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Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method

Author

Listed:
  • Xueting Cui

    (School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China)

  • Xiaoling Sun

    (Department of Management Science, School of Management, Fudan University, Shanghai 200433, P. R. China)

  • Shushang Zhu

    (Department of Finance and Investment, Sun Yat-Sen Business School, Sun Yat-Sen University, Guangzhou 510275, P. R. China)

  • Rujun Jiang

    (School of Data Science, Fudan University, Shanghai 200433, P. R. China)

  • Duan Li

    (Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon, Hong Kong)

Abstract

In this paper, we investigate a portfolio optimization methodology using nonparametric value at risk (VaR). In particular, we adopt kernel VaR and quadratic VaR as risk measures. As the resulting models are nonconvex and nonsmooth optimization problems, albeit with some special structures, we propose some specially devised block coordinate descent (BCD) methods for finding approximate or local optimal solutions. Computational results show that the BCD methods are efficient for finding local solutions with good quality and they compare favorably with the branch-and-bound method-based global optimal solution procedures. From the simulation test and empirical analysis that we carry out, we are able to conclude that the mean-VaR models using kernel VaR and quadratic VaR are more robust compared to those using historical VaR or parametric VaR under the normal distribution assumption, especially when the information of the return distribution is limited.

Suggested Citation

  • Xueting Cui & Xiaoling Sun & Shushang Zhu & Rujun Jiang & Duan Li, 2018. "Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 454-471, August.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:3:p:454-471
    DOI: 10.1287/ijoc.2017.0793
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    References listed on IDEAS

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    Cited by:

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    7. Francesco Cesarone & Manuel L. Martino & Fabio Tardella, 2023. "Mean-Variance-VaR portfolios: MIQP formulation and performance analysis," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 1043-1069, September.
    8. Jiapeng Liu & Miłosz Kadziński & Xiuwu Liao & Xiaoxin Mao, 2021. "Data-Driven Preference Learning Methods for Value-Driven Multiple Criteria Sorting with Interacting Criteria," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 586-606, May.
    9. Shicheng Hu & Danping Li & Junmin Jia & Yang Liu, 2021. "A Self-Learning Based Preference Model for Portfolio Optimization," Mathematics, MDPI, vol. 9(20), pages 1-17, October.

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