Partial Correlation Networks of Assets

Ordinary correlation between two stocks can be misleading in a group, because a shared driver — say, the overall market or an industry factor — pushes both up and down together even if neither one directly influences the other. Partial correlation answers a sharper question: how correlated are two assets after removing the linear influence of every other asset in the set? If two stocks are highly correlated only because both track the market, their partial correlation (with the market held fixed) collapses toward zero, while a pair with a genuine direct link — say, a supplier and its main customer — keeps a nontrivial partial correlation even after everything else is accounted for.

Computing it is a matter of inverting the covariance matrix: the partial correlation between assets $i$ and $j$ is read off from the precision matrix (the inverse covariance matrix), rescaled to lie between $-1$ and $1$. Drawing an edge between every pair whose partial correlation clears some threshold produces a network — a picture of which assets are directly, rather than indirectly, connected, once confounding co-movement is stripped away.

These networks are used to spot contagion channels: in a portfolio of forty stocks, raw correlation might show nearly every pair connected because of a common market factor, while the partial correlation network reduces to a sparse handful of genuine direct links — the pairs that actually move each other, which is what matters for diversification and stress testing.