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An Asset Allocation Model and Its Solving Method

Author

Listed:
  • Zhang Qingye

    (School of Management, University of Shanghai for Science and Technology, Shanghai, 200093, China)

  • Gao Yan

    (School of Management, University of Shanghai for Science and Technology, Shanghai, 200093, China)

Abstract

Asset allocation is an important issue in finance, and both risk and return are its fundamental ingredients. Rather than the return, the measure of the risk is complicated and of controversy. In this paper, we propose an appropriate risk measure which is precisely a convex combination of mean semi-deviation and conditional value-at-risk. Based on this risk measure, investors can trade-off flexibly between the volatility and the loss to tackle the incurring risk by choosing different convex coefficients. As the presented risk measure contains nonsmooth term, the asset allocation model based on it is nonsmooth. To employ traditional gradient algorithms, we develop a uniform smooth approximation of the plus function and convert the model into a smooth one. Finally, an illustrative empirical study is given. The results indicate that investors can control risk efficiently by adjusting the convex coefficient and the confidence level simultaneously according to their perceptions. Moreover, the effectiveness of the smoothing function proposed in the paper is verified.

Suggested Citation

  • Zhang Qingye & Gao Yan, 2017. "An Asset Allocation Model and Its Solving Method," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 163-175, April.
    • Handle: RePEc:bpj:jossai:v:5:y:2017:i:2:p:163-175:n:5
    DOI: 10.21078/JSSI-2017-163-13
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    References listed on IDEAS

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    1. 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.
    2. Shangmei Zhao & Qing Lu & Liyan Han & Yong Liu & Fei Hu, 2015. "A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution," Annals of Operations Research, Springer, vol. 226(1), pages 727-739, March.
    3. Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
    4. Churlzu Lim & Hanif Sherali & Stan Uryasev, 2010. "Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization," Computational Optimization and Applications, Springer, vol. 46(3), pages 391-415, July.
    5. Yuichi Takano & Keisuke Nanjo & Noriyoshi Sukegawa & Shinji Mizuno, 2015. "Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs," Computational Management Science, Springer, vol. 12(2), pages 319-340, April.
    6. 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.
    7. Alexander, S. & Coleman, T.F. & Li, Y., 2006. "Minimizing CVaR and VaR for a portfolio of derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 583-605, February.
    8. Fanwen Meng & Jie Sun & Mark Goh, 2011. "A smoothing sample average approximation method for stochastic optimization problems with CVaR risk measure," Computational Optimization and Applications, Springer, vol. 50(2), pages 379-401, October.
    9. 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.
    10. Pang, Li-Ping & Chen, Shuang & Wang, Jin-He, 2015. "Risk management in portfolio applications of non-convex stochastic programming," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 565-575.
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