There is no possible logical reason for being moral.
Logic only operates within an agreed model.
That means it is only possible to be logical about moral questions if both parties have agreed to work within a model for settling questions of right and wrong. In that sense there is logic within a Marxist, or Original Buddhist, or Zen Buddhist, or Islamic model of right and wrong. The amoral person is not one who is bad, but a person who refuses to discuss right and wrong at all.