Standard Deviation
Standard deviation measures how much a set of values is spread out from its average. It is the square root of the variance — the average of the squared differences between each value and the mean. In finance it quantifies how widely returns vary around their average, so it is the standard way to express the volatility, and therefore the risk, of an investment. A larger standard deviation means more dispersion.
Worked example
Take five annual returns: 2%, 4%, 6%, 8%, 10%. The mean is (2 + 4 + 6 + 8 + 10) ÷ 5 = 6%. The squared deviations from the mean are 16, 4, 0, 4 and 16, summing to 40. The variance is 40 ÷ 5 = 8, and the standard deviation is √8 = 2.83%.
Why it matters
Standard deviation matters because it converts a scatter of returns into a single, comparable number for risk, and it underpins tools such as the Sharpe ratio and the bell-curve assumptions behind much of finance. A key pitfall is that it assumes returns are roughly symmetric and normally distributed; real markets have fat tails and crashes, so standard deviation can understate the chance of extreme losses.
Frequently asked questions
What is the difference between variance and standard deviation?
Variance is the average of the squared deviations from the mean. Standard deviation is its square root, which returns the figure to the same units as the original data and is therefore easier to interpret.
What is the difference between population and sample standard deviation?
Population standard deviation divides the summed squared deviations by the number of values (n). Sample standard deviation divides by n − 1 to correct for estimating from a sample, giving a slightly larger result.
Related terms: Volatility, Sharpe Ratio