Optimization of a long–short portfolio under nonconvex transaction cost

The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long–short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long–short strategy leads to a portfolio with significantly better risk–return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.