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

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 |  Includes: BND, DIA, IEF, QQQ, SPY
by: David Van Knapp

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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

Click to enlarge

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%

Click to enlarge

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.