We’re in the latter half of our earnings season and I thought I’d take some time to share some information on how to calculate expected stock price movement around a binary event like an earnings report. This involves analyzing the expected movement in the underlying options.

The expected move of a stock for a binary event can be found by calculating a IV percentage of the value of the front month at the money (ATM) straddle. That is to say, you would add the price of the front month ATM call and the price of the front month ATM put, then multiply this value by 84%.

This is derived from the formula for a confidence interval:

Using a standard distribution curve, this implies a 16% chance that the underlying will end up outside of our standard deviation range.

The Implied Volatility percentage can be used as a proxy for the standard deviation of movement. The sample size would be the number of days until expiration. Since we’re aiming to do these calculations right before earnings, this becomes small and negligible. Doing this right before earnings minimizes the effects of theta (time) on the option prices. And since we’re calculating the 1 standard deviation move then the Z-value would simply be 1.

Another easy way to calculate the expected move for a binary event is to take the ATM straddle, plus the 1st OTM strangle and then divide the sum by 2.

However, one thing to note is that the word “expected” move might be misleading. Here in this scenario, the “expected” move is literally derived from the option strikes where traders are most willing to buy/sell. This applies pressure towards stock prices through the forces of supply and demand. Because the expected move is derived this way, it opens up the vulnerability of human error.

If traders are buying and selling at a certain strike price, it’s because that’s where they “expect” it to move. As a result, our calculations are at the mercy of these “expectations”.

But moving on…

I will illustrate this example using Regeneron Pharmaceuticals (REGN) since their earnings report is tomorrow.

The stock is currently trading at **$340.58**

Note the ATM (at-the-money) straddle:

- Take the ATM call (4 NOV 16 340.0 strike): The bid-ask spread is 15.20-17.60 so the midpoint is $
**16.40** - Take the ATM put (4 NOV 16 342.5 strike): The bid-ask spread is 14.70-16.80 so the midpoint is $
**15.75**

The current implied volatility is around 59.72% so take 59.72% of this sum and you get .5972*(16.40+15.75) = **19.20**

**The expected stock movement for REGN is 340.58 +/- 19.20. Between 359.78 to 321.38**

Which means by tomorrow, there is a 68% chance (1 standard deviation) of the stock ending up at 359.78 or 321.38. Traders are expecting a 5.6% movement after the earnings release.

### The quick and dirty way

First note our ATM straddle price of 16.40+15.75 = **32.15**

Note the 1st OTM (out-of-the-money) strangle:

- The first OTM call (4 NOV 16 342.5 strike): The bid-ask spread is 13.20-16.30 so the midpoint is $
**14.75** - The first OTM put (4 NOV 16 340.0 strike): The bid-ask spread is 13.50-15.70 so the midpoint is
**$14.60**

If we add all these values together, 32.15+14.75+14.60 = 61.50 , and divide it by 2 we get = **30.75**

The expected stock movement for REGN becomes 340.58 +/- 30.75. Which means by tomorrow, there is a 50% chance of the stock ending up at 309.83 or 371.33. Traders are expecting a 9.02% movement after the earnings release.

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