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A novel methodology for portfolio selection in fuzzy multi criteria environment using risk-benefit analysis and fractional stochastic
Department of Industrial Engineering, Yazd University, Yazd Iran |
This article proposes an efficient approach for solving portfolio type problems. It is highly suitable to help fund allocators and decision makers to set up appropriate portfolios for investors. Stock selection is based upon the risk benefits analysis using MADM approach in fuzzy environment. This sort of analysis allows decision makers to identify the list of acceptable portfolios where they can assign some portions of their asset to them. The purpose of this article is two folds; first, to introduce a methodology to select the list of stocks for investment purpose, and second, to employ a stochastic fractional programming model to assign money into selected stocks. This article proposes a hybrid methodology for finding an optimal or new optimal solution of the problem. This hybrid approach considers risks and benefits at the time of stocks prioritization. This is followed by solving a fractional programming to determine the percentages of the budget to be allocated to stocks while dealing with two sets of suitable and non-suitable stocks. For clarification purposes, a sample example problem is solved.
References:
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show all references
References:
[1] |
M. Abdel-Baset and I. M. Hezam, An improved flower pollination algorithm for ratio optimization problems, Applied Mathematics and Information Sciences Letters, 3 (2015). 83-91. |
[2] |
L. Adam, M. Branda, H. Heitsch and R. Henrion,
Solving joint chance constrained problems using regulation and benders' decomposition, Annals of Operations Research, 292 (2020), 683-709.
doi: 10.1007/s10479-018-3091-9. |
[3] |
A. Alinedjad and Y. Zare Mehrjerdi, A new approach for portfolio performance evaluation in MVS modeling using data envelopment analysis: (Case study: Iran stock market), Sharif Industrial Journal of Management and Industrial Engineering, 2013. |
[4] |
M. Amiri,
An integrated eigenvector-DEA-TOPSIS methodology for portfolio risk evaluation in the FOREX spot market, Expert Systems with Applications, 37 (2010), 509-516.
|
[5] |
M. Amiri, M. Shariatpanah and M. Benekar,
Optimal portfolio selection using multi criterion decision making, Journal of Securities Exchange, 11 (2010), 5-24.
|
[6] |
S. Amirian and M. Amiri, The effects of using fuzzy multi attributes approaches on selective portfolio returns in Tehran securities exchange market, in The 10th International Industrial Engineering Conference, Tehran University, Tehran, Iran, 2013. |
[7] |
H. Arsham and A. B. Kahn,
A complete algorithm for linear fractional programs, Computers & Mathematics with Applications, 20 (1990), 11-23.
doi: 10.1016/0898-1221(90)90344-J. |
[8] |
E. Babaee Tirkolaee, A. Mardani, Z. Dashtian, M. Soltani and G. W. Weber, A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design, Journal of Cleaner Production, 250 (2019). |
[9] |
A. Baykasoglu and I. Golcuk,
Development of a novel multiple-attribute decision making model via fuzzy cognitive maps and hierarchical fuzzy TOPSIS, Information Sciences, 301 (2015), 75-98.
|
[10] |
A. Baykasoglu and I. Golcuk,
Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS, Expert Systems with Applications, 70 (2017), 37-57.
|
[11] |
A. Baykasoglu, V. Kaplanoglu, Z. D. U. Durmusoglu and C. Sahin, Integrating fuzzy DEMATEL and fuzzy hierarchical TOPSIS methods for truck selection, Expert Systems with Applications, 40 (2013), 899-907. |
[12] |
M. S. Bazzara and C. M. Shetty, Nonlinear Programming, Theory and Algorithms, Wiley, New York, 1979. |
[13] |
S. K. Bhatt,
Equivalence of various linearization algorithms for linear fractional programming, ZOR-Methods and Models of Operations Research, 33 (1989), 39-43.
doi: 10.1007/BF01415516. |
[14] |
A. Bilbao-Terol, B. Pérez-Gladish, M. Arenas-Parra, M. Victoria and R. Ura,
Fuzzy compromise programming for portfolio selection, Applied Mathematics and Computations, 173 (2006), 251-264.
doi: 10.1016/j.amc.2005.04.003. |
[15] |
A. Biswas and K. Bose, Fuzzy goal programming approach for quadratic fractional bilevel programming, in Proceedings of the 2011 International Conference on Scientific Computing (CSC 2011), CSREA Press, Las Vegas, (2011), 143-149. |
[16] |
P. Brockett, William W. Abraham Charnes, Cooper Kuyuk Kwon and W. Timothy Ruefli, Chance Constrained Programming Approach to Empirical Analyses of Mutual Fund Investment Strategies, National Science Foundation under Grant SES 8722504 and by the IC., 1992. |
[17] |
G. F. Can and S. Demirok,
Universal usability evaluation by using an integrated fuzzy multi criteria decision making approach, International Journal of Intelligent Computing and Cybernetics, 12 (2019), 194-223.
|
[18] |
A. Charnes and W. W. Cooper,
Programming with linear fractional functions, Naval Research Logistics Quarterly, 9 (1962), 181-186.
doi: 10.1002/nav.3800090303. |
[19] |
A. Charnes and W. W. Cooper,
Chance-constrained Programming, Management Science, 6 (1962), 73-79.
doi: 10.1287/mnsc.6.1.73. |
[20] |
Z. Chen, S. Peng and A. Lisser,
A sparse chance constrained portfolio selection model with multiple constraints, Journal of Global Optimization, 77 (2020), 825-852.
doi: 10.1007/s10898-020-00901-3. |
[21] |
Z. Chen, S. Peng and J. Liu,
Data-driven robust chance constrained problems: a mixture model approach, J. Optim. Theory Appl., 179 (2018), 1065-1085.
doi: 10.1007/s10957-018-1376-4. |
[22] |
P. Chunhachinda, K. Dandapani, S. Hamid and A. J. Prakash,
Portfolio selection and skewness: Evidence from international stock markets, Journal of Banking and Finance, 21 (1997), 143-167.
|
[23] |
H. Dalman, An interactive fuzzy goal programming algorithm to solve decentralized bi-level multi-objective fractional programming problem, Available at http://sciencewise.info/media/pdf/1606.00927v1.pdf. |
[24] |
M. L. De Prado, R. Vince and Q. J. Zhu,
Optimal risk budgeting under a finite investment horizon, Risks, 7 (2019), 1-15.
|
[25] |
W. Dinkelbach,
On non-linear fractional programming, Management Science, 13 (1967), 492-498.
doi: 10.1287/mnsc.13.7.492. |
[26] |
M. Doumpos and Zo pounidis,
Multi-objective optimization models in finance and investment, Journal of Golobal optimization, 76 (2020), 243-244.
doi: 10.1007/s10898-019-00873-z. |
[27] |
M. D{ü}r, C. Khompatraporn and Z. B. Zabinsky,
Solving fractional problems with dynamic multistart improving hit-and-run, Ann. Oper. Res., 156 (2007), 25-44.
doi: 10.1007/s10479-007-0232-y. |
[28] |
D. Dutta, R. N. Tiwari and J. R. Rao,
Multiple objectives linear fractional programming, A Fuzzy Set Theoretic Approach, Fuzzy Sets and Systems, 52 (1992), 39-45.
doi: 10.1016/0165-0114(92)90034-2. |
[29] |
M. Elahi, M. Yousefi and Y. Zare Mehrjerdi,
Portfolio optimization with mean-variance approach using hunting search meta-heuristic algorithm, Financial Research Journal, 16 (2011), 37-56.
|
[30] |
S. Fallahpour, H. Safari and N. Omrani,
Portfolio selection using fuzzy logarithm modeling and PROMETE approach, Financial Strategic Management Journal, 2 (2013), 103-120.
|
[31] |
T. B. Farag, A Parametric Analysis on Multicriteria Integer Fractional Decision-Making Problems, PhD Thesis, Faculty of Science, Helwan University, Helwan, Egypt, 2012. |
[32] |
G. Guastaroba, R. Mansini and Sp eranza,
On the effectiveness of scenario generation techniques in single-period portfolio optimization, European Journal of Operational Research, 192 (2009), 500-511.
doi: 10.1016/j.ejor.2007.09.042. |
[33] |
P. Guo, X. Chen, M. Li and J. Li, Fuzzy chance constrained linear fractional programming approach for optimal water allocation, Stoch. Environ. Res. Risk Assess, (2014), 1601-1612. |
[34] |
S. N. Gupta,
A chance constrained approach to fractional programming with random numerator, Journal of Math. Model Algorithm, 24 (2009), 1-5.
doi: 10.1007/s10852-009-9110-8. |
[35] |
G. A. Hanasusanto, V. Roitch, D. Kuhn and W. Wiesemann,
Ambiguous joint chance constraints under mean and dispersion information, Oper. Res., 65 (2017), 751-767.
doi: 10.1287/opre.2016.1583. |
[36] |
K. Hassanlou,
A multi period portfolio selection using chance constrained programming, Decision Science Letters, 6 (2017), 221-232.
|
[37] |
I. M. Hezam, O. A. Raouf and Os ama Abdel,
Solving fractional programming problems using metaheuristic algorithms under uncertainty, Intern. J. Adv. Comput., 46 (2013c), 1261-1270.
|
[38] |
I. M. Hezam and O. A. Raouf,
Particle swarm optimization programming for solving complex variable fractional programming problems, International Journal of Engineering, 2 (2013), 123-130.
|
[39] |
M. Ivanova and L. Dospatleiv,
Application of Markowitz portfolio optimization on Bulgarian stock market from 2013 to 2016, International Journal of Pure and Applied Mathematics, 17 (2017), 291-307.
|
[40] |
J. Jia and J. S. Dyer,
A standard measure of risk and risk-value models, Management Science, 42 (1996), 1691-1705.
|
[41] |
H. Jiao, Y. Guo and P. Shen,
Global optimization of generalized linear fractional programming with nonlinear constraints, Appl. Math. Comput., 183 (2006), 717-728.
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Variants of Fuzzy | Authors and years | |
TOPSIS and MADM | of publications | |
1 | Fuzzy TOPSIS | Mirabi et al. (2012), |
Baykasoglu and Golcuk(2015) | ||
2 | Hierarchical fuzzy TOPSIS | Zare Mehrjerdi (2020), |
Baykasoglu (2013) | ||
3 | Type-2 fuzzy TOPSIS | Baykasoglu and |
Golcuk (2017) | ||
4 | Interval value fuzzy TOPSIS | Zare Mehrjerdi (2013) |
5 | Group DM Fuzzy TOPSIS | Wange (2008), |
Zare Mehrjerdi (2013) | ||
6 | AHP and Fuzzy AHP | Aydein Celen (2014) |
7 | ANP and Fuzzy ANP | Pahlavan et al. (2012), |
Amiri, M. (2010) | ||
8 | ELECTRE | Chen-Tung-Chen (2009), |
Thien Phue Ho Quang (2014) | ||
9 | Compromise Programming | Bilbao-Terol et al. (2006) |
10 | PROMEETHE | Fallahpour et al. (2014) |
Variants of Fuzzy | Authors and years | |
TOPSIS and MADM | of publications | |
1 | Fuzzy TOPSIS | Mirabi et al. (2012), |
Baykasoglu and Golcuk(2015) | ||
2 | Hierarchical fuzzy TOPSIS | Zare Mehrjerdi (2020), |
Baykasoglu (2013) | ||
3 | Type-2 fuzzy TOPSIS | Baykasoglu and |
Golcuk (2017) | ||
4 | Interval value fuzzy TOPSIS | Zare Mehrjerdi (2013) |
5 | Group DM Fuzzy TOPSIS | Wange (2008), |
Zare Mehrjerdi (2013) | ||
6 | AHP and Fuzzy AHP | Aydein Celen (2014) |
7 | ANP and Fuzzy ANP | Pahlavan et al. (2012), |
Amiri, M. (2010) | ||
8 | ELECTRE | Chen-Tung-Chen (2009), |
Thien Phue Ho Quang (2014) | ||
9 | Compromise Programming | Bilbao-Terol et al. (2006) |
10 | PROMEETHE | Fallahpour et al. (2014) |
CCP and its Variants | Authors and Years | |
rough variables | of publications | |
1 | CCP with random | Tavana, M., Khanjani, R., |
and Di Caprio, D. (2019) | ||
2 | CCP with multi period | Hassanlou, K. (2017) |
portfolio selection | ||
3 | Joint CCP and | Adam, L., Branda, M., Heitsch, |
Portfolio selection | H., and Henrion, R. (2018) | |
4 | CCP with Multi objective modeling | Miryekemani, S.A., Sadeh, |
of Portfolio selection and GA | E., Amini Sabegh, Z. (2017) | |
5 | Sparse CCP | Chen, Z., Peng, S., |
Portfolio selection | and Lisser, A. (2020). | |
6 | CCP and Robust and | Sengupta, R.N., |
reliable portfolio optimization | and Kumar, R. (2017). | |
7 | CCP and Data | Chen, Z., Peng, |
driven robust | S., Liu, J.(2018) | |
8 | Ambiguous joint CCP | Hanasusanto, G.A., Roitch, V., |
Kuhn, D., Wiesemann, W. (2017) | ||
9 | CCP and Type-2 fuzzy fractional | Zhou, C., Huang, G., |
integrated modeling | and Chen, J. (2019). | |
10 | CCP with a sparse model | Xu, F., Wang, M., Dai, |
Y.H., Xu, D. (2018) | ||
11 | CCP and Data | Alinedjad and Zare |
envelop analysis | Mehrjerdi (2013) | |
12 | CCP and Fuzzy computer | Liu (2009), |
simulation | Zare Mehrjerdi et al. (2010) |
CCP and its Variants | Authors and Years | |
rough variables | of publications | |
1 | CCP with random | Tavana, M., Khanjani, R., |
and Di Caprio, D. (2019) | ||
2 | CCP with multi period | Hassanlou, K. (2017) |
portfolio selection | ||
3 | Joint CCP and | Adam, L., Branda, M., Heitsch, |
Portfolio selection | H., and Henrion, R. (2018) | |
4 | CCP with Multi objective modeling | Miryekemani, S.A., Sadeh, |
of Portfolio selection and GA | E., Amini Sabegh, Z. (2017) | |
5 | Sparse CCP | Chen, Z., Peng, S., |
Portfolio selection | and Lisser, A. (2020). | |
6 | CCP and Robust and | Sengupta, R.N., |
reliable portfolio optimization | and Kumar, R. (2017). | |
7 | CCP and Data | Chen, Z., Peng, |
driven robust | S., Liu, J.(2018) | |
8 | Ambiguous joint CCP | Hanasusanto, G.A., Roitch, V., |
Kuhn, D., Wiesemann, W. (2017) | ||
9 | CCP and Type-2 fuzzy fractional | Zhou, C., Huang, G., |
integrated modeling | and Chen, J. (2019). | |
10 | CCP with a sparse model | Xu, F., Wang, M., Dai, |
Y.H., Xu, D. (2018) | ||
11 | CCP and Data | Alinedjad and Zare |
envelop analysis | Mehrjerdi (2013) | |
12 | CCP and Fuzzy computer | Liu (2009), |
simulation | Zare Mehrjerdi et al. (2010) |
Portfolio Application areas | Authors and Years of publications | |
1 | Multi-objective capital allocation | Mizgier, Kamil, J., Joseph M. |
for supplier development under risk | Pasia, Srinivas Talluri (2017) | |
2 | Multi-objective Optimization of Credit | Mizgier, Kamil J., Pasia, Joseph (2016), |
Capital Allocation in Financial Institutions | Doumpos, M., and Zopounidis, (2020 | |
3 | Large Scale Portfolio optimization | Qu, B.Y., Zhoi, Q., Xiao, J.M., |
using Multi-objective Programming | Liang, J.J., Suganthan, P.N (2017) | |
4 | Financial portfolio optimization, | Özceylan, Eren, Kabak, Mehmet, |
Bank portfolio management | Dağdeviren, Metin (2016), Soleymani, F., | |
monetary policy, economic uncertainty | and Paquet, E. (2020), Amirian, S., Amiri, | |
M. (2013), Udomrachtavanich, W. (2005) | ||
5 | Application of Markowitz portfolio | Ivanova, M., Dospatleiv, L. (2016) |
optimization on Bulgarian stock market | ||
6 | Behavioral portfolio selection | Simo-Kengne, B.D., Ababio, |
and optimization | K.A., Ur Koumba, J.M (2018) | |
7 | Scenario-based portfolio selection | Liesiö, J., Salo A. (2012) |
8 | Nonlinear bi-level programming approach | Ma, S. (2016) |
for product portfolio management | ||
9 | Effectiveness of scenario generation | Guastaroba, G., Mansini, |
techniques in single-period | R., Speranza, (2009) | |
portfolio optimization | ||
10 | Optimal risk budgeting under | De Prado, M.L., Vince, |
a finite investment horizon | R., and Zhu, Q.J. (2019) |
Portfolio Application areas | Authors and Years of publications | |
1 | Multi-objective capital allocation | Mizgier, Kamil, J., Joseph M. |
for supplier development under risk | Pasia, Srinivas Talluri (2017) | |
2 | Multi-objective Optimization of Credit | Mizgier, Kamil J., Pasia, Joseph (2016), |
Capital Allocation in Financial Institutions | Doumpos, M., and Zopounidis, (2020 | |
3 | Large Scale Portfolio optimization | Qu, B.Y., Zhoi, Q., Xiao, J.M., |
using Multi-objective Programming | Liang, J.J., Suganthan, P.N (2017) | |
4 | Financial portfolio optimization, | Özceylan, Eren, Kabak, Mehmet, |
Bank portfolio management | Dağdeviren, Metin (2016), Soleymani, F., | |
monetary policy, economic uncertainty | and Paquet, E. (2020), Amirian, S., Amiri, | |
M. (2013), Udomrachtavanich, W. (2005) | ||
5 | Application of Markowitz portfolio | Ivanova, M., Dospatleiv, L. (2016) |
optimization on Bulgarian stock market | ||
6 | Behavioral portfolio selection | Simo-Kengne, B.D., Ababio, |
and optimization | K.A., Ur Koumba, J.M (2018) | |
7 | Scenario-based portfolio selection | Liesiö, J., Salo A. (2012) |
8 | Nonlinear bi-level programming approach | Ma, S. (2016) |
for product portfolio management | ||
9 | Effectiveness of scenario generation | Guastaroba, G., Mansini, |
techniques in single-period | R., Speranza, (2009) | |
portfolio optimization | ||
10 | Optimal risk budgeting under | De Prado, M.L., Vince, |
a finite investment horizon | R., and Zhu, Q.J. (2019) |
Authors | Purpose of research | Solution methodology | |
1 | Dalman, H. (2016) | bi-level multi-objective fractional | Interactive fuzzy goal |
programming problem | programming algorithm | ||
2 | Xiao, L. (2010) | Solving linear fractional | Neural network method |
programming | |||
3 | Farag, T.B. (2012) | integer fractional | Parametric analysis |
decision-making problems | |||
4 | Hezam, I.M., | solving fractional programming | Meta-heuristic algorithms, |
Raouf MMH (2013) | problems and complex variable | Particle swarm optimization | |
Osama Abdel, Hezam | fractional programming | ||
IM, Raouf OA (2013) | |||
5 | Dür M, | Solving fractional problems | Dynamic multi-start |
Khompatraporn C, | improving hit-and-run | ||
Zabinsky ZB (2007) | |||
6 | Udhayakumar, | solving chance constrained | Simulation based |
et al. (2010) | fractional programming | genetic algorithm | |
7 | Sameeullah | Linear fractional | Genetic Algorithm |
et al. (2008) | programming. | ||
8 | Gupta (2009) | chance constrained approach | Convex programming |
to fractional programming | |||
with random numerator | |||
9 | Wang C-F, | linear fractional | Global optimization |
Shen P-P (2008) | programming | algorithm | |
10 | Biswas and | quadratic fractional | Goal programming |
Bose (2011) | bi-level programming. | approach | |
11 | Charnes and | converted the fractional | Linear programming |
Cooper (1962, 1973) | programming (FP) into | ||
equivalent linear | |||
programming | |||
12 | Pal (2003, 2013), | Fractional chance | Fuzzy modeling and goal |
Zare Mehrjerdi (2011) | constraint programming | programming approach | |
13 | Zhang, Li, | Two stage stochastic | Decision support system |
and Guo (2017) | chance constrained | ||
fractional programming | |||
14 | Zare Mehrjerdi | Linear fractional | Optimization |
and Faregh (2017), | programming Arsham | ||
(1990), Dutta (1992) | |||
15 | Amiri, M., | The effects of using fuzzy multi | Multi attribute decision |
Shariatpanah, | attributes approaches on selective | making | |
M., Benekar, | portfolio returns in Tehran | ||
M. (2010) | securities exchange market | ||
16 | Phuc Ho Quang, | Applications in Portfolio | Multiple criteria |
T. (2014) | Selection Problems | decision making | |
17 | Y. Simaan. (1997 | Estimation risk in | mean variance model |
portfolio selection | and the mean-absolute | ||
deviation model | |||
18 | Zhu, H., Hung, | Stochastic linear fractional | linear fractional |
G. H. (2011) | programming approach for | programming | |
sustainable waste management |
Authors | Purpose of research | Solution methodology | |
1 | Dalman, H. (2016) | bi-level multi-objective fractional | Interactive fuzzy goal |
programming problem | programming algorithm | ||
2 | Xiao, L. (2010) | Solving linear fractional | Neural network method |
programming | |||
3 | Farag, T.B. (2012) | integer fractional | Parametric analysis |
decision-making problems | |||
4 | Hezam, I.M., | solving fractional programming | Meta-heuristic algorithms, |
Raouf MMH (2013) | problems and complex variable | Particle swarm optimization | |
Osama Abdel, Hezam | fractional programming | ||
IM, Raouf OA (2013) | |||
5 | Dür M, | Solving fractional problems | Dynamic multi-start |
Khompatraporn C, | improving hit-and-run | ||
Zabinsky ZB (2007) | |||
6 | Udhayakumar, | solving chance constrained | Simulation based |
et al. (2010) | fractional programming | genetic algorithm | |
7 | Sameeullah | Linear fractional | Genetic Algorithm |
et al. (2008) | programming. | ||
8 | Gupta (2009) | chance constrained approach | Convex programming |
to fractional programming | |||
with random numerator | |||
9 | Wang C-F, | linear fractional | Global optimization |
Shen P-P (2008) | programming | algorithm | |
10 | Biswas and | quadratic fractional | Goal programming |
Bose (2011) | bi-level programming. | approach | |
11 | Charnes and | converted the fractional | Linear programming |
Cooper (1962, 1973) | programming (FP) into | ||
equivalent linear | |||
programming | |||
12 | Pal (2003, 2013), | Fractional chance | Fuzzy modeling and goal |
Zare Mehrjerdi (2011) | constraint programming | programming approach | |
13 | Zhang, Li, | Two stage stochastic | Decision support system |
and Guo (2017) | chance constrained | ||
fractional programming | |||
14 | Zare Mehrjerdi | Linear fractional | Optimization |
and Faregh (2017), | programming Arsham | ||
(1990), Dutta (1992) | |||
15 | Amiri, M., | The effects of using fuzzy multi | Multi attribute decision |
Shariatpanah, | attributes approaches on selective | making | |
M., Benekar, | portfolio returns in Tehran | ||
M. (2010) | securities exchange market | ||
16 | Phuc Ho Quang, | Applications in Portfolio | Multiple criteria |
T. (2014) | Selection Problems | decision making | |
17 | Y. Simaan. (1997 | Estimation risk in | mean variance model |
portfolio selection | and the mean-absolute | ||
deviation model | |||
18 | Zhu, H., Hung, | Stochastic linear fractional | linear fractional |
G. H. (2011) | programming approach for | programming | |
sustainable waste management |
MADM | MODM | Integrating | |
approaches | approaches | approaches | |
(1) risks and benefits | hierarchical | gp (this study) | this research |
analysis for portfolio | fuzzy topsis | ||
analysis | (hftopsis) (this study) | ||
(2) assessment of | this study | x | this study |
portfolio alternatives | |||
and prioritization | |||
of them | |||
portfolio analysis | optimization | madm and | |
approaches | modm integration | ||
approach |
MADM | MODM | Integrating | |
approaches | approaches | approaches | |
(1) risks and benefits | hierarchical | gp (this study) | this research |
analysis for portfolio | fuzzy topsis | ||
analysis | (hftopsis) (this study) | ||
(2) assessment of | this study | x | this study |
portfolio alternatives | |||
and prioritization | |||
of them | |||
portfolio analysis | optimization | madm and | |
approaches | modm integration | ||
approach |
Portfolio Risks | Descriptions |
Broker (C1) | Since investors in the developing countries have |
little access to brokers on the international markets so | |
the risk can be relatively high for investors. | |
Technical Analysis (C2) | Access to professional technical analysts |
is not a simple task. This because (1) there are not too | |
many of such analysts and (2) they are far less | |
experienced in this task in general. | |
Capital management (C3) | Capital management techniques are related |
to three categories of: Tools, Objectives and Costs. | |
More on these terminologies can be studied in | |
the work of Amiri, et al. (2010). | |
Trading System (C4) | A good on-line trading system with fast access to |
internet may help capital management to | |
access the main trading board and then buy or | |
sell as required. Most likely in developing countries the | |
internet access is not fast and always available for | |
political and social reasons as it is in many | |
middle eastern countries. | |
Technology (C5) | Due to the fact that foreign exchange is rapidly |
growing and will continue to do so and | |
reaching over 3 trillion dollars (Amiri et al. 2010), | |
hence we there is a need to spend more on | |
technology and expect a good level of risk at | |
any level of trading. | |
Trading Psychology (C6) | The most effective factors in trading |
psychology can be identified as: trading commitment, | |
personal trading style, personal discipline, | |
trading coach, courage, and familiar with the | |
secrets of successful traders. |
Portfolio Risks | Descriptions |
Broker (C1) | Since investors in the developing countries have |
little access to brokers on the international markets so | |
the risk can be relatively high for investors. | |
Technical Analysis (C2) | Access to professional technical analysts |
is not a simple task. This because (1) there are not too | |
many of such analysts and (2) they are far less | |
experienced in this task in general. | |
Capital management (C3) | Capital management techniques are related |
to three categories of: Tools, Objectives and Costs. | |
More on these terminologies can be studied in | |
the work of Amiri, et al. (2010). | |
Trading System (C4) | A good on-line trading system with fast access to |
internet may help capital management to | |
access the main trading board and then buy or | |
sell as required. Most likely in developing countries the | |
internet access is not fast and always available for | |
political and social reasons as it is in many | |
middle eastern countries. | |
Technology (C5) | Due to the fact that foreign exchange is rapidly |
growing and will continue to do so and | |
reaching over 3 trillion dollars (Amiri et al. 2010), | |
hence we there is a need to spend more on | |
technology and expect a good level of risk at | |
any level of trading. | |
Trading Psychology (C6) | The most effective factors in trading |
psychology can be identified as: trading commitment, | |
personal trading style, personal discipline, | |
trading coach, courage, and familiar with the | |
secrets of successful traders. |
Portfolio's Benefits | Descriptions |
Dividend (C7) | Dividend can be defined according to following formula |
where dai is the nominal annual revenue and Ph, i is the | |
highest price of asset i in the year before. | |
Dividend of a portfolio is defined as the weighted sum | |
of the dividends of individual stocks in the portfolio. | |
Short term and long | Some researchers considered short term and long term |
term returns (C8) | returns for 12 months performance and 36 months |
Related formulas for these performances are shown below where | |
price of asset i at periods |
|
The short term performance for asset |
|
The long term performance for asset i is as shown below | |
Liquidity (C9) | For a specific asset, liquidity is set to be a proportion |
of that asset which is called turnover rate. | |
Often investors prefer to deal with greater liquidity. | |
Standard and Poor's | Based upon the Standard & Poor fund services, |
Star Ranking (C10) | the performance ranking which is based on an annual |
basis is shown by star ranking. Taking |
|
of stars assigned to investment fund |
|
objective function for the problem under study. | |
where |
|
assigned to investment fund |
|
Financial System reporting | This means that accounting system is in good |
such as ERP system (C11) | health and organization deals with low risk to |
do stock trading. ERP financial systems are able to | |
report the status of the company in the right time | |
and at the right amount of information needed for | |
making right decisions. | |
Green Vision of | This vision of company indicates that |
the Company (C12) | risks are low and benefits are high. |
Portfolio's Benefits | Descriptions |
Dividend (C7) | Dividend can be defined according to following formula |
where dai is the nominal annual revenue and Ph, i is the | |
highest price of asset i in the year before. | |
Dividend of a portfolio is defined as the weighted sum | |
of the dividends of individual stocks in the portfolio. | |
Short term and long | Some researchers considered short term and long term |
term returns (C8) | returns for 12 months performance and 36 months |
Related formulas for these performances are shown below where | |
price of asset i at periods |
|
The short term performance for asset |
|
The long term performance for asset i is as shown below | |
Liquidity (C9) | For a specific asset, liquidity is set to be a proportion |
of that asset which is called turnover rate. | |
Often investors prefer to deal with greater liquidity. | |
Standard and Poor's | Based upon the Standard & Poor fund services, |
Star Ranking (C10) | the performance ranking which is based on an annual |
basis is shown by star ranking. Taking |
|
of stars assigned to investment fund |
|
objective function for the problem under study. | |
where |
|
assigned to investment fund |
|
Financial System reporting | This means that accounting system is in good |
such as ERP system (C11) | health and organization deals with low risk to |
do stock trading. ERP financial systems are able to | |
report the status of the company in the right time | |
and at the right amount of information needed for | |
making right decisions. | |
Green Vision of | This vision of company indicates that |
the Company (C12) | risks are low and benefits are high. |
Goal | |
Risks | |
Benefits |
Goal | |
Risks | |
Benefits |
Risks | Benefits | |
Risk1 (C1) | ||
Risk1 (C2) | ||
Risk1 (C3) | ||
Risk1 (C4) | ||
Risk1 (C5) | ||
Risk1 (C6) | ||
Ben1 (C7) | ||
Ben2 (C8) | ||
Ben3 (C9) | ||
Ben4 (C10) | ||
Ben5 (C11) | ||
Ben6 (C12) | ||
Weights |
Risks | Benefits | |
Risk1 (C1) | ||
Risk1 (C2) | ||
Risk1 (C3) | ||
Risk1 (C4) | ||
Risk1 (C5) | ||
Risk1 (C6) | ||
Ben1 (C7) | ||
Ben2 (C8) | ||
Ben3 (C9) | ||
Ben4 (C10) | ||
Ben5 (C11) | ||
Ben6 (C12) | ||
Weights |
Risk1(C1) | Risk2(C2) | Risk3(C3) | Risk4(C4) | Risk5(C5) | Risk6(C6) | |
Index funds | (48, 68, 86) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (43, 62, 78) | (48, 68, 84) |
Computer | (51, 71, 87) | (50, 70, 87) | (43, 63, 82) | (43, 63, 80) | (31, 49, 68) | (46, 66, 83) |
Durable goods | (50, 70, 87) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (24, 39, 58) | (27, 45, 63) |
Pharmaceutical | (53, 73, 89) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (31, 48, 66) | (38, 57, 74) |
Chip Industry | (49, 69, 86) | (50, 70, 87) | (34, 53, 71) | (43, 63, 80) | (30, 48, 67) | (28, 46, 65) |
Real States | (46, 66, 83) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (37, 55, 72) | (38, 56, 74) |
Life Insurance | (44, 64, 82) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (29, 47, 66) | (33, 51, 69) |
Health | (43, 63, 82) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (35, 53, 71) | (41, 59, 76) |
Insurance | ||||||
Tourism | (50, 70, 88) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (34, 52, 70) | (32, 49, 68) |
industry | ||||||
Auto industry | (50, 70, 87) | (50, 70, 87) | (36, 54, 72) | (43, 63, 80) | (33, 50, 68) | (37, 53, 70) |
Benefit1 | Benefit2 | Benefit3 | Benefit4 | Benefit5 | Benefit6 | |
(C7) | (C8) | (C9) | (C10) | (C11) | (C12) | |
Index funds | (58, 78, 94) | (50, 70, 87) | (55, 75, 93) | (63, 83, 96) | (63, 83, 97) | ((25, 41, 61) |
Computer | (48, 68, 85) | (47, 66, 84) | (51, 71, 87) | (45, 65, 82) | (48, 68, 85) | (40, 60, 78) |
Durable goods | (25, 42, 61) | (32, 49, 68) | (44, 63, 80) | (32, 49, 67) | (53, 73, 87) | (19, 35, 54) |
Pharmaceutical | (39, 57, 74) | (43, 61, 78) | (42, 62, 78) | (44, 63, 78) | (52, 72, 86) | (19, 33, 52) |
Chip Industry | (35, 53, 69) | (41, 59, 76) | (44, 63, 78) | (52, 71, 85) | (53, 73, 87) | (12, 26, 46) |
Real States | (35, 54, 72) | (37, 57, 74) | (20, 37, 56) | (21, 37, 56) | (53, 73, 88) | (16, 30, 49) |
Life Insurance | (46, 65, 81) | (47, 67, 82) | (21, 37, 57) | (33, 50, 68) | (53, 73, 87) | (42, 61, 78) |
Health | (43, 63, 79) | (46, 66, 82) | (30, 47, 64) | (26, 43, 61) | (54, 74, 88) | (22, 38, 57) |
Insurance | ||||||
Tourism | (47, 67, 82) | 47, 67, 82) | (22, 40, 59) | (40, 58, 73) | (53, 73, 87) | (27, 43, 62) |
industry | ||||||
Auto industry | (49, 68, 83) | (50, 69, 84) | (38, 56, 71) | (31, 48, 64) | (53, 73, 87) | (22, 38, 56) |
(43, 63, 82) | (50, 70, 87) | (34, 53, 71) | (43, 63, 80) | (24, 39, 58) | (27, 45, 63) | |
(58, 78, 94) | (50, 70, 87) | (55, 75, 93) | (63, 83, 96) | (63, 83, 97) | (42, 61, 78) |
Risk1(C1) | Risk2(C2) | Risk3(C3) | Risk4(C4) | Risk5(C5) | Risk6(C6) | |
Index funds | (48, 68, 86) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (43, 62, 78) | (48, 68, 84) |
Computer | (51, 71, 87) | (50, 70, 87) | (43, 63, 82) | (43, 63, 80) | (31, 49, 68) | (46, 66, 83) |
Durable goods | (50, 70, 87) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (24, 39, 58) | (27, 45, 63) |
Pharmaceutical | (53, 73, 89) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (31, 48, 66) | (38, 57, 74) |
Chip Industry | (49, 69, 86) | (50, 70, 87) | (34, 53, 71) | (43, 63, 80) | (30, 48, 67) | (28, 46, 65) |
Real States | (46, 66, 83) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (37, 55, 72) | (38, 56, 74) |
Life Insurance | (44, 64, 82) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (29, 47, 66) | (33, 51, 69) |
Health | (43, 63, 82) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (35, 53, 71) | (41, 59, 76) |
Insurance | ||||||
Tourism | (50, 70, 88) | (50, 70, 87) | (49, 69, 87) | (43, 63, 80) | (34, 52, 70) | (32, 49, 68) |
industry | ||||||
Auto industry | (50, 70, 87) | (50, 70, 87) | (36, 54, 72) | (43, 63, 80) | (33, 50, 68) | (37, 53, 70) |
Benefit1 | Benefit2 | Benefit3 | Benefit4 | Benefit5 | Benefit6 | |
(C7) | (C8) | (C9) | (C10) | (C11) | (C12) | |
Index funds | (58, 78, 94) | (50, 70, 87) | (55, 75, 93) | (63, 83, 96) | (63, 83, 97) | ((25, 41, 61) |
Computer | (48, 68, 85) | (47, 66, 84) | (51, 71, 87) | (45, 65, 82) | (48, 68, 85) | (40, 60, 78) |
Durable goods | (25, 42, 61) | (32, 49, 68) | (44, 63, 80) | (32, 49, 67) | (53, 73, 87) | (19, 35, 54) |
Pharmaceutical | (39, 57, 74) | (43, 61, 78) | (42, 62, 78) | (44, 63, 78) | (52, 72, 86) | (19, 33, 52) |
Chip Industry | (35, 53, 69) | (41, 59, 76) | (44, 63, 78) | (52, 71, 85) | (53, 73, 87) | (12, 26, 46) |
Real States | (35, 54, 72) | (37, 57, 74) | (20, 37, 56) | (21, 37, 56) | (53, 73, 88) | (16, 30, 49) |
Life Insurance | (46, 65, 81) | (47, 67, 82) | (21, 37, 57) | (33, 50, 68) | (53, 73, 87) | (42, 61, 78) |
Health | (43, 63, 79) | (46, 66, 82) | (30, 47, 64) | (26, 43, 61) | (54, 74, 88) | (22, 38, 57) |
Insurance | ||||||
Tourism | (47, 67, 82) | 47, 67, 82) | (22, 40, 59) | (40, 58, 73) | (53, 73, 87) | (27, 43, 62) |
industry | ||||||
Auto industry | (49, 68, 83) | (50, 69, 84) | (38, 56, 71) | (31, 48, 64) | (53, 73, 87) | (22, 38, 56) |
(43, 63, 82) | (50, 70, 87) | (34, 53, 71) | (43, 63, 80) | (24, 39, 58) | (27, 45, 63) | |
(58, 78, 94) | (50, 70, 87) | (55, 75, 93) | (63, 83, 96) | (63, 83, 97) | (42, 61, 78) |
Risk1 | Risk2 | Risk3 | Risk4 | Risk5 | Risk6 | Total | |
Index funds | 0.0258 | 0.0000 | 0.0915 | 0.0000 | 0.1420 | 0.1363 | 0.3956 |
Computer | 0.0405 | 0.0000 | 0.0573 | 0.0000 | 0.613 | 0.1249 | 0.2840 |
Durable goods | 0.0339 | 0.0000 | 0.0915 | 0.0000 | 0.0000 | 0.0000 | 0.1254 |
Pharmaceutical | 0.0471 | 0.0000 | 0.0915 | 0.0000 | 0.0533 | 0.0723 | 0.2642 |
Chip Industry | 0.0290 | 0.0000 | 0.0000 | 0.0000 | 0.0523 | 0.0072 | 0.0885 |
Real States | 0.0112 | 0.0000 | 0.0915 | 0.0000 | 0.0985 | 0.0656 | 0.2668 |
Life Insurance | 0.0032 | 0.0000 | 0.0915 | 0.0000 | 0.0461 | 0.0367 | 0.1775 |
Health | |||||||
Insurance | 0.0000 | 0.0000 | 0.0915 | 0.0000 | 0.0834 | 0.0891 | 0.2640 |
Tourism | |||||||
industry | 0.0356 | 0.0000 | 0.0915 | 0.0000 | 0.0778 | 0.0278 | 0.2326 |
Auto industry | 0.0339 | 0.0000 | 0.0070 | 0.0000 | 0.0667 | 0.0539 | 0.1616 |
Risk1 | Risk2 | Risk3 | Risk4 | Risk5 | Risk6 | Total | |
Index funds | 0.0258 | 0.0000 | 0.0915 | 0.0000 | 0.1420 | 0.1363 | 0.3956 |
Computer | 0.0405 | 0.0000 | 0.0573 | 0.0000 | 0.613 | 0.1249 | 0.2840 |
Durable goods | 0.0339 | 0.0000 | 0.0915 | 0.0000 | 0.0000 | 0.0000 | 0.1254 |
Pharmaceutical | 0.0471 | 0.0000 | 0.0915 | 0.0000 | 0.0533 | 0.0723 | 0.2642 |
Chip Industry | 0.0290 | 0.0000 | 0.0000 | 0.0000 | 0.0523 | 0.0072 | 0.0885 |
Real States | 0.0112 | 0.0000 | 0.0915 | 0.0000 | 0.0985 | 0.0656 | 0.2668 |
Life Insurance | 0.0032 | 0.0000 | 0.0915 | 0.0000 | 0.0461 | 0.0367 | 0.1775 |
Health | |||||||
Insurance | 0.0000 | 0.0000 | 0.0915 | 0.0000 | 0.0834 | 0.0891 | 0.2640 |
Tourism | |||||||
industry | 0.0356 | 0.0000 | 0.0915 | 0.0000 | 0.0778 | 0.0278 | 0.2326 |
Auto industry | 0.0339 | 0.0000 | 0.0070 | 0.0000 | 0.0667 | 0.0539 | 0.1616 |
Benefit 1 | Benefit 2 | Benefit 3 | Benefit 4 | Benefit 5 | Benefit 6 | Total | |
Index | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1343 | 0.1343 |
funds | |||||||
Computer | 0.0559 | 0.0196 | 0.234 | 0.1051 | 0.878 | 0.0037 | 0.2954 |
Durable | 0.2326 | 0.1246 | 0.0664 | 0.2157 | 0.0583 | 0.1876 | 0.8852 |
goods | |||||||
Pharmac- | 0.1257 | 0.0521 | 0.0767 | 0.1213 | 0.0678 | 0.2041 | 0.6477 |
eutical | |||||||
Chip | 0.1568 | 0.0635 | .0714 | 0.0686 | 0.0618 | 0.2742 | 0.6963 |
Industry | |||||||
Real | 0.1442 | 0.0765 | 0.2570 | 0.3141 | 0.0558 | 0.2351 | 1.0827 |
States | |||||||
Life | 0.0743 | 0.0185 | 0.2518 | 0.2083 | 0.0618 | 0.0000 | 0.6148 |
Insurance | |||||||
Health | |||||||
Insurance | 0.0897 | 0.0218 | 0.1796 | 0.2660 | 0.0523 | 0.1628 | 0.7720 |
Tourism | |||||||
industry | 0.0647 | 0.0185 | 0.2298 | 0.1562 | 0.0583 | 0.1182 | 0.6458 |
Auto | 0.0540 | 0.0033 | 0.1167 | 0.2304 | 0.0618 | 0.1672 | 0.6334 |
industry |
Benefit 1 | Benefit 2 | Benefit 3 | Benefit 4 | Benefit 5 | Benefit 6 | Total | |
Index | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.1343 | 0.1343 |
funds | |||||||
Computer | 0.0559 | 0.0196 | 0.234 | 0.1051 | 0.878 | 0.0037 | 0.2954 |
Durable | 0.2326 | 0.1246 | 0.0664 | 0.2157 | 0.0583 | 0.1876 | 0.8852 |
goods | |||||||
Pharmac- | 0.1257 | 0.0521 | 0.0767 | 0.1213 | 0.0678 | 0.2041 | 0.6477 |
eutical | |||||||
Chip | 0.1568 | 0.0635 | .0714 | 0.0686 | 0.0618 | 0.2742 | 0.6963 |
Industry | |||||||
Real | 0.1442 | 0.0765 | 0.2570 | 0.3141 | 0.0558 | 0.2351 | 1.0827 |
States | |||||||
Life | 0.0743 | 0.0185 | 0.2518 | 0.2083 | 0.0618 | 0.0000 | 0.6148 |
Insurance | |||||||
Health | |||||||
Insurance | 0.0897 | 0.0218 | 0.1796 | 0.2660 | 0.0523 | 0.1628 | 0.7720 |
Tourism | |||||||
industry | 0.0647 | 0.0185 | 0.2298 | 0.1562 | 0.0583 | 0.1182 | 0.6458 |
Auto | 0.0540 | 0.0033 | 0.1167 | 0.2304 | 0.0618 | 0.1672 | 0.6334 |
industry |
Risk1 | Risk2 | Risk3 | Risk4 | Risk5 | Risk6 | Total | |
Index funds | 0.0200 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0200 |
Computer | 0.0060 | 0.0000 | 0.0295 | 0.0000 | 0.0683 | 0.0086 | 0.1124 |
Durable goods | 0.0121 | 0.0000 | 0.0000 | 0.0000 | 0.1420 | 0.1363 | 0.2904 |
Pharmaceutical | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0785 | 0.0540 | 0.1324 |
Chip Industry | 0.0169 | 0.0000 | 0.0915 | 0.0000 | 0.0784 | 0.1265 | 0.3133 |
Real States | 0.0349 | 0.0000 | 0.0000 | 0.0000 | 0.0355 | 0.0612 | 0.1316 |
Life Insurance | 0.0436 | 0.0000 | 0.0000 | 0.0000 | 0.0847 | 0.0908 | 0.2190 |
Health | |||||||
Insurance | 0.0471 | 0.0000 | 0.0000 | 0.0000 | 0.0494 | 0.0401 | 0.1366 |
Tourism | |||||||
industry | 0.0106 | 0.0000 | 0.0000 | 0.0000 | 0.0531 | 0.1014 | 0.1651 |
Auto industry | 0.0121 | 0.0000 | 0.0831 | 0.0000 | 0.645 | 0.0747 | 0.2344 |
Risk1 | Risk2 | Risk3 | Risk4 | Risk5 | Risk6 | Total | |
Index funds | 0.0200 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0200 |
Computer | 0.0060 | 0.0000 | 0.0295 | 0.0000 | 0.0683 | 0.0086 | 0.1124 |
Durable goods | 0.0121 | 0.0000 | 0.0000 | 0.0000 | 0.1420 | 0.1363 | 0.2904 |
Pharmaceutical | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0785 | 0.0540 | 0.1324 |
Chip Industry | 0.0169 | 0.0000 | 0.0915 | 0.0000 | 0.0784 | 0.1265 | 0.3133 |
Real States | 0.0349 | 0.0000 | 0.0000 | 0.0000 | 0.0355 | 0.0612 | 0.1316 |
Life Insurance | 0.0436 | 0.0000 | 0.0000 | 0.0000 | 0.0847 | 0.0908 | 0.2190 |
Health | |||||||
Insurance | 0.0471 | 0.0000 | 0.0000 | 0.0000 | 0.0494 | 0.0401 | 0.1366 |
Tourism | |||||||
industry | 0.0106 | 0.0000 | 0.0000 | 0.0000 | 0.0531 | 0.1014 | 0.1651 |
Auto industry | 0.0121 | 0.0000 | 0.0831 | 0.0000 | 0.645 | 0.0747 | 0.2344 |
Benefit 1 | Benefit 2 | Benefit 3 | Benefit 4 | Benefit 5 | Benefit 6 | Total | |
Index | 0.2326 | 0.1246 | 0.2570 | 0.3141 | 0.0878 | 0.1346 | 1.1506 |
funds | |||||||
Computer | 0.1736 | 0.1039 | 0.2323 | 0.2053 | 0.0000 | 0.2697 | 0.9848 |
Durable | 0.0000 | 0.0000 | 0.1881 | 0.0975 | 0.0310 | 0.0827 | 0.3993 |
goods | |||||||
Pharmac- | 0.1049 | 0.0717 | 0.1780 | 0.1914 | 0.0214 | 0.0694 | 0.6369 |
eutical | |||||||
Chip | 0.0753 | 0.0605 | 0.1842 | 0.2444 | 0.272 | 0.0000 | 0.5915 |
Industry | |||||||
Real | 0.0858 | 0.0472 | 0.0000 | 0.0000 | 0.0329 | 0.0384 | 0.2042 |
States | |||||||
Life | 0.1565 | 0.1055 | 0.0025 | 0.1045 | 0.0272 | 0.2742 | 0.6705 |
Insurance | |||||||
Health | |||||||
Insurance | 0.1409 | 0.1020 | 0.0771 | 0.0466 | 0.0367 | 0.1067 | 0.5100 |
Tourism | |||||||
industry | 0.1658 | 0.1055 | 0.0249 | 0.1583 | 0.0310 | 0.1516 | 0.6372 |
Auto | 0.1774 | 0.1213 | 0.1403 | 0.0860 | 0.0272 | 0.1040 | 0.6562 |
industry |
Benefit 1 | Benefit 2 | Benefit 3 | Benefit 4 | Benefit 5 | Benefit 6 | Total | |
Index | 0.2326 | 0.1246 | 0.2570 | 0.3141 | 0.0878 | 0.1346 | 1.1506 |
funds | |||||||
Computer | 0.1736 | 0.1039 | 0.2323 | 0.2053 | 0.0000 | 0.2697 | 0.9848 |
Durable | 0.0000 | 0.0000 | 0.1881 | 0.0975 | 0.0310 | 0.0827 | 0.3993 |
goods | |||||||
Pharmac- | 0.1049 | 0.0717 | 0.1780 | 0.1914 | 0.0214 | 0.0694 | 0.6369 |
eutical | |||||||
Chip | 0.0753 | 0.0605 | 0.1842 | 0.2444 | 0.272 | 0.0000 | 0.5915 |
Industry | |||||||
Real | 0.0858 | 0.0472 | 0.0000 | 0.0000 | 0.0329 | 0.0384 | 0.2042 |
States | |||||||
Life | 0.1565 | 0.1055 | 0.0025 | 0.1045 | 0.0272 | 0.2742 | 0.6705 |
Insurance | |||||||
Health | |||||||
Insurance | 0.1409 | 0.1020 | 0.0771 | 0.0466 | 0.0367 | 0.1067 | 0.5100 |
Tourism | |||||||
industry | 0.1658 | 0.1055 | 0.0249 | 0.1583 | 0.0310 | 0.1516 | 0.6372 |
Auto | 0.1774 | 0.1213 | 0.1403 | 0.0860 | 0.0272 | 0.1040 | 0.6562 |
industry |
Rows | Stocks Names | Si* | Si- | Si*+Si- | Ci | Rank |
1 | Index funds | 0.5298 | 1.1707 | 1.7005 | 0.6884 | 1 |
2 | Computer | 0.5795 | 1.0972 | 1.6767 | 0.6544 | 2 |
3 | Durable goods | 1.0106 | 0.6897 | 1.7003 | 0.4056 | 8 |
4 | Pharmaceutical | 0.9119 | 0.7693 | 1.6812 | 0.4576 | 7 |
5 | Chip Industry | 0.7848 | 0.9048 | 1.6897 | 0.5355 | 3 |
6 | Real States | 1.3496 | 0.3359 | 1.6854 | 0.1993 | 10 |
7 | Life Insurance | 0.7922 | 0.8895 | 1.6817 | 0.5289 | 4 |
8 | Health Insurance | 1.0359 | 0.6466 | 1.6825 | 0.3843 | 9 |
9 | Tourism industry | 0.8784 | 0.8023 | 1.6808 | 0.4774 | 6 |
10 | Auto industry | 0.7950 | 0.8906 | 1.6856 | 0.5284 | 5 |
Rows | Stocks Names | Si* | Si- | Si*+Si- | Ci | Rank |
1 | Index funds | 0.5298 | 1.1707 | 1.7005 | 0.6884 | 1 |
2 | Computer | 0.5795 | 1.0972 | 1.6767 | 0.6544 | 2 |
3 | Durable goods | 1.0106 | 0.6897 | 1.7003 | 0.4056 | 8 |
4 | Pharmaceutical | 0.9119 | 0.7693 | 1.6812 | 0.4576 | 7 |
5 | Chip Industry | 0.7848 | 0.9048 | 1.6897 | 0.5355 | 3 |
6 | Real States | 1.3496 | 0.3359 | 1.6854 | 0.1993 | 10 |
7 | Life Insurance | 0.7922 | 0.8895 | 1.6817 | 0.5289 | 4 |
8 | Health Insurance | 1.0359 | 0.6466 | 1.6825 | 0.3843 | 9 |
9 | Tourism industry | 0.8784 | 0.8023 | 1.6808 | 0.4774 | 6 |
10 | Auto industry | 0.7950 | 0.8906 | 1.6856 | 0.5284 | 5 |
Rows | Stocks Names | Rank by Hierarchical TOPSIS | Rank by SWA |
1 | Index funds | 1 | 1 |
2 | Computer | 2 | 2 |
3 | Durable goods | 8 | 7 |
4 | Pharmaceutical | 7 | 8 |
5 | Chip Industry | 3 | 4 |
6 | Real States | 10 | 10 |
7 | Life Insurance | 4 | 3 |
8 | Health Insurance | 9 | 9 |
9 | Tourism industry | 6 | 6 |
10 | Auto industry | 5 | 5 |
Rows | Stocks Names | Rank by Hierarchical TOPSIS | Rank by SWA |
1 | Index funds | 1 | 1 |
2 | Computer | 2 | 2 |
3 | Durable goods | 8 | 7 |
4 | Pharmaceutical | 7 | 8 |
5 | Chip Industry | 3 | 4 |
6 | Real States | 10 | 10 |
7 | Life Insurance | 4 | 3 |
8 | Health Insurance | 9 | 9 |
9 | Tourism industry | 6 | 6 |
10 | Auto industry | 5 | 5 |
Security | 1 | 2 | 3 | 4 | 5 |
Security | 6 | 7 | 8 | 9 | 10 |
Fuzzy | |||||
Security | 1 | 2 | 3 | 4 | 5 |
Security | 6 | 7 | 8 | 9 | 10 |
Fuzzy | |||||
Values | 2.30 | 1.70 | 2.60 | 1.95 | 2.025 | 2.275 | 2.25 | 2.90 | 1.50 | 2.2 |
Values | 2.30 | 1.70 | 2.60 | 1.95 | 2.025 | 2.275 | 2.25 | 2.90 | 1.50 | 2.2 |
[1] |
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