The impact of association measures within the portfolio dimensionality reduction problem

The dependency structure of random sources plays a crucial role in portfolio theory and in several pricing and risk management problems. In this paper, we discuss the possible usage of alternative association measures in portfolio problems. Among association measures, we highlight those that are consistent with the choices of riskaverse investors and we characterise semidefinite positive association measures. Additionally, we propose new portfolio selection problems that optimise the association between the portfolio and market benchmarks and follow a dimensionality reduction problem. Finally, by carrying out an empirical analysis, we show the impact of selected association measures within the portfolio problem. This analysis proves that the proper usage of both a risk measure and an association measure can increase the portfolio performance substantially.