Expected Move: Define the Metric Before Using the Number

Separate an option-implied volatility scale from expected absolute change, model intervals, straddle quotes, executable cost, breakevens, and realized profit or loss.

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

Expected move is market shorthand, not one universal statistic. A quoted number may mean a one-standard-deviation volatility scale, a model interval, a strict expected absolute change, an at-the-money straddle midpoint, an executable debit, or an expiration breakeven distance. Label the metric before interpreting it.

The common calculation S_0 x sigma_ann x sqrt(T) is a linearized one-standard-deviation dollar scale when sigma_ann is annualized volatility and T uses the matching year fraction. It is not automatically E[|Delta S|], a direction forecast, a probability guarantee, an option price, or a profitable-trade threshold.

Build and test the reference

Lock the underlying, valuation timestamp, horizon, expiration, spot or forward reference, strike convention, quantity, multiplier, deliverable, exercise style, and settlement method.
Save synchronized call and put bid, ask, size, package quote, spot or forward, rates, dividends, borrow, volatility surface, and event calendar.
Compute the horizon scale a = sigma_ann x sqrt(T) with the provider’s day-count and volatility convention; record any constant-variance or total-variance interpolation assumption.
Name the output. A linear dollar scale is s = S_ref x a. Under the teaching assumption Delta S = sZ with Z ~ N(0, 1), strict expected absolute change is E[|Delta S|] = s x sqrt(2 / pi), not s.
State the interval model and center. Linear markers are S_ref x (1 +/- a); log markers are S_ref x exp(+/-a) and are asymmetric in dollar space. A probability statement also needs a distribution, measure, drift, and stable parameters.
Separate straddle references: m_mid = C_mid + P_mid, m_buy = C_ask + P_ask, and m_sell = C_bid + P_bid. Leg sums do not guarantee simultaneous size or a package fill; record the actual complex-order execution.
Build entry, exit, and expiration ledgers with quantity q, multiplier M, all fees F, and actual fills. Compare realized moves over identical endpoints, then version the result when spot, time, surface, or events change.

An at-the-money straddle held to expiration has gross payoff q x M x |S_T - K|. If the package debit is p_fill, its net expiration P/L is q x M x (|S_T - K| - p_fill) - F. Under the controlled same-strike example, fee-adjusted breakevens are K +/- (p_fill + F / (q x M)). Before expiration, remaining time, the full volatility surface, rates, dividends, borrow, and executable exit quotes matter.

The familiar 68.268949% inside +/-1 sigma applies to a fixed centered normal model. Implied volatility is a model-derived, risk-neutral pricing input, and one ATM observation does not identify a physical return distribution or the full risk-neutral surface. VIX-style broad-strike variance methods are also different from a single-stock ATM shortcut.

Four worked examples

One sigma is not the strict expected absolute change. Let S_0 = $125, sigma_ann = 24%, and T = 30 / 365. Then a = 0.0688058615, the linear dollar scale is $8.600733, and the linear markers are $116.399267 and $133.600733. Under the centered-normal teaching assumption, E[|Delta S|] = $8.600733 x sqrt(2 / pi) = $6.862392, or 79.788456% of one sigma. Using 21 / 252 instead gives $8.660254, so the convention must be disclosed.
Linear and log markers differ. With S_ref = $100, sigma_ann = 40%, and T = 0.5, the horizon scale is a = 0.2828427125. Linear markers are $71.715729 and $128.284271; log markers around the stated reference are $75.363832 and $132.689644, corresponding to -24.636168% and +32.689644%. Neither pair is a guaranteed range, and a forward mean or lognormal median can require a different center.
Quote side changes the straddle number. A call quoted at $4.40 / $4.80 and put at $4.10 / $4.50 produce m_mid = $8.90, m_buy = $9.30, and m_sell = $8.50. The displayed buy-versus-sell width is $0.80/share = $80 for M = 100 before fees, but it is potential quote friction rather than a guaranteed round-trip loss or package fill.
A move above one sigma can still lose money. Buy one K = $125 straddle for an actual p_fill = $9.30, with M = 100 and total lifecycle fees F = $4. At expiration S_T = $133.80, gross payoff is $880, but net P/L is $880 - $930 - $4 = -$54. Fee-adjusted breakevens are $115.66 and $134.34. The $8.80 move exceeds the $8.600733 volatility scale but does not cover the executable debit and fees.

Seven-step controls and failure modes

The label can hide whether the number is sigma, expected absolute change, a quote, a debit, or a breakeven.
The timestamp, horizon, expiration, event window, or realized-move endpoints can be mismatched.
Spot, forward, risk-neutral mean, and lognormal median can be treated as the same center.
Volatility can be entered as a percentage instead of a decimal or paired with the wrong model convention.
Calendar-day and trading-day year fractions can be mixed or selected after seeing the answer.
Square-root-of-time scaling can fail when term variance, events, or regimes are not stable.
A spot-ATM strike can differ from forward ATM, Delta ATM, or an interpolated ATM coordinate.
A single ATM IV can hide skew, smile, tail prices, rates, dividends, borrow, and supply-demand effects.
Risk-neutral pricing information can be mislabeled as a real-world probability or forecast.
One sigma can be confused with strict E[|X|] or an arithmetic expected price change.
Linear symmetric markers can be presented as exact lognormal or nonnegative-price bounds.
The normal-model 68.268949% can be presented as a market guarantee despite jumps and fat tails.
Call, put, underlying, and volatility inputs can be stale, asynchronous, crossed, or too small.
A midpoint can be treated as executable, or leg sums can be confused with a package net market.
Partial fills, legging, rejected orders, bid-ask spread, impact, slippage, and fees can erase the thesis.
Quantity, multiplier, adjusted deliverable, exercise style, or physical versus cash settlement can be wrong.
Expiration payoff can be confused with a pre-expiration mark that still contains time and surface risk.
American exercise, writer assignment, halts, no-bid markets, and after-hours inventory can disrupt the plan.
A move beyond the headline scale can still fail to cover premium, fees, skew repricing, or exit spread.
Historical comparisons can contain corporate-action errors, inconsistent prices, survivorship, look-ahead, or data snooping.

Common misconceptions

“Expected move predicts direction.” It is a magnitude label only after the metric is defined.
“Expected means strict average absolute change, and one sigma guarantees 68%.” Those are different claims with model assumptions.
“An ATM straddle always equals one sigma.” It is a market-priced package with quote, carry, surface, and contract effects.
“A midpoint is executable and sets the real breakeven.” Actual fills, size, multiplier, and fees control the ledger.
“A realized move above the headline number guarantees a long-straddle profit.” Debit, strike, timing, repricing, and exit terms still matter.