Realized volatility measures how much an asset's price actually moved over a past period, calculated directly from observed returns. It looks backward at what happened, in contrast to forward-looking estimates that try to predict future price swings. The term answers a simple question: how bumpy was the ride?

Investors and risk managers use realized volatility as the empirical anchor for almost every risk calculation. It feeds position sizing, risk budgets, and the comparison between what a model predicted and what the market delivered. Because it is computed from real data rather than assumptions, it serves as the yardstick against which forecasting models are judged.

Definition

Realized volatility is the standard deviation of an asset's returns over a sample window, usually annualized so that different time horizons can be compared on a common scale. It is sometimes called historical volatility, though practitioners increasingly reserve "realized volatility" for measures built from high-frequency (intraday) data. The core idea stays the same: take the returns that occurred, measure their dispersion, and scale the result to a yearly figure.

How It Is Calculated

The calculation starts with periodic returns, typically the change in price from one observation to the next. Practitioners compute the standard deviation of those returns over the chosen window, then multiply by the square root of the number of periods in a year to annualize. Daily returns scale by the square root of roughly 252 (the number of trading days), while monthly returns scale by the square root of 12.

The square-root scaling follows from a foundational assumption: that returns are independent from one period to the next, so variance (the square of the standard deviation) grows linearly with time. This assumption is convenient and often roughly true, but it breaks down when returns cluster, which they frequently do during market stress. Understanding why the scaling works clarifies why it sometimes fails.

Interpretation and Use

A higher realized volatility means the asset's returns were more dispersed, swinging further from their average. Risk managers compare realized volatility against a target to decide whether to increase or reduce exposure, a practice that underpins volatility-aware position sizing. Analysts also compare realized volatility against implied volatility (the market's forward-looking estimate embedded in option prices); a persistent gap between the two is a studied phenomenon known as the variance risk premium.

Realized volatility tends to cluster: calm periods follow calm periods, and turbulent stretches follow turbulent ones. This persistence is why backward-looking estimates carry some forecasting value over short horizons, and it is the empirical motivation behind models that explicitly track changing volatility over time. The clustering also means a single recent estimate can understate risk just before conditions shift.

Known Limitations

Academic Origin

The use of return dispersion as a risk measure dates to the foundations of modern portfolio theory, where variance served as the central proxy for risk. The shift toward high-frequency realized measures came later, as intraday data became available and researchers showed that summing squared intraday returns produces a far more precise estimate of daily volatility than a single close-to-close return. This work, associated with Andersen, Bollerslev, and co-authors, reframed volatility as something that can be observed and measured rather than only inferred from a model.

Further Reading

• Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P. (2003). "Modeling and Forecasting Realized Volatility." Econometrica, 71(2), 579–625.
• Andersen, T.G. and Bollerslev, T. (1998). "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts." International Economic Review, 39(4), 885–905.
• Hull, J.C. (2017). Options, Futures, and Other Derivatives. 10th edition. Pearson.

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