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An Algorithm for Portfolio Optimization with Transaction Costs

Author

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  • Michael J. Best

    (Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada)

  • Jaroslava Hlouskova

    (Department of Economics and Finance, Institute for Advanced Studies, Stumpergasse 56, A-1060 Vienna, Austria)

Abstract

We consider the problem of maximizing an expected utility function of n assets, such as the mean-variance or power-utility function. Associated with a change in an asset's holdings from its current or target value is a transaction cost. This cost must be accounted for in practical problems. A straightforward way of doing so results in a 3n-dimensional optimization problem with 3n additional constraints. This higher dimensional problem is computationally expensive to solve. We present a method for solving the 3n-dimensional problem by solving a sequence of n-dimensional optimization problems, which accounts for the transaction costs implicitly rather than explicitly. The method is based on deriving the optimality conditions for the higher-dimensional problem solely in terms of lower-dimensional quantities. The new method is compared to the barrier method implemented in Cplex in a series of numerical experiments. With small but positive transaction costs, the barrier method and the new method solve problems in roughly the same amount of execution time. As the size of the transaction cost increases, the new method outperforms the barrier method by a larger and larger factor.

Suggested Citation

  • Michael J. Best & Jaroslava Hlouskova, 2005. "An Algorithm for Portfolio Optimization with Transaction Costs," Management Science, INFORMS, vol. 51(11), pages 1676-1688, November.
    • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:11:p:1676-1688
    DOI: 10.1287/mnsc.1050.0418
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    References listed on IDEAS

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    1. De Panne, C & Whinston, Andrew, 1969. "The Symmetric Formulation of the Simplex Method for Quadratic Programming," Econometrica, Econometric Society, vol. 37(3), pages 507-527, July.
    2. Robert R. Grauer & Nils H. Hakansson, 1993. "On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies," Management Science, INFORMS, vol. 39(7), pages 856-871, July.
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    Citations

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    Cited by:

    1. 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.
    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. Ying Fu & Kien Ng & Boray Huang & Huei Huang, 2015. "Portfolio optimization with transaction costs: a two-period mean-variance model," Annals of Operations Research, Springer, vol. 233(1), pages 135-156, October.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. David Bergman & Andre A. Cire, 2018. "Discrete Nonlinear Optimization by State-Space Decompositions," Management Science, INFORMS, vol. 64(10), pages 4700-4720, October.
    13. 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.
    14. Vasyl Golosnoy, 2010. "No-transaction bounds and estimation risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 487-493.
    15. 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.

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