Optimal portfolios using linear programming models

The classical Quadratic Programming formulation of the well known portfolio selection problem, is cumbersome, time consuming and relies on two important assumptions: (a) the expected return is multivariate normally distributed; (b) the investor is risk averter. This paper formulates two alternative models, (i) maximin, and (ii) minimization of absolute deviation. Data from a very simple problem, consisting of five securities over twelve months, is used, to examine if these various formulations provide similar portfolios or not. As expected, the maximin formulation has the highest return and risk, while the min σ (quadratic programming) has the lowest risk and return, with the min σ formulation being closed to min σ formulation.