L0-norm based Short-term Sparse Portfolio Optimization Algorithm Based on Alternating Direction Method of Multipliers

Abstract

This paper proposes a novel short-term sparse portfolio optimization (SSPO) model based on ℓ0-norm. Compared with existing approaches, this model selects the portfolio based on the short-term increasing potential of assets, and an ℓ0-norm constraint is introduced to directly control the maximum number of non-zero assets in selected portfolios. Unlike the ℓ1-norm based methods, the no-short-selling constraints can be directly used in our proposed model. Besides, a sparse regularization term is introduced to eliminate trivial trades in the SSPO system. Moreover, to solve the contained non-convex optimization system, an algorithm based on the concept of the alternating direction method of multipliers (ADMM) is developed. The convergence of the proposed algorithm is also investigated. Finally, the effectiveness of the proposed approach is demonstrated by some numerical experiments on four real-world datasets.