The three methods, worked through
The calculator's example values: one standard deviation and the range it gives.
| Method | Inputs | Arithmetic | One standard deviation |
|---|---|---|---|
| Implied volatility | SPY 768.40, IV 15%, 30 days | 768.40 × 0.15 × √(30 ÷ 365) | ±33.04 735.36 to 801.44 |
| Straddle | SPY 768.40, call 13.20 + put 12.90 | 26.10 ÷ 0.8 | ±32.71 735.69 to 801.11 |
| VIX | SPX 7,680.50, VIX 16, 1 session | 7,680.50 × 0.16 ÷ 15.87 | ±77.41 7,603.09 to 7,757.91 |
Why the straddle is divided by 0.8
At expiry an at-the-money straddle is worth the distance the price moved, either way, so its price today is the market's average move. For a normal curve the average distance from the middle is √(2/π), about 0.8, of one standard deviation: divide the straddle by 0.8 to compare it with the implied volatility method. tastylive quotes 85% of the straddle as its expected move, a smaller figure for the same options.
What the range means
About 68% of outcomes inside one standard deviation, 95% inside two, on the curve's own terms.
Where the curve is wrong
The method treats returns as normal. Real prices gap on earnings and fall faster than they rise, so moves past two standard deviations happen more often than 5% of the time. Read the range as what the options price today, re-read it as the implied volatility changes, and size the trade on the options profit calculator; for same-day SPX options the 0DTE calculator shows the decay into the close.