Standard Deviation

Symbol: $\sigma$

Standard deviation measures the average amount by which data points differ from the mean, indicating the volatility or total risk of a dataset.

Formula:

$$\sigma =\sqrt{\frac{\sum (X_i-\bar{X}{)}^2}{n-1}}$$

Where:

• $X$ is the variable.
• $X_i$ are individual data points.
• $\bar{X}$ is the mean of $X$.
• $n$ is the number of data points.

It is also the square root of Variance.

In finance, a higher standard deviation means more unpredictable returns and therefore greater risk.

Used to assess total (systemic + unsystematic) risk, unlike Beta, which only measures systematic risk.