The Quantitative Diversity Index in Multi-Objective Portfolio Model

Document Type : Original Article

Authors

1 Associate Prof., Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran. Pardis St. Molasadra Ave., Vanak Sq, Tehran 19395-1999, Iran

2 Ph.D. Candidate, Department of Financial Engineering, Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran. Pardis St. Molasadra Ave., Vanak Sq, Tehran 19395-1999, Iran

3 Assistant Prof., Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran.

Abstract

The primary purpose of investors is maximizing the utility that is characterized by two essential criteria include risk and return. Regarding investors' uncertainty about the future, one of the main ways to reduce risk is to diversify the investment portfolio. In this research, we proposed an index conducted by Euclidean distance for assessing portfolio diversity. Besides, we designed a multi-objective model to select optimal stock portfolios with considering value at risk (VaR), which is one of the critical indicators of unacceptable risk, portfolio Beta as systematic risk, and portfolio variance as unsystematic risk simultaneously. The model presented in this paper aims to maximize diversification while minimizing value at risk and stock risks. Furthermore, maximizing returns are considered as a limitation of this model. Since the proposed model is nonlinear and concerning computational complexity, it is NP-hard; therefore, we utilized the PSO and the GE metaheuristic algorithms that are improved for solving multi-objective problems to solve the model. The results of the model implementation in multiple iterations showed that the average yield of selected portfolios by the model is higher than the desirable condition. The evaluation of stock performance indicators also shows the satisfactory performance of the multi-objective model.

Keywords

References

Aluko, O. A., Fapetu, O., & Azeez, B. A. (2018). International portfolio diversification in the Nigerian stock market: A global financial crisis perspective. Future Business Journal, 4(2), 189-194.
Beaudreau, A. H., Chan, M. N., & Loring, P. A. (2018). Harvest portfolio diversification and emergent conservation challenges in an Alaskan recreational fishery. Biological Conservation, 222, 268-277.
Briere, M., Oosterlinck, K., & Szafarz, A. (2015). Virtual currency, tangible return: Portfolio diversification with bitcoin. Journal of Asset Management, 16(6), 365-373.
Chan Kim, W., Hwang, P., & Burgers, W. P. (1989). Global diversification strategy and corporate profit performance. Strategic management journal, 10(1), 45-57.
Chang, T. J., Yang, S. C., & Chang, K. J. (2009). Portfolio optimization problems in different risk measures using a genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537.
Chen, Y., Shi, Y., Wei, X., & Zhang, L. (2014). How does credit portfolio diversification affect banks’ return and risk? Evidence from Chinese listed commercial banks. Technological and Economic Development of Economy, 20(2), 332-352.
Dang, V. D. (2019). The effects of loan portfolio diversification on Vietnamese banks’ return. In International Econometric Conference of Vietnam (pp. 928-939). Springer, Cham.
Diyarbakırlıoğlu, E., & Satman, M. H. (2013). The maximum diversification index. Journal of Asset Management, 14(6), 400-409.
Eberhart, R., & Kennedy, J. (1995, October). A new optimizer using particle swarm theory. In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science (pp. 39-43). Ieee.
Francis, J. C., & Kim, D. (2013). Modern portfolio theory: Foundations, analysis, and new developments (Vol. 795). John Wiley & Sons.
Gagliardini, P., & Gouriéroux, C. (2013). Granularity adjustment for risk measures: Systematic vs unsystematic risks. International Journal of Approximate Reasoning, 54(6), 717-747.
Georgalos, K., Paya, I., & Peel, D. A. (2018). On the contribution of the Markowitz model of utility to explain risky choice in experimental research. Journal of Economic Behavior & Organization.
Holland, J. H. (1974). Erratum: Genetic algorithms and the optimal allocation of trials. SIAM Journal on Computing, 3(4), 326-326.
Jackwerth, J. C., & Slavutskaya, A. (2016). The total benefit of alternative assets to pension fund portfolios. Journal of Financial Markets, 31, 25-42.
Jadhao, G. and Chandra, A., (2017). Application of VIX and entropy indicators for portfolio rotation strategies. Research in International Business and Finance, 42, pp.1367-1371.
Jones, C. P. (2007). Investments: analysis and management. John Wiley & Sons.
Kajtazi, A., & Moro, A. (2019). The role of bitcoin in well diversified portfolios: A comparative global study. International Review of Financial Analysis, 61, 143-157.
Kalashnikov, V., Benita, F., López-Ramos, F., & Hernández-Luna, A. (2017). Bi-objective project portfolio selection in Lean Six Sigma. International Journal of Production Economics, 186, 81-88.
Kara, G., Özmen, A., & Weber, G. W. (2019). Stability advances in robust portfolio optimization under parallelepiped uncertainty. Central European Journal of Operations Research, 27(1), 241-261.
Kim, W., Kim, Y. M., Kim, T. H., & Bang, S. (2018). Multi-dimensional portfolio risk and its diversification: A note. Global Finance Journal, 35, 147-156.
Liu, W. (2018). Portfolio diversification across cryptocurrencies. Finance Research Letters.
Markowitz, H. M., & Todd, G. P. (2000). Mean-variance analysis in portfolio choice and capital markets (Vol. 66). John Wiley & Sons.
Oh, K. J., Kim, T. Y., & Min, S. (2005). Using genetic algorithm to support portfolio optimization for index fund management. Expert Systems with Applications, 28(2), 371-379.
Oloko, T. F. (2018). Portfolio diversification between developed and developing stock markets: The case of US and UK investors in Nigeria. Research in International Business and Finance, 45, 219-232.
Oyenubi, A. (2016). Diversification measures and the optimal number of stocks in a portfolio: An information theoretic explanation. Computational Economics, 1-29.
Paut, R., Sabatier, R., & Tchamitchian, M. (2019). Reducing risk through crop diversification: An application of portfolio theory to diversified horticultural systems. Agricultural Systems, 168, 123-130.
Platanakis, E., Sakkas, A., & Sutcliffe, C. (2019). Harmful diversification: Evidence from alternative investments. The British Accounting Review, 51(1), 1-23.
Pola, G. (2016). On entropy and portfolio diversification. Journal of Asset Management, 17(4), 218-228.
Reilly, F. K., & Brown, K. C. (2011). Investment analysis and portfolio management. Cengage Learning.
Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of risk, 2, 21-42.
Steinberg, J. B. (2018). International portfolio diversification and the structure of global production. Review of Economic Dynamics, 29, 195-215.
Taguchi, G. (1986). Introduction to quality engineering: designing quality into products and processes (No. 658.562 T3).
Zelany, M. (1974). A concept of compromise solutions and the method of the displaced ideal. Computers & Operations Research, 1(3-4), 479-496.
Iranian Journal of Finance
Volume 5, Issue 1
Winter 2021
Pages 122-146

Files

History

  • Receive Date: 13 December 2019
  • Revise Date: 13 December 2020
  • Accept Date: 24 January 2021

Share

How to cite

Statistics