A Systematic Literature Review on Mean-CVaR Based Financial Asset Portfolio Weight Allocation Using K-Means Clustering

Alim Jaizul Wahid, Riaman Riaman, Sukono Sukono

Abstract


This study aims to identify and analyze the application of the Mean-Conditional Value-at-Risk (Mean-CVaR) model in the allocation of financial asset portfolio weights combined with the K-Means Clustering algorithm. The Systematic Literature Review (SLR) method is used with the PRISMA protocol through the stages of identification, screening, eligibility, and inclusion. Data is obtained from Scopus, ScienceDirect, and Dimensions databases, then selected up to six relevant primary articles. The results of the study indicate that CVaR is the dominant risk measure in portfolio optimization, while K-Means Clustering serves as a method of grouping assets to increase diversification. The optimization methods used include Genetic Algorithm, Particle Swarm Optimization, Teaching Learning-Based Optimization, and Stochastic Programming. However, direct integration between Mean-CVaR and K-Means within a portfolio weight allocation framework is still rare. This research emphasizes the need to develop a hybrid model that combines both approaches in an integrated manner, applied to a multi-asset portfolio, and validated under various market conditions to produce an optimal, adaptive, and resilient investment strategy against extreme risks.

Keywords


Mean-Conditional Value-at-Risk; K-Means Clustering; Portfolio Weight Allocation; Financial Asset Portfolio

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References


[1] J. Fadika and Y. A. Indra, “Peran pasar modal dalam meningkatkan minat investasi pada generasi muda di era digital,” Journal of Management and Innovation Entrepreneurship, vol. 2, no. 1, pp. 1700–1712, 2024. doi: 10.70248/jmie.v2i1.1430.

[2] Y. Yang, “Clustering-based financial big data analysis for portfolio optimization,” in Proceedings of the 2025 International Conference on Big Data, Association for Computing Machinery, 2025, pp. 36–42. doi: 10.1145/3727505.3727511.

[3] M. A. Riswana and G. W. Yasa, “Influence of investment knowledge, minimum capital, influencers, technological progress on students interest in investing in the capital market,” International Journal of Business, Economics & Management, vol. 7, no. 1, pp. 18–26, 2024. doi: 10.21744/ijbem.v7n1.2249.

[4] L. H. Nguyen, L. X. D. Nguyen, and E. Adegbite, “Does mean-cvar outperform mean- variance? theoretical and practical perspectives,” Theoretical and Practical Perspectives, pp. 1–52, 2018. doi: https://dx.doi.org/10.2139/ssrn.3143827.

[5] L. Gubu, E. Cahyono, H. Budiman, and M. K. Djafar, “Cluster analysis for mean-variance portfolio selection: A comparison between k-means and k-medoids clustering,” Jurnal Riset dan Aplikasi Matematika, vol. 7, no. 2, pp. 104–115, 2023. doi: 10.26740/jram.v7n2.p10 4-115.

[6] U. Arif, D. Muhammad, T. Sohail, and M. I. Majeed, “Portfolio optimization with mean- variance & mean-cvar: Evidence from pakistan stock market,” International Journal of Management Research and Emerging Sciences, vol. 10, no. 2, pp. 215–226, 2020.

[7] S. Petchrompo, A. Wannakrairot, and A. K. Parlikad, “Pruning pareto optimal solutions for multi-objective portfolio asset management,” European Journal of Operational Research, vol. 297, no. 1, pp. 203–220, 2022. doi: 10.1016/j.ejor.2021.04.053.

[8] I. Lisnawati and R. Subekti, “Conditional value at risk (cvar) of portfolio using conditional copula,” Jurnal Kajian dan Terapan Matematika, vol. 7, no. 3, pp. 64–72, 2018. doi: 10.14710/j.gauss.v9i3.28913.

[9] M. Salahi, F. Mehrdoust, and F. Piri, “Cvar robust mean-cvar portfolio optimization,”

ISRN Applied Mathematics, vol. 2013, pp. 1–9, 2013. doi: 10.1155/2013/570950.

[10] F. Soleymani and M. Vasighi, “Efficient portfolio construction by means of cvar and k- means++ clustering analysis: Evidence from the nyse,” International Journal of Finance and Economics, vol. 27, no. 3, pp. 3679–3693, 2022. doi: 10.1002/ijfe.2344.

[11] M. Gulliksson, S. Mazur, and A. Oleynik, “Minimum var and minimum cvar optimal portfolios: The case of singular covariance matrix,” Results in Applied Mathematics, vol. 26, p. 100 557, 2025. doi: 10.1016/j.rinam.2025.100557.

[12] N. Abudurexiti, K. He, D. Hu, S. T. Rachev, H. Sayit, and R. Sun, “Portfolio analysis with mean-cvar and mean-cvar-skewness criteria based on mean–variance mixture models,” Annals of Operations Research, vol. 336, no. 1-2, pp. 945–966, 2024. doi: 10.1007/s10479- 023-05396-1.

[13] M. M. Kowsar, M. Mohiuddin, and S. Islam, “Mathematics for finance: A review of quantitative methods in loan portfolio optimization,” International Journal of Scientific Interdisciplinary Research, vol. 4, no. 3, pp. 1–29, 3. Available online.

[14] X. Guo, R. H. Chan, W. K. Wong, and L. Zhu, “Mean–variance, mean–var, and mean–cvar models for portfolio selection with background risk,” Risk Management, vol. 21, no. 2, pp. 73–98, 2019. doi: 10.1057/s41283-018-0043-2.

[15] C. Yu and Y. Liu, “A personalized mean-cvar portfolio optimization model for individual investment,” Mathematical Problems in Engineering, vol. 2021, p. 12, 2021. doi: 10.1155

/2021/8863597.

[16] R. Bedoui, R. Benkraiem, K. Guesmi, and I. Kedidi, “Portfolio optimization through hybrid deep learning and genetic algorithms vine copula-garch-evt-cvar model,” Technological Forecasting and Social Change, vol. 197, 2023. doi: 10.1016/j.techfore.2023.122887.

[17] V. Jain, R. R. Sahay, and Nupur, “Integrated robust em and todim approach with teaching learning based portfolio optimization,” Computational Economics, 2025. doi: 10.1007/s1 0614-025-11013-z.

[18] H. Firmansyah and D. Rosadi, “Construction of stock portfolios based on k-means clustering of continuous trend features,” Jurnal Matematika Integratif, vol. 20, no. 2, pp. 149–172, 2024. doi: 10.24198/jmi.v20.n2.53351.149-172.

[19] R. Siagian, P. Sirait, and A. Halima, “E-commerce customer segmentation using k-means algorithm and length, recency, frequency, monetary model,” Journal of Informatics and Telecommunication Engineering, vol. 5, no. 1, pp. 21–30, 2021. doi: 10.31289/jite.v5i1

.5182.

[20] D. Wu, X. Wang, and S. Wu, “Construction of stock portfolios based on k-means clustering of continuous trend features,” Knowledge-Based Systems, vol. 252, no. 2022, p. 109 358, 2022. doi: 10.1016/j.knosys.2022.109358.

[21] J. C. Mba and E. S. E. F. Angaman, “A k-means classification and entropy pooling portfolio strategy for small and large capitalization cryptocurrencies,” Entropy, vol. 25, no. 8, 2023. doi: 10.3390/e25081208.

[22] V. Bulani, M. Bezbradica, and M. Crane, “Improving portfolio management using clustering and particle swarm optimisation,” Mathematics, vol. 13, no. 10, 2025. doi: 10.3390/math1 3101623.

[23] M. Kaut, “Scenario generation by selection from historical data,” Computational Manage- ment Science, vol. 18, no. 3, pp. 411–429, 2021. doi: 10.1007/s10287-021-00399-4.

[24] M. J. Page, J. E. McKenzie, P. M. Bossuyt, et al., “The prisma 2020 statement: An updated guideline for reporting systematic reviews,” BMJ, n71, 2021. doi: 10.1136/bmj.n71.

[25] A. Z. Irmansyah, D. Chaerani, and E. Rusyaman, “A systematic review on integer multi- objective adjustable robust counterpart optimization model using benders decomposition,” JTAM (Jurnal Teori dan Aplikasi Matematika), vol. 6, no. 3, pp. 678–690, 2022. doi: 10.31764/jtam.v6i3.8578




DOI: https://doi.org/10.18860/cauchy.v10i2.36590

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