ATLASStandard deviation
Investing glossary · Risk and statistics
A measure of how far values typically fall from their average; in finance, the usual way to quantify risk.
Definition
The standard deviation measures how spread out a set of numbers is around its average. If weekly returns are tightly clustered around their mean, the standard deviation is small; if they are scattered, it is large. In finance, the standard deviation of returns is the usual definition of volatility.
It is useful because it is in the same units as the data: a weekly standard deviation of 3% means a typical week lands about 3 percentage points from the average. But it treats gains and losses the same, and it understates the chance of extreme events because real returns have fatter tails than a bell curve.
Formula
s = √( Σ (rᵢ − r̄)² ÷ (n − 1) )
rᵢ = return in period i, r̄ = average return, n = number of periods. Dividing by n − 1 gives the sample estimate.
Worked example
Over the last 53 weeks the weekly returns of Microsoft (MSFT) averaged +0.16% with a standard deviation of 5.14%. Scaling that to a year (multiplying by the square root of 52) gives an annualized volatility of about 37%.
The standard deviation says how wide the weekly swings were, not whether the stock went up or down; the average says that.
How ATLAS uses it
ATLAS uses the standard deviation of returns, blended with a long-run level, as the volatility input of its price-range model.
Related in ATLAS: Stock analysis →Browse all ATLAS tools →See it on a real stock
The example above uses these companies. Open their pages for the full numbers:
Frequently asked questions
What does one standard deviation mean?
For bell-shaped data, about 68% of observations fall within one standard deviation of the average and about 95% within two. Real stock returns have fatter tails, so extreme moves are more common than that rule suggests.
Why divide by n − 1?
When you estimate from a sample, dividing by n − 1 corrects a small bias and gives a better estimate of the true spread.
Related terms
Put the idea to work on your own stocks
Open any company in ATLAS to see its fair value, its odds of rising and its risk numbers side by side.
Try ATLAS →Not investment advice. ATLAS estimates are produced by statistical models from public data; they can be wrong and past performance does not predict future results. Consider your own situation before investing. Disclaimer