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

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