IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i3d10.1007_s10957-007-9252-7.html
   My bibliography  Save this article

An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 1: Theory

Author

Listed:
  • M. J. Best

    (University of Waterloo)

  • J. Hlouskova

    (Institute for Advanced Studies)

Abstract

A portfolio optimization problem consists of maximizing an expected utility function of n assets. At the end of a typical time period, the portfolio will be modified by buying and selling assets in response to changing conditions. Associated with this buying and selling are variable transaction costs that depend on the size of the transaction. A straightforward way of incorporating these costs can be interpreted as the reduction of portfolios’ expected returns by transaction costs if the utility function is the mean-variance or the power utility function. This results in a substantially higher-dimensional problem than the original n-dimensional one, namely (2K+1)n-dimensional optimization problem with (4K+1)n additional constraints, where 2K is the number of different transaction costs functions. The higher-dimensional problem is computationally expensive to solve. This two-part paper presents a method for solving the (2K+1)n-dimensional problem by solving a sequence of n-dimensional optimization problems, which account for the transaction costs implicitly rather than explicitly. The key idea of the new method in Part 1 is to formulate the optimality conditions for the higher-dimensional problem and enforce them by solving a sequence of lower-dimensional problems under the nondegeneracy assumption. In Part 2, we propose a degeneracy resolving rule, address the efficiency of the new method and present the computational results comparing our method with the interior-point optimizer of Mosek.

Suggested Citation

  • M. J. Best & J. Hlouskova, 2007. "An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 563-581, December.
  • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9252-7
    DOI: 10.1007/s10957-007-9252-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9252-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-007-9252-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Michael J. Best & Jaroslava Hlouskova, 2005. "An Algorithm for Portfolio Optimization with Transaction Costs," Management Science, INFORMS, vol. 51(11), pages 1676-1688, November.
    2. Grauer, Robert R & Hakansson, Nils H, 1986. "A Half Century of Returns on Levered and Unlevered Portfolios of Stocks, Bonds, and Bills, with and without Small Stocks," The Journal of Business, University of Chicago Press, vol. 59(2), pages 287-318, April.
    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. Zhang, Wei-Guo & Xiao, Wei-Lin & Xu, Wei-Jun, 2010. "A possibilistic portfolio adjusting model with new added assets," Economic Modelling, Elsevier, vol. 27(1), pages 208-213, January.
    2. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2013. "Portfolio rebalancing with an investment horizon and transaction costs," Omega, Elsevier, vol. 41(2), pages 406-420.
    3. Areski Cousin & Jérôme Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Working Papers hal-04086378, HAL.
    4. Areski Cousin & J'er^ome Lelong & Tom Picard, 2023. "Mean-variance dynamic portfolio allocation with transaction costs: a Wiener chaos expansion approach," Papers 2305.16152, arXiv.org, revised Jun 2023.
    5. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    6. Jiuping Xu & Xiaoyang Zhou & Steven Li, 2011. "A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 530-552, September.
    7. Michael J. Best & Xili Zhang, 2011. "Degeneracy Resolution for Bilinear Utility Functions," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 615-634, September.

    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. Júnior, Antonio Marcos Duarte, 1997. "A Framework for the Active Management of a Global Currency Fund," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 17(2), November.
    2. Michael Best & Robert Grauer & Jaroslava Hlouskova & Xili Zhang, 2014. "Loss-Aversion with Kinked Linear Utility Functions," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 45-65, June.
    3. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
    4. Vasyl Golosnoy, 2010. "No-transaction bounds and estimation risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 487-493.
    5. Cumming, Douglas & Helge Haß, Lars & Schweizer, Denis, 2013. "Private equity benchmarks and portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3515-3528.
    6. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    7. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2013. "Portfolio rebalancing with an investment horizon and transaction costs," Omega, Elsevier, vol. 41(2), pages 406-420.
    8. Grauer, Robert R. & Hakansson, Nils H., 1995. "Stein and CAPM estimators of the means in asset allocation," International Review of Financial Analysis, Elsevier, vol. 4(1), pages 35-66.
    9. Grauer, Robert R., 2013. "Limiting losses may be injurious to your wealth," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5088-5100.
    10. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    11. Grauer, Robert R. & Shen, Frederick C., 2000. "Do constraints improve portfolio performance?," Journal of Banking & Finance, Elsevier, vol. 24(8), pages 1253-1274, August.
    12. J J Glen, 2011. "Mean-variance portfolio rebalancing with transaction costs and funding changes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 667-676, April.
    13. Michael J. Best & Xili Zhang, 2011. "Degeneracy Resolution for Bilinear Utility Functions," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 615-634, September.
    14. M. J. Best & J. Hlouskova, 2007. "An Algorithm for Portfolio Optimization with Variable Transaction Costs, Part 2: Computational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 531-547, December.
    15. Andrew Chen & Frank Fabozzi & Dashan Huang, 2012. "Portfolio revision under mean-variance and mean-CVaR with transaction costs," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 509-526, November.
    16. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2014. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 59292, London School of Economics and Political Science, LSE Library.
    17. Patrizia Beraldi & Antonio Violi & Massimiliano Ferrara & Claudio Ciancio & Bruno Antonio Pansera, 2021. "Dealing with complex transaction costs in portfolio management," Annals of Operations Research, Springer, vol. 299(1), pages 7-22, April.
    18. Michael J. Best & Robert R. Grauer, 2017. "Humans, Econs and Portfolio Choice," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-30, June.
    19. Blomvall, Jorgen & Lindberg, Per Olov, 2003. "Back-testing the performance of an actively managed option portfolio at the Swedish Stock Market, 1990-1999," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1099-1112, April.
    20. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2016. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 65486, London School of Economics and Political Science, LSE Library.

    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:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9252-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.