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arXiv · 2602.19462

Zero Variance Portfolio

Jinyuan Chang·Yi Ding·Zhentao Shi·Bo Zhang
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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.

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Jinyuan Chang, Yi Ding, Zhentao Shi, Bo Zhang. 2026-02-23. Zero Variance Portfolio. https://arxiv.org/abs/2602.19462

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