Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911342738276352 |
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| author | Khalaf, Layla Abu Smyth, William |
| author_facet | Khalaf, Layla Abu Smyth, William |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control Khalaf, Layla Abu Smyth, William Portfolio Management 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. |
| title | Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control |
| topic | Portfolio Management |
| url | https://arxiv.org/abs/2512.23021 |