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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

    as
    1. Zaiwen Wen & Xianhua Peng & Xin Liu & Xiaoling Sun & Xiaodi Bai, 2013. "Asset Allocation under the Basel Accord Risk Measures," Papers 1308.1321, arXiv.org.
    2. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    3. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    4. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    5. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 227-255.
    6. QIU, Feng & AHMED, Shabbir & DEY, Santanu S & WOLSEY, Laurence A, 2014. "Covering linear programming with violations," LIDAM Reprints CORE 2618, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Feng Qiu & Shabbir Ahmed & Santanu S. Dey & Laurence A. Wolsey, 2014. "Covering Linear Programming with Violations," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 531-546, August.
    8. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    9. Benati, Stefano & Rizzi, Romeo, 2007. "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 423-434, January.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Steven Kou & Xianhua Peng & Chris C. Heyde, 2013. "External Risk Measures and Basel Accords," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 393-417, August.
    12. 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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    Cited by:

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    7. Ma, Shuai & Ma, Xiaoteng & Xia, Li, 2023. "A unified algorithm framework for mean-variance optimization in discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1057-1067.
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