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

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