A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem

In this paper, we consider an extension of the Markovitz model, in which the variance has been replaced with the Value-at-Risk. So a new portfolio optimization problem is formulated. We showed that the model leads to an NP-hard problem, but if the number of past observation Tor the number of assets K are low, e.g. fixed to a constant, polynomial time algorithms exist. Furthermore, we showed that the problem can be formulated as an integer programming instance. When K and T are large and alpha(VaR) is small-as common in financial practice-the computational results show that the problem can be solved in a reasonable amount of time. (c) 2005 Elsevier B.V. All rights reserved.