Using the following returns, calculate the arithmetic average returns, the varia
ID: 2795231 • Letter: U
Question
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y Returns 13% 20 Year 18% 39 -9 2 3 4 5 -21 -23 47 Requirement 1: (a) Calculate the arithmetic average return for X (Click to select) + (b) Calculate the arithmetic average return for Y. (Click to select)+ Requirement 2: (a) Calculate the variance for X. (Do not round intermediate calculations.) (Click to select) (b) Calculate the variance for Y. (Do not round intermediate calculations.) (Click to select) + Requirement 3: (a) Calculate the standard deviation for X. (Do not round intermediate calculations.) (Click to select) + (b) Calculate the standard deviation for Y. (Do not round intermediate calculations.) (Click to select)Explanation / Answer
------------------------------------------------------------------------------------------------------------------------
Arithmetic mean of X
The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Arithmetic mean = (Sum of all the values in the data set)/ Number of data
= (0.13 + 0.31 + 0.2 + (-0.21) + 0.22)/ 5
= 0.65/ 5
= 0.13
So arithmetic mean is 0.13 or 13%
------------------------------------------------------------------------------------------------------------------------
Variance of X
Variance = [Sigma(X-µ)^2/N-1)
Where,
X = Value in the data set
µ= Sum of att the data sent divided by number of data
N = Number of data points
Lets find the mean of the numbers
µ = (Sum of numbers in data set)/number of data
= (0.13 + 0.31 + 0.2 + -0.21 + 0.22 + 0 + 0 + 0 + 0 + 0)/ 5
= 0.65/ 5
= 0.13
Data (X)
(X-µ)
(X-µ)^2
0.13
0
0
0.31
0.18
0.0324
0.2
0.07
0.0049
-0.21
-0.34
0.1156
0.22
0.09
0.0081
Total
0.161
Lets find the variance by putting the values in the formula
Variance = 0.161/5-1
= 0.161/4
= 0.04
Variance is 0.04
------------------------------------------------------------------------------------------------------------------------
Standard deviation of X
Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. In finance, standard deviation is a statistical measurement; when applied to the annual rate of return of an investment, it sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, indicating a larger price range.
Standard deviation = UNDROOT[Sigma(X-µ)^2/N-1]
Where,
X = Value in the data set
µ= Sum of att the data sent divided by number of data
N = Number of data points
Lets find the mean of the numbers
µ = (Sum of numbers in data set)/number of data
= (0.13 + 0.31 + 0.2 + -0.21 + 0.22 + 0 + 0 + 0 + 0 + 0)/ 5
= 0.65/ 5
= 0.13
Data (X)
(X-µ)
(X-µ)^2
0.13
0
0
0.31
0.18
0.0324
0.2
0.07
0.0049
-0.21
-0.34
0.1156
0.22
0.09
0.0081
Total
0.16
Let’s put the values in the formula to find standard deviation
Standard deviation = UNDROOT[0.161/ (5- 1)]
= UNDROOT[0.161/ 4]
= UNDROOT[0.0403]
= 0.2
So standard deviation of numbers is 0.2
------------------------------------------------------------------------------------------------------------------------
Arithmetic mean of Y
The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables.
Arithmetic mean = (Sum of all the values in the data set)/ Number of data
= (0.18 + 0.39 + (-0.09) + (-0.23) + 0.47)/ 5
= 0.72/ 5
= 0.14
So arithmetic mean is 0.14
------------------------------------------------------------------------------------------------------------------------
Variance of Y
Variance = [Sigma(X-µ)^2/N-1)
Where,
X = Value in the data set
µ= Sum of att the data sent divided by number of data
N = Number of data points
Lets find the mean of the numbers
µ = (Sum of numbers in data set)/number of data
= (0.18 + 0.39 + -0.09 + -0.23 + 0.47 + 0 + 0 + 0 + 0 + 0)/ 5
= 0.72/ 5
= 0.14
Data (X)
(X-µ)
(X-µ)^2
0.18
0.04
0.0016
0.39
0.25
0.0625
-0.09
-0.23
0.0529
-0.23
-0.37
0.1369
0.47
0.33
0.1089
Total
0.3628
Lets find the variance by putting the values in the formula
Variance = 0.3628/5-1
= 0.3628/4
= 0.09
Variance is 0.09
------------------------------------------------------------------------------------------------------------------------
Standard deviation of Y
Standard deviation is a measure of the dispersion of a set of data from its mean. It is calculated as the square root of variance by determining the variation between each data point relative to the mean. In finance, standard deviation is a statistical measurement; when applied to the annual rate of return of an investment, it sheds light on the historical volatility of that investment. The greater the standard deviation of a security, the greater the variance between each price and the mean, indicating a larger price range.
Standard deviation = UNDROOT[Sigma(X-µ)^2/N-1]
Where,
X = Value in the data set
µ= Sum of att the data sent divided by number of data
N = Number of data points
Lets find the mean of the numbers
µ = (Sum of numbers in data set)/number of data
= (0.18 + 0.39 + -0.09 + -0.23 + 0.47 + 0 + 0 + 0 + 0 + 0)/ 5
= 0.72/ 5
= 0.14
Data (X)
(X-µ)
(X-µ)^2
0.18
0.04
0.0016
0.39
0.25
0.0625
-0.09
-0.23
0.0529
-0.23
-0.37
0.1369
0.47
0.33
0.1089
Total
0.36
Lets put the values in the formula to find standard deviation
Standard deviation = UNDROOT[0.3628/ (5- 1)]
= UNDROOT[0.3628/ 4]
= UNDROOT[0.0907]
= 0.3
So standard deviation of numbers is 0.3
------------------------------------------------------------------------------------------------------------------------
Hope this answer your query.
Feel free to comment if you need further assistance. J
Data (X)
(X-µ)
(X-µ)^2
0.13
0
0
0.31
0.18
0.0324
0.2
0.07
0.0049
-0.21
-0.34
0.1156
0.22
0.09
0.0081
Total
0.161
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.