Scandinavian Working Papers in Economics

Working Papers,
Copenhagen Business School, Department of Finance

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
Additional contact information
Bjarne Astrup Jensen: Department of Finance, Copenhagen Business School, Postal: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, A5, DK-2000 Frederiksberg, Denmark

Abstract: Abstract: Finding the mean-variance eÆcient 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 incorporated.

Keywords: Keywords: Mean variance efficient portfolios; short sale constraints; linear programming; multiple basis shifts; place- ment limits.

JEL-codes: G11

29 pages, February 2, 2001

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