Standard Deviation

Standard deviation measures how spread out a set of numbers is around its average.

In markets, it's the core ingredient of volatility.

If you want to express a return as “how many standard deviations from average,” see z-score.

The formula

$$\sigma = \sqrt{E[(r - \mu)^2]}$$

Where $r$ is the return series and $\mu$ is the average return.

What it captures (and what it doesn't)

• It treats upside and downside moves the same.
• A few big outliers can dominate it.
• It doesn't tell you direction (that's skew).

So standard deviation is a reasonable starting point but not a complete picture.