In this work is presented a linear multi-objective model that in each iteration is solved a linear programming problem, where the magnitude of the restrictions is obtained by a neighbourhood of the convex search space of feasible solutions. The selection of an investment portfolio through a multiobjective mathematical model indicates that it has several available portfolios. In our model the selection of one of them is performed with the same principle used by the Capital Assets Pricing Model, it is a single point that touches the border of optimal portfolios. The model is tested with a Mexican Stock investment portfolio selection during a period of debacle. This is possible because our model can be applied when there are no positive returns. The results show that using a neighbourhood search within feasible solutions is correct because is possible to obtain investment portfolios with positive profit in periods of debacle.