IDEAS home Printed from https://ideas.repec.org/p/hhs/cbsfin/2001_002.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://openarchive.cbs.dk/cbsweb/handle/10398/7186
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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(4), pages 1851-1872, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. C.Y. Kwan, Clarence, 1999. "A note on market-neutral portfolio selection," Journal of Banking & Finance, Elsevier, vol. 23(5), pages 773-800, May.
    2. Rambaud, Salvador Cruz & Pérez, José García & Sánchez Granero, Miguel Ángel & Trinidad Segovia, Juan Evangelista, 2009. "Markowitz's model with Euclidean vector spaces," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1245-1248, August.
    3. Levy, Moshe & Ritov, Yaacov, 2001. "Portfolio Optimization with Many Assets: The Importance of Short-Selling," University of California at Los Angeles, Anderson Graduate School of Management qt41x4t67m, Anderson Graduate School of Management, UCLA.
    4. Ravi Kashyap, 2024. "The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments," Papers 2407.09536, arXiv.org.
    5. Kwan, Clarence C. Y., 1995. "Optimal portfolio selection under institutional procedures for short selling," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 871-889, August.
    6. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    7. Bick, Avi, 2004. "The mathematics of the portfolio frontier: a geometry-based approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 337-361, May.
    8. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    9. Muhinyuza, Stanislas & Bodnar, Taras & Lindholm, Mathias, 2020. "A test on the location of the tangency portfolio on the set of feasible portfolios," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    10. Shuzhen Yang, 2019. "A varying terminal time mean-variance model," Papers 1909.13102, arXiv.org, revised Jan 2020.
    11. Felix Fie{ss}inger & Mitja Stadje, 2024. "Mean-Variance Optimization for Participating Life Insurance Contracts," Papers 2407.11761, arXiv.org.
    12. Zied Ftiti & Aviral Tiwari & Amél Belanès & Khaled Guesmi, 2015. "Tests of Financial Market Contagion: Evolutionary Cospectral Analysis Versus Wavelet Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 575-611, December.
    13. C.F. Sirmans & Elaine Worzala, 2003. "International Direct Real Estate Investment: A Review of the Literature," Urban Studies, Urban Studies Journal Limited, vol. 40(5-6), pages 1081-1114, May.
    14. Chiu-Ming Hsiao, 2022. "Economic Growth, CO 2 Emissions Quota and Optimal Allocation under Uncertainty," Sustainability, MDPI, vol. 14(14), pages 1-26, July.
    15. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Portfolio selection with a drawdown constraint," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3171-3189, November.
    16. Min Dai & Zuo Quan Xu & Xun Yu Zhou, 2009. "Continuous-Time Markowitz's Model with Transaction Costs," Papers 0906.0678, arXiv.org.
    17. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    18. Matus Medo & Chi Ho Yeung & Yi-Cheng Zhang, 2008. "How to quantify the influence of correlations on investment diversification," Papers 0805.3397, arXiv.org, revised Feb 2009.
    19. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    20. Peter Simmons & Yuanyuan Xie, 2013. "Financial Markets Around the Great Recession: East Meets West," Discussion Papers 13/29, Department of Economics, University of York.

    More about this item

    Keywords

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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:cbsfin:2001_002. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Lars Nondal (email available below). General contact details of provider: https://edirc.repec.org/data/cbschdk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.