Covariance
A measure of how two assets move together: positive when they tend to deviate from their averages in the same direction, negative when in opposite ones.
Formula
\mathrm{Cov}(a,b) = \frac{1}{n-1}\sum_{i=1}^{n}\left(r_{a,i}-\bar{r}_a\right)\left(r_{b,i}-\bar{r}_b\right)Computed on returns matched by date. The value depends on the scale of the returns themselves, so to compare pairs it is normalised — which gives correlation.
How to read the number
Portfolio risk is driven by covariances rather than by the individual dispersion of each holding: what a pair contributes is set by how they move together.
When the metric lies
Estimates from short histories are noisy, and the number of pairs grows with the square of the number of assets while the amount of data does not grow at all.
Also known as: return covariance