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Table 8 Mean, standard deviation (Std), median, minimum (Min) and maximum (Max) values of the performance metrics for the compared algorithms for the Mean-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 0.0080 0.0021 0.0082 0.0045 0.7888 0.6141 0.7795 0.6066 0.4172 0.4957 0.4120 0.3577 0.8327 0.8893 0.8224 1.1028
  Median 0.0074 0.0023 0.0074 0.0045 0.7922 0.5662 0.7774 0.6054 0.4188 0.3578 0.4108 0.3577 0.8193 1.1041 0.8177 1.1027
  Std 0.0028 0.0008 0.0025 0.0005 0.0293 0.1460 0.0328 0.0102 0.0127 0.2451 0.0115 0.0004 0.0314 0.3845 0.0252 0.0003
  Min 0.0044 0.0000 0.0050 0.0038 0.7340 0.5343 0.7277 0.5956 0.3910 0.3575 0.3955 0.3571 0.7866 0.1725 0.7898 1.1020
  Max 0.0155 0.0029 0.0153 0.0056 0.8532 1.0000 0.8469 0.6372 0.4361 0.9095 0.4360 0.3582 0.9013 1.1046 0.8962 1.1033
FF49Industries Mean 0.0085 0.0023 0.0083 0.0035 0.8015 0.6135 0.8026 0.6111 0.6740 0.5055 0.6787 0.5052 0.5184 0.9957 0.5103 0.9953
  Median 0.0083 0.0023 0.0082 0.0034 0.8023 0.6131 0.8030 0.6118 0.6792 0.5056 0.6804 0.5052 0.5171 0.9957 0.5089 0.9954
  Std 0.0018 0.0002 0.0015 0.0005 0.0208 0.0165 0.0255 0.0112 0.0162 0.0002 0.0136 0.0002 0.0134 0.0002 0.0115 0.0003
  Min 0.0061 0.0018 0.0053 0.0028 0.7702 0.5807 0.7529 0.5894 0.6404 0.5051 0.6473 0.5049 0.4992 0.9954 0.4924 0.9946
  Max 0.0115 0.0025 0.0111 0.0046 0.8508 0.6456 0.8556 0.6317 0.6970 0.5059 0.7021 0.5057 0.5592 0.9960 0.5416 0.9958
NASDAQ100 Mean 0.0044 0.0024 0.0044 0.0047 0.8454 0.5250 0.8410 0.6157 0.7159 0.3011 0.7179 0.3009 0.4227 1.1232 0.4132 1.1225
  Median 0.0044 0.0022 0.0044 0.0047 0.8487 0.5259 0.8399 0.6136 0.7223 0.3010 0.7245 0.3007 0.4169 1.1234 0.4106 1.1225
  Std 0.0007 0.0006 0.0006 0.0006 0.0140 0.0194 0.0137 0.0187 0.0165 0.0007 0.0175 0.0006 0.0154 0.0006 0.0141 0.0007
  Min 0.0031 0.0020 0.0031 0.0037 0.8158 0.4981 0.8131 0.5792 0.6785 0.2999 0.6767 0.2997 0.4024 1.1221 0.3920 1.1215
  Max 0.0060 0.0041 0.0056 0.0057 0.8634 0.5854 0.8716 0.6468 0.7366 0.3025 0.7441 0.3019 0.4523 1.1242 0.4506 1.1239
SP500 Mean 0.0017 0.0046 0.0017 0.0038 0.9455 0.6555 0.9445 0.6475 0.9658 0.3561 0.9658 0.3528 0.1886 1.0962 0.1877 1.1084
  Median 0.0017 0.0039 0.0017 0.0035 0.9464 0.6576 0.9438 0.6473 0.9660 0.3560 0.9660 0.3529 0.1889 1.0964 0.1868 1.1084
  Std 0.0003 0.0019 0.0003 0.0008 0.0050 0.0306 0.0047 0.0267 0.0028 0.0012 0.0030 0.0008 0.0030 0.0053 0.0038 0.0022
  Min 0.0012 0.0027 0.0013 0.0026 0.9383 0.6110 0.9363 0.5905 0.9606 0.3543 0.9599 0.3513 0.1843 1.0843 0.1828 1.1027
  Max 0.0025 0.0106 0.0026 0.0060 0.9559 0.7413 0.9594 0.6927 0.9709 0.3585 0.9717 0.3541 0.1951 1.1052 0.1952 1.1119
NASDAQComp Mean 0.0014 0.0062 0.0014 0.0044 0.9527 0.7833 0.9533 0.7366 0.9476 0.4536 0.9475 0.4497 0.2150 0.9999 0.2143 1.0210
  Median 0.0013 0.0051 0.0014 0.0040 0.9515 0.7882 0.9546 0.7343 0.9482 0.4507 0.9483 0.4504 0.2147 1.0054 0.2139 1.0225
  Std 0.0003 0.0035 0.0002 0.0014 0.0038 0.0381 0.0050 0.0267 0.0027 0.0114 0.0027 0.0053 0.0021 0.0173 0.0024 0.0068
  Min 0.0010 0.0033 0.0011 0.0029 0.9465 0.7014 0.9425 0.6977 0.9412 0.4434 0.9411 0.4388 0.2112 0.9573 0.2111 1.0037
  Max 0.0021 0.0190 0.0018 0.0089 0.9617 0.8544 0.9614 0.8029 0.9509 0.4952 0.9510 0.4585 0.2195 1.0287 0.2197 1.0341
  1. aNumbers in bold represent best results among the algorithms with respect to the corresponding performance metric