Many investors based their disbursements from their
401(k) plans on the 4 percent rule. One
version of the four percent rule involves an initial disbursement of 4 percent
of the 401(k) balance with subsequent disbursements linked to inflation. The question presented here involves
modeling the sustainability of the four percent rule under different financial
scenarios.
Question: A person starts her retirement with $500,000
in a stock fund. She disburses funds from the account based on the four percent
rule. Her initial disbursement is 4
percent of $500,000. Subsequent
disbursements are the initial disbursement protected against inflation.
The inflation rate is assumed
to be 2 percent every year.
The person wants you to calculate
the account balance after 15 disbursements under two financial scenarios.
The first financial scenario
involves losses of 6.0 percent per year for the first four years at the
beginning of the holding period followed by gains of 9 percent per year for 11
years.
The second scenario involves
gains of 9 percent per year for the first 11 years in the holding period
followed by losses of 6 percent per year for the final four years.
Create a spreadsheet that
allows you to estimate the balance in the investment account after 15 years for
both scenarios.
Construct the spreadsheet so
that it can easily consider different outcomes for different financial
scenarios, disbursement rates and inflation rates.
Analysis:
The spreadsheet for the first
scenario is laid out below.
Scenario One


Initial Disbursement Rate

0.04


Inflation Rate

0.02


Balance

Disburement

Stock Returns


0

$500,000

$20,000


1

$450,000

$20,400

0.06

2

$402,600

$20,808

0.06

3

$357,636

$21,224

0.06

4

$314,954

$21,649

0.06

5

$321,651

$22,082

0.09

6

$328,518

$22,523

0.09

7

$335,561

$22,974

0.09

8

$342,788

$23,433

0.09

9

$350,206

$23,902

0.09

10

$357,822

$24,380

0.09

11

$365,646

$24,867

0.09

12

$373,687

$25,365

0.09

13

$381,954

$25,872

0.09

14

$390,458

$26,390

0.09

15

$399,210

NA

0.09

The spreadsheet for the
second scenario is laid out below.
Scenario Two


Initial Disbursement Rate

0.04


Inflation Rate

0.02


Balance

Disbursement

Stock Returns


0

$500,000

$20,000


1

$525,000

$20,400

0.09

2

$551,850

$20,808

0.09

3

$580,709

$21,224

0.09

4

$611,748

$21,649

0.09

5

$645,157

$22,082

0.09

6

$681,139

$22,523

0.09

7

$719,919

$22,974

0.09

8

$761,738

$23,433

0.09

9

$806,861

$23,902

0.09

10

$855,576

$24,380

0.09

11

$908,198

$24,867

0.09

12

$828,839

$25,365

0.06

13

$753,744

$25,872

0.06

14

$682,647

$26,390

0.06

15

$615,299

NA

0.06

Discussion of Results:
Balance at year 15 for scenario
one where early returns are negative is $399,210.
Balance at year 15 for
scenario two where early returns are negative and later returns are positive is
$615,299.
The Lesson:
The four percent rule does not work well when a person
retires and returns immediately become negative. The rule leads to a much better outcome if
returns early in retirement are robust.
Financial path risk appears to be an even more
important problem in retirement when a person is actively disbursing funds than
during working years.
Discussion of Spreadsheet:
The disbursement rate top
cell in input area is multiplied by initial balance $500,000 top row of chart
to get initial disbursement.
Subsequent disbursement is
(1+inf)*previous period disbursement.
Stock returns are in farright
column.
Balance is (1+return) * previous
balance) – previous disbursement
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