# Standard Deviation in Options Trading

By Stephen L. Papale, Optionetics.com | Mon November 25, 2002 1:30PM PT

There are almost as many ways to make money trading options as there are options traders. Some focus on one or two strategies such as calendars or butterflies. Many incorporate charting or some other form of technical or directional analysis to form an opinion on movement of the underlying and then incorporate an appropriate strategy to capitalize on the expected move. Once the preliminary analysis is complete, the trader must decide on the appropriate strike price or prices to incorporate based on volatility, time to expiration and expected move.

Several options strategies aren’t so much interested in the direction of the move but rather the magnitude of the move. Once we have an idea of the magnitude of a move over a given time, we can decide and implement the appropriate strategy.

The easiest way to determine the expected magnitude of a future move in an underlying is to look at the implied volatility. This number gives the expected move in either direction of the underlying over the next year. For example, if the implied volatility of IBM were 30%, we would expect IBM to move 30% either up or down over the next year. If IBM were trading at 100, then the expected range would be 70 – 130. The statistical probability that IBM will trade within this range is 68%. This is also known as 1 standard deviation or sigma.

Using the concept of sigma can be a valuable tool in helping to determine how to place trades. Let’s say that we are looking at IBM options two months out. We can use some simple math to determine the 1 sigma or 1 standard deviation movement of IBM over the next two months. Let’s assume:

Days to expiration (D): 60

Implied Volatility (S): 20

IBM price (P): 100

The formula to calculate the expected move is as follows:

S (P) ( D/365) [S times P times the square root of D/365]

Using the above values we have:

.20 (100) ( 60/365) [.20 times the square root of 60/365]

=8.11 rounded off to 8

This indicates that over the next 60 days IBM will trade between 92 and 108 with a 68% probability. Again, this range is known as the 1-sigma range or 1 standard deviation. If we want a different statistical probability all we need to do is multiply 8 by the appropriate factor. For example, to get a 2 standard deviations move we simply multiply

8 by 2 = 16. Two standard deviations give 95% certainty that IBM will move between 84 (100-16) and 116 over the next 60 days.

Once we determine the range for the market we can use this information in helping us structure trades. In the above example, we are 68% certain that IBM should trade between 92 and 108. It should be noted however that this expected range is based on the implied volatility at 20%. Should the volatility change significantly, it would be wise to recalculate as the range could change. That said, having an idea of the expected range of an underlying could be very helpful in determining where to place verticals and condors. Additionally, this analysis combined with technical analysis, specifically moving averages and support and resistance levels, could add even a greater level of confidence when placing trades. **Stephen L. Papale***Contributing Writer and Trading StrategistOptionetics.com ~ Your Options Education Sitespapale@optionetics.com*

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