How do I stress test a correlation matrix?

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AcadiFi · Accepted Answer

Correlation stress testing applies shocks to the off-diagonal entries of your correlation matrix and revalues the portfolio under the stressed matrix. You can't just shift arbitrary correlations - the result must remain positive semi-definite. Four common approaches: One, apply a historical crisis correlation matrix from a past event (2008, 2020, 2011) and ensure PSD via eigenvalue decomposition. Two, scale all off-diagonals toward 1.0 by parameter alpha: rho_stressed = alpha + (1-alpha)*rho_baseline. Three, block correlation model: assets within risk-on bloc get rho=0.9, safe-haven bloc rho=0.9, cross-bloc rho=-0.7. Four, nearest-correlation-matrix projection: start with target shocked correlations, project to nearest PSD matrix via Higham algorithm. For a $1.8B global macro book with 45 positions, a correlation stress lifting all equity-credit-EM pairs to 0.9 and keeping safe-haven pairs unchanged might increase portfolio VaR from $28M to $51M - an 82% jump. The stress reveals the book had diversification benefits that disappear in crisis. ```mermaid graph TD A[Baseline
corr matrix] --> B[Apply
shock] B --> C{PSD?} C -->|No| D[Project] C -->|Yes| E[Revalue] D --> E ```

How do I stress test a correlation matrix?

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