Volatility

Volatility describes how far single years land from the average. It is most often stated as the standard deviation of yearly returns: take each year's return minus the average, square the differences, average the squares and take the square root. The result is in percentage points, the same unit as the returns.

A planner that simulates returns usually draws each year from a bell curve, a normal distribution, set by two numbers: the average and the standard deviation. Under that curve, about two years in three land within one standard deviation of the average. At a 6% average and a 13-point standard deviation, that is between −7% and 19%. One year in ten falls below −10.7%, one in ten rises above 22.7%, and about one year in three is a loss.

Some sources divide the sum of the squares by one fewer than the number of years, the sample standard deviation. On a short record it reads higher, 15.0 points instead of 13.0 in the example below; over decades of returns the two barely differ.

Two portfolios each average 6% a year over four years. The steady one returns 5%, 7%, 4% and 8%. The other returns 19%, −13%, 17% and 1%.

For the second, the differences from the 6% average are 13, −19, 11 and −5 points. Squared, they are 169, 361, 121 and 25, which add up to 676. Divided by the four years that is 169, and its square root is 13: a standard deviation of 13 points. The steady portfolio's squared differences add up to 10, for a standard deviation of about 1.6 points.

The average is the same; the growth is not. $10,000 in the steady portfolio ends the four years at $12,619, and in the other at $12,234, $385 less. A 13% loss takes a gain of about 15% to make up, so wider swings pull compound growth further below the average return: about 5.2% a year for the second portfolio against about 6.0% for the steady one.

Yearly returns

19%, −13%, 17%, 1%

Average

6%

Differences from the average

13, −19, 11, −5

Squared and added

676

Divided by 4 years

169

Standard deviation, √169

13 points

An average return does not say how a balance gets there. A plan that runs one flat return every year leaves volatility out, and its line lands in the same place whatever the swing. In the example, a flat 6% turns $10,000 into $12,625 in four years; the portfolio with the same 6% average and a 13-point standard deviation ends at $12,234.

When a plan is simulated, the standard deviation sets how far apart the runs land. A larger figure widens the range between the low and high paths, and while withdrawals are coming out, as in retirement or the college years, the order of the swings changes how many paths run out.

Taiga Finance's “College savings” planner and the public college savings calculator run the projection 600 times, drawing each year's return from a bell curve around the “Nominal annual return” with a standard deviation of 13 points. The figure is fixed; neither asks for it. The planner's chart shades the 10th to 90th percentile of those runs as a “Simulated range”, shown or hidden by a chip in the chart header; the calculator's legend reads “Simulated range (middle 80%)”, with a “Simulated range” switch, and its note says the yearly returns swing like a stock-heavy portfolio's. In the app, the working behind “College cost covered” states the range as 600 simulated futures with each year's return drawn around the return with a 13% standard deviation, and the working behind “Chance of hitting target” calls that spread a stock-heavy portfolio's year-to-year swing.

The Retirement savings planner fixes its volatility rather than asking for it: a 12-point standard deviation of yearly real (inflation-adjusted) returns around the “Real return” set under “Assumptions”. The info note beside “Real return” gives the source of both figures, a 60/40 portfolio's 1928–2024 record, which compounded about 5% a year after inflation “with single years spread about 12% around that”. Opened, the “Chance money lasts” figure lists the “Return spread” beside the number of “Simulated return sequences”.