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


  • Jensen, Bjarne Astrup

    (Department of Finance, Copenhagen Business School)


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.

Suggested Citation

  • Jensen, Bjarne Astrup, 2001. "Mean variance efficient portfolios by linear programming: A review of some portfolio selection criteria of Elton, Gruber and Padberg," Working Papers 2001-2, Copenhagen Business School, Department of Finance.
  • Handle: RePEc:hhs:cbsfin:2001_002

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    References listed on IDEAS

    1. Elton, Edwin J & Gruber, Martin J & Padberg, Manfred W, 1976. "Simple Criteria for Optimal Portfolio Selection," Journal of Finance, American Finance Association, vol. 31(5), pages 1341-1357, December.
    2. Kwan, Clarence C Y, 1984. " Portfolio Analysis Using Single Index, Multi-index, and Constant Correlation Models: A Unified Treatment," Journal of Finance, American Finance Association, vol. 39(5), pages 1469-1483, December.
    3. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
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    Keywords: Mean variance efficient portfolios; short sale constraints; linear programming; multiple basis shifts; place- ment limits.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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