A New Mean-Risk Quality Portfolio Optimization Model
Keywords:
risk-quality, portfolio optimization model, reality constraints, genetic algorithms
Abstract
This paper introduces a new mean-risk quality portfolio optimization model, grounded in uncertainty theory. It assumes that the return of assets is an uncertain variable and utilizes data estimated by experts to test the model. The approach begins by using the expected value of return and risk quality to represent the return and risk of the portfolio respectively. A new risk measure, termed “risk quality,” is introduced, leading to the establishment of the mean-risk quality portfolio optimization model. Next, to more closely align with real financial markets, the paper integrates constraints reflecting realistic financial market characteristics. These include transaction costs, financing constraints, and threshold constraints. By doing so, it establishes a mean-risk quality model with minimized risk, providing a more robust portfolio optimization framework. Finally, both the basic mean-risk-quality model and the version incorporating realistic constraints are empirically analyzed using genetic algorithms. Sensitivity tests are conducted on the robust portfolio model with minimized risk to further validate its effectiveness.
References
Al-Nator, M. S., Al-Nator, S. V., & Kasimov, Y. F. (2020). Multi-period Markowitz model and optimal self-financing strategy with commission. Journal of Mathematical Sciences, 248(1), 33-45. https://doi.org/10.1007/s10958-020-04853-7
Baptista, A. M. (2012). Portfolio selection with mental accounts and background risk. Journal of Banking & Finance, 36(4), 968-980. https://doi.org/10.1016/j.jbankfin.2011.10.015
Chiu, W.-Y. (2022). Another look at portfolio optimization with mental accounts. Applied Mathematics and Computation, 419, 126851. https://doi.org/10.1016/j.amc.2021.126851
Das, S., Markowitz, H., Scheid, J., & Statman, M. (2010). Portfolio optimization with mental accounts. Journal of Financial and Quantitative Analysis, 45(2), 311-334. https://doi.org/10.1017/s0022109010000141
de Melo, M. K., Cardoso, R. T. N., & Jesus, T. A. (2022). Multi-objective dynamic optimization of investment portfolio based on model predictive control. SIAM Journal on Control and Optimization, 60(1), 104-123. https://doi.org/10.1137/20M1346420
de Melo, M. K., Cardoso, R. T. N., & Jesus, T. A. (2022). Multi-objective model predictive control for portfolio optimization with cardinality constraint. Expert Systems with Applications, 205, 117639. https://www.sciencedirect.com/science/article/pii/S0957417422009459
Deliktaş, D., & Ustun, O. (2022). Multi-objective genetic algorithm based on the fuzzy MULTIMOORA method for solving the cardinality constrained portfolio optimization. Applied Intelligence, 53(12), 14717-14743. https://doi.org/10.1007/s10489-022-04240-6
Guo, S., Gu, J. W., Fok, C. H., & Ching, W. K. (2023). Online portfolio selection with state-dependent price estimators and transaction costs. European Journal of Operational Research, 311(1), 333-353. https://www.sciencedirect.com/science/article/pii/S0377221723003454
Guo, W., Zhang, W., Liu, Y. J., & Xu, W. (2022). Modeling of linear uncertain portfolio selection with uncertain constraint and risk index. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4182793
Guo, X., Chan, R. H., Wong, W.-K., & Zhu, L. (2018). Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk. Risk Management, 21(2), 73-98. https://doi.org/10.1057/s41283-018-0043-2
Huang, X. (2012). A risk index model for portfolio selection with returns subject to experts’ estimations. Fuzzy Optimization and Decision Making, 11(4), 451-463. https://doi.org/10.1007/s10700-012-9125-x
Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284-296. https://doi.org/10.1016/j.amc.2015.12.018
Huang, X., & Di, H. (2020). Uncertain portfolio selection with mental accounts. International Journal of Systems Science, 51(12), 2079-2090. https://doi.org/10.1080/00207721.2019.1648706
Huang, X., & Ma, D. (2022). Uncertain mean-chance model for portfolio selection with multiplicative background risk. International Journal of Systems Science: Operations & Logistics, 10(1). https://doi.org/10.1080/23302674.2022.2158443
Hübner, G., & Lejeune, T. (2022). Portfolio choice and mental accounts: A comparison with traditional approaches. Finance, 43(1), 95-121. https://doi.org/10.3917/fina.431.0095
Indarwati, E., & Kusumawati, R. (2021). Estimation of the portfolio risk from conditional value at risk using Monte Carlo simulation. Jurnal Matematika, Statistika dan Komputasi, 17(3), 370-380. https://doi.org/10.20956/j.v17i3.11340
James, C. T. M. (1970). Models of capital budgeting, E-V vs E-S. Journal of Finance and Quantitative Analysis, 4(5), 657-675. https://www.jstor.org/stable/2330119
Jiang, G., Huang, X., & Yang, T. (2023). Multiple risks and uncertain portfolio management. International Journal of Information Technology & Decision Making, 1-29. https://doi.org/10.1142/S0219622023500190
Khanjani Shiraz, R., Tavana, M., & Fukuyama, H. (2020). A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk. Soft Computing, 24(22), 17167-17186. https://doi.org/10.1007/s00500-020-05010-7
Khodamoradi, T., & Salahi, M. (2022). Extended mean-conditional value-at-risk portfolio optimization with PADM and conditional scenario reduction technique. Computational Statistics, 38(2), 1023-1040. https://doi.org/10.1007/s00180-022-01263-y
Khodamoradi, T., Salahi, M., & Najafi, A. R. (2023). Multi-intervals robust mean-conditional value-at-risk portfolio optimisation with conditional scenario reduction technique. International Journal of Applied Decision Sciences, 16(2), 237. https://doi.org/10.1504/ijads.2023.129475
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), 519-531. https://doi.org/10.1287/mnsc.37.5.519
Lam, W. S., Lam, W. H., & Jaaman, S. H. (2021). Portfolio optimization with a mean–absolute deviation–entropy multi-objective model. Entropy, 23(10), 1266. https://doi.org/10.3390/e23101266
Li, B., & Huang, Y. (2023). Uncertain random portfolio selection with different mental accounts based on mixed data. Chaos, Solitons & Fractals, 168, 113198. https://doi.org/10.1016/j.chaos.2023.113198
Li, J. (2018). A mean-fuzzy random VaR portfolio selection model in hybrid uncertain environment. Uncertainty and Operations Research, 125–147. https://doi.org/10.1007/978-981-10-7817-0_13
Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Application, 1(1). https://doi.org/10.1186/2195-5468-1-1
Liu, B. (2014). Introduction. Springer Uncertainty Research, 1–8. https://doi.org/10.1007/978-3-662-44354-5_1
Liu, D. B. (2007). Uncertainty theory. Springer Berlin Heidelberg, 205-234. https://doi.org/10.1007/978-3-540-73165-8_5
Liu, Y., Zhou, Y., & Niu, J. (2023). Portfolio optimization: A multi-period model with dynamic risk preference and minimum lots of transaction. Finance Research Letters, 55, 103964. https://www.sciencedirect.com/science/article/pii/S1544612323003367
Lv, L., Zhang, B., Peng, J., & Ralescu, D. A. (2020). Uncertain portfolio selection with borrowing constraint and background risk. Mathematical Problems in Engineering, 2020, 1-13. https://doi.org/10.1155/2020/1249829
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://www.jstor.org/stable/2975974
Meng, X., & Shan, Y. (2021). A fuzzy mean semi-absolute deviation-semi-variance-proportional entropy portfolio selection model with transaction costs. Proceedings of the 2021 40th Chinese Control Conference (CCC). IEEE. https://doi.org/10.23919/ccc52363.2021.9550714
Pitera, M., & Stettner, Ł. (2023). Discrete‐time risk sensitive portfolio optimization with proportional transaction costs. Mathematical Finance, n/a(n/a). https://onlinelibrary.wiley.com/doi/abs/10.1111/mafi.12406
Primbs, J. A. (2018). Applications of MPC to finance. Control Engineering, 665–685. https://doi.org/10.1007/978-3-319-77489-3_27
Ramedani, A. M., Mehrabian, A., & Didehkhani, H. (2022). Sustainable project portfolio selection under uncertainty with consideration of conflicting projects. https://doi.org/10.21203/rs.3.rs-2128708/v1
Salahi, M., Khodamoradi, T., & Najafi, A. R. (2023). Multi-intervals robust mean-conditional value-at-risk portfolio optimization with conditional scenario reduction technique. International Journal of Applied Decision Sciences, 1(1), 1. https://doi.org/10.1504/ijads.2023.10045206
Siew, L. W. (2020). Portfolio optimization of financial companies with fuzzy TOPSIS-mean-semi absolute deviation model. Journal of Dynamic Control Systems, 12(SP4), 1488-1495. https://doi.org/10.5373/jardcs/v12sp4/20201627
Tversky, A., & Kahneman, D. (1986). Rational choice and the framing of decisions. Journal of Business, 59(4), S251-S278. https://www.jstor.org/stable/2352759
Uryasev, S., & Rockafellar, R. T. (2001). Conditional value-at-risk: Optimization approach. In S. Uryasev & P. M. Pardalos (Eds.), Stochastic optimization: Algorithms and applications (pp. 411-435). Springer US. https://doi.org/10.1007/978-1-4757-6594-6_17
Vukovic, D. B., Maiti, M., & Frömmel, M. (2022). Inflation and portfolio selection. Finance Research Letters, 50, 103202. https://www.sciencedirect.com/science/article/pii/S154461232200407X
Wang, X., & Huang, X. (2019). A risk index to model uncertain portfolio investment with options. Economic Modelling, 80, 284-293. https://doi.org/10.1016/j.econmod.2018.11.014
World Bank. (2021). Portfolio risk assessment using risk index. In World Bank (Ed.). https://doi.org/10.1596/35490
Yang, T., & Huang, X. (2022). Two new mean–variance enhanced index tracking models based on uncertainty theory. North American Journal of Economics and Finance, 59. https://doi.org/10.1080/23302674.2022.2158443
Yang, X. Y., Chen, S. D., Liu, W. L., & Zhang, Y. (2022). A multi-period fuzzy portfolio optimization model with short selling constraints. International Journal of Fuzzy Systems, 24(6), 2798-2812. https://doi.org/10.1007/s40815-022-01294-z
Zhang, J., & Li, Q. (2019). Credibilistic mean-semi-entropy model for multi-period portfolio selection with background risk. Entropy, 21(10), 944. https://doi.org/10.3390/e21100944
Zhang, J., Jin, Z., & An, Y. (2017). Dynamic portfolio optimization with ambiguity aversion. Journal of Banking & Finance, 79, 95-109. https://doi.org/10.1016/j.jbankfin.2017.03.007
Zhang, P. (2018). Multiperiod mean absolute deviation uncertain portfolio selection with real constraints. Soft Computing, 23(13), 5081-5098. https://doi.org/10.1007/s00500-018-3176-z
Baptista, A. M. (2012). Portfolio selection with mental accounts and background risk. Journal of Banking & Finance, 36(4), 968-980. https://doi.org/10.1016/j.jbankfin.2011.10.015
Chiu, W.-Y. (2022). Another look at portfolio optimization with mental accounts. Applied Mathematics and Computation, 419, 126851. https://doi.org/10.1016/j.amc.2021.126851
Das, S., Markowitz, H., Scheid, J., & Statman, M. (2010). Portfolio optimization with mental accounts. Journal of Financial and Quantitative Analysis, 45(2), 311-334. https://doi.org/10.1017/s0022109010000141
de Melo, M. K., Cardoso, R. T. N., & Jesus, T. A. (2022). Multi-objective dynamic optimization of investment portfolio based on model predictive control. SIAM Journal on Control and Optimization, 60(1), 104-123. https://doi.org/10.1137/20M1346420
de Melo, M. K., Cardoso, R. T. N., & Jesus, T. A. (2022). Multi-objective model predictive control for portfolio optimization with cardinality constraint. Expert Systems with Applications, 205, 117639. https://www.sciencedirect.com/science/article/pii/S0957417422009459
Deliktaş, D., & Ustun, O. (2022). Multi-objective genetic algorithm based on the fuzzy MULTIMOORA method for solving the cardinality constrained portfolio optimization. Applied Intelligence, 53(12), 14717-14743. https://doi.org/10.1007/s10489-022-04240-6
Guo, S., Gu, J. W., Fok, C. H., & Ching, W. K. (2023). Online portfolio selection with state-dependent price estimators and transaction costs. European Journal of Operational Research, 311(1), 333-353. https://www.sciencedirect.com/science/article/pii/S0377221723003454
Guo, W., Zhang, W., Liu, Y. J., & Xu, W. (2022). Modeling of linear uncertain portfolio selection with uncertain constraint and risk index. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4182793
Guo, X., Chan, R. H., Wong, W.-K., & Zhu, L. (2018). Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk. Risk Management, 21(2), 73-98. https://doi.org/10.1057/s41283-018-0043-2
Huang, X. (2012). A risk index model for portfolio selection with returns subject to experts’ estimations. Fuzzy Optimization and Decision Making, 11(4), 451-463. https://doi.org/10.1007/s10700-012-9125-x
Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284-296. https://doi.org/10.1016/j.amc.2015.12.018
Huang, X., & Di, H. (2020). Uncertain portfolio selection with mental accounts. International Journal of Systems Science, 51(12), 2079-2090. https://doi.org/10.1080/00207721.2019.1648706
Huang, X., & Ma, D. (2022). Uncertain mean-chance model for portfolio selection with multiplicative background risk. International Journal of Systems Science: Operations & Logistics, 10(1). https://doi.org/10.1080/23302674.2022.2158443
Hübner, G., & Lejeune, T. (2022). Portfolio choice and mental accounts: A comparison with traditional approaches. Finance, 43(1), 95-121. https://doi.org/10.3917/fina.431.0095
Indarwati, E., & Kusumawati, R. (2021). Estimation of the portfolio risk from conditional value at risk using Monte Carlo simulation. Jurnal Matematika, Statistika dan Komputasi, 17(3), 370-380. https://doi.org/10.20956/j.v17i3.11340
James, C. T. M. (1970). Models of capital budgeting, E-V vs E-S. Journal of Finance and Quantitative Analysis, 4(5), 657-675. https://www.jstor.org/stable/2330119
Jiang, G., Huang, X., & Yang, T. (2023). Multiple risks and uncertain portfolio management. International Journal of Information Technology & Decision Making, 1-29. https://doi.org/10.1142/S0219622023500190
Khanjani Shiraz, R., Tavana, M., & Fukuyama, H. (2020). A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk. Soft Computing, 24(22), 17167-17186. https://doi.org/10.1007/s00500-020-05010-7
Khodamoradi, T., & Salahi, M. (2022). Extended mean-conditional value-at-risk portfolio optimization with PADM and conditional scenario reduction technique. Computational Statistics, 38(2), 1023-1040. https://doi.org/10.1007/s00180-022-01263-y
Khodamoradi, T., Salahi, M., & Najafi, A. R. (2023). Multi-intervals robust mean-conditional value-at-risk portfolio optimisation with conditional scenario reduction technique. International Journal of Applied Decision Sciences, 16(2), 237. https://doi.org/10.1504/ijads.2023.129475
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), 519-531. https://doi.org/10.1287/mnsc.37.5.519
Lam, W. S., Lam, W. H., & Jaaman, S. H. (2021). Portfolio optimization with a mean–absolute deviation–entropy multi-objective model. Entropy, 23(10), 1266. https://doi.org/10.3390/e23101266
Li, B., & Huang, Y. (2023). Uncertain random portfolio selection with different mental accounts based on mixed data. Chaos, Solitons & Fractals, 168, 113198. https://doi.org/10.1016/j.chaos.2023.113198
Li, J. (2018). A mean-fuzzy random VaR portfolio selection model in hybrid uncertain environment. Uncertainty and Operations Research, 125–147. https://doi.org/10.1007/978-981-10-7817-0_13
Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Application, 1(1). https://doi.org/10.1186/2195-5468-1-1
Liu, B. (2014). Introduction. Springer Uncertainty Research, 1–8. https://doi.org/10.1007/978-3-662-44354-5_1
Liu, D. B. (2007). Uncertainty theory. Springer Berlin Heidelberg, 205-234. https://doi.org/10.1007/978-3-540-73165-8_5
Liu, Y., Zhou, Y., & Niu, J. (2023). Portfolio optimization: A multi-period model with dynamic risk preference and minimum lots of transaction. Finance Research Letters, 55, 103964. https://www.sciencedirect.com/science/article/pii/S1544612323003367
Lv, L., Zhang, B., Peng, J., & Ralescu, D. A. (2020). Uncertain portfolio selection with borrowing constraint and background risk. Mathematical Problems in Engineering, 2020, 1-13. https://doi.org/10.1155/2020/1249829
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://www.jstor.org/stable/2975974
Meng, X., & Shan, Y. (2021). A fuzzy mean semi-absolute deviation-semi-variance-proportional entropy portfolio selection model with transaction costs. Proceedings of the 2021 40th Chinese Control Conference (CCC). IEEE. https://doi.org/10.23919/ccc52363.2021.9550714
Pitera, M., & Stettner, Ł. (2023). Discrete‐time risk sensitive portfolio optimization with proportional transaction costs. Mathematical Finance, n/a(n/a). https://onlinelibrary.wiley.com/doi/abs/10.1111/mafi.12406
Primbs, J. A. (2018). Applications of MPC to finance. Control Engineering, 665–685. https://doi.org/10.1007/978-3-319-77489-3_27
Ramedani, A. M., Mehrabian, A., & Didehkhani, H. (2022). Sustainable project portfolio selection under uncertainty with consideration of conflicting projects. https://doi.org/10.21203/rs.3.rs-2128708/v1
Salahi, M., Khodamoradi, T., & Najafi, A. R. (2023). Multi-intervals robust mean-conditional value-at-risk portfolio optimization with conditional scenario reduction technique. International Journal of Applied Decision Sciences, 1(1), 1. https://doi.org/10.1504/ijads.2023.10045206
Siew, L. W. (2020). Portfolio optimization of financial companies with fuzzy TOPSIS-mean-semi absolute deviation model. Journal of Dynamic Control Systems, 12(SP4), 1488-1495. https://doi.org/10.5373/jardcs/v12sp4/20201627
Tversky, A., & Kahneman, D. (1986). Rational choice and the framing of decisions. Journal of Business, 59(4), S251-S278. https://www.jstor.org/stable/2352759
Uryasev, S., & Rockafellar, R. T. (2001). Conditional value-at-risk: Optimization approach. In S. Uryasev & P. M. Pardalos (Eds.), Stochastic optimization: Algorithms and applications (pp. 411-435). Springer US. https://doi.org/10.1007/978-1-4757-6594-6_17
Vukovic, D. B., Maiti, M., & Frömmel, M. (2022). Inflation and portfolio selection. Finance Research Letters, 50, 103202. https://www.sciencedirect.com/science/article/pii/S154461232200407X
Wang, X., & Huang, X. (2019). A risk index to model uncertain portfolio investment with options. Economic Modelling, 80, 284-293. https://doi.org/10.1016/j.econmod.2018.11.014
World Bank. (2021). Portfolio risk assessment using risk index. In World Bank (Ed.). https://doi.org/10.1596/35490
Yang, T., & Huang, X. (2022). Two new mean–variance enhanced index tracking models based on uncertainty theory. North American Journal of Economics and Finance, 59. https://doi.org/10.1080/23302674.2022.2158443
Yang, X. Y., Chen, S. D., Liu, W. L., & Zhang, Y. (2022). A multi-period fuzzy portfolio optimization model with short selling constraints. International Journal of Fuzzy Systems, 24(6), 2798-2812. https://doi.org/10.1007/s40815-022-01294-z
Zhang, J., & Li, Q. (2019). Credibilistic mean-semi-entropy model for multi-period portfolio selection with background risk. Entropy, 21(10), 944. https://doi.org/10.3390/e21100944
Zhang, J., Jin, Z., & An, Y. (2017). Dynamic portfolio optimization with ambiguity aversion. Journal of Banking & Finance, 79, 95-109. https://doi.org/10.1016/j.jbankfin.2017.03.007
Zhang, P. (2018). Multiperiod mean absolute deviation uncertain portfolio selection with real constraints. Soft Computing, 23(13), 5081-5098. https://doi.org/10.1007/s00500-018-3176-z
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2025-03-06
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