## Tuesday, September 17, 2019

### The path of stock returns and financial risk for 401(k) investors

The path of stock returns and financial risk for 401(k) investors

This post compares terminal wealth in a 401(k) plan for two stock return scenarios.   The average return for the two scenarios are identical.  One scenario has a bad year at the beginning of the holding period.   The other scenario has a bad return at the end of the holding period.

This problem is solved using basic math in an Excel spreadsheet.

Question:   Consider a 401(K) plan with a \$300,000 balance ten years prior to retirement. The person contributes \$10,000 every year to her 401(k) plan.  For simplicity of calculation assume the entire annual \$10,000 contribution goes into the account at the beginning of the year.

Calculate wealth at retirement for two financial scenarios.   Scenario one involves a negative 20 percent return in the first year followed by positive 8 percent returns in the following nine years.   Scenario two involves positive 8 percent returns for the first nine years followed by a negative 20 percent return in the year leading up to retirement.

What is the average stock market return during the 10-year period?

What is 401(k) wealth at retirement for both scenarios?

Financial advisors often recommend holding stock in 401(k) plans over long time horizons because stocks tend to have higher returns than other financial assets.  Financial advisors also recommend starting 401(k) savings early because wealth accumulation is enhanced by compounding of returns.

What does the result presented here suggest about the risks associated with 401(k) investing?

Analysis:   The holding period return can be measured by the geometric mean of (1+r) minus 1.   The calculation is laid out in the table below.

 Scenario One Scenario Two 1 0.8 1.08 2 1.08 1.08 3 1.08 1.08 4 1.08 1.08 5 1.08 1.08 6 1.08 1.08 7 1.08 1.08 8 1.08 1.08 9 1.08 1.08 10 1.08 0.8 Geomean minus one 4.81% 4.81%

The wealth for each period is beginning balance multiplied by (1+r).   The calculation for wealth at retirement for scenario one where the bad stock return year is the first year of the last ten years prior to retirement is laid out in the table below.

 Wealth Calculation Scenario One Time 401(k) Balance Contribution made at beginning of year r for  scenario one 0 \$300,000 \$10,000 1 \$248,000 \$10,000 -0.2 2 \$278,640 \$10,000 0.08 3 \$311,731 \$10,000 0.08 4 \$347,470 \$10,000 0.08 5 \$386,067 \$10,000 0.08 6 \$427,753 \$10,000 0.08 7 \$472,773 \$10,000 0.08 8 \$521,395 \$10,000 0.08 9 \$573,906 \$10,000 0.08 10 \$630,619 0.08

The wealth calculation for scenario two where the bad stock return is the year prior to retirement is laid out in the following table.

 Wealth Calculation Scenario Two Time 401(k) Balance Contribution made at beginning of year r for scenario two 0 \$300,000 \$10,000 1 \$334,800 \$10,000 0.08 2 \$372,384 \$10,000 0.08 3 \$412,975 \$10,000 0.08 4 \$456,813 \$10,000 0.08 5 \$504,158 \$10,000 0.08 6 \$555,290 \$10,000 0.08 7 \$610,514 \$10,000 0.08 8 \$670,155 \$10,000 0.08 9 \$734,567 \$10,000 0.08 10 \$595,654 -0.2

Wealth in scenario one where you get the bad year over sooner rather than later is around \$35,000 higher than in scenario two where the bad return year is the last year prior to retirement.  The difference is 5.87 percent of wealth at the end of scenario two.

The reason for the lower end of period wealth in the second scenario is the market downturn impacts a larger value of assets.

This example understates financial path risk because stock downturns can and do last more than one year.

Financial advisors generally favor taking advantage of higher returns on stocks and compounding by starting 401(k) investments as soon as a worker enters the workforce.  The calculations supporting this recommendation do not account for financial return path risk shown in this post.  Often workers will be better off by immediately eliminating student debt rather than increase exposure to the market.