IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v53y2012i3p681-709.html
   My bibliography  Save this article

A local relaxation method for the cardinality constrained portfolio optimization problem

Author

Listed:
  • Walter Murray

    ()

  • Howard Shek

    ()

Abstract

The NP-hard nature of cardinality constrained mean-variance portfolio optimization problems has led to a number of different algorithms with varying degrees of success in reaching optimality given limited computational resources and under the presence of strict time constraints present in practice. The proposed local relaxation algorithm explores the inherent structure of the objective function. It solves a sequence of small, local, quadratic-programs by first projecting asset returns onto a reduced metric space, followed by clustering in this space to identify sub-groups of assets that best accentuate a suitable measure of similarity amongst different assets. The algorithm can either be cold started using a suitable heuristic method such as the centroids of initial clusters or be warm started based on the last output. Results, using a basket of up to 3,000 stocks and with different cardinality constraints, indicates that the proposed algorithm can lead to significant performance gain over popular branch-and-cut methods. One key application of this algorithm is in dealing with large scale cardinality constrained portfolio optimization under tight time constraint, such as for the purpose of index tracking or index arbitrage at high frequency. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Walter Murray & Howard Shek, 2012. "A local relaxation method for the cardinality constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 53(3), pages 681-709, December.
  • Handle: RePEc:spr:coopap:v:53:y:2012:i:3:p:681-709
    DOI: 10.1007/s10589-012-9471-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-012-9471-1
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    4. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    5. Peter Reinhard Hansen & Zhuo Huang & Howard Howan Shek, 2012. "Realized GARCH: a joint model for returns and realized measures of volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 877-906, September.
    6. Hiroshi Konno & Rei Yamamoto, 2005. "Integer programming approaches in mean-risk models," Computational Management Science, Springer, vol. 4(4), pages 339-351, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:spr:coopap:v:70:y:2018:i:2:d:10.1007_s10589-018-9985-2 is not listed on IDEAS
    2. repec:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2447-x is not listed on IDEAS
    3. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-016-2111-x is not listed on IDEAS

    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:spr:coopap:v:53:y:2012:i:3:p:681-709. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.