Knowledge Economy Studies

Intelligent Risk Processing and Opportunity Formation in Financial Markets: The Superior Performance of HERC Algorithm in Efficient Portfolio Construction

Document Type : Original Article

Authors

Mahsa Safavi Iranji 1
Majid Zanjirdar 2

1 Department of Financial engineering, Qom Branch, Islamic Azad University, Qom, Iran.

2 Department of Finance, Ar.C., Islamic Azad University, Arak, Iran

https://doi.org/10.22034/kes.2026.2077852.1088
Abstract
Hierarchical portfolio optimization methods, particularly the Hierarchical Equal Risk Contribution (HERC) approach, have become increasingly prominent in financial research due to their effectiveness in balancing risk and enhancing diversification. Unlike traditional methods such as Equal-Weight (EW) and Inverse Volatility (IV), which rely on oversimplified assumptions and often underperform in volatile markets, HERC allocates capital by distributing risk more efficiently across the assets. This study examined the performance of the HERC model relative to EW and IV to determine its ability to convert risk into investment opportunities under fluctuating market conditions. The methodology followed a structured process that includes deriving variables from multiple data sources, conducting thorough data cleaning and normalization, and implementing traditional allocation models as benchmarks. Advanced hierarchical clustering techniques were then applied to provide a more innovative allocation framework. Rigorous hypothesis testing was used to validate the results, and portfolio performance was evaluated using established statistical metrics. Findings revealed that HERC—especially its single linkage and average linkage versions—delivers substantially higher risk-adjusted returns, as measured by the Sharpe and Sortino ratios, compared to EW and IV. The proposed methodology not only improves overall investment outcomes but also enables more effective risk and return management, making it a strong alternative to conventional portfolio construction and risk evaluation approaches.

Keywords

Asset Allocation
Hierarchical Equal Risk Contribution (HERC)
Risk Management
Unsupervised Learning

Subjects

Asawa, Y. (2021). Modern machine learning solutions for portfolio selection. IEEE Engineering Management Review, 50(1), 94–112. https://ieeexplore.ieee.org/abstract/document/9627810.
Cajas, D. (2023). A graph theory approach to portfolio optimization. SSRN Working Paper. https://dx.doi.org/10.2139/ssrn.4602019.
Ciciretti, V., & Bucci, A. (2023). Building optimal regime-switching portfolios. Economic Modelling and Finance, 64, S1062940822001723. https://doi.org/10.1016/j.najef.2022.101837.
Deković, D., & Šimović, P. P. (2025). Hierarchical risk parity: Efficient implementation and real world analysis. Future Generation Computer Systems, 107, 107744. https://doi.org/10.1016/j.future.2025.107744.
DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915–1953. https://doi.org/10.1093/rfs/hhm075.
Dogan, A., & Birant, D. (2022). K-centroid link: A novel hierarchical clustering linkage method. Applied Intelligence, 52, 1–24. https://doi.org/10.1007/s10489-021-02624-8.
Duarte, F. G., & De Castro, L. N. (2020). A framework to perform asset allocation based on partitional clustering. IEEE Access, 8, 110775–110788. https://doi.org/10.1109/access.2020.3001944.
Ferretti, S. (2022). On the modeling and simulation of portfolio allocation schemes: An approach based on network community detection. Computational Economics, 62(3), 969–1005. https://link.springer.com/article/10.1007/s10614-022-10288-w.
Ferri, R. (2010). All about asset allocation (2nd ed.). McGraw-Hill Education. https://search.worldcat.org/title/663882714.
Hallin, M., & Trucíos, C. (2023). Forecasting value-at-risk and expected shortfall in large portfolios: A general dynamic factor model approach. Econometrics and Statistics, 27, 1–5. https://doi.org/10.1016/j.ecosta.2021.04.006.
Huang, W., & Gao, X. (2021). Evaluating hierarchical equal risk contribution portfolios in the Chinese stock market. Journal of Mathematical Finance, 12(1), 179–195. https://doi.org/10.4236/jmf.2022.121011.
Jain, P., & Jain, S. (2019). Can machine learning-based portfolios outperform traditional risk-based portfolios? The need to account for covariance misspecification. Risks, 7(3), 74. https://doi.org/10.3390/risks7030074.
Lim, T., & Ong, C. (2020). Portfolio diversification using shape-based clustering. Journal of Financial Data Science, 3(1), 111. https://doi.org/10.3905/jfds.2020.1.054.
López de Prado, M. (2016). Building diversified portfolios that outperform out of sample. Journal of Portfolio Management, 42(4), 59–69. https://doi.org/10.3905/jpm.2016.42.4.059.
Maillard, S., Roncalli, T., & Teïletche, J. (2010). The properties of equally weighted risk contribution portfolios. Journal of Portfolio Management, 36(4), 60–70. https://doi.org/10.3905/jpm.2010.36.4.060.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91. https://doi.org/10.2307/2975974.
Menvouta, E. J., Serneels, S., & Verdonck, T. (2023). Portfolio optimization using cellwise robust association measures and clustering methods with application to highly volatile markets. Journal of Financial Data Science, 9, 100097. https://doi.org/10.1016/j.jfds.2023.100097.
Millea, A., & Edalat, A. (2022). Using deep reinforcement learning with hierarchical risk parity for portfolio optimization. International Journal of Financial Studies, 11(1), 10. https://doi.org/10.3390/ijfs11010010.
Nourahmadi, M., & Sadeqi, H. (2021). Hierarchical risk parity as an alternative to conventional methods of portfolio optimization: A study of Tehran Stock Exchange. Iranian Journal of Finance, 5(4), 1–24. https://doi.org/10.30699/ijf.2021.289848.1242.
Nourahmadi, M., & Sadeqi, H. (2022). A machine learning-based hierarchical risk parity approach: A case study of a portfolio consisting of stocks of the top 30 companies on the Tehran Stock Exchange. Financial Research Journal, 24(2), 236–256. https://doi.org/10.22059/frj.2021.319092.1007146.
Nourahmadi, M., & Sadeqi, H. (2023). Portfolio diversification based on clustering analysis. Iranian Journal of Accounting, Auditing and Finance, 7(3), 1–16. https://doi.org/10.22067/ijaaf.2023.43078.1092.
Nourahmadi, M., rasti, F., & Sadeqi, H. (2021). A Review of Research on Financial Time Series Clustering: A Bibliometrics Approach. ADVANCES IS FINANCE AND INVESTMENT, 2(2 ), 23-57. SID. https://sid.ir/paper/391770/en
Nourahmadi, M. , Rahimi, A. and Sadeqi, H. (2024). Designing a Stock Recommender System Using the Collaborative Filtering Algorithm for the Tehran Stock Exchange. Financial Research Journal, 26(2), 318-346. 10.22059/frj.2023.360955.1007479
Raffinot, T. (2017). Hierarchical clustering-based asset allocation. Journal of Portfolio Management, 44(2), 89–102. https://doi.org/10.3905/jpm.2018.44.2.089.
Raffinot, T. (2018). The hierarchical equal risk contribution portfolio. SSRN Electronic Journal. https://dx.doi.org/10.2139/ssrn.3237540.
Rostami, M. , Rasti, F. and Abbasi, E. (2025). Copula-Based Risk Modeling: A Comparative Analysis of MCAViaR and Gaussian Copulas for Global Indices. Journal of Mathematics and Modeling in Finance, 5(2), 77-106. 10.22054/jmmf.2025.86227.1187
Safavi Iranji, M., Zanjirdar, M., Safa, M., & Jahangirnia, H. (2024). Asset allocation using nested clustered optimization algorithm: A novel approach to risk management in portfolio. Journal of Mathematical Modeling in Finance, 4(2), 137–157. https://doi.org/10.22054/jmmf.2025.82388.1149.
Sajadi, S. M. A., Barak, S., & Fereydooni, A. (2024). Online portfolio selection using macroeconomic pattern matching. SSRN Electronic Journal. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4960922.
Schwendner, P., Papenbrock, J., Jaeger, M., & Krügel, S. (2021). Adaptive seriational risk parity and other extensions for heuristic portfolio construction using machine learning and graph theory. Journal of Financial Data Science, 3(4), 65–83. DOI: 10.3905/jfds.2021.1.078.
Sen, J., & Dutta, A. (2023). Portfolio optimization for the Indian stock market. In Encyclopedia of Data Science and Machine Learning (pp. 1904–1951). IGI Global. https://www.igi-global.com/chapter/portfolio-optimization-for-the-indian-stock-market/317595.
Sen, J., & Mehtab, S. (2021). A comparative study of optimum risk portfolio and eigen portfolio on the Indian stock market. International Journal of Business Forecasting and Marketing Intelligence, 7(2), 143–193. https://doi.org/10.1504/IJBFMI.2021.120155.
Seyfi, S. M., Sharifi, A., & Arian, H. (2021). Portfolio value-at-risk and expected shortfall using an efficient simulation approach based on Gaussian mixture model. Mathematics and Computers in Simulation, 190, 1056–1079. https://doi.org/10.1016/j.matcom.2021.05.029.
Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119–138. https://www.jstor.org/stable/2351741?searchText=Mutual%20fund%20performance&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3DMutual%2Bfund%2Bperformance%26so%3Drel&ab_segments=0%2Fbasic_search_gsv2%2Fcontrol&refreqid=fastly-default%3A32de7d5ea9a6a553b1e108b638c1f88f.
Sjöstrand, D., Behnejad, N., & Richter, M. (2020). Exploration of hierarchical clustering in long-only risk-based portfolio optimization (Doctoral dissertation). Copenhagen Business School, Copenhagen. https://research.cbs.dk/files/62178444/879726_Master_Thesis_Nima_Daniel_15736.pdf.
Venugopal, M., & Sophia, S. (2020). Examining Sharpe ratio, ASR, Sortino, Treynor and information ratio in Indian equity mutual funds during the pandemic. International Journal of Management, 11(11). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3780440.
Zhao, Y., & Karypis, G. (2002). Evaluation of hierarchical clustering algorithms for document datasets. In Proceedings of the International Conference on Information and Knowledge Management (pp. 515–524). https://doi.org/10.1145/584792.584877.
 
Knowledge Economy Studies
Volume 3, Issue 1
April 2026
Pages 11-20

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