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Solving norm constrained portfolio optimization via coordinate-wise descent algorithms

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  • Yen, Yu-Min
  • Yen, Tso-Jung

Abstract

A fast method based on coordinate-wise descent algorithms is developed to solve portfolio optimization problems in which asset weights are constrained by lq norms for 1≤q≤2. The method is first applied to solve a minimum variance portfolio (mvp) optimization problem in which asset weights are constrained by a weighted l1 norm and a squared l2 norm. Performances of the weighted norm penalized mvp are examined with two benchmark data sets. When the sample size is not large in comparison with the number of assets, the weighted norm penalized mvp tends to have a lower out-of-sample portfolio variance, lower turnover rate, fewer numbers of active constituents and shortsale positions, but higher Sharpe ratio than the one without such penalty. Several extensions of the proposed method are illustrated; in particular, an efficient algorithm for solving a portfolio optimization problem in which assets are allowed to be chosen grouply is derived.

Suggested Citation

  • Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
    • Handle: RePEc:eee:csdana:v:76:y:2014:i:c:p:737-759
    DOI: 10.1016/j.csda.2013.07.010
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    Cited by:

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    3. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    4. Vanita Garg & Kusum Deep, 2019. "Portfolio optimization using Laplacian biogeography based optimization," OPSEARCH, Springer;Operational Research Society of India, vol. 56(4), pages 1117-1141, December.
    5. Hongxin Zhao & Lingchen Kong & Hou-Duo Qi, 2021. "Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 853-881, December.
    6. Hongxin Zhao & Yilun Jiang & Yizhou Yang, 2023. "Robust and Sparse Portfolio: Optimization Models and Algorithms," Mathematics, MDPI, vol. 11(24), pages 1-20, December.
    7. Stefania Corsaro & Valentina Simone, 2019. "Adaptive $$l_1$$ l 1 -regularization for short-selling control in portfolio selection," Computational Optimization and Applications, Springer, vol. 72(2), pages 457-478, March.
    8. Michele Costola & Bertrand Maillet & Zhining Yuan & Xiang Zhang, 2024. "Mean–variance efficient large portfolios: a simple machine learning heuristic technique based on the two-fund separation theorem," Annals of Operations Research, Springer, vol. 334(1), pages 133-155, March.
    9. Giovanni Bonaccolto, 2021. "Quantile– based portfolios: post– model– selection estimation with alternative specifications," Computational Management Science, Springer, vol. 18(3), pages 355-383, July.
    10. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    11. Margherita Giuzio & Sandra Paterlini, 2019. "Un-diversifying during crises: Is it a good idea?," Computational Management Science, Springer, vol. 16(3), pages 401-432, July.
    12. Dai, Zhifeng & Wang, Fei, 2019. "Sparse and robust mean–variance portfolio optimization problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1371-1378.
    13. Stefania Corsaro & Valentina De Simone & Zelda Marino & Francesca Perla, 2020. "$$l_1$$ l 1 -Regularization for multi-period portfolio selection," Annals of Operations Research, Springer, vol. 294(1), pages 75-86, November.
    14. Qifa Xu & Junqing Zuo & Cuixia Jiang & Yaoyao He, 2021. "A large constrained time‐varying portfolio selection model with DCC‐MIDAS: Evidence from Chinese stock market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 3417-3435, July.
    15. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989, arXiv.org, revised Feb 2020.
    16. Giovanni Bonaccolto, 2019. "Critical Decisions for Asset Allocation via Penalized Quantile Regression," Papers 1908.04697, arXiv.org.
    17. Stefania Corsaro & Valentina De Simone, 2018. "Adaptive l1-regularization for short-selling control in portfolio selection," Papers 1808.00982, arXiv.org.

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