Mathematics · Core
Correlation
Correlation is standardized covariance, ρ ∈ [−1, 1]. It is a linear association, not causation, and it is unstable exactly when you need it.
Definition
Pearson ρ = Cov/(σ_x σ_y). It is silent on tail dependence (copulas) and on nonlinear links. Rank correlations (Spearman, Kendall) are more robust to outliers and still do not give you a causal graph.
Why it matters
‘Uncorrelated alpha’ is the sales pitch. Crisis ρ → 1 is the live book. Know both.
Case
Equity–bond ρ flipped from negative (2010s) to positive (2022 inflation shock). A constant-ρ risk model was a regime bet.
How to read it
State the window and whether you mean Pearson or tail dependence. A single ρ on a slide is a vibe.
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