Mean variance efficient portfolios by linear programming: A review of some portfolio selection criteria of Elton, Gruber and Padberg

Abstract: Finding the mean-variance eÆcient frontier is <p> a quadratic programming problem with an analytical solu- <p> tion, whenever the portfolio choice is unrestricted. The an- <p> alytical solution involves an inversion of the covariance ma- <p> trix. When short-sale constraints are added to the problem <p> it is usually thought of as adding considerable complexity <p> to the quadratic programming problem. This paper shows <p> that such problems can be handled by a simple linear pro- <p> gramming procedure, which allows for multiple changes of <p> basis variables. We show how some classical selection cri- <p> teria from models with particular covariance matrices fall <p> into this framework. Furthermore, adding linear constraints <p> like maximum placement limits for subsets of assets is easily <p> incorporated.