A discretization scheme for a portfolio selection problem is discussed. The model is a benchmark relative, mean-variance optimization problem in continuous time. In order to make the model computationally tractable, it is discretized in time and space. This approximation scheme is designed in such a way that the optimal values of the approximate problems yield bounds on the optimal value of the original problem. The convergence of the bounds is discussed as the granularity of the discretization is increased. A threshold accepting algorithm that attempts to find the most accurate discretization among all discretizations of a given complexity is also proposed. Promising results of a numerical case study are provided.