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Table 2 The in-sample results of Markowitz model and semiparametric method with VaR

From: Stressed portfolio optimization with semiparametric method

Period

Markowitz model

VOO

TLT

LQD

IAU

VNQ

Volatility

Return

SR

VaR

2015.10–2015.12

0.177457

0.236393

0.237593

0.251497

0.097060

0.004914

0.030581

0.306925

0.006247

2015.11–2016.01

0.191533

0.189183

0.330781

0.151453

0.137050

0.002987

− 0.005483

− 0.098757

0.007346

2015.12–2016.02

0.194609

0.355099

0.082842

0.298886

0.068564

0.004341

0.005303

0.056277

0.006773

2016.01–2016.03

0.260998

0.075808

0.533044

0.059611

0.070539

0.002181

0.008187

0.178133

0.003308

2016.02–2016.04

0.438323

0.064790

0.067393

0.369232

0.060262

0.002125

0.035512

0.825654

0.001020

2016.03–2016.05

0.390102

0.240234

0.210918

0.075207

0.083540

0.001978

0.012604

0.308068

0.002448

2016.04–2016.06

0.479150

0.070969

0.089529

0.298833

0.061519

0.002832

0.007287

0.121279

0.004774

2016.05–2016.07

0.738519

0.068578

0.061201

0.072736

0.058966

0.002899

0.016837

0.283215

0.003153

2016.06–2016.08

0.320867

0.055845

0.230660

0.336898

0.055729

0.005984

0.001661

0.010396

0.013003

2016.07–2016.09

0.050000

0.050000

0.050000

0.050000

0.800000

0.006583

0.027021

0.202071

0.011142

2016.08–2016.10

0.139885

0.050013

0.050025

0.710035

0.050042

0.006969

− 0.048987

− 0.354452

0.015765

2016.09–2016.11

0.050087

0.091749

0.050325

0.757647

0.050192

0.003759

− 0.003168

− 0.047676

0.006812

2016.10–2016.12

0.438323

0.064790

0.067393

0.369232

0.060262

0.002109

0.035072

0.821653

0.001010

2016.11–2017.01

0.390102

0.240234

0.210918

0.075207

0.083540

0.001967

0.012639

0.310623

0.002446

2016.12–2017.02

0.479150

0.070969

0.089529

0.298833

0.061519

0.002872

0.007412

0.121802

0.004850

2017.01–2017.03

0.738519

0.068578

0.061201

0.072736

0.058966

0.002898

0.016696

0.280854

0.003139

2017.02–2017.04

0.052075

0.081504

0.053957

0.750060

0.062405

0.005907

0.008514

0.068544

0.010037

2017.03–2017.05

0.050000

0.050000

0.050000

0.050000

0.800000

0.006613

0.027088

0.201664

0.011180

2017.04–2017.06

0.268480

0.506691

0.100368

0.066477

0.057984

0.003795

0.003241

0.037208

0.007439

2017.05–2017.07

0.050087

0.091749

0.050325

0.757647

0.050192

0.003773

− 0.003187

− 0.047763

0.006848

2017.06–2017.08

0.158318

0.147202

0.286875

0.077530

0.330075

0.003091

0.008758

0.134928

0.004218

2017.07–2017.09

0.068086

0.099889

0.581654

0.196896

0.053475

0.002464

0.011891

0.232854

0.003164

2017.08–2017.10

0.054063

0.324698

0.054747

0.226128

0.340363

0.004020

0.052083

0.642620

0.003341

2017.09–2017.11

0.694957

0.056122

0.065574

0.125798

0.057549

0.002685

0.013336

0.240615

0.004102

2017.10–2017.12

0.294399

0.078843

0.166064

0.401023

0.059670

0.003378

0.017698

0.255765

0.005440

2017.11–2018.01

0.050000

0.050000

0.050000

0.050000

0.800000

0.006603

0.026934

0.200794

0.011140

2017.12–2018.02

0.689011

0.050565

0.051537

0.156637

0.052250

0.008303

− 0.012137

− 0.075602

0.015948

2018.01–2018.03

0.050087

0.091749

0.050325

0.757647

0.050192

0.003766

− 0.003195

− 0.047956

0.006847

2018.02–2018.04

0.158318

0.147202

0.286875

0.077530

0.330075

0.003057

0.008730

0.135977

0.004188

2018.03–2018.05

0.068086

0.099889

0.581654

0.196896

0.053475

0.002495

0.011707

0.226234

0.003159

2018.04–2018.06

0.054063

0.324698

0.054747

0.226128

0.340363

0.004048

0.052520

0.643533

0.003367

2018.05–2018.07

0.694957

0.056122

0.065574

0.125798

0.057549

0.002736

0.013147

0.232666

0.004110

2018.06–2018.08

0.325014

0.342751

0.141088

0.076066

0.115081

0.003133

− 0.015913

− 0.260602

0.005865

2018.07–2018.09

0.227873

0.050683

0.242898

0.428362

0.050185

0.005906

0.032595

0.272428

0.009340

2018.08–2018.10

0.050000

0.050000

0.050000

0.800000

0.050000

0.015891

− 0.004267

− 0.014737

0.036630

2018.09–2018.11

0.583894

0.054994

0.249566

0.055026

0.056520

0.006741

0.064711

0.476899

0.006162

2018.10–2018.12

0.158318

0.147202

0.286875

0.077530

0.330075

0.003061

0.008743

0.136008

0.004196

2018.11–2019.01

0.068086

0.099889

0.581654

0.196896

0.053475

0.002444

0.011862

0.234118

0.003148

2018.12–2019.02

0.054063

0.324698

0.054747

0.226128

0.340363

0.004022

0.052921

0.652735

0.003368

2019.01–2019.03

0.694957

0.056122

0.065574

0.125798

0.057549

0.002692

0.013332

0.239855

0.004107

2019.02–2019.04

0.178815

0.345249

0.250347

0.082559

0.143030

0.003362

0.005718

0.078847

0.005336

2019.03–2019.05

0.227873

0.050683

0.242898

0.428362

0.050185

0.005817

0.032549

0.276187

0.009269

2019.04–2019.06

0.050000

0.050000

0.050000

0.800000

0.050000

0.016006

− 0.004323

− 0.014807

0.037009

2019.05–2019.07

0.583894

0.054994

0.249566

0.055026

0.056520

0.006845

0.065511

0.475499

0.006247

2019.06–2019.08

0.059228

0.520589

0.060882

0.063095

0.296206

0.007853

− 0.017620

− 0.114845

0.014456

2019.07–2019.09

0.185526

0.312187

0.109350

0.328851

0.064085

0.003799

− 0.005244

− 0.074500

0.006928

2019.08–2019.10

0.069817

0.050163

0.050104

0.050025

0.779891

0.005226

0.016017

0.149260

0.007558

2019.09–2019.11

0.354102

0.143553

0.259630

0.157578

0.085137

0.002090

0.019192

0.449085

0.001906

2019.10–2019.12

0.450722

0.062094

0.089300

0.325553

0.072330

0.002482

0.026369

0.522830

0.003108

2019.11–2020.01

0.227873

0.050683

0.242898

0.428362

0.050185

0.005841

0.032588

0.275389

0.009291

2019.12–2020.02

0.050000

0.050000

0.050000

0.800000

0.050000

0.015897

− 0.004250

− 0.014678

0.036575

2020.01–2020.03

0.583894

0.054994

0.249566

0.055026

0.056520

0.006741

0.065250

0.480855

0.006186

2020.02–2020.04

0.256336

0.353002

0.113060

0.160268

0.117334

0.007432

0.009408

0.060487

0.011529

2020.03–2020.05

0.400734

0.051429

0.066797

0.429053

0.051987

0.008963

0.001657

0.006922

0.021945

2020.04–2020.06

0.069817

0.050163

0.050104

0.050025

0.779891

0.005254

0.016093

0.149191

0.007597

2020.05–2020.07

0.050059

0.409585

0.243612

0.246698

0.050045

0.007639

− 0.027503

− 0.182747

0.016412

2020.06–2020.08

0.050112

0.050673

0.796835

0.052323

0.050057

0.002337

0.027782

0.585563

0.002510

2020.07–2020.09

0.129021

0.324443

0.074690

0.414853

0.056993

0.009845

− 0.014013

− 0.073286

0.022706

2020.08–2020.10

0.074008

0.425982

0.067759

0.050285

0.381966

0.004700

0.017964

0.186668

0.004731

2020.09–2020.11

0.327937

0.110332

0.315693

0.055792

0.190245

0.003739

0.009645

0.123414

0.006185

Period

Semiparametric method

VOO

TLT

LQD

IAU

VNQ

Volatility

Return

SR

VaR

2015.10–2015.12

0.160183

0.201954

0.389901

0.155095

0.092867

0.003968

0.023492

0.290764

0.004389

2015.11–2016.01

0.216752

0.131119

0.448274

0.112298

0.091557

0.002686

− 0.004560

− 0.092644

0.006486

2015.12–2016.02

0.172940

0.343354

0.067331

0.351387

0.064988

0.004277

0.002737

0.027125

0.006675

2016.01–2016.03

0.287010

0.051091

0.560270

0.050384

0.051246

0.002134

0.008876

0.198229

0.002867

2016.02–2016.04

0.530729

0.080792

0.096155

0.230098

0.062226

0.001641

0.035218

1.060395

0.000373

2016.03–2016.05

0.399718

0.218111

0.252014

0.062924

0.067233

0.001865

0.012726

0.329927

0.002181

2016.04–2016.06

0.407809

0.055219

0.058044

0.425151

0.053778

0.002812

0.010829

0.185165

0.003766

2016.05–2016.07

0.687917

0.086119

0.068683

0.096677

0.060604

0.002701

0.016116

0.290572

0.002939

2016.06–2016.08

0.295074

0.058944

0.345485

0.241187

0.059309

0.005659

0.000088

− 0.002902

0.012696

2016.07–2016.09

0.169464

0.063972

0.058819

0.053705

0.654040

0.005967

0.026090

0.215117

0.009871

2016.08–2016.10

0.490535

0.078949

0.127607

0.210662

0.092247

0.003839

− 0.007447

− 0.102409

0.005604

2016.09–2016.11

0.053734

0.255260

0.067222

0.565168

0.058617

0.002900

0.000532

0.001990

0.004256

2016.10–2016.12

0.530729

0.080792

0.096155

0.230098

0.062226

0.001617

0.034387

1.050693

0.000369

2016.11–2017.01

0.399718

0.218111

0.252014

0.062924

0.067233

0.001847

0.012803

0.335297

0.002178

2016.12–2017.02

0.407809

0.055219

0.058044

0.425151

0.053778

0.002863

0.011203

0.188381

0.003825

2017.01–2017.03

0.687917

0.086119

0.068683

0.096677

0.060604

0.002702

0.015835

0.285352

0.002926

2017.02–2017.04

0.059820

0.299233

0.074893

0.404997

0.161057

0.004510

0.009389

0.099466

0.007155

2017.03–2017.05

0.169464

0.063972

0.058819

0.053705

0.654040

0.006025

0.026201

0.213990

0.009905

2017.04–2017.06

0.349012

0.250337

0.257934

0.077485

0.065231

0.003048

0.008530

0.133072

0.005830

2017.05–2017.07

0.053734

0.255260

0.067222

0.565168

0.058617

0.002923

0.000539

0.002094

0.004277

2017.06–2017.08

0.121561

0.082417

0.495424

0.060742

0.239856

0.002705

0.007115

0.123810

0.003664

2017.07–2017.09

0.073791

0.114737

0.509979

0.248497

0.052996

0.002456

0.011837

0.232526

0.003139

2017.08–2017.10

0.074851

0.306618

0.072666

0.167985

0.377880

0.003839

0.048566

0.627128

0.002693

2017.09–2017.11

0.775866

0.052707

0.055846

0.061907

0.053674

0.002652

0.017581

0.323599

0.003499

2017.10–2017.12

0.334962

0.071289

0.272083

0.263743

0.057923

0.002980

0.017407

0.285051

0.005007

2017.11–2018.01

0.169464

0.063972

0.058819

0.053705

0.654040

0.006003

0.025920

0.212413

0.009870

2017.12–2018.02

0.275426

0.065573

0.140699

0.386802

0.131500

0.004183

0.002988

0.030737

0.006914

2018.01–2018.03

0.053734

0.255260

0.067222

0.565168

0.058617

0.002910

0.000541

0.002142

0.004278

2018.02–2018.04

0.121561

0.082417

0.495424

0.060742

0.239856

0.002646

0.007070

0.125743

0.003638

2018.03–2018.05

0.073791

0.114737

0.509979

0.248497

0.052996

0.002485

0.011472

0.222401

0.003134

2018.04–2018.06

0.074851

0.306618

0.072666

0.167985

0.377880

0.003891

0.049404

0.629415

0.002714

2018.05–2018.07

0.775866

0.052707

0.055846

0.061907

0.053674

0.002735

0.017075

0.304586

0.003507

2018.06–2018.08

0.527862

0.270079

0.069391

0.057903

0.074765

0.002891

− 0.011236

− 0.201531

0.004917

2018.07–2018.09

0.163395

0.117267

0.299596

0.369493

0.050250

0.005635

0.026281

0.229476

0.009048

2018.08–2018.10

0.469976

0.153788

0.057899

0.266291

0.052046

0.007470

0.019957

0.130787

0.017045

2018.09–2018.11

0.485838

0.061267

0.326615

0.062098

0.064182

0.005929

0.057045

0.477570

0.005171

2018.10–2018.12

0.121561

0.082417

0.495424

0.060742

0.239856

0.002656

0.007093

0.125695

0.003643

2018.11–2019.01

0.073791

0.114737

0.509979

0.248497

0.052996

0.002434

0.011858

0.234983

0.003122

2018.12–2019.02

0.074851

0.306618

0.072666

0.167985

0.377880

0.003844

0.050094

0.646250

0.002715

2019.01–2019.03

0.775866

0.052707

0.055846

0.061907

0.053674

0.002669

0.017557

0.321148

0.003503

2019.02–2019.04

0.185337

0.143157

0.531074

0.067048

0.073384

0.002593

0.009933

0.183488

0.003530

2019.03–2019.05

0.163395

0.117267

0.299596

0.369493

0.050250

0.005476

0.026232

0.235693

0.008973

2019.04–2019.06

0.469976

0.153788

0.057899

0.266291

0.052046

0.007581

0.020493

0.132420

0.017219

2019.05–2019.07

0.485838

0.061267

0.326615

0.062098

0.064182

0.006122

0.058396

0.473563

0.005243

2019.06–2019.08

0.092558

0.397549

0.119787

0.104515

0.285590

0.006938

− 0.014984

− 0.110994

0.012743

2019.07–2019.09

0.174315

0.320654

0.315521

0.106787

0.082724

0.003515

− 0.009353

− 0.138969

0.006173

2019.08–2019.10

0.402554

0.081189

0.056218

0.051299

0.408739

0.004420

0.019300

0.213619

0.005823

2019.09–2019.11

0.462187

0.133589

0.120307

0.221211

0.062705

0.001887

0.023460

0.610738

0.001066

2019.10–2019.12

0.302124

0.051589

0.053442

0.540133

0.052713

0.002479

0.030260

0.601898

0.002362

2019.11–2020.01

0.163395

0.117267

0.299596

0.369493

0.050250

0.005517

0.026285

0.234431

0.008997

2019.12–2020.02

0.469976

0.153788

0.057899

0.266291

0.052046

0.007489

0.019791

0.129359

0.017014

2020.01–2020.03

0.485838

0.061267

0.326615

0.062098

0.064182

0.005933

0.057920

0.484621

0.005193

2020.02–2020.04

0.272085

0.162933

0.233367

0.201392

0.130223

0.007076

0.017931

0.123754

0.011220

2020.03–2020.05

0.211447

0.054567

0.294013

0.384679

0.055294

0.006421

0.006489

0.047289

0.015313

2020.04–2020.06

0.402554

0.081189

0.056218

0.051299

0.408739

0.004465

0.019502

0.213715

0.005853

2020.05–2020.07

0.062204

0.342805

0.350125

0.186273

0.058592

0.006584

− 0.024562

− 0.189698

0.013904

2020.06–2020.08

0.055680

0.294309

0.415059

0.181089

0.053865

0.002336

0.040450

0.856912

0.001602

2020.07–2020.09

0.201736

0.393465

0.188655

0.144974

0.071170

0.006108

− 0.013680

− 0.115384

0.012968

2020.08–2020.10

0.051031

0.603457

0.050679

0.050169

0.244664

0.004696

0.023206

0.242621

0.004484

2020.09–2020.11

0.225476

0.057092

0.474217

0.051103

0.192112

0.003403

0.006678

0.092000

0.005677

  1. This table reports the optimal weights (five ETFs: VOO, TLT, LQD, IAU, VNQ), volatility (the standard deviation of return in the estimation window), return, Sharpe ratios (adjusted) and VaR of quarterly in-sample for asset allocation portfolios which are constructed using Markowitz model and semiparametric method with VaR (\(\alpha =0.05\)). All the results are reported for the total sample period (October 2015-November 2020) and estimation window is 3 months