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基本指数-最小下半方差投资组合优化研究

张鹏 李欣茵 曾永泉

张鹏, 李欣茵, 曾永泉. 基本指数-最小下半方差投资组合优化研究[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 93-101. doi: 10.6054/j.jscnun.2021047
引用本文: 张鹏, 李欣茵, 曾永泉. 基本指数-最小下半方差投资组合优化研究[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 93-101. doi: 10.6054/j.jscnun.2021047
ZHANG Peng, LI Xinyin, ZENG Yongquan. The Mixture of Fundamental Indexing and Minimum Semi-variance Portfolio Selection[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(3): 93-101. doi: 10.6054/j.jscnun.2021047
Citation: ZHANG Peng, LI Xinyin, ZENG Yongquan. The Mixture of Fundamental Indexing and Minimum Semi-variance Portfolio Selection[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(3): 93-101. doi: 10.6054/j.jscnun.2021047

基本指数-最小下半方差投资组合优化研究

doi: 10.6054/j.jscnun.2021047
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

湖北省技术创新专项软科学项目 2019ADC030

详细信息
    通讯作者:

    张鹏,Email: 20181021@m.scnu.edu.cn

  • 中图分类号: F830.91

The Mixture of Fundamental Indexing and Minimum Semi-variance Portfolio Selection

  • 摘要: 为了克服方差作为风险度量无法区分收益和损失的局限性,同时弥补经典均值-方差模型忽略了企业基本面状况的缺陷,该文结合下半方差和基本指数的优点,分别考虑1-、2-范数交易成本,构建了基于期望效用最大化的基本指数-最小下半方差投资组合模型(简称“FI-semiv模型”),并运用不等式组的旋转算法进行求解. 文章通过“滚动窗口”的方法,对FI-semiv模型进行了样本外检验与分析,并进一步将该模型与最小方差模型、最小下半方差模型和等比例投资模型的夏普比率进行对比. 结果表明:基于FI-semiv模型构建的投资组合的夏普比率得到了有效提高,FI-semiv投资组合的风险更小,投资效率更高.
  • 图  1  具有1-范数交易成本的投资组合的夏普比率

    Figure  1.  The sharp ratio of portfolios with 1-norm transaction

    图  2  具有2-范数交易成本的投资组合夏普比率

    Figure  2.  The sharp ratio of portfolios with 2-norm transaction

    表  1  具有1-范数交易成本的FI-semiv投资组合相关指标

    Table  1.   The related indicators of 1-P-FI-semiv portfolios

    时期 c d 收益率 方差 夏普比率 时期 c d 收益率 方差 夏普比率
    1 0.000 0 1.000 0 -0.054 7 0.001 0 -1.754 1 31 1.000 0 0.000 0 0.024 0 0.002 8 0.451 0
    2 0.000 0 1.000 0 0.022 0 0.001 0 0.702 1 32 1.000 0 0.000 0 -0.021 9 0.002 8 -0.411 3
    3 0.000 0 1.000 0 0.005 6 0.000 8 0.191 8 33 0.000 0 1.000 0 -0.019 3 0.000 7 -0.746 8
    4 0.000 0 1.000 0 0.011 2 0.000 8 0.390 5 34 1.000 0 0.000 0 -0.026 9 0.002 5 -0.534 5
    5 1.000 0 0.000 0 0.001 6 0.003 3 0.028 3 35 1.000 0 0.000 0 0.073 8 0.002 1 1.592 8
    6 0.000 0 1.000 0 0.003 5 0.000 8 0.125 2 36 0.000 0 1.000 0 0.027 1 0.000 5 1.185 3
    7 1.000 0 0.000 0 -0.012 7 0.003 2 -0.224 0 37 0.000 0 1.000 0 0.009 6 0.000 5 0.416 4
    8 1.000 0 0.000 0 0.026 2 0.002 9 0.484 0 38 0.000 0 1.000 0 0.059 8 0.000 5 2.605 3
    9 0.000 0 1.000 0 -0.009 6 0.000 7 -0.357 6 39 0.000 0 1.000 0 0.002 8 0.000 6 0.115 2
    10 0.000 0 1.000 0 0.052 7 0.000 7 1.962 5 40 1.000 0 0.000 0 -0.003 7 0.002 0 -0.084 0
    11 1.000 0 0.000 0 0.029 2 0.002 8 0.550 1 41 0.000 0 1.000 0 0.024 9 0.000 6 1.040 4
    12 0.000 0 1.000 0 0.001 7 0.000 7 0.063 9 42 1.000 0 0.000 0 0.020 2 0.001 9 0.462 5
    13 0.000 0 1.000 0 0.007 5 0.000 7 0.278 5 43 0.000 0 1.000 0 -0.000 9 0.000 5 -0.039 1
    14 1.000 0 0.000 0 0.088 5 0.002 7 1.707 1 44 0.000 0 1.000 0 -0.003 4 0.000 5 -0.152 7
    15 0.000 0 1.000 0 -0.001 4 0.000 7 -0.052 6 45 1.000 0 0.000 0 0.009 5 0.001 8 0.221 9
    16 0.000 0 1.000 0 -0.042 5 0.000 7 -1.636 7 46 1.000 0 0.000 0 0.024 9 0.001 8 0.583 9
    17 1.000 0 0.000 0 0.020 4 0.003 1 0.365 4 47 1.000 0 0.000 0 0.072 7 0.001 8 1.719 0
    18 1.000 0 0.000 0 0.006 4 0.003 1 0.116 3 48 1.000 0 0.000 0 0.024 6 0.001 8 0.579 4
    19 1.000 0 0.000 0 0.039 6 0.003 0 0.727 1 49 1.000 0 0.000 0 0.021 8 0.001 7 0.526 3
    20 0.000 0 1.000 0 -0.045 0 0.000 6 -1.821 7 50 1.000 0 0.000 0 -0.021 9 0.001 7 -0.531 9
    21 1.000 0 0.000 0 0.016 0 0.002 9 0.294 5 51 0.000 0 1.000 0 0.023 5 0.000 5 1.031 2
    22 0.000 0 1.000 0 0.077 4 0.000 6 3.156 3 52 1.000 0 0.000 0 0.030 5 0.001 7 0.742 4
    23 1.000 0 0.000 0 -0.004 9 0.002 7 -0.093 9 53 1.000 0 0.000 0 0.018 4 0.001 7 0.449 4
    24 0.000 0 1.000 0 0.012 4 0.000 7 0.482 6 54 0.000 0 1.000 0 0.017 4 0.000 5 0.798 5
    25 1.000 0 0.000 0 -0.015 2 0.002 8 -0.285 0 55 1.000 0 0.000 0 0.031 3 0.001 7 0.764 1
    26 0.000 0 1.000 0 -0.001 1 0.000 7 -0.041 4 56 1.000 0 0.000 0 0.035 4 0.001 7 0.862 9
    27 0.000 0 1.000 0 0.046 7 0.000 6 1.844 6 57 0.836 8 0.163 2 0.004 8 0.001 3 0.130 6
    28 0.000 0 1.000 0 0.000 4 0.000 7 0.016 7 58 0.000 0 1.000 0 -0.063 2 0.000 4 -3.033 5
    29 0.000 0 1.000 0 0.019 5 0.000 6 0.768 3 59 0.000 0 1.000 0 0.018 5 0.000 5 0.854 0
    30 0.000 0 1.000 0 0.045 7 0.000 6 1.792 7 60 1.000 0 0.000 0 -0.087 7 0.001 7 -2.135 0
    下载: 导出CSV

    表  2  具有2-范数交易成本的FI-semiv投资组合相关指标

    Table  2.   The related indicators of 2-P-FI-semiv portfolios

    时期 c d 收益率 方差 夏普比率 时期 c d 收益率 方差 夏普比率
    1 0.000 0 1.000 0 -0.056 6 0.001 0 -1.761 2 31 1.000 0 0.000 0 0.030 0 0.002 8 0.563 7
    2 0.000 0 1.000 0 0.027 1 0.001 0 0.847 0 32 1.000 0 0.000 0 -0.015 9 0.002 8 -0.298 9
    3 0.000 0 1.000 0 0.012 4 0.000 9 0.421 7 33 0.000 0 1.000 0 -0.014 8 0.000 7 -0.561 3
    4 0.000 0 1.000 0 0.020 2 0.000 8 0.696 5 34 1.000 0 0.000 0 -0.020 9 0.002 5 -0.415 3
    5 1.000 0 0.000 0 0.007 6 0.003 3 0.132 6 35 1.000 0 0.000 0 0.079 8 0.002 1 1.722 2
    6 0.000 0 1.000 0 0.010 2 0.000 8 0.358 0 36 0.000 0 1.000 0 0.032 9 0.000 6 1.356 6
    7 1.000 0 0.000 0 -0.006 7 0.003 2 -0.118 4 37 0.000 0 1.000 0 0.013 3 0.000 6 0.541 0
    8 1.000 0 0.000 0 0.032 2 0.002 9 0.594 5 38 0.000 0 1.000 0 0.065 2 0.000 6 2.673 7
    9 0.000 0 1.000 0 -0.007 8 0.000 7 -0.288 6 39 1.000 0 0.000 0 0.008 6 0.002 0 0.190 9
    10 0.000 0 1.000 0 0.050 7 0.000 7 1.869 2 40 1.000 0 0.000 0 0.002 2 0.002 0 0.050 4
    11 1.000 0 0.000 0 0.035 2 0.002 8 0.663 0 41 0.000 0 1.000 0 0.032 0 0.000 7 1.238 9
    12 0.000 0 1.000 0 0.004 8 0.000 7 0.177 2 42 1.000 0 0.000 0 0.026 2 0.001 9 0.599 6
    13 0.000 0 1.000 0 0.010 6 0.000 7 0.391 6 43 0.000 0 1.000 0 0.002 2 0.000 5 0.095 6
    14 1.000 0 0.000 0 0.094 5 0.002 7 1.822 7 44 0.000 0 1.000 0 0.007 1 0.000 5 0.303 7
    15 0.000 0 1.000 0 0.004 5 0.000 7 0.169 9 45 1.000 0 0.000 0 0.015 4 0.001 8 0.362 6
    16 0.000 0 1.000 0 -0.047 3 0.000 7 -1.811 9 46 1.000 0 0.000 0 0.030 9 0.001 8 0.724 5
    17 1.000 0 0.000 0 0.026 4 0.003 1 0.472 7 47 1.000 0 0.000 0 0.078 7 0.001 8 1.860 7
    18 1.000 0 0.000 0 0.012 4 0.003 1 0.224 5 48 1.000 0 0.000 0 0.030 6 0.001 8 0.720 6
    19 1.000 0 0.000 0 0.045 6 0.003 0 0.837 1 49 1.000 0 0.000 0 0.027 8 0.001 7 0.671 2
    20 0.000 0 1.000 0 -0.041 9 0.000 6 -1.668 6 50 1.000 0 0.000 0 -0.015 9 0.001 7 -0.386 5
    21 1.000 0 0.000 0 0.022 0 0.002 9 0.404 9 51 0.000 0 1.000 0 0.028 1 0.000 5 1.212 0
    22 0.000 0 1.000 0 0.084 5 0.000 6 3.397 3 52 1.000 0 0.000 0 0.036 5 0.001 7 0.888 2
    23 1.000 0 0.000 0 0.001 1 0.002 7 0.021 7 53 1.000 0 0.000 0 0.024 4 0.001 7 0.596 0
    24 0.000 0 1.000 0 0.013 2 0.000 7 0.506 1 54 0.000 0 1.000 0 0.019 6 0.000 5 0.881 2
    25 1.000 0 0.000 0 -0.009 2 0.002 8 -0.172 7 55 1.000 0 0.000 0 0.037 3 0.001 7 0.910 4
    26 0.000 0 1.000 0 0.000 2 0.000 7 0.007 0 56 1.000 0 0.000 0 0.041 4 0.001 7 1.009 1
    27 0.000 0 1.000 0 0.048 1 0.000 7 1.876 0 57 0.000 0 1.000 0 0.014 6 0.000 5 0.678 9
    28 0.000 0 1.000 0 0.012 2 0.000 7 0.469 5 58 0.000 0 1.000 0 -0.055 0 0.000 4 -2.597 0
    29 0.000 0 1.000 0 0.021 9 0.000 7 0.848 7 59 0.000 0 1.000 0 0.026 1 0.000 5 1.180 9
    30 0.000 0 1.000 0 0.053 6 0.000 7 2.075 3 60 1.000 0 0.000 0 -0.081 7 0.001 7 -1.989 0
    下载: 导出CSV

    表  3  8个模型的相关指标

    Table  3.   The related indicators of measured models

    模型 平均收益率 平均标准差 平均夏普比率
    1-P-min 0.010 7 0.055 7 0.228 9
    1-P-semiv 0.012 8 0.058 1 0.259 2
    1-P-ew 0.004 2 0.036 0 0.142 0
    1-P-FI-semiv 0.011 2 0.038 1 0.320 7
    2-P-min 0.013 6 0.055 7 0.285 2
    2-P-semiv 0.015 8 0.058 1 0.314 8
    2-P-ew 0.007 2 0.036 0 0.229 2
    2-P-FI-semiv 0.016 5 0.038 5 0.470 8
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-10-26
  • 网络出版日期:  2021-07-06
  • 刊出日期:  2021-06-25

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