STATGB 3302 : Statistical Inference And Regression Analysis
Comparison of the stock prices has been done in the following figures 2.1, 2.2 and 2.3. The stock prices of S&P, Boeing and IBM have been plotted in the graph over the selected time frame. It has been observed that the stock prices for both the companies Boeing and IBM follow an increasing trend. The S&P stock prices also follow an increasing trend.
1.2 Computation of Returns
The returns on the closing stock prices for S&P, BE and IBM are given in the following table:
|
Date |
Price Series |
Returns |
|||||
|
S&P |
Boeing |
IBM |
US TN (10 Year) |
Return S&P |
Return Boeing |
Return IBM |
|
|
2/1/2010 |
1104.49 |
63.16 |
127.16 |
3.595 |
– |
– |
– |
|
3/1/2010 |
1169.43 |
72.61 |
128.25 |
3.833 |
5.71 |
13.94 |
0.85 |
|
4/1/2010 |
1186.69 |
72.43 |
129 |
3.663 |
1.47 |
-0.25 |
0.58 |
|
5/1/2010 |
1089.41 |
64.18 |
125.26 |
3.301 |
-8.55 |
-12.09 |
-2.94 |
|
6/1/2010 |
1030.71 |
62.75 |
123.48 |
2.951 |
-5.54 |
-2.25 |
-1.43 |
|
7/1/2010 |
1101.6 |
68.14 |
128.4 |
2.907 |
6.65 |
8.24 |
3.91 |
|
8/1/2010 |
1049.33 |
61.13 |
123.13 |
2.477 |
-4.86 |
-10.86 |
-4.19 |
|
9/1/2010 |
1141.2 |
66.54 |
134.14 |
2.517 |
8.39 |
8.48 |
8.56 |
|
10/1/2010 |
1183.26 |
70.64 |
143.6 |
2.612 |
3.62 |
5.98 |
6.81 |
|
11/1/2010 |
1180.55 |
63.77 |
141.46 |
2.797 |
-0.23 |
-10.23 |
-1.50 |
|
12/1/2010 |
1257.64 |
65.26 |
146.76 |
3.305 |
6.33 |
2.31 |
3.68 |
|
1/1/2011 |
1286.12 |
69.48 |
162 |
3.378 |
2.24 |
6.27 |
9.88 |
|
2/1/2011 |
1327.22 |
72.01 |
161.88 |
3.414 |
3.15 |
3.58 |
-0.07 |
|
3/1/2011 |
1325.83 |
73.93 |
163.07 |
3.454 |
-0.10 |
2.63 |
0.73 |
|
4/1/2011 |
1363.61 |
79.78 |
170.58 |
3.296 |
2.81 |
7.62 |
4.50 |
|
5/1/2011 |
1345.2 |
78.03 |
168.93 |
3.05 |
-1.36 |
-2.22 |
-0.97 |
|
6/1/2011 |
1320.64 |
73.93 |
171.55 |
3.158 |
-1.84 |
-5.40 |
1.54 |
|
7/1/2011 |
1292.28 |
70.47 |
181.85 |
2.805 |
-2.17 |
-4.79 |
5.83 |
|
8/1/2011 |
1218.89 |
66.86 |
171.91 |
2.218 |
-5.85 |
-5.26 |
-5.62 |
|
9/1/2011 |
1131.42 |
60.51 |
174.87 |
1.924 |
-7.45 |
-9.98 |
1.71 |
|
10/1/2011 |
1253.3 |
65.79 |
184.63 |
2.175 |
10.23 |
8.37 |
5.43 |
|
11/1/2011 |
1246.96 |
68.69 |
188 |
2.068 |
-0.51 |
4.31 |
1.81 |
|
12/1/2011 |
1257.6 |
73.35 |
183.88 |
1.871 |
0.85 |
6.56 |
-2.22 |
|
1/1/2012 |
1312.41 |
74.18 |
192.6 |
1.799 |
4.27 |
1.13 |
4.63 |
|
2/1/2012 |
1365.68 |
74.95 |
196.73 |
1.977 |
3.98 |
1.03 |
2.12 |
|
3/1/2012 |
1408.47 |
74.37 |
208.65 |
2.216 |
3.09 |
-0.78 |
5.88 |
|
4/1/2012 |
1397.91 |
76.8 |
207.08 |
1.915 |
-0.75 |
3.22 |
-0.76 |
|
5/1/2012 |
1310.33 |
69.61 |
192.9 |
1.581 |
-6.47 |
-9.83 |
-7.09 |
|
6/1/2012 |
1362.16 |
74.3 |
195.58 |
1.659 |
3.88 |
6.52 |
1.38 |
|
7/1/2012 |
1379.32 |
73.91 |
195.98 |
1.492 |
1.25 |
-0.53 |
0.20 |
|
8/1/2012 |
1406.58 |
71.4 |
194.85 |
1.562 |
1.96 |
-3.46 |
-0.58 |
|
9/1/2012 |
1440.67 |
69.6 |
207.45 |
1.637 |
2.39 |
-2.55 |
6.27 |
|
10/1/2012 |
1412.16 |
70.44 |
194.53 |
1.686 |
-2.00 |
1.20 |
-6.43 |
|
11/1/2012 |
1416.18 |
74.28 |
190.07 |
1.606 |
0.28 |
5.31 |
-2.32 |
|
12/1/2012 |
1426.19 |
75.36 |
191.55 |
1.756 |
0.70 |
1.44 |
0.78 |
|
1/1/2013 |
1498.11 |
73.87 |
203.07 |
1.985 |
4.92 |
-2.00 |
5.84 |
|
2/1/2013 |
1514.68 |
76.9 |
200.83 |
1.888 |
1.10 |
4.02 |
-1.11 |
|
3/1/2013 |
1569.19 |
85.85 |
213.3 |
1.852 |
3.54 |
11.01 |
6.02 |
|
4/1/2013 |
1597.57 |
91.41 |
202.54 |
1.675 |
1.79 |
6.28 |
-5.18 |
|
5/1/2013 |
1630.74 |
99.02 |
208.02 |
2.164 |
2.06 |
8.00 |
2.67 |
|
6/1/2013 |
1606.28 |
102.44 |
191.11 |
2.478 |
-1.51 |
3.40 |
-8.48 |
|
7/1/2013 |
1685.73 |
105.1 |
195.04 |
2.593 |
4.83 |
2.56 |
2.04 |
|
8/1/2013 |
1632.97 |
103.92 |
182.27 |
2.749 |
-3.18 |
-1.13 |
-6.77 |
|
9/1/2013 |
1681.55 |
117.5 |
185.18 |
2.615 |
2.93 |
12.28 |
1.58 |
|
10/1/2013 |
1756.54 |
130.5 |
179.21 |
2.542 |
4.36 |
10.49 |
-3.28 |
|
11/1/2013 |
1805.81 |
134.25 |
179.68 |
2.741 |
2.77 |
2.83 |
0.26 |
|
12/1/2013 |
1848.36 |
136.49 |
187.57 |
3.026 |
2.33 |
1.65 |
4.30 |
|
1/1/2014 |
1782.59 |
125.26 |
176.68 |
2.668 |
-3.62 |
-8.59 |
-5.98 |
|
2/1/2014 |
1859.45 |
128.92 |
185.17 |
2.658 |
4.22 |
2.88 |
4.69 |
|
3/1/2014 |
1872.34 |
125.49 |
192.49 |
2.723 |
0.69 |
-2.70 |
3.88 |
|
4/1/2014 |
1883.95 |
129.02 |
196.47 |
2.648 |
0.62 |
2.77 |
2.05 |
|
5/1/2014 |
1923.57 |
135.25 |
184.36 |
2.457 |
2.08 |
4.72 |
-6.36 |
|
6/1/2014 |
1960.23 |
127.23 |
181.27 |
2.516 |
1.89 |
-6.11 |
-1.69 |
|
7/1/2014 |
1930.67 |
120.48 |
191.67 |
2.556 |
-1.52 |
-5.45 |
5.58 |
|
8/1/2014 |
2003.37 |
126.8 |
192.3 |
2.343 |
3.70 |
5.11 |
0.33 |
|
9/1/2014 |
1972.29 |
127.38 |
189.83 |
2.508 |
-1.56 |
0.46 |
-1.29 |
|
10/1/2014 |
2018.05 |
124.91 |
164.4 |
2.335 |
2.29 |
-1.96 |
-14.38 |
|
11/1/2014 |
2067.56 |
134.36 |
162.17 |
2.194 |
2.42 |
7.29 |
-1.37 |
|
12/1/2014 |
2058.9 |
129.98 |
160.44 |
2.17 |
-0.42 |
-3.31 |
-1.07 |
|
1/1/2015 |
1994.99 |
145.37 |
153.31 |
1.675 |
-3.15 |
11.19 |
-4.55 |
|
2/1/2015 |
2104.5 |
150.85 |
161.94 |
2.002 |
5.34 |
3.70 |
5.48 |
|
3/1/2015 |
2067.89 |
150.08 |
160.5 |
1.934 |
-1.75 |
-0.51 |
-0.89 |
|
4/1/2015 |
2085.51 |
143.34 |
171.29 |
2.046 |
0.85 |
-4.59 |
6.51 |
|
5/1/2015 |
2107.39 |
140.52 |
169.65 |
2.095 |
1.04 |
-1.99 |
-0.96 |
|
6/1/2015 |
2063.11 |
138.72 |
162.66 |
2.335 |
-2.12 |
-1.29 |
-4.21 |
|
7/1/2015 |
2103.84 |
144.17 |
161.99 |
2.205 |
1.95 |
3.85 |
-0.41 |
From the results of the summary statistics, it can be seen that BE provides higher returns than IBM. It can also be seen that the returns provided by BE is less than S&P 500. On the other hand, it can be said that BE experiences higher risks than IBM. The risks suffered by IBM has a similarity with that of the S&P 500.
|
Summary Statistics |
Return S&P |
Return Boeing |
Return IBM |
|
Mean |
0.99 |
1.27 |
0.37 |
|
Standard Error |
0.45 |
0.74 |
0.57 |
|
Median |
1.47 |
1.65 |
0.33 |
|
Mode |
#N/A |
#N/A |
#N/A |
|
Standard Deviation |
3.65 |
5.97 |
4.57 |
|
Sample Variance |
13.34 |
35.58 |
20.85 |
|
Kurtosis |
0.46 |
-0.32 |
0.56 |
|
Skewness |
-0.34 |
-0.22 |
-0.47 |
|
Range |
18.78 |
26.04 |
24.26 |
|
Minimum |
-8.55 |
-12.09 |
-14.38 |
|
Maximum |
10.23 |
13.94 |
9.88 |
|
Sum |
64.44 |
82.53 |
24.21 |
|
Count |
65 |
65 |
65 |
From the Jarque-Berra test, it can be seen that the returns provided by BE and IBM are normally distributed. Normality test is performed on the data because any test performed on a data which is not normal might not give a proper result on performing any tests.
|
|
Jarque Berra Test |
||
|
Return S&P |
Return Boeing |
Return IBM |
|
|
Test Statistic |
1.850 |
0.793 |
3.254 |
|
P-Value |
0.396 |
0.673 |
0.197 |
To test whether the returns on Boeing stocks exceeds 3 percent, z-test has to be conducted. From the comparison of the returns on Boeing stock, it has been observed that the returns on the Boeing stocks do not exceed 3 percent.
|
Hypothesis Test for µ |
|||
|
|
|||
|
Hypotheses |
|||
|
Null Hypothesis H0: |
µ |
≤ |
3 |
|
Alternative Hypothesis HA: |
µ |
> |
3 |
|
Test Type |
|
|
Upper |
|
Level of significance |
|||
|
|
|
alpha α set to: |
0.05 |
|
Critical Region |
|||
|
Degrees of Freedom |
64 |
||
|
Critical Value |
1.6690 |
||
|
|
|
||
|
Sample Data |
|||
|
Sample Standard Deviation s |
5.97 |
||
|
Sample Mean x bar |
1.27 |
||
|
Sample Size n |
65 |
||
|
Is Pop StDev known? Y/N |
N |
||
|
Standard Error of the Mean |
0.7399 |
||
|
t Sample Statistic |
-2.3385 |
||
|
p-value from the t distribution |
0.0112 |
||
|
|
|
|
|
|
Hypothesis test decision: |
|||
|
Reject the Null Hypothesis |
Decision has to be made on which stock would be better to invest. In order to do that, the risks of the stocks have to be compared. From the results of the comparison of stock returns of BE and IBM, it can be seen that the variation in the returns are not same. Moreover, the variation is higher in case of BE. Thus, IBM would be a preferred choice for investment.
|
F-Test Two-Sample for Variances |
||
|
|
Boeing |
IBM |
|
Mean |
94.97 |
174.97 |
|
Variance |
905.08 |
582.33 |
|
Observations |
66 |
66 |
|
df |
65 |
65 |
|
F |
1.554 |
|
|
P(F<=f) one-tail |
0.039 |
|
|
F Critical one-tail |
1.508 |
|
Further, it has to be compared whether both the stocks have the same average returns. From the results of the analysis, it has been observed that the average stock returns for both the companies BE and IBM are same. There is no significant difference between the average returns on the stocks of BE as well as IBM.
|
t-Test: Two-Sample Assuming Equal Variances |
||
|
|
Return Boeing |
Return IBM |
|
Mean |
1.27 |
0.37 |
|
Variance |
35.58 |
20.85 |
|
Observations |
65 |
65 |
|
Pooled Variance |
28.22 |
|
|
Hypothesized Mean Difference |
0 |
|
|
df |
128 |
|
|
t Stat |
0.963 |
|
|
P(T<=t) one-tail |
0.169 |
|
|
t Critical one-tail |
1.657 |
|
|
P(T<=t) two-tail |
0.337 |
|
|
t Critical two-tail |
1.979 |
|
Thus, from the analysis above it has been observed that the stocks of BE and IBM provide same returns with lesser risk in case of IBM and higher risk in case of BE. Thus, the preferred choice of investment will be in the stocks of BE.
1.7 Calculation of Excess Returns
|
Date |
US TN (10 Year) |
Return S&P |
Return IBM |
Excess Return (Yt) |
Excess Market Return (Xt) |
|
2/1/2010 |
3.595 |
|
|
|
|
|
3/1/2010 |
3.833 |
5.7133 |
0.8535 |
-2.9795 |
1.8803 |
|
4/1/2010 |
3.663 |
1.4651 |
0.5831 |
-3.0799 |
-2.1979 |
|
5/1/2010 |
3.301 |
-8.5532 |
-2.9421 |
-6.2431 |
-11.8542 |
|
6/1/2010 |
2.951 |
-5.5388 |
-1.4312 |
-4.3822 |
-8.4898 |
|
7/1/2010 |
2.907 |
6.6516 |
3.9071 |
1.0001 |
3.7446 |
|
8/1/2010 |
2.477 |
-4.8612 |
-4.1910 |
-6.6680 |
-7.3382 |
|
9/1/2010 |
2.517 |
8.3928 |
8.5643 |
6.0473 |
5.8758 |
|
10/1/2010 |
2.612 |
3.6193 |
6.8148 |
4.2028 |
1.0073 |
|
11/1/2010 |
2.797 |
-0.2293 |
-1.5015 |
-4.2985 |
-3.0263 |
|
12/1/2010 |
3.305 |
6.3256 |
3.6782 |
0.3732 |
3.0206 |
|
1/1/2011 |
3.378 |
2.2393 |
9.8798 |
6.5018 |
-1.1387 |
|
2/1/2011 |
3.414 |
3.1457 |
-0.0741 |
-3.4881 |
-0.2683 |
|
3/1/2011 |
3.454 |
-0.1048 |
0.7324 |
-2.7216 |
-3.5588 |
|
4/1/2011 |
3.296 |
2.8097 |
4.5025 |
1.2065 |
-0.4863 |
|
5/1/2011 |
3.05 |
-1.3593 |
-0.9720 |
-4.0220 |
-4.4093 |
|
6/1/2011 |
3.158 |
-1.8426 |
1.5390 |
-1.6190 |
-5.0006 |
|
7/1/2011 |
2.805 |
-2.1708 |
5.8307 |
3.0257 |
-4.9758 |
|
8/1/2011 |
2.218 |
-5.8468 |
-5.6211 |
-7.8391 |
-8.0648 |
|
9/1/2011 |
1.924 |
-7.4467 |
1.7072 |
-0.2168 |
-9.3707 |
|
10/1/2011 |
2.175 |
10.2307 |
5.4311 |
3.2561 |
8.0557 |
|
11/1/2011 |
2.068 |
-0.5072 |
1.8088 |
-0.2592 |
-2.5752 |
|
12/1/2011 |
1.871 |
0.8497 |
-2.2159 |
-4.0869 |
-1.0213 |
|
1/1/2012 |
1.799 |
4.2660 |
4.6332 |
2.8342 |
2.4670 |
|
2/1/2012 |
1.977 |
3.9787 |
2.1217 |
0.1447 |
2.0017 |
|
3/1/2012 |
2.216 |
3.0851 |
5.8826 |
3.6666 |
0.8691 |
|
4/1/2012 |
1.915 |
-0.7526 |
-0.7553 |
-2.6703 |
-2.6676 |
|
5/1/2012 |
1.581 |
-6.4699 |
-7.0933 |
-8.6743 |
-8.0509 |
|
6/1/2012 |
1.659 |
3.8793 |
1.3798 |
-0.2792 |
2.2203 |
|
7/1/2012 |
1.492 |
1.2519 |
0.2043 |
-1.2877 |
-0.2401 |
|
8/1/2012 |
1.562 |
1.9571 |
-0.5783 |
-2.1403 |
0.3951 |
|
9/1/2012 |
1.637 |
2.3947 |
6.2660 |
4.6290 |
0.7577 |
|
10/1/2012 |
1.686 |
-1.9988 |
-6.4304 |
-8.1164 |
-3.6848 |
|
11/1/2012 |
1.606 |
0.2843 |
-2.3194 |
-3.9254 |
-1.3217 |
|
12/1/2012 |
1.756 |
0.7043 |
0.7756 |
-0.9804 |
-1.0517 |
|
1/1/2013 |
1.985 |
4.9198 |
5.8402 |
3.8552 |
2.9348 |
|
2/1/2013 |
1.888 |
1.1000 |
-1.1092 |
-2.9972 |
-0.7880 |
|
3/1/2013 |
1.852 |
3.5355 |
6.0241 |
4.1721 |
1.6835 |
|
4/1/2013 |
1.675 |
1.7924 |
-5.1762 |
-6.8512 |
0.1174 |
|
5/1/2013 |
2.164 |
2.0550 |
2.6697 |
0.5057 |
-0.1090 |
|
6/1/2013 |
2.478 |
-1.5113 |
-8.4785 |
-10.9565 |
-3.9893 |
|
7/1/2013 |
2.593 |
4.8278 |
2.0355 |
-0.5575 |
2.2348 |
|
8/1/2013 |
2.749 |
-3.1798 |
-6.7716 |
-9.5206 |
-5.9288 |
|
9/1/2013 |
2.615 |
2.9316 |
1.5839 |
-1.0311 |
0.3166 |
|
10/1/2013 |
2.542 |
4.3630 |
-3.2770 |
-5.8190 |
1.8210 |
|
11/1/2013 |
2.741 |
2.7663 |
0.2619 |
-2.4791 |
0.0253 |
|
12/1/2013 |
3.026 |
2.3289 |
4.2975 |
1.2715 |
-0.6971 |
|
1/1/2014 |
2.668 |
-3.6231 |
-5.9812 |
-8.6492 |
-6.2911 |
|
2/1/2014 |
2.658 |
4.2213 |
4.6934 |
2.0354 |
1.5633 |
|
3/1/2014 |
2.723 |
0.6908 |
3.8770 |
1.1540 |
-2.0322 |
|
4/1/2014 |
2.648 |
0.6182 |
2.0466 |
-0.6014 |
-2.0298 |
|
5/1/2014 |
2.457 |
2.0812 |
-6.3619 |
-8.8189 |
-0.3758 |
|
6/1/2014 |
2.516 |
1.8879 |
-1.6903 |
-4.2063 |
-0.6281 |
|
7/1/2014 |
2.556 |
-1.5195 |
5.5787 |
3.0227 |
-4.0755 |
|
8/1/2014 |
2.343 |
3.6964 |
0.3282 |
-2.0148 |
1.3534 |
|
9/1/2014 |
2.508 |
-1.5635 |
-1.2928 |
-3.8008 |
-4.0715 |
|
10/1/2014 |
2.335 |
2.2936 |
-14.3826 |
-16.7176 |
-0.0414 |
|
11/1/2014 |
2.194 |
2.4237 |
-1.3657 |
-3.5597 |
0.2297 |
|
12/1/2014 |
2.17 |
-0.4197 |
-1.0725 |
-3.2425 |
-2.5897 |
|
1/1/2015 |
1.675 |
-3.1533 |
-4.5458 |
-6.2208 |
-4.8283 |
|
2/1/2015 |
2.002 |
5.3439 |
5.4764 |
3.4744 |
3.3419 |
|
3/1/2015 |
1.934 |
-1.7549 |
-0.8932 |
-2.8272 |
-3.6889 |
|
4/1/2015 |
2.046 |
0.8485 |
6.5064 |
4.4604 |
-1.1975 |
|
5/1/2015 |
2.095 |
1.0437 |
-0.9621 |
-3.0571 |
-1.0513 |
|
6/1/2015 |
2.335 |
-2.1236 |
-4.2075 |
-6.5425 |
-4.4586 |
|
7/1/2015 |
2.205 |
1.9550 |
-0.4128 |
-2.6178 |
-0.2500 |
|
Date |
CAPM |
Date |
CAPM |
|
2/1/2010 |
|
11/1/2012 |
-3.56455 |
|
3/1/2010 |
-2.98785 |
12/1/2012 |
-1.76906 |
|
4/1/2010 |
-3.04909 |
1/1/2013 |
1.17901 |
|
5/1/2010 |
-4.97757 |
2/1/2013 |
-2.99866 |
|
6/1/2010 |
-3.84307 |
3/1/2013 |
1.372211 |
|
7/1/2010 |
-0.56164 |
4/1/2013 |
-5.34834 |
|
8/1/2010 |
-5.23661 |
5/1/2013 |
-0.86307 |
|
9/1/2010 |
2.515487 |
6/1/2013 |
-7.85119 |
|
10/1/2010 |
1.390917 |
7/1/2013 |
-1.51123 |
|
11/1/2010 |
-3.792 |
8/1/2013 |
-6.97573 |
|
12/1/2010 |
-0.94387 |
9/1/2013 |
-1.79999 |
|
1/1/2011 |
2.792546 |
10/1/2013 |
-4.71902 |
|
2/1/2011 |
-3.29795 |
11/1/2013 |
-2.68279 |
|
3/1/2011 |
-2.83062 |
12/1/2013 |
-0.3962 |
|
4/1/2011 |
-0.43582 |
1/1/2014 |
-6.4445 |
|
5/1/2011 |
-3.62345 |
2/1/2014 |
0.069555 |
|
6/1/2011 |
-2.1584 |
3/1/2014 |
-0.46782 |
|
7/1/2011 |
0.673323 |
4/1/2014 |
-1.53805 |
|
8/1/2011 |
-5.95061 |
5/1/2014 |
-6.54798 |
|
9/1/2011 |
-1.30356 |
6/1/2014 |
-3.73579 |
|
10/1/2011 |
0.813767 |
7/1/2014 |
0.671498 |
|
11/1/2011 |
-1.32939 |
8/1/2014 |
-2.39976 |
|
12/1/2011 |
-3.66299 |
9/1/2014 |
-3.48857 |
|
1/1/2012 |
0.556555 |
10/1/2014 |
-11.3636 |
|
2/1/2012 |
-1.08317 |
11/1/2014 |
-3.34162 |
|
3/1/2012 |
1.064031 |
12/1/2014 |
-3.14822 |
|
4/1/2012 |
-2.79936 |
1/1/2015 |
-4.96399 |
|
5/1/2012 |
-6.45982 |
2/1/2015 |
0.94685 |
|
6/1/2012 |
-1.34161 |
3/1/2015 |
-2.89502 |
|
7/1/2012 |
-1.95643 |
4/1/2015 |
1.547989 |
|
8/1/2012 |
-2.47621 |
5/1/2015 |
-3.03515 |
|
9/1/2012 |
1.650793 |
6/1/2015 |
-5.16013 |
|
10/1/2012 |
-6.11967 |
7/1/2015 |
-2.76733 |
The CAPM is calculated from the regression analysis. The calculation of the CAPM is given by the following equation:
CAPM = -1.17 + 0.61 * Excess Return
|
Regression Statistics |
|
|
Multiple R |
0.4951 |
|
R Square |
0.2452 |
|
Adjusted R Square |
0.23 |
|
Standard Error |
3.96 |
|
Observations |
65 |
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
-1.17 |
0.53 |
-2.225 |
0.03 |
-2.22 |
-0.12 |
|
Xt |
0.61 |
0.13 |
4.524 |
0.000 |
0.34 |
0.88 |
The coefficients of the regression analysis show that, if the excess return on the stocks is zero, then the market return of the stocks will be -1.17. With one-unit increase in the excess return of the stocks, the market return of the stocks will increase by 0.61.
The coefficient of determination (R Square) value indicates that the excess return on the stocks will be able to explain 24.51 percent of the variability in the market return of the stocks. The average excess stock returns of IBM are supposed to lie between 0.34 and 0.88 with 95 percent confidence.
1.9 Determination of Neutral Stock
It can be seen clearly from the computations of the confidence interval that the average return on the stocks of IBM lies between -0.76 and 1.50 with 95 percent confidence. There is always a possibility that the stocks will not have any returns. Thus, this stock can be termed as a neutral stock.
|
Confidence Interval for the mean |
|
|
Data |
|
|
Sample Standard Deviation |
4.5661 |
|
Sample Mean |
0.37 |
|
Sample Size |
65 |
|
Confidence Level |
95% |
|
Is Pop StDev known? Y/N |
N |
|
Intermediate Calculations |
|
|
Standard Error of the Mean |
0.5664 |
|
Degrees of Freedom |
64 |
|
t Value |
1.9977 |
|
Margin of Error |
1.1314 |
|
Confidence Interval |
|
|
Interval Lower Limit |
-0.76 |
|
Interval Upper Limit |
1.50 |
From the results of the Jarque-Berra test, it can be said that the errors in the developed model of prediction of CAPM is normally distributed. The following figure also shows that the errors are normally distributed as they follow a linear trend.
|
Test for Normality of Residuals |
|
|
Skewness |
-0.755 |
|
Kurtosis |
2.915 |
|
Count |
65 |
|
Jarque-Berra test Statistic |
29.181 |
|
P-Value |
0.000 |
There is availability of two different stocks in the market. One is the stock prices of Boeing company and the other is the stock prices of IBM (International Business Machines). Historical data on the monthly stock prices of these two companies have been collected from finance.yahoo.com for the time frame of 2nd Feb, 2010 to 31st July, 2015. The S&P price index of this time frame and the interest rate of the 10 year US Treasury Note has been collected from the same website. The client is interested to invest in the stocks of one of two available companies Boeing or IBM. Thus, the main interest of this study is to identify which of the two stocks will be better and safer to invest. For this, the risk on the stock prices and the returns from the stocks are to be compared over the time frame to assess which stock would be better to invest. The necessary analysis will be conducted using appropriate statistical techniques and on Microsoft Excel.
Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J., 2016. Statistics for business & economics. Nelson Education.
Siegel, A., 2016. Practical business statistics. Academic Press.
Ruppert, D., 2014. Statistics and finance: an introduction. Springer.
Swift, L. and Piff, S., 2014. Quantitative methods: for business, management and finance. Palgrave Macmillan.
Asongu, S.A. and Moulin, B., 2016. Research in International Business and Finance.
Sullivan III, M., 2015. Fundamentals of statistics. Pearson.