Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost

In this paper, we propose a sparse equity portfolio optimization model that aims at minimizing transaction cost by avoiding small investments while promoting diversification to help mitigate the volatility in the portfolio. The former is achieved by including the ℓ0-norm regularization of the asset weights to promote sparsity. Subjected to a minimum expected return, the proposed model turns out to be an objective function consisting of discontinuous and nonconvex terms. The complexity of the model calls for proximal method, which allows us to handle the objective terms separately via the corresponding proximal operators. We develop an efficient algorithm to find the optimal portfolio and prove its global convergence. The efficiency of the algorithm is demonstrated using real stock data and the model is promising in portfolio selection in terms of generating higher expected return while maintaining good level of sparsity, and thus minimizing transaction cost.