Volume 2 Issue 2 pp. 225-236 Spring, 2011


A Portfolio Selection Using Fuzzy Analytic Hierarchy Process: A Case Study of Iranian pharmaceutical industry


Solmaz Ghazanfar Ahari, Nader Ghaffari-Nasab, Ahmad Makui, and Seyed Hassan Ghodsypour


Portfolio selection is one of the important problems encountered by any investor. The purpose of this paper is to solve a real stock portfolio selection problem in Iran. According to the uncertain environments in which financial decisions are made, most of the recent works in this field use fuzzy sets theory in order to incorporate these uncertainties into their analysis. The problem is to determine how to allocate a limited fund among the stocks of some pharmaceutical companies in Tehran stock exchange. For this purpose we apply two fuzzy analytic hierarchy process (FAHP) methods to this problem. Finally, the results obtained from the two methods are compared in terms of the solution quality.


DOI: 10.5267/j.ijiec.2010.03.001

Keywords: Fuzzy AHP, Portfolio Selection, Decision Making, Nonlinear Programming, Finance
References

Anagnostopoulos, K.P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables, Computers and Operations Research, 37(7), 1285-1297.

Buckley, J.J. (1985). Fuzzy hierarchical analysis, Fuzzy Sets and Systems, 17, 233–247.

Branke, J., Scheckenbach, B., Stein, M., Deb, K., & Schmeck, H. (2009). Portfolio optimization with an envelope-based multi-objective evolutionary algorithm, European Journal of Operational Research, 199 (3), 684-693.

Chang, D.-Y. (1996). Applications of the Extent Analysis Method on Fuzzy AHP, European Journal of Operational Research, 95, 649–655.

Enea, M., & Piazza, T. (2004). Project selection by constrained fuzzy AHP, Fuzzy Optimization and Decision Making, 3, 39–62.

Fortemps, F., & Roubens, M. (1996). Ranking and Defuzzification Methods Based on Area Compensation, Fuzzy Sets and Systems, 82, 319–330.

Gao, J., & Chu, Z. (2010). A new particle swarm optimisation based on MATLAB for portfolio selection problem, International Journal of Modelling, Identification and Control, 9(1-2), 206-211.

Giove, S., Funari, S., & Nardelli, C. (2006). An interval portfolio selection problem based on regret function, European Journal of Operational Research, 170(1), 253–264.

Grant, M., Boyd, S. (2009). www.stanford.edu/~boyd/cvxbook/.

Huang, J.-J., Tzeng, G.-H., & Ong, C.-S., (2006). A novel algorithm for uncertain portfolio selection, Applied Mathematics and Computation, 173(1), 350–359.

Lacagnina, V., & Pecorella, A. (2006). A stochastic soft constraints fuzzy model for a portfolio selection problem, Fuzzy Sets and Systems, 157(10), 1317–1327.

Inuiguchi, M & Ramik, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets and Systems, 111(1), 3–28.

Inuiguchi, M., & T. Tanino, T. (2000). Portfolio selection under independent possibilistic information, Fuzzy Sets and Systems, 115(1), 83–92.

Kahraman, C. (Ed.). (2008). Fuzzy multi-criteria decision making, Springer, New York.

Klir, G. J. (1997). Fuzzy Arithmetic with Requisite Constraints, Fuzzy Sets and Systems, 91, 165–175.

Markowitz, H. M. (1991). Foundations of portfolio theory, The Journal of Finance, 46(2), 469–477.

Mikhailov, L. (2000). A fuzzy programming method for deriving priorities in the analytic hierarchy process, Journal of Operational Research Society, 51, 341–349.

Ong, C.-S., Huang, J. J., & Tzeng, G.-T. (2005). A novel hybrid model for portfolio selection, Applied Mathematics and Computation, 169(2), 1195–1210.

Parra, M. A., Terol, A. B., & Uria, M. V. R. (2001). A fuzzy goal programming approach to portfolio selection, European Journal of Operational Research, 113(2), 287–297.

Ruoning, X., & Xiaoyan, Z. (1992). Extension of the Analytic Hierarchy Process in Fuzzy Environment, Fuzzy Sets and Systems, 52, 251–257.

Saaty, T.L. (1980). The Analytic Hierarchy Process, McGraw-Hill, New York.

Saaty, T.L., Rogers, P.C., & Bell, R. (1980). Portfolio selection through hierarchies, The Journal of Portfolio Management , 16–21.

Seçme, N.Y., Bayrakdaroǧlu, & A., Kahraman, C. (2009). Fuzzy performance evaluation in Turkish Banking Sector using Analytic Hierarchy Process and TOPSIS, Expert Systems with Applications, 36(9), 11699-11709.

Tanaka, H., & Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research, 114, 115–126.

Tanaka, H., Guo, P., & Türksen, I. B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Sets and Systems, 111(3), 387–397.

Terol, A. B., Gladish, B. P., Parra, M. A., & Uria, M. V. R. (2006). Fuzzy compromise programming for portfolio selection, Applied Mathematics and Computation, 173 (1), 251–264.

Tiryaki, F., & Ahlatcioğlu, B. (2009). Fuzzy portfolio selection using fuzzy analytic hierarchy process, Information Science, 179, 53-69.

Van Laarhoven, P. J. M., & Pedrycz, W. (1983). A Fuzzy Extension of Saaty’s Priority Theory, Fuzzy Sets and Systems, 11, 229–241.

Wang, S., & Zhu, S. (2002). On fuzzy portfolio selection problems, Fuzzy Optimization and Decision Making, 1, 361–377.

Xia, Y., Liu, B., Wang, S., & Lai, K.K. (2000). A model for portfolio selection with order of expected returns, Computers and Operations Research, 27 (5), 409–422.

Yang, J. (2009). Integrative performance evaluation for supply chain system based on logarithm triangular fuzzy number-AHP method, Kybernetes, 38(10), 1760-1770.

Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., & Nie, Z.-K. (2007). Possibilistic mean–variance models and efficient frontiers for portfolio selection problem, Information Sciences, 177(13), 2787–2801.