Analysis of the performance of stocks is essential
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.
Herein we present the time line charts of prices of stocks
Figure 1: Comparison of prices of Stocks
Figure 3: Closing stock prices of Boeing
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.
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 
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.
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 JarqueBera test is used to test for normality of the data. Skewness and Kurtosis are two important statistical features which are used to calculate the JarqueBera Statistics.
The formula for JarqueBera statistics is:
The JarqueBera statistics follows a Chsquare 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 JarqueBera statistics for Boeing:
Time line charts of prices of stocks
Since the pvalue 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.
To test if the average return of the stock prices of Boeing is at least 3% the onesample ttest is used. The onesample ttest 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%
Alternate hypothesis: The average return of the stock prices of Boeing is at least 3%
Statistics 
Value 
count 
65 
mean 
1.0140 
standard deviation 
5.9877 
standard error 
0.7427 
Hypothesized mean 
0.03 
a 
0.05 
Tails 
1 
df 
64 
t stat 
1.3249 
p value 
0.0950 
t crit 
0.0630 
sig 
No 
The tstatistics is calculated as :
Since the tstat 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%
In order to compare the risks associated with both the stocks independent sample ttest assuming unequal variance was used.
Null Hypothesis: The risk on stock prices of both the stocks are similar
Alternate Hypothesis: The risks on stock prices of both the stocks are similar
tTest: TwoSample 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) onetail 
0.1670 

t Critical onetail 
1.6572 

P(T<=t) twotail 
0.3340 

t Critical twotail 
1.9793 
From the above test we find that at 0.05 level of significance pvalue is 0.3340. Since the pvalue is more than the level of significance hence we do not reject Null Hypothesis.
Thus the risks associated on both the stocks is similar.
In order to compare the risks associated with both the stocks independent sample ttest assuming unequal variance was used.
Null Hypothesis: The average return on stock prices of both the stocks are similar
Alternate Hypothesis: The average return on stock prices of both the stocks are similar
tTest: TwoSample 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) onetail 
0.1670 

t Critical onetail 
1.6568 

P(T<=t) twotail 
0.3339 

t Critical twotail 
1.9787 
From the above test we find that at 0.05 level of significance pvalue is 0.3339. Since the pvalue 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.
The excess return and excess return for IBM is calculated using the stated formula.
CAPM has been calculated using the regression model.
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.
From the above tables we find that R^{2} 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 R^{2} 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
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: à 0.3959, 1.0450
Thus the 95% confidence interval for the coefficient of the market return of IBM is 0.3959, 1.0450.
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.
BA 
IBM 

Skewness 
0.0927 
0.3866 
Kurtosis 
0.8889 
1.7733 
JarqueBera 
12.1631 
5.6947 
χ2(0.05,2) 
0.0023 
0.0580 
The distribution of the error term was analysed using the JarqueBera 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.