Glossary
Standard deviation
QM1.01Also called dispersion, sd of a sample.
The square root of the average squared deviation from the mean. It measures how spread out a set of numbers is.
A series of 6, 8, 10, 12 and 14 has a mean of 10 and a standard deviation of 2.828.
In finance it is applied to returns, where its interpretation depends on a distributional assumption that markets do not satisfy. Under a normal distribution, a three-standard-deviation day should occur about once every few years, and markets deliver them far more often.
The measure is fine. The assumption usually attached to it is not.