Cleaning a covariance matrix with Marchenko–Pastur

With $N$ assets and $T$ observations, a sample correlation matrix of pure noise still has spread-out eigenvalues. Random matrix theory says where they land.

Eigenvalues inside that band are indistinguishable from noise. Clipping replaces them with their average, keeping the trace, and leaves the signal eigenvalues alone.

Why it matters for VaR

Noisy small eigenvalues make the optimizer and the Monte Carlo engine trust directions that don’t exist. Cleaning them tightens out-of-sample risk estimates.