Volatility
How much an investment's returns swing around their average, usually measured by the standard deviation of annual returns.
Compound (geometric) return ≈ Average (arithmetic) return − σ² ÷ 2
Explanation
Volatility is most often expressed as the standard deviation (σ) of returns. A diversified US stock index has historically had annual volatility in the high teens; high-quality bonds much lower. If returns roughly followed a bell curve, about two-thirds of years would fall within one standard deviation of the average, and about 95% within two. Real markets have “fat tails”: extreme years happen more often than a bell curve predicts.
Volatility is not just discomfort. It has two concrete costs in planning:
- Volatility drag. Losses hurt more than equal-sized gains help. A 50% loss followed by a 50% gain leaves you down 25%. As a rule of thumb, the compound return is roughly the average return minus half the variance (σ² ÷ 2).
- Timing risk with withdrawals. When you are taking money out, a volatile portfolio can be depleted by bad years early on, even if the long-run average is fine (sequence-of-returns risk).
Volatility is also not the whole story. A low-volatility asset like cash can still lose to inflation, and an asset’s long-run return matters as much as its swings.
In scenarios, the deterministic projection uses a single average return, while Monte Carlo mode draws random returns based on each asset’s expected return and volatility (and their correlations). Raising the volatility setting widens the spread between good and bad outcomes.
Example
A stock portfolio has a 7% average annual return and 15% volatility.
- One standard deviation: 7% ± 15%, so about two-thirds of years between −8% and +22%
- Two standard deviations: 7% ± 30%, so about 95% of years between −23% and +37%
Volatility drag:
- Approximate compound return: 7% − (0.15 × 0.15) ÷ 2 = 7% − 1.125% = 5.875%
- Two-year illustration: $100,000 × 1.50 = $150,000, then × 0.50 = $75,000. The average return was 0%, but you lost 25%.