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An Algorithm for Portfolio Optimization with Transaction Costs

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Author Info

  • 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.

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File URL: http://dx.doi.org/10.1287/mnsc.1050.0418
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 51 (2005)
Issue (Month): 11 (November)
Pages: 1676-1688

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Handle: RePEc:inm:ormnsc:v:51:y:2005:i:11:p:1676-1688

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Related research

Keywords: convex programming; portfolio optimization; transaction costs;

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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. 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.
  3. 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.
  4. 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.

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