For the 1990 retirement period it had a lot higher withdrawals than the standard Bengen method.  For the 1971 retirement period it had mixed results.  It was robbing from withdrawals early on and the giving higher ones at the end.

A method with similar results that allows you to use the same method every year is the Modified RMD method.  It doesn’t rob quite as much from the middle years.  I like it.  If I thought there was enough discretionary income that would be the method I used.  At this time I'm not estimating enough discretionary income to make the mid-retirement years work.

Please remember I’m not an expert and have done extremely limited testing.  Different funds and different time periods could have very different results.

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Re: Bengen's 4% Distribution Method


@PatMorgan wrote:

@Mustang wrote:

@PatMorgan wrote:

Taking an initial withdrawal of 4%, with later withdrawals adjusted for inflation, lasted longer when starting for 1968 than it would have for some other starting years.  The number of years depend on details of how the calculation is done.  My calculation adjust for inflation using the average CPI-U over 12 month periods, rather than the change for a month, such as December, from a year ago.  I spent during each month of the year and not only during one month.


I used the inflation Year to Year inflation numbers from the link below.  How is that wrong?  Why would average be better than year to year?


As I wrote: "I spent during each month of the year and not only during one month."  Using the average of the CPI-U over 12 months is a better measure of spending that was done during those months than the CPI-U of only one month of the year.


I'm not using a single month's rate.  I'm using year-to-year rates that cover the entire year.

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Re: Bengen's 4% Distribution Method


@Mustang wrote:


I'm not using a single month's rate.  I'm using year-to-year rates that cover the entire year.


The inflation rate you are using for a year is the percent difference between the CPI-U for December of a year and for December of the previous year.  Tables you have posted have an inflation rate of 1.7% for 1997.  That is the difference between the CPI-U of 160.5 for Dec. 1997 and  156.9 for Dec. 1996.  However, the difference between the average of the CPI-U for 1997 and for 1996 is 2.3%.

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Re: Bengen's 4% Distribution Method

For anyone concerned that an initial withdrawal of 4%, with later withdrawals adjusted for inflation, taken from an account in the Wellington fund starting in 1968, resulted in the withdrawal for 1979 being 10% of the balance at that time, here is a table for some other staring years of the withdrawal percentage for the tenth year, using the initial withdrawal rate that resulted in account depletion at 30 years.

197010.19%
197110.34%
197212.19%
197311.65%
197410.76%
197511.12%

A withdrawal of more than 10% at the tenth year has not prevented the approach from lasting 30 years.

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Re: Bengen's 4% Distribution Method

Mustang,

Here is another method I had in mind:

Start with Bengen 4% (or any other appropriate x percentage).    At the first five year review, you calculate what the original Bengen withdrawal would give and (the current portfolio balance times new swr) and take the maximum.   Call it W5.   Adjust the W5 for inflation for 4 more years of withdrawal.   At the second review, compute W5 adjusted for 5 years of inflation and (the new balance times new swr) and take the maximum, etc.

I am not an expert either.   But this problem is interesting and potentially useful. 

 

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Re: Bengen's 4% Distribution Method

A variable real withdrawal amount approach described by Bengen is the Floor-and-Ceiling approach:

  • Allow withdrawals to increase during a bull market, but to not more than 25 percent above the real value of the first year's withdrawal
  • Allow withdrawals to decline during a bear market, but not more than ten percent below the real value of the first year's withdrawal.

With an account in the Wellington fund, using an initial withdrawal rate of 4%, when starting for 1968, the real amount withdrawn became the floor amount with the third withdrawal and stayed there until the account was depleted after 34 years. When starting for 1990, the amount withdrawn became the ceiling amount with the eighth withdrawal and as of the end of 2019 the account balance adjusted for inflation was 2.9 times the initial balance.

It is possible that the real withdrawal for a year to be less than the one for the previous year. A lower floor percent or higher ceiling percent could be used.

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Re: Bengen's 4% Distribution Method


@PatMorgan wrote:

@Mustang wrote:


I'm not using a single month's rate.  I'm using year-to-year rates that cover the entire year.


The inflation rate you are using for a year is the percent difference between the CPI-U for December of a year and for December of the previous year.  Tables you have posted have an inflation rate of 1.7% for 1997.  That is the difference between the CPI-U of 160.5 for Dec. 1997 and  156.9 for Dec. 1996.  However, the difference between the average of the CPI-U for 1997 and for 1996 is 2.3%.


Got it.  Here a table with the numbers you are talking about.  This is going to be an easy fix.  Thank you for explaining that.

https://inflationdata.com/Inflation/Consumer_Price_Index/HistoricalCPI.aspx?reloaded=true

 

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Re: Bengen's 4% Distribution Method


@PatMorgan wrote:

A variable real withdrawal amount approach described by Bengen is the Floor-and-Ceiling approach:

  • Allow withdrawals to increase during a bull market, but to not more than 25 percent above the real value of the first year's withdrawal
  • Allow withdrawals to decline during a bear market, but not more than ten percent below the real value of the first year's withdrawal.

With an account in the Wellington fund, using an initial withdrawal rate of 4%, when starting for 1968, the real amount withdrawn became the floor amount with the third withdrawal and stayed there until the account was depleted after 34 years. When starting for 1990, the amount withdrawn became the ceiling amount with the eighth withdrawal and as of the end of 2019 the account balance adjusted for inflation was 2.9 times the initial balance.

It is possible that the real withdrawal for a year to be less than the one for the previous year. A lower floor percent or higher ceiling percent could be used.

Interesting, I read about ceilings and floors but never worked anything with them.  After I'm done mowing I'll fix my interest rates and test that against the Inflation -1% option.  That might be an easier system then trying to mate it with Kitces' ratchet-up method.


 

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Re: Bengen's 4% Distribution Method

@PatMorgan @Mustang 

For what it’s worth: Below is what Pfau shows in his 2018 table for “Bengen’s Dollar-Floor-and-Ceiling”rule, compared with Kitces and Modified RMD. I have no explanation of exactly what Pfau there took the Floor-and-Ceiling rule to be, but he evidently used +20% as a ceiling and -15% as a floor. Pfau assumes a 4% initial withdrawal for each strategy from a $100,000 accumulation, using a 50-50 allocation. Not sure what stock and bond funds were used. (The results are based on rolling 30-year periods from 1926 to 2015.)

1. Bengen’s Dollar-Floor-and-Ceiling Withdrawals
Real spending in 10/20/30 years, 90th percentile: $4800/$4800/$4800
Real spending in 10/20/30 years, 50th percentile: $4,070/$4,390//$4720
Real spending in 10/20/30 years, 10th percentile: $3,400/$3,400/$3,400
Remaining wealth after 30 years, 90th//50th/10th percentile: $292,880/$122,070/$68,660

2. Kitces Ratcheting Rule
Real spending in 10/20/30 years, 90th percentile: $4,840/$6,440/$9,430
Real spending in 10/20/30 years, 50th percentile: $4,000/$5,320/$7,090
Real spending in 10/20/30 years, 10th percentile: $4,000/$4000/$4000
Remaining wealth after 30 years, 90th/50th/10th percentile: $236,960/$79,500/$25,630

3. Modified RMD Rule (1.24 times the RMD)
Real spending in 10/20/30 years, 90th percentile: $7,510/$11,690/$10,180
Real spending in 10/20/30 years, 50th percentile: $5,080/$6,650/$6,220
Real spending in 10/20/30 years, 10th percentile: $3,200/$3,620/$4,250
Remaining wealth after 30 years, 90th/50th/10th percentile: $70,160/$41,570/$30,250


For “Vanguard’s Percentage Floor and Ceiling Withdrawals,” Pfau shows results that are better than #1's at the 90th percentile, but substantially worse at the 50th and (especially) 10th percentiles.

I give extra credit to rules that front-load the withdrawals. The value of a withdrawal depends not just on its size but on the likelihood one will still be around to take it. That’s a comparative merit of Kitces in 10th percentile scenarios and of Modified RMD in 50th and 90th percentile scenarios. (To that end, a variation of the Modified RMD, offered by an AAII author, uses RMD + 2 percentile points, which is more aggressive early, less aggressive late. And I recall that Pfau somewhere caps the Modified RMD at 8.6% of end-of-year balance, providing the IRS doesn't require more.)

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Re: Bengen's 4% Distribution Method

@PatMorgan 

From the US Bureau of Labor Statistics:

“Another consideration is whether to use a particular monthly index from one year to the next, such as December to December, or use annual averages. From a statistical perspective, each of these types of indexes has its advantages. A 12-month percent change from, say, December-to-December, is arguably a more recent estimate of price change than an annual average percent change. Said another way, the December-to-December percent change is the most recent 12-month percent change in a year, while the annual average percent change reflects the change in the average index for all 12 months of one year to the average index for all 12 months the next year. The December-to-December index percent change, however, tends to be more volatile than the percent change in the annual average index. Annual average indexes are based on 12 monthly data points which, when averaged, reduce volatility by smoothing out the highs and lows.”

https://www.bls.gov/cpi/questions-and-answers.htm

From The Balance:

“The best way to compare inflation rates is to use the end-of-year CPI. This creates an image of a specific point in time. For example, in 1933, January began with a CPI of -9.8%. By the end of the year, CPI had increased to 0.8%. If you were to calculate the average for the year, the average would be -5.1%. This gives you the idea that prices had fallen over the year when they had actually risen.”

https://www.thebalance.com/u-s-inflation-rate-history-by-year-and-forecast-3306093

The December to December percent is the most recent 12-month percent change and a calculation can create a negative number can be misleading giving the reader the idea that prices have fallen.  We are using end of year balances to calculate withdrawals and in 2009 using averages resulted in a negative 0.4%.  And the 30-year inflation didn’t differ much.  For December to December it was 354%.  For Average it was 361%.  Since I did all the calculations I decided to compare the two.. 

The 1968 retirement still failed showing 5 years of negative balances.  The 1971 retirement’s ending balances were very close: $1,318,000 for year-to-year and $1,322,000 for averages.  Final withdrawals were also pretty close:  $84,342 for year-to-year and $85,879.  Not bad for 30-years of cumulative differences.  The 1990 retirement’s ending balances pretty close: $3,102,000 for year-to-year and $3,075,000 for averages. So were the withdrawals: $38,872 for year-to-year and $40,501 for averages.  Again, not bad for 30-years of cumulative differences.

Bottom line.  It’s not worth the change.  The differences wouldn't change anything that we have discussed.  I’ll stick with the year-to-year inflation rates for the reasons given in the Bureau of Labor Statistics and The Balanced quotes above.

I can post spreadsheets and comparisons if you wish.  Now, onward to ceilings and floors.

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Re: Bengen's 4% Distribution Method


@Mustang wrote:

 

From The Balance:

“The best way to compare inflation rates is to use the end-of-year CPI. This creates an image of a specific point in time. For example, in 1933, January began with a CPI of -9.8%. By the end of the year, CPI had increased to 0.8%. If you were to calculate the average for the year, the average would be -5.1%. This gives you the idea that prices had fallen over the year when they had actually risen.”

https://www.thebalance.com/u-s-inflation-rate-history-by-year-and-forecast-3306093

 


My opinion differs from that of The Balance.

The difference between CPI-U for January 1932 and January 1933 was -9.8%, and the difference between December 1932 and 1933 was 0.8%. Spending would have been 9.8% less in January 1933 than it would have been in January 1932, using the CPI-U as an indicator of spending.

Because spending would have been done during the entire year, and not only in December, the difference in the average price of -5.1% accurately reflects the change in spending for the entire year. The spending during the entire year of 1933 would have fallen relative to the spending during the entire year of 1932.

There may be little difference in the calculated results using the average CPI-U over a 12-month period versus using the CPI-U for a single month of the year. However, when examining the calculations in detail, it is useful to state what is being used as the adjustment for inflation. I use use the average CPI-U over 12-month periods because it accurately indicates spending during entire years.

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Re: Bengen's 4% Distribution Method

@PatMorgan   I know that you know this.  I just wanted to clarify for anyone else who might be reading this. The inflation rate I'm using is year-to-year.  It covers the price increases for a full year. For example, the increase from December 2018 to December 2019.  Not just one month, example November 2019 to December 2019. 

The problem I see with using each year's 12-month average is that depending upon each month's weight  that average might fall in April of one year and September of the next.  I think that is the primary difference.  But, we agree.  The 30-year accumulated difference is very small.  For those that look at small differences I will specify the method I'm using.  According to the experts, both are correct.

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Re: Bengen's 4% Distribution Method

For some, a table of with dollar values may make it clearer.  Here is a table for the previously mentioned years of 1932 and 1933, with spending for the first month set to $1,000.

 CPI-U  Spending 
 19321933 19321933
Jan.14.312.9 $1,000$902
Feb.14.112.7 $986$888
Mar.14.012.6 $979$881
Apr.13.912.6 $972$881
May13.712.6 $958$881
June13.612.7 $951$888
July13.613.1 $951$916
Aug.13.513.2 $944$923
Sep.13.413.2 $937$923
Oct.13.313.2 $930$923
Nov.13.213.2 $923$923
Dec.13.113.2 $916$923
average13.612.9 $954$904
change -5.19%  -5.19%

 

The -5.19% shown here differs from the reported -5.1% because the -5.19% is calculated from averages that have not been rounded. The percent difference between 13.6 and 12.9 is -5.1% with the percent rounded to 1 digit after the decimal point.

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Re: Bengen's 4% Distribution Method

What Vanguard uses as floors and ceilings in "From assets to income: A goals-based approach to retirement spending" is not what Bengen uses as Floor-and-Ceiling withdrawals.

Vanguard applies a floor and ceiling to the withdrawal amount for the current year relative to the withdrawal amount for the previous year. The withdrawal amount can decrease every year by the floor percentage, -2.5% in the Vanguard article. If the real return of the portfolio is less than the floor percentage for each year over 7 years, the withdrawal amount at the 7th year is -16% relative to the start of that sequence of negative real returns.

Bengen restricts the real withdrawal amount so that it is always at least 90% of the withdrawal amount of the first year, a -10% floor. With a usual withdrawal of 4% of the current balance, the real withdrawal amount for any year will never be less than 3.6% of the initial balance.

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Re: Bengen's 4% Distribution Method

@PatMorgan

Thank you for pointing that out.  I had known about Vanguard's method a long time.  I have a copy of their October 2013 paper on my drive. I must have read it a long time ago be cause I had an inkling Bengen's method was different but when I went looking for his 2001 paper yesterday I didn't have permission to read it. Most of the things I've read talked about the differences in the percentages used.  After your comments I went looking.  I still don't have permission to actually read Bengen's work but I did discover an article by Wade Pfau that agrees.  It says the ceiling is 20% above the real value of the first year's withdrawal and the floor is 15% below the real value of the first year's withdrawal.

That is a completely different method.  It will most likely change everything.  Since I already have the spreadsheets set up I'll alter them to Vanguard's method first and look at Bengen's later.  I'll delete my other posts and put up ones that are accurate later.

Thanks for pointing that out.  It looks like I'll have something to do if it rains tomorrow besides watching the news.

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Re: Bengen's 4% Distribution Method

There is a huge difference between Vanguard’s ceilings and floors methodology and Bengen’s ceiling and floors methodology. A huge difference.  Both use the initial rate times the end of year balance but Vanguard has no mechanism to include inflation.  Bengen’s ceilings and floors are adjusted for inflation.  This is particularly important during periods of very high inflation such as the 1970s. 

Wellington’s performance back then did not match the general market data that Bengen used.  It failed to last 30 years for a 1968 retirement.  Our journey along this thread was to find a method that allowed Wellington to succeed.  My complaint with most of the other proposed alternatives is that they would only work if the retiree had significant discretionary income.  Most of the other proposals cut the retiree’s standard of living in half during mie-retirement.  Bengen’s ceiling and floors didn’t.

I have may have found a new favorite withdrawal method.  Bengen’s ceilings and floors.  It made it through the first hurdle which was to provide a livable income during the the 1968 retirement.  Now I need to see how it does during a very good retirement period where people make money almost by accident.

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Re: Bengen's 4% Distribution Method

Is the Bengen ceilings-and-floor rule you're referring to the same one that Pfau tested? That one had a floor of 85% of the real initial withdrawal and a ceiling of 120% of the initial real withdrawal. Pfau's table shows the Kitces rule decidedly superior to that rule for 90th, 50th, and 10th percentile scenarios.  

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Re: Bengen's 4% Distribution Method

Here are charts of the results of my calculations using Bengen and Vanguard floor and ceiling withdrawals from the Vanguard Wellington fund (VWELX). The charts are for the two starting years that have been previous mentioned.

 

vwelx-fnc-1968-2001.svg

When starting in 1968, with the Bengen method, the withdrawal for all but the first two years is the floor amount. With the Vanguard method, the withdrawal for most years from the 2nd to 28th decreases by the floor percent from the withdrawal for the previous year; the withdrawal for later years increases by the ceiling percent. Because of the usually higher withdrawals by the Bengen method, there is not enough of a balance to take the withdrawal for the 35th year; with the Vanguard method the real balance after 34 years is 0.83 times of the initial balance.

 

vwelx-fnc-1990-2019.svg

When starting in 1990, with the Bengen method, the withdrawal starting with the 8th year is the ceiling amount. With the Vanguard method, the withdrawal for 16 of the years increased by the ceiling percent relative to the previous year; the withdrawal for 8 years decreased by the floor percent. Because of the usually lower withdrawals with the Bengen method, real balance after 30 years is 2.9 times the initial balance, with the Vanguard method it is 2.2 times the initial balance.

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Re: Bengen's 4% Distribution Method

@Mustang 

Mustang, I evidently don't understand the Ceilings & Floors rule, or else don't understand how to read the table for 1990-2020, the first part of which is copied below. In 1991, how could the beginning balances differ for the three rules, given that during 1990 the same $20K was withdrawn for all three rules, from the same 1990 beginning balance, and all using Wellington?  

 

Bengen 4%

Rule

Ceilings &

Floors

Kitces

Ratchet-up

year

Beg Bal

Withdraw

Beg Bal

Withdraw

Beg Bal

Withdraw

1990

$500,000

$20,000

$500,000

$20,000

$500,000

$20,000

1991

$466,512

$21,220

$498,048

$19,922

$466,512

$21,220

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