What is a one-standard-deviation move?
In one line: A one-standard-deviation move is the range, up or down, that an option's implied volatility says the stock should stay inside about 68% of the time over a given period.
How it works
Implied volatility is quoted as a yearly number, like 32%. Scale it to the days you care about and you get the one-standard-deviation move for that period.
The rough formula: price × IV × √(days ÷ 365). On a $50 stock with 32% IV and 30 days to go: $50 × 0.32 × √(30 ÷ 365) ≈ $50 × 0.32 × 0.29 ≈ $4.60. So the market expects XYZ between about $45.40 and $54.60 at expiry, about two times in three.
That's the "one SD" range. Two standard deviations is double it, about 95% of the time. Sellers in the wheel strategy often sell the put near the bottom of the one-SD range, which lines up with a delta around 0.16 to 0.20.
An example (hypothetical)
XYZ trades at $50, IV 32%, 30 days (an illustration, not a trade idea). One SD ≈ $4.60. You sell the $45 put, just outside the range, for $0.70 ($70).
| Where XYZ lands | How often, roughly | Result |
|---|---|---|
| Inside $45.40 to $54.60 | About two times in three | +$70 |
| Above $54.60 | About one time in six | +$70 |
| Below $45.40, say $44 | About one time in six | Assigned at $45: −$100 + $70 = −$30 |
| Far below, say $36 | Rare, but inside that one in six | Assigned at $45: −$900 + $70 = −$830 |
The range told you how often you'd be outside it. It never said how far outside. The $36 row lives in the same "one in six" as the $44 row.
Why it matters for sellers
The one-SD move is the most useful number on the chain, because it turns IV into dollars on your stock. A $45 strike is not "far away" on its own. It's far away if the one-SD move is $2 and close if it's $8.
It's also the most misread number. It's the market's estimate, from today's option prices, assuming moves spread out in a bell shape. Real stocks gap. Earnings, news and crashes land outside the range more often than the bell curve says, and when they do they don't stop at the edge.
So use it to pick the strike and to sanity-check the premium. Don't use it as a wall. The size of a bad month is set by the stock, not the SD. Our expected move guide works through the formula on a real chain.
Questions
How do I calculate a one-standard-deviation move?
Stock price × implied volatility × the square root of (days ÷ 365). A $50 stock at 32% IV over 30 days: about $4.60 either way.
Does a one-SD move mean the stock can't go further?
No. It means the market expects the stock inside that range about 68% of the time. The other third includes moves well past the edge, especially around news.
What delta is the one-standard-deviation strike?
Roughly 0.16. That's why many sellers talk about "16-delta" puts: it's the strike about one SD below the price, by the option's own math.
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