Variance is the average of the squared deviations of a series from its mean. It is the building block of standard deviation (its square root) and of more elaborate risk measures like covariance, correlation, and portfolio variance.
Variance is convenient for math (it adds across independent variables) but not for interpretation (it lives in squared-return units). For most trading reporting, standard deviation is reported instead because it shares units with the original returns.
Sample variance divides by N − 1 rather than N (Bessel's correction) to give an unbiased estimate. Most spreadsheet and statistical libraries default to the N − 1 version.
Formula
Var = Σ(x_i − x̄)^2 / (N − 1)
Example
Returns [0.01, -0.02, 0.00, 0.015, -0.005]. Mean = 0. Squared deviations sum to ≈0.000805. Variance = 0.000805 / 4 ≈ 0.000201.
How Noon Barbari uses Variance
Every concept here is implemented in the platform. Open the relevant docs or tool to see it in action.
Volatility calculator →Related terms
- Statistics
Standard deviation
Square root of variance — the most common volatility measure in trading.
- Statistics
Sharpe ratio
Excess return over the risk-free rate per unit of total volatility.
- Indicators
Bollinger Bands
A moving average flanked by ±k standard deviations of price. k = 2 by default.
- Statistics
Mean
Arithmetic average of a series. In trading: average return per period.