Expected move vs standard deviation: why two "expected" numbers disagree
Both numbers come from the option prices. The standard deviation move uses implied volatility in a formula. The expected move from the straddle is a quick shortcut, and it comes out about 0.8 of a standard deviation. That gap changes which put you sell.
The short answer
Use the standard deviation move when you want a range with known odds behind it. Under the normal model the market uses, the stock stays inside one standard deviation about two times out of three. Use the straddle expected move when you want a fast read off the chain with no math. It is smaller, about 0.8 of one standard deviation, so price leaves that range more often, a little over four times in ten.
Neither one is a forecast. Both are the market's own price for the move, turned into dollars.
A Standard deviation is a way to measure how far price usually strays from where it started. The Expected move is the dollar range the option market is pricing in until expiry.
Side by side
| Standard deviation move | Straddle expected move | |
|---|---|---|
| Where it comes from | Implied volatility, put into a formula | The price of the at-the-money call plus put |
| The math | Price × IV × √(days ÷ 365) | Add the two premiums |
| Size | One standard deviation | About 0.8 of one standard deviation |
| Price ends outside it, both sides | About 32% of the time (model) | About 42% of the time (model) |
| Price ends below the low end | About 16% (model) | About 21% (model) |
| Best for | Picking a strike with stated odds | A quick look before earnings or a news day |
| Weak spot | Needs the IV and a calculator | Easy to mistake for the "max" move |
The 0.8 is not a rule of thumb someone made up. When moves follow a bell curve, the average size of a move is about 0.8 of one standard deviation. A straddle is priced near that average, so that is where its price lands.
A worked example (hypothetical)
Take a made-up stock, Northwind Freight, at $100. Its options show 30% implied volatility, and expiry is 30 days away.
The standard deviation move:
- √(30 ÷ 365) is about 0.287.
- $100 × 0.30 × 0.287 = about $8.60.
- The range is $91.40 to $108.60.
The straddle expected move:
- The $100 call and the $100 put each cost about $3.43 in this example.
- Together that is about $6.86, call it $6.90.
- The range is $93.10 to $106.90.
Check: $6.90 ÷ $8.60 is about 0.80. The two methods agree on the shape and differ on the size, exactly as the table says.
The put a seller would pick from each
Say you sell a Cash-secured put just under the low end of each range.
- From the straddle range: the $93 put, for about $0.90 ($90).
- From the standard deviation range: the $91 put, for about $0.55 ($55).
The $93 put pays more because it sits closer to the price. That extra $35 is pay for more risk, not a better deal. Here is how each one ends at three prices (hypothetical, before fees):
| Stock at expiry | Sold the $93 put | Sold the $91 put |
|---|---|---|
| $96 | Expires: +$90 | Expires: +$55 |
| $92 | Assigned at $93: −$100 + $90 = −$10 | Expires: +$55 |
| $88 | Assigned at $93: −$500 + $90 = −$410 | Assigned at $91: −$300 + $55 = −$245 |
At $92 the stock moved less than one standard deviation, yet the $93 seller is already assigned. At $88 both are assigned, and the closer strike loses more.
A range is a price, not a promise. In this model, price leaves the one-standard-deviation range about a third of the time. Over a year of monthly trades, that is several months.
Which one should you use?
| Pick the standard deviation move if… | Pick the straddle expected move if… |
|---|---|
| You are choosing a strike and want stated odds | You want a quick number with no math |
| You sell puts and want a wider cushion | You are sizing up an earnings move |
| You compare strikes across stocks | You only need a rough range for the week |
Many sellers use both. They read the straddle to see what the market fears, then pick the strike from the standard deviation range. That keeps the strike outside the "average" move, not on top of it.
The expected move calculator does the formula for you. The expected move guide covers the details, and the options strategy comparison chart shows where a put fits among the other choices. If you run the wheel strategy, the strike you pick here is the price you may end up paying for the shares.
Questions
Is the expected move one standard deviation?
Not when it comes from the straddle. The straddle price is about 0.8 of one standard deviation. Some platforms show a "one standard deviation expected move" from the IV formula instead. Check which one your platform shows before you pick a strike from it.
How often does a stock move more than the expected move?
Under the normal model, price ends outside one standard deviation about 32% of the time, and outside the straddle range about 42% of the time. Real stocks have more big moves than the model expects, so these are a floor, not a ceiling.
Why is the straddle price only 0.8 of a standard deviation?
A straddle pays the size of the move, whichever way it goes. On a bell curve, the average size of a move is about 0.8 of one standard deviation. The straddle is priced near that average.
Should I sell puts at one standard deviation?
Many sellers do, because it gives a stated cushion. It still finishes below the strike about one time in six in the model, and you need the cash to buy the shares when it does.
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