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Table 9 Mean, standard deviation (Std), median, minimum (Min) and maximum (Max) values of the performance metrics for the compared algorithms for the Mean-semi-variance-CVaR portfolio optimization problem

From: Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures

Dataset Statistic S Δ IGD HV
   NSGA-IIb NSGA-IIa SPEA 2b SPEA 2a NSGA-IIb NSGA-IIa SPEA 2b SPEA 2a NSGA-IIb NSGA-IIa SPEA 2b SPEA 2a NSGA-IIb NSGA-IIa SPEA 2b SPEA 2a
DowJones Mean 0.0113 0.1829 0.0122 0.0047 0.7356 0.9073 0.7304 0.5973 0.4643 0.5827 0.4685 0.4243 0.9383 0.9160 0.9349 1.1504
  Median 0.0096 0.0040 0.0111 0.0046 0.7322 0.6091 0.7278 0.5938 0.4655 0.4232 0.4703 0.4243 0.9378 1.1538 0.9353 1.1507
  Std 0.0056 0.5373 0.0051 0.0003 0.0235 0.6294 0.0219 0.0129 0.0106 0.2935 0.0097 0.0013 0.0235 0.4254 0.0213 0.0011
  Min 0.0055 0.0000 0.0068 0.0042 0.7058 0.5683 0.6987 0.5840 0.4371 0.4216 0.4480 0.4225 0.8930 0.0259 0.8970 1.1487
  Max 0.0315 1.7121 0.0269 0.0057 0.8140 2.3622 0.7761 0.6263 0.4836 1.3523 0.4842 0.4274 0.9936 1.1556 0.9650 1.1516
FF49Industries Mean 0.0149 0.0048 0.0130 0.0051 0.6899 0.6116 0.6875 0.6264 0.7604 0.5661 0.7592 0.5663 0.4675 0.9934 0.4676 0.9923
  Median 0.0131 0.0048 0.0122 0.0052 0.6973 0.6095 0.6877 0.6293 0.7613 0.5662 0.7615 0.5663 0.4634 0.9935 0.4646 0.9921
  Std 0.0056 0.0004 0.0025 0.0003 0.0188 0.0106 0.0161 0.0110 0.0203 0.0012 0.0213 0.0009 0.0222 0.0006 0.0191 0.0007
  Min 0.0090 0.0040 0.0106 0.0046 0.6452 0.5942 0.6577 0.6071 0.7231 0.5633 0.7126 0.5647 0.4371 0.9924 0.4394 0.9910
  Max 0.0284 0.0056 0.0209 0.0060 0.7161 0.6322 0.7275 0.6430 0.7878 0.5681 0.7861 0.5682 0.5135 0.9944 0.5212 0.9937
NASDAQ100 Mean 0.0060 0.0065 0.0060 0.0087 0.7885 0.5807 0.7862 0.6090 0.7007 0.3603 0.7013 0.3600 0.5367 1.2166 0.5348 1.2143
  Median 0.0058 0.0051 0.0060 0.0073 0.7846 0.5844 0.7847 0.5979 0.7071 0.3603 0.7065 0.3598 0.5331 1.2167 0.5318 1.2154
  Std 0.0012 0.0045 0.0010 0.0033 0.0131 0.0380 0.0097 0.0326 0.0174 0.0013 0.0187 0.0009 0.0180 0.0009 0.0198 0.0029
  Min 0.0044 0.0041 0.0048 0.0054 0.7720 0.5141 0.7711 0.5572 0.6494 0.3583 0.6499 0.3584 0.5155 1.2148 0.4940 1.2061
  Max 0.0090 0.0249 0.0081 0.0157 0.8123 0.6846 0.8026 0.6820 0.7173 0.3631 0.7353 0.3621 0.5875 1.2177 0.5867 1.2179
SP500 Mean 0.0025 0.0117 0.0024 0.0131 0.9130 0.6531 0.9114 0.6480 1.0043 0.4065 1.0042 0.4057 0.1793 1.1797 0.1795 1.1822
  Median 0.0024 0.0103 0.0023 0.0114 0.9127 0.6511 0.9104 0.6431 1.0049 0.4059 1.0049 0.4053 0.1784 1.1819 0.1786 1.1841
  Std 0.0004 0.0053 0.0003 0.0070 0.0054 0.0345 0.0050 0.0311 0.0049 0.0038 0.0050 0.0021 0.0041 0.0112 0.0042 0.0072
  Min 0.0018 0.0032 0.0018 0.0049 0.8997 0.5986 0.9060 0.5846 0.9939 0.4017 0.9937 0.4019 0.1718 1.1413 0.1722 1.1611
  Max 0.0033 0.0204 0.0031 0.0325 0.9220 0.7283 0.9257 0.7103 1.0104 0.4183 1.0111 0.4108 0.1880 1.1929 0.1881 1.1913
NASDAQComp Mean 0.0027 0.0106 0.0026 0.0123 0.8967 0.6113 0.8968 0.5986 1.0450 0.5133 1.0450 0.5132 0.1612 1.0369 0.1612 1.0417
  Median 0.0027 0.0099 0.0025 0.0100 0.8957 0.6068 0.8967 0.5950 1.0448 0.5119 1.0449 0.5144 0.1615 1.0396 0.1614 1.0425
  Std 0.0004 0.0045 0.0003 0.0051 0.0068 0.0289 0.0068 0.0247 0.0021 0.0083 0.0021 0.0065 0.0017 0.0119 0.0017 0.0080
  Min 0.0021 0.0054 0.0022 0.0063 0.8869 0.5638 0.8850 0.5521 1.0421 0.5025 1.0420 0.5019 0.1581 1.0050 0.1579 1.0245
  Max 0.0038 0.0248 0.0030 0.0233 0.9106 0.6863 0.9140 0.6397 1.0499 0.5377 1.0499 0.5268 0.1644 1.0576 0.1646 1.0537
  1. aNumbers in bold represent best results among the algorithms with respect to the corresponding performance metric