Covariance vs correlation

Closely related but not the same. What each one measures and why correlation is usually preferred in finance.

Play with it

Correlation and covariance. Dial a correlation from −1 to +1 and watch two assets move together, apart, or not at all.

Open full screen

Correlation+0.70

Scale of asset B's moves1×

Same pattern, measured in bigger units.

Measured correlation+0.66always between −1 and +1

Covariance10.5changes with scale

120 monthly returns, one dot per month

The same two assets as prices over ten years

These two assets move strongly in the same direction, with a measured correlation of 0.66. Now drag the scale dial and watch which number changes.

Try this

Set correlation to +1: the two friends always walk in the same direction.
Set it to −1 and watch the dots line up like a seesaw.
Set it to 0. Knowing asset A's month tells you nothing about asset B's.
Scale asset B by 100×. The covariance explodes, the correlation stays put.

The math

\rho_{A,B} = \frac{\operatorname{Cov}(A,B)}{\sigma_A\,\sigma_B}

$\rho_{A,B}$: correlation, from −1 to +1
$\operatorname{Cov}(A,B)$: covariance, in the data's own units
$\sigma_A, \sigma_B$: each asset's standard deviation

Quick check

Two questions to see if it clicked. Answers explain themselves.

Why is a covariance of 500 hard to interpret on its own?

Correlation is…