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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)