Standard deviation measures how much an asset's returns swing around its average return over time. In investing it's used interchangeably with "volatility" — a higher standard deviation means returns are more dispersed and the investment is considered riskier.
Why It Matters
Volatility is the raw input behind nearly every other risk metric in this glossary — VaR, Sharpe Ratio, and options pricing (via implied volatility) all start here. It's also the number that determines position sizing: a risk manager setting exposure limits needs to know how much a position can plausibly move before deciding how large it should be.
How It Works in Practice
- 1Collect a return series (daily, monthly, or annual)
- 2Calculate the mean (average) return over the period
- 3Sum the squared deviations of each return from the mean, divide by the number of observations, and take the square root
- 4Annualize daily or monthly volatility by multiplying by the square root of the number of periods in a year
Common Pitfalls
Standard deviation treats upside and downside moves identically, even though investors generally only care about downside risk
It assumes returns are roughly normally distributed, which understates the frequency of extreme moves ('fat tails') that markets actually exhibit
Realized (historical) volatility and implied volatility (derived from options prices) can diverge sharply — implied volatility reflects the market's forward-looking risk expectation, not just the past