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Mathematically Calculating 1SD Expected Move Using a Probability Analysis Chart

9/24/2016

8 Comments

 
As discussed in the "Expected Move" post, the expected movement of a stock can be calculated with the following formula, where S subscript 0 is the stock's current price, IV is implied volatility, and the final term is the square root of days to expiration divided by 365:
Picture
Though an intimidating formula at first glance, it provides traders with the approximate range in which a stock's price may travel in a given amount of time or days to expiration (DTE). Note: The image above should say plus or minus preceding the square root sign.

To visualize, let's look at an example. Assume a SPY stock's price on low for the year on Feb 11th 2016 as $182.86, with an implied volatility of 28.14%. To calculate the expected move in 30 days, we substitute "DTE" with actual number of dates and solve for EM. 
The plus or minus range for each expiration will approximately equate to the EM calculations using the mid-price fills of EM spreads and the MMM value. 
Picture
Picture
So, in the above example, there's a 68% probability (1 SD) that SPY would stay in a range of +/- $14.75 from the current price of $182.86 in 30 days from now. There's a 95% (2 SD) probability that the stock price would stay in a range of +/- $29.49 from the current price of $182.86 in 30 days from now. And so for for 3 SD.

Now if we go for 60 days from now, you'll see that the numbers are as follows:
  • 1 SD = +/- $20.86
  • 2 SD = +/- $41.71
  • 3 SD = +/- $62.57

Geek stuff - ​Putting the Equation Into Perspective:
​The equation itself is a transformation of an inverse parabolic function. What? The most basic parabola is y=x^2. When we take the inverse of this function we arrive at y= +/- SQUAREROOT(x). The inverse function and the EM graph are the same shape! The formula of the EM graph is a transformation of the inverse function. Think of the product of (S0) and (IV) as the coefficient, DTE as the independent variable (x), and EM as the dependent variable (y). See the correlation?
Picture
8 Comments
WAYNE YONG link
7/4/2017 10:33:40 am

Hi Nisha,

I enjoyed learning about you on Tastytrade. I developed an Excel spreadsheet that contains your similar calculations that would help you calculate the expected move of a stock during earnings announcements. If you're interested, then let me know how I may send it to you.

Happy trading!
Wayne Yong

Reply
samuel
5/18/2018 11:26:26 pm

pl send

Reply
raju
2/4/2019 08:19:45 am

how did you calculate 2sd and 3sd

Reply
Anon
3/9/2022 08:05:10 pm

+2sd = stock price + (expected move * 2)
-2sd = stock price - (expected move * 2)
+3sd = stock price + (expected move * 3)
-3sd = stock price - (expected move * 3)

Reply
british essay writers review link
1/3/2020 02:32:05 am

I admit the fact that I am hot really familiar with the world of stocks so I find the article really hard to understand. But still I want to make a research and read more article about this, that's why I came here. I am not familiar with Probability Analysis Chart that's why I want to thank you for teaching me the ways on how to deal with it. It may be hard at first, but if you are devoted to understand it even more, I am sure that you will get it eventually!

Reply
don
12/10/2021 12:34:40 pm

i'm lost. i think you jumped ahead and forgot to include some formulas.
how did you go from expected move to bell curve probability?
if the expected move price isn't the 1std dev, how do you find the 1std dev price?

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Barb link
4/20/2022 07:53:19 am

Can this be used on all timeframes as is or do I have to make changes in the formula. Ex Can I use 1yr. 1 day for the time frame and leave formula as is. Thks for any inf.

Reply
Dinakar Nathan
4/21/2022 07:56:33 am

Interesting concept.....how can we estimate on Friday, the expected move for an underlying one week from now and 4 weeks from now ?

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    Nisha

    Ninteen year-old trader,  future connoisseur of options.

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