Equally weighted cardinality constrained portfolio selection via factor models

In this work a proposal and discussion of two different 0-1 optimization models is carried out in order to solve the cardinality constrained portfolio problem by using factor models. Factor models are used to build portfolios based on tracking the market index, among other objectives, and require to estimate smaller number of parameters than the classical Markowitz model. The addition of the cardinality constraints limits the number of securities in the portfolio. Restricting the number of securities in the portfolio allows to obtain a concentrated portfolio while also limiting transaction costs. To solve this problem a new quadratic combinatorial problem is presented to obtain an equally weighted cardinality constrained portfolio. For a single factor model, some theoretical results are presented. Computational results from the 0-1 models are compared with those using a state-of-the-art Quadratic MIP solver.