Zero Variance Portfolio

TL;DR

This paper introduces the Ridgelet estimator for zero variance portfolios, showing it improves out-of-sample performance and generalizability in high-dimensional settings, unlike traditional pseudoinverse methods.

Contribution

The paper proposes a novel Ridgelet estimator for zero variance portfolios that achieves better out-of-sample risk and demonstrates the double descent phenomenon in high-dimensional portfolio optimization.

Findings

Ridgelet estimator outperforms pseudoinverse in out-of-sample tests.

Portfolio risk exhibits double descent with Ridgelet in overparameterized regimes.

Empirical results confirm the method's competitiveness in high-dimensional settings.

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.