Calculation Methodology

Last updated: May 11, 2026

This page explains how Expected Move and ±1σ price ranges are computed. The methodology is grounded in standard options pricing concepts, but the published values should be interpreted as a probabilistic reference — not a guaranteed boundary on future price movement.

1. Core Concept

Expected Move estimates the likely magnitude of price movement over a specific period, derived from implied volatility (IV) observed in the options market.

The ±1σ range represents approximately a 68% probability cone under a normal distribution assumption. In other words, if option market expectations are accurate and price follows a lognormal distribution, the asset will close within the ±1σ range about two-thirds of the time over the specified horizon.

Real markets, however, do not strictly follow a normal distribution. Tail risk, gap events, regime shifts, and non-Gaussian behavior can — and do — cause prices to exceed the ±1σ range more often than the model predicts.

2. Input Variables

• Reference Price (S) — Current intraday price or applicable closing price for the period.
• Time to Expiration (T) — Trading days (or fraction thereof) remaining until the option series expires. This directly impacts the magnitude of the expected move.
• Implied Volatility (σ_imp) — Annualized IV extracted from the relevant options chain (typically at-the-money or near-the- money strikes).
• Optional adjustments — Interest rates and dividends may be incorporated in simplified form where material.

3. Calculation Steps

1. Determine remaining time to expiration in standardized units (e.g., trading days converted to years).
2. Convert annualized implied volatility to the relevant horizon:
   σ_period = σ_annual × √(T / 252)
3. Compute expected move magnitude:
   EM = S × σ_period
4. Generate upper and lower bounds:
   Upper (+1σ) = S + EM
   Lower (−1σ) = S − EM
5. Apply formatting rules (price precision, ticker-specific rounding) for display.

4. Example

For SPY trading at $694.46 with a weekly at-the-money implied volatility of roughly 12% (annualized) and 5 trading days to expiration:

Illustrative numbers only. Actual published values use the most recent observable IV from the relevant options chain.

5. Important Caveats

• 0DTE sensitivity — Same-day expected moves change rapidly with minute-by-minute time decay and IV crush. Treat 0DTE numbers as short-horizon snapshots.
• Event impact — Earnings, FOMC, CPI, NFP, and other scheduled events significantly inflate IV and the resulting expected move ranges. The ±1σ band may widen meaningfully heading into known events.
• Liquidity & spreads — Wide bid-ask spreads or sparse strike coverage degrade IV reliability, which propagates into our calculations.
• Tail risk — Markets gap and dislocate. Actual price moves can — and regularly do — exceed ±1σ by meaningful amounts.

6. Intended Use

Expected Move values should be used as one of multiple inputs in your trading research, alongside fundamental analysis, technical structure, order flow, sector context, and risk management discipline. They are not standalone trading signals.

7. Contact

Questions about a specific calculation or value? usstocksigma@gmail.com