probability
Standard Deviation Range
Maps standard deviation multiples to probability ranges. Tells you the chance of the stock staying within N standard deviations.
Formula
1σ ≈ 68.2%, 2σ ≈ 95.4%, 3σ ≈ 99.7% Range = S ± N × S × IV × √(DTE/365)
Variables
- 1σ
- 68.2% of outcomes fall within ±1 std dev
- 2σ
- 95.4% of outcomes fall within ±2 std devs
- 3σ
- 99.7% of outcomes fall within ±3 std devs
- S
- Current stock price
- IV
- Implied volatility
Worked Example
Inputs
- S
- $200
- IV
- 25%
- DTE
- 30
Calculation Steps
- 1
1σ move = 200 × 0.25 × √(30/365) = $14.34 - 2
1σ range: $185.66 — $214.34 (68% confidence) - 3
2σ range: $171.32 — $228.68 (95% confidence) - 4
3σ range: $156.98 — $243.02 (99.7% confidence)
Result: 68% chance: $185.66–$214.34 | 95% chance: $171.32–$228.68
Intuition
Sell iron condors at 1σ wings for ~68% POP, or 2σ for ~95% POP (but very thin credit). In practice, stocks have "fat tails" — 3σ moves happen more often than the math predicts. Never assume the normal distribution is perfectly accurate.