## Thursday, December 30, 2010

### Using Implied Volatility to Determine the Expected Range of a Stock

When there is an event that is likely to impact the price of an equity (e.g., earnings; FDA ruling; new product release; etc.,) you will see an increase in the option pricing. This rise pricing is attributed to an increase in the option's implied volatility. When the implied volatility is high, that means that the market anticipates a greater movement in the stock price.

I am often asked "How can I determine how far a stock is likely to move?" I will give you two methods to estimate the expected movement: one that requires a calculator and a quick and dirty way that you can do in your head.
First a little theory:

When we talk about historical volatility, we are measuring the zigzaggedness of a stock. How much did it zig and how much did it zag? If it zigged and zagged a lot, the historic volatility is high. In mathematical terms we determine the zigzaggedness by measuring the "standard deviation."

Remember the bell curve or the normal distribution?

If a distribution is considered "normal," 68% of the time, you will be within 1 standard deviation of the peak of that curve. For the most part, stock exhibit a normal distribution. (Actually, it's a lognormal distribution, but let's keep this simple.)

The historic volatility is the movement that did occur. The implied volatility is the movement that is expected to occur in the future. When we are estimating future prices, we use the implied volatility.
Using the calculator:

The following calculation can be done to estimate a stocks potential movement:
(Stock price) x (Annualized Implied Volatility) x (Square Root of [days to expiration / 365]) = 1 standard deviation.

Take for example AAPL that is trading at \$323.62 this morning. It has earnings next month. The current Implied Volatility is 31.6%. JAN options expire in 22 days, that would indicate that standard deviation is:

\$323.62 x 31.6% x SQRT (2/365) = \$25.11
That means that there is a 68% chance that RIMM will be between \$298.51 and \$348.73 in January expiration.

Quick and Dirty:

Now, for those of you that have not touched the square-root key since you took algebra back in high school, you can just use an options chain to get an estimate of where the stock could move. Find the price of the at-the-money straddle and the out-of-the-money strangle and add them together and divide by two. That is about equal to the 50% probability movement.

For AAPL this is the 320 straddle (320 call and put) and the 310/330 strangle (330 call and 310 put.) Add those together and you will get \$30.58. If you divide that by two (\$30.58 / 2 = \$15.29) and add and subtract that from the current stock price, you get very close to 50% probability range. That means that AAPL has about a 50% chance of being at \$308.33 and \$338.91 by January expiration.

This method is a enough to make a mathematician cringe. However, it works out to be a pretty good "SWAG," as they say.
Thoughts on what these numbers mean:

I don't use these calculations as a price target to build a strategy. I use them more as a warning sign. Considering the potential movement, you may want to reconsider your delta neutral strategy (e.g., call calendar, put calendar, iron condor, etc.) which profits from a stagnant trend. While the premiums look good now, you might want to wait until after the event for that stagnant strategy. Or, you may be looking at a straddle or strangle knowing that there is going to be a big movement. If you look at those estimated moves, you'll see that a straddle or strangle is probably not that attractive - especially when you consider the volatility crush that is likely to occur after the event.

For example the current JAN 320 straddle on AAPL. It's pricing at \$19.40. That means that you need the stock to move to at least \$304.22 or \$343.02 just to break even by expiration. Now, consider the estimates made above. Does this look like a trade that you'd want to be in? Unless you know something that the market doesn't know - like the iPhone cures the common cold - you probably are best advised to avoid this sort of trade. (Another factor that must be considered is the dramatic changes in implied volatility. But, I will leave that for another post.)

Unless you have a strong sentiment, I believe the most prudent approach is to consider a protective strategy. For stock ownership, I believe that a collar trade is typically best strategy around earnings. It protects you from downward movement in the stock. Also, because there is a long and a short option, the impacts of volatility crush is mitigated. The art is picking the right options and that is what we teach you at OptionsAnimal.

By Eric Hale
OptionsAnimal Instructor

Source: http://www.optionsanimal.com/using-implied-volatility-determine-expected-range-stock