Retirement's 4% Rule: The Importance of Return Sequence

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 30-year 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 2000-2009. That 10-year span will simply be repeated to get the 30-year 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: Two-thirds 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 out-gain the S&P 500 by 5% each and every year, in good years and in bad.
• Just for fun, we’ll run the 30-year sequence twice.
  • Trial 1: The sequence will be run forward, just as it happened. This is a real stress test, because the 2000-2009 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’ 30-year 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 30-year 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 10-year 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 2000-2009, 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 30-year 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 30-year 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 30-year 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 2000-2009 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 2000-2009 were given? The way they actually happened, the first three years (the collapse of the tech-telecom 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 10-year span?

S&P 500, 2000-2009	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 2000-2009, 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.