Invest Glossary

Plain-English definitions, reviewed by an independent investor

Covariance

Covariance shows whether two assets tend to move together and by how much.

Covariance shows whether two assets tend to move together and by how much.

Covariance = Average of (X−MeanX)(Y−MeanY)

Common mix-ups

Its scale depends on the assets, so correlation (normalised) is easier to read.

Picture this

A portfolio pairs stocks with gold, whose prices have historically shown low or negative covariance with equities. In a market selloff, stocks fall while gold often holds or rises, so the products of their deviations are negative and the overall portfolio wobbles less than stocks alone. The scenario is covariance at work: it is the mathematical reason a “boring” gold allocation improves a portfolio even when gold’s own return is unimpressive — what matters is how it moves alongside everything else.

How to apply it

You will almost never quote covariance directly; correlation is its readable form. Understand that negative covariance between assets is the mathematical basis of diversification — it is what makes the whole portfolio smoother than its parts.

What it means for you

It feeds correlation and portfolio risk maths directly.

A quick example

Covariance multiplies each asset’s deviation from its own average and averages the products. If both assets are above their averages at the same time, the products are positive and covariance is positive; if they move opposite, the products are negative. The sign tells you the direction of co-movement, and the size reflects how strongly they swing together. The problem is that scale makes raw covariance hard to compare across pairs — which is why analysts divide by the two standard deviations to get correlation, a tidy −1 to +1 number.

Key takeaway

Covariance shows whether two assets move together and by how much, and its sign and size feed directly into correlation and portfolio risk. Positive means co-movement, negative means the opposite — and negative covariance between assets is the mathematical basis of diversification. Raw covariance is hard to compare across pairs, so analysts normalise it into correlation. You will rarely quote it, but every smooth, diversified portfolio you own is built on negative covariances working quietly in the background.

Definitions reviewed by the Investing Glossary editorial team.

Answers to Common Questions

Covariance vs correlation?

Correlation is covariance divided by the two SDs, from −1 to +1.

Negative covariance?

Means the assets tend to move opposite, useful for hedging.

Why is covariance scale-dependent?

Volatile assets produce large products, so size alone distorts comparisons.

Where is it used?

In portfolio construction, where the covariance matrix drives optimal weights.

Related concepts

CorrelationVarianceDiversification