Definition
Volatility measures how widely an asset's returns vary around their average, most often as the standard deviation of returns, usually quoted as an annualized percentage. Higher volatility means larger price swings in both directions, not a particular direction.
How it works
Historical (realized) volatility is computed from past returns, while implied volatility is inferred from option prices and reflects market expectations. To annualize a daily figure, multiply by √252, the conventional count of trading days in a year; weekly data uses √52, and markets that trade every day, such as many crypto markets, often use 365.
This square-root-of-time rule assumes returns are independent and identically distributed with a stable variance. Volatility tends to cluster in calm and turbulent spells, so a figure from a quiet year can badly understate the next stressful one.
Formula / convention
σ = √(Σ (r(i) − mean r)² ÷ (n − 1)); Annualized σ ≈ σ(period) × √(periods per year)
Illustrative example
Illustrative: a fictional share's daily returns have a standard deviation of 1.2%, so annualized volatility is 1.2% × √252 = 1.2% × 15.87 ≈ 19.0%. For an asset that trades every calendar day, the same 1.2% daily figure would be annualized with √365 and give about 22.9%, so the day count must match the market's calendar.
What to watch for
Volatility treats upward and downward moves alike and says nothing about direction or the chance of permanent loss. Estimates depend on the window and return frequency, and the square-root scaling breaks down when returns are autocorrelated or volatility itself changes.