Standard Deviation and How To Use It

Twitter@LoneStarQuant

A number of attendees had questions about standard deviation at the Festival of Traders. As promised, I am going to give you a definition and intuitive example so you understand why it is important to rely on low standard deviation samples.

Definition: "In statistcs and probability theory, the standard deviation (SD) (represented by the Greek letter sigma, σ) shows how much variation or dispersion from the average exists. A low standard deviation indicates that the data points tend to be very close to the mean (also called expected value); a high standard deviation indicates that the data points are spread out over a large range of values." 

Example: Low Standard Deviation

You will notice that the standard deviation for the above pattern is 0.30%. If you look at each year from 2008 to 2013, the return over the 56 days follows a tight range between 0.60% and 1.60%, giving a low standard deviation.  

Here is a hypothetical example:

Notice in this chart that the average is clearly 1.5% since (1.5%+1.5%+1.5%+1.5%+1.5%+1.5%)/6 =1.5%. Then what is the standard deviation? It is 0. Why is it zero? Because every year the return is exactly 1.5%, so there is no 'dispersion' in the data.

An example with a higher standard deviation:

Based on the first two examples, it should come as no surprise that Camden has a larger standard deviation (because each sample average is different).  In this particular case, the average move of 8.8% is greater than the standard deviation of 5.6%, making this a quality candidate.

It is always important to identify instances where the standard deviation is lower than the average move. This helps you eliminate noise from your decision making. Stay smart and trade safe!