Historical volatility (HV) — also called realized volatility — is the actual measured volatility of an asset’s price returns over a defined historical period. It is typically calculated as the annualized standard deviation of daily log returns over the past 20, 30, 60, or 252 trading days. Historical volatility is backward-looking: it measures what volatility has been, not what it is expected to be going forward.

Calculating Historical Volatility

The calculation involves three steps. First, compute the daily log return for each trading day: ln(today’s price / yesterday’s price). Second, compute the standard deviation of these daily returns over the chosen lookback period. Third, annualize by multiplying by the square root of 252 (the approximate number of trading days in a year). The result is expressed as a percentage — for example, a 20% historical volatility means that, on an annualized basis, the asset’s returns have been fluctuating with a standard deviation of 20%.

Historical vs. Implied Volatility

Historical volatility and implied volatility (IV) measure different things. HV is backward-looking and based on actual price data. IV is forward-looking and derived from option prices — reflecting the market’s collective expectation of future volatility. The spread between IV and HV is the volatility risk premium: the amount by which the market pays above realized historical volatility for options protection. When implied volatility is significantly above historical volatility, options are “expensive” relative to recent realized moves — and vice versa when it is below.

Use in Active Risk Management

Historical volatility is a critical input for active risk management. Rising historical volatility signals increasing market risk and uncertainty — often prompting a reduction in portfolio exposure through volatility targeting or other dynamic risk management approaches. Falling historical volatility signals calmer conditions — often allowing a gradual increase in portfolio exposure. Many systematic risk management systems use historical volatility as the primary input for position sizing: as volatility rises, position sizes shrink; as it falls, they expand.

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