Cardinality Constrained Portfolio Optimization via Alternating Direction Method of Multipliers

Area of Science:

• Quantitative Finance
• Optimization Theory
• Computational Finance

Background:

• The Markowitz mean-variance model is widely used in portfolio optimization.
• Sparse regularization is popular for achieving sparse portfolios.
• Existing penalty-based methods lack explicit control over portfolio size (cardinality).

Purpose of the Study:

• To reformulate the mean-variance model as a cardinality-constrained nonconvex optimization problem.
• To develop an algorithm that explicitly controls the number of assets in a portfolio.
• To address the limitation of regularization parameter dependency in existing methods.

Main Methods:

• Formulation of the mean-variance model with an L0-norm (cardinality) constraint.
• Application of the alternating direction method of multipliers (ADMMs) to solve the nonconvex problem.
• Derivation of the dynamic behavior of the proposed algorithm.

Main Results:

• The proposed algorithm allows explicit control over portfolio cardinality.
• Numerical results show superior performance compared to state-of-the-art algorithms.
• Demonstrated effectiveness on four real-world datasets.

Conclusions:

• The developed ADMM-based algorithm effectively solves the cardinality-constrained nonconvex portfolio optimization problem.
• This approach offers explicit control over portfolio size, a key advantage over traditional methods.
• The findings suggest a more precise and controllable method for sparse portfolio construction.