Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control

ArXiv ID: 2512.23021 “View on arXiv”

Authors: Layla Abu Khalaf, William Smyth

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.

Keywords: Portfolio Optimization, Covariance Matrix Estimation, Positive Semidefiniteness, Spectral Conditioning, Gerber Statistics, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper is highly mathematical, featuring dense algebraic derivations, convex-like combinations, and closed-form spectral control, while also presenting empirical backtests with transaction costs and Sharpe ratio comparisons against standard estimators.

  flowchart TD
    A["Research Goal<br>Improve Covariance Estimation<br>for Portfolio Optimization"] --> B["Data & Setup<br>Equities, Co-movement Evidence, Tangency Portfolio Backtests"]
    B --> C["Methodology: Atomic-IQ Framework<br>Squeezing Identity & Convex-Like Combination"]
    C --> D["Computational Process<br>Constructive PSD Guarantee via Atomic Eigenvalues"]
    D --> E["Analytic Eigen-Floor<br>Control Spectral Conditioning & Repair PSD Violations"]
    E --> F["Outcomes<br>Higher Out-of-sample Sharpe Ratios<br>More Stable Risk Profile"]