Building an optimal portfolio using a mean-VaR framework

The area of finance has been a continuous source of challenging problems that have influenced research efforts on analytical and numerical solution methods for complex decision problems. In this paper we propose an original algorithm for portfolio optimization. We attack the problem in three stages: selecting assets, risk estimation, portfolio optimization. We select assets in the portfolio using principal components analysis in order to construct the initial portfolio, then we select from each of the classes obtained those assets that correspond to the minimum measure Value-at-Risk at a fixed probability level. Finally we solve the optimization problem. One numerical example is also presented for the sake of illustration.