Quick answer
Standard deviation is the square root of the variance, the average squared distance of values from their mean [1]. In investing it measures how far returns typically land from their average, and it is the most common gauge of volatility.
#How is standard deviation calculated?
The NIST statistics handbook defines the sample variance as the sum of squared differences from the mean divided by N − 1, and the standard deviation as its square root [1]. Squaring gives more weight to values far from the center, and taking the square root brings the result back to the original units, here percentage points [1].
Worked example
Five years of returns, step by step
A hypothetical fund returned 12%, −4%, 9%, 15% and −2% in five years.
- Mean ((12 − 4 + 9 + 15 − 2) ÷ 5)
- 6%
- Differences from the mean
- 6, −10, 3, 9, −8
- Squared differences
- 36, 100, 9, 81, 64
- Sum of squares
- 290
- Variance (290 ÷ (5 − 1))
- 72.5
- Standard deviation (√72.5)
- 8.51 percentage points
A typical year landed roughly 8.5 points away from the 6% average; one standard deviation either side spans about −2.5% to +14.5%.
Hypothetical returns. Calculated in code with the N − 1 formula.
#How do investors use standard deviation?
It is a way to compare how bumpy different investments have been. FINRA describes volatility as prices moving up some days and down on others [2]; standard deviation turns that into one figure. Two funds with similar average returns but very different standard deviations gave their owners very different rides. See volatility for a side-by-side example.
| Standard deviation | What it suggests about past returns |
|---|---|
| Low | Returns stayed close to their average |
| High | Returns swung widely around their average |
| Zero | Returns were the same every period |
#What are its limits?
- It treats upside and downside the same. A surprise gain raises standard deviation just as a loss does.
- It looks backward. Past spread is not a forecast of future spread.
- It is not the whole risk picture. It ignores how an investment moves with the market, which beta addresses, and risks such as default or liquidity. FINRA's beta discussion makes the same point from the other side: a stock can be volatile yet have a low beta [2].
Related terms
Frequently asked questions
Is a lower standard deviation always better?
Not by itself. Lower usually means a smoother ride, but often comes with lower expected returns. It depends on your goals and how long you can stay invested.
Why divide by N − 1 instead of N?
When you calculate from a sample, such as a few years of returns, dividing by N − 1 is the standard formula in the NIST handbook. With many data points the difference is small.
Sources
Grade A = primary source (regulator, government agency, official rulebook or the index provider's own documents). Numbers in brackets in the text point here.
- National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods — 1.3.5.6 Measures of Scale (2026). Accessed 2026-10-03.A
- FINRA. Volatility (2026). Accessed 2026-10-03.A
This page is general education, not personal financial, tax or legal advice. Figures in worked examples are hypothetical and calculated before taxes and fees unless stated. Rules and limits change; check the linked primary sources for the current version. How we check every page.
