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具有现实约束的均值-VaR投资组合绩效评价

曾永泉 张鹏

曾永泉, 张鹏. 具有现实约束的均值-VaR投资组合绩效评价[J]. 华南师范大学学报(自然科学版), 2020, 52(4): 95-103. doi: 10.6054/j.jscnun.2020066
引用本文: 曾永泉, 张鹏. 具有现实约束的均值-VaR投资组合绩效评价[J]. 华南师范大学学报(自然科学版), 2020, 52(4): 95-103. doi: 10.6054/j.jscnun.2020066
ZENG Yongquan, ZHANG Peng. Measuring the Efficiency of Mean-VaR Portfolio Selection with Real Constraints[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(4): 95-103. doi: 10.6054/j.jscnun.2020066
Citation: ZENG Yongquan, ZHANG Peng. Measuring the Efficiency of Mean-VaR Portfolio Selection with Real Constraints[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(4): 95-103. doi: 10.6054/j.jscnun.2020066

具有现实约束的均值-VaR投资组合绩效评价

doi: 10.6054/j.jscnun.2020066
基金项目: 

国家自然科学基金项目 71271161

广东省软科学项目 2019A101002066

广东省软科学项目 2019A101002052

广东省软科学项目 2018A070712030

详细信息
    通讯作者:

    张鹏,教授,Email:zhangpeng300478@aliyun.com

  • 中图分类号: O221.2;F830.91

Measuring the Efficiency of Mean-VaR Portfolio Selection with Real Constraints

  • 摘要: 考虑交易成本、借款约束、上下界约束和基数约束等实际约束条件,提出了均值-VaR投资组合优化模型;该投资组合优化模型非常复杂,难以获得真实前沿面的解析解,给投资组合理论的应用带来了很大的困难,因此,进一步提出了具有实际约束的均值-VaR投资组合DEA绩效评价模型,通过构建DEA模型的前沿面来逼近真实前沿面,从而对构建的投资组合绩效评价模型进行效率评价;最后,运用上海证券市场的股票周交易数据进行实证研究.研究结果表明:随着样本数据量的增大,DEA前沿面逐渐接近于真实前沿面.
  • 图  1  分段线性凸交易成本函数

    Figure  1.  The piecewise linear convex transaction cost function

    图  2  投资组合效率

    Figure  2.  The portfolio efficiency

    图  3  投资组合真实前沿面

    Figure  3.  The real frontier of portfolio

    图  4  投资组合7种前沿面

    Figure  4.  The seven frontiers of portfolio

    图  5  收益率均值分布

    Figure  5.  The mean return distribution

    表  1  股票收益率均值及其相关性

    Table  1.   The expected return of stock and its correlation

    股票代码 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
    收益率均值 0.002 53 0.002 70 0.002 93 0.002 64 0.001 71 0.001 64 0.002 71 0.002 32 0.002 54 0.004 37
    相关系数 0.259 42 0.418 26 0.259 31 0.424 06 0.507 93 0.250 49 0.431 61 0.324 97 0.489 24 0.403 57
    股票代码 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20
    收益率均值 0.005 49 0.003 91 0.006 47 0.005 35 0.005 41 0.002 04 0.002 42 0.001 88 0.002 98 0.001 83
    相关系数 0.249 43 0.161 08 0.384 82 0.223 37 0.382 54 0.308 39 0.496 61 0.338 87 0.345 69 0.469 35
    股票代码 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30
    收益率均值 0.003 11 0.002 04 0.002 71 0.003 11 0.002 24 0.003 92 0.004 15 0.001 83 0.001 53 0.002 97
    相关系数 0.524 21 0.334 95 0.396 09 0.438 01 0.510 86 0.390 27 0.431 78 0.331 44 0.033 17 0.406 50
    下载: 导出CSV

    表  2  投资组合的净收益率(VaR0∈[0, 0.089])

    Table  2.   The portfolio return when VaR0 ∈[0, 0.089]

    VaR0 0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.024 0.027 0.030
    净收益率 0.000 40 0.000 66 0.000 93 0.001 19 0.001 44 0.001 69 0.001 94 0.002 19 0.002 43 0.002 67 0.002 91
    VaR0 0.033 0.036 0.039 0.042 0.045 0.048 0.051 0.054 0.057 0.060 0.063
    净收益率 0.003 15 0.003 39 0.003 63 0.003 86 0.004 09 0.004 32 0.004 54 0.004 76 0.004 98 0.005 18 0.005 38
    VaR0 0.066 0.069 0.072 0.075 0.078 0.081 0.084 0.087 0.089
    净收益率 0.005 57 0.005 75 0.005 92 0.006 07 0.006 21 0.006 33 0.006 43 0.006 51 0.006 55
    下载: 导出CSV

    表  3  模型(14)的不同风险和样本数据量下的净收益率

    Table  3.   The net return according to different risk and sample sizes in Model(14)

    VaR0 m/只
    100 200 500 1 000 2 000 4 000
    0 0.000 34 0.000 34 0.000 34 0.000 34 0.000 34 0.000 34
    0.003 0.000 52 0.000 54 0.000 57 0.000 57 0.000 57 0.000 58
    0.006 0.000 67 0.000 78 0.000 80 0.000 81 0.000 82 0.000 82
    0.009 0.000 86 0.000 97 0.000 98 0.000 99 0.001 03 0.001 05
    0.012 0.001 04 0.001 17 0.001 21 0.001 22 0.001 25 0.001 28
    0.015 0.001 22 0.001 38 0.001 43 0.001 45 0.001 48 0.001 50
    0.018 0.001 41 0.001 57 0.001 62 0.001 65 0.001 72 0.001 73
    0.021 0.001 59 0.001 76 0.001 81 0.001 86 0.001 94 0.001 96
    0.024 0.001 77 0.001 95 0.001 99 0.002 06 0.002 18 0.002 19
    0.027 0.001 95 0.002 13 0.002 17 0.002 26 0.002 38 0.002 41
    0.030 0.002 14 0.002 30 0.002 36 0.002 47 0.002 61 0.002 64
    0.033 0.002 32 0.002 47 0.002 54 0.002 67 0.002 86 0.002 87
    0.036 0.002 50 0.002 65 0.002 83 0.002 87 0.003 10 0.003 10
    0.039 0.002 66 0.002 82 0.002 91 0.003 08 0.003 31 0.003 32
    0.042 0.002 81 0.002 99 0.003 09 0.003 28 0.003 52 0.003 55
    0.045 0.002 97 0.003 16 0.003 28 0.003 48 0.003 75 0.003 78
    0.048 0.003 12 0.003 33 0.003 46 0.003 69 0.003 97 0.004 01
    0.051 0.003 28 0.003 51 0.003 65 0.003 89 0.004 21 0.004 24
    0.054 0.003 43 0.003 68 0.003 83 0.004 09 0.004 38 0.004 46
    0.057 0.003 59 0.003 85 0.004 02 0.004 30 0.004 65 0.004 69
    0.060 0.003 74 0.004 01 0.004 20 0.004 50 0.004 90 0.004 92
    0.063 0.003 90 0.004 15 0.004 38 0.004 67 0.005 13 0.005 15
    0.066 0.004 05 0.004 30 0.004 57 0.004 84 0.005 36 0.005 37
    0.069 0.004 21 0.004 44 0.004 75 0.005 02 0.005 54 0.005 57
    0.072 0.004 36 0.004 58 0.004 94 0.005 19 0.005 54 0.005 57
    0.075 0.004 52 0.004 73 0.005 12 0.005 36 0.005 54 0.005 57
    0.078 0.004 67 0.004 80 0.005 22 0.005 42 0.005 54 0.005 57
    0.081 0.004 70 0.004 80 0.005 22 0.005 42 0.005 54 0.005 57
    0.084 0.004 70 0.004 80 0.005 22 0.005 42 0.005 54 0.005 57
    0.087 0.004 70 0.004 80 0.005 22 0.005 42 0.005 54 0.005 57
    0.089 0.004 70 0.004 80 0.005 22 0.005 42 0.005 54 0.005 57
    下载: 导出CSV

    表  4  收益、风险导向效率PEr、PEv与DEA效率值θ间的相关系数

    Table  4.   The correlation coefficents between PEr or PEv and θ

    比较因子 m/只
    100 200 500 1 000 2 000 4 000
    PErθ 0.944 3 0.964 2 0.981 0 0.993 5 0.994 0 0.994 4
    PEvθ 0.969 1 0.982 4 0.987 2 0.991 1 0.993 0 0.993 6
    下载: 导出CSV

    表  5  不同风险和不同样本数据量下的净收益率与理想期望收益率的差值

    Table  5.   The distance value between the rate of net return and the rate of ideal expected return according to different risk and sample sizes

    m/只 VaR0
    0.036 0.051 0.075 0.089
    100 0.000 77 0.001 26 0.001 55 0.001 85
    200 0.000 61 0.001 03 0.001 34 0.001 75
    500 0.000 56 0.000 90 0.000 95 0.001 33
    1 000 0.000 52 0.000 65 0.000 71 0.001 12
    2 000 0.000 32 0.000 33 0.000 50 0.000 98
    4 000 0.000 29 0.000 31 0.000 50 0.000 98
    下载: 导出CSV

    表  6  不同样本数据量下的运行时间

    Table  6.   The operation time for different sizes of sample data  s

    m/只 100 200 500 1 000 2 000 4 000
    运行时间 24.8 62.7 367.7 1 070.8 8 502.8 35 470.8
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-06-27
  • 刊出日期:  2020-08-25

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