Scandinavian Working Papers in Economics
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Department of Finance, Copenhagen Business School Working Paper Series, Department of Finance, Copenhagen Business School

No 2001-2:
Mean variance efficient portfolios by linear programming: A review of some portfolio selection criteria of Elton, Gruber and Padberg

Bjarne Astrup Jensen

Abstract: Abstract: Finding the mean-variance e∆cient frontier is

a quadratic programming problem with an analytical solu-

tion, whenever the portfolio choice is unrestricted. The an-

alytical solution involves an inversion of the covariance ma-

trix. When short-sale constraints are added to the problem

it is usually thought of as adding considerable complexity

to the quadratic programming problem. This paper shows

that such problems can be handled by a simple linear pro-

gramming procedure, which allows for multiple changes of

basis variables. We show how some classical selection cri-

teria from models with particular covariance matrices fall

into this framework. Furthermore, adding linear constraints

like maximum placement limits for subsets of assets is easily


Keywords: Keywords: Mean variance efficient portfolios; short sale constraints; linear programming; multiple basis shifts; place- ment limits.; (follow links to similar papers)

JEL-Codes: G11; (follow links to similar papers)

29 pages, February 2, 2001

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