Financial Analysis of Boeing and IBM

The assignment presents a comparative analysis of Boeing and IBM's financial performance. It calculates the volatility of each company's stock prices and compares their sensitivity to market returns using R-squared values. The study also constructs 95% confidence intervals for the coefficient of market return, highlighting the potential range of future market influence on IBM's stock price. Additionally, it employs the Jarque-Bera test to assess the normality of the error terms in both cases.

Running Head: STATISTICS FOR FINANCE AND BUSINESS
Statistics for Finance and Business
Name of the Student
Name of the University
Author Note

1SFFBSTATISTICS FOR FINANCE AND BUSINESS
Table of Contents
Introduction......................................................................................................................................2
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................4
Part b............................................................................................................................................4
Part c............................................................................................................................................5
Answer 3..........................................................................................................................................6
Answer 4..........................................................................................................................................7
Answer 5..........................................................................................................................................7
Answer 6..........................................................................................................................................8
Answer 7..........................................................................................................................................8
Part a............................................................................................................................................8
Part b............................................................................................................................................8
Part c............................................................................................................................................9
Part d............................................................................................................................................9
Answer 8..........................................................................................................................................9
Answer 9..........................................................................................................................................9

2SFFBSTATISTICS FOR FINANCE AND BUSINESS
Introduction
In order to make the right decision in the investment of stocks, analysis of the
performance of stocks is essential. The two factors which are essential in stocks are the risk
factors and return on stocks. In the present report we analyse the performance of stocks of
Boeing and IBM for the period starting 1/12/2010 and ending at 31/05/2016. The closing prices
of the stocks have been obtained from yahoo finance. In addition, the prices of S&P 500 index
and US TN have also been used for the analysis.
The analysis in the report provides information for the stated period based on which
investment decision can be made.
Answer 1
Herein we present the time line charts of prices of stocks
12/1/2010
3/1/2011
6/1/2011
9/1/2011
12/1/2011
3/1/2012
6/1/2012
9/1/2012
12/1/2012
3/1/2013
6/1/2013
9/1/2013
12/1/2013
3/1/2014
6/1/2014
9/1/2014
12/1/2014
3/1/2015
6/1/2015
9/1/2015
12/1/2015
3/1/2016
0.00
500.00
1000.00
1500.00
2000.00
2500.00
Comparison of prices of Stocks
S&P BA IBM
Time Line
Prices
Figure 1: Comparison of prices of Stocks

3SFFBSTATISTICS FOR FINANCE AND BUSINESS
12/1/2010
6/1/2011
12/1/2011
6/1/2012
12/1/2012
6/1/2013
12/1/2013
6/1/2014
12/1/2014
6/1/2015
12/1/2015
0.00
500.00
1000.00
1500.00
2000.00
2500.00
Price of S&P
Time Line
Prices
Figure 2: Closing stock prices of S&P
12/1/2010
4/1/2011
8/1/2011
12/1/2011
4/1/2012
8/1/2012
12/1/2012
4/1/2013
8/1/2013
12/1/2013
4/1/2014
8/1/2014
12/1/2014
4/1/2015
8/1/2015
12/1/2015
4/1/2016
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
Stock Prices of Boeing
TimeLine
Price
Figure 3: Closing stock prices of Boeing

4SFFBSTATISTICS FOR FINANCE AND BUSINESS
12/1/2010
4/1/2011
8/1/2011
12/1/2011
4/1/2012
8/1/2012
12/1/2012
4/1/2013
8/1/2013
12/1/2013
4/1/2014
8/1/2014
12/1/2014
4/1/2015
8/1/2015
12/1/2015
4/1/2016
0.00
50.00
100.00
150.00
200.00
250.00
Stock Prices of IBM
TimeLine
Price
Figure 4: Closing stock prices of IBM
From the above chart it is clear that the prices of S&P is way above the prices of Boeing and
IBM during the same period. In addition, it is also seen that the prices of Boeing show a steady
growth during the period while the prices of IBM initially rose and then fell during the period.
Moreover, the prices of both IBM and Boeing are very close to each other.
Answer 2
Part b
Table 1: Statistics for the returns on stock prices of Boeing and IBM
Statistics BA IBM
Mean 1.0140 0.0715
Standard Error 0.7427 0.6267
Median 1.1997 -0.0741
Mode #N/A #N/A
Standard Deviation 5.9877 5.0523
Sample Variance 35.8520 25.5255
Kurtosis 0.6987 0.6553
Skewness -0.4699 -0.1368
Range 30.8197 28.8656
Minimum -18.5328 -14.3826
Maximum 12.2870 14.4829
Sum 65.9092 4.6464
Count 65 65

5SFFBSTATISTICS FOR FINANCE AND BUSINESS
From the above table it is found that the average returns on the stock prices of Boeing
during the period of 1/12/2010 to 31/05/2016 is higher than the returns on IBM. However, it is
found that the risk associated with the stock prices of IBM is lower than that of Boeings. The
higher average return associated with the stocks of Boeing can be attributed to the higher risks
for the prices of the organizations.
Hence it is found that the stock prices of IBM is relatively riskier than that of Boeings.
Part c
In order to further analyse the data a basic requirement is the presence of normality. The
requirement of normality of the data checks whether the data follows a normal distribution. The
Jarque-Bera test is used to test for normality of the data. Skewness and Kurtosis are two
important statistical features which are used to calculate the Jarque-Bera Statistics.
The formula for Jarque-Bera statistics is:
Jarque−Bera=n∗[ skewnes s2
6 + ( kurtosis−3 )2
24 ]
The Jarque-Bera statistics follows a Ch-square distribution with 2 degrees of Freedom.
Organization Skewness kurtosis Count
BA -0.4699 0.6987 65
IBM -0.1368 0.6553 65
From the above calculations the Jarque-Bera statistics for Boeing:
Boeing=65∗[ ( −0.4699 ) 2
6 + ( 0.6987−3 ) 2
24 ] =17.353
Hence Jarque-Bera statistics for Boeing = 17.353
The p-value of the statistics = 0.0002.
Since the p-value is less than 0.05 hence it can be inferred that the data for Boeing
follows a normal distribution.
From the above calculations the Jarque-Bera statistics for IBM:
IBM=65∗[ (−0.1368 )2
6 + ( 0.6553−3 )2
24 ]=15.0915
Hence Jarque-Bera statistics for IBM = 15.0915

6SFFBSTATISTICS FOR FINANCE AND BUSINESS
The p-value of the statistics = 0.0005.
Since the p-value is less than 0.05 hence it can be inferred that the data for IBM follows a
normal distribution.
Thus it is found that the data for both Boeing and IBM follows normal distribution. Hence the
returns on the closing stock prices can be used for further calculations.
Answer 3
To test if the average return of the stock prices of Boeing is at least 3% the one-sample t-
test is used. The one-sample t-test is used since the test is used to assess how a sample data
compares with a given value. In the present condition we have to compare if the average return
of the stock prices of Boing is less than or greater than 3%.
Null hypothesis: The average return of the stock prices of Boeing is less than 3%
H0 : μ<3 %
Alternate hypothesis: The average return of the stock prices of Boeing is at least 3%
H A : μ ≥3 %
Statistics Value
count 65
mean 1.0140
standard deviation 5.9877
standard error 0.7427
Hypothesized mean 0.03
 0.05
Tails 1
df 64
t stat 1.3249
p value 0.0950
t crit 0.0630
sig No
The t-statistics is calculated as : 1.0140−0.03
0.7427 =13249
Since the t-stat is more than the critical value hence we do not have sufficient evidence to
reject the Null Hypothesis. Thus, it is found that the average return of the stock prices of Boeing
is less than 3%

7SFFBSTATISTICS FOR FINANCE AND BUSINESS
Answer 4
In order to compare the risks associated with both the stocks independent sample t-test
assuming unequal variance was used.
Null Hypothesis: The risk on stock prices of both the stocks are similar
H0 :σ Boeing=σIBM
Alternate Hypothesis: The risks on stock prices of both the stocks are similar
H A :σ Boeing ≠ σ IBM
t-Test: Two-Sample Assuming Unequal Variances
BA IBM
Mean 1.0140 0.0715
Variance 35.8520 25.5255
Observations 65 65
Hypothesized Mean Difference 0
df 124
t Stat 0.9699
P(T<=t) one-tail 0.1670
t Critical one-tail 1.6572
P(T<=t) two-tail 0.3340
t Critical two-tail 1.9793
From the above test we find that at 0.05 level of significance p-value is 0.3340. Since the
p-value is more than the level of significance hence we do not reject Null Hypothesis.
Thus the risks associated on both the stocks is similar.
Answer 5
In order to compare the risks associated with both the stocks independent sample t-test assuming
unequal variance was used.
Null Hypothesis: The average return on stock prices of both the stocks are similar
H0 : μBoeing=μIBM
Alternate Hypothesis: The average return on stock prices of both the stocks are similar
H A : μBoeing≠ μIBM

8SFFBSTATISTICS FOR FINANCE AND BUSINESS
t-Test: Two-Sample Assuming Equal Variances
BA IBM
Mean 1.0140 0.0715
Variance 35.8520 25.5255
Observations 65 65
Pooled Variance 30.6887
Hypothesized Mean Difference 0
Df 128
t Stat 0.9699
P(T<=t) one-tail 0.1670
t Critical one-tail 1.6568
P(T<=t) two-tail 0.3339
t Critical two-tail 1.9787
From the above test we find that at 0.05 level of significance p-value is 0.3339. Since the
p-value is more than the level of significance hence we do not reject Null Hypothesis.
Thus the risks associated on both the stocks is similar.
However, since the risk of IBM is lower than that of Boeing hence we would choose IBM
for further analysis.
Answer 6
The excess return and excess return for IBM is calculated using the stated formula.
Answer 7
Part a
CAPM has been calculated using the regression model.
Part b
From the above regression analysis, we find that the coefficient for market return of
Boeing is 1.1193 and for IBM is 0.7204. Thus, we can say that the volatility of Boeing is
111.93% as against 72.04% for IBM. Since the market returns for IBM is less volatile hence the
stock prices are less risky and thus may be more profitable.

9SFFBSTATISTICS FOR FINANCE AND BUSINESS
Part c
From the above tables we find that R2 for Boeing is 0.4048 and for IBM is 0.2380. R2
defines the relation of excess market return of the stocks with excess return. From the values of
R2 we find that the correlation of the returns for Boeing is 40.48% and for IBM is 23.80%. Thus,
the prices of Boeing is more closely associated with the market returns.
Hence it would be wise to invest in the stocks of IBM
Part d
At 0.05 level of significance and 63 degrees of freedom the critical value is 1.9983.
For IBM:
Coefficient = 0.7204
Standard Error = 0.1624
Thus the confidence interval: 0.7204 ± 1.9983∗0.1624  0.3959, 1.0450
Thus the 95% confidence interval for the coefficient of the market return of IBM is 0.3959,
1.0450.
Answer 8
Statistics Values
Mean 0.0715
Standard Deviation 5.0523
Count 65
Standard Error 0.6267
confidence Level 95%
Lower critical value -1.9600
Upper critical value 1.9600
Margin of Error +/- 1.2282
Confidence Interval Lower Limit -1.1567
Confidence Interval Upper Limit 1.2997
The 95% confidence interval for IBM is -1.1567, 1.2297. Hence, it is reasonable to
suggest that the prices of IBM are within the interval at 5% risk. In other words, we can say that
when stock prices of another period is taken then there is a 95% chance that the returns would lie
between -1.1567 and 1.2297.
Answer 9

10SFFBSTATISTICS FOR FINANCE AND BUSINESS
0 20 40 60 80 100 120
-25
-20
-15
-10
-5
0
5
10
15
Normal Probability Plot (BA)
Sample Percentile
ytBA
0 20 40 60 80 100 120
-20
-15
-10
-5
0
5
10
15
Normal Probability Plot (IBM)
Sample Percentile
ytIBM
BA IBM
Skewness 0.0927 -0.3866
Kurtosis 0.8889 1.7733
Jarque-Bera 12.1631 5.6947
χ2(0.05,2) 0.0023 0.0580
The distribution of the error term was analysed using the Jarque-Bera test. From the test
results it is found that while the error term of the market return for Boeing is normally
distributed, the error term for IBM is not normally distributed.