Standard deviation

Standard deviation is calculated from a series of returns: take each return’s difference from the average, square it, average those squares, and take the square root. The result is in the same units as the returns, such as percentage points a year. A fund with an average return of 7% and a standard deviation of 15% has much more widely scattered returns than one with the same average and a standard deviation of 5%. If returns followed a normal distribution, about two-thirds of years would fall within one standard deviation of the average and about 95% within two.

Standard deviation is the most common measure of investment risk and underpins the Sharpe ratio and much of portfolio theory. Its limits matter. It treats unexpectedly large gains as just as ‘risky’ as large losses. Real market returns have fatter tails than a normal distribution, so extreme falls happen more often than the formula implies. And it is estimated from the past, which may not resemble the future. It measures bumpiness along the way, not the risk of permanent loss or of failing to meet a goal.