Definition
Variance is a measure of how much the individual values in a data set differ from their average, computed as the average of the squared deviations from the mean and expressed in squared units of the data.
Why it matters
Variance is the primitive that standard deviation is built from, the square of the standard deviation. It appears directly in portfolio construction, risk decomposition, and covariance analysis, where working in squared units is analytically convenient because variances add across independent components while standard deviations do not.
How it works
Variance is computed by taking each value in the data set, subtracting the average, squaring the difference, and then averaging those squared differences. It is the mean squared deviation from the mean. The result is expressed in squared units, which is why variance of a return series measured in percentage points has units of squared percentage points, a quantity that is analytically useful but not directly interpretable in the way standard deviation is. Two properties make variance analytically convenient: the variance of a sum of independent variables equals the sum of their variances, and the variance scales in known ways when a variable is multiplied by a constant. Worked example: taking the same three-year return series of six, eight, and ten percent, the deviations from the eight percent average are minus two, zero, and plus two percentage points. Squared, these are four, zero, and four. Their average is approximately two point sixty-seven squared percentage points, which is the variance of the series. Its square root, approximately one point sixty-three percentage points, is the corresponding standard deviation.
In practice
For an individual reading fund disclosures or performance reports, variance is rarely reported directly; the same information is conveyed as standard deviation, which is easier to interpret because it shares units with the underlying returns. Variance shows up under the surface, however, whenever a portfolio's overall risk is being decomposed into contributions from different asset classes, or whenever a Monte Carlo model is being parameterized. A professional working with risk analysis uses variance whenever the additive property matters, for example when combining independent return streams or when decomposing total return variability into systematic and idiosyncratic components. Plan fiduciaries encounter variance in target date fund glide path analysis and in the risk-based capital calculations that carriers submit to regulators.
Related terms
- Standard deviation
- Correlation
- Volatility drag
- Sharpe ratio
- Risk-adjusted return
- Monte Carlo simulation
- Geometric Brownian motion
- Risk-based capital