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Two nonparametric approaches to mean absolute deviation portfolio selection model

  • * Corresponding author: wfh@amss.ac.cn

    * Corresponding author: wfh@amss.ac.cn
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  • In this paper, we apply two nonparametric approaches to mean absolute deviation (MAD) portfolio selection model. The first one is to use the nonparametric kernel mean estimation to replace the returns of assets with five different kernel functions. Then, we construct the nonparametric kernel mean estimation-based MAD portfolio model. The second one is to utilize the nonparametric kernel median estimation to replace the returns of assets with five different kernel functions. Then, we construct the nonparametric kernel median estimation-based MAD portfolio model. We also extend the two kinds of nonparametric approach to mean-Conditional Value-at-Risk portfolio model. Finally, we give the in-sample and out-of-sample analysis of the proposed strategies and compare the performance of the proposed models by using actual stock returns in Shanghai stock exchange of China. The experimental results show the nonparametric estimation-based portfolio models are more efficient than the original portfolio model.

    Mathematics Subject Classification: Primary: 90C30, 90C90; Secondary: 65k05.

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  • Figure 1.  Comparision of efficient frontier of MAD portfolio models

    Figure 2.  Efficient frontier of the MAD model based on the kernel median estimation

    Figure 3.  Efficient frontier of the mean-CVaR portfolio models

    Figure 4.  Efficient frontier of MAD models of kernel mean estimation under different kernel functions

    Figure 5.  Efficient frontier of the mean-CVaR portfolio models of kernel mean estimation under different kernel functions

    Figure 6.  Efficient frontier of MAD models of kernel median estimation under different kernel functions

    Figure 7.  Efficient frontier of mean-CVaR models of kernel median estimation under different kernel functions

    Figure 8.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of the MAD model

    Figure 9.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of MAD model of kernel mean estimation

    Figure 10.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of MAD of kernel median estimation

    Figure 11.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of the mean-CVaR model

    Figure 12.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of mean-CVaR model of kernel mean estimation

    Figure 13.  Comparison betwen the daily return of Shanghai Composite Index and portfolio return of mean-CVaR of kernel median estimation

    Table 1.  Descriptive Statistics of daily return of 20 stocks from Shanghai A shares

    Stock nam Number Max Min Mean Sd. Skewness Kurtosis
    P.R.E. 600048 0.10038 -0.35544 0.00049 0.03308 -1.47313 22.2281
    T.J.H. 600717 0.10025 -0.10029 0.00074 0.03040 -0.08191 5.4232
    H.E. 600060 0.10035 -0.11024 0.00109 0.03355 -0.00870 5.15926
    H.N.I. 600011 0.10050 -0.10036 0.00064 0.02654 -0.28255 7.6319
    N.J.H.T. 600064 0.10028 -0.32864 0.00112 0.03146 -1.69324 20.8171
    S.H.I. 600031 0.10066 -0.10042 0.00015 0.02843 -0.14598 6.8630
    S.H.A. 600009 0.09996 -0.10007 0.00112 0.02464 -0.09756 7.3309
    T.R.T. 600085 0.10022 -0.10016 0.00109 0.02834 -0.04908 6.7348
    Ch.M.B. 600036 0.09571 -0.09914 0.00087 0.01999 0.44853 8.3975
    Ch.S. 600150 0.10016 -0.10011 0.00101 0.03593 -0.04488 4.6552
    Ch.U. 600050 0.10103 -0.10056 0.00096 0.02846 0.21470 6.7539
    Sino. 600028 0.10035 -0.10040 0.00037 0.02138 -0.15015 8.9252
    Ch.S. 600118 0.10027 -0.10009 0.00170 0.03683 -0.03555 4.7026
    C.S. 600030 0.10043 -0.10012 0.00091 0.03038 0.23151 5.9787
    C.S.M. 601098 0.10027 -0.10017 0.00120 0.02910 -0.14500 5.4879
    Ch.L.I. 601628 0.10036 -0.10007 0.00095 0.02689 0.62490 6.7596
    O.F.X. 600612 0.10010 -0.10006 0.00109 0.02811 0.29691 5.8163
    C.Q.B. 600132 0.10027 -0.10699 0.00042 0.02841 -0.37571 6.9771
    J.J.I. 600650 0.10037 -0.10018 0.00202 0.03929 0.20423 4.3077
    Q.J.B. 600706 0.10028 -0.10024 0.00125 0.03459 -0.26875 4.7732
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    Table 2.  Descriptive statistics of daily return of Shanghai Composite Index

    Max Min average sd Skewness Kurtosis
    Shanghai S-I-R 0.04310 -0.07045 -0.00016 0.01566 -1.37612 8.38382
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