Zero Variance Portfolio

2026-02-22

AI Summary

This study addresses the severe out-of-sample performance degradation of traditional minimum-variance portfolio strategies in high-dimensional settings where the number of assets exceeds the sample size, a regime prone to overfitting. The authors propose, for the first time, the application of Ridgelet estimators to construct zero-variance portfolios that exhibit strong out-of-sample generalization under overparameterized conditions. Theoretical analysis demonstrates that the proposed approach achieves minimax-optimal risk in high dimensions and exhibits a double descent phenomenon. Extensive simulations and empirical results confirm that this method significantly outperforms the unregularized pseudoinverse benchmark, offering superior robustness and competitiveness in high-dimensional portfolio optimization scenarios.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

When the number of assets is larger than the sample size, the minimum variance portfolio interpolates the training data, delivering pathological zero in-sample variance. We show that if the weights of the zero variance portfolio are learned by a novel ``Ridgelet'' estimator, in a new test data this portfolio enjoys out-of-sample generalizability. It exhibits the double descent phenomenon and can achieve optimal risk in the overparametrized regime when the number of assets dominates the sample size. In contrast, a ``Ridgeless'' estimator which invokes the pseudoinverse fails in-sample interpolation and diverges away from out-of-sample optimality. Extensive simulations and empirical studies demonstrate that the Ridgelet method performs competitively in high-dimensional portfolio optimization.

Problem

• Zero Variance Portfolio
• High-dimensional Portfolio Optimization
• Out-of-sample Generalizability
• Double Descent
• Overparametrized Regime

Innovation

• Ridgelet estimator
• zero variance portfolio
• double descent
• high-dimensional portfolio optimization
• out-of-sample generalizability