Working Papers,
Copenhagen Business School, Department of Finance

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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