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Sparse portfolio selection with uncertain probability distribution

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Abstract

Designed as remedies for uncertain parameters and tiny optimal weights in the portfolio selection problem, we consider a class of distributionally robust portfolio optimization models with cardinality constraints. For considering the statistical significance and tractability, we construct two kinds of ambiguity sets based on L1-norm and moment information, respectively. The nominal distribution, as the core of the first ambiguity set, is determined by non-parametric estimation method. To reduce the disturbing error of the second ambiguity set, we apply a shrinkage estimation method to determine the moment information based on historical data. By introducing a binary variable, the proposed sparse portfolio optimization model can be converted equivalently to a tractable mixed-integer 0-1 programming problem, which can be dealt with efficiently by a modified primal-dual Benders’ decomposition method. Through the actual market data, we test the proposed models and show their validity. Furthermore, performances measured by net portfolio return, Sharpe ratio, and cumulative return are superior to the classical portfolio selection models in the back-testing of out-of-sample data.

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Notes

  1. Given N historical data, \(\boldsymbol {\xi }^{j}\in \mathbb {R}^{n}, j=1,...,N\), \(\boldsymbol {X}^{j}=\boldsymbol {\xi }^{j}-\frac {1}{N}{\sum }^{N}_{j=1}\boldsymbol {\xi }^{j}\).

  2. https://finance.yahoo.com/

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Acknowledgments

This research has been supported by National Natural Science Foundation of China (71571055) and partially supported by the NSF of Anhui Educational Committe (KJ2020A0712). Meanwhile, this research was also supported by Initial Scientific Research Fund of Chuzhou University (2020qd39).

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Authors and Affiliations

  1. School of Mathematics and Finance, Chuzhou University, Anhui, People’s Republic of China

    Ripeng Huang

  2. Nanjing University of Information Science and Technology, Nanjing, People’s Republic of China

    Shaojian Qu

  3. Business School, University of Shanghai for Science and Technology, Shanghai, People’s Republic of China

    Shaojian Qu

  4. National University of Singapore, Singapore, Singapore

    Shaojian Qu

  5. Academy of Mathematics and Systems Science CAS, Beijing, People’s Republic of China

    Xiaoguang Yang

  6. School of Economics and Finance, Xi’an Jiaotong University, Xi’an, Shaanxi, People’s Republic of China

    Fengmin Xu

  7. Business School, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Zeshui Xu

  8. School of Finance, Yunnan University of Finance and Economics, Kunming, Yunnan, People’s Republic of China

    Wei Zhou

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  1. Ripeng Huang
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Correspondence to Shaojian Qu.

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Huang, R., Qu, S., Yang, X. et al. Sparse portfolio selection with uncertain probability distribution. Appl Intell 51, 6665–6684 (2021). https://doi.org/10.1007/s10489-020-02161-w

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