Dimensionless linear-comovement measure ρ_X,Y = dfracCov(X,Y)σ_X σ_Y in [-1, +1] — the normalised covariance. Captures only linear dependence; ρ = 0 does not imply independence (e.g. Y = X^2 with X symmetric). Sample correlation has standard error ≈ 1/√(n) for iid Gaussian data — far too noisy to invert into a stable covariance matrix without shrinkage (Ledoit-Wolf) or factor-structure imposition. Tail correlation rises sharply in crises (correlation breakdown).