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SVNexus · Contagion

Correlation networks

Also called: asset networks, minimum spanning tree, market graph

A correlation network represents assets as nodes and their dependence as weighted links, making clusters and central assets visible.

Definition

A correlation network is a graph in which each node is an asset and each link carries a measure of dependence between two assets, most often return correlation. Because a full correlation matrix has a link for every pair, networks are usually filtered to keep only the most important links.

The same construction works with other dependence measures, such as tail dependence or transfer entropy, which turn it into a directed or crash-focused network.

Intuition

A correlation matrix of 100 assets has 4,950 pairwise numbers, which is unreadable. A network shows the structure: clusters of assets that move together, bridges between clusters, and hubs connected to many others. Diversification looks very different when you can see that half a portfolio sits in one tight cluster.

Watching the network over time shows how structure tightens in stress, when clusters merge and the graph becomes denser.

How it's calculated

A classic construction (Mantegna, 1999) converts correlation into a distance:

dij = √(2 · (1 − ρij))

which runs from 0 (perfectly correlated) to 2 (perfectly anti-correlated). Filtering options:

  • Minimum spanning tree: the N − 1 links connecting all assets with the smallest total distance.
  • Threshold network: keep links with |ρ| above a cut-off.
  • Planar maximally filtered graph: keeps more links than a tree while staying planar.

Node importance is then summarized with measures such as degree (number of links), strength (sum of link weights) and betweenness (how often a node lies on shortest paths).

Example: a correlation of 0.8 maps to a distance of √(2 × 0.2) ≈ 0.63, and a correlation of 0 to √2 ≈ 1.41. In spanning trees of broad equity universes, stocks from the same sector typically cluster together, often linked through a few large names that appear as hubs.

How to read it

Look for clusters, hubs and how they change. A hub in a stress period is an asset whose moves are shared by many others. Tree length, the sum of distances in the spanning tree, shrinks when markets become more correlated.

Choose the window carefully: short windows show fast changes but add noise; long windows hide them. Animated or replayed networks help separate persistent structure from one-off links.

Common mistakes

  • Reading filtered networks as if missing links meant zero dependence.
  • Using correlations from mixed time zones or different sampling frequencies.
  • Ignoring estimation noise, which in large universes produces many spurious links.
  • Treating network centrality as a measure of causal influence.

In Saqrid

SVNexus draws an animated force-directed network of how assets in a universe move together and spill over, built from return correlation, DCC correlation, transfer entropy, tail dependence or implied-vol spillover links.

A time scrubber replays the network and its metrics at earlier dates.

Open SVNexus.

  • DCC correlationDynamic conditional correlation (DCC) models correlations that change over time, built on GARCH volatilities for each asset.
  • Cross-asset contagionCross-asset contagion is a rise in linkages between markets after a shock, beyond normal interdependence, so losses spread further than usual.
  • Diebold–Yilmaz connectednessThe Diebold–Yilmaz index measures how much of each market's forecast-error variance comes from shocks to other markets, summarized as total connectedness.
  • Tail dependenceTail dependence measures the chance that two assets suffer extreme moves together, which ordinary correlation can understate badly.

Go deeper

Saqrid Institute lesson: Volatility Spillover (Diebold–Yilmaz). Lesson text is open to read without an account.

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