Dependence✓ Mathematical
◆ The PatternCorrelations shift in crises — diversification can vanish when you need it most
In calm markets, asset correlations are moderate and diversification works. During stress, correlations spike toward 1 — a phenomenon called correlation breakdown.
σ²p = w′ Σ w
Copula models separate marginal distributions from the dependence structure, allowing non-linear tail dependence to be modeled explicitly. Regime-switching models capture correlation shifts.
// Interactive — stress level and correlation regime shift
Stress level
2008 lesson. Structured-credit losses soared because default correlations jumped far beyond historical norms.
Pattern bridge: Correlation and covariance matrices are explored in The Toolkit — Correlation.