Developing a robust portfolio rebalancing model by considering fundamental factors

Document Type : Research Note

Authors

1 Faculty of Industrial Engineering, K. N. Toosi University of Technology

2 Faculty of Industrial Engineering, K. N. Toosi University of Technology.

Abstract

Portfolio rebalancing is one of the most important parts of investment management. After forming a portfolio by an investor, due to changing prices in the market, the portfolio value deviates from its initial amount. Therefore, the investor must rebalance the investment portfolio to achieve their goal. On the other hand, the fundamental factors of companies do not remain constant over time due to reasons such as changes in the country's economic situation and changes in policies related to the purchase, production, and sale of the company’s products. Furthermore, to select the best stocks that are prone to grow, it is essential to pay attention to the fundamental factors of companies by examining important financial ratios, including net profit ratio, return on assets (ROA), return on equity ratio (ROE), debt ratio (DR) and other ratios. In this research, a multi-objective model for the portfolio rebalancing problem is developed to consider the fundamental factors of stocks. To include the fundamental factors to the model, the TOPSIS technique is applied. In addition, due to considering several goals in the model, multi-choice fuzzy ideal programming is used to solve the model. Also, due to the variety of investors' expectations and the uncertainty of some parameters, including the ratio P/E and expected stock return, the uncertainty in the parameters of the model has been taken into account and the model is formulated using Bertsimas and Sim's approach from robust optimization approaches. In addition, by adopting Constant Proportion Portfolio Insurance strategy (CPPI) and maintaining the stop loss in specific time periods such as three months, the developed model is solved using the real data of the Tehran Stock Exchange and its results have been analyzed. In summary, the results show that the return and the Sharp ratio of the proposed portfolio are better than the traditional models.

Keywords

Main Subjects


1. Najafi, A. B. and Aghaei, M., 2019. Proposing a
Portfolio Rebalancing Model for Small Investors.
Journal of Investment knowledge, 8(31), pp.317-
337. [In Persian].
2. Markowitz, H., 1952. Portfolio selection. The
journal of finance, 7(1), pp. 77-91.
https://doi.org/10.1111/j.1540-
6261.1952.tb01525.x
3. Markowitz, M., 1967. Portfolio Selection. Efficient
Diversification of Investments, Wiley, New York.
https://doi.org/10.2307/3006625.
4. Smith, K. V., 1967. A transition model for portfolio
revision. The Journal of Finance, 22(3), pp. 425-
439. https://doi.org/10.1111/j.1540-
6261.1967.tb02978.x.
5. Pogue, G. A., 1970. An extension of the Markowitz
portfolio selection model to include variable
transaction costs. The Journal of Finance, 22(5), pp.
1005-1027. https://doi.org/10.1111/j.1540-
6261.1970.tb00865.x.
6. Kumar, P., Panda, G. and Gupta, U. C., 2015.
Portfolio rebalancing model with transaction costs
using interval optimization. OPSEARCH, 52, pp.
827-860. https://doi.org/10.1007/s12597-015-0210-
0.
7. Woodside, M., Lucas, C. and Beasley, J. E., 2013.
Portfolio rebalancing with an investment horizon
and transaction costs. Omega, 41(2), pp. 406-420.
https://doi.org/10.1016/j.omega.2012.03.003.
8. Glen, J. J., 2011. Mean-variance portfolio
rebalancing with transaction costs and funding
changes. Journal of the Operational Research
Society, 62(4), pp. 667-676.
https://doi.org/10.1057/jors.2009.148.
9. Zandieh, M. and Mohaddesi, S. O., 2019. Portfolio
rebalancing under uncertainty using meta-heuristic
algorithm. International Journal of Operational
Research, 36(1), pp.12-29. https://doi.org/
10.1504/ijor.2019.102068.
10. Fang, Y., Lai, K. K. and Wang, S. Y., 2006. Portfolio
rebalancing model with transaction costs based on
fuzzy decision theory. European Journal of
Operational Research, 175(2), pp. 879-893.
https://doi.org/ 10.1016/j.ejor.2005.05.020.
11. Najafi, A. B. and Fazeli, E., 2015. The dualobjective model of index tracker portfolio review
considering transaction costs and solving it with
meta-heuristic algorithms. Financial Knowledge of
Securities Analysis, 7(24), pp. 79-95. [In Persian].
12. Tarczynski, W., 2014. Different variant of
fundamental portfolio. Folio Oeconomica
Stetinensia, 14(22), pp. 47-62.
https://doi.org/10.2478/foli-2014-0104.
13. Ghahtarani, A. and Najafi, A. A., 2013. Robust goal
programming for multi-objective portfolio selection
problem. Economic Modelling, 33, pp.588–592.
https://doi.org/10.1016/j.econmod.2013.05.006.
14. Khodamoradi, T., Salahi, M. and Najafi, A. A.,
2020. Robust ccmv model with short selling and
risk-neutral interest rate. Phys A Stat Mech Appl
124429.
https://doi.org/10.1016/j.physa.2020.124429.
15. Swain, P. and Ojha, A., 2021. Robust approach for
uncertain portfolio allocation problems under box
uncertainty. Recent trends in applied mathematics,
select proceedings of AMSE 2019, pp 347–35.
https://doi.org/10.1007/978-981-15-9817-3_23 .
16. Ghahtarani, A., Saif, A. and Ghasemi, A., 2022.
Robust portfolio selection problems: a
comprehensive review. Operational Research, 22,
pp. 3203–3264. https://doi.org/10.1007/s12351-
022-00690-5 .
17. Zadeh, L. A., 1965. Fuzzy sets. Information and
Control, 8, pp. 338–353.
https://doi.org/10.1016/S0019-9958(65)90241-X .
18. Narasimhan, R., 1980. Goal programming in a fuzzy
environment. Decision Sciences, 11, pp. 325–336.
مهندسی صنایع و مدیریت شریف، )زمستان 1403( ، دوره ی ،40 شماره ی ،2 صص،164-152. )یادداشت فنی(
164
https://doi.org/10.1111/j.1540-
5915.1980.tb01142.x.
19. Hannan, E. L., 1981. On fuzzy goal programming.
Decision Sciences, 12, pp. 522–531.
https://doi.org/10.1111/j.1540-
5915.1981.tb00102.x.
20. Kim, J. S. and Whang, K. M., 1998. A tolerance
approach to the fuzzy goal programming problems
with unbalanced triangular membership function.
European Journal of Operational Research, 107, pp.
614–624. https://doi.org/10.1016/S0377-
2217(96)00363-3.
21. Chang, C. T., 2008. Multi-choice goal
programming. The International Journal of
Management Science, 34 (4), pp. 389–396.
https://doi.org/10.1016/j.omega.2005.07.009 .
22. Chiang, L., Hocine, A., Kouaissah, N. and Zhuang,
Z. Y., 2020. Weighted-additive Fuzzy Multi Choice
Goal Programming (WA-FMCGP). European
Journal of Operational Research, 285, pp. 642-654.
https://doi.org/10.1016/j.ejor.2020.02.009.
23. Savage, A., 2010. Optimal Portfolio Rebalancing
Strategy: Evidence from Finnish Stocks. Lambert
Academic Publishing, English.
24. Cont, R. and Tankov, P., 2009. Constant proportion
portfolio insurance in the presence of jumps in asset
prices. Mathematical Finance, 19, pp. 379-401.
https://doi.org/10.1111/j.1467-9965.2009.00377.x .
25. Ahmadi, M., 2015. Preparation for capital market
principles test. Ariana Qalam Publications, Tehran,
Fourth edition. [In Persian].
26. Hwang, C. L. and Yoon, K. P., 1981. Multiple
attribute decision making. Methods and
27. Mirghafori, S. H. A., 2015. Multi-criteria decision
making methods. Academic Jihad Publications,
Tehran, First edition. [In Persian].
28. Mulvey, J. M., Vanderbei, R. J. and Zenios, S. A.,
1995. Robust optimization of large scale systems.
Operation Research, 43 (2), pp. 264–281.
https://doi.org/10.1287/opre.43.2.264.
29. Soyster, A., 1973. Convex programming with setinclusive constraints and applications to inexact
linear programming. Operations Research, 21, pp.
1154–1157. https://doi.org/10.1287/opre.21.5.1154.
30. Ben-Tal, A. and Nemirovski, A., 2000. Robust
solutions of linear programming problems
contaminated with uncertain data. Mathematical
Programming, 88, pp. 411–424.
https://doi.org/10.1007/PL00011380 .
31. Bertsimas, D. and Sim, M., 2003. Robust discrete
optimization and network flows. Mathematical
Programming, 98, pp. 49–71.
https://doi.org/10.1007/s10107-003-0396-4.
32. Bertsimas, D. and Sim, M., 2004. The price of
robustness. Operations Research, 52, pp. 35–53.
https://doi.org/10.1287/opre.1030.0065.
33. Konno, H. and Yamazaki, H., 1991. Mean-absolute
deviation portfolio optimization model and its
application to Tokyo stock market. Management
Science, 37, pp. 519–531.
https://doi.org/10.1287/mnsc.37.5.519.
34. Charnes, A. and Cooper, W. W., 1959. Chance
constrained programming. Management science,
6(1), pp. 73-79.
https://doi.org/10.1287/mnsc.6.1.73.