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.

翻译：当资产数量大于样本容量时，最小方差投资组合会对训练数据进行插值，从而产生病态化的零样本内方差。我们证明，若通过一种新型"Ridgelet"估计量学习零方差投资组合的权重，该投资组合在新测试数据中具备样本外泛化能力。该方法呈现双下降现象，并能在资产数量主导样本容量的过参数化状态下实现最优风险。相比之下，采用伪逆的"无岭"估计量无法实现样本内插值，且会偏离样本外最优性。大量模拟与实证研究表明，Ridgelet方法在高维投资组合优化中具有竞争优势。