Volatility

Volatility describes how much and how quickly an asset's price or returns fluctuate, independent of direction — a highly volatile asset can be volatile on the way up as easily as down. It is the standard shorthand for risk in most quantitative finance, even though it treats desirable upside swings and undesirable downside swings the same way.

Historical, or realized, volatility is usually calculated as the standard deviation of an asset's periodic returns, annualized by multiplying by the square root of the number of periods in a year. This differs from implied volatility, which is not calculated from past prices at all but backed out from current option prices using a model such as Black-Scholes model, and reflects the market's expectation of future volatility rather than its recent history.

Volatility feeds directly into risk measures such as the sharpe ratio and value at risk, into position sizing, and into options pricing. A common pitfall is assuming volatility is stable: it clusters, so calm periods and turbulent periods each tend to persist, and it spikes sharply around news and market stress, so a volatility figure estimated from a quiet period can badly understate the risk of a turbulent one that follows.