Distance Measures for Portfolio Selection

The classical Markowitz approach to the portfolio selection problem (PSP) consists of selecting the portfolio that minimises the return variance for a given level of expected return. By solving the problem for different values of this expected return we obtain the Pareto efficient frontier, which is composed of non-dominated portfolios. The final user has to discriminate amongst these points by resorting to an external criterion in order to decide which portfolio to invest in. We propose to define an external portfolio that corresponds to a desired criterion, and to assess its distance from the Markowitz frontier in market allowing for short-sellings or not. We show that this distance is able to give us useful information about out-of-sample performances. The pursued objective is to provide an operational method for discriminating amongst non-dominated portfolios considering the investors’ preferences