Portfolio selection is a relevant problem arising in finance and economics. While its basic formulations can be efficiently solved through linear or quadratic programming, its more practical and realistic variants, which include various kinds of constraints and objectives, have in many cases to be tackled by approximate algorithms. In this work, we present a hybrid technique that combines a local search, as master solver, with a quadratic programming procedure, as slave solver. Experimental results show that the approach is very promising and achieves results comparable with, or superior to, the state of the art solvers.