The expected move formula is price × implied volatility × √(days ÷ 365), and the result is a one-standard-deviation range around the current price. Traders who count only trading sessions use √(sessions ÷ 252) instead. Plug in the S&P 500 at 7,659.44 and the VIX at 19.99 (both October 16, 2026 closes) and the math gives a one-session expected move of about ±96 points (±1.26%) and a 21-session move of about ±442 points (±5.77%).
That's the whole formula. The useful part is knowing what the number does and doesn't promise, and how often the market has actually stayed inside it. Short version: more often than textbook statistics predict, with some brutal exceptions.
The Expected Move Formula, Step by Step
Implied volatility (IV) is quoted as an annualized standard deviation. An IV of 20% means the options market is pricing roughly a 20% one-standard-deviation move over a full year. To shrink that annual figure to your window, multiply it by the square root of the fraction of a year you care about.
- Take the price. The S&P 500 closed at 7,659.44 on October 16, 2026.
- Convert IV to a decimal. A VIX of 19.99 becomes 0.1999.
- Scale for time. For 21 trading sessions, √(21 ÷ 252) ≈ 0.2887.
- Multiply. 7,659.44 × 0.1999 × 0.2887 ≈ 442 points, or 5.77% of the index.
Why the square root of time? If daily moves are roughly independent, variance adds up in a straight line as days pass, and standard deviation is the square root of variance. So volatility grows with the square root of time. Four times as many days means twice the expected move, not four times.
Calendar days or trading days? Both conventions are in use and they land close together. At the October 16, 2026 close, 30 calendar days on the 365-day convention gives ±438.96 points (5.73%), while 21 sessions on the 252-day convention gives ±442.00 points (5.77%). The real error is mixing them, such as counting trading days and then dividing by 365.
What "one standard deviation" means. Under a normal distribution, about 68% of outcomes land within ±1 standard deviation and about 95% within ±2. The formula draws a probability band, not a target. If returns were perfectly normal, a close outside the 1-SD band would happen roughly one time in three. They aren't, and that's where it gets interesting.
Worked Example: S&P 500 at the October 16, 2026 Close
Here the VIX stands in for implied volatility. Cboe describes the VIX as a measure of market expectations of near-term volatility conveyed by S&P 500 (SPX) option prices, on a roughly one-month horizon. Stretching a one-month IV over one day or one week is an approximation, since short-dated options can trade at a different IV.
| Window | Time factor | 1-SD move (points) | 1-SD move (%) | Implied range |
|---|---|---|---|---|
| 1 session | √(1/252) | ±96.45 | ±1.26% | 7,562.99 to 7,755.89 |
| 5 sessions | √(5/252) | ±215.67 | ±2.82% | 7,443.77 to 7,875.11 |
| 21 sessions | √(21/252) | ±442.00 | ±5.77% | 7,217.44 to 8,101.44 |
| 30 calendar days | √(30/365) | ±438.96 | ±5.73% | 7,220.48 to 8,098.40 |
Inputs: S&P 500 7,659.44 and VIX 19.99, October 16, 2026 closes. The VIX had jumped from 16.46 a session earlier, and a higher IV input widens every row. For what a VIX near 20 has historically meant for stocks, see our breakdown of what a VIX above 20 means.
The Straddle Shortcut
Many trading platforms print an "expected move" right on the options chain, and it is often built from the at-the-money straddle (a call plus a put at the same strike) rather than from the IV formula. The two are linked. Under standard option-pricing assumptions, an at-the-money straddle is worth approximately:
Straddle ≈ S × σ × √t × √(2/π) ≈ 0.798 × the 1-SD move
Flip it around and the 1-SD move ≈ straddle ÷ 0.798 ≈ 1.25 × the straddle. Using the 21-session S&P 500 figure: 0.798 × 442 ≈ 352.7 points. In other words, a straddle priced near 353 index points would be consistent with a ±442-point one-standard-deviation band.
Why 0.798? A straddle pays off the absolute size of the move, and the average absolute move of a normal distribution is about 0.798 standard deviations. So the straddle price is the market's estimate of the average move, which is smaller than one standard deviation.
That's why "expected move" figures differ between platforms. Some show the raw straddle (about 0.8 SD), some scale it up, some blend the straddle with nearby strangles, and some use the IV formula. Check which one you're reading before comparing it to anything else.
How Often the Market Beats the Expected Move
We tested the formula against more than 36 years of history: S&P 500 and VIX daily closes from January 2, 1990, through October 16, 2026 (FMP data). On every session, we compared the index's actual percentage change over the next 21 sessions with the VIX-implied 1-SD move, VIX ÷ 100 × √(21/252). Windows overlap and returns exclude dividends.
| Test | Sessions tested | Actual exceed rate | Normal distribution |
|---|---|---|---|
| 21 sessions, beyond 1 SD | 9,245 | 15.7% | ~31.7% |
| 21 sessions, beyond 2 SD | 9,245 | 0.98% | ~4.6% |
| 21 sessions since 2010, beyond 1 SD | 4,202 | 15.7% | ~31.7% |
| 1 session, beyond 1 SD | 9,265 | 18.3% | ~31.7% |
Implied volatility usually runs rich. The VIX was higher than the S&P 500's subsequent 21-session realized volatility on 85.3% of days, by an average of 4.06 points. That gap is the volatility risk premium: option sellers charge extra for insuring against crashes. On October 16, 2026, the index's trailing 21-day realized volatility was 10.20% against a VIX of 19.99. That is a backward-looking snapshot, not a forecast, but it fits the same pattern.
The tails are still fat, and they lean down. Fewer misses is not the same as small misses. The 2-SD breaks were lopsided: 0.85% of windows fell below −2 SD versus 0.13% that rose above +2 SD. The worst case started February 13, 2020: the S&P 500 fell 29.28% over the next 21 sessions against an implied 1-SD move of 4.08%, about 7.2 standard deviations. A ±1 SD band is a working range, not a floor or a ceiling.
One caveat. This is an index, which diversifies away single-company shocks. Individual stocks, especially around earnings, behave differently, and this backtest says nothing about how often any one ticker breaks its implied move. Spikes in volatility demand, like the one covered in our report on the VIX breaking above 22, are when traders watch the band most closely.
Common Expected Move Mistakes
- Mixing day counts. Trading days go with 252; calendar days go with 365. Never cross them.
- Using the wrong expiry's IV. Each expiration has its own implied volatility. Pull IV from the expiry that matches your window.
- Ignoring event IV. Options that span an earnings report or a major data release carry extra premium for that event. Once the news is out, that IV typically collapses, and the post-event expected move shrinks with it.
- Treating 1 SD as a ceiling. Even with the volatility premium, the S&P 500 broke its 21-session band 15.7% of the time from 1990 through October 16, 2026.
- Assuming symmetry. Puts usually trade at higher IV than equally distant calls (skew), and the backtest above shows the biggest misses skewed to the downside.
Applying It to Earnings
The most popular use of the formula is the earnings trade. Traders compare the move implied by options that span the report with how far the stock actually moved after its past several reports. If the implied move has consistently been bigger than the realized moves, options look rich; if the stock routinely blows through it, they look cheap. That comparison is a clue, not a verdict, since every quarter brings new information. See how that setup looked in options positioning ahead of Micron earnings and in options traders bracing for more tech volatility.
Hypothetical example (for illustration only, not market data): a hypothetical $100 stock with 60% IV and seven calendar days to expiration. The math: $100 × 0.60 × √(7 ÷ 365) ≈ $100 × 0.60 × 0.1385 ≈ $8.31. That is a 1-SD band of roughly $91.69 to $108.31. The matching at-the-money straddle would price near 0.798 × $8.31 ≈ $6.63.
Desk Notes
What the numbers say: The VIX-implied 21-session band held about 84% of the time from 1990 through October 16, 2026, and the VIX topped later realized volatility on 85.3% of days. Implied volatility has usually overpriced the S&P 500's actual swings.
What they don't: They don't cap the downside. The breaks that did happen leaned hard to the downside, including a 29.28% drop against a 4.08% band in early 2020. They also say nothing about single stocks around earnings.
For more volatility and options coverage, head to the Wall Street War Room homepage.
FAQ
Is the expected move 1 or 2 standard deviations?
The standard formula gives 1 standard deviation, which covers about 68% of outcomes under a normal distribution. Double it for a 2-SD band (about 95%). Platform "expected move" figures built from the raw straddle sit closer to 0.8 SD.
Should I use calendar days or trading days?
Either works if it's consistent: calendar days over 365, or trading sessions over 252. At the October 16, 2026 close they gave ±438.96 and ±442.00 S&P 500 points for roughly one month.
Why does the straddle price differ from the formula?
An at-the-money straddle prices the average absolute move, about 0.798 of one standard deviation. Skew, dividends, interest rates and bid-ask spreads add further small differences.
How accurate is the expected move?
For the S&P 500, the VIX-implied 21-session band was exceeded 15.7% of the time from 1990 to October 16, 2026, about half the rate a normal distribution implies. The misses that do happen can be severe.