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Task A: Downloading the data
Download the data for S&P 500 index, Boeing Stock Price, General Dynamics Corp. Stock Price, and US TN (10 Year)
Calculations
rt_S&P

rt_Boeng

rt_GD

S&P (xxb)

Boeng(xxb)

GD(xxb)


0.00

0.00

0.00

0.06

1.02

1.11


0.08

1.36

1.31

0.02

0.34

0.20


0.07

1.26

1.38

0.01

0.24

0.27


0.07

1.29

1.36

0.01

0.27

0.25


0.08

1.36

1.35

0.02

0.34

0.24


0.08

1.43

1.48

0.02

0.41

0.37


0.08

1.51

1.57

0.02

0.49

0.46


0.09

1.67

1.77

0.03

0.65

0.66


0.08

1.53

1.57

0.02

0.51

0.46


0.08

1.47

1.53

0.02

0.45

0.42


0.08

1.37

1.52

0.02

0.35

0.41


0.08

1.36

1.46

0.02

0.34

0.35


0.07

1.34

1.37

0.01

0.32

0.26


0.07

1.35

1.37

0.01

0.33

0.26


0.07

1.31

1.49

0.01

0.29

0.38


0.08

1.45

1.57

0.02

0.43

0.46


0.07

1.36

1.53

0.01

0.34

0.42


0.07

1.36

1.59

0.01

0.34

0.48


0.07

1.41

1.54

0.01

0.39

0.43


0.07

1.45

1.52

0.01

0.43

0.41


0.07

1.43

1.48

0.01

0.41

0.37


0.07

1.36

1.52

0.01

0.34

0.41


0.07

1.34

1.45

0.01

0.32

0.34


0.07

1.36

1.52

0.01

0.34

0.41


0.07

1.31

1.48

0.01

0.29

0.37


0.06

1.17

1.43

0.00

0.15

0.32


0.06

1.10

1.36

0.00

0.08

0.25


0.06

1.02

1.31

0.00

0.00

0.20


0.06

0.98

1.28

0.00

0.04

0.17


0.06

0.96

1.18

0.00

0.06

0.07


0.06

0.97

1.21

0.00

0.05

0.10


0.06

0.85

1.15

0.00

0.17

0.04


0.06

0.77

1.16

0.00

0.25

0.05


0.06

0.75

1.10

0.00

0.27

0.01


0.05

0.74

1.05

0.01

0.28

0.06


0.06

0.80

0.99

0.00

0.22

0.12


0.05

0.78

0.92

0.01

0.24

0.19


0.05

0.80

0.92

0.01

0.22

0.19


0.05

0.78

0.92

0.01

0.24

0.19


0.05

0.74

0.85

0.01

0.28

0.26


0.05

0.79

0.86

0.01

0.23

0.25


0.05

0.83

0.86

0.01

0.19

0.25


0.05

0.79

0.81

0.01

0.23

0.30


0.05

0.79

0.79

0.01

0.23

0.32


0.05

0.80

0.72

0.01

0.22

0.39


0.05

0.75

0.69

0.01

0.27

0.42


0.05

0.77

0.73

0.01

0.25

0.38


0.05

0.69

0.75

0.01

0.33

0.36


0.05

0.67

0.72

0.01

0.35

0.39


0.05

0.67

0.74

0.01

0.35

0.37


0.05

0.70

0.73

0.01

0.32

0.38


0.05

0.71

0.72

0.01

0.31

0.39


0.05

0.72

0.71

0.01

0.30

0.40


0.05

0.70

0.67

0.01

0.32

0.44


0.05

0.77

0.69

0.01

0.25

0.42


0.05

0.77

0.73

0.01

0.25

0.38


0.05

0.68

0.68

0.01

0.34

0.43


0.05

0.69

0.69

0.01

0.33

0.42


0.05

0.69

0.73

0.01

0.33

0.38


0.05

0.84

0.75

0.01

0.18

0.36


0.05

0.85

0.74

0.01

0.17

0.37


0.05

0.79

0.76

0.01

0.23

0.35


0.06

1.02

1.11

0.02

0.16

0.02

Sum

0.01

0.31

0.34





62

62

62

JB test






K3

183.43933

0.08719

0.007307




K4

15724.1905

3.28337

2.97871



JB

n[(K3)^2/6 + (k4)^2/24]

639077317

27.92822

22.9217




K3^2

33649.9879

0.007602

5.34E05




K3^2/6

5608.33131

0.001267

8.9E06




K4^2

247250168

10.78051

8.872705




K4^2/24

10302090.3

0.449188

0.369696




K3^2/6 + K4^2/24

10307698.7

0.450455

0.369705



JB

n[(K3)^2/6 + (k4)^2/24]

639077317

27.92822

22.9217


JB Test calculation

n[(K3)^2/6 + (k4)^2/24]

6.39E+08


33649.99

K3^2/6

5608.331

K4^2

2.47E+08

K4^2/24

10302090


10307699


6.39E+08

Null Hypothesis H0: The mean stock returns of GD is not equal to 2.8 percent

Alternate Hypothesis H1: The mean return of GD stock is equal to 2.8%


OneSample Statistics

N

Mean

Std. Deviation

Std. Error Mean

rt_GD

62

1.1102

.37165

.04720

OneSample Test

Test Value = 2.8


t

Df

Sig. (2tailed)

Mean Difference

95% Confidence Interval of the Difference


Lower

Upper

rt_GD

35.802

61

.000

1.68984

1.7842

1.5955








There exists mean difference of 1.68 for GD stock returns from t test statistics, t (61) = 35.8, 0.00<0.005 at 95% C.I. Hence, null hypothesis stating mean stock returns of GD is not equal to 0 is accepted
rt_Boeng

rt_GD

0

0

1.361862

1.31477

1.261369

1.382765

1.289841

1.356505

1.361862

1.351007

1.429208

1.478442

1.50696

1.572854

1.666428

1.773411

1.531658

1.570137

1.466517

1.52535

1.372705

1.517249

1.357241

1.456478

1.343204

1.37497

1.35375

1.37214

1.310635

1.492565

1.446994

1.574588

1.355034

1.52768

1.362233

1.588848

1.410461

1.538255

1.447203

1.523955

1.429821

1.479755

1.355402

1.515181

1.335847

1.454148

1.362976

1.519786

1.308919

1.482167

1.17166

1.428392

1.1

1.361306

1.015031

1.305502

0.980977

1.284869

0.95603

1.178703

0.966939

1.208474

0.854706

1.149174

0.769235

1.161049

0.747667

1.096983

0.735351

1.052088

0.801543

0.991973

0.778699

0.917101

0.800068

0.922346

0.778093

0.917859

0.742118

0.850201

0.789083

0.861703

0.833477

0.860072

0.79177

0.814668

0.78815

0.789956

0.803798

0.718084

0.747053

0.690324

0.772324

0.729291

0.690277

0.753526

0.665117

0.723174

0.668541

0.739484

0.700087

0.730891

0.714187

0.716028

0.723487

0.708268

0.696042

0.672905

0.768171

0.691231

0.766581

0.727541

0.677647

0.675313

0.689896

0.685122

0.694013

0.730677

0.835916

0.75036

Risk returns of Boeng and GD are computed and depicted in above table. F statistical testing was performed to observe differences
FTest TwoSample for Variances
FTest TwoSample for Variances





rt_Boeng

rt_GD

Mean

1.01746

1.110295

Variance

0.111919

0.138301

Observations

62

62

Df

61

61

F

0.809245


P(F<=f) onetail

0.205428


F Critical onetail

0.654094


F (61) = 0.80, F critical is greater than F statistics suggesting a slight mean variation between risk returns of the Boeng and GD stocks.

Correlation



rt_Boeng

rt_GD

rt_Boeng

1


rt_GD

0.952110318

1

So, we get r=0.95 which is based upon the correlation statistical testing which is just performed, since r value is positive and close to 1, it can be inferred that the risks associated with the Boeng and GD company stocks are same.
Regression Model
CAPM
SUMMARY OUTPUT


















Regression Statistics









Multiple R

0.602263437








R Square

0.362721247








Adjusted R Square

0.352099934








Standard Error

0.507227183








Observations

62

















ANOVA










df

SS

MS

F

Significance F




Regression

1

8.786175

8.786175

34.15032

2.24E07




Residual

60

15.43676

0.257279






Total

61

24.22294

















Coefficients

Standard Error

t Stat

Pvalue

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.604712092

0.294961

2.05014

0.044728

0.014702

1.194723

0.014702

1.194723

xt_GD

0.001012065

0.000173

5.84383

2.24E07

0.00136

0.00067

0.00136

0.00067




























RESIDUAL OUTPUT





PROBABILITY OUTPUT













Observation

Predicted Yt_GD

Residuals

Standard Residuals


Percentile

Yt_GD



1

0.604712092

0.60471

1.20209


0.806452

2.13923



2

0.735735938

1.40349

2.78996


2.419355

1.97391



3

0.774073496

1.13916

2.2645


4.032258

1.91323



4

0.755412526

0.93808

1.86478


5.645161

1.80699



5

0.73048338

1.07651

2.13996


7.258065

1.80065



6

0.701713067

0.62484

1.24211


8.870968

1.7409



7

0.6273589

0.01779

0.03536


10.48387

1.73014



8

0.538672197

0.388083

0.771456


12.09677

1.71804



9

0.662159101

0.057297

0.113898


13.70968

1.69593



10

0.655808446

0.113158

0.224944


15.32258

1.6935



11

0.666671778

0.312921

0.622045


16.93548

1.67603



12

0.722158779

0.379637

0.754666


18.54839

1.6543



13

0.776085718

0.174056

0.345999


20.16129

1.64402



14

0.819381229

0.02448

0.04866


21.77419

1.62673



15

0.80873752

0.386303

0.767917


23.3871

1.61692



16

0.719962769

0.71355

1.418442


25

1.6068



17

0.772511255

0.641191

1.274602


26.6129

1.54053



18

0.789870919

0.886719

1.762677


28.22581

1.53832



19

0.817411016

0.793666

1.577701


29.83871

1.53288



20

0.851875221

0.73883

1.468694


31.45161

1.5321



21

0.823038825

0.616794

1.226102


33.06452

1.52833



22

0.827182664

0.736363

1.46379


34.67742

1.50877



23

0.837333113

0.535481

1.064464


36.29032

1.50368



24

0.910093428

0.444879

0.88436


37.90323

1.47569



25

0.926918127

0.521085

1.035847


39.51613

1.46583



26

0.982224601

0.558616

1.110453


41.12903

1.44071



27

1.01101954

0.697326

1.386189


42.74194

1.4143



28

1.04467578

0.186177

0.370095


44.35484

1.38095



29

1.019955171

0.17318

0.34425


45.96774

1.37897



30

1.100388947

0.31391

0.62401


47.58065

1.33246



31

1.046981339

0.49354

0.9811


49.19355

1.32656



32

1.096261131

0.36957

0.73465


50.80645

1.31511



33

1.172242391

0.20871

0.41488


52.41935

1.27883



34

1.22212869

0.42189

0.83866


54.03226

1.19452



35

1.265204452

0.70871

1.40882


55.64516

1.19313



36

1.198573916

0.47745

0.94911


57.25806

1.18064



37

1.27638435

0.46451

0.92339


58.87097

1.02188



38

1.289408258

0.51125

1.01629


60.48387

1.00346



39

1.30118056

0.42896

0.85272


62.09677

0.92147



40

1.341314986

0.26548

0.52775


63.70968

0.8585



41

1.378369798

0.27593

0.54851


65.32258

0.84386



42

1.348408287

0.34752

0.69082


66.93548

0.64515



43

1.422027586

0.1063

0.21132


68.54839

0.60486



44

1.390576308

0.32747

0.65096


70.16129

0.60203



45

1.436872584

0.18004

0.3579


71.77419

0.54265



46

1.487037371

0.01664

0.03307


73.3871

0.46521



47

1.478247151

0.037539

0.074622


75

0.42361



48

1.413649192

0.492175

0.978378


76.6129

0.42243



49

1.524505922

0.245679

0.488377


78.22581

0.40583



50

1.487450643

0.292935

0.582315


79.83871

0.35375



51

1.505251423

0.190142

0.377976


81.45161

0.34252



52

1.527381021

0.148409

0.295016


83.06452

0.31369



53

1.482557579

0.14417

0.2866


84.67742

0.30185



54

1.52380675

0.00829

0.01648


86.29032

0.20625



55

1.390485216

0.11828

0.23513


87.90323

0.15059



56

1.337707601

0.005248

0.010433


89.51613

0.13132



57

1.499050031

0.023363

0.046443


91.12903

0.11304



58

1.500100106

0.03278

0.06516


92.74194

0.09082



59

1.463185951

0.07514

0.14936


94.35484

0.02374



60

1.358091228

0.177451

0.352749


95.96774

0.00641



61

1.349970557

0.346514

0.688822


97.58065

0



62

1.479078582

0.457199

0.90885


99.19355

0.096848



The CAPM for regression model infers that Boeng = 0.001GD + 0.60
This infers that there is no difference in CAMP of both stocks are fair value and no variation in their risk level
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Task B: Hypothesis Testing of Means and Variances Equality
Question 1: Calculate returns for these three series in Excel or any software of your choice using the transformation: rt = 100*ln(Pt / Pt1) and perform the JarqueBerra test of normally distributed returns for each of Boeing and GD. What do you infer about the distribution of the two stock returns series? Describe also the risk and average return relationship in each of the two stocks.
Answer:
JB_Boeng

JB_GD







27.9282161

22.9217












JB Test calculation







n[(K3)^2/6 + (k4)^2/24]

6.39E+08


The chi square critical value




33649.99







K3^2/6

5608.331


H0: Normal distribution of data



K4^2

2.47E+08


H1: Means there is no normal distribution of data


K4^2/24

10302090








10307699








6.39E+08










JB

Boeng

27.92

p<0.05> 0.01




JB

GD

22.92

p<0.05> 0.01












We usually do not take Null theory into account when the significance level is 5%

Question 2:
Test a hypothesis that the average return on GD stock is different from 2.8%. Which test statistic would you choose to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null hypothesis.
Answer:
OneSample Statistics


N

Mean

Std. Deviation

Std. Error Mean

rt_GD

62

1.1102

.37165

.04720

The mean GD stock rate is 1.11% with deviation of 0.37
OneSample Test


Test Value = 2.8


t

df

Sig. (2tailed)

Mean Difference

95% Confidence Interval of the Difference


Lower

Upper

rt_GD

35.802

61

.000

1.68984

1.7842

1.5955

In regards to a Student Ttest was led to assess the accompanying expressed theory
M1 = 28% normal returns of GD stocks are 2.8%.
H0: The mean returns of GD isn't approach to 2.8 percent
H1: The mean GD stock return is 2.8%
The outcomes propose that t(61) = 35.80, alpha = 0.000< 0.005 has a measurable noteworthy mean distinction 1.68. The mean supply of GD esteem is observed to be 1.11 which isn't rise to conjectured mean stock esteem 2.8% in this test. It is henceforth deduced that invalid speculation expressing that the normal return isn't rise to 2.8 percent for GD Stock is acknowledged
Question 3: Before investing in one of the two stocks, you first want to compare risk associated with each of the two stocks. Perform an appropriate hypothesis test using 5% significance level and interpret your results.
Answer:
FTest TwoSample for Variances





rt_Boeng

rt_GD

Mean

1.01746

1.110295

Variance

0.111919

0.138301

Observations

62

62

Df

61

61

F

0.809245


P(F<=f) onetail

0.205428


F Critical onetail

0.654094


Invalid theory H0: There is no mean distinction between hazard returns of Boeng and GD.
Interchange theory H1: The danger of putting resources into GD stocks is higher than Boeng stocks. A F test is led to assess the distinctions in mean hazard free return rates. The F(61) = 0.80, p<0.25 is lesser than F basic esteem (0.65). This construes recommending that there is a noteworthy variety in hazard related with GD and Boeng stocks. Henceforth, invalid theory is rejected. The hazard related with GD is higher than Boeng since mean returns of GD is higher than Boeng stocks.
Question 4: Besides, you want to determine whether both stocks have same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns. Report your findings and also mention which stock will you prefer and why?
Answer:
H0: There is no mean varieties in normal returns of GD and Beong stocks
H1: There is a measurable critical mean contrast in populace normal returns of GD and Boeng stocks
Connection investigation was performed to evaluate whether there is any connection between populace normal returns of GD and Boeng stocks. The r esteem near 1 to  1 demonstrates the positive to negative relationship held between factors

rt_Boeng

rt_GD

rt_Boeng

1

1

rt_GD

0.95216012

1

As per the mentioned connection grid detailed that the loads of GD and Boeng have comparative populace mean returns, since, Pearson's r esteem is 0.95 at 95% C.I. This deduces recommending that populace normal of GD and Boeng stock returns have solid positive connection between them. Thus, invalid speculation is acknowledged.
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Task C: Regression Analysis and Inference
Question 5: Compute excess return on your preferred stock as yt = rt  rf,t and excess market return as xt = rM,t  rf,t and perform the following tasks.
Answer:
a. Estimate the CAPM using linear regression by regressing the excess return on your preferred stock (yt) on excess market return (xt) and properly report your regression results.
Relapse investigation is led to evaluate the peril of putting resources into GD stocks. The overabundance returns and market returns of GD stock were determined by subtracting the SP 500 returns and CBOE US treasury premium returns. CAMP Beta coefficient esteem is assessed utilizing relapse.
b. Interpret the estimated CAPM betacoefficient in terms of the stock's riskiness in comparison with the market.

Coefficients

Standard Error

t Stat

Pvalue

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

0.604712

0.294961

2.05014

0.044728

0.014702

1.194723

0.014702

1.194723

xt_GD

0.00101

0.000173

5.84383

2.24E07

0.00136

0.00067

0.00136

0.00067

The Beta coefficient of CAMP GD stock is  0.00101 is seen from the above determined Regression results.
c. Interpret the value of R2.
Regression Statistics

Multiple R

0.602263

R Square

0.362721

Adjusted R Square

0.3521

Standard Error

0.507227

Observations

62

The R squared estimation of the assessed CAPM model for GD stock is 0.36. This gathers this model gauges the danger of contributing GD stocks 36% correctly. Expanded dimension of standard blunder rate is the purpose behind less R squared esteem.
d. Interpret 95% confidence interval for the slope coefficient.
Question 6: Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether your preferred stock is a neutral stock.
Answer:
H0: The abundance market returns of GD stock is seen to impartial
H1: The abundance market returns of GD stock is certainly not an unbiased stock
The t( 5.85) has p esteem = 2.24 more noteworthy than p<0.005 at 95% C.I. Henceforth, it is obvious that invalid speculation is rejected. This gathers overabundance market returns of GD stock is certainly not an impartial stock and it is less hazardous in nature.
Question 7: One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.
Answer:
The blunder term in relapse model as a rule gauges the likelihood of expectation of relapse model. The evaluated standard blunder is 0.50.
Invalid Hypothesis H0: The mistake term isn't regularly disseminated
Substitute Hypothesis H1: The blunder term is dispersed ordinarily
The standard blunder of beta coefficient esteem is observed to be 0.00 at 5% hugeness dimension in the relapse table. This construes, invalid speculation expressing that blunder term isn't circulated regularly is acknowledged.
Moreover, the likelihood plot likewise displays the negative straight pattern suggesting that blunder term isn't regularly appropriated
Proposal
The mean stock returns of GD and Boeng were thought about by figuring the normal hazard free returns, abundance returns and market returns. The normal stock returns of GD are nearly higher than Boeng. Likewise, the hazard free return for GD stock is seen to be bigger than Boeng's without hazard return rate. Factual test were performed to looking at the populace mean of normal return and a positive solid connection was seen among GD and Boeng. Notwithstanding, results acquired from relapse testing has registered estimation of CAPM Beta Coefficient of GD stocks. This uncovered CAPM of GD stocks is exceedingly less secure at 5% Significance dimension. The overabundance returns of stock additionally delineate the solid negative association with the abundance market returns. Henceforth, it is more dangerous to put resources into GD stocks.
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