Volatility

Volatility is the standard deviation of an asset's returns — a statistical measure of how widely results scatter around their average, quoted as an annualized percentage. A stock with 20% annualized volatility is expected to land within 20 percentage points of its mean return in roughly two out of three years, if returns behaved normally (they do not, quite — real markets produce more extreme days than the bell curve predicts).

Realized and implied are different animals. Realized (historical) volatility is computed from past price changes; implied volatility is backed out of current option prices and represents the market's forecast. The gap between them is a traded quantity — options tend to price implied above subsequently realized volatility most of the time, which is the premium option sellers harvest and occasionally choke on.

Scaling follows the square root of time: annualized volatility = daily volatility x sqrt(252), using 252 trading days per year. Volatility also clusters — quiet periods and violent periods each persist — so the recent number is informative but regime shifts arrive fast.