In FirmTape’s sample, the SPX close finished within one intraday at-the-money implied expected move in 72.4% of eligible readings, above the 68.3% lognormal one-sigma benchmark. But the study also found the variance forecast was essentially unbiased. The result is better read as a difference in distribution shape than as proof that implied volatility simply overstated the move.
What “expected move” means in this study
Here, the expected move (EM) is a band around the current SPX level, not a forecast of direction. FirmTape calculates it from spot, at-the-money implied volatility and the time remaining until the regular-session close: EM = S · σ · √τ, where S is spot, σ is implied volatility and τ is the year fraction remaining until 16:00.
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For each five-minute frame, the authors average per-strike call and put implied volatilities, interpolate that value at spot and compare the session’s eventual close with the resulting band. So the question is: when the screen shows a band around SPX at an intraday moment, how often does that day’s close land inside it?
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What the 1,088-session calibration found
FirmTape’s study, published August 27, 2026, covers SPX regular sessions from April 14, 2022, through August 26, 2026: 1,088 trading days and 82,378 five-minute readings. The headline excludes readings with less than 15 minutes until the close. Its figures are publisher-produced and were not independently audited.
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| Band around spot | Lognormal benchmark coverage | Measured close coverage |
|---|---|---|
| Within 1.0× EM | 68.3% | 72.4% ± 0.9 percentage points |
| Within 0.8× EM | 57.5% | 62.0% ± 0.9 percentage points |
| Within 0.5× EM | 38.3% | 42.4% ± 0.8 percentage points |
The study describes the 0.8× band as an approximate straddle breakeven. These are close-containment rates, not option-trade returns.
How to read the variance result
FirmTape also reports day-clustered E[z²] = 1.034 ± 0.062, describing it as an essentially unbiased variance forecast. Coverage and variance measure different things: coverage counts how often the close falls within a band, while E[z²] assesses squared normalized movement and therefore the scale of the variance forecast.
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In the study’s interpretation, more closes fell near the center than a lognormal one-sigma model would imply, while the distribution also had fatter tails. That combination can produce higher-than-benchmark coverage without an overstated variance forecast. The study summarizes this as “the expected move has the right variance and the wrong shape.” This is its interpretation of the findings, not a guarantee about future sessions.
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In the study’s comparison, the implied quote had a QLIKE loss of 1.50 versus 2.05 for a trailing-realized-volatility benchmark; lower is better. This is a forecast-loss comparison, not evidence that a particular options strategy was profitable.
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Coverage ranged from 71.0% to 73.6% across the reported intraday buckets through the final half hour. The final quarter hour, excluded from the headline, had 76.3% coverage. By year, the reported rates were 71.8% in 2022, 71.6% in 2023, 72.4% in 2024, 74.2% in 2025 and 71.4% in 2026. The 2026 sample ends August 26, so it is not a full-year figure. FirmTape says the readings are averaged by session before sessions are averaged, rather than treating roughly 76 frames per session as independent observations.
What the result does—and does not—tell you
It is about the close, not the intraday path
A move beyond the band during the session that later reverses is counted as inside if the close is within the band. The calibration therefore does not measure how often SPX touches or crosses the expected-move boundary intraday.
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It excludes overnight moves and trading costs
The test uses regular-session readings and that session’s close; it does not measure overnight movement. Nor does containment establish that selling an option or straddle would make money after spreads, fees and execution. FirmTape describes the work as “measurement, not a signal.”
The final minutes and gamma-state observation need caution
Readings with less than 15 minutes remaining are left out of the headline because the shrinking σ√τ makes the ratio noisy; the study reports those readings separately. It also says the short-gamma difference is only two to three standard errors and cautions against leaning on it. Treat that subgroup observation as tentative, not as a usable trading signal.
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Why other “expected move” hit rates may not match
Hit rates are comparable only when the forecast input, horizon, endpoint and sampling method align. FirmTape uses intraday at-the-money implied volatility and tests the eventual session close against each frame’s band. A separate Theta Desk analysis uses VIX-scaled bands and close-to-close endpoints at one-day, one-week and one-month horizons over a long historical sample. Its higher containment rates are not an apples-to-apples replication of FirmTape’s result.
The Theta Desk analysis also notes overlapping horizons, dependence among stress episodes and that its VIX-based measure sits somewhat above at-the-money straddle levels. Do not combine its percentages with FirmTape’s intraday-to-close rates as if they measured the same thing.
- Volatility input: intraday at-the-money implied volatility, VIX or a straddle-derived measure.
- Horizon: time remaining at the reading, or a fixed one-day, one-week or one-month period.
- Endpoint: a boundary touch, session close or close-to-close change.
- Sampling: whether intraday readings are clustered by day and whether overnight gaps count.
- Claim being tested: band coverage, variance calibration or actual trade returns.
How FirmTape describes using the estimate
FirmTape says sizing against the expected move as a one-sigma estimate is reasonable within the tested setup, but warns that the 28% outside the one-times band should not be treated as lognormal tails. That is a study-specific caution, not a promise that any chosen position size is safe. The findings apply to the sample, calculation and close endpoint described above.
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