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Realized variance
Definition
Realized variance is an ex-post measure of variation calculated by summing squared returns over subintervals within a specified period. In financial econometrics, the returns are often intraday log returns. Under suitable assumptions and increasingly fine observation, the sum estimates the quadratic variation of the underlying price process. It is a realized historical quantity, distinct from a forecast of future variance, and its definition should specify the return convention, sampling frequency and observation window.
What it means
The measure captures movement along a price path rather than only the net change between its endpoints. A price can rise and fall substantially and finish near its starting level; its net return may be small while realized variance is large. It is also different from the usual sample variance of returns, which centers observations and divides by a sample-size factor. The square root is commonly called realized volatility, although terminology in the literature should be checked carefully.
How it works
Choose a time window and a sampling scheme, calculate successive returns consistently, square them and add them. Clean price data for obvious recording problems and define the treatment of missing intervals, overnight changes and market closures. Assess the impact of sampling frequency. In an ideal continuous-time setting, finer sampling improves the quadratic-variation approximation, but observed market prices contain microstructure effects that can make extremely fine sampling problematic. Specialized estimators address noise or separate jump and continuous components when those are the intended targets.
Three practical examples
Example 1: A researcher summarizes a day's intraday price variation using regularly sampled log returns. Example 2: A model uses past realized variance as an input when forecasting future volatility. Example 3: An analyst compares ordinary realized variance with a noise-robust estimator to assess sensitivity to market microstructure. These are measurement and modeling uses. A historical variance figure is not a trading recommendation or a complete description of future loss risk.
Think of it this way
Think of measuring how much a traveler moved up and down along a route rather than only the difference between the starting and ending heights. Squaring each movement prevents opposite directions from canceling. The analogy also highlights why the observation spacing matters: a coarse record can miss movements that occurred between its recorded points. Financial returns add further complications because the recorded prices themselves may contain noise.
Worked example
Suppose four intraday log returns, expressed as decimals, are 0.010, -0.020, 0.015 and -0.005. Their sum is zero, but realized variance is 0.010 squared + 0.020 squared + 0.015 squared + 0.005 squared = 0.00075. Its square root is approximately 0.027386, or 2.7386% in return units. If the same path is observed only at every second interval, the two log returns are -0.010 and 0.010, producing realized variance 0.0002. The coarse measure misses within-pair movement. Expressing the original returns in percentage points gives squared-sum 7.5, which is 10,000 times the decimal-unit variance. The underlying path is unchanged; only the units changed.
Illustrative case study
Fictional case study: Willow Analytics compares daily realized variance across two datasets and finds large discrepancies. The team discovers that one calculation includes an overnight return while the other covers only trading hours, and that the price sampling rules differ. Analysts align definitions before comparing models. This fictional case illustrates measurement discipline rather than a claim of superior investment performance. It also shows why a familiar label is insufficient without its operational specification.
Common misconceptions and mistakes
Common mistakes include squaring only the total daily return, treating realized variance as the ordinary sample variance, and mixing decimal and percentage units. Finer sampling is not automatically better when price observations contain microstructure noise. With jumps, quadratic variation includes squared jumps as well as integrated continuous variance. Omitting overnight movement changes the target. Annualisation adds assumptions and conventions; it should not be performed silently or interpreted as a guaranteed future level of variability.
Business use
Business use: Realized variance supports risk measurement, volatility research and evaluation of forecasting models. Document the asset, return definition, time window and data-cleaning rules. Compare estimates under plausible sampling choices and distinguish measured past variation from predicted future uncertainty. Review whether the target includes jumps and overnight changes. When communicating results, give units and avoid presenting one variance measure as a complete account of liquidity, tail losses or other risks.
People also ask
Can realized variance be positive when the total return is zero?
Yes; opposing subinterval returns can cancel in the total while their squares remain positive. Q: Is realized volatility the same numerical quantity? A: Usually it is the square root, so the units differ. Q: Does sampling every available tick always improve the estimate? A: No; microstructure noise can distort very high-frequency calculations.
Check your understanding
Why is the example's coarse realized variance smaller?
Answer: Movements within each combined interval cancel before squaring.
Why does percentage-unit variance equal 7.5 rather than 0.00075?
Answer: Multiplying returns by 100 multiplies their squares by 10,000. Consistent units are essential when comparing values.
Related terms
- Log returns are logarithms of price ratios
Learn next
Calculate realized variance at several sampling frequencies for a synthetic return path. Compare it with the squared total return and ordinary sample variance. Add small observation noise to see why finer sampling can become misleading. Then study the distinction between quadratic variation and integrated variance before interpreting empirical financial data.
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Sources
Sources: Barndorff-Nielsen and Shephard, Estimating quadratic variation using realized variance: https://onlinelibrary.wiley.com/doi/10.1002/jae.691 ; Barndorff-Nielsen and Shephard, Econometric analysis of realised volatility and its use in estimating stochastic volatility models, author-hosted research paper: https://www.nuffield.ox.ac.uk/economics/papers/2001/w4/realised.pdf . These primary research sources ground the squared-return and quadratic-variation interpretation. The four-return calculation and fictional data-comparison case are original educational illustrations.
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