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Expected Volatility

A number somebody predicted, forever mistaken for a number the market priced.

Quick answer: Expected volatility is a forecast of how much an asset will move over a future period, produced by a statistical model from the return history — which makes it somebody's prediction, not the market's price, and that distinction is the whole point.

In simple words

Expected volatility answers the question "how much do I think NIFTY will move over the next month?" with a number you compute rather than a number you read off a screen. You take the recent daily returns — say NIFTY has been moving about 0.8% a day — and you build a model that turns that history into a forecast for the future. If the model says 0.8% a day will continue, it scales that up to roughly 12.7% a year. That 12.7% is an expected volatility: it is a forecast, and like every forecast it can be wrong.

The word "expected" is doing quiet, dangerous work here. Expected volatility is what a forecasting model expects. Implied volatility is what the option market charges. They are usually close, they are labelled with the same percentage sign, and they are constantly swapped for one another in conversation — which is precisely why so many people believe that "implied volatility predicts the move". It does not predict anything. A forecast predicts. A price is just a price.

Not to be confused with: Implied volatility, which is not a forecast at all — it is the volatility figure backed out of an option's market price. Expected volatility is what a model such as GARCH or EWMA predicts the future will realise; implied volatility is what a seller of optionality is charging for it today. The two coincide only by accident, and the systematic gap between them is the volatility risk premium.

A forecast against the outcome it was forecasting

Biased high in the calm, catastrophically low at the shock

An EWMA forecast of NIFTY volatility plotted against the volatility that subsequently arrived.

5%10%15%20%25%30%20d70d120d170dIV is biased high in the calm……and catastrophically low right before the shockDay the forecast was madeAnnualised volatilityimplied volatility (the forecast, made today)realised volatility over the NEXT 20 days (the outcome)
The forecast tracks the outcome closely and sits slightly above it for long, quiet stretches — which is exactly what makes it feel trustworthy. Then a shock arrives, realised volatility triples in a session, and the forecast is left far below it because a model built from yesterday's returns cannot know about tomorrow's news. The picture proves that the error you can measure and the error that can ruin you are two different distributions.

Professional explanation

Expected volatility is a forecast, and every forecast has a model behind it

There is no such thing as "the" expected volatility, only the volatility expected by a particular model fed a particular history. The two workhorses are EWMA and GARCH. EWMA — the exponentially weighted moving average, standardised by RiskMetrics with a decay of 0.94 — treats tomorrow's variance as a blend of today's variance and today's squared return, weighting recent days more heavily than old ones. GARCH adds one idea EWMA lacks: a long-run average volatility that the forecast is pulled back toward, so that a spike decays not to nothing but to a normal level. Both are backward-looking machines. They can only extrapolate the movement that has already happened, dressed up as a statement about movement that has not.

Why implied volatility usually beats the statistical forecast

Run a fair contest — forecast next month's realised volatility with GARCH, and separately read it off the option market's implied volatility — and across almost every liquid market the implied number wins on average. This is not because option traders own a better time-series model. It is because the option price contains information that is simply not in the return history: a scheduled RBI policy meeting next week, a Union Budget, an election count, a build-up of hedging demand that nobody has yet had to act on. A GARCH model fitted to past returns is blind to a known future event until the event moves the returns. The option market prices it the moment the date is known. That informational edge, not statistical sophistication, is why implied volatility is the forecast to beat.

The forecast fails hardest exactly where it matters

The uncomfortable truth about every volatility forecast is that its errors are not evenly distributed. In calm markets a model like EWMA is slightly too high, over and over, because it is still carrying a memory of the last disturbance while the market drifts quietly — a small, comfortable, profitable-looking bias. Then a regime changes: a bank blows up, a currency gaps, a policy surprises, and realised volatility triples in a single session. At that exact moment the forecast is at its lowest and its most confident, because it was built from the quiet days immediately preceding. The forecast is most wrong precisely when being wrong costs the most. A volatility model is an umbrella that works on every day except the one it rains.

Volatility clusters, which is the only reason forecasting works at all

If returns were independent from one day to the next, yesterday's move would tell you nothing about today's and no forecast could beat the long-run average. The reason EWMA and GARCH earn their keep is that volatility clusters: large moves are followed by large moves and quiet by quiet, a property visible in every equity index ever measured. GARCH formalises this as mean-reverting variance — high volatility decays back toward a long-run level at a measurable speed, low volatility drifts back up. This is genuinely useful and genuinely limited. Clustering tells you that a turbulent week will probably be followed by a turbulent day. It says nothing about the jump that starts the turbulence, because that jump is, by definition, not in yesterday's data.

How the forecast is actually used, and mis-used

An expected volatility is an input, not a conclusion. Risk managers feed it into value-at-risk and margin models; option traders compare it against implied volatility to decide whether options look rich or cheap; portfolio managers scale position sizes so that expected risk stays roughly constant as volatility changes. The recurring error is to treat the forecast as if it were a fact and then lever against it. A model that has been quietly right for two years builds exactly the confidence that makes the eventual miss expensive, because that confidence is what let the position grow large. The forecast is most trusted at the moment before it is most wrong.

Formula

EWMA — the RiskMetrics variance forecast

σ²_t = λ·σ²_{t−1} + (1 − λ)·r²_{t−1}, λ ≈ 0.94

Tomorrow's variance forecast is a weighted blend of today's variance forecast and today's squared return. The decay λ controls memory: at 0.94 (the RiskMetrics daily standard) a day's influence halves roughly every eleven days. EWMA has no long-run average built in, so a spike decays toward the prevailing level rather than toward a normal one — which is exactly the feature GARCH adds.

  • σ²_tThe variance forecast for day t — the quantity being produced. Its square root, annualised by multiplying by √252, is the expected volatility.
  • σ²_{t−1}The previous day's variance forecast, carried forward. This is what gives EWMA its memory.
  • r²_{t−1}The previous day's squared return (log return of the underlying), the newest piece of information entering the forecast.
  • λThe decay factor, between 0 and 1. RiskMetrics fixes it at 0.94 for daily data; a higher λ means a longer, smoother memory and a slower reaction to new moves.

GARCH(1,1) — variance with a long-run anchor

σ²_t = ω + α·r²_{t−1} + β·σ²_{t−1}

GARCH(1,1) adds a constant ω so the forecast mean-reverts to a long-run variance of ω / (1 − α − β) rather than drifting. EWMA is the special case ω = 0, α = 1 − λ, β = λ with α + β = 1. The persistence α + β, usually near 0.95 for an equity index, sets how slowly a volatility spike decays; the symbols α and β are the weights on the newest squared return and the previous variance respectively.

How to build an EWMA volatility forecast, step by step

  1. Collect a clean series of daily closing prices for the underlying — NIFTY, say — and convert them to daily log returns: r = ln(price today ÷ price yesterday).
  2. Seed the recursion. Take a simple variance of the first stretch of returns (say the first 30 days) as your starting σ² so the model has somewhere to begin.
  3. Fix the decay. Use λ = 0.94 for a daily forecast unless you have a specific reason to change it; a longer horizon uses a higher λ.
  4. Step forward one day at a time: σ²_t = 0.94 × σ²_{t−1} + 0.06 × r²_{t−1}. Each new day updates the forecast with that day's squared return.
  5. Take the square root of the final σ² to get a daily volatility, then annualise it by multiplying by √252 — the number of trading days in a year.
  6. Sanity-check the result against implied volatility and India VIX. If your forecast is 12% and the option market is charging 14%, that two-point gap is the volatility risk premium, not necessarily a mistake by either side.
  7. Never report the forecast without its horizon and its model. "12.7%, EWMA λ=0.94, one-month annualised" is a number. "12.7%" alone is an invitation to confuse it with an implied volatility.

Practical example

NIFTY worked example

NIFTY is at 24,000 and your EWMA forecast currently stands at 12% annualised, which is a daily volatility of 12% ÷ √252 ≈ 0.756%, so σ²_{t−1} ≈ 0.00756² ≈ 0.0000572. Today NIFTY falls 1.5% on an unexpected headline, so r = 0.015 and r² = 0.000225 — a much bigger squared return than the forecast was carrying. Update: σ²_t = 0.94 × 0.0000572 + 0.06 × 0.000225 ≈ 0.0000537 + 0.0000135 = 0.0000672. The new daily volatility is √0.0000672 ≈ 0.820%, and annualised that is 0.820% × √252 ≈ 13.0%. So one 1.5% day dragged the forecast from 12% to 13%. Interpret that: EWMA reacts, but it reacts gently — a single shock nudges the forecast by a point, which is comforting on a normal day and dangerously slow on the day a genuine regime change begins.

BANKNIFTY worked example

The same recursion on BANKNIFTY teaches the opposite lesson about persistence. BANKNIFTY at 52,000 realises more volatility than NIFTY — say a forecast sitting at 16% annualised, a daily σ of about 1.008%. Suppose it then goes quiet: several sessions of roughly 0.5% moves, well below the forecast. Each quiet day pulls σ²_t down, but only by six percent of the gap, because λ = 0.94 keeps ninety-four percent of yesterday. After five calm sessions the forecast has barely fallen from 16% to about 15%. A trader who sold BANKNIFTY volatility expecting the forecast — and the option premium — to collapse as fast as the market went quiet would be waiting a long time. EWMA is deliberately sticky: it forgets slowly on the way down just as it reacts slowly on the way up, and that asymmetry between how fast volatility spikes and how slowly forecasts of it decay is where a lot of money is lost.

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. An expected volatility that has been accurate for months is the most dangerous number on the desk, because its track record is exactly what justifies sizing the position larger. Every statistical forecast is blind to the jump that is not yet in the data, and position sizes scaled to a calm forecast are largest at the moment the calm ends. A forecast is a reason to size a position, never a reason to believe the position is safe.

Advantages & limitations

What it is good for

  • It is explicit and reproducible. Unlike implied volatility, which depends on a live market and a pricing model, an EWMA or GARCH forecast can be computed from public price history by anyone, audited, and compared across assets on identical terms.
  • It captures volatility clustering. Because it weights recent returns most heavily, it reacts to a genuine change in regime faster than a plain rolling-window historical volatility, which mechanically forgets old shocks all at once when they fall out of the window.
  • It has a long-run anchor, in the GARCH form. Mean reversion means a spike is forecast to decay toward a normal level rather than persist forever, which matches how volatility actually behaves and prevents the forecast from over-committing to a single turbulent week.
  • It is a genuine forecast you can score. Because it makes a falsifiable prediction about a future period, you can measure its error after the fact and improve it — something you cannot honestly do with a price, which was never a prediction in the first place.
  • It needs no option market. For an underlying with illiquid or non-existent options, a statistical forecast is the only forward-looking volatility estimate available at all.

Where it breaks down

  • It is blind to scheduled events. A GARCH model fitted to past returns cannot see an RBI policy meeting or a Union Budget sitting in next week's calendar until the event actually moves prices, so it systematically under-forecasts volatility ahead of known catalysts — precisely where implied volatility does its best work.
  • It cannot forecast a jump. The whole apparatus assumes volatility evolves smoothly from its recent path; a gap caused by news that was not in yesterday's returns is, by construction, outside what the model can predict. The forecast is lowest and most confident just before the discontinuity.
  • It is sensitive to the decay and the window. Change λ from 0.94 to 0.97 and the same data produce a visibly different, smoother forecast; there is no objectively correct choice, only a choice suited to a horizon, and two analysts can defend two different numbers from identical prices.
  • It assumes the future resembles the estimation sample. When the market's regime changes — a shift in policy, liquidity, or market structure — a model calibrated on the old regime keeps forecasting the old regime until enough new data accumulates to retrain it, and the lag is largest exactly when it matters.
  • It says nothing about the shape of the tail. EWMA and standard GARCH forecast a variance under a roughly normal assumption; they do not tell you the probability of the six-standard-deviation day, which is the one that determines whether a short-volatility book survives.

Common mistakes

  • Calling an expected volatility an implied volatility, or vice versa. They are a forecast and a price. Once you conflate them, "IV predicts the move" sounds true, and every downstream decision inherits the error.
  • Trusting a forecast more the longer it has been right. A model quietly accurate through a calm stretch has taught you nothing about its behaviour in a shock, and the accumulated confidence is exactly what makes the eventual miss large, because it is what let the position grow.
  • Reading a low forecast as a low-risk environment. A quiet forecast means the recent past was quiet; it is silent about the jump, and historically the lowest-volatility periods are when leverage and short-volatility exposure build up across the whole market.
  • Using a single decay or window for every horizon. A λ tuned for a one-day forecast produces a jumpy, over-reactive estimate of one-month volatility. Match the memory of the model to the horizon you are forecasting.
  • Feeding a shock day's return into the recursion without checking it is real. A fat-fingered print, a stale close or a corporate action can inject a spurious squared return that inflates the forecast for weeks, because EWMA forgets it only slowly.
  • Forecasting variance and then forgetting to annualise consistently. Mixing a daily variance with a √365 scaling, or comparing a 252-day-annualised forecast against a broker's 365-based number, produces a discrepancy that gets blamed on the model rather than on the arithmetic.

Professional usage

On a professional desk, expected volatility is the number the trade is measured against, not the trade itself. A volatility arbitrage desk generates its own realised-volatility forecast — often a GARCH or a more elaborate high-frequency estimator — and trades the difference between that forecast and the option market's implied volatility, delta-hedging so that the profit and loss depends on which volatility was closer to the truth. If their forecast is 12% and implied is 14%, they may sell the option and hedge, betting the underlying realises nearer their number, and their entire edge is the quality of the forecast, which is why enormous effort goes into it.

Risk managers use expected volatility to set the size of value-at-risk and the level of margin, deliberately preferring a forward EWMA or GARCH estimate to a naive trailing average because the exponential weighting reacts to a regime change days sooner. But the sophisticated ones treat the forecast as a floor on risk, not a measurement of it: they stress the book against volatility levels the model considers improbable, precisely because the model's job is to describe the normal days and its blind spot is the abnormal one that sets the margin call in motion.

Key takeaways

  • Expected volatility is a forecast produced by a model; implied volatility is a price backed out of the option market. Conflating the two is the reason people wrongly believe IV predicts the move.
  • EWMA and GARCH are the standard forecasts. Both extrapolate volatility clustering from past returns; GARCH adds a long-run mean the forecast reverts toward, EWMA does not.
  • Implied volatility usually beats the statistical forecast on average, because option prices contain information about scheduled events and hedging demand that is not yet in the return history.
  • Every volatility forecast is biased slightly high in calm markets and catastrophically low right before a shock, because the shock is not in the data the model was built from.
  • A forecast is a reason to size a position, never a reason to believe it is safe — and it is most trusted at the moment before it is most wrong.

Treat expected volatility as a forecast with a model and a horizon stapled to it, and half the confusion around implied volatility disappears. The option market is not forecasting anything when it quotes 14%; a GARCH model genuinely is when it says 12%. The gap between them is information and risk premium, not a contradiction. And the number to distrust most is the one that has been right the longest, because its track record was earned entirely on the days that do not matter.

Frequently asked questions

What is expected volatility?
Expected volatility is a forecast of how much an asset will move over a future period, produced by a statistical model such as EWMA or GARCH from the recent return history. It is a prediction you compute, not a price you read off a screen, and like any prediction it can be wrong.
How is expected volatility different from implied volatility?
Expected volatility is a model's forecast of future movement; implied volatility is the volatility figure backed out of an option's market price. One is a prediction, the other is a price. They are labelled with the same percentage sign and constantly confused, which is why people wrongly think implied volatility predicts the move.
What is EWMA in volatility forecasting?
EWMA, the exponentially weighted moving average, forecasts tomorrow's variance as a blend of today's variance forecast and today's squared return, weighting recent days more heavily. RiskMetrics standardised it with a decay of 0.94 for daily data, which makes a day's influence halve roughly every eleven days.
What is GARCH and how does it differ from EWMA?
GARCH(1,1) forecasts variance from a constant, the last squared return, and the last variance, which gives it a long-run average that the forecast mean-reverts toward. EWMA is the special case with no constant, so a GARCH spike decays back to a normal level while an EWMA spike only decays toward whatever level currently prevails.
Does expected volatility predict the direction of the market?
No. Volatility of any kind measures the size of expected movement, not its sign. A forecast of 13% is equally consistent with the market rising sharply or falling sharply. Direction and dispersion are separate questions, and no volatility forecast answers the first one.
Why does implied volatility usually beat a statistical forecast?
Because the option price contains information the return history does not — a scheduled RBI meeting, a Budget, an election count, a build-up of hedging demand. A model fitted to past returns is blind to a known future event until the event moves prices, while the option market prices it the moment the date is known.
Can a volatility forecast be trusted?
It can be used, not trusted. Every statistical forecast is slightly too high in calm markets and far too low right before a shock, because the shock is not in the data it was built from. Treat a forecast as an input with a known blind spot, not as a fact.
What is a normal expected volatility for NIFTY?
A one-month EWMA or GARCH forecast for NIFTY typically sits somewhere between roughly 11% and 16% annualised in ordinary conditions, broadly in line with India VIX around 13. These are conventions drawn from recent history, not fixed rules, and a genuine stress period pushes the number well above the range.
What does the decay factor lambda control?
Lambda controls the memory of an EWMA forecast. At 0.94 the model keeps 94% of yesterday's variance and adds 6% of today's squared return, so it reacts slowly and smoothly. A higher lambda means a longer memory and a gentler reaction; a lower one makes the forecast jumpy and over-sensitive to single days.
Why is expected volatility annualised?
By convention, so that forecasts over different horizons are comparable on one scale. A daily variance forecast is turned into a daily volatility by taking its square root, then annualised by multiplying by √252, the number of trading days in a year. Always report the horizon alongside the number.
Can expected volatility be negative?
No. Volatility is the square root of a variance, and a variance is a sum of squared returns, so it cannot be negative. If a forecasting routine returns a negative number, there is a coding error — most often a variance that went negative because of a badly chosen constant in a GARCH fit.
Why does my volatility forecast lag a market crash?
Because it is built from past returns, and a crash is news that was not in those returns. EWMA updates by only 6% of the new squared return each day at lambda 0.94, so even a violent move nudges the forecast gently at first. The forecast catches up over the following sessions, which is exactly too late.
What is volatility clustering and why does it matter?
Volatility clustering is the tendency of large moves to be followed by large moves and quiet by quiet, visible in every equity index. It is the only reason forecasting beats a constant guess: if returns were independent, yesterday's move would tell you nothing about today's and no model could add value.
How many days of history do I need to forecast volatility?
Enough to estimate the model stably — a few hundred daily returns is a common minimum for a GARCH fit — but EWMA needs only a seed variance and then updates forever. More history stabilises the parameters but also mixes in old regimes that may no longer apply, so more is not always better.
Is expected volatility the same as historical volatility?
No, though they are cousins. Historical volatility is a plain backward-looking measurement of what already happened; expected volatility uses that history to make a forward-looking forecast. A rolling historical volatility forgets old shocks abruptly when they leave the window, whereas EWMA lets them fade gradually.
Should I use expected volatility or implied volatility to price a position?
Options are priced off implied volatility because that is the volatility the market will transact at. Expected volatility is what you compare that price against to decide whether it looks rich or cheap. Using your own forecast to price a trade only makes sense if you also plan to hedge and capture the difference between the two.
What happens to a forecast when I feed it a bad data point?
A spurious spike — a fat-fingered print, a stale close, an unadjusted corporate action — injects a large false squared return that inflates the forecast for weeks, because EWMA forgets it only at 6% a day. Cleaning the return series before it enters the recursion is not optional.
Does expected volatility mean revert?
In the GARCH form, yes, by design: the forecast is pulled back toward a long-run average variance at a speed set by the model's persistence. Plain EWMA does not mean revert at all — it has no long-run anchor, so a spike decays only toward the currently prevailing level, not toward any normal one.
Why do two analysts get different expected volatilities from the same data?
Because they chose different models, decay factors, or estimation windows, all of which are defensible. An EWMA at lambda 0.94 and a GARCH(1,1) fitted to the same returns will disagree, and neither is wrong. This is why a forecast should always be reported with the method that produced it.
Can expected volatility be used for position sizing?
Yes, and it commonly is: many managers scale positions so that forecast risk stays roughly constant as volatility changes. The hazard is that a calm forecast produces the largest position sizes just before a regime change, so volatility-targeting can quietly build maximum exposure at the worst possible moment.
Is India VIX an expected volatility?
Not in the statistical sense. India VIX is a model-free summary of the near-dated NIFTY option chain — it is derived from implied volatilities, which are prices, not from a forecasting model. It is often read as the market's expected volatility, but it is a price aggregate, and it carries the volatility risk premium that a pure forecast does not.

Voice search & related questions

Natural-language questions people ask about expected volatility.

What does expected volatility actually mean?
It means the amount of movement a model predicts an asset will show over some future window. You compute it from recent returns using something like EWMA or GARCH, and it comes out as an annualised percentage — a forecast, not a market price.
Is expected volatility the same thing as IV?
No, and this is the confusion worth clearing up. Expected volatility is a forecast your model makes. Implied volatility is a price the option market sets. They look identical on the screen because both are percentages, but one predicts and the other charges, and only the second is something you can actually transact at.
Why does my forecast always seem a bit too high?
Because in calm markets it is. EWMA and GARCH carry a memory of the last disturbance while the market drifts quietly, so they sit slightly above the realised volatility for long stretches. That small persistent bias feels like the model working — until a shock arrives and the same model is suddenly far too low.
Which is better, EWMA or GARCH?
GARCH is richer because it adds a long-run average that the forecast reverts toward, so a spike decays to a normal level rather than drifting. EWMA is simpler, needs no fitting, and is the RiskMetrics standard. For many everyday purposes their forecasts are close; GARCH earns its extra complexity mainly around regime changes.
Can I make money trading expected volatility against implied?
That is exactly what a volatility arbitrage desk attempts: forecast realised volatility, compare it with implied, trade the gap, and delta-hedge so direction drops out. Whether it works depends entirely on whose number was closer to the truth, and short-volatility positions carry theoretically unlimited loss, so nothing here is a promise of profit.
How far ahead can expected volatility forecast?
Usefully, not very far. Volatility clustering makes tomorrow and next week forecastable from recent data, but the predictive power fades quickly with horizon and collapses entirely at any jump the data could not foresee. A one-month forecast is reasonable; a one-year forecast is mostly the long-run average with a label.
Why did my forecast miss the crash completely?
Because a crash is news, and news is not in yesterday's returns. Your model can only extrapolate the movement that already happened, so it was at its lowest and most confident right before the move that mattered. That is not a bug you can tune away; it is the defining limit of any backward-looking forecast.

Sources & references

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

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