Comprehensive Analysis of MSFT and APPL Stock Investment Strategies

This project undertakes a detailed financial analysis of Microsoft (MSFT) and Apple (APPL) stocks. It begins with hypothesis testing, including the Jarque-Berra test for normality of returns and a t-test to assess if the average return on APPL differs from 3%. The project then compares the risks associated with both stocks using statistical measures like mean, variance, and correlation. Furthermore, regression analysis is employed to evaluate the excess market return, estimate the Capital Asset Pricing Model (CAPM) beta coefficient, interpret the coefficient of determination (R2), and test whether a stock is aggressive. The analysis involves interpreting statistical outputs such as coefficients, t-stats, p-values, and confidence intervals to draw conclusions about the investment characteristics of MSFT and APPL. The project aims to provide insights into stock performance and investment strategies through rigorous financial modeling and statistical analysis.

Which stock should I invest in

Contents
TASK 2: HYPOTHESIS TESTING OF MEANS AND VARIANCE EQUALITY......................1
(i) Jarque-Berra test of normally distributed returns for each of the two stocks, MSFT and
APPL......................................................................................................................................1
(ii) Hypothesis test of average return on APPL is different form 3% at 5% of significant level
................................................................................................................................................2
(iii) Compare the risks associated with the two stocks...........................................................2
(iv) Compare the risks associated with the two stocks...........................................................3
TASK 3: REGRESSION ANALYSIS AND INFERENCE............................................................4
(i) The excess market return...................................................................................................4
(ii) Estimate the Capital Asset Pricing...................................................................................5
(iii) Interpretation of estimated CAPM beta coefficient.........................................................7
(iv) The 95% confidence interval for the slope coefficient....................................................7
(v) Interpret the value of the coefficient of determination R2................................................7
(vi) Test of hypothesis if stock is an aggressive stock at the 5% level of significance..........8

TASK 2: HYPOTHESIS TESTING OF MEANS AND VARIANCE
EQUALITY
(i) Jarque-Berra test of normally distributed returns for each of the two stocks, MSFT and APPL
R_MSFT (%) R_APPL (%)
Mean 0.02102106 Mean 0.015649
Standard Error 0.00793276 Standard Error 0.00964
Median 0.020157713 Median 0.016623
Mode #N/A Mode #N/A
Standard Deviation 0.061956837 Standard Deviation 0.075295
Sample Variance 0.00383865 Sample Variance 0.005669
Kurtosis 0.990361162 Kurtosis 0.032881
Skewness 0.247615246 Skewness -0.2614
Range 0.326509211 Range 0.380271
Minimum -0.130247554 Minimum -0.18404
Maximum 0.196261658 Maximum 0.196227
Sum 1.282284677 Sum 0.954596
Count 61 Count 61
Largest(1) 0.196261658 Largest(1) 0.196227
Smallest(1) -0.130247554 Smallest(1) -0.18404
Confidence
Level(95.0%) 0.015867883
Confidence
Level(95.0%) 0.019284
R_MSFT (%) R_APPL (%)
Jarque-Berra test 4.31E+00 3.93E+00
Kurtosis 0.990361162 0.032880786
Skewness 0.247615246 -0.261404072
1

(ii) Hypothesis test of average return on APPL is different form 3% at 5% of significant level
H0: μ < a > 3%
Hα: μ ≠ 3%
t-Test: Paired Two Sample for
Means
0.03
Mean 0.014743271
Variance 0.005714462
Observations 60
Hypothesized Mean Difference 3
df 59
t Stat -305.8930622
P(T<=t) one-tail 1.98256E-96
t Critical one-tail 1.671093032
P(T<=t) two-tail 3.96513E-96
t Critical two-tail 2.000995378
(iii) Compare the risks associated with the two stocks
Risk associated with stocks of MSFT
MFST Risk factors
Mean 75.2464999 2.224596
Variance 820.4634249 0.127095676
Observations 60 60
Pearson Correlation
-
0.079934271
Hypothesized Mean
Difference 0
df 59
t Stat 19.72576961
P(T<=t) one-tail 5.85638E-28
2

t Critical one-tail 1.671093032
P(T<=t) two-tail 1.17128E-27
t Critical two-tail 2.000995378
Risk associated with Apple Stock
APPL Risk factors
Mean 145.4299996 2.224596
Variance 1414.709765 0.127095676
Observations 60 60
Pearson Correlation
-
0.048936862
Hypothesized Mean
Difference 0
df 59
t Stat 29.47681233
P(T<=t) one-tail 2.67005E-37
t Critical one-tail 1.671093032
P(T<=t) two-tail 5.3401E-37
t Critical two-tail 2.000995378
(iv) Compare the risks associated with the two stocks
R_MSFT
(%) R_F (%)
Mean 0.02102106 2.218768525
Variance 0.00383865 0.127048942
Observations 61 61
Pearson Correlation
-
0.128598301
Hypothesized Mean
Difference 0
3

df 60
t Stat -46.4482176
P(T<=t) one-tail 4.83934E-49
t Critical one-tail 1.670648865
P(T<=t) two-tail 9.67868E-49
t Critical two-tail 2.000297822
R_APPL
(%) R_F (%)
Mean 0.015649119 2.218768525
Variance 0.005669275 0.127048942
Observations 61 61
Pearson Correlation
-
0.097365459
Hypothesized Mean
Difference 0
df 60
t Stat
-
46.32878629
P(T<=t) one-tail 5.6245E-49
t Critical one-tail 1.670648865
P(T<=t) two-tail 1.1249E-48
t Critical two-tail 2.000297822
TASK 3: REGRESSION ANALYSIS AND INFERENCE
(i) The excess market return
Excess market return of Microsoft company
Regression Statistics
Multiple R 0.99978577
R Square 0.99957159
4

Adjusted R Square 0.98290492
Standard Error 0.04696757
Observations 61
ANOVA
df SS MS F
Significance
F
Regression 1 308.814201 308.814 139991.3 2.8E-101
Residual 60 0.13235718 0.00221
Total 61 308.946558
Excess market return of Apple company
Regression Statistics
Multiple R 0.99944795
R Square 0.9988962
Adjusted R Square 0.98222953
Standard Error 0.07632728
Observations 61
ANOVA
df SS MS F
Significance
F
Regression 1 316.329267 316.329 54297.5 3.67E-89
Residual 60 0.34955119 0.00583
Total 61 316.678818
(ii) Estimate the Capital Asset Pricing
5

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(iii) Interpretation of estimated CAPM beta coefficient
The coefficients are analysed as 0.21922 and t Stat are considered as 3.78171. it states the
significant difference upper than 95% level was 0.13266 it means the stock price of apple varied
during the months more than
(iv) The 95% confidence interval for the slope coefficient
Coefficients
Standard
Error t Stat
P-
value
Lower
95% Upper 95%
Lower
95.0%
Upper
95.0%
Intercept 0 #N/A #N/A #N/A #N/A #N/A #N/A #N/A
X (RM - RF) 0.9940825 0.00265688 374.154
9.3E-
103 0.988768 0.999397048 0.988767946 0.999397
The confidence intervals in respect of slope between rates are also collected in various
forms.
(v) Interpret the value of the coefficient of determination R2
7

(vi) Test of hypothesis if stock is an aggressive stock at the 5% level of significance
8

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