The report discusses about the volatility and risk of stock market, return and market return. Usually, it is observed that stock market is volatile and unsteady (Berenson et al. 2012). Therefore, it is hard for evaluating the market performance. The report focuses to indicate the method of evaluating the company’s Price indexes through its market price movements. The price indexes for Boeing and International Business Machines (IBM) has been chosen for demonstrating (Freed, Bergquist and Jones 2014). However, the historical price movements of the individual price indexes from 1^{st} December 2010 and 31^{st} May 2016 cannot depict the appropriate outputs. Therefore, the historical index prices of S&P500 index and the 10 years’ US Treasury Bill are involved in the evaluation method for computing the effective outcomes. S&P500 index represents the summarisation of the market and the 10 years’ US Treasury Bill refers the riskfree return of the market.
The method of price index evaluation is divided in some parts. They are the compared and their market returns are calculated in the first part. In the next part, hypotheses are tested and CAPM is calculated using linear regression model. The whole evaluation is incorporated based on Capital Asset Pricing Model.
The movement of the price indexes for a defined timeperiod depicts trends of price indexes. The first line chart involves all the three types of trend lines of price indexes. The second, third and fourth line charts involve the line charts individually. The price indexes of IBM and BA in the line charts are shown below:
It could be inferred from the above line charts that the price indexes of both S&P500 and BA have increased from 01/12/2010 to 31/05/2016. The IBM price index has increased and then decreased within this period. It has better stationary trend in case of IBM price index than BA price index.

Price Indexes 



Price Returns 


Date 
S& P 500 price 
Boeing (BA) price 
IBM price 
TBill price 
S&P 500 price return 
Boeing (BA) price return 
IBM Price return 
12/1/2010 
1257.64 
65.26 
146.76 
3.305 
S&P 500 price return 
Boeing (BA) price return 
IBM Price return 
1/1/2011 
1286.12 
69.48 
162 
3.378 
2.239296944 
6.265966274 
9.879776981 
2/1/2011 
1327.22 
72.01 
161.88 
3.414 
3.145657708 
3.576604148 
0.074098434 
3/1/2011 
1325.83 
73.93 
163.07 
3.454 
0.104786202 
2.631367353 
0.73242485 
4/1/2011 
1363.61 
79.78 
170.58 
3.296 
2.809693855 
7.615413437 
4.502480722 
5/1/2011 
1345.2 
78.03 
168.93 
3.05 
1.359291933 
2.217947863 
0.972002012 
6/1/2011 
1320.64 
73.93 
171.55 
3.158 
1.842618552 
5.397465574 
1.539040029 
7/1/2011 
1292.28 
70.47 
181.85 
2.805 
2.170835635 
4.793159804 
5.830741764 
8/1/2011 
1218.89 
66.86 
171.91 
2.218 
5.846750175 
5.258620558 
5.621109711 
9/1/2011 
1131.42 
60.51 
174.87 
1.924 
7.446710096 
9.979228837 
1.707170481 
10/1/2011 
1253.3 
65.79 
184.63 
2.175 
10.23065919 
8.365925872 
5.431103736 
11/1/2011 
1246.96 
68.69 
188 
2.068 
0.507155381 
4.313579104 
1.808811334 
12/1/2011 
1257.6 
73.35 
183.88 
1.871 
0.849656569 
6.563881998 
2.21585647 
1/1/2012 
1312.41 
74.18 
192.6 
1.799 
4.2660044 
1.125209474 
4.633213239 
2/1/2012 
1365.68 
74.95 
196.73 
1.977 
3.978734502 
1.032661246 
2.121667944 
3/1/2012 
1408.47 
74.37 
208.65 
2.216 
3.085147563 
0.776850947 
5.882596833 
4/1/2012 
1397.91 
76.8 
207.08 
1.915 
0.752569988 
3.215200416 
0.755297659 
5/1/2012 
1310.33 
69.61 
192.9 
1.581 
6.469930807 
9.829642967 
7.093331288 
6/1/2012 
1362.16 
74.3 
195.58 
1.659 
3.879271978 
6.520274255 
1.37976243 
7/1/2012 
1379.32 
73.91 
195.98 
1.492 
1.251888486 
0.526280118 
0.204307969 
8/1/2012 
1406.58 
71.4 
194.85 
1.562 
1.957060987 
3.455029356 
0.578253022 
9/1/2012 
1440.67 
69.6 
207.45 
1.637 
2.394711887 
2.553335875 
6.266026974 
10/1/2012 
1412.16 
70.44 
194.53 
1.686 
1.998784252 
1.199677342 
6.430394465 
11/1/2012 
1416.18 
74.28 
190.07 
1.606 
0.284267279 
5.3080411 
2.319392548 
12/1/2012 
1426.19 
75.36 
191.55 
1.756 
0.704336761 
1.443492052 
0.775642462 
1/1/2013 
1498.11 
73.87 
203.07 
1.985 
4.919779205 
1.996981139 
5.840189485 
2/1/2013 
1514.68 
76.9 
200.83 
1.888 
1.099992755 
4.019907037 
1.109199265 
3/1/2013 
1569.19 
85.85 
213.3 
1.852 
3.535529388 
11.00956615 
6.024085053 
4/1/2013 
1597.57 
91.41 
202.54 
1.675 
1.792416591 
6.275336138 
5.17622762 
5/1/2013 
1630.74 
99.02 
208.02 
2.164 
2.055020242 
7.996689421 
2.669688481 
6/1/2013 
1606.28 
102.44 
191.11 
2.478 
1.511292881 
3.395546122 
8.478506442 
7/1/2013 
1685.73 
105.1 
195.04 
2.593 
4.827772796 
2.5634978 
2.035544611 
8/1/2013 
1632.97 
103.92 
182.27 
2.749 
3.179826758 
1.129090574 
6.771550366 
9/1/2013 
1681.55 
117.5 
185.18 
2.615 
2.931559129 
12.28169805 
1.583916104 
10/1/2013 
1756.54 
130.5 
179.21 
2.542 
4.362997098 
10.49348932 
3.27699456 
11/1/2013 
1805.81 
134.25 
179.68 
2.741 
2.766329003 
2.833050663 
0.261911042 
12/1/2013 
1848.36 
136.49 
187.57 
3.026 
2.328947407 
1.654765511 
4.297469436 
1/1/2014 
1782.59 
125.26 
176.68 
2.668 
3.623140749 
8.585979544 
5.981199928 
2/1/2014 
1859.45 
128.92 
185.17 
2.658 
4.221337488 
2.880044837 
4.693416414 
3/1/2014 
1872.34 
125.49 
192.49 
2.723 
0.690824862 
2.696598325 
3.876991905 
4/1/2014 
1883.95 
129.02 
196.47 
2.648 
0.618164318 
2.774140392 
2.046552269 
5/1/2014 
1923.57 
135.25 
184.36 
2.457 
2.081219595 
4.715745562 
6.361937971 
6/1/2014 
1960.23 
127.23 
181.27 
2.516 
1.887899662 
6.112842199 
1.690271874 
7/1/2014 
1930.67 
120.48 
191.67 
2.556 
1.519468737 
5.451270678 
5.578747831 
8/1/2014 
2003.37 
126.8 
192.3 
2.343 
3.696364432 
5.112727671 
0.328153535 
9/1/2014 
1972.29 
127.38 
189.83 
2.508 
1.563543608 
0.456365573 
1.292772286 
10/1/2014 
2018.05 
124.91 
164.4 
2.335 
2.293639895 
1.958121139 
14.38264992 
11/1/2014 
2067.56 
134.36 
162.17 
2.194 
2.423747367 
7.292926219 
1.365729073 
12/1/2014 
2058.9 
129.98 
160.44 
2.17 
0.419738458 
3.314221049 
1.072510203 
1/1/2015 
1994.99 
145.37 
153.31 
1.675 
3.153277922 
11.19016204 
4.545805109 
2/1/2015 
2104.5 
150.85 
161.94 
2.002 
5.343887644 
3.700382334 
5.476390633 
3/1/2015 
2067.89 
150.08 
160.5 
1.934 
1.754919723 
0.51175068 
0.893196604 
4/1/2015 
2085.51 
143.34 
171.29 
2.046 
0.848472245 
4.594909592 
6.506404307 
5/1/2015 
2107.39 
140.52 
169.65 
2.095 
1.043672976 
1.98695468 
0.962052978 
6/1/2015 
2063.11 
138.72 
162.66 
2.335 
2.123555928 
1.289233562 
4.207529853 
7/1/2015 
2103.84 
144.17 
161.99 
2.205 
1.954968325 
3.853562471 
0.412752153 
8/1/2015 
1972.18 
130.68 
147.89 
2.2 
6.46247309 
9.824161178 
9.106588838 
9/1/2015 
1920.03 
130.95 
144.97 
2.06 
2.679873126 
0.206401488 
1.994191606 
10/1/2015 
2079.36 
148.07 
140.08 
2.151 
7.97193795 
12.28696342 
3.431312911 
11/1/2015 
2080.41 
145.45 
139.42 
2.218 
0.050474186 
1.785281788 
0.472275654 
12/1/2015 
2043.94 
144.59 
137.62 
2.269 
1.768565854 
0.593024094 
1.299471827 
1/1/2016 
1940.24 
120.13 
124.79 
1.931 
5.206761723 
18.53276586 
9.786389491 
2/1/2016 
1932.23 
118.18 
131.03 
1.74 
0.413690564 
1.636557884 
4.879396445 
3/1/2016 
2059.74 
126.94 
151.45 
1.786 
6.390499042 
7.150566372 
14.48292207 
4/1/2016 
2065.3 
134.8 
145.94 
1.819 
0.269576165 
6.00776711 
3.705992562 
5/1/2016 
2096.95 
126.15 
153.74 
1.834 
1.520836665 
6.632052979 
5.20673044 
Summary Statistics:
Boeing (BA) Price return 
IBM Price return 






Mean 
1.0139883 
Mean 
0.071483586 
Standard Error 
0.7426766 
Standard Error 
0.626657713 
Median 
1.1996773 
Median 
0.074098434 
Standard Deviation 
5.9876504 
Standard Deviation 
5.052276003 
Sample Variance 
35.851957 
Sample Variance 
25.52549281 
Kurtosis 
0.6987056 
Kurtosis 
0.655346526 
Skewness 
0.4699036 
Skewness 
0.136800306 
Range 
30.819729 
Range 
28.86557199 
Minimum 
18.532766 
Minimum 
14.38264992 
Maximum 
12.286963 
Maximum 
14.48292207 
Sum 
65.909237 
Sum 
4.646433103 
Count 
65 
Count 
65 
Confidence Level (95.0%) 
1.4836671 
Confidence Level (95.0%) 
1.251892683 
The average return of Boeing (BA) is greater than average returns of IBM (1.0139883>0.071483586). The risk is determined by standard deviation of returns of close rates of price index. The risk in terms of standard deviation shows that Boeing return is more volatile than IBM return (5.9876504>5.052276003).
The risk is relatively greater for Boeing price return for its greater variability in terms of standard deviation.
JerqueBera test is carried out for testing the normality of price indexes that are Boeing and IBM.
The JerqueBera test statistic (JB) is given as
JB = n *
JarqueBera test 








Skewness 
Kurtosis 
n 
JB 
α 
χ2 (0.05,2) 
Decision 
Boeing (BA) 
0.469903619 
0.698706 
65 
16.7353157 
0.05 
5.991464547 
Normality is Rejected 
IBM 
0.136800306 
0.655347 
65 
15.0915299 
0.05 
5.991464547 
Normality is Rejected 
Firstly, the JB test statistics of both the price indexes are calculated. For BA price return and IBM price return, they are 16.7353157 and 15.0915299. Then applying significant test statistic, we have tested Chisquare tests at 5% level of significance (χ2 (0.05, 2) = 5.99). For both one and twotail Chisquare tests, Boeing and IBM price returns failed to attain normality. Hence, none of the price returns is normally distributed at 95% confidence limit.
One sample ttest 
Boeing Close return (BA) 


Average (Xbar) = 
1.01398826 
hypothetical mean (μ) = 
3% 
(Xbar  μ) = 
0.98398826 
Standard deviation = 
5.987650369 
sample size (n) = 
65 
degrees of freedom= 
64 
Standard error = 
0.742676624 
tstatistic = 
1.324921544 
T(critical) = 
1.997729633 
Decision making = 
Null hypothesis rejected 
A onesample ttest determines whether the average price return of Boeing Close return (BA) is at least 3%. The tstatistic is  . The tstatistic is 1.324921544. At 5% level of significance, we reject the null hypothesis of average price return greater than or equal to 0.03 as T_{0.05 }< T_{cric}.
Therefore, the average price return of Boeing is not at least 3%.

Boeing (BA) return 
IBM return 
Variance 
35.85195694 
25.52549281 
Degrees of freedom 
64 
64 
Fstatistic 
1.404554937 

pvalue of Fstatistic 
0.088449703 

level of significance 
0.05 

decision making 
Null hypothesis accepted 

The riskiness of returns of two price returns could be more effectively compared by Ftest of two samples variances. The Ftest for comparing the riskiness of the price returns of IBM and GE are conducted here.
Hypotheses:
Null hypothesis (H_{0}): σ_{1}^{2 }= σ_{2}^{2}
Alternative hypothesis (H_{A}): σ_{1}^{2 }≠ σ_{2}^{2}
The F value for twotail test is computed as F = F_{1α/2, N11, N21}
Here, α=0.05, N_{1}1=64 and N_{2}1=64.
The risk associated with each of the two price returns is compared with the help of Fstatistic. The calculated Fstatistics (F = is 1.404554937.
For Boeing and IBM price returns, pvalue of the Fstatistic is 0.088449703. It is greater than 0.05. The null hypothesis is accepted at 5% level of significance.
Hence, it could be depicted that level of volatility of the two price returns for the given period are almost equal to each other (Groebner et al. 2008).
The average return is indicated by the mean of returns of the price returns. Hence, for comparing the average return of Boeing (BA) and IBM price returns, two sample ztest (for unequal samples) and two sample ttest (for equal samples) can be conducted on the calculated returns of the two price returns.
Hypotheses:
Null hypothesis (H0): μ_{BA} = μ_{IBM}
Alternative hypothesis (H_{A}): μ_{BA} ≠ μ_{IBM}
The zstatistic is given as z and tstatistic is given as .
Ztest of equality of means of two samples:
zTest: Two Sample for Means 



Boeing (BA) returns 
IBM returns 
Mean 
1.01398826 
0.071483586 
Known Variance 
35.8519 
25.5254 
Observations 
65 
65 
Hypothesized Mean Difference 
0 

z 
0.969920863 

P(Z<=z) onetail 
0.16604297 

z Critical onetail 
1.644853627 

P(Z<=z) twotail 
0.33208594 

z Critical twotail 
1.959963985 

decision making 
Null hypothesis accepted 

For comparing the average returns of each of the two investing price returns, a ztest is applied. The variances are known for each of the price returns. The calculated zstatistic is 0.9699. The pvalue for twotail zstatistic is 0.332 (>0.05). Therefore, we can reject the null hypothesis of equality of averages of returns of two price returns at 5% level of significance.
Twosample ttest of equality of means for unequal variances:
tTest: TwoSample Assuming Unequal Variances 



Boeing (BA) return 
IBM return 
Mean 
1.01398826 
0.07148359 
Variance 
35.85195694 
25.5254928 
Observations 
65 
65 
Hypothesized Mean Difference 
0 

df 
124 

t Stat 
0.96991968 

P(T<=t) onetail 
0.166987311 

t Critical onetail 
1.657234971 

P(T<=t) twotail 
0.333974621 

t Critical twotail 
1.979280091 

decision making 
Null hypothesis accepted 

The ttest assuming equal variances of BA and IBM price returns gives the tstatistic 0.96991968. The pvalue of the twotail ttest is found to be 0.333974621. The level of significance is 5%, which is lesser than calculated pvalue. Therefore, we cannot reject the null hypothesis of equality of averages of both the price returns.
Inference:
According to the price return averages and price return standard deviations (risk), an equality is established. Hence, we cannot draw firm decision to choose any one price returns between BA and IBM. Hence, we further proceed with both of them. Next, we are willing to excess price return, excess market return and CAPM of both the price returns. With the help of these, we can find the volatility of both the price returns. The preferable price return would be distinguished after that.
Excess Return 
Excess Return 
Excess Market Return 
Boeing Excess return (BA) 
IBM Excess return 

BA 
IBM 

y_{tBA} 
y_{tIBM} 
x_{t} 
2.887966274 
6.501776981 
1.138703056 
0.162604148 
3.488098434 
0.268342292 
0.822632647 
2.72157515 
3.558786202 
4.319413437 
1.206480722 
0.486306145 
5.267947863 
4.022002012 
4.409291933 
8.555465574 
1.618959971 
5.000618552 
7.598159804 
3.025741764 
4.975835635 
7.476620558 
7.839109711 
8.064750175 
11.90322884 
0.216829519 
9.370710096 
6.190925872 
3.256103736 
8.055659186 
2.245579104 
0.259188666 
2.575155381 
4.692881998 
4.08685647 
1.021343431 
0.673790526 
2.834213239 
2.4670044 
0.944338754 
0.144667944 
2.001734502 
2.992850947 
3.666596833 
0.869147563 
1.300200416 
2.670297659 
2.667569988 
11.41064297 
8.674331288 
8.050930807 
4.861274255 
0.27923757 
2.220271978 
2.018280118 
1.287692031 
0.240111514 
5.017029356 
2.140253022 
0.395060987 
4.190335875 
4.629026974 
0.757711887 
0.486322658 
8.116394465 
3.684784252 
3.7020411 
3.925392548 
1.321732721 
0.312507948 
0.980357538 
1.051663239 
3.981981139 
3.855189485 
2.934779205 
2.131907037 
2.997199265 
0.788007245 
9.157566153 
4.172085053 
1.683529388 
4.600336138 
6.85122762 
0.117416591 
5.832689421 
0.505688481 
0.108979758 
0.917546122 
10.95650644 
3.989292881 
0.0295022 
0.557455389 
2.234772796 
3.878090574 
9.520550366 
5.928826758 
9.666698047 
1.031083896 
0.316559129 
7.951489318 
5.81899456 
1.820997098 
0.092050663 
2.479088958 
0.025329003 
1.371234489 
1.271469436 
0.697052593 
11.25397954 
8.649199928 
6.291140749 
0.222044837 
2.035416414 
1.563337488 
5.419598325 
1.153991905 
2.032175138 
0.126140392 
0.601447731 
2.029835682 
2.258745562 
8.818937971 
0.375780405 
8.628842199 
4.206271874 
0.628100338 
8.007270678 
3.022747831 
4.075468737 
2.769727671 
2.014846465 
1.353364432 
2.051634427 
3.800772286 
4.071543608 
4.293121139 
16.71764992 
0.041360105 
5.098926219 
3.559729073 
0.229747367 
5.484221049 
3.242510203 
2.589738458 
9.515162035 
6.220805109 
4.828277922 
1.698382334 
3.474390633 
3.341887644 
2.44575068 
2.827196604 
3.688919723 
6.640909592 
4.460404307 
1.197527755 
4.08195468 
3.057052978 
1.051327024 
3.624233562 
6.542529853 
4.458555928 
1.648562471 
2.617752153 
0.250031675 
12.02416118 
11.30658884 
8.66247309 
1.853598512 
4.054191606 
4.739873126 
10.13596342 
5.582312911 
5.82093795 
4.003281788 
2.690275654 
2.167525814 
2.862024094 
3.568471827 
4.037565854 
20.46376586 
11.71738949 
7.137761723 
3.376557884 
3.139396445 
2.153690564 
5.364566372 
12.69692207 
4.604499042 
4.18876711 
5.524992562 
1.549423835 
8.466052979 
3.37273044 
0.313163335 
The Capital Asset Pricing Model (CAPM) is known as CAPM, which is one of the fundamental models in the financial field. The CAPM elaborates variability in the rate of return (r_{t}) as a function of the rate of return on a market portfolio (r_{M,t}) consisting all publicly traded price returns. Usually, the rate of return of any price return can be measured using opportunity cost that is the return on a risk free asset (r_{f,t}). The difference between the return and risk free rate is known as “risk premium” as it is the reward or punishment for performing a risky investment (Peirson et al. 2014). In accordance to CAPM, the risk premium on a security (r_{t }–r_{f,t}) is proportional to the risk premium on the market portfolio (r_{M,t }– r_{f,t}). According to CAPM,
(r_{t }–r_{f,t}) = β_{M}*(r_{M,t }– r_{f,t}) ……………….(1)
Equation (1) is called economic model as it describes association between excess price returns and excess market return.
The CAPM beta is crucial from the viewpoints of investors as it discloses the volatility of market price returns. Particularly, the bête (slope) measures the sensitivity of variation of given return of security in the whole price market. Value of beta defines whether the price return is a defensive, a neutral price index or an aggressive price index. Including an intercept (β_{0}) and an error term (u_{t}) in the model, we have a simple linear regression model –
(r_{t}  r_{f,t}) = β_{0 }+ β_{M} (r_{M,t}  r_{f,t}) +u_{t} ………………..(2)
Boeing (BA) Excess return:
SUMMARY OUTPUT 













Regression Statistics 






Multiple R 
0.63626059 





R Square 
0.40482754 





Adjusted R Square 
0.39538036 





Standard Error 
4.65767923 





Observations 
65 












ANOVA 







df 
SS 
MS 
F 
Significance F 

Regression 
1 
929.6231383 
929.6231 
42.85167 
1.22694E08 

Residual 
63 
1366.720475 
21.69398 



Total 
64 
2296.343613 












Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Intercept 
0.4017602 
0.629404328 
0.638318 
0.52558 
0.856003975 
1.659524372 
x_{t} 
1.11931665 
0.170989356 
6.546119 
1.23E08 
0.777621689 
1.461011607 
IBM Excess return:
SUMMARY OUTPUT 













Regression Statistics 






Multiple R 
0.487837632 





R Square 
0.237985555 





Adjusted R Square 
0.225890087 





Standard Error 
4.424020742 





Observations 
65 












ANOVA 







df 
SS 
MS 
F 
Significance F 

Regression 
1 
385.0900093 
385.09 
19.6756 
3.757E05 

Residual 
63 
1233.03345 
19.57196 



Total 
64 
1618.123459 












Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Intercept 
1.12349158 
0.597829448 
1.87928 
0.064833 
2.3181584 
0.07117523 
x_{t} 
0.720411483 
0.162411454 
4.435718 
3.76E05 
0.3958581 
1.04496487 
The calculated βvalue for Boeing excess return and Excess market return is 1.11931665. The calculated βvalue for IBM excess return and Excess market return is 0.720411483. The calculated βvalues define that BA price indexes are 111.93% less volatile than the market, whereas the volatility level of IBM compared to the market is 72.04%. Therefore, it can be stated that Boeing (BA) is highly volatile than IBM. Therefore, Boeing (BA) is considered to be more profitable than IBM price returns.
The linear regression tables describe that the values of R^{2} of BA and IBM are 0.40482754 and 0.237985555. The R^{2} indicates the relationship of the dependent variable with the independent variable. Hence, from the values of multiple R^{2} of the two price returns it could be stated that Boeing (BA) excess return (40.48%) is more associated than the association of IBM (23.80%).
Confidence Interval of IBM Price Return:
 For Boeing (BA) price return, slope (β_{1}) = 1.11931665, Standard Error = 170989356, d.f. = 64, tvalue = 6.546119. Hence, the 95% confidence interval for the slope coefficient would be (0.777621689, 1.461011607).
 For IBM price return, slope (β_{1}) = 0.720411483, Standard Error = 162411454, d.f. = 64, tvalue = 4.435718. Hence, the 95% confidence interval for the slope coefficient would be (0.3958581, 1.04496487).
The testing of aggressiveness of the excess price returns needs the following hypothesis:
Null hypothesis (H_{0}): β_{1} = 1
Alternative hypothesis (H_{1}): β_{1} < 1
For BA price returns, β_{1} is 1.11931665 along with the standard error (SE) 0.170989356. The “residual degrees of freedom” is 63 and calculated pvalue is 0.0. Hence, t = β_{1}/ SE = 6.546119.
For IBM price indexes, β_{1} is 0.720411483 along with the standard error (SE) 0.162411454. The “residual degrees of freedom” is 63 and calculated pvalue is 0.0. Hence, t = β_{1}/ SE = 4.435718.
For both the excess price returns, the pvalues are positive tvalue and equal degrees of freedom 64. The 95% confidence intervals for beta values of both BA and IBM price returns are (0.777621689, 1.461011607) and (0.3958581, 1.04496487). The confidence intervals near to 0 refers more neutral nature for price excess return. The confidence intervals of tstatistics indicate that IBM price return is more neutral (Moffett, Stonehill and Eiteman 2014).
IBM Ecess Price return residual plot:
The method of ordinary least squares (OLS) helps to establish the normality with diagram. The error terms in the model are graphically shown in normal probability plot. It shows that the error terms are not following normal distributions for IBM price indexes. The distributions of residual values are not symmetric for both the market return values.
JarqueBera test 








Skewness 
Kurtosis 
n 
JB 
α 
χ2 (0.05,2) 
Decision 
IBM 
0.039955804 
0.40782718 
65 
18.21556 
0.05 
5.99146455 
Normality is Rejected 
Besides, we perform a JarqueBera test for examining the normality of the residual values. The JB statistic of IBM (18.21) refers that normality of residual values of the regression is rejected at 5% level of significance.
Berenson, M., Levine, D., Szabat, K. A., & Krehbiel, T. C. (2012). Basic business statistics: Concepts and applications. Pearson Higher Education AU.
Freed, N., Bergquist, T., & Jones, S. (2014). Understanding business statistics. John Wiley & Sons.
Groebner, D.F., Shannon, P.W., Fry, P.C. and Smith, K.D., 2008. Business statistics. Pearson Education.
Moffett, M. H., Stonehill, A. I., & Eiteman, D. K. (2014). Fundamentals of multinational finance. Pearson.
Peirson, G., Brown, R., Easton, S., & Howard, P. (2014). Business finance. McGrawHill Education Australia.
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