A heuristic algorithm for a portfolio optimization model applied to the Milan stock market

In this paper the authors present a model which takes into account characteristics of the portfolio optimization problem which are disregarded in most optimization models. These are transaction costs, minimum transaction units and limits on minimum holdings. The model is a mixed integer linear model which generalizes one of the linear models which recently appeared in the literature as an alternative to the classical Markowitz model. Unfortunately, in order to obtain a greater realism in the problem modelling a set of binary and integer variables needs to be introduced. Computational experiments are carried out to evaluate the complexity of the model, which is applied to the Milan stock market. The results show that the presence of the integer variables dramatically increases the computational complexity of the model compared with the continuous version. For this reason the paper analyzes a heuristic solution procedure based on two phases, which reflect the investor’s empirical approach to the problem. The computational results show that the heuristic procedure generates an error lower than 4.1% and that the error decreases when the capital invested increases.