Standard deviation of return measures the average deviations of a return series from its mean, and is often used as a measure of risk. A large standard deviation implies that there have been large swings in the return series of the manager.

Standard deviation can be calculated in two ways:

1. Standard Deviation assumes that the returns series is a sample of the population. This is the calculation most commonly used. The standard deviation of the return series is the square root of the variance:
   
   StdDev(r₁, …, r_n) =
   
   where r₁, …, r_n is a return series, i.e., a sequence of returns for n time periods.
2. Population Standard Deviation assumes that the return series is the population. Population Standard Deviation is the square root of the population variance:
   
   PStdDev(r₁, …, r_n) =

Standard Deviation and Population Standard Deviation are the square root of Variance and Population Variance.

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