Using Binary Variables to Obtain Small Optimal Portfolios

Abstract

Binary modeling may be used in order to constrain the number of stocks in an optimal portfolio. Such modeling allows an exact resolution of the number problem raised by Jansen and van Dijk in an earlier issue; their solution is only approximate. Binary variable modeling allows imposition of a minimum threshold for portfolio weights, whether by itself or along with the numerical constraint. A manager can thus limit transaction and administrative costs when tracking a benchmark or constructing an efficient portfolio.