Using Binary Variables to Obtain Small Optimal Portfolios

摘要

The use of binary variables allows us to obtain exact solutions for two types of problem, the search for an optimal portfolio of a relatively small size, and the search for an optimal portfolio whose weights are greater than a given threshold or are zero. These two constraints can be introduced separately or together. The purpose of the optimization can be to track a benchmark or to construct an efficient portfolio (Markowitz model). The role of the constraints is to reduce transaction and administrative costs. The proposed models are quadratic integer programming problems. For a universe of 100 stocks, the solution using specialized software is simple and exact (one obtains a global optimum). For a universe of 250 stocks, the solutions take longer and, for low values of m, only an can be reached in reasonable computation time. But, even in this case, solutions are approximation better than those obtained by the Jansen-van Dijk method.