Invest Glossary

Plain-English definitions, reviewed by an independent investor

Variance

Variance is the average of squared deviations from the mean — the squared cousin of standard deviation.

Variance is the average of squared deviations from the mean — the squared cousin of standard deviation.

Variance = Average of (Return − Mean)²

A quick example

A stock’s returns swing around their average; variance squares each deviation so that ups and downs both count, then averages them. Because the deviations are squared, the result is in units of percent-squared, which is hard to interpret — that is why standard deviation, the square root, is the number people actually quote. Variance matters mathematically: it is the input for portfolio optimisation, and combining assets with low covariance lets you cut portfolio variance without cutting expected return. It is the engine behind the whole idea of diversification.

What it means for you

It is the raw risk measure that standard deviation tames by square-rooting.

Picture this

Two portfolios have the same expected return. Portfolio A holds five nearly identical tech stocks; portfolio B holds stocks, bonds, and cash. Portfolio A’s variance is far higher because its components move together, and squaring the swings makes the joint risk even clearer. The maths of variance is exactly why diversification works: spreading across low-covariance assets shrinks the squared deviations, and the portfolio becomes smoother than any of its parts. The number nobody quotes, variance, is quietly doing the work.

Common mix-ups

Its squared units make it awkward to quote, so SD is preferred in practice.

How to apply it

You rarely need to calculate variance yourself; funds report standard deviation, which is variance’s readable form. Understand the link — SD is the square root of variance — so the risk numbers on a factsheet are not mysterious.

Key takeaway

Variance is the squared cousin of standard deviation, the raw risk measure nobody quotes because its units are unreadable — and the mathematical engine behind diversification. Squaring deviations makes ups and downs both count, and combining assets with low covariance shrinks portfolio variance without cutting expected return. You rarely need to calculate it; funds report standard deviation, its square root. Understand the link and the idea: portfolio risk is about how the parts move together, not how they move alone.

Definitions reviewed by the Investing Glossary editorial team.

Common Questions, Answered

Variance vs SD?

SD is the square root of variance, in the same units as returns.

Why square deviations?

So ups and downs both add up instead of cancelling.

Where is variance used?

Portfolio optimisation and risk models that need exact inputs.

Can variance be negative?

No, squares are always non-negative; zero means no variation.

Keep reading

Standard DeviationCovariance