# How to Calculate Monthly Return Volatility for a Stock

The monthly return volatility for a stock is a numerical representation of that stock's risk; the technical term for volatility is standard deviation. A stock with high volatility tends to move more than a stock with lower volatility over the course of a typical month. In addition to being helpful in selecting the ideal stocks for your investment portfolio, volatility figures also allow you to calculate a fair price for stock options. Stock options are financial instruments that give you the right, but not the obligation, to buy or sell stocks at a predetermined price on a specific date.

## Calculate a Stock's Monthly Returns

The return for any given month equals the last trading price for the last business day of the month, divided by the last trading price for the previous month, minus one. Assume, for instance, that you wish to calculate the return for April and the last business day in April was April 29, while the last trading day of the prior month was March 31. Divide the closing price of April 29 by the closing price of March 31 and subtract 1 from the result. Do this for every month in the time range.

## Determine Average Monthly Return

To calculate the average monthly return, add up all returns and divide them by the number of months. Now subtract the return for each month from this average. As a result, you will obtain the deviation of each month's return from the mean. Naturally, you will have positive as well as negative deviations, since the return for some months will be below the average return, and other months will have above-average returns.

Then square each of the variances. Remember that whether you start with a negative or positive figure, the square is always a positive number. Use at least a year's worth of monthly data to obtain workable results.

## Find the Standard Deviation

Add up the squares of the deviations you have calculated previously. Then divide this total by the number of months to find out the average of the squared deviations. This average is your variance.

To calculate the monthly volatility, you must take the square-root of the variance. The result will be the standard deviation of the stock's monthly returns, and this is the most commonly used parameter when financial professionals talk about risk and volatility. By using this standard deviation of returns, it is also possible to calculate how likely a stock is to drop or rise more than a particular threshold over the course of a typical month.