Analysis of Apple Stock Returns and Market Returns

MG3002-Assignment -2019
Student Name:
Instructor Name:
Course Number:
15th May 2019

Part A
Calculate the returns using the following formula:
Returns=ln (Stock Price)t −ln( Stock Price)t−1
Calculate also the square returns and the absolute returns.
Do a full descriptive statistics analysis for the returns, square returns and absolute
returns including the following:
a. Graphs (for example, t-plots, histograms).
Answer
Figure 1: Time series plot for the returns on APPLE
Figure 2: Time series plot for the square returns of the APPLE

Figure 3: Time series plot for the absolute returns of APPLE
Figure 4: Histogram for the returns on APPLE
Figure 5: Histogram for the square returns of the APPLE

Figure 6: Histogram for the absolute returns of APPLE
b. Arithmetic measures (for example, mean, median maximum, minimum,
standard deviation). Provide brief comments on your findings.
Answer
Table 1: Descriptive (Summary) Statistics
APPLE
Returns
Square
returns
APPLE
Absolute
returns
APPLE
S & P
Returns
Square
returns S &
P
Absolute S
& P
Mean 4.96E-06 0.000366 0.013023 0.000164 9.13E-05 0.006444
Standard
Error
0.001209 6.14E-05 0.000885 0.000604 1.43E-05 0.000446
Median 0.001326 7.86E-05 0.008867 0.000676 1.64E-05 0.004052
Standard
Deviation
0.019159 0.000973 0.014028 0.009573 0.000226 0.00707
Sample
Variance
0.000367 9.46E-07 0.000197 9.16E-05 5.12E-08 5E-05
Kurtosis 5.179957 61.23986 9.680335 4.240517 44.03966 7.076903
Skewness -0.68957 6.718747 2.598877 -0.16071 5.686191 2.296106
Range 0.172977 0.011009 0.104878 0.08182 0.002343 0.048396
Minimum -0.10492 2.17E-09 4.65E-05 -0.03342 4.72E-11 6.87E-06
Maximum 0.068053 0.011009 0.104924 0.048403 0.002343 0.048403
Sum 0.001245 0.091764 3.268687 0.041281 0.022919 1.61756
Count 251 251 251 251 251 251
Table 1 above presents the descriptive statistics for both the stock (Apple) and the
market (S & P 500). From the above table, we can clearly see that the distribution of
the apple returns is slightly negative (left) skewed as the skewness value is given as -
0.69 (a value less than -0.5). However, the distribution of the market returns (S & P
500 index) is seen to follow a normal distribution (skewness value closer to zero). The
standard deviation for the Apple stock returns is much larger than that of the market