Table 10 Comparisons of P-GE-NoVaS and P-GA-NoVaS methods

500 simulated data

M1-1step

0.85483

0.84138

0.02

M1-5steps

0.40510

0.40137

0.01

M1-30steps

0.03293

0.03290

0.00

M2-1step

0.98431

0.99658

0.01

M2-5steps

0.90156

0.91980

0.02

M2-30steps

0.49761

0.48396

0.03

M3-1step

0.99360

0.98407

0.01

M3-5steps

0.94456

0.94073

0.00

M3-30steps

0.92128

0.90855

0.01

M4-1step

0.97484

0.99640

0.02

M4-5steps

0.90862

0.95338

0.05

M4-30steps

0.68266

0.67594

0.01

M5-1step

0.96936

0.97151

0.00

M5-5steps

0.82810

0.82747

0.00

M5-30steps

0.53026

0.47311

0.11

M6-1step

0.90196

0.93509

0.04

M6-5steps

0.75922

0.80311

0.05

M6-30steps

0.40790

0.41112

0.01

M7-1step

0.96081

0.95932

0.00

M7-5steps

0.84889

0.85127

0.00

M7-30steps

0.69698

0.71391

0.02

M8-1step

0.92557

0.93452

0.01

M8-5steps

0.92549

0.93178

0.01

M8-30steps

0.33834

0.33853

0.00

250 simulated data

M1-1step

0.83168

0.83034

0.00

M1-5steps

0.43772

0.43247

0.01

M1-30steps

0.22659

0.23035

0.02

M2-1step

0.88781

0.87614

0.01

M2-5steps

0.52872

0.51712

0.02

M2-30steps

0.73604

0.75251

0.02

M3-1step

0.94635

0.93693

0.01

M3-5steps

0.96361

0.99977

0.04

M3-30steps

0.98872

0.99818

0.01

M4-1step

0.92829

0.92811

0.00

M4-5steps

0.67482

0.67894

0.01

M4-30steps

0.71003

0.81115

0.12

M5-1step

0.78087

0.79075

0.01

M5-5steps

0.34396

0.35155

0.02

M5-30steps

0.00201

0.00194

0.03

M6-1step

0.94661

0.93863

0.01

M6-5steps

0.84719

0.85851

0.01

M6-30steps

0.70301

0.70420

0.00

M7-1step

0.73553

0.83216

0.12

M7-5steps

0.46618

0.48020

0.03

M7-30steps

0.06479

0.06507

0.00

M8-1step

0.76586

0.83340

0.08

M8-5steps

0.38107

0.45665

0.17

M8-30steps

0.00918

0.00983

0.07

Previous 2-year real-world data

AAPL-1step

0.98261

0.97836

0.00

AAPL-5steps

1.00090

0.96999

0.03

AAPL-30steps

0.97326

0.96174

0.01

BAC-1step

1.00416

1.02780

0.02

BAC-5steps

0.97542

0.99399

0.02

BAC-30steps

0.99533

1.00363

0.01

MSFT-1step

0.97376

0.96185

0.01

MSFT-5steps

0.96601

0.95271

0.01

MSFT-30steps

0.91046

0.88515

0.03

MCD-1step

0.98873

0.99005

0.00

MCD-5steps

0.98059

0.97777

0.00

MCD-30steps

0.99512

0.99418

0.00

1-year stock data

MCD18-1step

0.95332

0.94412

0.01

MCD18-5steps

0.88773

0.88151

0.01

MCD18-30steps

0.61097

0.61153

0.00

MCD19-1step

0.93141

0.94559

0.01

MCD19-5steps

0.90061

0.90602

0.01

MCD19-30steps

0.80805

0.77976

0.04

AAPL18-1step

0.96311

0.89283

0.07

AAPL18-5steps

0.85114

0.71233

0.16

AAPL18-30steps

0.35731

0.37081

0.04

AAPL19-1step

0.80948

0.81872

0.01

AAPL19-5steps

0.68191

0.68792

0.01

AAPL19-30steps

0.73823

0.72892

0.01

BAC18-1step

0.93031

0.92619

0.00

BAC18-5steps

0.86387

0.72512

0.16

BAC18-30steps

0.81429

0.87630

0.07

BAC19-1step

0.97757

0.98605

0.01

BAC19-5steps

0.89571

0.95436

0.06

BAC19-30steps

1.01175

1.03482

0.02

MSFT18-1step

0.94507

0.95921

0.01

MSFT18-5steps

0.76646

0.74237

0.03

MSFT18-30steps

0.68741

0.64717

0.06

MSFT19-1step

0.98469

0.95347

0.03

MSFT19-5steps

1.02387

0.95417

0.07

MSFT19-30steps

0.97585

0.98476

0.01

Tesla18-1step

0.95885

0.86238

0.10

Tesla18-5steps

1.02036

1.01560

0.00

Tesla18-30steps

1.22256

1.25005

0.02

Tesla19-1step

0.98646

0.98955

0.00

Tesla19-5steps

0.97523

0.96107

0.01

Tesla19-30steps

0.87158

0.84366

0.03

Bitcoin18-1step

0.99967

0.97734

0.02

Bitcoin18-5steps

1.02008

0.93826

0.08

Bitcoin18-30steps

0.95020

0.91364

0.04

Bitcoin19-1step

0.86795

0.87256

0.01

Bitcoin19-5steps

0.55620

0.56789

0.02

Bitcoin19-30steps

0.00624

0.00631

0.01

1-year index data

NASDAQ18-1step

0.94837

0.92421

0.03

NASDAQ18-5steps

0.83585

0.78823

0.06

NASDAQ18-30steps

0.74660

0.67389

0.10

NASDAQ19-1step

0.93558

0.93843

0.00

NASDAQ19-5steps

0.84459

0.84051

0.00

NASDAQ19-30steps

0.58924

0.59218

0.00

NYSE18-1step

0.95793

0.96619

0.01

NYSE18-5steps

0.87919

0.75822

0.14

NYSE18-30steps

0.79466

0.61830

0.22

NYSE19-1step

0.90407

0.92193

0.02

NYSE19-5steps

0.69822

0.71038

0.02

NYSE19-30steps

0.18173

0.18116

0.00

Smallcap18-1step

0.91299

0.91101

0.00

Smallcap18-5steps

0.73541

0.73223

0.00

Samllcap18-30steps

0.48461

0.46312

0.04

Smallcap19-1step

0.98731

0.98482

0.00

Smallcap19-5steps

0.87700

0.85490

0.03

Samllcap19-30steps

0.88825

0.90360

0.02

Djones18-1step

0.84931

0.91192

0.07

Djones18-5steps

0.86017

0.76226

0.11

Djones18-30steps

0.66418

0.56854

0.14

Djones19-1step

0.96365

0.96977

0.01

Djones19-5steps

0.89542

0.91238

0.02

Djones19-30steps

0.80304

0.81803

0.02

S &P500-18-1step

0.90469

0.88405

0.02

S &P500-18-5steps

0.90544

0.75646

0.16

S &P500-18-30steps

0.83210

0.72104

0.13

S &P500-19-1step

0.92183

0.93162

0.01

S &P500-19-5steps

0.75579

0.77434

0.02

S &P500-19-30steps

0.29796

0.30127

0.01

BSE18-1step

0.94676

0.92568

0.02

BSE18-5steps

0.82886

0.84408

0.02

BSE18-30steps

0.44818

0.44092

0.02

BSE19-1step

0.67694

0.66667

0.02

BSE19-5steps

0.23665

0.23603

0.00

BSE19-30steps

0.02890

0.02888

0.00

BIST18-1step

0.92271

0.94138

0.02

BIST18-5steps

0.80837

0.81417

0.01

BIST18-30steps

1.09665

1.09900

0.00

BIST19-1step

0.95467

0.98234

0.03

BIST19-5steps

0.82898

0.85370

0.03

BIST19-30steps

0.88511

0.85743

0.03

Volatile 1-year stock data

NKE-1step

0.65295

0.65594

0.00

NKE-5steps

0.22550

0.22226

0.01

NKE-30steps

0.00337

0.00340

0.01

AMZN-1step

0.90200

0.90487

0.00

AMZN-5steps

0.71789

0.72850

0.01

AMZN-30steps

0.53460

0.53310

0.00

IBM-1step

0.80744

0.79509

0.02

IBM-5steps

0.40743

0.38413

0.06

IBM-30steps

0.00918

0.00879

0.04

MSFT-1step

0.84502

0.81582

0.03

MSFT-5steps

0.37528

0.38022

0.01

MSFT-30steps

0.00732

0.00784

0.07

SBUX-1step

0.69943

0.66743

0.05

SBUX-5steps

0.30528

0.26856

0.12

SBUX-30steps

0.00289

0.00236

0.18

KO-1step

0.81309

0.77035

0.05

KO-5steps

0.39679

0.33405

0.16

KO-30steps

0.01963

0.01582

0.19

MCD-1step

0.58018

0.56414

0.03

MCD-5steps

0.17887

0.17439

0.03

MCD-30steps

0.00001

0.00001

0.02

Tesla-1step

0.89253

0.88782

0.01

Tesla-5steps

0.66177

0.66937

0.01

Tesla-30steps

0.22460

0.22395

0.00

Bitcoin-1step

0.36346

0.36326

0.00

Bitcoin-5steps

0.01321

0.01322

0.00

Bitcoin-30steps

0.00000

0.00000

0.00

Volatile 1-year currency data

CADJPY-1step

0.48712

0.48367

0.01

CADJPY-5steps

0.13549

0.14376

0.06

CADJPY-30steps

0.00394

0.00482

0.18

EURJPY-1step

0.94206

0.95133

0.01

EURJPY-5steps

0.76727

0.75636

0.01

EURJPY-30steps

0.15350

0.18189

0.16

USDCNY-1step

0.96766

0.95757

0.01

USDCNY-5steps

0.86364

0.83523

0.03

USDCNY-30steps

0.60121

0.60131

0.00

GBPJPY-1step

0.86553

0.87160

0.01

GBPJPY-5steps

0.49208

0.48842

0.01

GBPJPY-30steps

0.17246

0.17262

0.00

USDINR-1step

0.98975

0.93140

0.06

USDINR-5steps

0.81103

0.75693

0.07

USDINR-30steps

0.17966

0.11380

0.37

CNYJPY-1step

0.79877

0.74586

0.07

CNYJPY-5steps

0.40569

0.34839

0.14

CNYJPY-30steps

0.06270

0.05444

0.13

Volatile 1-year index data

S &P500-1step

0.92349

0.92854

0.01

S &P500-5steps

0.75183

0.77060

0.02

S &P500-30steps

0.29793

0.30115

0.01

NASDAQ-1step

0.75350

0.77753

0.03

NASDAQ-5steps

0.33519

0.36428

0.08

NASDAQ-30steps

0.00599

0.00696

0.14

NYSE-1step

0.57174

0.54598

0.05

NYSE-5steps

0.10182

0.07798

0.23

NYSE-30steps

0.00001

0.00001

0.01

Smallcap-1step

0.60931

0.57773

0.05

Smallcap-5steps

0.10337

0.09628

0.07

Smallcap-30steps

0.00006

0.00004

0.39

BSE-1step

0.39745

0.39851

0.00

BSE-5steps

0.04109

0.04170

0.01

BSE-30steps

0.00002

0.00002

0.05

DAX-1step

0.64727

0.66097

0.02

DAX-5steps

0.10356

0.11085

0.07

DAX-30steps

0.00007

0.00008

0.06

USDX future-1step

0.99640

1.03693

0.04

USDX future-5steps

0.54834

0.51997

0.05

USDX future-30steps

0.10278

0.10063

0.02

Bovespa-1step

0.57558

0.60656

0.05

Bovespa-5steps

0.07447

0.09395

0.21

Bovespa-30steps

2.04E−6

3.19E−6

0.36

Djones-1step

0.57550

0.54422

0.05

Djones-5steps

0.11554

0.08698

0.25

Djones-30steps

0.00001

0.00003

0.53

BIST-1step

0.90832

0.92418

0.02

BIST-5steps

0.47480

0.49279

0.04

BIST-30steps

0.05550

0.05671

0.02