Get Instant Help From 5000+ Experts For
question

Writing: Get your essay and assignment written from scratch by PhD expert

Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost

Editing:Proofread your work by experts and improve grade at Lowest cost

And Improve Your Grades
myassignmenthelp.com
loader
Phone no. Missing!

Enter phone no. to receive critical updates and urgent messages !

Attach file

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

Guaranteed Higher Grade!
Free Quote
wave
Question:
This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest rate. We will use this variable to compute excess returns on our preferred stock (either Boeing or IBM) and Market excess returns.
 
1.Comparison of Stock Returns
1.1 Graphical Display
1.2 Computation of Returns
1.3 Summary of Returns
1.4 Hypothesis Testing on Stock Returns
1.5 Comparison of Risks
1.6 Comparison of mean Return
1.7 Calculation of Excess Returns
1.8 Estimation of CAPM for IBM
1.9 Determination of Neutral Stock
Answer:
1.Comparison of Stock Returns
1.1 Graphical Display

Comparison of the stock prices has been done in the following figures 2.1, 2.2 and 2.3. The stock prices of S&P, Boeing and IBM have been plotted in the graph over the selected time frame. It has been observed that the stock prices for both the companies Boeing and IBM follow an increasing trend. The S&P stock prices also follow an increasing trend.

 

                                                                              

                                                                                

1.2 Computation of Returns

The returns on the closing stock prices for S&P, BE and IBM are given in the following table:

Date

Price Series

Returns

S&P

Boeing

IBM

US TN (10 Year)

Return S&P

Return Boeing

Return IBM

2/1/2010

1104.49

63.16

127.16

3.595

3/1/2010

1169.43

72.61

128.25

3.833

5.71

13.94

0.85

4/1/2010

1186.69

72.43

129

3.663

1.47

-0.25

0.58

5/1/2010

1089.41

64.18

125.26

3.301

-8.55

-12.09

-2.94

6/1/2010

1030.71

62.75

123.48

2.951

-5.54

-2.25

-1.43

7/1/2010

1101.6

68.14

128.4

2.907

6.65

8.24

3.91

8/1/2010

1049.33

61.13

123.13

2.477

-4.86

-10.86

-4.19

9/1/2010

1141.2

66.54

134.14

2.517

8.39

8.48

8.56

10/1/2010

1183.26

70.64

143.6

2.612

3.62

5.98

6.81

11/1/2010

1180.55

63.77

141.46

2.797

-0.23

-10.23

-1.50

12/1/2010

1257.64

65.26

146.76

3.305

6.33

2.31

3.68

1/1/2011

1286.12

69.48

162

3.378

2.24

6.27

9.88

2/1/2011

1327.22

72.01

161.88

3.414

3.15

3.58

-0.07

3/1/2011

1325.83

73.93

163.07

3.454

-0.10

2.63

0.73

4/1/2011

1363.61

79.78

170.58

3.296

2.81

7.62

4.50

5/1/2011

1345.2

78.03

168.93

3.05

-1.36

-2.22

-0.97

6/1/2011

1320.64

73.93

171.55

3.158

-1.84

-5.40

1.54

7/1/2011

1292.28

70.47

181.85

2.805

-2.17

-4.79

5.83

8/1/2011

1218.89

66.86

171.91

2.218

-5.85

-5.26

-5.62

9/1/2011

1131.42

60.51

174.87

1.924

-7.45

-9.98

1.71

10/1/2011

1253.3

65.79

184.63

2.175

10.23

8.37

5.43

11/1/2011

1246.96

68.69

188

2.068

-0.51

4.31

1.81

12/1/2011

1257.6

73.35

183.88

1.871

0.85

6.56

-2.22

1/1/2012

1312.41

74.18

192.6

1.799

4.27

1.13

4.63

2/1/2012

1365.68

74.95

196.73

1.977

3.98

1.03

2.12

3/1/2012

1408.47

74.37

208.65

2.216

3.09

-0.78

5.88

4/1/2012

1397.91

76.8

207.08

1.915

-0.75

3.22

-0.76

5/1/2012

1310.33

69.61

192.9

1.581

-6.47

-9.83

-7.09

6/1/2012

1362.16

74.3

195.58

1.659

3.88

6.52

1.38

7/1/2012

1379.32

73.91

195.98

1.492

1.25

-0.53

0.20

8/1/2012

1406.58

71.4

194.85

1.562

1.96

-3.46

-0.58

9/1/2012

1440.67

69.6

207.45

1.637

2.39

-2.55

6.27

10/1/2012

1412.16

70.44

194.53

1.686

-2.00

1.20

-6.43

11/1/2012

1416.18

74.28

190.07

1.606

0.28

5.31

-2.32

12/1/2012

1426.19

75.36

191.55

1.756

0.70

1.44

0.78

1/1/2013

1498.11

73.87

203.07

1.985

4.92

-2.00

5.84

2/1/2013

1514.68

76.9

200.83

1.888

1.10

4.02

-1.11

3/1/2013

1569.19

85.85

213.3

1.852

3.54

11.01

6.02

4/1/2013

1597.57

91.41

202.54

1.675

1.79

6.28

-5.18

5/1/2013

1630.74

99.02

208.02

2.164

2.06

8.00

2.67

6/1/2013

1606.28

102.44

191.11

2.478

-1.51

3.40

-8.48

7/1/2013

1685.73

105.1

195.04

2.593

4.83

2.56

2.04

8/1/2013

1632.97

103.92

182.27

2.749

-3.18

-1.13

-6.77

9/1/2013

1681.55

117.5

185.18

2.615

2.93

12.28

1.58

10/1/2013

1756.54

130.5

179.21

2.542

4.36

10.49

-3.28

11/1/2013

1805.81

134.25

179.68

2.741

2.77

2.83

0.26

12/1/2013

1848.36

136.49

187.57

3.026

2.33

1.65

4.30

1/1/2014

1782.59

125.26

176.68

2.668

-3.62

-8.59

-5.98

2/1/2014

1859.45

128.92

185.17

2.658

4.22

2.88

4.69

3/1/2014

1872.34

125.49

192.49

2.723

0.69

-2.70

3.88

4/1/2014

1883.95

129.02

196.47

2.648

0.62

2.77

2.05

5/1/2014

1923.57

135.25

184.36

2.457

2.08

4.72

-6.36

6/1/2014

1960.23

127.23

181.27

2.516

1.89

-6.11

-1.69

7/1/2014

1930.67

120.48

191.67

2.556

-1.52

-5.45

5.58

8/1/2014

2003.37

126.8

192.3

2.343

3.70

5.11

0.33

9/1/2014

1972.29

127.38

189.83

2.508

-1.56

0.46

-1.29

10/1/2014

2018.05

124.91

164.4

2.335

2.29

-1.96

-14.38

11/1/2014

2067.56

134.36

162.17

2.194

2.42

7.29

-1.37

12/1/2014

2058.9

129.98

160.44

2.17

-0.42

-3.31

-1.07

1/1/2015

1994.99

145.37

153.31

1.675

-3.15

11.19

-4.55

2/1/2015

2104.5

150.85

161.94

2.002

5.34

3.70

5.48

3/1/2015

2067.89

150.08

160.5

1.934

-1.75

-0.51

-0.89

4/1/2015

2085.51

143.34

171.29

2.046

0.85

-4.59

6.51

5/1/2015

2107.39

140.52

169.65

2.095

1.04

-1.99

-0.96

6/1/2015

2063.11

138.72

162.66

2.335

-2.12

-1.29

-4.21

7/1/2015

2103.84

144.17

161.99

2.205

1.95

3.85

-0.41

 
 
1.3 Summary of Returns

From the results of the summary statistics, it can be seen that BE provides higher returns than IBM. It can also be seen that the returns provided by BE is less than S&P 500. On the other hand, it can be said that BE experiences higher risks than IBM. The risks suffered by IBM has a similarity with that of the S&P 500.

Summary Statistics

Return S&P

Return Boeing

Return IBM

Mean

0.99

1.27

0.37

Standard Error

0.45

0.74

0.57

Median

1.47

1.65

0.33

Mode

#N/A

#N/A

#N/A

Standard Deviation

3.65

5.97

4.57

Sample Variance

13.34

35.58

20.85

Kurtosis

0.46

-0.32

0.56

Skewness

-0.34

-0.22

-0.47

Range

18.78

26.04

24.26

Minimum

-8.55

-12.09

-14.38

Maximum

10.23

13.94

9.88

Sum

64.44

82.53

24.21

Count

65

65

65

 

From the Jarque-Berra test, it can be seen that the returns provided by BE and IBM are normally distributed. Normality test is performed on the data because any test performed on a data which is not normal might not give a proper result on performing any tests.

 

Jarque Berra Test

Return S&P

Return Boeing

Return IBM

Test Statistic

1.850

0.793

3.254

P-Value

0.396

0.673

0.197

 
 
1.4 Hypothesis Testing on Stock Returns


To test whether the returns on Boeing stocks exceeds 3 percent, z-test has to be conducted. From the comparison of the returns on Boeing stock, it has been observed that the returns on the Boeing stocks do not exceed 3 percent.

Hypothesis Test for µ

 

Hypotheses

Null Hypothesis H0:

 µ

3

Alternative Hypothesis HA:

 µ

>

3

Test Type

 

 

Upper

Level of significance

 

 

alpha α set to:

0.05

Critical Region

Degrees of Freedom

64

Critical Value

1.6690

 

 

Sample Data

Sample Standard Deviation s

5.97

Sample Mean x bar

1.27

Sample Size n

65

Is Pop StDev known? Y/N

N

Standard Error of the Mean

0.7399

t Sample Statistic

-2.3385

p-value from the t distribution

0.0112

 

 

 

 

Hypothesis test decision:

Reject the Null Hypothesis

 
 
1.5 Comparison of Risks

Decision has to be made on which stock would be better to invest. In order to do that, the risks of the stocks have to be compared. From the results of the comparison of stock returns of BE and IBM, it can be seen that the variation in the returns are not same. Moreover, the variation is higher in case of BE. Thus, IBM would be a preferred choice for investment.

F-Test Two-Sample for Variances

 

Boeing

IBM

Mean

94.97

174.97

Variance

905.08

582.33

Observations

66

66

df

65

65

F

1.554

 

P(F<=f) one-tail

0.039

 

F Critical one-tail

1.508

 

 
 
1.6 Comparison of mean Return

Further, it has to be compared whether both the stocks have the same average returns. From the results of the analysis, it has been observed that the average stock returns for both the companies BE and IBM are same. There is no significant difference between the average returns on the stocks of BE as well as IBM.

 

t-Test: Two-Sample Assuming Equal Variances

 

Return Boeing

Return IBM

Mean

1.27

0.37

Variance

35.58

20.85

Observations

65

65

Pooled Variance

28.22

 

Hypothesized Mean Difference

0

 

df

128

 

t Stat

0.963

 

P(T<=t) one-tail

0.169

 

t Critical one-tail

1.657

 

P(T<=t) two-tail

0.337

 

t Critical two-tail

1.979

 

 
 

Thus, from the analysis above it has been observed that the stocks of BE and IBM provide same returns with lesser risk in case of IBM and higher risk in case of BE. Thus, the preferred choice of investment will be in the stocks of BE.

1.7 Calculation of Excess Returns

 

Date

US TN (10 Year)

Return S&P

Return IBM

Excess Return (Yt)

Excess Market Return (Xt)

2/1/2010

3.595

 

 

 

 

3/1/2010

3.833

5.7133

0.8535

-2.9795

1.8803

4/1/2010

3.663

1.4651

0.5831

-3.0799

-2.1979

5/1/2010

3.301

-8.5532

-2.9421

-6.2431

-11.8542

6/1/2010

2.951

-5.5388

-1.4312

-4.3822

-8.4898

7/1/2010

2.907

6.6516

3.9071

1.0001

3.7446

8/1/2010

2.477

-4.8612

-4.1910

-6.6680

-7.3382

9/1/2010

2.517

8.3928

8.5643

6.0473

5.8758

10/1/2010

2.612

3.6193

6.8148

4.2028

1.0073

11/1/2010

2.797

-0.2293

-1.5015

-4.2985

-3.0263

12/1/2010

3.305

6.3256

3.6782

0.3732

3.0206

1/1/2011

3.378

2.2393

9.8798

6.5018

-1.1387

2/1/2011

3.414

3.1457

-0.0741

-3.4881

-0.2683

3/1/2011

3.454

-0.1048

0.7324

-2.7216

-3.5588

4/1/2011

3.296

2.8097

4.5025

1.2065

-0.4863

5/1/2011

3.05

-1.3593

-0.9720

-4.0220

-4.4093

6/1/2011

3.158

-1.8426

1.5390

-1.6190

-5.0006

7/1/2011

2.805

-2.1708

5.8307

3.0257

-4.9758

8/1/2011

2.218

-5.8468

-5.6211

-7.8391

-8.0648

9/1/2011

1.924

-7.4467

1.7072

-0.2168

-9.3707

10/1/2011

2.175

10.2307

5.4311

3.2561

8.0557

11/1/2011

2.068

-0.5072

1.8088

-0.2592

-2.5752

12/1/2011

1.871

0.8497

-2.2159

-4.0869

-1.0213

1/1/2012

1.799

4.2660

4.6332

2.8342

2.4670

2/1/2012

1.977

3.9787

2.1217

0.1447

2.0017

3/1/2012

2.216

3.0851

5.8826

3.6666

0.8691

4/1/2012

1.915

-0.7526

-0.7553

-2.6703

-2.6676

5/1/2012

1.581

-6.4699

-7.0933

-8.6743

-8.0509

6/1/2012

1.659

3.8793

1.3798

-0.2792

2.2203

7/1/2012

1.492

1.2519

0.2043

-1.2877

-0.2401

8/1/2012

1.562

1.9571

-0.5783

-2.1403

0.3951

9/1/2012

1.637

2.3947

6.2660

4.6290

0.7577

10/1/2012

1.686

-1.9988

-6.4304

-8.1164

-3.6848

11/1/2012

1.606

0.2843

-2.3194

-3.9254

-1.3217

12/1/2012

1.756

0.7043

0.7756

-0.9804

-1.0517

1/1/2013

1.985

4.9198

5.8402

3.8552

2.9348

2/1/2013

1.888

1.1000

-1.1092

-2.9972

-0.7880

3/1/2013

1.852

3.5355

6.0241

4.1721

1.6835

4/1/2013

1.675

1.7924

-5.1762

-6.8512

0.1174

5/1/2013

2.164

2.0550

2.6697

0.5057

-0.1090

6/1/2013

2.478

-1.5113

-8.4785

-10.9565

-3.9893

7/1/2013

2.593

4.8278

2.0355

-0.5575

2.2348

8/1/2013

2.749

-3.1798

-6.7716

-9.5206

-5.9288

9/1/2013

2.615

2.9316

1.5839

-1.0311

0.3166

10/1/2013

2.542

4.3630

-3.2770

-5.8190

1.8210

11/1/2013

2.741

2.7663

0.2619

-2.4791

0.0253

12/1/2013

3.026

2.3289

4.2975

1.2715

-0.6971

1/1/2014

2.668

-3.6231

-5.9812

-8.6492

-6.2911

2/1/2014

2.658

4.2213

4.6934

2.0354

1.5633

3/1/2014

2.723

0.6908

3.8770

1.1540

-2.0322

4/1/2014

2.648

0.6182

2.0466

-0.6014

-2.0298

5/1/2014

2.457

2.0812

-6.3619

-8.8189

-0.3758

6/1/2014

2.516

1.8879

-1.6903

-4.2063

-0.6281

7/1/2014

2.556

-1.5195

5.5787

3.0227

-4.0755

8/1/2014

2.343

3.6964

0.3282

-2.0148

1.3534

9/1/2014

2.508

-1.5635

-1.2928

-3.8008

-4.0715

10/1/2014

2.335

2.2936

-14.3826

-16.7176

-0.0414

11/1/2014

2.194

2.4237

-1.3657

-3.5597

0.2297

12/1/2014

2.17

-0.4197

-1.0725

-3.2425

-2.5897

1/1/2015

1.675

-3.1533

-4.5458

-6.2208

-4.8283

2/1/2015

2.002

5.3439

5.4764

3.4744

3.3419

3/1/2015

1.934

-1.7549

-0.8932

-2.8272

-3.6889

4/1/2015

2.046

0.8485

6.5064

4.4604

-1.1975

5/1/2015

2.095

1.0437

-0.9621

-3.0571

-1.0513

6/1/2015

2.335

-2.1236

-4.2075

-6.5425

-4.4586

7/1/2015

2.205

1.9550

-0.4128

-2.6178

-0.2500

 
1..8 Estimation of CAPM for IBM
 
 

Date

CAPM

Date

CAPM

2/1/2010

 

11/1/2012

-3.56455

3/1/2010

-2.98785

12/1/2012

-1.76906

4/1/2010

-3.04909

1/1/2013

1.17901

5/1/2010

-4.97757

2/1/2013

-2.99866

6/1/2010

-3.84307

3/1/2013

1.372211

7/1/2010

-0.56164

4/1/2013

-5.34834

8/1/2010

-5.23661

5/1/2013

-0.86307

9/1/2010

2.515487

6/1/2013

-7.85119

10/1/2010

1.390917

7/1/2013

-1.51123

11/1/2010

-3.792

8/1/2013

-6.97573

12/1/2010

-0.94387

9/1/2013

-1.79999

1/1/2011

2.792546

10/1/2013

-4.71902

2/1/2011

-3.29795

11/1/2013

-2.68279

3/1/2011

-2.83062

12/1/2013

-0.3962

4/1/2011

-0.43582

1/1/2014

-6.4445

5/1/2011

-3.62345

2/1/2014

0.069555

6/1/2011

-2.1584

3/1/2014

-0.46782

7/1/2011

0.673323

4/1/2014

-1.53805

8/1/2011

-5.95061

5/1/2014

-6.54798

9/1/2011

-1.30356

6/1/2014

-3.73579

10/1/2011

0.813767

7/1/2014

0.671498

11/1/2011

-1.32939

8/1/2014

-2.39976

12/1/2011

-3.66299

9/1/2014

-3.48857

1/1/2012

0.556555

10/1/2014

-11.3636

2/1/2012

-1.08317

11/1/2014

-3.34162

3/1/2012

1.064031

12/1/2014

-3.14822

4/1/2012

-2.79936

1/1/2015

-4.96399

5/1/2012

-6.45982

2/1/2015

0.94685

6/1/2012

-1.34161

3/1/2015

-2.89502

7/1/2012

-1.95643

4/1/2015

1.547989

8/1/2012

-2.47621

5/1/2015

-3.03515

9/1/2012

1.650793

6/1/2015

-5.16013

10/1/2012

-6.11967

7/1/2015

-2.76733

 

The CAPM is calculated from the regression analysis. The calculation of the CAPM is given by the following equation:

CAPM = -1.17 + 0.61 * Excess Return

Regression Statistics

Multiple R

0.4951

R Square

0.2452

Adjusted R Square

0.23

Standard Error

3.96

Observations

65

 
 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-1.17

0.53

-2.225

0.03

-2.22

-0.12

Xt

0.61

0.13

4.524

0.000

0.34

0.88

 

The coefficients of the regression analysis show that, if the excess return on the stocks is zero, then the market return of the stocks will be -1.17. With one-unit increase in the excess return of the stocks, the market return of the stocks will increase by 0.61.

The coefficient of determination (R Square) value indicates that the excess return on the stocks will be able to explain 24.51 percent of the variability in the market return of the stocks. The average excess stock returns of IBM are supposed to lie between 0.34 and 0.88 with 95 percent confidence.

 

1.9 Determination of Neutral Stock

It can be seen clearly from the computations of the confidence interval that the average return on the stocks of IBM lies between -0.76 and 1.50 with 95 percent confidence. There is always a possibility that the stocks will not have any returns. Thus, this stock can be termed as a neutral stock.

Confidence Interval for the mean

Data

Sample Standard Deviation

4.5661

Sample Mean

0.37

Sample Size

65

Confidence Level

95%

Is Pop StDev known? Y/N

N

Intermediate Calculations

Standard Error of the Mean

0.5664

Degrees of Freedom

64

t Value

1.9977

Margin of Error

1.1314

Confidence Interval

Interval Lower Limit

-0.76

Interval Upper Limit

1.50

 

From the results of the Jarque-Berra test, it can be said that the errors in the developed model of prediction of CAPM is normally distributed. The following figure also shows that the errors are normally distributed as they follow a linear trend.

Test for Normality of Residuals

Skewness

-0.755

Kurtosis

2.915

Count

65

Jarque-Berra test Statistic

29.181

P-Value

0.000

 
 
                                                                                         
Introduction:

There is availability of two different stocks in the market. One is the stock prices of Boeing company and the other is the stock prices of IBM (International Business Machines). Historical data on the monthly stock prices of these two companies have been collected from finance.yahoo.com for the time frame of 2nd Feb, 2010 to 31st July, 2015. The S&P price index of this time frame and the interest rate of the 10 year US Treasury Note has been collected from the same website. The client is interested to invest in the stocks of one of two available companies Boeing or IBM. Thus, the main interest of this study is to identify which of the two stocks will be better and safer to invest. For this, the risk on the stock prices and the returns from the stocks are to be compared over the time frame to assess which stock would be better to invest. The necessary analysis will be conducted using appropriate statistical techniques and on Microsoft Excel.

Referance:

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2016. Statistics for business & economics. Nelson Education.

Siegel, A., 2016. Practical business statistics. Academic Press.

Ruppert, D., 2014. Statistics and finance: an introduction. Springer.

Swift, L. and Piff, S., 2014. Quantitative methods: for business, management and finance. Palgrave Macmillan.

Asongu, S.A. and Moulin, B., 2016. Research in International Business and Finance.

Sullivan III, M., 2015. Fundamentals of statistics. Pearson.

Cite This Work

To export a reference to this article please select a referencing stye below:

My Assignment Help. (2020). Comparison Of Stock Returns. Retrieved from https://myassignmenthelp.com/free-samples/statgb-3302-statistical-inference-and-regression-analysis.

My Assignment Help (2020) Comparison Of Stock Returns [Online]. Available from: https://myassignmenthelp.com/free-samples/statgb-3302-statistical-inference-and-regression-analysis
[Accessed 12 July 2024].

My Assignment Help. 'Comparison Of Stock Returns' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/statgb-3302-statistical-inference-and-regression-analysis> accessed 12 July 2024.

My Assignment Help. Comparison Of Stock Returns [Internet]. My Assignment Help. 2020 [cited 12 July 2024]. Available from: https://myassignmenthelp.com/free-samples/statgb-3302-statistical-inference-and-regression-analysis.

Get instant help from 5000+ experts for
question

Writing: Get your essay and assignment written from scratch by PhD expert

Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost

Editing: Proofread your work by experts and improve grade at Lowest cost

loader
250 words
Phone no. Missing!

Enter phone no. to receive critical updates and urgent messages !

Attach file

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

Plagiarism checker
Verify originality of an essay
essay
Generate unique essays in a jiffy
Plagiarism checker
Cite sources with ease
support
Whatsapp
callback
sales
sales chat
Whatsapp
callback
sales chat
close