Q1. A.) Histogram of stock return:- Ans:- Consider the following figure for histogram of stock return
Figure 1.1- Histogram of Stock return
The following is the bin range and the frequency:-
The histogram above provides us with a visual impression of our stock return.
The distribution is not symmetric.
Higher frequency of return is more on the right hand side of the distribution.
The returns occur most frequently around negative 2% to positive 6%.
Between 3% and 6%, the stock has highest frequency of positive return.
Hence from the above histogram we can conclude that the stock’s overall return is positive.
B.) Histogram of Market Return:-
Bin Range:-
Bin
Frequency
-7.85664
1
-5.34354
4
-2.83043
7
-0.31733
10
2.195769
21
4.708871
12
7.221973
5
More
0
The distributional features are as follows:- The distribution is not symmetric.
Higher frequency of return is more on the right hand side of the distribution.
The returns occur most frequently around 0% to positive 4%.
Between 2% and 4%, the stock has highest frequency of positive return.
Hence from the above histogram we can conclude that the market’s overall return is positive.
Q2.)
Stock Return
Market Return
Mean
0.52%
0.18%
Median
1.10%
0.31%
A.) Mean and Median of the stock return:-
Mean= 0.52
Median= 1.10
Mean and Median are the measures of central tendency and represent the most likely outcome of any random variable. Here for our NAB stock from DEC 1 2009 to DEC 31 2014, the most likely outcome according to mean is 0.52%, and according to median it is 1.10%. Due to asymmetric distribution, the two measures are slightly different.
B.) Mean and Median of Market return:-
Mean=0.18%
Median=0.31%
Here for the market return, the most likely outcome is 0.18% according to mean, and 0.31% according to median. Here from the values of mean and median, we can see that the values are very near to each other, and so they tend to show some symmetric values.
C.) Expected return of the stock is 0.52%, and that of market is 0.18%. Hence by these values we come to know that the NAB stock has outperformed the market and is giving higher returns. Here the median is used to separate higher half of the return from the lower half. So here also, the median of stock return which is 1.10% is higher then the market return which is 0.31%. Here the values are different because the distribution is not symmetric.
Q3.)
Stock Return
Market Return
Standard Deviation
6.037%
3.57%
Interquartile Range
8.11%
5.45%
A.) The Standard Deviation measures the average deviation of the returns of the stock and the market around the mean. Here for NAB stock the standard deviation is 6.037%, which indicates that the average return is deviated 6.037% from the mean.
Interquartile Range:- The distance between the 75th percentile and the 25th percentile, which represents 50% of data around the median. Here the statistics indicate that 50% of data points are located between -3.58% and 4.52%, and the length of that interval is 8.11% B.) The Standard deviation of the market return is 3.57%, which means that the average return of the market is deviated by 3.57% from the mean.
Interquartile range:- Here for the market return the 75th percentile and 25th percentile are -2.19% and 3.25%, and the length of the interval is 5.45% .
C.) Here the variability or riskness of the NAB stock return is more as compared to the riskness of the market return. Its just the double of market return. So the NAB stock is more risky and has more return as compared to the market return.
Skewness:- Measures the degree of asymmetry of the distribution.
Kurtosis:- Measures how frequently extreme observations occur in comparison with normal distribution.
A.) Here the skewness of NAB stock is -0.22%, which means that our return
