Theory of portfolios: New considerations on classic models and the Capital Market Line

The aim of this paper is to present an alternative method to obtain the efficient portfolio in Roy's model starting from the concepts of critical return and risk which are introduced here. This method will permit resolution of the main problem of Roy's model, that is to say, the impossibility of obtaining the portfolio in certain situations. The introduction of these new concepts will also allow the detection and solution of a problem associated with the calculation of the Capital Market Line. This work concludes by considering the possibility that investors allocate part of their budget for buying zero-risk assets.