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In FirmTape’s study of SPX regular sessions from April 14, 2022, through August 26, 2026, the session close landed within one intraday at-the-money implied expected move in 72.4% of eligible readings. A lognormal one-standard-deviation model would predict 68.3%. The study also found that normalized squared movement was close to its forecast level, so the higher containment rate does not by itself show that implied volatility was simply too high.
What “expected move” means in this study
The expected move (EM) is a range around the current SPX level, not a forecast of direction. At each intraday reading, FirmTape calculated it as EM = S · σ · √τ, where S is spot, σ is interpolated at-the-money implied volatility, and τ is the fraction of a year remaining until the 16:00 close. The question tested was whether that session’s close finished between spot minus EM and spot plus EM.
For each frame, the study averaged per-strike call and put implied volatilities, interpolated at spot, and paired the result with one-minute index prints. Its sample comprised 82,378 five-minute readings across 1,088 regular sessions, from April 14, 2022, to August 26, 2026. The study was published August 27, 2026. Read FirmTape’s study and methodology.
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How often the close landed inside the band
FirmTape compared observed containment with the theoretical coverage under a lognormal model. Its reported uncertainty figures accompany the measured coverage estimates.
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| Band around spot | Lognormal theoretical coverage | Measured close containment |
|---|---|---|
| 0.5× EM | 38.3% | 42.4% ± 0.8 percentage points |
| 0.8× EM (described by the study as approximate straddle breakeven) | 57.5% | 62.0% ± 0.9 percentage points |
| 1.0× EM | 68.3% | 72.4% ± 0.9 percentage points |
These are close-at-the-endpoint results, not the percentage of sessions in which SPX stayed inside the band at every moment. A reading counted as contained if the close was inside, even if the index had crossed outside the band earlier.
Why higher coverage does not mean volatility was simply overstated
Coverage and variance measure different properties. Coverage asks how often an endpoint falls inside a chosen range. Variance checks the average squared size of normalized movement. FirmTape reports day-clustered E[z²] = 1.034 ± 0.062 and describes that result as an essentially unbiased variance forecast.
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The study’s interpretation is that the distribution was more concentrated near the center, while also having fatter tails, than the lognormal model would suggest. That shape can produce more closes inside a one-sigma band without making the variance forecast too large. FirmTape summarizes its finding as “the expected move has the right variance and the wrong shape.” The reported 72.4% containment should therefore not be read as evidence that outcomes outside the band are as unlikely as a lognormal model implies.
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Intraday readings and close endpoint
The headline estimate excludes frames with less than 15 minutes remaining before the close, when the shrinking σ√τ makes the normalized ratio noisy. Those final-quarter-hour readings were reported separately: containment was 76.3%. Across the listed intraday buckets through the final half hour, reported coverage ranged from 71.0% to 73.6%.
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Readings within a session are not independent observations in the study’s headline calculation. The authors first averaged readings by session and then averaged across sessions. Reproduction instructions also specify dropping frames with fewer than three finite near-the-money IVs and clipping implied volatility to 1%–200%.
Not a test of intraday touches or option-trading returns
The result does not count an intraday excursion that reverses before the close as a breach. It also excludes overnight movement and does not establish whether selling a straddle or another options position would have been profitable after bid-ask spreads, fees, and execution.
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Other reported comparisons
By year, FirmTape reports containment of 71.8% in 2022, 71.6% in 2023, 72.4% in 2024, 74.2% in 2025, and 71.4% in 2026. Its QLIKE comparison reports a loss of 1.50 for the implied-volatility quote versus 2.05 for a trailing-realized-volatility benchmark; lower is better in that comparison. These are study-reported descriptive results, not a promise that implied volatility will outperform for a particular trade or period.
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How to compare expected-move accuracy claims
Two containment percentages are comparable only if they use similar inputs, horizons, endpoints, and treatment of repeated observations. Check what each estimate actually measures before drawing conclusions:
- Volatility input: intraday at-the-money implied volatility, VIX, or a straddle price can produce different bands.
- Horizon: an intraday reading with time left to the close differs from a one-day, one-week, or one-month forecast.
- Endpoint: a close inside the range is not the same as never touching or crossing the range during the period.
- Sampling and dependence: repeated readings or overlapping periods can be related; determine whether estimates account for clustering and whether overnight gaps are included.
- Evaluation metric: containment, variance calibration, and realized trade returns answer different questions.
The separate Theta Desk analysis uses VIX-scaled bands and close-to-close endpoints at one-day, one-week, and one-month horizons over a longer historical sample. It reports materially higher containment rates, but its measure, horizons, and sampled observations differ from FirmTape’s intraday ATM-IV-to-close test. Theta Desk also notes overlapping horizons, dependence among stress episodes, and that its VIX-based measure sits somewhat above ATM straddle levels. The two sets of hit rates should not be combined as if they were replications. See Theta Desk’s analysis and its stated caveats.
What the result is useful for
Within this specific setup, the findings give a historical calibration for interpreting an intraday, ATM-IV-based band around SPX spot: the close fell inside 1× EM more often than a lognormal one-sigma benchmark predicts, while the study’s variance check remained near one. That can inform how a reader thinks about band coverage, but it is not a directional forecast, a path-risk measure, or proof of a profitable strategy. FirmTape describes the work as “measurement, not a signal.”
For general context, Fidelity explains the use of at-the-money options in implied-volatility calculations and the one-standard-deviation convention for expected-move scaling. That educational explanation is not evidence for FirmTape’s SPX findings. Read Fidelity’s volatility overview.
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