The Impact of Transaction Costs on Rebalancing an Investment Portfolio in Portfolio Optimization

Authors: B. Marasović, S. Pivac, S. V. Vukasović

Abstract:

Constructing a portfolio of investments is one of the most significant financial decisions facing individuals and institutions. In accordance with the modern portfolio theory maximization of return at minimal risk should be the investment goal of any successful investor. In addition, the costs incurred when setting up a new portfolio or rebalancing an existing portfolio must be included in any realistic analysis. In this paper rebalancing an investment portfolio in the presence of transaction costs on the Croatian capital market is analyzed. The model applied in the paper is an extension of the standard portfolio mean-variance optimization model in which transaction costs are incurred to rebalance an investment portfolio. This model allows different costs for different securities, and different costs for buying and selling. In order to find efficient portfolio, using this model, first, the solution of quadratic programming problem of similar size to the Markowitz model, and then the solution of a linear programming problem have to be found. Furthermore, in the paper the impact of transaction costs on the efficient frontier is investigated. Moreover, it is shown that global minimum variance portfolio on the efficient frontier always has the same level of the risk regardless of the amount of transaction costs. Although efficient frontier position depends of both transaction costs amount and initial portfolio it can be concluded that extreme right portfolio on the efficient frontier always contains only one stock with the highest expected return and the highest risk.

Keywords: Croatian capital market, Fractional quadratic programming, Markowitz model, Portfolio optimization, Transaction costs.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1099840

References:

[1] C. J. Adcock, and N. Meade, “A simple algorithm to incorporate transactions costs in quadratic optimization,” European Journal of Operational Research, vol. 79, no. 1, 1994, pp. 85-94.
[2] Z. Aljinović, B. Marasović, and N. Tomić-Plazibat, “The selection of the optimal portfolio on the Croatian capital market,” in Proceedings of Sixth International Conference on Enterprise in Transition, May 2005. pp. 299-301.
[3] Z. Aljinović, B. Marasović, B. Šego, Financijsko modeliranje. Ekonomski fakultet u Splitu, Split, 2011.
[4] A. Bouri, J. M. Martel and H. Chabchoub, “A Multi-criterion approach for selecting attractive portfolio,” Journal of Multi-Criteria Decision Analysis, vol. 11, 2002, pp. 269-277.
[5] T. J. Chang, N. Meade, J. E. Beasley and Y. M. Sharaiha, “Heuristics for cardinality constrained portfolio optimization,” Computers and Operations Research, vol. 27, 2000, pp. 1271-1302.
[6] A. Charnes and W. W. Cooper, “Programming with linear fractional functionals,” Naval Research Logistics Quarterly, vol. 9, 1962, pp. 181- 186.
[7] O. L. V. Costa and A. C. Paiva, “Robust portfolio selection using linearmatrix inequalities,” Journal of Economic Dynamics and Control, vol. 26, 2002, pp 889-909.
[8] E. De Giorgi, “A Note on Portfolio Selection under Various Risk Measures”, Working Paper, no. 9, National Centre of Competence in Research Financial Valuation and Risk Management, 2002. http://www.nccr-finrisk.unizh.ch/media/pdf/wp/WP009_3.pdf
[9] N. Khoury, J. M. Martel and M. Veilleux, “Methode multicritere de selection de portefeuilles indiciels interantionaux,“ Acualite Economique vol. 69, no. 1, 1993, pp. 171–190.
[10] H. Konno, H. Waki and A. Yuuki, “Portfolio optimization under lower partial risk measures,” Financial Engineering and the Japanese Markets, vol. 9, no. 2, 2002, pp. 127-140.
[11] B. Marasović, Z. Babić, “Two-step multi-criteria model for selecting optimal portfolio,” International Journal of Production Economics, vol. 134, 2011, pp. 58-66.
[12] H. M. Markowitz, “Portfolio Theory,” Journal of Finance, vol. 7, 1952, pp. 77-91.
[13] H. M. Markowitz and P. Todd, Mean-Variance Analysis in Portfolio Choice and Capital Markets. John Wiley & Sons, 2000.
[14] J. E. Mitchell and S. Braun, Rebalancing an Investment Portfolio in the Presence of Transaction Costs, Working Paper, Department of Rensselaer Polytechnic Institute, 2002.
[15] W. Ogryczak, “Multiple criteria linear programming model for portfolio selection,” Annals of Operations Research, vol. 97, 2000, pp. 143-162.
[16] R. T. Rockafaller and S. Uryasev, “Optimization of Conditional Valueat- Risk,” Journal of Risk, vol. 2, 2000, pp. 21-41.
[17] B. Škarica and Z. Lukač, “A Comparison of Basic and Extended Markowitz Model on Croatian Capital Market”, Croatian Operational Research Review, vol. 3, 2012, pp. 236-245.
[18] P. Venkataraman, Applied Optimization with MATLAB Programming, John Wiley & Sons, 2002.
[19] The Zagreb Stock Exchange. History Trading 2011 and 2012. http://zse.hr/default.aspx?id=44101&index=CROBEX10 (Accessed July 2013).
[20] S. A. Zenios, “Asset/liability management under uncertainty for fixed income securities,” Annals of Operations Research, vol. 59, 1995, pp. 77-98, reprinted in World Wide Asset and Liability Modeling, editors: W. T. Ziemba and J. M. Mulvey, Cambridge University Press, 1998.
[21] C. Zopounidis, “Multicriteria decision aid in financial management,” European Journal of Operational Research, vol. 119, 1999, pp. 404– 415.
[22] Poslovni dnevnik. http://www.poslovni.hr/burze/brokeri-u-hrvatskoj-sukonkurentniji- od-slovenskih-evo-zasto-222728 (Accessed Oct. 2013).