Expected Move Explained
A stock's "expected move" represents the one standard deviation expected range for a stock's price in the future.
A one standard deviation range encompasses 68% of the expected outcomes, so a stock's expected move is the magnitude of that stock's future price movements with 68% certainty.
There are three variables that go into the expected move formula:
1) The current stock price
2) The stock's implied volatility
3) The desired expected move period (expressed as the number of days)
Since a stock can have multiple implied volatilities depending on the expiration cycle, it's important to use the implied volatility of the options in the expiration cycle closest to the desired time period. For example, when looking at the option chain on a stock, you might see something similar to the following:
Expiration | Days to Expiration | Implied Volatility |
---|---|---|
November 2016 | 7 | 27.50% |
December 2016 | 35 | 25.25% |
January 2017 | 70 | 24.50% |
March 2017 | 126 | 26.00% |
If you wanted to calculate the expected move for this stock over the next 75 days, it wouldn't make sense to use the 7-day implied volatility.
Instead, it would be better to use the implied volatility of the 70-day options. Why? Because the 7-day implied volatility is 27.50% while the 70-day implied volatility is 24.50%. If you used 27.50% for a 70-day expected move calculation, the result would be overstated.
Expected Move Formula
Now that you know some of the best practices, it's time to perform some calculations. Here is the expected move formula:
If you wish to use trading days instead of calendar days, just change the denominator from 365 to 252, since there are 252 trading days in a year. Both calculations will result in virtually the same number.
Using the formula and table from above, let's calculate the expected move for each time period. Let's assume the current stock price is $200:
Expiration | Days to Exp. | IV | Expected Move |
---|---|---|---|
November 2016 | 7 | 27.50% | $200 x 27.50% x √(7/365) = ±$7.62 |
December 2016 | 35 | 25.25% | $200 x 25.25% x √(35/365) = ±$15.64 |
January 2017 | 70 | 24.50% | $200 x 24.50% x √(70/365) = ±$21.46 |
March 2017 | 126 | 26.00% | $200 x 26.00% x √(126/365) = ±$30.55 |
The expected moves in this table suggest the following:
➜ The 7-day option prices are implying a 68% probability that the stock price is ±$7.62 from $200 in seven days (between $192.38 and $207.62).
➜ The 35-day option prices are implying a 68% probability that the stock price is ±$15.64 from $200 in 35 days (between $184.36 and $215.64).
➜ The 70-day option prices are implying a 68% probability that the stock price is ±$21.46 from $200 in 70 days (between $178.54 and $221.46).
➜ The 126-day option prices are implying a 68% probability the stock price is ±$30.55 from $200 in 126 days (between $169.45 and $230.55).
The following chart serves as a visualization for the table above:
Why does this matter to you as an options trader? Knowing how much a stock's price is expected to fluctuate over various time periods can give you a reasonable expectation for a stock's future prices. Additionally, if you want to calculate a stock's expected range over a specific period of time, you have the ability to do so.