Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control

TL;DR

This paper introduces a new method for estimating covariance matrices that guarantees positive semidefiniteness and controls spectral conditioning, improving portfolio optimization stability and performance.

Contribution

It proposes a novel atomic-IQ parameterization and an analytic eigen floor for covariance estimation, ensuring PSD and conditioning control without ex-post adjustments.

Findings

Improved out-of-sample Sharpe ratios in back tests.

More stable risk profiles compared to standard estimators.

Constructive PSD guarantees within an explicit feasibility region.

Abstract

We revisit Gerber's Informational Quality (IQ) framework, a data-driven approach for constructing correlation matrices from co-movement evidence, and address two obstacles that limit its use in portfolio optimization: guaranteeing positive semidefinite ness (PSD) and controlling spectral conditioning. We introduce a squeezing identity that represents IQ estimators as a convex-like combination of structured channel matrices, and propose an atomic-IQ parameterization in which each channel-class matrix is built from PSD atoms with a single class-level normalization. This yields constructive PSD guarantees over an explicit feasibility region, avoiding reliance on ex-post projection. To regulate conditioning, we develop an analytic eigen floor that targets either a minimum eigenvalue or a desired condition number and, when necessary, repairs PSD violations in closed form while remaining compatible with the squeezing identity. In long-only tangency back tests with transaction costs, atomic-IQ improves out-of-sample Sharpe ratios and delivers a more stable risk profile relative to a broad set of standard covariance estimators.