Expected Move: The Range Implied by IV

Implied vs Realized Volatility introduced IV as a forward-looking annualized estimate of how much the underlying will move. The practical question is the next one: how much is that in dollars over the period you actually care about? The answer is the expected move — the 1-σ range derived from IV. This article covers the formula (a short one), the ATM-straddle shortcut (works without any math), the probabilistic interpretation, how the range scales with time, why 0DTE expected moves behave the way they do, and where the formula breaks down.

What expected move is

Expected move is the one-standard-deviation range the underlying is expected to land in over a given time period, computed from the current implied volatility.

The 68% / 95% labels come from the normal distribution. They're approximations — option pricing models assume lognormal returns, and the real distribution of returns has fatter tails. But for short-dated options near the money, the approximations are close enough to be useful as planning numbers.

The formula

S is the current underlying price, σ_IV is the implied volatility (as a decimal — 0.15 for 15%), and T is the number of calendar days to expiration.

A worked example. SPX at 5000, IV at 15%, one trading day to expiration:

EM ≈ 5000 × 0.15 × √(1/365) = 5000 × 0.15 × 0.0523 ≈ $39

So the 1-σ range is roughly 4961 to 5039 — about $80 wide. The 2-σ range is roughly 4922 to 5078.

The intuition: IV is annualized, so over a single day the underlying gets only 1/√365 ≈ 5.2% of the full annual move. That's where the small-but-not-tiny daily numbers come from.

The ATM straddle shortcut

You don't actually have to compute the formula. The market is already pricing it for you — it's the ATM straddle.

A straddle is one ATM call plus one ATM put. At expiration, the straddle is worth |S − K| — exactly the absolute move from the strike. Today, the straddle's premium is roughly what the market expects that absolute move to be. The exact relationship under BSM is:

ATM straddle ≈ S × σ_IV × √(2T / (365π))

That's roughly 80% of the formula above. For practical purposes, traders treat the ATM straddle as the market-implied expected move and skip the math. Read the ATM straddle price off the chain, and that's your expected move number — incorporating whatever IV the market is actually pricing right now.

This shortcut has another advantage: it uses the actual ATM IV that the market is trading, not a single "official" IV like VIX or VIX1D, which can be smoothed or interpolated.

See it interactively

The cone below shows the ±1σ band (darker) and ±2σ band (lighter) fanning out across a single trading session from SPX at 5000. The shape is the √-of-time scaling law in miniature — the range widens fast in the morning and flattens into the afternoon, because expected move grows with the square root of elapsed time, not linearly. Drag IV up and the whole cone widens. Drag the marker to read the expected move from the open through any point in the session — about ±$28 by midday, about ±$39 by the close at 15% IV.

Notice the ATM straddle estimate panel — it's roughly 80% of the ±1σ number, exactly as the formula predicts.

The square-root-of-time scaling law

Expected move scales with the square root of time, not linearly. Variance accumulates linearly as time passes — the defining property of a random walk — and the standard deviation, which is what expected move measures, is the square root of variance. So halving the time left doesn't halve the expected move; it scales it by √0.5 ≈ 0.71.

On 0DTE this plays out within a single session. Treating the trading day (9:30am to 4:00pm) as carrying roughly one day's expected move — about ±$39 at SPX 5000 and 15% IV — the move still to come shrinks with the square root of the time left to the close:

Two things to notice. First, the decay is slow early and fast late: losing the first hour of the session trims the remaining move by only about $3 (±$39 to ±$36), but losing the last full hour takes it from ±$15 to nearly nothing. That acceleration — the square-root curve steepening as it approaches zero — is the same force behind the way gamma and theta accelerate in the final hour. Second, the morning expected move is large relative to where strikes sit: ±$39 at 15% IV is plenty of room for an at-the-money strike to be tested, which is why a 50-delta short option on 0DTE is essentially a coin flip on the close.

What the shrink means for your strikes

The shrinking expected move cuts in the premium seller's favor when the underlying sits still. A 5050 short call against SPX at 5000 is about 1.3σ away at the open (full session, IV=15%, ±$39). If SPX hasn't moved by 3pm, that same strike is now further away in probability terms, not closer — with an hour left the remaining expected move is only about ±$15, so 50 points is more than 3σ. That's theta working for the seller: as long as the underlying stays put, every passing hour pushes a fixed OTM strike further out in σ terms.

The flip side is that intraday strike selection has to use the remaining expected move, not the morning's. A strike chosen to sit "1σ out" at 2pm is far closer to the money in points than one chosen at the open — "1σ" is a ±$39 cushion at 9:30am but only an ~$15 cushion with an hour to go. Same label, very different distance.

The cone above shows the open's-eye view — the range fanning out from 9:30am. The remaining-move view here is the same square-root-of-time law measured from a later starting point.

Using expected move in practice

Three concrete uses, in roughly increasing sophistication.

Strike selection. Short strikes outside ±1σ are high-probability OTM at expiration — under the ~68% rule, only about 16% of paths cross each side. Picking a 16-delta strike (covered in Moneyness: ITM, ATM, OTM) ends up roughly at the edge of the 1-σ band, which is why "sell the 16-delta strangle" is a common discipline.

Sanity-checking credit vs distance. When sizing a short premium trade, the credit collected per unit of expected move tells you something the credit alone doesn't. A $1.00 credit on a strike that's 0.5σ away is a different trade from a $1.00 credit on a strike that's 1.5σ away — same dollar income, very different risk profile. Expected move gives you the denominator for that comparison.

Reality check on IV. If today's expected move feels disconnected from what the underlying has actually been doing — implied move much larger than recent realized ranges, or much smaller — that's information about whether IV is rich or cheap. Pair this with Implied vs Realized Volatility for the underlying framework.

Where the formula breaks down

Three honest caveats.

The lognormal assumption. Real return distributions have fatter tails than the lognormal model assumes. The ±2σ band is sometimes cited as "95% confidence," but in real markets the actual probability of staying within ±2σ is closer to 90% — and during stress regimes, lower. Treat ±2σ as "usually contained" rather than "almost certainly contained."

Skew. On SPX, OTM puts trade at higher IV than equivalent OTM calls (the structural fingerprint of dealer hedging and downside-protection demand). That means the real-world expected move is asymmetric — the downside half of the ±1σ band is genuinely wider than the upside half. The symmetric formula above is an average across the chain; reading the ATM straddle gives you the same average. For the skew-aware version, you can read put-side and call-side OTM premium separately. See The Volatility Smile and SPX Skew.

Jumps. News-driven gaps (CPI, FOMC, earnings for equities) push the underlying through prices without traversing every intermediate level in continuous time. Expected move is an average-case framing; individual event days look nothing like it. The model assumes continuous paths and constant IV — both are wrong around scheduled events.

Key takeaways