Document Type : Original Article


1 MSc., University of Yazd.

2 Ph.D., Tarbiat Modares University.

3 Assistant Professor, Tarbiat Modares University.


In the selection of a collection of investment assets, the expected utility of investor is determined via risk and return criteria. Regarding the uncertainty of the investor about the future, portfolio diversification is a common path towards risk reduction in investment problem. In this study, not only the Euclidean Distance Criterion (EDI) was introduced to be a measure of portfolio diversification, but also a multi-objective model was designed for portfolio selection. This model intended to maximize the return and diversification of portfolio, and also to minimize non-systematic risk of it.  Since this is a non-linear model and in terms of complexity is among "NP-hard", regarding the computational efficiency of the Genetic Algorithms (GA) in optimization, it was used for solving the model. Results from the implementation of the dual-objective model (return and diversification) and triple-objective model (return, diversification, and non-systematic risk) with multiple-repetition showed that the average return of the portfolio selected by perposed model was higher than the favorable level. Investigation into portfolio performance indices indicates the efficiency of the dual-objective model (return and diversification).


1. Agarwal, M. (2015). Developments in Mean-Variance Efficient Portfolio Selection. Published by Palgrave Macmillan.
2. Akbari, M., Zandieh, M., & Dorri, B. (2012). Scheduling part-time and mixed-skilled workers using genetic algorithm approach, Journal of Industrial Management Perspective, 7, 87-102, (In Persian).
3. Aslan, O., Kantar, M.Y. Usta, I. (2015). Genetic Algorithms for Solving Portfolio Allocation Models based on Relative-Entropy, Mean and Variance. Journal of Scientific Research and Development 2 (12), 7-12.
4. Carmichael, B., & Koumou, G. B., & Moran, K. (2015). Unifying Portfolio Diversification Measures Using Rao's Quadratic Entropy.CIRANO (Center for Interuniversity Researchand Analysis of Organizations) Working Papers.
5. Chang, Tun J., & Yang, S. C., & Chang, K. J. (2009). Portfolio optimization Problems in Different Risk Measures Using Genetic Algorithm. Expert Systems with Applications36 (7), 10529-10537.
6. Diyarbakırlıoğlu, E., & Satman, M. H. (2013). The Maximum Diversification Index. Journal of Asset Management14(6), 400-409.
7. El hachloufi, M., & Guennoun, Z., & Hamza, F. (2012). Stocks Portfolio Optimization Using Classification and Genetic Algorithms. Applied Mathematical Sciences, 6, pp. 4673-4684.
8. Eom, C., & Kim, Y. H., & Park, J., & Kaizoji, T. (2015). Effects of the Market Factor on Portfolio Diversification: The Case of Market Crashes. Investment Analysts Journal44(1), 71-83.
9. Farzi, S., & Shavazi, A. R., & Pandari, A. R. (2013). Using quantum-behaved particle swarm optimization for portfolio selection problem. International Arab Journal of Information Technology, 10(2), 111-119.
10. Francis, J. C., Kim, D. (2013). Modern Portfolio Theory: Foundations, Analysis, and New Developments. John Wiley & Sons.
11. Garkaz, M., & Abasi, E. & Moghadasi, M. (2010). Selecting and Optimizing the Portfolio Using the Genetic Algorithm Based on Different Definitions of Risk Portfolio, Journal of Industrial Management, 5(11), 115-136.
12. Hattingh, j.j. (2004).Portfolio management: The use of alternative investments for the purpose of diversification. Thesis. Rand Afrikaans University, Johannesburg.
13. Jones, C. P. (2008). Investments: Analysis and management, translation to Persian by Reza Tehrani, Asgar Noorbakhsh, Negah Danesh, Iran.
14. Kirchner, U., & Zunckel, C. (2011). Measuring Portfolio Diversification, Quantitative Finance Paper, No. 1102.4722.
15. Moutameni, A., & Sharifi, S.A. (2012). Propounding a Model for Portfolio Selection in Stock Exchange by Using of MCDM (Case Study: 50 Better Companies), Journal of Industrial Management Perspective, 5, 73-89, (In Persian).
16. Oh, K. J., & Kim, T. Y., & Min, S. (2005). Using Genetic Algorithm to Support Portfolio Optimization for Index Fund Management. Expert Systems with Application28(2), 371-379.
17. Oyenubi, A. (2016). Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation. Computational Economics, 1.
18. Pandari, A.R., & Azar, A., & Shavazi, A.R. (2012). Genetic algorithms for portfolio selection problem with non-linear objectives. African Journal of Business Management6, 6209-6216.
19. Parque, V., & Mabu, S., & Hirasawa, K., (2009). Global portfolio diversification by genetic relation algorithm. ICROS-SICE International Joint Conference (ICCAS-SICE 2009). 2567-2572.
20. Rahnama, R.F., & Nikoomaram, H., & Toloie, E.A., & Lotfi, H.F., & Bayat, M. (2015). Reviewing the efficiency of portfolio optimization based on a stable model with classical optimization in risk prediction and portfolio returns, Financial engineering and securities management, 6(22), 29-60.
21. Ravindran, A. (2009). Operations Research Methodologies. CRC Press Taylor & Francis Group.
22. Reily, F.K., & Brown, K.C. 2012. Investment analysis and portfolio management. 10th edition. South- Western College Publication
23. Rudin, A. M., & Morgan, S. (2006). A Portfolio Diversification Index. The Journal of Portfolio Management32(2), 81-89.
24. Shahrabadi, A. & Bashiri, N. (2015). Investment Management in the Stock Exchange, Exchange Sharing Publishing. (In Persian).
25. Sharpe, William F., Gordon J. Alexander. 1990. Investments. Fourth Edition, Prentice-Hall.
26. Stirling, A. (2006). On the economics and analysis of diversity.SPRU ElectronicWorking Paper, Number 28. University of Sussex.
27. Stirling, A. (2007). A general framework for analysing diversity in science, technology and society. Journal of the Royal Society Interface.
28. Taghizadeh, R., & Fazli, S. (2011). Corporate Performance Measurement Method using Grey Relation Analysis and Fuzzy TOPSIS, Journal of Industrial Management Perspective, 2, 125-150, (In Persian).
29. Terra, C. (2015), Principles of International Finance and Open Economy Macroeconomics: Theories, Applications, and Policies. Elsevier Academic Press.
30. Yibing, C., & Yong, S., & Xianhua W., & Lingling, Z. (2014). How Does Credit Portfolio Diversification Affect Banks’ Return and Risk? Evidence from Chinese Listed Commercial Banks. Technological and Economic Development of Economy20(2), 332–352.