How to estimate the expected move of a stock from implied volatility
An expected move is the one-standard-deviation range read from implied volatility. The usual estimate is the price, times implied volatility, times the square root of the year fraction. This page works that arithmetic, says what the roughly 68% figure counts, and connects the band to the chance of finishing beyond a price or touching it.
Price times IV times the square root of time
Implied volatility is an annualized standard deviation of the log of the price. It is the volatility that makes a pricing model match an option's market price. A shorter window scales with the square root of time. The dollar figure people call the expected move is that width, multiplied by the price.
| price | Stock price today |
|---|---|
| IV | Implied volatility, annualized, as a decimal. 20% is 0.20 |
| days | Calendar days until the date |
| 365 | Day count used for the year fraction on this page |
move = price × IV × √(days / 365) lower = price − move upper = price + move
The band is centered on today's price, and it is the same number of dollars up and down. Use the implied volatility of the expiry you care about, near the spot. The next strike can imply a different volatility. That pattern is the skew. Historical volatility, the standard deviation of past returns, is a different input. This page does not use it.
The lognormal model puts the standard deviation on the log of the price, so the dollar distances up and down are not exactly equal. With zero interest and zero dividends, one standard deviation either side of the mean of the log is:
T = days / 365 log band = price × exp(−IV² × T / 2 ± IV × √T)
With a nonzero interest rate r and dividend yield q, that log band is centered on ln(price) + (r − q − IV²/2) × T. The dollar shortcut above still centers on the price. At a modest volatility and a short horizon the two bands sit close together. The worked example shows both.
A worked example
Suppose the stock is at $100, implied volatility is 20%, and the horizon is 91.25 days. That is a quarter of a 365-day year, so the year fraction is exactly 0.25 and the square root is 0.5. These inputs are a teaching example. They are not a quote for any ticker. The probability rows use zero interest and zero dividends, the same setting as the companion guide.
| Question | Result |
|---|---|
| Expected move, price × IV × √(days/365) | $10.00 |
| Dollar band, price minus the move through price plus the move | $90.00 to $110.00 |
| Lognormal one-standard-deviation band, zero rates | $90.03 to $109.97 |
| Model probability inside the lognormal band | 68.3% |
| Model probability inside the dollar band | 68.4% |
| Finishes above $110.00 | 15.8% |
| Finishes below $90.00 | 15.8% |
| Touches $110.00 at some point before the date | 32.4% |
| Touches $90.00 at some point before the date | 30.8% |
Step 1. The year fraction is 91.25 / 365 = 0.25. The square root of 0.25 is 0.5.
Step 2. Scale the volatility. 0.20 × 0.5 = 0.10. Over this window the standard deviation of the log return is 0.10.
Step 3. The dollar move is 100 × 0.20 × 0.5 = 10. The band is $90.00 to $110.00.
Step 4. The log band uses the same 0.10, and a downward shift of the log. With zero interest and zero dividends the mean of the log return is −IV²T/2 = −0.005. One standard deviation either side of that mean, measured from the spot, is $90.03 to $109.97. The dollar band and the log band differ by a few cents at these inputs.
Actual/365 and a 252-day year are both in use. This page divides by 365. Plugging the same 91.25 days into 252 instead produces a move of $12.04, because the year fraction becomes 0.3621 rather than 0.25. That is a different convention, not a second observation. The rows above keep the year fraction at 0.25.
The gap grows with time. The same $100 price and the same 20% volatility over a full 365-day year give a dollar move of $20.00, so the shortcut band is $80.00 to $120.00. The zero-rate lognormal band is $80.25 to $119.72, and the model probability of finishing inside the dollar band is 68.9%. Equal steps in the log are unequal steps in dollars, and with zero rates the median sits below the spot. The shortcut ignores both.
What the roughly 68% counts
For a normal random variable, the probability of landing within one standard deviation of the mean is N(1) − N(−1). With the normal distribution function used on this site, that is 68.3%. People round it to about 68%.
If the log of the price is normal, 68.3% is the model probability of finishing inside the log band, between $90.03 and $109.97. The band is centered on the mean of the log, which is the median of the price. The figure is a property of the normal curve. It is not a count of how often prices have stayed inside an implied-volatility range.
The normal curve puts 15.9% of its probability more than one standard deviation below the mean, and the same share above the mean. The dollar band is a close stand-in at these inputs, not the same interval. The model probability of finishing between $90.00 and $110.00 is 68.4%. The chance of finishing above $110.00 is 15.8%, and the chance of finishing below $90.00 is 15.8%. In this continuous model an exact price has probability zero, so the endpoints do not change the percentage.
What the range does not mean
Fat tails
A normal curve for the log price has thin tails. Equity prices put more mass on very large moves than a constant-volatility lognormal does, especially over a few days. The band is the model's one-standard-deviation range. Moves past it happen more often than that curve says. Far from the spot, wing option prices are the correction, when the quotes are real.
Not a forecast guarantee
Implied volatility matches an option price inside a model. The expected-move band rescales that number to the window and multiplies by the price. It is the width the option price is consistent with. It is not a guarantee that the stock finishes inside the band, and it is not a forecast of the move that will occur.
One width for the whole window
Implied volatility over a window is an average. If most of the uncertainty is an earnings announcement, a trial result, or a deal decision on one day, the formula still spreads that width across the whole horizon. It gives one range for the date. It does not say how much of the move happens on the announcement. Around a known event the price on the expiry can have two humps. A single lognormal has one hump by construction.
The dollar shortcut can also print a negative lower price when the product is larger than the spot. A stock price stays positive. The log band, built from an exponential, stays positive.
Finishing beyond the band, and touching it
The expected move answers a range question: where a one-standard-deviation finish would sit. Finishing above a price, and touching that price at any time before the date, are different events. On the example inputs, finishing above $110.00 is 15.8% and finishing below $90.00 is 15.8%. Those are N(d2) values in the lognormal model. They are risk-neutral weights, the weights that reproduce option prices, not a replay of history.
Touching is the chance the price trades at the edge at least once before the date, even if it finishes back inside the band. The continuous-monitoring probability of touching $110.00 is 32.4%, and of touching $90.00 is 30.8%. The ratio of touching to finishing beyond the level is 2.05 on the upside and 1.95 on the downside, against a rule of thumb of 2. The formula watches the path continuously and has no overnight gap. How to estimate the probability a stock reaches a price by a date derives N(d2), the touch formula, and that roughly 2× rule, using these same $100, 20%, quarter-year inputs.
Read the distribution the option chain is pricing
The calculator plots the risk-neutral distribution for a listed US stock or ETF and one expiry, from the option chain rather than from one volatility. Switch the chart to the cumulative curve and you can read the probability of finishing at or below a price, skew included. It does not draw the expected-move band on this page. A high value there is still the price of insurance in the options market, not a forecast and not a recommendation.
The desk is free to use. Methodology and limits on the calculator page covers the smile fit, American exercise, and the confidence flag for wide markets.
Common questions
How do you estimate the expected move of a stock from implied volatility?
Multiply the stock price by implied volatility, as a decimal, and by the square root of the year fraction. On a 365-day count that is price × IV × √(days/365). Subtract that dollar amount from the price and add it to get the usual band. The product approximates a one-standard-deviation move. It is a model width read from the option price, not a forecast of the move that will happen.
Why do people say the expected move is about a 68% range?
About 68% is the probability that a normal random variable lands within one standard deviation of its mean. When the logarithm of the stock price is normal, that share of the model probability lies inside the one-standard-deviation log band. The symmetric dollar band is an approximation of that interval. The percentage is a property of the normal curve, not a count of past prices. Equity prices have fatter tails than the curve, and implied volatility is not a guarantee that the price finishes inside the band.
How does the expected move relate to finishing above a price or touching it?
The expected move is a range for the price on the horizon date. The probability of finishing above a chosen price is N(d2) in the lognormal model, which is a different object from the width of the band. Touching that price at any time before the date is more likely than finishing beyond it. For a short horizon the touch probability is roughly twice the chance of finishing beyond the level. Both figures are risk-neutral calculations.
Is this financial advice?
No. This page is educational only. It explains a model. It is not financial advice, not a prediction of where a stock will trade, and not a claim about returns.