Basis Immunity: Isotropy as a Regularizer for Uncertainty

ArXiv ID: 2511.13334 “View on arXiv”

Authors: Florent Segonne

Abstract

Diversification is a cornerstone of robust portfolio construction, yet its application remains fraught with challenges due to model uncertainty and estimation errors. Practitioners often rely on sophisticated, proprietary heuristics to navigate these issues. Among recent advancements, Agnostic Risk Parity introduces eigenrisk parity (ERP), an innovative approach that leverages isotropy to evenly allocate risk across eigenmodes, enhancing portfolio stability. In this paper, we review and extend the isotropy-enforced philosophy of ERP proposing a versatile framework that integrates mean-variance optimization with an isotropy constraint acting as a geometric regularizer against signal uncertainty. The resulting allocations decompose naturally into canonical portfolios, smoothly interpolating between full isotropy (closed-form isotropic-mean allocation) and pure mean-variance through a tunable isotropy penalty. Beyond methodology, we revisit fundamental concepts and clarify foundational links between isotropy, canonical portfolios, principal portfolios, primal versus dual representations, and intrinsic basis-invariant metrics for returns, risk, and isotropy. Applied to sector trend-following, the isotropy constraint systematically induces negative average-signal exposure – a structural, parameter-robust crash hedge. This work offers both a practical, theoretically grounded tool for resilient allocation under signal uncertainty and a pedagogical synthesis of modern portfolio concepts.

Keywords: Agnostic Risk Parity, Eigenrisk parity (ERP), Isotropy, Mean-variance optimization, Portfolio construction, Multi-asset

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents advanced mathematical concepts, including tensor algebra, eigen-decompositions, isotropy constraints, and the derivation of a closed-form isotropic-mean allocation, requiring a high level of theoretical understanding. While it discusses practical applications and crash hedging, the explicit exclusion of empirical studies and backtesting details indicates it is primarily theoretical rather than implementation-ready.

  flowchart TD
    A["Research Goal: Integrate isotropy as a regularizer<br>for robust portfolio construction"] --> B["Key Methodology: Extension of ERP framework<br>Mean-Variance + Isotropy Constraint"]
    B --> C["Inputs: Asset Returns, Covariance Matrix"]
    C --> D["Process: Compute Eigenmodes &<br>Isotropic-Mean Allocation"]
    D --> E["Process: Apply Tunable Penalty<br>to interpolate: Isotropic <-> Mean-Variance"]
    E --> F["Key Finding: Decayed portfolios &<br>Basis-Invariant Metrics"]
    F --> G["Outcome: Negative Signal Exposure<br>acting as Crash Hedge"]