Last week, we looked at a retirement withdrawal strategy that crashed and burned for Mr. and Mrs. Growth. They were withdrawing from a $1,000,000 nest egg using the familiar 4% rule. That rule starts with a 4% withdrawal in Year 1 and then adds 3% each year to the withdrawal amount to keep up with inflation. It turned out that the growth in the Growth’s retirement assets just could not keep up with the compounding effect of that 3% per year inflation increment. Their average annual return also equaled 3%. They ran out of money in Year 25 of a 30year plan.
If you recall, the Growths’ financial advisor set them up with a conservative asset allocation to match their conservative risk profile. In last week’s article, the return on their portfolio exactly matched the rate of inflation at 3% per year, and it just wasn’t enough.
The Growths’ advisor recommended an asset allocation and a withdrawal strategy to meet their goals. The advisor adjusted their asset allocations according to his understanding of Modern Portfolio Theory. In addition to his formal training, he keeps up with his field by reading journals, newsletters, and the Wall Street Journal every day. He believed that the best path to follow was a total return strategy.
The Growths seemingly had already done the hard part by accumulating the $1,000,000. In a total return strategy, a withdrawal plan is mandatory. That is because the portfolio is not constructed to generate all the income needed. Rather, it is designed to have parts of the nest egg be sold off each year to obtain the cash needed for living expenses. The most common guideline is the 4% rule as described above, with 3% withdrawal increments each year to cover inflation.
Assumptions
Several commenters objected to the “unrealistic” nature of the assumptions in last week’s sample. So let’s revisit the situation and run other trials using different assumptions.
 Instead of the flat 3% return every year, the returns will follow the pattern actually achieved by the stock market in 20002009. That 10year span will simply be repeated to get the 30year total return sequence.
 The Growths requested a conservative portfolio. I use two models to reflect what their advisor has achieved through asset allocation.
 Model A: Twothirds of the S&P 500’s returns are achieved each year. This not only reflects the conservative construction of their asset allocation (it’s heavy on bonds), but it also dampens the volatility of their portfolio, as bonds tend to do.
 Model B: Here, their advisor hits a home run. He manages to outgain the S&P 500 by 5% each and every year, in good years and in bad.

Just for fun, we’ll run the 30year sequence twice.
 Trial 1: The sequence will be run forward, just as it happened. This is a real stress test, because the 20002009 period started with three bad years.
 Trial 2: The sequence will be run backward. This produces positive returns in 6 of the first 7 years and should get the portfolio off to a great start in its quest to achieve the Growths’ 30year retirement goal.
Other assumptions remain the same:
 Mr. and Mrs. Growth start off with $1,000,000 on the day they both retire.
 Following their advisor’s recommendation, they follow the 4% + inflation rule for making withdrawals from their retirement nest egg.
 Transaction costs are ignored.
 Taxes are ignored.
 Each withdrawal is made at the beginning of the year.
 The nest egg’s balance at the end of each year—after that year’s annual growth—equals its beginning balance for the next year.
Discussion:
I lied. Running the return sequence forward and backward is not just for fun. It is, in fact, a main point of this article. I want to demonstrate the surprising impact that the sequence of returns has on the entire 30year strategy.
One suggestion by commenters last week was that the Growths not make their first withdrawal at the beginning of the first year but rather at the end of the year. I thought about making this change but then realized that it does not conform to the basic premise. It would impact the results if someone handed the Growths $40,000 to live on in their first year. But they need to fund their first year of retirement themselves—that’s what the nest egg is for. So either we can say that they have $1,000,000 and take $40,000 out for the first year, or we can say that they have the first year covered but a portfolio of only $960,000. They can’t have it both ways. We can’t just add $40,000 to the portfolio that they do not have.
Here’s the return series. The table below shows:
 Actual year.
 Year number in the Growths’ retirement. The 10year series will be repeated to total 30 years. The series will be run both forward (Trial 1) and backward (Trial 2).
 The actual total returns including dividends of the S&P 500 (according to MoneyChimp) in 20002009, rounded to the nearest whole percent.
 Model A: Volatility cut down to 2/3 of what it actually was.
 Model B: Five percent added to each year’s returns.
Year  2000  2001  2002  2003  2004  2005  2006  2007  2008  2009 
Year#  1  2  3  4  5  6  7  8  9  10 
Actual  9%  12  22  29  11  5  16  6  37  27 
A  6%  8  15  19  7  3  11  4  25  18 
B  4%  7  17  34  16  10  16  11  32  32 
This will give us four shots at a successful 30year retirement for the Growths: 1A, 2A, 1B, and 2B. Do you think any of them will work? Here are the trials:
 1A: Years run forward; volatility dampened to 2/3 of actual.
 2A: Years run backward, volatility same as 1A
 1B: Years run forward; returns 5% better than S&P 500.
 2B: Years run backward; returns same as in 1B.
Run 1A: Sequence Run Forward and Volatility Dampened to 2/3 of S&P 500’s Volatility
First Decade:
Year Number 
Beginning Balance $  Amount Withdrawn $  Amount Remaining $  Annual Return %  End Balance $ 
1  1,000,000  40,000  960,000  6  902,400 
2  902,400  41,200  861,200  8  792,304 
3  792,304  42,436  749,868  15  637,388 
4  637,388  43,709  593,679  19  706,478 
5  706,478  45,020  661,458  7  707,760 
6  707.760  46,371  661,389  3  681,230 
7  681,230  47,762  633,468  11  703,150 
8  703,150  49,195  653,955  4  680,113 
9  680,113  50,671  629,442  25  472,082 
10  472,082  52,191  419,891  18  495,471 
Second Decade:
11  495,471  53,757  441,714  6  415,211 
12  415,211  55,370  359,841  8  331,054 
13  331,054  57,031  274,023  15  232,919 
14  232,919  58,742  174,177  19  207,271 
15  207,271  60,504  146,767  7  157,041 
16  157,041  62,319  94,722  3  97,563 
17  97,563  64,189  33,374  11  37,045 
18  37,045  66,115  (29,609)  0  0 
19  0  0  0  0  0 
20  0  0  0  0  0 
Third Decade:
There is no third decade. The Growths ran out of money in Year 18 of their planned 30year retirement.
Run 2A: Sequence Run Backward and Volatility Dampened to 2/3 of S&P 500’s Volatility
First Decade:
Year Number 
Beginning Balance $  Amount Withdrawn $  Amount Remaining $  Annual Return %  End Balance $ 
1  1,000,000  40,000  960,000  18  1,132,800 
2  1,132,800  41,200  1,091,600  25  818,700 
3  818,700  42,436  776,254  4  807,315 
4  807,315  43,709  763,606  11  847,602 
5  847,602  45,020  802,582  3  826,660 
6  826,660  46,371  780289  7  834,909 
7  834,909  47,762  787,147  19  936,705 
8  936,705  49,195  887,510  15  754,383 
9  754,383  50,671  703,712  8  647,415 
10  647,415  52,191  595,224  6  559,511 
Second Decade:
11  559,511  53,757  505,754  18  596,790 
12  596,790  55,370  540949  25  405,711 
13  405,711  57,031  348,680  4  362,628 
14  362,628  58,742  303,886  11  337,313 
15  337,313  60,504  276,809  3  285,113 
16  285,113  62,319  222,794  7  238,390 
17  238,390  64,189  174,201  19  207,299 
18  207,299  66,115  141,184  15  120,006 
19  120,006  68,098  51,908  8  47,755 
20  47,755  70,141  (22,386)  0  0 
Third Decade:
Once again, there is no third decade. The Growths ran out of money in Year 20 of their planned 30year retirement. The resequencing of returns did get them an extra two years.
Run 2A: Sequence Run Forward and Returns 5% Better than S&P 500 Every Year
First Decade:
Year Number 
Beginning Balance $  Amount Withdrawn $  Amount Remaining $  Annual Return %  End Balance $ 
1  1,000,000  40,000  960,000  4  921,600 
2  921,600  41,200  880,400  7  818,772 
3  818,772  42,436  776,336  17  644,359 
4  644,359  43,709  600,650  34  804,871 
5  804,871  45,020  759,851  16  881,427 
6  881,427  46,371  835,056  10  918,562 
7  918,562  47,762  870,800  16  1,010,127 
8  1,010,127  49,195  960,932  11  1,066,635 
9  1,066,635  50,671  1,015,964  32  690,856 
10  690,857  52,191  638,665  32  843,037 
Second Decade:
11  843,037  53,757  789,280  4  757,709 
12  757,709  55,370  702,339  7  653,175 
13  653,175  57,031  596,144  17  494,800 
14  494,800  58,742  436,058  34  584,317 
15  584,317  60,504  523,813  16  607,623 
16  607,623  62,319  545,303  10  599,835 
17  599,835  64,189  535,646  16  621,349 
18  621,349  66,115  555,234  11  616,310 
19  616,310  68,098  548,212  32  372,784 
20  372,784  70,141  302,643  32  399,489 
Third Decade:
21  399,489  72,245  327,244  4  314,154 
22  314,154  74,413  239,741  7  222,959 
23  222,959  76,645  146,314  17  121,441 
24  121,441  78,944  42,497  34  56,946 
25  56,946  81,312  (24,366)  0  0 
26  0  0  0  0  0 
27  0  0  0  0  0 
28  0  0  0  0  0 
29  0  0  0  0  0 
30  0  0  0  0  0 
Once again, this withdrawal scheme fails, this time in Year 25.
Run 2B: Sequence Run Backward and Annual Returns 5% Better than S&P 500
First Decade:
Year Number 
Beginning Balance $  Amount Withdrawn $  Amount Remaining $  Annual Return %  End Balance $ 
1  1,000,000  40,000  960,000  32  1,267,200 
2  1,267,200  41,200  1,226,000  32  833,680 
3  833,680  42,436  791,244  11  878,281 
4  878,281  43,709  834,572  16  968,103 
5  968,103  45,020  923,083  10  1,015,392 
6  1,015,392  46,371  969,021  16  1,124,064 
7  1,124,064  47,762  1,076,302  34  1,442,244 
8  1,442,244  49,195  1,393.049  17  1,156,231 
9  1,156,231  50,671  1,105,560  7  1,028,171 
10  1,028,171  52,191  975,980  4  936,941 
Second Decade:
11  936,941  53,757  883,184  32  1,165,802 
12  1,165,802  55,370  1,110,432  32  755,094 
13  755,094  57,031  698,063  11  774,850 
14  774,850  58,742  716,108  16  830,685 
15  830,685  60,504  770,181  10  847,199 
16  847,199  62,319  784,880  16  910,461 
17  910,461  64,189  846,272  34  1,134,005 
18  1,134,005  66,115  1,067,890  17  886,349 
19  886,349  68,098  818,251  7  760,973 
20  760,973  70,141  690,832  4  663,199 
Third Decade:
21  663,199  72,245  590,954  32  780,059 
22  780,059  74,413  705,646  32  479,839 
23  479,839  76,645  403,194  11  447,546 
24  447,546  78,944  368,602  16  427,578 
25  427,578  81,312  346,266  10  380,893 
26  380,893  83,751  297,142  16  344,684 
27  344,684  86,264  258,420  34  346,283 
28  346,283  88,852  257,431  17  213,668 
29  213,668  91,517  122,151  7  113,600 
30  113,600  94,264  19,336  4  18,563 
Finally, a Total Return plan that squeaks through, barely. If taxes were counted, this would have failed too. It will fail in Year 31.
More Discussion:
As with last week, I had no preconceived notions of how any trial would end up. I simply wanted to illustrate the importance of return sequencing on total returns. I was aware that using 20002009 as a starting decade would provide a severe stress test on the 4% strategy. That's what a stress test should do.
Let’s talk about return sequencing for a minute. In preparing this article, I discovered that I made misleading statements in last week’s comments about sequencing. I implied that sequencing by itself makes a difference in compounded returns. That is not true.
Remember the first table, where the S&P’s annual returns for 20002009 were given? The way they actually happened, the first three years (the collapse of the techtelecom bubble) were really bad, while 6 of the last 7 years had increases, including +27% the final year. What do you suppose the total arithmetic and compound growth was for the S&P 500 during that 10year span?
S&P 500, 20002009  Forward  Backward 
Arithmetic total  +14%  +14% 
Compounded total  8%  8% 
While the compounded total differs from the arithmetic total, it is the same no matter how the returns are sequenced. (Try it.) According to MoneyChimp, the compounded total will always be less than the arithmetic total (which is the same as saying that the arithmetic annual average is smaller than CAGR—compound annual growth rate). They state that the CAGR is usually about a percent or two less than the simple average.
So why is the sequencing important when you are making withdrawals? Because the withdrawals go relentlessly up (the result of the 3% annual increment), and sometimes an increased withdrawal coincides with a particularly bad annual return year. The combination can be lethal. In each run, the backwards sequence did better than the forward sequence. That’s because the smallest withdrawals coincide with the best returns in each decade when you run the sequence backward.
Here are some other takeaways:
 If you have the misfortune to retire in a flat market, it is really hard to make the 4% rule work for 30 years. The likelihood that your portfolio will outperform the S&P 500 by 5% every year for 30 straight years is practically nil. Yet that’s what it took here to get a single successful trial.
 In the lost decade of 20002009, the arithmetic average of each year’s returns was actually positive. But the compound average was negative. As some people say, down years have more impact than up years. The most common example of this is that returns of 50% and +100% do not yield +25% as their arithmetic average would suggest. They actually leave you at 0%, right where you started.
 Getting off to a bad start in a withdrawal plan can cause psychological problems. In Run 1A, the portfolio was down more than 1/3 after the first three years. I imagine that can cause sleepless nights when you know that the portfolio is supposed to last for 30 years.
 When portfolios are failing, their plunge to zero is sickeningly fast and steep in the last few years.
For me personally, this is my takeaway: Don’t rely on a total return strategy and portfolio withdrawals to fund retirement. Don’t employ automatic inflation escalators in your withdrawals every year. How this method has gained dominance in the retirement industry is a mystery to me. The risks of failure, and fear of failure, are just so great.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.