Volatility Impact Calculator

Two portfolios quoting the same average return can end at very different places. On the sample figures used on this page, a starting amount of 100,000 at a 10% average return over 30 years projects to about 1,745,000 at that average, while the compound rate implied by 20% volatility projects to about 1,006,000. The gap of roughly 739,000 comes from the volatility alone, with the headline average unchanged.

Average return against compounded return

Average return and compounded return are not the same number, and volatility is the reason. A portfolio that falls 50% then rises 50% averages zero and is down 25%, because the rise applies to a smaller base than the fall did. The calculator applies the standard variance approximation, subtracting half the variance from the arithmetic mean to estimate the compound rate, so on the sample figures a 10% average paired with 20% volatility compounds at about 8%.

What moves the number most

Raising each input by 1% of its own value, on the sample figures, moves the gap by 3.67% for years, 2.69% for the average return, 1.51% for volatility and exactly 1.00% for principal. Three of those four are continuous gradients rather than moves the field will accept. The return is the exception, since it steps in tenths of a percentage point, so entering 10.1 in place of 10 reproduces the 2.69% exactly. The years figure comes from 30 to 30.3, where the smallest step available is a whole year, and that one-year step adds 12.72% instead. Principal is exactly linear because it multiplies both projections equally, so it can never shift the percentage rows at all. The ranking is not general either. The volatility lever grows in relative terms as volatility falls, reaching 1.98% at a 5% standard deviation and dropping to 1.02% at 30%, so where volatility places in the ordering depends on where the starting figure sits.

Where the approximation holds

Subtracting half the variance is a second-order estimate, and which way it errs depends on where the two inputs sit. For a symmetric two-point distribution the estimate sits below the true compound return whenever the average return exceeds a quarter of the variance, which comes to one percentage point at a 20% standard deviation and covers most ordinary settings: on the sample figures the estimate gives 8.00% against about 8.17%, so the drag reported is roughly 0.17 percentage points on the high side. That overstatement grows to about 0.50 points near a 46% standard deviation, then shrinks, reaching zero at about 63% and reversing beyond it. The threshold moves with the return as well, and at a 30% standard deviation the sign flips once the average return falls below 2.25%.

Past the crossover the divergence stops being a rounding matter. At a 10% average return with volatility at 100% the estimate puts the compound rate at -40% where the two-point benchmark gives about -54%, and at a 0% average return the same volatility puts the estimate at -50% against a benchmark of -100%. Both corners sit inside the ranges the sliders reach. That second comparison also sits on the benchmark's own edge, because the down state of a two-point distribution is the return minus the standard deviation, which stops being defined once volatility passes one plus the return. The approximation treats volatility as constant besides, whereas in practice it clusters. The output is useful for showing that two portfolios quoting the same average can finish far apart, rather than for predicting where either one lands.

Which volatility figure to enter

The input is an annual standard deviation of returns, the same quantity a fund factsheet reports as volatility or standard deviation, usually measured over three or five years. Where only monthly figures are available, the annual equivalent is the monthly standard deviation multiplied by the square root of twelve. The half-variance step is an identity in logarithmic terms, where the log of one plus the compound return equals the log of one plus the average minus half the variance. This calculator applies the result as a plain annual rate instead, so it remains an approximation on either basis. Pairing a standard deviation measured on log returns with an arithmetic average return, for instance, overstates the thirty-year multiple by about 5%.

What the model leaves out

Returns are treated as drawn from one unchanging distribution, so nothing here captures the order in which gains and losses arrive. That ordering matters a great deal once money is being paid in or taken out, which is a separate effect from the one measured here. Costs, taxes and contributions are absent, and a single compound rate stands in for a path that in practice never repeats the same number twice.