A Hand Calculation for 2000 to 2005.

Research on Safe Withdrawal Rates

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JWR1945
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A Hand Calculation for 2000 to 2005.

Post by JWR1945 »

Here are my hand calculations for a 100% stock portfolio that started in January 2000.

These are the inputs from Professor Robert Shiller's database. I copied these numbers today. I have limited my own precision to two decimal places for dividend yields when making my hand calculations.

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Date   Price   Dividend         CPI   
2000   1425.59   16.57333333   168.8      
2001   1335.63   16.17         175.1   
2002   1140.21   15.73666667   177.1
2003    895.84   16.12         181.7   
2004   1132.52   [?]           185.2 


Here are some approximate numbers for January 2005. The original source is the cbs.marketwatch.com website. I have used today's dividend yield of 1.65% for 2004.

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I have used an index value of 1185.00 for January 2005.
I have used a dividend yield of 1.65% for 2004.
You must always make all of these steps.

January 2000.

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Start with $1000000 in January 2000.
To be as favorable as possible, we withdraw at the end of the year.
Dividend yield is 16.57 divided by 1425.59.  This equals 1.16%.
Dividend amount in 2000 is the initial balance times yield or $11600.
Price change equals 2001 index value divided by 2000 index value.
Price adjustment equals 1335.63/1425.59 or 0.9369.
Price at the end of 2000 equals $936900.
Add the dividend amount.
Balance before withdrawals: $948500.
Withdraw $40000.
Balance after withdrawals: $908500.
January 2001.

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Start with $908500 in January 2001.
To be as favorable as possible, we withdraw at the end of the year.
Dividend yield is 16.17 divided by 1335.63.  This equals 1.21%.
Dividend amount in 2001 is the initial balance times yield or $10993.
Price change equals 2002 index value divided by 2001 index value.
Price adjustment equals 1140.21/1335.63 or 0.8537.
Price at the end of 2001 equals $775586.
Add the dividend amount.
Balance before withdrawals: $786579.
Withdraw $40000.
Balance after withdrawals: $746579.
January 2002.

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Start with $746579 in January 2002.
To be as favorable as possible, we withdraw at the end of the year.
Dividend yield is 15.74 divided by 1140.21.  This equals 1.38%.
Dividend amount in 2002 is the initial balance times yield or $10303.
Price change equals 2003 index value divided by 2002 index value.
Price adjustment equals 895.84/1140.21 or 0.7857.
Price at the end of 2002 equals $586587.
Add the dividend amount.
Balance before withdrawals: $596890.
Withdraw $40000.
Balance after withdrawals: $556890.
January 2003.

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Start with $556890 in January 2003.
To be as favorable as possible, we withdraw at the end of the year.
Dividend yield is 16.12 divided by 895.84.  This equals 1.80%.
Dividend amount in 2003 is the initial balance times yield or $10024.
Price change equals 2004 index value divided by 2003 index value.
Price adjustment equals 1132.52/895.84 or 1.2642.
Price at the end of 2003 equals $707020.
Add the dividend amount.
Balance before withdrawals: $717044.
Withdraw $40000.
Balance after withdrawals: $677044.
January 2004.

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Start with $677044 in January 2004.
To be as favorable as possible, we withdraw at the end of the year.
Dividend yield is unknown.   We shall use today's value of 1.65%.
Dividend amount in 2004 is the initial balance times yield or $11171.
Price change equals 2005 index value divided by 2004 index value.
Price adjustment equals 1185.00/1132.52 or 1.0463.
Price at the end of 2004 equals $708391.
Add the dividend amount.
Balance before withdrawals: $719562.
Withdraw $40000.
Balance after withdrawals: $679562.
The starting balance in January 2005 is $679562.

Here are the inflation adjustment calculations.

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Inflation adjustment for 2000 through 2004:      
Starting index value:     168.8
Ending index value:  185.2
Ratio:   0.9114 or 91.14%   
Estimated inflation adjustment for 2004 to 2005:
Assume 3%.
Multiplier equals 97% or 0.9114.

Estimated inflation adjustment for 2000 to 2005:
Multiply 0.9114 by 0.97.
Adjustment for inflation equals 0.8841 or 88.41%.


SUMMARY:

We started with $1 000 000 in January 2000.

I have examined a portfolio with 100% stocks. [Please don't ask for anything more complicated. These hand calculations are difficult enough as is.]

We have made four withdrawals of $40000 with no adjustments for inflation.
The balance in January 2005 is $679562 (nominal) before adjusting for inflation.
The balance in January 2005 is $600801 (real) after adjusting for inflation.

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A retiree who started with $1.0 million in January 2000

and

who withdrew $40000 at the end of each year (without increasing his withdraws to match inflation)

would now have

$679562 (nominal).
His buying power would now be $600801 (real) in year 2000 dollars.

His withdrawals have remained at $40000 (nominal). His withdrawal in January 2005 has a buying power of $35364 (real) in year 2000 dollars.


This may help to put things into perspective. If our retiree had placed all of his money ($1000000) in cash at zero percent interest, he would have $840000 (nominal) in January 2005. His buying power in January 2005 would now be $742644 (real) in year 2000 dollars.

Even though our retiree has cut back since 2000 (because the stock market has done poorly), he has suffered a major loss of capital. If he has maintained a high exposure to stocks, his portfolio could be down by as much as 40% of its original buying power. Even cash without interest would have been limited to a loss of 26% of its original buying power.

Have fun.

John R.
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Post by ben »

My lazy buggar couch potato unclemick stylke buys the VBINX consisting of total US stock market 60% and total US bond market 40 % and takes the first 40k out already on 1st Jan 2000(how the heck can he pull END year!? :lol: cat food for a year!?). He had much more left at the end of 2004 according to my nos:
year w/r+CPI VBINX Balance end year
2000 40000 -2 940800
2001 40640 -3 873155.2
2002 41615 -9.5 752543.5552
2003 42364 19.9 851504.7633
2004 43847 9.3 882769.7257
So he has 883k left. Note that JWR juses SP500 and some shiller base. I use a REAL FUND with real results for a total market portfolio 60/40. No cat food yet for him. :D

JWR am I missing something? I don't think so? Cheers, Ben
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Post by unclemick »

Chickenheartedness being my favorite investment theory(at least currently). Bogle, JWR and Ben notwithstanding, if I couldn't make the portfolio yield do the work of 40k(by being cheap), then I would change the portfolio to up the yield.

Still old school - heh,heh,heh. Doesn't mean it wouldn't work - BUT Bogle's 1999 stocks for the next decade calc comes in roughly 1.8% - not to far from some of the SWR Research to date.

And Bogle has that buried in his article for Philanthropic - read 5% take out to keep the IRS happy.

So Bogle is more toward Ben as to take out numbers over a period - but by his own method of calc circa 1999(aka 2000) the stock side looks hand grenade close to to some of JWR's data runs.

One more wild card - the correlation between earnings yield and risk free interest rate since 1926 is 0.42 per Bogle - so he takes interest projections as the current yield and does not try adjust P/E - ?? uses historical values to 'guess' what average P/E might be reasonable.

Hmmm - either set of numbers are interesting. But I would struggle for a Ben Graham margin of safety - if it were me.

Tongue in cheek - Bogle and Ben are optimists - while JWR and I are more conservative - er not pesimists - just conservative.
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Post by JWR1945 »

Here is a comparison of S&P500 returns and Ben's fund holdings (conceptual) when there are no withdrawals.

S&P500 stocks

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S&P500 return = price gain + dividend yield = total return         
Year   Prices   Dividends   Total
2000    -6.31   1.16     -5.15
2001   -14.61   1.21    -13.40
2002   -21.43   1.38    -20.05
2003    26.42   1.80     28.22
2004     4.63   1.65      6.28
Gain multipliers = 1 + r where r is the total return as a decimal fraction
Year Gain multiplier
2000 0.9485
2001 0.8660
2002 0.7995
2003 1.2822
2004 1.0628


100% S&P500 stock portfolio

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Product of gain multipliers = 0.8949.
Cumulative nominal return equals -10.51%.
Fifth root of gain multiplier product = 0.9780.
Annualized nominal return = -2.20%.
Inflation adjustment = 0.8841
Product of gain multipliers*Inflation adjustment = 0.7912.
Cumulative real return equals -20.88%.
Fifth root of gain multiplier product (real) = 0.9542.
Annualized real return = -4.58%.

60% S&P500 stocks and 40% cash

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Gain multiplier = 1 + 0.60*r where r is the total return for the S&P500.   
Cash has an interest rate of zero percent.   
Year   Gain multiplier
2000   0.9641
2001   0.9196
2002   0.8797
2003   1.1693
2004   1.0377

Portfolio with 60% S&P500 stocks and 40% cash

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Product of gain multipliers = 0.9513.
Cumulative nominal return equals -4.87%.
Fifth root of gain multiplier product = 0.9901.
Annualized nominal return = -0.99%.
Inflation adjustment = 0.8841
Product of gain multipliers*Inflation adjustment = 0.8410.
Cumulative real return equals -15.90%.
Fifth root of gain multiplier product (real) = 09660.
Annualized real return = -3.40%.

Ben's Holdings (conceptual)

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Year   Return   Gain multiplier
2000   -2.0%   0.980
2001   -3.0%   0.970
2002   -9.5%   0.905
2003   19.9%   1.199
2004    9.3%   1.093

Ben's Portfolio (conceptual)

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Product of gain multipliers = 1.127.
Cumulative nominal return equals 12.7%.
Fifth root of gain multiplier product = 1.0242.
Annualized nominal return = 2.42%.
Inflation adjustment = 0.8841
Product of gain multipliers*Inflation adjustment = 0.9964.
Cumulative real return equals -0.36%.
Fifth root of gain multiplier product (real) = 0.9993.
Annualized real return = -0.07%.

SUMMARY:

Ben has had us consider an investment portfolio that has matched inflation almost exactly between January 2000 and January 2005.

Ben's portfolio (conceptual) has done much better than the S&P500. The S&P500 lost 20.88% in buying power during the same time frame. This is an annualized real loss of 4.58% per year over 5 years.

Ben's portfolio (conceptual) consists of 60% stocks and 40% bonds. A portfolio consisting of 60% stocks as represented by the S&P500 index and 40% cash without interest would have lost 15.90% in buying power from January 2000 to January 2005. This is an annualized real loss of 3.40% per year over 5 years.

[I use cash with zero percent interest because I am making my calculations manually. In addition, I have no data for commercial paper and/or bonds.]

A portfolio that matches inflation exactly every year has a true 30-year Safe Withdrawal Rate of 3.33% (of the initial balance) plus inflation.

SUPPLEMENTAL CALCULATIONS:

Ben's fund portfolio (conceptual) using my method. This allows us to make direct comparisons.

All withdrawals are $40000 in nominal dollars. This is Ben's approach when stocks do poorly.

Ben's Holdings (conceptual)
Year, Gain multiplier, Initial Balance, Interim Balance, After $40000 withdrawal

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2000   0.980   $1,000,000  $980,000   $940,000
2001   0.970    $940,000   $911,800   $871,800
2002   0.905    $871,800   $788,979   $748,979
2003   1.199    $748,979   $898,026   $858,026
2004   1.093    $858,026   $937,822   $897,822
January 2005 balance: $897,822 (nominal dollars).
Inflation adjustment = 0.8841.
January 2005 balance in terms of year 2000 dollars: $793764.

Here is what happens when we withdraw $40000 at the beginning of 2000.
Year, Gain multiplier, Initial Balance, Interim Balance, After $40000 withdrawal

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2000   0.980   $960,000   $940,800   $900,800
2001   0.970   $900,800   $873,776   $833,776
2002   0.905   $833,776   $754,567   $714,567
2003   1.199   $714,567   $856,766   $816,766
2004   1.093   $816,766   $892,725   $852,725
NOTE: The 2004 interim balance was $893K. After the 2004 withdrawal, the balance was $853K. This is why we got different numbers.
January 2005 balance: $852725 (nominal dollars).
Inflation adjustment = 0.8841.
January 2005 balance in terms of year 2000 dollars: $753894.

Have fun.

John R.
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Post by JWR1945 »

From my earlier thread:
Calculated Rates of the Last Decade dated Wed Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657

With 50% stocks for 2000:
The Safe Withdrawal rate was 2.54%.
The Calculated Rate was 3.55%.
The High Risk Rate was 4.56%.

With 80% stocks for 2000:
The Safe Withdrawal rate was 1.59%.
The Calculated Rate was 3.17%.
The High Risk Rate was 4.75%.

Remember that the Calculated Rate corresponds to 50-50 odds.

Withdrawing $40000 nominal corresponds to a real withdrawal rate varying from 4.0% to 3.5%.

With the 100% S&P500 stock portfolio, we would expect that the likelihood of failure is greater than 50%. From a previous investigation (reported during the very early days of the FIRE board), if a portfolio falls below 50% of the initial balance (in nominal dollars) within the first eleven years, it is almost certain to fail. Anything below 70% is in danger.

The 100% stock portfolio is in danger. There is still a little bit of hope.

With a 60% S&P500 stock portfolio, we would estimate that the likelihood of failure is close to 50%. The Calculated Rate, which has a 50% chance of success, with a 50% stock portfolio is 3.55% and we have gradually cut our withdrawals down to 3.5%.

Ben's investments use (corporate) bonds instead of commercial paper. This has kept his (nominal) balance up to 85% to 90% of his initial balance. This is in a favorable region. However, his nominal balance did fall to 75% earlier. This suggests that he should continue to monitor its progress carefully. Currently, his odds are slightly in favor success. Within the next six years, his portfolio is likely to have grown sufficiently or lost badly enough for him to declare success or failure with confidence.

Have fun.

John R.
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Post by hocus2004 »

Currently, his odds are slightly in favor of success.

I made a bit of a case in favor of the Ben approach in the other thread (the one started by Ben that is titled something like "The Year 2000 Retiree"). In Ben's real portfolio, he does not have just stocks and bonds. He also has things like timber and gold (as I recall). These are asset classes that tend to do well when stocks do poorly. So the real Ben portfolio (not the 60-40 simplified version described in his post) might enjoy better odds of success. My guess is that it does.
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Post by hocus2004 »

From a previous investigation (reported during the very early days of the FIRE board), if a portfolio falls below 50% of the initial balance (in nominal dollars) within the first eleven years, it is almost certain to fail. Anything below 70% is in danger.

Here is a link to a thread from the Good Old Days at the FIRE board titled "A Helpful Detour:"

http://nofeeboards.com/boards/viewtopic.php?t=1000

The research discussed in that thread was updated a little bit in a discussion held at the bottom (for now) of this thread, one that I think of endearingly as the "Makes Me Wanna Be Sick"Â￾ thread (it's true title is "Juicy SWR Thread on Early Retirement Forum"Â￾):

http://nofeeboards.com/boards/viewtopic.php?t=1516
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Post by unclemick »

Careful Hocus - slicing and dicing is addictive like caffeine in coffee - I was there in the 1980's/early 90's before I became a 'born again Boglehead'. With 75% Vg Lifestrategy mod (not a 'pure' 60/40) plus REIT's and dividend stocks - even I am backsliding somewhat.

Seriously - the big benefit of these exercises puts well crafted numbers forward which the individual can use to construct 'his' retirement - with a real feel for the options/odds and most importantly what to watch/monitor in case he/she needs to adjust in the stretch.

Me - heh, heh -perhaps I can downsize my 1.8 - 5% handgrenade to an economy model.

As of 1/19/05 Vg posts 2.39% yield for Balanced Index.
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Post by ben »

Hocus is ofcourse right - my own portfolio is different from the Mr. lazy-buggar-couch-potato-2000-retiree (LBCP) I am describing. :D

I am however using LBCP an example to compare with as buying VBINX is as simple as it gets - and makes much more sense than buying only PARTS of the US equity and bond market now that we HAVE such a great fund tool to use. It simply has 60% tot US equity and 40% tot US bonds.

I don't understand JWR comment that I use (corporate) bonds instead of commercial paper - I USE ! TOTAL BOND FUND THAT CONTAINS ALL US BONDS BUT MOSTLY OF COURSE GOV BONDS.

I also do not understand why JWR compare the VBINX with SP500 60% and CASH 40% portfolio? Should at least be commercial papers for the 40%.

Also not quite clear what JWR means with Bens holdings "conceptual"? It is LBCP holding VBINX - nothing conceptual there?

We also do still not agree on the end number as my IS $893k AFTER the $40k pulled (say 31st dec 2003 eve) for the year 2004. Below are my numbers with no inflation adjustment at all:

year w/r VBINX balance end year
2000 40000 -2 940800
2001 40000 -3 873776
2002 40000 -9.5 754567
2003 40000 19.9 856766
2004 40000 9.3 892725

Is this really rocket science since we cant even agree on something this simple? Cheers, ben
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Post by JWR1945 »

ben wrote:Hocus is of course right - my own portfolio is different from the Mr. lazy-buggar-couch-potato-2000-retiree (LBCP) I am describing. :D

I am however using LBCP an example to compare with as buying VBINX is as simple as it gets - and makes much more sense than buying only PARTS of the US equity and bond market now that we HAVE such a great fund tool to use. It simply has 60% tot US equity and 40% tot US bonds.

I don't understand JWR comment that I use (corporate) bonds instead of commercial paper - I USE ! TOTAL BOND FUND THAT CONTAINS ALL US BONDS BUT MOSTLY OF COURSE GOV BONDS.

I also do not understand why JWR compare the VBINX with SP500 60% and CASH 40% portfolio? Should at least be commercial papers for the 40%.

Also not quite clear what JWR means with Bens holdings "conceptual"? It is LBCP holding VBINX - nothing conceptual there?

We also do still not agree on the end number as my IS $893k AFTER the $40k pulled (say 31st dec 2003 eve) for the year 2004. Below are my numbers with no inflation adjustment at all:

year w/r VBINX balance end year
2000 40000 -2 940800
2001 40000 -3 873776
2002 40000 -9.5 754567
2003 40000 19.9 856766
2004 40000 9.3 892725

Is this really rocket science since we cant even agree on something this simple? Cheers, ben
OK. The fund has whatever it has. My main points are that it is very likely to be better than commercial paper (or a money market fund) and that it is almost certain to be better than cash at zero percent interest.

The main reason for my comparisons with cash at zero percent interest is that I AM DOING ALL OF THIS BY HAND! In addition, I don't have the data for anything else.

I looked at 60% stocks and 40% cash without interest as an approximation that I could calculate and do so without too much effort.

I knew very well that you have not presented your actual holdings and your actual withdrawal procedure (especially since you are not yet making withdrawals). You have presented a portfolio that is conceptual in the sense of its being your own portfolio.

Rocket science is much easier.

I have provided all of my calculations to avoid misunderstandings regarding the details. There are almost always differences in how people calculate their numbers. For example, the level of precision influences calculated balances slightly.

Look at my calculations, starting with:
SUPPLEMENTAL CALCULATIONS:
Ben's fund portfolio (conceptual) using my method. This allows us to make direct comparisons.
...
Scroll down to:
Here is what happens when we withdraw $40000 at the beginning of 2000.
Year, Gain multiplier, Initial Balance, Interim Balance, After $40000 withdrawal

Read my Interim Balance for 2004. It is exactly $892,725.

This lets us both know exactly what is going on.

Have fun.

John R.
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Post by ben »

But what IS interim balance? MINE is the END year balance of 2004. Yours is obviously not?
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Post by ben »

Ah reading it again you use the word interim for same as my END year. He ENDED 2004 with $893k(in todays USD) and about 20k less if he had adjusted the w/d for inflation. Phew...we agree! :D
Looking at 2005 he would then have pulled $40k out but they are STILL in his ING Orange account(most of them) so does not give a correct picture to say that he falls to $853 as such - still has the $40k on top.

All that said; a slight adjustment to the portfolio we usually throw around, by using VBINX, Mr. LBCP still has close to $900k in todays USD.

A (very little) bit of diversification has, as JWR pointed out, made a HUGE difference. That is great news for a full blown diversifier like me! :D Historical nos with REITs/commodities Etc. for the time periods we have had that also indicated an improvement of the SWR through diversification.

We will see whether the VBINX is enough diversification to make Mr. LBCP last 30 years at the 4% w/r. Cheers, Ben
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Post by JWR1945 »

That is why I presented all of my numbers.

My procedure includes a withdrawal at the very end of each year.

My original calculations had no withdrawal at the beginning of 2000. This corresponds to what FIRECalc produces.

My second set of calculations has a withdrawal at the beginning of 2000. Otherwise, the procedure is identical to that used with my original calculations. This corresponds to what FIRECalc produces when you place a special checkmark in the right box.

I have aligned my own procedures to match those of dory36's FIRECalc. (Splitting withdrawals into two portions, which is what happens with the Retire Early Safe Withdrawal Calculator, would just make things harder for me.)

You may have guessed this already: there is no single, standard procedure.

Have fun.

John R.
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Post by ben »

You may have guessed this already: there is no single, standard procedure.
Yes you can say that again! :lol:

for a real life retiree 31st Dec 1999 the situation is however that he would need to pull some money out for spending - he can certainly not wait untill end 2000....

With VBINX doing so well for the period I thought of Hocus mention of Browne. And the PRPFX fund I mentioned being more diversified. Here are the returns 00-04: 5.9% 3.8% 14.4% 20.5% 12%. My quick typing
tells me that he would be having $1.4M in his portfolio at end of 2004 (and a little less if adjusted w/r for inflation). Sweet....
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Post by JWR1945 »

dory36 started out programming FIRECalc your way:
for a real life retiree 31st Dec 1999 the situation is however that he would need to pull some money out for spending - he can certainly not wait until end 2000....
Originally, you had to check the box to make the first withdrawal at the end of the first year.

Retire Early generalized and compromised. You can split your allocation into any percentage between the beginning and the end of a year. The default setting, which is the compromise, is for 50% at the beginning of the year and 50% at the end.

To convert that $1.4 million into year 2000 dollars, multiply by 0.8841 (roughly 88%). The buying power of this portfolio is growing.

Have fun.

John R.
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Post by JWR1945 »

For ben:

Here are the returns of stocks, commercial paper and a ladder of 5-year Treasury Notes for 2000-2004.

Year, Returns of VBINX, Stocks, Commercial Paper and the Ladder

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2000   -2.0    -5.15   6.22   6.30
2001   -3.0   -13.40   3.95   4.81
2002   -9.5   -20.02   1.76   4.19
2003   19.9    28.22   dummy  dummy
2004    9.3     6.28   dummy  dummy

Baseline = 0.6*stocks+0.4*ladder
dummy values of 0.4*Ladder were 1.5% for 2003 and 2004
Year, Returns of VBINX an the Baseline

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2000   -2.0    -0.57
2001   -3.0    -6.12
2002   -9.5   -10.35
2003   19.9     18.4
2004    9.3      5.3
Tabulated Results
Start: 1000000 960000 960000

Code: Select all

2000   Gain   994300   954528   940800
   Withdrawal   -40000  -40000  -40000
   Balance    954300   914528   900800
            
2001   Gain   895897   858559   873776
   Withdrawal   -40000  -40000  -40000
   Balance    855897   818559   833776
            
2002   Gain   767312   733838   754567
   Withdrawal   -40000  -40000  -40000
   Balance    727312   693838   714567
            
2003   Gain   861137   824504   856765
   Withdrawal   -40000  -40000  -40000
   Balance    821137   784504   816766
            
2004   Gain   864657   826083   892725
   Withdrawal   -40000  -40000  -40000
   Balance    824657   786083   852725
5-year inflation multiplier = 0.8841
2004 Before Withdrawal 764443 730340 789258
2004 After Withdrawal 729079 694976 753894

The bolded numbers form the comparison.

VBINX did slightly better than have a ladder of 5-year Treasury Notes for the (40% non-stock) fixed income component.

These results are much closer than previously calculated.

Have fun.

John R.
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