Expected Move Calculator: 1-Sigma Implied Range from IV

The expected move is the 1-standard-deviation price range the options market is pricing into a given expiration. This calculator computes it two ways and shows both side by side: from at-the-money implied volatility using sigma * S * sqrt(T), and from the ATM straddle using approximately 1.25 * straddle (the Brenner-Subrahmanyam 1988 identity). Under Black-Scholes assumptions the two methods agree to high precision; deviations in real markets reflect carry, discounting, and skew adjustments.

How to Read the Output

The 1-sigma range brackets roughly 68% of the implied terminal distribution; the 2-sigma range brackets approximately 95%. Real equity returns are fat-tailed, so both buckets understate the probability of large adverse moves. Use the computed ranges as market-implied guide rails, not as probabilistic guarantees. The output is anchored on the spot price you enter; if you want the range projected from a different reference (the closing print, the after-hours mid), enter that as spot.

When the Two Methods Disagree

Under pure Black-Scholes the IV-based and straddle-based estimates are mathematically equivalent up to the 1.25 factor. In live markets they diverge for three reasons: carry costs (rate and dividend yield enter the IV computation but are absorbed into the straddle quote), bid-ask spreads on the straddle (use the mid for the cleanest comparison), and skew (away from ATM the smile makes the lognormal assumption less accurate). When the IV method and the straddle method disagree by more than a few percent, look at the surface: skew or a quote-staleness issue is usually the cause.

Common Use Cases

Sizing earnings moves: enter the front-month IV before the print and the calculator returns the implied 1-sigma range for the report. Compare the implied range to the actual reported move on the per-ticker IV vs HV page to see how the market typically pays for that name's events. Sizing FOMC moves: do the same with index ETFs (SPY, QQQ, IWM) using the front-week IV. Sizing event hedges: pick the strikes you want to hedge, compute the move, and adjust the hedge thickness to match the expected range plus a buffer.

Limitations

The Brenner-Subrahmanyam approximation is exact only at zero rate and zero dividend yield; at typical SPY-like rates and yields the constant is closer to 1.253. The calculator uses 1.25 as a useful round number; for high-rate environments or high-yield underlyings the difference is small but visible in the digits. The lognormal terminal-distribution assumption breaks down in the wings; for tail-risk hedging that needs accurate wing pricing, use the main pricing calculator with a fat-tail model (Jump Diffusion or Variance Gamma).

Expected Move vs Risk-Neutral Density

The 1-sigma expected move is a parametric estimate that assumes lognormal terminal returns. The risk-neutral density (RND) is a non-parametric estimate of the same distribution, extracted from the call-price function via Breeden-Litzenberger butterfly differentiation. For an at-the-money expiration with smooth quotes, the two methods agree closely. For expirations with pronounced skew or fat tails, the RND captures structural information the 1-sigma estimate cannot: the implied probability is asymmetric, with downside fatter than upside, and the integration of the RND across any threshold gives the implied probability of finishing above or below that level. The standalone calculator emits the parametric 1-sigma estimate; the per-ticker probability page on the platform exposes the full RND for each available expiration.

Worked Example

Suppose SPY spot is 600, the front-week ATM IV is 12% (annualized), and there are 5 calendar days to expiration. The IV-based estimate is 600 * 0.12 * sqrt(5/365) = 600 * 0.12 * 0.117 = 8.4 dollars. The 1-sigma range is therefore approximately 591.6 to 608.4. If the front-week ATM straddle is trading at $7.00, the straddle-based estimate is 1.25 * 7 = 8.75 dollars, giving a range of 591.25 to 608.75. The two methods agree to within 4%, well within the noise floor for a one-week window. If they had disagreed by 30%, the divergence would warrant a closer look at skew, term structure, or quote staleness on the straddle.