Standard Deviation
A statistical measure of expected price range for stocks and options.
Standard deviation is a statistical measure of how much a data set varies from its average. In options trading, it quantifies the expected price range of a stock over a given time period. A one standard deviation move encompasses approximately 68% of all expected outcomes, meaning the stock is expected to stay within that range about two-thirds of the time. Implied volatility is expressed as an annualized one standard deviation move.
Why It Matters
Standard deviation is the bridge between implied volatility and actual dollar amounts. When someone says a stock has 30% IV, standard deviation translates that into a concrete price range you can use to select strikes, size positions, and evaluate trade probabilities. Without this translation, IV is just an abstract percentage.
Option sellers frequently use standard deviation to define their strike selection. Selling a put at one standard deviation out means there is roughly a 68% chance the stock stays above that strike — giving you a 68% probability of keeping the full premium. Selling at two standard deviations out gives roughly a 95% probability. This framework turns strike selection from guesswork into a probabilistic decision.
How It Works
To calculate the expected one standard deviation move for a stock:
1 SD Move = Stock Price x IV x sqrt(Days to Expiration / 365)
Standard deviation ranges and probabilities:
- 1 SD (68.2%): The stock is expected to stay within this range about 68% of the time
- 2 SD (95.4%): The stock is expected to stay within this range about 95% of the time
- 3 SD (99.7%): The stock is expected to stay within this range about 99.7% of the time
Important caveats: These probabilities assume returns are normally distributed, which is only an approximation. Real stock returns have fatter tails than the normal distribution predicts — meaning 3 SD moves happen more frequently than the 0.3% the math suggests. This is why selling far OTM options is not as safe as the standard deviation math implies.
How traders use standard deviation:
- Strike selection: Sell options at 1 SD out for higher probability trades, or at 0.5 SD for more premium
- Expected move calculation: The options market's expected move for an earnings event is approximately one standard deviation, derived from ATM straddle pricing
- Position sizing: Knowing the 2 SD range helps you define worst-case scenarios for risk management
- Comparing stocks: A $100 stock with 40% IV has a larger expected range than a $100 stock with 20% IV — standard deviation makes this concrete
Quick Example
Stock ABC trades at $200 with IV of 40%. You want to sell a put expiring in 30 days.
1 SD move = $200 x 0.40 x sqrt(30/365) = $200 x 0.40 x 0.287 = $22.90
One standard deviation below: $200 - $22.90 = $177.10. Selling a put at the $177 strike gives you approximately a 68% + 16% = 84% chance of the stock staying above that level (since 68% is within the range, and 16% is the portion above the range).
Two standard deviations: $200 - $45.80 = $154.20. A $154 strike put has roughly a 97.5% chance of expiring worthless — but the premium will be much smaller.