You might ask, “what does probability have to do with option investing?”, and the answer is “a lot”. The probability of having a safe flight on an airline is better than 99.99999%, and the probability of a safe automobile trip is 99.98%, and generally people feel safe flying or driving to their destinations. But if the probabilities for safe flying and driving were significantly different say 95%, people might not feel so safe flying and driving, and rightly so.

As with flying and driving, probabilities for stock option investing for a stock option strategy can generally be estimated in order to determine risk versus reward for various stock investment strategies. For an option trader, it wouldn’t be too difficult to determine whether to select a stock options investment strategy with a 95% probability of returning 2% with a 5% probability of losing 15% versus a stock options investment strategy with a 2% probability of returning 95% with a 98% chance of losing 100%. For the option trader who would select the stock options investment strategy of 2% probability of returning 95% with a 98% chance of losing 100%, he/she might as well go to Las Vegas and have some fun and excitement while losing their money.

Suppose for example we have the option of purchasing an out-of-the-money call option on the S&P 100 Index (symbol OEX) that is 1% away from being in-the-money with one day left until expiration. And, we would like to know the probability of the position finishing in-the-money at expiration based on the index’s past 52-week behavior. The appropriate set of data to use for this analysis would be the last twelve month’s one day to expiration and day of expiration values, 12 data points, but that’s not really enough data, so instead we could use a proxy for the appropriate data and use the data over the last 52 weeks of the percent change from one day to the following day, a total of 252 data points.

To do this analysis we must perform some stock research, we obtain the data for the S&P 100 index from the Yahoo! Finance web site and load it into a spreadsheet, in this case Microsoft’s Excel spreadsheet is used. A new column is created showing the percentage change from one day’s closing value to the following day’s closing value. This column along with a column for the “bins” is then analyzed using Tools/Data Analysis/Histogram in Excel. Historically, the results from this analysis indicate there is about a 6% probability (15 data points out of 252) of finishing in-the-money for an OEX option that is 1% out-of-the-money and one day from expiration (see Table 1). Based on this analysis we should probably let the Vegas option trader use this stock options investment strategy.

It should be noted we haven’t taken into account changes in volatility and other factors that can affect probability calculations, and the method for calculating probabilities outlined in this article is a “quick-and-dirty” approach and as with any probability calculation should be used with care.

The spreadsheet used for this analysis may be downloaded at:

http://www.poweropt.com/Probability.xls

A free Excel viewer may be downloaded from Microsoft’s web site to view it at www.microsoft.com (search for Excel viewer).

[tags]stock research, option trader, stock option investing, stock investment strategies[/tags]

## Ira Kierstein

WHAT DOES “BIN” REPRESENT IN YOUR DATA?? THANK YOU, IRA

## Greg Zerenner

Hi Ira:

A “BIN” is like a bucket for data. When you analyze how often something was to happen, you need to separate the “SOMETHINGS” into buckets, then count the occurances of the “SOMETHINGS” for each bucket/bin.

In this case, each “BIN” is a % change, and the frequency is how many times the data shows a % change that is in the range of the bin.

So for example, if you wanted to count how many times RED, GREEN, or BLUE came up in a random box of mixed crayons…You would have 3 bins. 1 for RED, 1 for BLUE, and 1 for GREEN.

Hope this helps.

## Allen Forsythe

A quick theoretical question about probabilities for Iron Condors. Because the outcome of each leg of the spread is mutually exclusive, shouldn’t the probability that the entire strategy will finish in the money just be the greatest of the probabilities of either leg?

I can’t quite grasp this concept and would appreciate any input you have.

Thanks!

Allen

## Charles Webster

Allen…I am a perennial Options STUDENT who seems never smart enough to graduate…but I think the crucial positions

to calculate the probability of touching would be the SHORT

STRIKES of an IC………traderkip