*On any given day a stock can do one of three things. It can go up, it can go down or it can go sideways. That’s pretty much all it can do. Figuring out which one of the three the stock’s going to do on any given day is pretty much what investing is all about. If I think about how I define these three things, I can start to get an idea of the probability of any of the three happening. For instance, if I define sideways as the price remaining exactly the same at the end of the day as at the beginning, then the probability of that happening is almost zero while the probability of the price going up is 50% and of going down is 50%. Not the kind of percentages you want to see when you’re trying to decide whether to go long or short.*

*As trading occurs throughout the day and the stock’s price is pushed up and down from the opening price, the volatility of the price will create a variance from the mean (opening price). This volatility will approximate the bell curve and standard deviations (SD) can be approximated.*

*If I define sideways as one SD from the mean then the probability of the price going sideways is 68% and the probability of the price rising more than one SD 16% and of decreasing more than one SD is 16%. If I define sideways as two SD then the probability of rising more than two SD is 2.5% and decreasing more than two SD is 2.5%. (If you’ve had more classes in statistics than you ever thought was possible, then this is probably second nature to you. If not, simply refer to the graphic below.)*

*Assuming that nothing drastic is pushing a stock in one direction or another, like a new product line or the resignation of the CEO, I can expect an increased probability of the stock going sideways as I increase my definition of sideways. Stated another way, the more I increase the definition of sideways, the less likely the stock price will be categorized as going either up or down.*

*This may all sound confusing but understanding this has provided me with the guidelines I use for selling puts and calls. Selling calls and puts more than one SD from the mean tells me that there’s a 16% chance of either having the stock called or put to me, respectively. Selling calls and puts that are two SD from the mean tells me that there’s a 2.5% chance of having the stock called or put to me. The greater distance from the mean that I sell a call or put the greater the probability that the option will expire worthless. Unfortunately the greater distance I sell an option from the mean, the less that option will be worth and the less money I will make.*

*All this information is priceless and has helped me build my strategy for selling puts and calls. But how do I find these SD limits? It just so happens that there’s a market indicator called Bollinger Bands that plots these limits based upon a 20 day moving average as the mean. The bands that it creates tell me where the SD lines are located. These lines don’t always line up exactly with the options strike prices that are available for option selling but they will allow me to approximate the probability of successfully selling puts and calls by knowing the proximity of the SD lines to the strike prices.*

*With this information I now have one piece of knowledge I use to make a judgement call of whether I want to sell an option. That judgement will be based upon the price I can sell an option for and the probability of the option expiring worthless. I then combine this information with information gathered from other indicators to look for confirmation of my decision. One of the other indicators I use is the MACD. I've discussed that indicator as well as how to trade options using the MACD in other posts. As the indicators begin to line up in one direction the probability of a successful trade begins to increase. In the end, however, nothing is certain. It’s all expectations and probability.*

*I’ll have more to say about Bollinger Bands in a future post but for this post I simply want to lay out how I use the Bell Curve and SDs to decide which strike price I’m going to use to sell puts and calls.*