Optimal Selection of Stock Portfolios Using Multi-Criteria Decision-Making Methods
Abstract
:1. Introduction
2. Research Literature
2.1. Modern Portfolio Theory
- Investors are risk-averse and have increasing expected utility, and the final utility curve of their wealth is decreasing;
- Investors choose their stock portfolio based on the average and variance of expected returns. Therefore, their indifference curves are a function of the expected rate of return and variance;
- Every investment option is infinitely divisible;
- Investors have a “one-period” “time” horizon, and this is the same for all investors;
- Investors prefer higher returns at a certain level of risk, and vice versa; for a certain level of return, they want the lowest risk (anti-recession assumption).
2.2. Portfolio and MCDM Approaches
2.3. Optimization Algorithms
2.4. MADM Approaches
2.4.1. TOPSIS
2.4.2. ARAS
2.4.3. Taxonomy Method
2.4.4. VIKOR
2.4.5. COPRAS
2.4.6. WASPAS
2.4.7. DEA Method
2.4.8. Mean Rank Method
Borda Count Method
Copeland Method
3. Research Method
3.1. Population
3.2. Evaluation Metrics
4. Findings
5. Discussion and Conclusions
Research Limitations
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Metric | Formula | |
---|---|---|
1 | Sales growth rate = | (Current period sales − prior period sales)/prior period sales |
2 | Net income growth rate = | (Current period net income − prior period net income)/prior period net income |
3 | EPS growth rate = | (Current period EPS − prior period EPS)/prior period EPS |
4 | EPS = | Net income/total number of shares |
5 | Net profit margin = | Net profits/net Sales |
6 | Operating margin = | Operating income/revenue (or sales) |
7 | ROA = | Net income/total assets |
8 | ROE = | Net income/total equity |
9 | Total asset turnover = | Net sales/total assets |
10 | Accounts receivable turnover = | Net sales/average account receivables |
11 | Inventory turnover = | Cost of goods sold/average inventories |
12 | Beta = | |
13 | Financial risk = | Total debts/total assets |
14 | Price to EPS = | Price per share EPS |
15 | Price to BVPS = | Price per share/total number of shares/equities |
Companies Numbers | VIKOR | COPRAS | TOPSIS | WASPAS | Taxonomy |
---|---|---|---|---|---|
1 | 2 | 24 | 6 | 23 | 1 |
2 | 11 | 19 | 13 | 22 | 12 |
3 | 16 | 14 | 19 | 9 | 11 |
4 | 5 | 7 | 4 | 3 | 3 |
5 | 10 | 5 | 5 | 6 | 4 |
6 | 24 | 16 | 12 | 20 | 24 |
7 | 4 | 10 | 22 | 5 | 16 |
8 | 20 | 15 | 16 | 14 | 19 |
9 | 22 | 22 | 24 | 24 | 22 |
10 | 18 | 21 | 17 | 17 | 14 |
11 | 15 | 11 | 11 | 11 | 6 |
12 | 7 | 1 | 1 | 1 | 21 |
13 | 21 | 9 | 9 | 19 | 20 |
14 | 8 | 20 | 18 | 7 | 9 |
15 | 12 | 4 | 3 | 10 | 7 |
16 | 3 | 23 | 20 | 15 | 15 |
17 | 13 | 8 | 8 | 13 | 13 |
18 | 14 | 12 | 21 | 18 | 17 |
19 | 19 | 3 | 7 | 12 | 18 |
20 | 1 | 6 | 10 | 2 | 2 |
21 | 23 | 2 | 2 | 16 | 23 |
22 | 6 | 18 | 23 | 8 | 5 |
23 | 9 | 13 | 15 | 4 | 8 |
24 | 17 | 17 | 14 | 21 | 10 |
Companies Numbers | Taxonomy | ARAS | WASPAS | TOPSIS | COPRAS | VIKOR | Mean Rank | Final Rank |
---|---|---|---|---|---|---|---|---|
1 | 1 | 3 | 23 | 6 | 24 | 2 | 9.8 | 6 |
2 | 12 | 9 | 22 | 13 | 19 | 11 | 14.3 | 17 |
3 | 11 | 14 | 9 | 19 | 14 | 16 | 13.8 | 14 |
4 | 3 | 6 | 3 | 4 | 7 | 5 | 4.6 | 2 |
5 | 4 | 15 | 6 | 5 | 5 | 10 | 7.5 | 4 |
6 | 24 | 21 | 20 | 12 | 16 | 24 | 19.5 | 23 |
7 | 16 | 22 | 5 | 22 | 10 | 4 | 13.1 | 13 |
8 | 19 | 4 | 14 | 16 | 15 | 20 | 14.6 | 19 |
9 | 22 | 12 | 24 | 24 | 22 | 22 | 21 | 24 |
10 | 14 | 18 | 17 | 17 | 21 | 18 | 17.5 | 21 |
11 | 6 | 13 | 11 | 11 | 11 | 15 | 11.1 | 8 |
12 | 21 | 2 | 1 | 1 | 1 | 7 | 5.5 | 3 |
13 | 20 | 17 | 19 | 9 | 9 | 21 | 15.8 | 20 |
14 | 9 | 11 | 7 | 18 | 20 | 8 | 12.1 | 11 |
15 | 7 | 19 | 10 | 3 | 4 | 12 | 9.1 | 5 |
16 | 15 | 8 | 15 | 20 | 23 | 3 | 14 | 16 |
17 | 13 | 10 | 13 | 8 | 8 | 13 | 10.8 | 7 |
18 | 17 | 23 | 18 | 21 | 12 | 14 | 17.5 | 22 |
19 | 18 | 24 | 12 | 7 | 3 | 19 | 13.8 | 15 |
20 | 2 | 5 | 2 | 10 | 6 | 1 | 4.3 | 1 |
21 | 23 | 1 | 16 | 2 | 2 | 23 | 11.1 | 9 |
22 | 5 | 16 | 8 | 23 | 18 | 6 | 12.6 | 12 |
23 | 8 | 20 | 4 | 15 | 13 | 9 | 11.5 | 10 |
24 | 10 | 7 | 21 | 14 | 17 | 17 | 14.3 | 18 |
Company 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | Total Wins | Borda Count | Difference between Wins and Losses | Copeland | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Company 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 17 | 5 | 15 | 4 | |
2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 14 | −8 | 15 | |
3 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 8 | 9 | −2 | 12 | |
4 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 19 | 3 | 17 | 3 | |
5 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 18 | 4 | 15 | 4 | |
6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | −21 | 20 | |
7 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 7 | 10 | −1 | 11 | |
8 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 6 | 11 | −6 | 14 | |
9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | −22 | 21 | |
10 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 14 | −13 | 18 | |
11 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 12 | 7 | 5 | 7 | |
12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 23 | 1 | 23 | 1 | |
13 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 3 | 14 | −12 | 17 | |
14 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 8 | 9 | 2 | 9 | |
15 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 15 | 6 | 10 | 5 | |
16 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 12 | −8 | 15 | |
17 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 11 | 8 | 5 | 7 | |
18 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 15 | −15 | 19 | |
19 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 13 | −9 | 16 | |
20 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 20 | 2 | 19 | 2 | |
21 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 8 | 9 | 7 | 6 | |
22 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 8 | 9 | 1 | 10 | |
23 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 11 | 8 | 3 | 8 | |
24 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 12 | −5 | 13 | |
Total losses | 2 | 11 | 10 | 2 | 3 | 21 | 8 | 12 | 22 | 16 | 7 | 0 | 15 | 6 | 5 | 13 | 6 | 17 | 13 | 1 | 1 | 7 | 8 | 10 | 216 |
Companies Number | Rank by Borda Count | Rank by Copeland | Rank by Mean Rank |
---|---|---|---|
1 | 5 | 4 | 6 |
2 | 14 | 15 | 17 |
3 | 9 | 12 | 14 |
4 | 3 | 3 | 2 |
5 | 4 | 4 | 4 |
6 | 16 | 20 | 23 |
7 | 10 | 11 | 13 |
8 | 11 | 14 | 19 |
9 | 16 | 21 | 24 |
10 | 14 | 18 | 21 |
11 | 7 | 7 | 8 |
12 | 1 | 1 | 3 |
13 | 14 | 17 | 20 |
14 | 9 | 9 | 11 |
15 | 6 | 5 | 5 |
16 | 12 | 15 | 16 |
17 | 8 | 7 | 7 |
18 | 15 | 19 | 22 |
19 | 13 | 16 | 15 |
20 | 2 | 2 | 1 |
21 | 9 | 6 | 9 |
22 | 9 | 10 | 12 |
23 | 8 | 8 | 10 |
24 | 12 | 13 | 18 |
Companies | Sales Growth (1) | Net Income Growth (2) | EPS Growth (3) | Net Profit Margin (4) | Operating Margin (5) | ROA (6) | ROE (7) | Total Assets Turnover (8) | Financial Risk (9) | β Coefficient (10) |
---|---|---|---|---|---|---|---|---|---|---|
1 | 1/9404 | 1/9611 | −1/9611 | 0/0074 | 0/0076 | 0/0430 | 0/2129 | 3/7761 | 0/7931 | 0/0399 |
4 | 0/5572 | 0/8219 | −0/0890 | 0/6213 | 0/6399 | 0/5423 | 0/8020 | 0/8728 | 0/3035 | 0/6841 |
5 | 0/9013 | 0/9935 | 0/9935 | 0/3286 | 0/3873 | 0/2339 | 0/7790 | 0/7118 | 0/6460 | 0/3720 |
12 | 0/1774 | 1/2144 | 1/2144 | −0/1549 | −0/1348 | −0/2298 | 0/0987 | 1/4829 | 0/9867 | 1/2314 |
20 | 0/8756 | 3/3155 | 3/3155 | 0/3543 | 0/4779 | 0/2550 | 0/5979 | 0/7197 | 0/4246 | 0/3366 |
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Jing, D.; Imeni, M.; Edalatpanah, S.A.; Alburaikan, A.; Khalifa, H.A.E.-W. Optimal Selection of Stock Portfolios Using Multi-Criteria Decision-Making Methods. Mathematics 2023, 11, 415. https://doi.org/10.3390/math11020415
Jing D, Imeni M, Edalatpanah SA, Alburaikan A, Khalifa HAE-W. Optimal Selection of Stock Portfolios Using Multi-Criteria Decision-Making Methods. Mathematics. 2023; 11(2):415. https://doi.org/10.3390/math11020415
Chicago/Turabian StyleJing, Dongmei, Mohsen Imeni, Seyyed Ahmad Edalatpanah, Alhanouf Alburaikan, and Hamiden Abd El-Wahed Khalifa. 2023. "Optimal Selection of Stock Portfolios Using Multi-Criteria Decision-Making Methods" Mathematics 11, no. 2: 415. https://doi.org/10.3390/math11020415
APA StyleJing, D., Imeni, M., Edalatpanah, S. A., Alburaikan, A., & Khalifa, H. A. E.-W. (2023). Optimal Selection of Stock Portfolios Using Multi-Criteria Decision-Making Methods. Mathematics, 11(2), 415. https://doi.org/10.3390/math11020415