If you watch stock prices, you surely have noticed that the prices are continually fluctuating. A few simple tools from statistics are useful when analyzing stock prices. When we talk about the “average” price we are technically referring to the mean. That means you add up the prices and divide by the number of prices listed. The mode is the price that is more prevalent than all the others. The median is the number where half of the values are above this level and the other half are below.
The variance refers to how much the prices vary around the mean. It is the sum of the squares of the deviations around the mean. The squares are used since the direction (positive or negative) from the mean is eliminated when a number is squared. You can look at the variance directly or take its square root, also known as the standard deviation.
Fortunately you won’t have to do this by hand, but you could. You subtract a price from the mean, square it, add up all the deviations, and then take the square root. The STDDEVP function in Excel will calculate all of this for you. The P in STDDEVP is for the population, assuming there are at least 30 data points (invoking the central limit theorem).
If you want to get a sense of how volatile your stock is, download its price history (from MSN Money or Yahoo Finance, for example) and run STDDEVP on the data in Excel. Volatility is one measure of risk since it shows the chance of a price different from what you paid at some point in the future.
We are also assuming the data are “normative” and follow a bell curve. Other ways of interpreting the standard deviation: 2/3 of the data will be within one standard deviation from the mean. 95% will be within 2 standard deviations. 99% will be within 3 standard deviations.
As an example, let’s say the S&P 500 is trading at 1500 with a standard deviation of 50. That implies that 2/3 of all closing prices will be between 1450 (1500 – one standard deviation) and 1550 (1500 + one standard deviation). 95% will be within 1400 (1500 – two standard deviations) and 1600 (1500 + two standard deviations). 99% will be within 1350 (1500 – three standard deviations) and 1650 (1500 + three standard deviations).
Now you understand a powerful statistical tool and you know how to use it. If you must choose only one stock to purchase between two options, this can be helpful. Compare the returns, growth, and dividend yield of the two options. If the yields are similar, you should choose the one with the lower volatility (smaller standard deviation).