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The spreadsheet Group Report Data.xlsx contains monthly returns on ten Australian industry indices from January 2016 to July 2021. The industry abbreviations are in the

The spreadsheet Group Report Data.xlsx contains monthly returns on ten Australian industry indices from January 2016 to July 2021. The industry abbreviations are in the table below. Investor utility is represented by: U = E(R) - A2 . There are two investors with different risk aversion coefficients (A). Angela has a risk aversion coefficient of 5 and Boris has a risk aversion coefficient of 2. Investors are able to short-sell each industry throughout the report. Investors are unable to borrow or lend at the risk-free rate except for part 5 of the report. The expected returns per month to be used throughout the report are in the following table.

Industry Abbreviation Expected Return

Consumer Discretionary COND 0.96%

Consumer Staples CONS 0.83%

Energy ENGY 1.09%

Health Care HC 0.86%

Industrials INDU 0.92%

Information Technology IT 1.00%

Materials MATL 0.87%

Telecom TELE 0.90%

Utilities UTIL 0.80%

Financials FIN 0.90%

Real Estate RE 0.96%

Calculate the expected utility for both investors if they invested solely in each industry. Which industries does each investor prefer? What are the reasons for their preference?

Consider the MATL and HC industries. What is the optimal portfolio for both Boris and Angela that contains these two industries? Discuss what happens to each investor's utility and portfolio risk for this portfolio compared holding these two industries individually. Will you always reach this conclusion or is specific to these two portfolios?

Date

COND

CONS

ENGY

HC

INDU

IT

MATL

TELE

UTIL

FIN

RE

1/29/16

-0.0265

-0.0018

-0.0649

-0.0258

-0.0269

-0.0491

-0.0912

0.0070

0.0073

-0.0737

0.0022

2/29/16

-0.0157

-0.0484

0.0028

0.0064

0.0584

-0.0546

0.0912

-0.0547

0.0123

-0.0532

0.0276

3/31/16

0.0513

0.0300

0.0616

0.0035

0.0227

0.0563

0.0605

0.0471

0.0130

0.0589

0.0278

4/29/16

-0.0171

0.0105

0.0747

0.0334

0.0151

0.0258

0.1430

0.0046

-0.0032

0.0169

0.0207

5/31/16

0.0564

-0.0089

-0.0161

0.0939

0.0256

0.0705

-0.0301

0.0496

0.0354

0.0470

0.0278

6/30/16

-0.0018

-0.0402

-0.0081

-0.0248

-0.0099

-0.0760

0.0059

-0.0128

0.0563

-0.0418

0.0291

7/29/16

0.0890

0.0855

0.0023

0.0700

0.0717

0.0389

0.0779

0.0423

0.0704

0.0589

0.0545

8/31/16

-0.0046

0.0186

0.0236

-0.0317

-0.0427

0.0458

0.0001

-0.0650

-0.0568

-0.0165

-0.0230

9/30/16

0.0028

0.0162

0.0009

-0.0033

-0.0025

0.0146

0.0568

-0.0395

-0.0324

-0.0065

-0.0399

10/31/16

-0.0613

-0.0383

-0.0198

-0.0805

-0.0411

-0.0659

0.0116

-0.0433

-0.0303

0.0074

-0.0737

11/30/16

-0.0033

0.0056

0.0329

-0.0163

0.0135

0.0010

0.0225

-0.0041

0.0366

0.0600

0.0069

12/30/16

0.0421

0.0173

0.0608

0.0086

0.0243

0.0403

0.0383

0.0052

0.0868

0.0551

0.0671

1/31/17

-0.0430

-0.0104

0.0072

0.0456

-0.0441

-0.0418

0.0477

-0.0168

0.0108

-0.0205

-0.0460

2/28/17

0.0151

0.0602

-0.0213

0.0390

0.0341

0.0185

-0.0319

-0.0314

0.0307

0.0413

0.0433

3/31/17

0.0473

0.0547

0.0433

0.0560

0.0435

0.0363

0.0022

0.0028

0.0628

0.0389

0.0095

4/28/17

0.0070

-0.0253

-0.0055

0.0340

0.0409

0.0352

-0.0025

-0.0948

0.0308

0.0191

0.0249

5/31/17

-0.0032

-0.0044

0.0152

-0.0238

0.0469

0.0022

-0.0024

0.0338

0.0100

-0.0771

-0.0075

6/30/17

0.0087

-0.0243

-0.0684

0.0608

-0.0025

0.0188

0.0063

-0.0166

-0.0269

0.0167

-0.0413

7/31/17

-0.0063

0.0097

0.0062

-0.0750

-0.0274

-0.0049

0.0348

-0.0421

-0.0528

0.0125

-0.0017

8/31/17

-0.0154

0.0517

0.0518

0.0025

0.0457

0.0099

0.0452

-0.0720

0.0322

-0.0212

0.0137

9/29/17

-0.0006

-0.0187

0.0112

0.0227

-0.0111

0.0060

-0.0138

-0.0446

-0.0364

0.0111

0.0119

10/31/17

0.0544

0.0534

0.0641

0.0548

0.0418

0.0844

0.0444

0.0235

0.0496

0.0326

0.0132

11/30/17

0.0087

0.0324

0.0433

0.0296

0.0221

0.0450

0.0201

-0.0158

0.0298

0.0000

0.0474

12/29/17

0.0368

0.0167

0.0652

-0.0048

-0.0095

0.0294

0.0611

0.0546

-0.0448

0.0042

0.0038

1/31/18

-0.0020

0.0021

-0.0028

0.0311

-0.0201

0.0249

0.0046

0.0077

-0.0435

-0.0074

-0.0323

2/28/18

-0.0119

0.0210

-0.0375

0.0696

-0.0037

0.0166

0.0037

-0.0620

-0.0159

0.0064

-0.0187

3/30/18

-0.0226

-0.0135

-0.0249

-0.0332

-0.0114

-0.0219

-0.0424

-0.0620

-0.0075

-0.0585

-0.0013

4/30/18

0.0295

0.0574

0.1072

0.0719

0.0308

0.0276

0.0744

0.0194

0.0216

0.0011

0.0410

5/31/18

0.0527

-0.0000

0.0041

0.0545

0.0124

0.0203

0.0197

-0.1005

0.0103

-0.0006

0.0301

6/29/18

0.0209

0.0594

0.0774

0.0250

0.0064

0.0590

0.0165

-0.0549

0.0591

0.0399

0.0256

7/31/18

0.0175

-0.0088

0.0118

0.0223

0.0316

-0.0112

-0.0025

0.0759

-0.0143

0.0204

0.0099

8/31/18

0.0359

0.0264

-0.0122

0.1042

0.0326

0.1221

-0.0486

0.1302

0.0061

0.0005

0.0261

9/28/18

-0.0383

-0.0267

0.0427

-0.0730

-0.0215

-0.0065

0.0406

0.0297

-0.0310

-0.0222

-0.0186

10/31/18

-0.0834

-0.0490

-0.1028

-0.0725

-0.0529

-0.1137

-0.0518

-0.0398

-0.0403

-0.0602

-0.0380

11/30/18

-0.0453

-0.0292

-0.1068

-0.0397

-0.0060

0.0099

-0.0475

-0.0412

-0.0176

0.0141

-0.0259

12/31/18

-0.0194

0.0120

-0.0220

0.0272

-0.0029

-0.0408

0.0513

-0.0326

0.0277

-0.0313

0.0107

1/31/19

0.0428

0.0273

0.1146

0.0391

0.0338

0.0882

0.0697

0.0809

0.0592

-0.0025

0.0585

2/28/19

0.0669

-0.0139

0.0784

0.0133

0.0644

0.0748

0.0640

0.0338

0.0403

0.0907

0.0219

3/29/19

0.0139

0.0368

-0.0415

0.0131

0.0198

0.0255

0.0340

0.0551

0.0132

-0.0262

0.0541

4/30/19

0.0546

0.0733

0.0155

0.0314

0.0315

0.0735

-0.0205

0.0178

-0.0049

0.0440

-0.0167

5/31/19

0.0204

-0.0416

-0.0380

0.0354

0.0025

-0.0312

0.0311

0.0711

-0.0062

0.0262

0.0258

6/28/19

-0.0151

0.0292

0.0217

0.0442

0.0555

0.0105

0.0617

0.0302

0.0308

0.0342

0.0324

7/31/19

0.0475

0.0959

0.0149

0.0596

0.0335

0.0511

0.0117

0.0204

0.0185

0.0177

0.0319

8/30/19

0.0064

0.0010

-0.0562

0.0343

-0.0250

0.0067

-0.0734

-0.0460

-0.0224

-0.0258

0.0240

9/30/19

0.0333

0.0174

0.0446

-0.0215

-0.0013

0.0011

0.0295

-0.0425

0.0201

0.0423

-0.0229

10/31/19

0.0055

-0.0224

0.0031

0.0727

0.0289

-0.0319

-0.0176

-0.0081

0.0123

-0.0288

0.0177

11/29/19

0.0422

0.0810

0.0729

0.0881

0.0397

0.1055

0.0444

0.0945

-0.0053

-0.0201

0.0233

12/31/19

-0.0221

-0.0775

-0.0138

-0.0266

-0.0305

-0.0389

0.0182

-0.0761

0.0078

-0.0156

-0.0448

1/31/20

0.0427

0.0781

0.0057

0.1201

0.0186

0.1024

0.0163

0.0872

0.0098

0.0474

0.0600

2/28/20

-0.0874

-0.0740

-0.1742

-0.0395

-0.0841

-0.1631

-0.1169

-0.0744

-0.0396

-0.0492

-0.0449

3/31/20

-0.2642

-0.0355

-0.3764

-0.0564

-0.2301

-0.1758

-0.1325

-0.1062

-0.0674

-0.2770

-0.3558

4/30/20

0.1644

0.0259

0.2521

0.0487

0.1282

0.2184

0.1437

0.0095

0.0323

0.0289

0.1412

5/29/20

0.0690

-0.0049

0.0474

-0.0510

0.0381

0.1431

0.0839

0.0642

0.0305

0.0535

0.0706

6/30/20

0.0506

0.0475

-0.0212

0.0339

-0.0157

0.0370

0.0217

-0.0256

0.0085

0.0434

-0.0145

7/31/20

0.0288

0.0323

-0.0626

-0.0384

-0.0380

0.0484

0.0591

0.0530

-0.0023

-0.0102

-0.0010

8/31/20

0.0971

-0.0031

0.0342

0.0402

0.0462

0.1515

0.0116

-0.0853

-0.0480

0.0135

0.0761

9/30/20

-0.0242

-0.0658

-0.1074

0.0082

-0.0032

-0.0639

-0.0286

-0.0359

-0.0332

-0.0613

-0.0134

10/30/20

0.0107

0.0456

-0.0097

0.0096

-0.0348

0.0858

-0.0105

-0.0344

-0.0149

0.0627

0.0029

11/30/20

0.0843

-0.0066

0.2824

0.0289

0.1198

0.0414

0.0766

0.1290

0.0147

0.1612

0.1323

12/31/20

0.0139

0.0221

-0.0069

-0.0469

-0.0218

0.0857

0.0877

-0.0280

-0.0538

-0.0050

0.0012

1/29/21

0.0478

0.0202

0.0096

-0.0170

-0.0307

0.0020

-0.0100

0.0448

-0.0009

0.0226

-0.0428

2/26/21

-0.0262

-0.0450

0.0250

-0.0282

-0.0184

-0.0802

0.0706

0.0150

-0.0802

0.0515

-0.0146

3/31/21

0.0668

0.0274

-0.0022

0.0243

0.0344

-0.0267

-0.0307

0.0587

0.0681

0.0429

0.0556

4/30/21

0.0344

-0.0237

-0.0468

0.0287

0.0415

0.0979

0.0748

0.0304

-0.0116

0.0320

0.0278

5/31/21

0.0316

0.0237

-0.0154

0.0347

-0.0112

-0.0910

0.0179

0.0206

-0.0662

0.0565

0.0147

6/30/21

0.0453

0.0543

0.0415

0.0214

0.0310

0.1236

0.0008

0.0563

0.0345

-0.0018

0.0481

7/31/21

-0.0055

0.0150

-0.0241

0.0111

0.0409

-0.0636

0.0706

-0.0148

0.0160

-0.0142

0.0085

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