## Thursday, July 18, 2019

### The Four Percent Rule under Different Return Scenarios

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.

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 far-right column.

Balance is (1+return) * previous balance) – previous disbursement