On the impact of semidefinite positive correlation measures in portfolio theory

In this paper potential usage of different correlation measures in portfolio problems is studied. We characterize especially semidefinite positive correlation measures consistent with the choices of risk-averse investors. Moreover, we propose a new approach to portfolio selection problem, which optimizes the correlation between the portfolio and one or two market benchmarks. We also discuss why should correlation measures be used to reduce the dimensionality of large scale portfolio problems. Finally, through an empirical analysis, we show the impact of different correlation measures on portfolio selection problems and on dimensionality reduction problems. In particular, we compare the ex post sample paths of several portfolio strategies based on different risk measures and correlation measures.