A Reference Point Approach to Bi-Objective Dynamic Portfolio Optimization

Authors

DOI:

https://doi.org/10.7494/dmms.2009.3.2.73

Keywords:

Dynamic Portfolio, Mixed Integer Programming, Reference Point Method, Bi-Objective Optimization, Value-at-Risk

Abstract

The portfolio selection problem presented in this paper is formulated as a biobjective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize by reference point method the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used.

References

Alves M.J. & Clímaco J. (2007). A review of interactive methods for multiobjective integer and mixed-integer programming. European Journal of Operational Research, 180(1), pp. 99–115. DOI: https://doi.org/10.1016/j.ejor.2006.02.033.

Anagnostopoulos K.P. & Mamanis G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), pp. 1285–1297. DOI: https://doi.org/10.1016/j.cor.2009.09.009.

Benati S. & Rizzi R. (2007). A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem. European Journal of Operational Research, 176(1), pp. 423–434. DOI: https://doi.org/10.1016/j.ejor.2005.07.020.

Bowman V.J. Jr. (1976). On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. In: H. Thiriez & S. Zionts (Eds.), Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, 130. Berlin–Heidelberg: Springer, pp. 76–86. DOI: https://doi.org/10.1007/978-3-642-87563-2_5.

Ehrgott M. (2005). Multicriteria Optimization. 2nd ed. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/3-540-27659-9.

Esch L., Kieffer R., Lopez T., Berbé C., Damel P., Debay M. & Hannosset J.-F. (2005). Asset and Risk Management: Risk Oriented Finance. Chichester: John Wiley & Sons. DOI: https://doi.org/10.1002/9781118673515.

Fourer R., Gay D.M. & Kernighan B.W. (1990). A modeling language for mathematical programming. Management Science, 36(5), pp. 519–554. DOI: https://doi.org/10.1287/mnsc.36.5.519.

Gaivoronski A.A., Krylov S. & van der Wijst N. (2005). Optimal portfolio selection and dynamic benchmark tracking. European Journal of Operational Research, 163(1), pp. 115–131. DOI: https://doi.org/10.1016/j.ejor.2003.12.001.

Lin C.-C. (2009). Comments on “A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem”. European Journal of Operational Research, 194(1), pp. 339–341. DOI: https://doi.org/10.1016/j.ejor.2008.01.041.

Markowitz H.M. (1952). Portfolio selection. The Journal of Finance, 7(1), pp. 77–91. DOI: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x.

Markowitz H.M. (1991). Portfolio Selection: Efficient Diversification of Investments. 2nd ed. Cambridge, MA: Basil Blackwell. ISBN: 978-1-55786-108-5.

Nemhauser G.L. & Wolsey L.A. (1999). Integer and Combinatorial Optimization. New York: John Wiley & Sons. ISBN: 978-0-471-35943-2.

Ogryczak W. (2000). Multiple criteria linear programming model for portfolio selection. Annals of Operations Research, 97(1–4), pp. 143–162. DOI: https://doi.org/10.1023/A:1018980308807.

Sawik B. (2009a). Lexicographic and weighting approach to multi-criteria portfolio optimization by mixed integer programming. In: K.D. Lawrence & G. Kleinman (Eds.), Financial Modeling Applications and Data Envelopment Applications. Applications of Management Science, 13. Bingley: Emerald Group Publishing, pp. 3–18. DOI: https://doi.org/10.1108/S0276-8976(2009)0000013003.

Sawik B. (2009b). A multi-objective dynamic portfolio optimization with short selling variables. Paper presented at the INFORMS Annual Meeting, San Diego, CA, USA, October 11–14, 2009.

Sawik B. (2009c). A weighted-sum mixed integer program for bi-objective dynamic portfolio optimization. Automatyka, 13(2), pp. 563–571.

Sawik B. (2009d). A lexicographic approach for multi-objective dynamic portfolio optimization. Paper presented at the 23rd European Conference on Operational Research – EURO XXIII, Bonn, Germany, July 5–8, 2009.

Sawik B. (2009e). Portfolio optimization of a multi-period investment by mixed integer programming. In: H. Howaniec & W. Waszkielewicz (Eds.), Conditions of Development of Management Systems. Bielsko-Biała: University of Bielsko-Biała, pp. 112–120.

Sawik B. (2009f). A dynamic MIP approach to multi-objective portfolio optimization. Paper presented at the CORS–INFORMS International Meeting, Toronto, Canada, June 14–17, 2009.

Sawik B. (2009g). Bi-objective dynamic portfolio optimization by mixed integer programming. Paper presented at the 22nd Conference of the European Chapter on Combinatorial Optimization – ECCO XXII, Jerusalem, Israel, May 17–20, 2009.

Sawik B. (2008). A three-stage lexicographic approach for multi-criteria portfolio optimization by mixed integer programming. Przegląd Elektrotechniczny, 84(9), pp. 108–112.

Speranza M.G. (1993). Linear programming models for portfolio optimization. Finance, 14, pp. 107–123.

Steuer R.E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons. ISBN: 978-0-471-88846-8.

Young M.R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), pp. 673–683. DOI: https://doi.org/10.1287/mnsc.44.5.673.

Downloads

Published

2009-12-21

Issue

Section

Articles

How to Cite

Sawik, B. (2009). A Reference Point Approach to Bi-Objective Dynamic Portfolio Optimization. Decision Making in Manufacturing and Services, 3(2), 73-85. https://doi.org/10.7494/dmms.2009.3.2.73

Most read articles by the same author(s)