volatilityhistorical

Historical volatility, abbreviated as HV, is a measure of how much the price of a security has fluctuated over a specified past period. It is an ex-post statistic used to describe past risk and variability, based on historical price data rather than forward-looking expectations.

To compute HV, collect price data for the chosen look-back window, calculate the period returns (either daily log returns or simple returns), and determine the standard deviation of those returns. If desired, annualize the result by multiplying the standard deviation by the square root of the number of trading periods in a year (commonly 252 for stock markets). This yields an annualized volatility figure that is easy to compare across assets.

HV is widely used in risk management, portfolio construction, and performance analysis. It helps quantify historical risk, set position sizing, and calibrate models that assume a level of price variability. In options markets, HV is often contrasted with implied volatility, which reflects market expectations of future volatility embedded in option prices. While HV provides a backward-looking view, implied volatility offers a forward-looking perspective.

Limitations include sensitivity to the chosen look-back window and data frequency, non-stationarity of volatility over time, and susceptibility to outliers. HV assumes past behavior is indicative of the near future only within the chosen window and does not account for structural changes or regime shifts. It is one tool among many for assessing risk and is often complemented by models that forecast volatility, such as GARCH-type approaches.