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Table 5 The Table presents percentiles of ten performance statistics for three investment strategies

From: Zero covariation returns

Performance statistics     
Percentile ZCP MVA MVBGEV Percentile ZCP MVA MVBGEV
Total returns Sharpe ratios
5 193.2717 68.9452 76.7186 5 0.4656 0.1947 0.2326
25 255.4264 120.9758 127.8869 25 0.6057 0.2951 0.3367
50 306.5203 161.9877 174.9696 50 0.6931 0.3797 0.4392
75 367.5754 233.1460 258.1319 75 0.7969 0.5046 0.5674
95 493.4716 444.3992 454.0174 95 0.9288 0.7307 0.7309
Gain loss ratios Proportion positive
5 1.1344 1.0667 1.0875 5 0.4541 0.4354 0.4392
25 1.1699 1.0880 1.1091 25 0.4601 0.4433 0.4475
50 1.1928 1.1074 1.1334 50 0.4652 0.4506 0.4539
75 1.2257 1.1461 1.1665 75 0.4711 0.4550 0.4608
95 1.2504 1.2088 1.2028 95 0.4769 0.4656 0.4696
Acceptability index Max draw down
5 0.0225 0.0113 0.0146 5 35.9336 43.5110 39.9070
25 0.0282 0.0148 0.0179 25 50.1653 62.3000 49.4967
50 0.0318 0.0179 0.0215 50 60.4912 80.1955 64.5189
75 0.0365 0.0236 0.0268 75 71.4947 106.1338 94.8317
95 0.0400 0.0326 0.0314 95 114.6504 170.1741 149.8968
Skewness Kurtosis
5 7.0578 5.4547 6.2779 5 183.2202 150.5144 160.6891
25 11.4880 11.7356 12.6388 25 349.2345 370.6285 394.1370
50 15.0425 16.6281 20.6671 50 493.9739 558.1219 751.9566
75 18.6804 23.0900 26.7035 75 658.1477 868.8013 1053.7356
95 23.6825 29.3793 34.2800 95 900.6095 1194.4466 1464.7390
Peakedness Tailweightedness
5 0.8146 0.8313 0.8322 5 0.0106 0.0062 0.0029
25 0.8386 0.8598 0.8611 25 0.0159 0.0119 0.0095
50 0.8600 0.8781 0.8953 50 0.0220 0.0194 0.0159
75 0.8807 0.9039 0.9213 75 0.0282 0.0287 0.0276
95 0.9030 0.9387 0.9625 95 0.0342 0.0417 0.0406
  1. They are zero covariation (ZCP) returns modeling with local bilateral gamma parameters of motion depending nonlinearly on all ten asset prices. Support vector machine regressions estimate the dependence. Also shown are mean variance portfolio selection with sample averages for means (MVA) and bilateral gamma exponential variations for the means (MVBGEV)