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Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration

  • * Corresponding author: Nan-jing Huang

    * Corresponding author: Nan-jing Huang
This work was supported by the National Natural Science Foundation of China (11471230, 11671282, 11801462)
Abstract Full Text(HTML) Figure(6) / Table(5) Related Papers Cited by
  • In this paper, we consider a multi-objective robust cross-market mixed portfolio optimization model under hierarchical risk integration in the international financial market consisting of finite sub-markets. It is difficult to describe the dependent structure accurately by the traditional copula theory because of the dependent structures of the risk assets in finite sub-markets are different usually. By employing the hierarchical risk integration method, we establish the multi-objective robust cross-market mixed portfolio model in which the worst-case value at risk is used as the risk measurement and the transaction costs, skewness and investment proportion limitation are all considered. We provide a new algorithm to calculate the worst-case value at risk of the cross-market mixed portfolio and give a numerical experiment to show the superiority of the model considered in this paper.

    Mathematics Subject Classification: 91G50, 91G60, 91B30, 62H20, 62E17, 62P99, 65C20.


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  • Figure 1.  The Structure of Financial Market

    Figure 2.  Cross-Market Mixed Portfolio

    Figure 3.  Index Trend from January 2010 to March 2017

    Figure 4.  Standardized Index Trend from January 2010 to March 2017

    Figure 5.  Rate of Return from January 2010 to December 2016

    Figure 6.  Return Curve of Model 4

    Table 1.  Moment information of daily return rate from January 2010 to December 2016

    Name Mean(%) Variance Skewness Kurtosis
    SZZS 0.0170 2.1816 -0.3702 7.6127
    HSI 0.0072 1.3876 -0.0621 6.0437
    DAX 0.0483 1.7579 -0.1611 5.2904
    AEX 0.0243 1.3845 -0.1214 5.8596
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    Table 2.  Correlation Coefficient Matrix

    SZZS 1.0000 0.5265 0.1463 0.1700
    HSI 1.0000 0.3596 0.3900
    DAX 1.0000 0.9146
    AEX 1.0000
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    Table 3.  Rank Correlation Coefficient Kendall's $ \tau $

    DJIA 1.0000 0.3575 0.0865 0.1060
    DAX 1.0000 0.2321 0.2458
    SZZS 1.0000 0.7144
    N225 1.0000
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    Table 4.  Model Settings

    Model 1 Model 2 Model 3 Model 4
    Risk Measurement Variance WCVaR WCVaR WCVaR
    Hierarchical Risk Integration NO NO YES YES
    Skewness NO NO NO YES
    Transaction Cost YES YES YES YES
    Investment Proportion Limitation YES YES YES YES
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    Table 5.  Statistic Comparison

    Item Model 1 Model 2 Model 3 Model 4
    WCVaR of optimal portfolio - 1.7816 1.7254 1.6914
    Total Rate of Return(%) 15.4084 16.1731 17.6015 18.3447
    Daily Rate of Return(%) 0.0518 0.0541 0.0586 0.0609
    Variance 0.8661 0.8876 0.9833 1.0135
    Daily Maximum Loss(%) -5.6033 -5.3498 -5.1381 -4.9078
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