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Fast algorithms for sparse portfolio selection considering industries and investment styles

Author

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  • Zhi-Long Dong

    (Xi’an Jiaotong University)

  • Fengmin Xu

    (Xi’an Jiaotong University)

  • Yu-Hong Dai

    (Chinese Academy of Sciences, Beijing)

Abstract

In this paper, we consider a large scale portfolio selection problem with and without a sparsity constraint. Neutral constraints on industries are included as well as investment styles. To develop fast algorithms for the use in the real financial market, we shall expose the special structure of the problem, whose Hessian is the summation of a diagonal matrix and a low rank modification. Specifically, an interior point algorithm taking use of the Sherman–Morrison–Woodbury formula is designed to solve the problem without any sparsity constraint. The complexity in each iteration of the proposed algorithm is shown to be linear with the problem dimension. In the occurrence of a sparsity constraint, we propose an efficient three-block alternating direction method of multipliers, whose subproblems are easy to solve. Extensive numerical experiments are conducted, which demonstrate the efficiency of the proposed algorithms compared with some state-of-the-art solvers.

Suggested Citation

  • Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:4:d:10.1007_s10898-020-00911-1
    DOI: 10.1007/s10898-020-00911-1
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    1. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    2. Xingju Cai & Deren Han & Xiaoming Yuan, 2017. "On the convergence of the direct extension of ADMM for three-block separable convex minimization models with one strongly convex function," Computational Optimization and Applications, Springer, vol. 66(1), pages 39-73, January.
    3. Rosenberg, Barr, 1974. "Extra-Market Components of Covariance in Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(2), pages 263-274, March.
    4. X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    5. Andre F. Perold, 1984. "Large-Scale Portfolio Optimization," Management Science, INFORMS, vol. 30(10), pages 1143-1160, October.
    6. Duan Li & Xiaoling Sun & Jun Wang, 2006. "Optimal Lot Solution To Cardinality Constrained Mean–Variance Formulation For Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 83-101, January.
    7. J. Gondzio & F. N. C. Sobral, 2019. "Quasi-Newton approaches to interior point methods for quadratic problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 93-120, September.
    8. Stephen Wright & Daniel Ralph, 1996. "A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 815-838, November.
    9. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    10. Grauer, Robert R. & Hakansson, Nils H. & Shen, Frederick C., 1990. "Industry rotation in the U.S. stock market : 1934-1986 returns on passive, semi-passive, and active strategies," Journal of Banking & Finance, Elsevier, vol. 14(2-3), pages 513-538, August.
    11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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