Portfolio optimization through a network approach: Network assortative mixing and portfolio diversification

Abstract

The paper deals with the classical problem of selecting a portfolio in the financial market and follows a risk-return optimization approach. The main issue in portfolio selection is capturing the dependency structure of the returns of the different assets. In the well-known Markowitz models this is measured by the variance/covariance matrix of the assets’ returns. Recent works have focused on a new way of modeling the dependency between returns of different assets by means of the so called “market graph” or “correlation graph”.Basing on this graph, the paper introduces new mixed integer linear formulations for the portfolio selection problem in which the portfolio expected return is maximized, while controlling the worst case loss. There are two innovative aspects related to the market graph. One is the introduction of a set of constraints over the neighborhood of each node. These constraints force the model to include in the portfolio a subset of assets which correspond to nodes poorly connected in the correlation graph. The second is the use of a measure from the area of complex network analysis called ‘assortativity’. A local assortativity coefficient is computed for each node, and it is used to formulate linear objective functions in the optimization models. We propose two Mixed Integer Linear Programs for finding the most ‘disassortative’ portfolios by using either the ‘local degree’ or the ‘local strength’ assortativity coefficients.A set of computational experiments is performed over real-world data sets to test the performance of the proposed models. The experimental results show that combining the assortativity criterion and the neighborhood constraints leads to an effective strategy to obtain portfolios with a good out-of-sample performance under the risk-return viewpoint.