This survey compares different portfolio selection frameworks, namely the common mean-variance analysis versus different mean-downside risk analysis, to determine which of these frameworks leads to the most efficient portfolio selection. An empirical simulation of portfolios generated by the different frameworks is implemented following the practitioners' point of view. The results show the mean-index tracking portfolio to over performs the mean-variance portfolio in terms of return per unit of risk, downside excess return and stability of optimization solutions when different estimations of expected returns are used