We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio optimization is ill-posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.