Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach
Abstract
:1. Introduction
2. L-R Fuzzy Numbers and Credibility Theory
2.1. L-R Power Fuzzy Numbers
2.2. Credibility Theory
- Definition 1.Credibility measure [61]. Let ξ be a fuzzy variable with membership function µ and x a real number. The credibility measure of a fuzzy event, characterised by ξ ≤ x, is defined by Equation (1).
- Definition 2.Expected value [61]. Let ξ be a fuzzy variable. Then the expected value of ξ is defined by Equation (2) provided that at least one of the two integrals is finite.
- Definition 3.Mean-absolute semi-deviation [64]. Let ξ be a fuzzy variable with finite expected value = . Its below-mean absolute semi-deviation is defined by Equation (4).
3. The Mean-Downside Risk-Socially Responsible Portfolio Selection Model
- : L-R fuzzy return of the i-th asset, that is, ,
- : L-R fuzzy ESG score of the i-th, that is, ,
- L-R fuzzy return of the portfolio, that is, ,
- expected return of the portfolio,
- : upper bound of the proportion invested in the i-th asset,
- : lower bound of the proportion invested in the i-th asset,
- k: the number of assets held in the portfolio,
- : the proportion of wealth invested in the i-th asset,
- : a binary variable indicating whether the i-th asset is contained in the portfolio. It takes value 1, if the i-th asset is included in the portfolio, otherwise it takes value 0.
3.1. Objective Functions
3.1.1. Return
3.1.2. ESG score
3.1.3. Risk
3.2. Real-World Constraints
- (i)
- Capital budget constraint on the assets is defined as
- (ii)
- Maximum number of assets held in the portfolio is defined as
- (iii)
- Maximal proportion of the capital that can be invested in a single asset is defined as
- (iv)
- Minimal proportion of the capital that can be invested in a single asset is defined as
- (v)
- No short selling of assets is defined as
4. Solution Methodology
5. Experimental Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Return | Risk | ESG Score | |
---|---|---|---|
Return | 1.000 | ||
Risk | 0.957 ** | 1.000 | |
ESG score | −0.614 ** | 0.449 ** | 1.000 |
VaR | Return | ESG Score | |
---|---|---|---|
SPDR Dow Jones ETF (DIA) | 0.0157 | 0.0426 | 0.6381 |
SR Optimal Portfolio | 0.0182 | 0.1433 | 0.7110 |
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García, F.; González-Bueno, J.; Oliver, J.; Riley, N. Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability 2019, 11, 2496. https://doi.org/10.3390/su11092496
García F, González-Bueno J, Oliver J, Riley N. Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability. 2019; 11(9):2496. https://doi.org/10.3390/su11092496
Chicago/Turabian StyleGarcía, Fernando, Jairo González-Bueno, Javier Oliver, and Nicola Riley. 2019. "Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach" Sustainability 11, no. 9: 2496. https://doi.org/10.3390/su11092496