Zero Variance Portfolio

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.