What is tail correlation and why differ from normal correlation?

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AcadiFi · Accepted Answer

Pearson correlation measures linear co-movement averaged across all observations. Tail correlation measures co-movement conditional on extreme returns, capturing what happens when both assets move together in the tails. The Pearson 0.35 reflects overall weak linear link, but the tail 0.78 says: when both move beyond 2 standard deviations, they move together 78% of the time. This pattern is very common for risky assets. EM equities and HY credit might have 0.45 Pearson correlation but 0.85 tail correlation because in normal markets they respond to idiosyncratic drivers, while in stress both respond to global risk-off selling. Gaussian copulas underestimate tail risk exactly because they force symmetric thinning of the tail dependence - a Gaussian copula with rho=0.45 has asymptotic tail dependence of zero. Remedies: use Student-t copulas (low degrees of freedom give fat tails and nonzero tail dependence), Clayton copula (lower-tail dependence), or Gumbel copula (upper-tail dependence). For risk metrics, report Kendall tau and tail dependence coefficients alongside Pearson. Calculate lambda_L = 2*P(U<=u | V<=u) for small u. ```mermaid graph TD A[Pearson=0.35
average] --> C[Misleading] B[Tail=0.78
conditional] --> D[True stress
link] C --> E[Use copulas] D --> E ```

What is tail correlation and why differ from normal correlation?

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