Multiobjective Optimization of Investments of two Businesses in Ghana

Jones Akanyare1 and Stephen B. Twum2
1Department of Mathematics, University for Development Studies, Tamale, Ghana
2Department of Mathematics, C. K. Tedam University of Technology & Applied Sciences, Ghana
DOI- http://doi.org/10.37502/IJSMR.2022.5612

Abstract

Portfolio optimization is a major concern of individuals and businesses across the world for sustainable financial and economic management of their funds. This work, as the first part of a portfolio optimization study of two selected businesses in Ghana, is aimed at optimizing separately the investments of the two businesses, to maximize their returns and minimize their risks under their operational constraints. The problems, being multi-objective in character, were modeled with the expected returns on their investments and the variances/standard deviations of the returns over fixed periods of time as the objective functions. To ensure dimensional uniformity, the objective functions were normalized and the Weighted Sum scalarization method employed in MATLAB to find Pareto optimal solutions of the models, using data from the two businesses. The results reveal that weight variations do not necessarily lead to many varied or diversified Pareto optimal solutions. The three distinct Pareto optimal solutions obtained for one of the businesses, however, suggest that the business could make respectively about 104.45M, 15.70M, and 15.72M Ghana Cedis returns on its investments with risk to return margins of 0.225%, 1.77%, and 1.76% respectively. The other business with only two distinct Pareto optimal solutions could make 14.67M or 30.36M Ghana Cedis returns with the corresponding risk to return margins of 0.016% and 0.017% respectively. It is recommended therefore that the businesses could select the solution with the least risk to return margins for implementation. A second part of the work, which will be reported in another paper, would investigate the models under post-optimality analysis and the prospects for a joint investment by the two businesses.

Keywords: Bi-criteria Optimization, Investment, Risk, Return, Standard Deviation, Pareto Optimal Solution.

References

  • Qu B. Y., Zhou Q., Liang J. J., and Suganthan P. N. (2017) Large-Scale Portfolio Optimization using Multiobjective Evolutionary Algorithms and Preselection Methods, Hindawi Mathematical Problems in Engineering, https//doi.org/10.115/2017/4197914
  • Markowitz, H. “Portfolio selection,” The Journal of Finance, vol. 7, no. 1, pp. 77–91, 1952.
  • Souza J. D. and Megginson W. L. (2002) The Financial & Operating Performance of Privitized Firms during the 1990s, Wiley Online Library, https//doi.org/10.1111/0022-108200150
  • Markowitz H. M. (1959) Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons Inc.,New York.
  • Fama, E. F., & French, K. R. (2004). The Capital Asset Pricing Model : Theory and Evidence. 18(3), 25–46.
  • N. Kolm, R. Tutuncu, and F. J. Fabozzi (2014) “60 Years of ¨ portfolio optimization: practical challenges and current trends,” European Journal of Operational Research, vol. 234, no. 2, pp. 356 – 371.
  • Bagchi, T. P. (2014). Pareto-Optimal Solutions for Multi-objective Production Scheduling Problems, Lecture Notes in Computer Science, January 1993, pp 458 – 471.
  • Keshavarz, E., & Toloo, M. (2015). Efficiency status of a feasible solution in the Multi-Objective Integer Linear Programming problems: A DEA methodology. Applied Mathematical Modelling, 39(12), 3236–3247. https://doi.org/10.1016/j.apm.2014.11.032.
  • Ponsich, A. L. Jaimes, and C. A. C. Coello (2013) “A survey on multiobjective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications,” IEEE Transactions on Evolutionary Computation, vol. 17, no. 3, pp. 321–344.
  • Skolpadungket, K. Dahal, and N. Harnpornchai (2007) “Portfolio optimization using multi-objective genetic algorithms,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’07), pp. 516–523, Singapore, September 2007.
  • Vedarajan, L. C. Chan, and D. Goldberg (1997) “Investment portfolio optimization using genetic algorithms, Proceedings of the Late Breaking Papers at the Genetic Programming Conference, pp. 255–263.
  • Kamil, A. A, & Kwan, M. (2004). Extension of Markowitz Model for Portfolio Analysis. WSEAS Transactions on Mathematics, 3(3), pp 641–646.
  • Wagner, N. (2002). On a model of portfolio selection with benchmark. Journal of Asset Management, 3(1), 55–65. https://doi.org/10.1057/palgrave.jam.2240065
  • Pandey, M. (2012). Application of Markowitz model in analysing risk and return: A case study of bse stock. Risk Governance and Control: Financial Markets and Institutions, 2(1), 7–15. https://doi.org/10.22495/rgcv2i1art1
  • Miettinen, K., & Mäkelä, M. M. (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24(2), 193–213. https://doi.org/10.1007/s00291-001-0092-9
  • Marler, R., & Arora, J. (2004). Survey of Multi-Objective Optimization Methods for Engineering. Structural and Multidisciplinary Optimization, 26, 369–395. https://doi.org/10.1007/s00158-003-0368-6
  • Deb, Multi-Objective Optimization Using Evolutionary Algorithms (2001) John Wiley & Sons, West Sussex, UK.
  • Miettinen . K. M. (2000). Nonlinear Multiobjective Optimization, SIAM Review 42 (2) 339 – 341.
  • Ehrgott, M. (2008). Multiobjective Optimization. AI Magazine, 29(4), 47–57. https://doi.org/10.1609/aimag.v29i4.2198
  • Li and Q. Zhang (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II, IEEE Transactions on Evolutionary Computation, vol. 13, no. 2, pp. 284–302.
  • Marler, R. T., & Arora, J. S. (2010). The weighted sum method for multi-objective optimization : new insights. June. https://doi.org/10.1007/s00158-009-0460-7 .