PARTIAL · portfolio tool
Hypothesis
Most eigenvalues of an empirical correlation matrix are noise (within the Marchenko–Pastur band); cleaning them yields a more stable correlation estimate for risk and hedging.
Math — Marchenko–Pastur noise band
Eigenvalues below $\lambda_+$ are statistically indistinguishable from noise, where:
$$ \lambda_{\pm} = \sigma^2\Big(1 \pm \sqrt{N/T}\Big)^2 $$
Method
Clip/shrink eigenvalues inside the MP band, rebuild $C$, use for minimum-variance hedge weights vs raw sample $C$.
Results
| Out-of-sample hedge variance | lower vs sample $C$ |
| Weight stability | higher |
| Directional edge | none (risk tool) |
A real improvement to risk estimation — cleaned correlations give more stable hedges and minimum-variance weights out-of-sample. No alpha by itself; adopted on the risk side, where most durable value lives.
A sample correlation matrix is mostly noise. Knowing which eigenvalues to trust is worth more than any single signal — but it is a risk tool, not a return tool.