Analytical Methods in Economics and Finance - Assignment Example

The paper "Analytical Methods in Economics and Finance" is a worthy example of an assignment on macro and microeconomics.

1.a

The fluctuation of the two variables XOM and MKT shows that XOM when registering positive returns has on several occasions outperformed the market return. Also, XOM has been registering less negative returns than the market portfolio expected returns when they are negative. Thus, XOM has generally been able to beat the market consistently over the ten years period.

(b) The MSFT and MKT premium risk from 1998 to 2008 is as follows;

OBS

MST premium risk

MKT premium risk

Jan-98

0.122152

-0.027574

Feb-98

0.104051

0.041127

Mar-98

0.023944

0.019219

Apr-98

-0.02512

-0.021241

May-98

-0.091049

-0.057858

Jun-98

0.245716

-0.000149

Jul-98

-0.017685

-0.055367

Aug-98

-0.159448

-0.18977

Sep-98

0.115128

0.031733

Oct-98

-0.07015

0.042254

Nov-98

0.120199

0.029883

Dec-98

0.10468

0.03095

Jan-99

0.229727

0.006243

Feb-99

-0.174246

-0.070208

Mar-99

0.161902

0.005759

Apr-99

-0.124851

0.016897

May-99

-0.039789

-0.052823

Jun-99

0.085635

0.018917

Jul-99

-0.080613

-0.062738

Aug-99

0.046557

-0.042086

Sep-99

-0.05371

-0.05497

Oct-99

-0.010019

0.029945

Nov-99

-0.048477

0.004753

Dec-99

0.250203

0.051822

Jan-00

-0.193773

-0.071856

Feb-00

-0.118948

-0.000333

Mar-00

0.156708

0.021449

Apr-00

-0.375632

-0.09157

May-00

-0.13515

-0.07115

Jun-00

0.246618

0.019546

Jul-00

-0.159447

-0.049208

Aug-00

-0.032103

0.043708

Sep-00

-0.168182

-0.083242

Oct-00

0.109866

-0.056667

Nov-00

-0.199072

-0.134649

Dec-00

-0.276112

-0.011757

Jan-01

0.375678

0.00743

Feb-01

-0.06588

-0.13137

Mar-01

-0.105196

-0.102393

Apr-01

0.206754

0.051801

May-01

-0.010996

-0.021542

Jun-01

0.023115

-0.049584

Jul-01

-0.125391

-0.050424

Aug-01

-0.17019

-0.091183

Sep-01

-0.135171

-0.123643

Oct-01

0.104305

-0.004136

Nov-01

0.07211

0.046631

Dec-01

-0.000332

-0.014262

Jan-02

-0.070443

-0.048163

Feb-02

-0.116391

-0.053808

Mar-02

0.001665

0.01259

Apr-02

-0.16558

-0.081752

May-02

-0.057935

-0.042561

Jun-02

0.042342

-0.102346

Jul-02

-0.154955

-0.11324

Aug-02

-0.009177

-0.024119

Sep-02

-0.140905

-0.132078

Oct-02

0.190348

0.042855

Nov-02

0.046633

0.029173

Dec-02

-0.135778

-0.085412

Jan-03

-0.114115

-0.055533

Feb-03

-0.029996

-0.047511

Mar-03

-0.010584

-0.02177

Apr-03

0.023659

0.050694

May-03

-0.06927

0.031404

Jun-03

0.00975

-0.015771

Jul-03

-0.002072

-0.008973

Aug-03

-0.027938

-0.007195

Sep-03

0.016162

-0.041205

Oct-03

-0.08606

0.028228

Nov-03

-0.048553

-0.015496

Dec-03

0.032463

0.013429

Jan-04

-0.021873

-0.009039

Feb-04

-0.072609

-0.016636

Mar-04

-0.092412

-0.042788

Apr-04

0.016032

-0.056333

May-04

-0.028276

-0.017976

Jun-04

0.056727

-0.01054

Jul-04

-0.034554

-0.069784

Aug-04

-0.071064

-0.029389

Sep-04

-0.019282

-0.011548

Oct-04

-0.02053

-0.014293

Nov-04

0.036542

0.01614

Dec-04

-0.03546

0.003077

Jan-05

-0.04857

-0.05866

Feb-05

-0.071677

-0.009408

Mar-05

-0.071451

-0.04904

Apr-05

0.014649

-0.057285

May-05

-0.009178

0.005813

Jun-05

-0.069312

-0.020572

Jul-05

-0.001105

0.011228

Aug-05

0.040134

-0.038046

Sep-05

-0.092366

-0.021494

Oct-05

-0.033269

-0.052887

Nov-05

0.048053

0.008303

Dec-05

-0.087378

-0.028627

Jan-06

0.044379

0.008009

Feb-06

-0.074376

-0.033747

Mar-06

-0.01945

-0.013043

Apr-06

-0.144562

-0.019135

May-06

-0.090488

-0.063145

Jun-06

-0.003405

-0.032499

Jul-06

0.000515

-0.034005

Aug-06

0.039801

-0.007018

Sep-06

0.032099

-0.012651

Oct-06

0.017623

0.004983

Nov-06

-0.00598

-0.008387

Dec-06

-0.015073

-0.02128

Jan-07

0.001387

-0.012665

Feb-07

-0.11603

-0.046101

Mar-07

-0.042753

-0.019154

Apr-07

0.04217

0.00779

May-07

-0.00371

0.006791

Jun-07

-0.071859

-0.046861

Jul-07

-0.048391

-0.063856

Aug-07

-0.037622

-0.02048

Sep-07

-0.006694

0.0088

Oct-07

0.217388

-0.006261

Nov-07

-0.116319

-0.081382

Dec-07

0.027421

-0.036445

Jan-08

-0.116373

-0.094408

Feb-08

-0.194376

-0.054143

Mar-08

0.011283

-0.042573

Apr-08

-0.02717

0.019041

May-08

-0.035259

-0.008278

Jun-08

-0.060705

-0.110728

Jul-08

-0.09717

-0.045253

Aug-08

0.033216

-0.021061

Sep-08

-0.054089

-0.130163

Oct-08

-0.19546

-0.216829

Nov-08

-0.120773

-0.117309

Dec-08

-0.070679

-0.010621

(c) Measures of central tendency and deviation of DIS, GE, GM and IBM respectively.

MEAN

-0.26779

-0.2349

-0.38931

-0.22645

         

MEDIAN

0.005859

-0.00472

-0.01302

0.006482

STD

0.080866

0.069934

0.127328

0.090485

                   

The mean of the four variables shows that the companies on average, in the period of ten years they registered negative returns. That means the company's returns in the last ten years were making a loss on aggregate. The median of the four variables shows the middle rate of return during the ten years fluctuation. From the calculation above, two companies registered positive returns at the center of ten years fluctuation while the other two had negative returns. The standard deviation of the four variables shows how the returns are spread on either side from the mean returns. DIS returns are relatively spread from the average return of -0.26779 by 0.080866, GE returns are spread far from the average return of -0.2349 by 0.069934, GM returns are spread by 0.127328 from the average return of -0.38931 and IBM returns are spread from the average return of -0.22645 by 0.090485.

(d) CAPM = rf + Ba(rm – rf)

MISFT ra = 0.032 + 0.574488* - 0.023771242

MISFT ra = 0.032 + - 0.0133656

MISFT ra = 0.0186

GM ra = 0.032 + 0.338807* -0.023771242

GM ra = 0.032 + -0.008054

GM ra = 0.0239

The beta value of the two variables is less than one which means the stocks of the two companies are less than one which means the value of the stock is defensive. Thus, the two variables of stock values are valued at a lower price than the market value.

(e) rj – rf = αj + βj (rm – rf)

In the case of MSFT;

0.0186 – 0.032103 = αj + - 0.0133656

-0.0135103 + 0.0133656 = αj

- 0.0001447 = αj

In the case of GM;

0.0239 - 0.032103 = αj -0.008054

0 = αj

In the case of MSFT, the value of alpha is not equal to zero but in the case of GM the value of alpha is equal to zero.

(f) The null hypothesis in this case is that the beta value of Microsoft is 1. The test statistics is as follows.

t = (bk – βk)/ se(bk)

N- 2 = 131 – 2 = 129 degree of freedom, the critical value is the 99th percentile of the t- distribution, t(0.99,129) = 1.282. Thus, if the null hypothesis t value calculated amounts to 1.282< t < 1.282, the null hypothesis is rejected. If t =1, the null hypothesis will not be rejected.

t = 0.574488/ -0.0716

t = -8.024

The null hypothesis is rejected.

(g) The risk premium for Microsoft when the market premium risk is 2% and 7% respectively.

0.0186 – 0.032103 = Bm * 0.02

-0.013503 = Bm* 0.02

-0.013503/ 0.02 = Bm

-0.67515 = Bm

Thus, the risk of holding Microsoft is 1- 0.675 = 0.325

Under 7%;

0.0186 – 0.032103 = Bm * 0.07

-0.013503 = Bm* 0.07

-0.013503/ 0.07 = Bm

-0.1929 = Bm

Thus, the risk of holding on the Microsoft stock under market premium risk of 7% is 1- 0.1929 = 0.807.

(h) t = (bk – βk)/ se(bk)

The null hypothesis is that alpha and beta values are equal. Thus, the difference between the two is zero.

Under the first half;

 

beta

 

0.704079

alpha

 

-0.0151

 The difference between the two = 0.71919

Degree of freedom = 50 – 2 = 48 and the significance level is 5% t (0.95.48)­ = 1.671

t = (0.71919)/ 0.024099

t = 29.84, the null hypothesis is rejected.

Under the second half;

beta

 

-0.15519

alpha

 

-0.02587

 The difference between the two is 0.12932;

t (0.95.48)­ = 1.671

t = 0.12932/ 0.010845

t = 11.92

The null hypothesis is rejected because it is not equal to the t statistic.

(i) Microsoft stock has a beta value which is less than one which means the stock volatility during fluctuation of the stock market is relatively low. With a beta value that is less than one, it means that the stock value has to be undervalued.

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