A Motif-Based Framework for Decomposing Risk Spillovers

Connectedness measures quantify aggregate risk spillovers but obscure the local interaction patterns that generate systemic risk. We develop a motif-based framework that first extracts multiscale backbones from quantile connectedness networks and then identifies directed triadic motifs whose frequencies exceed randomization baselines. To distinguish how assets' sectoral identities shape local spillover structures, we introduce colored motifs under sector partitions of increasing granularity. Using orbit positions that capture each node's structural role within directed triadic motifs, we construct portfolio strategies that exploit an asset's place in the spillover architecture. Applying the framework to 39 commodity and equity futures across lower, median, and upper conditional quantiles, we find that motif-based portfolios outperform minimum correlation and minimum connectedness benchmarks on risk-adjusted returns. We further show that in tail networks, assets with greater orbit-position diversity tend to act as net spillover transmitters rather than receivers, establishing positional diversity as a tail-specific marker of systemic influence. These findings demonstrate that local triadic topology carries portfolio-relevant information that aggregate connectedness measures miss.