Volatility Metrics Advanced Sum of squared returns over a period Backward-looking

Realized Variance

A realised-variance number is not the average of a period — it is a portrait of its five worst days.

Quick answer: Realized variance is the sum of the squared returns of an asset over a period, and because squaring makes the largest moves dominate the total, it is less an average of the period than a summary of its handful of worst days.

In simple words

Realized variance is what volatility actually turned out to be, measured after the fact by adding up the squared returns of every period. The squaring is the whole story. A 3% day contributes nine times as much as a 1% day and thirty-six times as much as a 0.5% day, so the biggest sessions swamp everything else. On the illustrative 120-day series used on this site, the five largest days account for the large majority of the entire period's realised variance. This means a single realised-variance figure is not telling you what a typical day looked like — it is telling you, almost entirely, what the worst few days looked like.

That property is exactly why realised variance, not realised volatility, is what a variance swap settles on. The buyer of a variance swap is paid the realised variance and pays a fixed strike agreed upfront, so they are effectively paid for the worst days of the period. In a calm stretch realised variance comes in low and the buyer loses the strike; in a crisis a few enormous squared returns send realised variance far above the strike and the buyer is paid many times over. The instrument is built directly on the fact that squared returns concentrate in the tail.

Not to be confused with: Realized volatility, which is the square root of realised variance and is quoted as an annualised percentage. Realised variance is the raw additive quantity in squared units that a variance swap settles on; realised volatility is its readable square root. Because of the square root, realised volatility understates how violently the tail days dominate the underlying variance.

How a few days dominate realised variance

Five days, most of the variance

The daily contributions of squared returns to total realised variance over the illustrative 120-day series, sorted by size.

The squared-return contributions are wildly unequal: a small number of large days tower over the rest, and the five biggest account for the large majority of the whole period's realised variance. This is the visual proof that a realised-variance figure is a portrait of a period's worst sessions, not an average of its typical ones.

Professional explanation

Squaring means the biggest days are everything

Realised variance sums squared returns, and squaring is not a neutral operation — it is a magnifying glass aimed at the extremes. A day that moves 4% contributes 0.0016 to the sum; a day that moves 0.5% contributes 0.000025. The large day is sixty-four times the small one, though it is only eight times larger in raw return. Over a long window the consequence is stark: the total realised variance is not built evenly out of every day but is dominated by a handful of sessions. On the site's illustrative 120-day series, the five largest days account for the large majority of the whole period's variance, which means removing those five days would change the realised-variance figure beyond recognition. A realised-variance number therefore answers the question 'how bad were the worst days' far more than 'how did the period behave on average', and reading it as an average is the central error to avoid.

This is what a variance swap settles on, and why the payoff is convex

A variance swap does not settle on realised volatility; it settles on realised variance, the raw sum of squared returns, annualised. The buyer receives the realised variance and pays a fixed variance strike agreed at inception, so the payoff is linear in variance — but variance is the square of volatility, which makes the payoff convex in volatility. Double the realised volatility and the realised variance quadruples, so the payoff to a long position more than doubles. This convexity concentrates the entire economics of the contract in the period's most violent days, exactly the days the squaring amplifies. Sellers of variance swaps collect a small premium in the many calm periods when realised variance undershoots the strike, and pay enormously in the rare periods when a few catastrophic days send it far above — which is precisely why short-variance positions blew up in 2008 and 2020, when a handful of sessions produced more variance than years of calm had earned.

Five-minute sampling versus daily closes

How often you sample the price changes the realised-variance figure materially. Computing realised variance from daily closing prices captures only the close-to-close moves and misses everything that happened intraday. Sampling every five minutes captures far more of the true path and produces a more accurate, less noisy estimate of the period's actual variance — this is the insight behind high-frequency realised variance, which sums intraday squared returns to estimate a single day's variance with far more precision than one close-to-close return can. But higher-frequency sampling introduces its own problem: microstructure noise, the bid-ask bounce and discrete tick sizes, inflates the sum if you sample too finely. Five minutes is the conventional compromise — frequent enough to capture the path, coarse enough to escape most of the noise. The choice of sampling frequency is not a detail; two desks measuring the 'realised variance' of the same day can get different numbers because they sampled it differently.

Jump contamination and why bipower variation exists

Realised variance cannot tell the difference between two very different things: a day of continuous, agitated trading and a day that gapped violently on a single piece of news. Both produce a large squared return, and both inflate realised variance identically, yet they mean different things for risk and for hedging. This is jump contamination — the realised-variance figure blends the continuous diffusion of ordinary volatility with the discrete jumps of news shocks, and cannot separate them. Bipower variation exists to solve exactly this. Instead of squaring each return, it multiplies the absolute values of adjacent returns, which is robust to isolated jumps: a single enormous return has no adjacent partner of similar size to multiply against, so its contribution is suppressed. Subtracting bipower variation from realised variance isolates the jump component, letting a researcher measure how much of a period's variance came from continuous movement and how much from discrete shocks. This decomposition matters because the two components behave differently and are hedged differently, and a variance swap seller who cannot tell them apart is blind to which risk they are actually short.

Formula

Realized variance as the sum of squared returns

RV = Σ_{t=1}^{n} r_t²

The plain sum of squared returns over the n periods observed. Because each return is squared, the largest moves dominate the total, so realised variance is concentrated in a period's worst few sessions. To express it on an annual scale, use the annualised form below.

RVRealized variance — the accumulated squared return over the period, in squared units (%² or fraction²).
r_tThe return of period t, usually the log return from the close of t−1 to the close of t (or an intraday interval for high-frequency RV).
nThe number of return observations in the period.
Σ_{t=1}^{n}Summation over every period t from 1 to n.

Annualised realized variance

RV_annual = (252 ÷ n) × Σ_{t=1}^{n} r_t²

Multiplying the mean squared daily return by 252 annualises the figure, since there are about 252 trading days in a year. Its square root is the realised volatility that gets quoted. The 252 assumes daily returns; high-frequency estimators rescale differently.

How to compute realized variance

Choose a sampling frequency. Daily closes are simplest; five-minute intervals give a more accurate estimate but require intraday data and introduce microstructure noise if sampled too finely.
Compute the return for each interval, usually the log return from one sampled price to the next.
Square each return. This is the step that makes the largest moves dominate the eventual total.
Sum the squared returns over the whole period. That sum is the raw realised variance in squared units.
Annualise if needed by multiplying the mean squared return by 252, or by the appropriate factor for your sampling frequency.
Take the square root to report a realised volatility, but keep in mind that the square root hides how concentrated the underlying variance was in a few days.
If you need to separate jumps from continuous movement, also compute bipower variation and subtract it from realised variance to isolate the jump contribution.

Practical example

NIFTY worked example

Take a 20-day window on a NIFTY-like series where nineteen days are quiet, moving about ±0.5%, and one day drops 5%. Each quiet day contributes 0.005² = 0.000025 to realised variance, and nineteen of them sum to 0.000475. The single 5% day contributes 0.05² = 0.0025 — more than five times the other nineteen days combined. Total realised variance is 0.000475 + 0.0025 = 0.002975, of which that one session is 0.0025 ÷ 0.002975 ≈ 84%. Annualise: (252 ÷ 20) × 0.002975 = 12.6 × 0.002975 ≈ 0.0375, and the realised volatility is √0.0375 ≈ 19.4%. Interpret it: without that one day, realised volatility would have been about 7.9%; a single session nearly tripled the figure. The realised-variance number does not describe those twenty days — it describes the one that mattered.

BANKNIFTY worked example

BANKNIFTY illustrates the sampling problem. Suppose on a turbulent banking day BANKNIFTY opens at 52,000, trades violently intraday between 51,000 and 52,800, but closes almost flat at 52,050. Measured close-to-close, the day's return is a mere 0.1%, contributing almost nothing to realised variance — the daily-close estimator records a calm day. Measured at five-minute intervals, the same session accumulates a large sum of squared intraday returns and registers as one of the most volatile days of the month. Both figures are 'realised variance' of the same day, and they disagree completely, because one samples the path and the other only its endpoints. For a variance-swap desk this is not academic: the contract's settlement convention specifies the sampling, and a trader who hedges against close-to-close variance while the swap settles on something finer is mismatched exactly on the wild days that decide the payoff.

Lot sizes used above (NIFTY 75, BANKNIFTY 30) are those in force at the time of writing; NSE revises them periodically. Figures exclude brokerage, STT, exchange charges, stamp duty and GST. Examples are teaching scenarios built on round numbers — they are not historical quotes, not backtests and not trade calls.

Risk note. Realised variance's history is routinely used to argue that selling variance is a reliable premium because realised almost always comes in below implied. It almost always does — and the word 'almost' is carrying the entire risk. Because realised variance is squared returns, a single crisis fortnight can deliver more variance than years of calm collected in premium, and the concentration in a few days means the danger is invisible right up until it is total. A short-variance position is not harvesting a steady yield; it is accumulating small credits against a liability that squares itself in the tail.

Advantages & limitations

What it is good for

It is a direct, model-free measurement of the dispersion that actually occurred, requiring no distributional assumption — just the observed returns, squared and summed.
It is exactly the quantity a variance swap settles on, so it is the precise object a variance trader is long or short, not an approximation of it.
It becomes far more accurate with high-frequency sampling: summing five-minute squared returns estimates a single day's variance with a precision one close-to-close return cannot approach.
It is additive across time by construction, since it is a sum, so the realised variance of a quarter is simply the sum of the realised variances of its days.
Combined with bipower variation, it can be decomposed into continuous and jump components, giving a richer picture of what actually drove a period's risk.

Where it breaks down

It is dominated by a handful of extreme days, so a single realised-variance figure describes a period's worst sessions far more than its typical behaviour, and reading it as an average is misleading.
It depends heavily on sampling frequency: close-to-close and five-minute estimators of the same period can differ substantially, and neither is uniquely correct.
At very high sampling frequencies it is contaminated by microstructure noise — the bid-ask bounce and tick discreteness — which inflates the sum unless corrected.
It cannot distinguish a continuous volatile day from a single violent jump, since both produce the same squared return; separating them requires bipower variation.
It is purely backward-looking, describing a period that has finished and carrying no direct forecast of the next, however tempting it is to extrapolate.
Its convexity makes it a treacherous thing to be short: the same squaring that concentrates it in a few days turns a crisis into a loss far larger than the calm-period premium ever justified.

Common mistakes

Reading a realised-variance figure as the average behaviour of a period. Because squaring concentrates it in a few days, the number is a summary of the worst sessions, and the typical day may have been nothing like it.
Selling variance swaps on the reasoning that realised almost always undershoots implied. It usually does, and then a few days deliver more variance than years of premium collected — the concentration in the tail is exactly what makes the strategy dangerous.
Ignoring the sampling frequency when comparing realised-variance figures. A close-to-close number and a five-minute number for the same period are different quantities, and treating them as interchangeable produces false comparisons.
Sampling too finely and mistaking microstructure noise for volatility. Below a few minutes the bid-ask bounce inflates realised variance, so the higher figure is measuring the tick, not the market.
Treating a jump day and a continuously volatile day as the same because they have the same realised variance. They carry different risks and hedge differently, and only bipower variation can tell them apart.
Extrapolating realised variance directly into a forecast of future variance without acknowledging that it is a backward-looking measurement that a single future day can overturn.
Confusing realised variance with implied variance. Realised is the squared movement that happened; implied is the price the option market charged for movement in advance, and the gap between them is the volatility risk premium, not an error.

Professional usage

Realized variance is the settlement quantity of the variance-swap market, so a volatility-arbitrage desk treats it as the thing it is directly long or short. The desk sells a variance swap struck at the implied variance, delta-hedges the option strip that replicates it, and its profit is the difference between the strike and the realised variance that arrives — a bet that implied variance exceeds what the underlying will actually deliver. Because realised variance concentrates in a few days, the desk's entire quarter can be decided by one session, so risk managers watch not just the level of realised variance but how much of it a single day could contribute. High-frequency desks compute intraday realised variance in near real time as their live estimate of the day's delivered volatility, updating their hedge as the sum accumulates.

Volatility researchers use realised variance as the benchmark that every volatility forecast is scored against, because it is the closest thing to a direct observation of the latent quantity that models like GARCH and stochastic-volatility models try to predict. The high-frequency realised-variance literature — summing five-minute squared returns, then correcting for microstructure noise and decomposing jumps with bipower variation — exists to build the cleanest possible measurement of what volatility actually was, so that a forecast of what it would be can be judged honestly. When a paper claims a model forecasts volatility well, the yardstick it is measured against is almost always a realised-variance estimator of exactly this kind.

Key takeaways

Realized variance is the sum of squared returns over a period, and because squaring amplifies the largest days, it is a summary of a period's worst few sessions rather than its average.
It is exactly what a variance swap settles on, and because variance is squared volatility, the payoff is convex — a few violent days can deliver more variance than years of calm.
The choice of sampling frequency matters: five-minute realised variance is far more accurate than close-to-close, but too-fine sampling lets microstructure noise inflate the figure.
Realized variance cannot separate a continuous volatile day from a single jump; bipower variation, which multiplies adjacent absolute returns, exists to isolate the jump component.
It is purely backward-looking — a measurement of a finished period — and the gap between it and implied variance is the volatility risk premium, not a forecasting error.

Realized variance is the honest reckoning of what volatility actually was, and its defining feature is that it refuses to be an average. Squaring the returns hands the entire figure to a few catastrophic days, which is why a variance swap built on it is convex, why short-variance positions look calm for years and then detonate, and why measuring it well requires arguing about sampling frequency and jumps. The uncomfortable lesson a marketing department would cut is this: because realised variance hides its whole magnitude in a handful of sessions you cannot see coming, any strategy that is short it is quietly holding a liability that stays invisible until the day it becomes the only thing that matters.

Frequently asked questions

What is realized variance?

Realized variance is the sum of the squared returns of an asset over a period — the variance that actually occurred, measured after the fact. Because each return is squared, the largest moves dominate the total, so the figure is concentrated in a period's worst few days rather than spread evenly across it.

How is realized variance calculated?

Take the return of each period, square it, and sum the squares over the whole window: RV = Σ r_t². To annualise, multiply the mean squared daily return by 252. The square root of realised variance is the realised volatility that gets quoted as a percentage.

What is the difference between realized variance and realized volatility?

Realized variance is the raw sum of squared returns in squared units; realized volatility is its square root, expressed as an annualised percentage. Variance is what a variance swap settles on and what adds across time; volatility is the readable form. The square root hides how concentrated the variance was in a few days.

Why do a few days dominate realized variance?

Because squaring is disproportionate: a 4% day contributes sixty-four times what a 0.5% day does, though it is only eight times larger. Over a long window a handful of extreme sessions swamp all the quiet ones, so the total is a portrait of the worst days, not an average of the period.

What does a variance swap settle on?

A variance swap settles on realized variance — the annualised sum of squared returns over the contract's life — against a fixed variance strike agreed upfront. The buyer receives realised variance and pays the strike, so the payoff is linear in variance and convex in volatility.

Why is a variance swap's payoff convex?

Because it settles on variance, which is the square of volatility. Double the realised volatility and the realised variance quadruples, so the payoff to a long position more than doubles. This convexity concentrates the contract's economics in the most violent days, which is why short positions can lose catastrophically.

Why did variance swap sellers blow up in 2008 and 2020?

Because realized variance is squared returns concentrated in a few days, and in those crises a handful of sessions produced more variance than years of calm premium had earned. The convexity that let short-variance books look steady for years turned a short crisis window into a loss many times the premium collected.

How does sampling frequency affect realized variance?

Substantially. Close-to-close sampling captures only end-of-day moves and misses the intraday path; five-minute sampling captures far more and gives a more accurate estimate. But sampling too finely lets microstructure noise inflate the figure, so five minutes is the conventional compromise between accuracy and noise.

What is high-frequency realized variance?

It is realized variance computed from intraday returns — commonly five-minute intervals — summed to estimate a single day's variance far more precisely than one close-to-close return can. It is the modern benchmark against which volatility forecasts are scored, once corrected for microstructure noise.

What is microstructure noise?

Microstructure noise is the distortion introduced by the mechanics of trading — the bid-ask bounce, discrete tick sizes and order flow — that inflates realised variance when prices are sampled too finely. Below a few minutes it can dominate the true signal, so estimators either sample coarser or correct for it explicitly.

What is bipower variation?

Bipower variation is a robust variance estimator that multiplies the absolute values of adjacent returns instead of squaring single returns. Because a lone jump has no similarly large neighbour to multiply against, its influence is suppressed, so bipower variation estimates the continuous part of variance and, subtracted from realised variance, isolates the jumps.

What is jump contamination?

Jump contamination is the fact that realized variance blends continuous, diffusive volatility with discrete news jumps and cannot separate them — both a violently agitated day and a single gap produce a large squared return. Distinguishing the two requires bipower variation, and it matters because the two components behave and hedge differently.

Why can't realized variance tell a jump from a volatile day?

Because it only sees squared returns, and a large squared return can come equally from a day of continuous agitation or a single violent gap. The figure records the magnitude but not the character of the move, so it treats a diffusion and a jump identically unless a separate estimator like bipower variation is used.

Is realized variance backward-looking or forward-looking?

Purely backward-looking. It measures the variance of a period that has already finished, using observed returns. It carries no direct forecast of the next period, and extrapolating it forward ignores that a single future day can overturn it — which is exactly what distinguishes it from implied variance.

What is the difference between realized variance and implied variance?

Realized variance is the squared movement that actually happened, measured after the fact; implied variance is the price the option market charged in advance for expected movement. The gap between implied and realised is the volatility risk premium — implied usually exceeds realised, which is why option sellers are compensated.

How do you annualise realized variance?

Multiply the mean squared daily return by 252, the approximate number of trading days in a year: RV_annual = (252 ÷ n) × Σ r_t². For higher-frequency sampling the scaling factor changes accordingly. Take the square root of the annualised variance to report an annualised realised volatility.

Why is realized variance additive across time?

Because it is defined as a sum of squared returns, so the realised variance of a quarter is exactly the sum of the realised variances of its days. This additivity is the same property that makes variance, not volatility, the natural quantity for combining dispersion across periods.

Can removing a few days really change realized variance that much?

Yes. On the illustrative 120-day series here, the five largest days account for the large majority of the whole period's realised variance, so removing them would change the figure beyond recognition. This is the concrete meaning of saying realised variance is concentrated in the tail.

Is realized variance a good measure of a period's risk?

It is a precise measurement of what dispersion occurred, but a poor description of typical behaviour, because it is dominated by a few days. It also cannot see skew, cannot separate jumps from diffusion without bipower variation, and is backward-looking — so it is a benchmark to measure against, not a complete risk picture.

Why do researchers use realized variance as a benchmark?

Because it is the closest thing to a direct observation of the latent volatility that models like GARCH and stochastic-volatility models try to forecast. A forecast can only be scored against something measurable, and high-frequency realised variance — noise-corrected and jump-decomposed — is the cleanest available measurement of what volatility actually was.

What does it mean that realized variance concentrates in a few days?

It means the sum is not built evenly from every session but is dominated by a small number of extreme ones, because squaring magnifies large returns. A realised-variance figure therefore answers 'how bad were the worst days' far more than 'how did the period behave typically', which is the single most important thing to understand about it.

Voice search & related questions

Natural-language questions people ask about realized variance.

What does realized variance actually measure?

Realized variance is what volatility actually turned out to be, measured by adding up the squared returns over a period. Because the returns are squared, the biggest days dominate the total, so the number is really a summary of a period's worst few sessions rather than an average of all of them.

Why is realized variance dominated by a few days?

Because squaring blows up the large moves: a 4% day counts sixty-four times a 0.5% day. Over a long stretch a handful of violent sessions swamp all the quiet ones, so on the 120-day series here the five biggest days carry the large majority of the whole figure. It is a portrait of the worst days.

Why does a variance swap use realized variance instead of volatility?

Because variance is the quantity that adds across time and can be replicated from a strip of options, so it can be traded cleanly. Settling on variance also makes the payoff convex — squared — which is the whole character of the instrument: it pays disproportionately in the crises where a few days deliver enormous variance.

Is selling variance a safe way to earn premium?

No. Realized variance usually comes in below the implied strike, so a seller collects small credits for a long time — and then a few crisis days deliver more variance than years of premium, because the payoff is squared and concentrated in the tail. It looks calm right up until it is total. None of this is investment advice.

Does it matter how often I sample prices for realized variance?

Yes, a lot. Close-to-close sampling misses the intraday path, while five-minute sampling captures far more and is more accurate — but sample too finely and the bid-ask bounce inflates the figure. Two desks measuring the same day can disagree entirely if they sampled it differently.

What is bipower variation for?

It separates a genuine jump from ordinary continuous volatility, which realised variance cannot do on its own. By multiplying adjacent absolute returns instead of squaring single ones, a lone jump gets suppressed because it has no large neighbour, so subtracting bipower variation from realised variance reveals how much came from jumps.

How is realized variance different from the VIX?

The VIX is forward-looking — the market's price today for future variance — while realised variance is backward-looking, the variance that actually happened. The difference between what the VIX implied and what realised variance delivered is the volatility risk premium, and it is usually positive, which is why option sellers are paid on average.

Sources & references

Last reviewed 10 July 2026. Educational content only — not investment advice.