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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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    7. Hongxin Zhao & Yilun Jiang & Yizhou Yang, 2023. "Robust and Sparse Portfolio: Optimization Models and Algorithms," Mathematics, MDPI, vol. 11(24), pages 1-20, December.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Giovanni Bonaccolto, 2019. "Critical Decisions for Asset Allocation via Penalized Quantile Regression," Papers 1908.04697, arXiv.org.
    13. Stefania Corsaro & Valentina De Simone, 2018. "Adaptive l1-regularization for short-selling control in portfolio selection," Papers 1808.00982, arXiv.org.
    14. 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.
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