Adaptive l1-regularization for short-selling control in portfolio selection

TL;DR

This paper introduces an adaptive l1-regularization method for portfolio selection that controls short-selling constraints by updating the regularization parameter within a Bregman iteration framework, ensuring sparsity and compliance with financial restrictions.

Contribution

It proposes a novel updating rule for the regularization parameter in Bregman iteration to effectively manage sparsity and short-selling constraints in portfolio optimization.

Findings

The method effectively controls short positions in portfolios.

Numerical tests demonstrate the approach's effectiveness.

The scheme preserves properties of the original Bregman iteration.

Abstract

We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The l1-penalty term can also be interpreted in terms of short sales, on which several financial markets have posed restrictions. The choice of the regularization parameter plays a key role to obtain optimal portfolios that meet the financial requirements. We propose an updating rule for the regularization parameter in Bregman iteration to control both the sparsity and the number of short positions. We show that the modified scheme preserves the properties of the original one. Numerical tests are reported, which show the effectiveness of the approach.