Standard deviation is the statistical measurement of dispersion about an average, which depicts how widely a stock or portfolio’s returns varied over a certain period of time. Investors use the standard deviation of historical performance to try to predict the range of returns that is most likely for a given investment. When a stock or portfolio has a high standard deviation, the predicted range of performance is wide, implying greater volatility.
Benefits
If the returns for a stock or portfolio follow a normal distribution, then approximately 68 percent of the time they will fall within one standard deviation of the mean return, and 95 percent of the time within two standard deviations. For example, if the mean annual return is 10 percent and the standard deviation is 2 percent, you would expect the return to be between 8 and 12 percent about 68 percent of the time, and between 6 and 14 percent about 95 percent of the time.
Origin
Morningstar calculates standard deviation for stocks and portfolios using the trailing monthly total returns for the appropriate time period. All of the monthly standard deviations are then annualized.
For the Pros
Morningstar first calculates the monthly standard deviation and then annualizes it to put it in a more useful one-year context. The formula for monthly standard deviation is:
where
s M = Monthly standard deviation
Ri = Return of the portfolio in month i
n = Number of periods
= Average monthly total return for the portfolio
is also called the arithmetic mean, and it is calculated by adding together all the monthly returns for the portfolio and dividing by the number of months.
Morningstar annualizes the monthly standard deviation by multiplying it by the square root of 12.
