The main goal of this paper is to formulate a robust mean-semivariance portfolio selection problem in terms of a linear matrix inequalities (LMI) optimization problem. The mean-semivariance model takes as the risk function a convex combination of the semivariances (below and above the expected return) of the tracking error (the difference between the investor's portfolio and a benchmark portfolio). We consider different forms of calculating the mean and semivariance of the tracking error. It is desired to minimize an objective function defined as a convex combination of the risk function minus the expected return of the tracking error. By a robust solution we mean a feasible portfolio which leads to a worst case value function lower than any other worst case value function evaluated at any other feasible portfolio. Numerical simulations will be presented with data from São Paulo Stock Exchange (BOVESPA).
Mean-semivariance; portfolio optimization; linear matrix inequalities; computational tool
