Sparse Extended Mean-Variance-CVaR Portfolios with Short-selling

Abstract: This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The proposed algorithm solves a sequence of penalty subproblems using a block coordinate descent (BCD) method while striving to fully exploit each component of the objective function or constraints. Through rigorous analysis, the well-posed nature of each subproblem of the BCD method is established, and closed-form solutions are derived where possible. A comprehensive theoretical convergence analysis is provided to confirm the efficacy of the introduced algorithm in reaching a local minimizer of this intractable optimization problem in finance, whereas generic optimization techniques either only capture a partial minimum or are not efficient. Numerical experiments conducted on real-world datasets validate the practical applicability, effectiveness, and robustness of the introduced algorithm across various criteria. Notably, the existence of closed-form solutions within the BCD subproblems prominently underscores the efficiency of our algorithm when compared to state-of-the-art methods.