Question

In: Finance

The rate of return on Cherry Jalopies, Inc., stock over the last five years was 15...

The rate of return on Cherry Jalopies, Inc., stock over the last five years was 15 percent, 11 percent, -1 percent, 4 percent, and 13 percent. Over the same period, the return on Straw Construction Company’s stock was 16 percent, 20 percent, -3 percent, 1 percent, and 12 percent.

Calculate the variances and the standard deviations for Cherry and Straw. (Enter variance as a decimal and standard deviation as a percent. Round your variance to 5 decimal places and standard deviation to 2 decimal places. Omit the "%" sign in your response.)

Solutions

Expert Solution

Standard deviation of Cherry Jalopies, Inc.

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 = √[∑(X-µ)^2/N-1]

Where,

                X = Value in the data set

                 µ= Sum of all the data sent divided by number of data

               N = Number of data points

Let's find the mean of the numbers

µ = (Sum of numbers in data set)/number of data

   = (0.15 + 0.11 + -0.01 + 0.04 + 0.13)/ 5

   = 0.42/ 5

   = 0.084

Data (X)

(X-µ)

(X-µ)^2

0.15

0.066

0.0044

0.11

0.026

0.0007

-0.01

-0.094

0.0088

0.04

-0.044

0.0019

0.13

0.046

0.0021

Total

0.0179

Let's put the values in the formula to find standard deviation

Standard deviation = UNDROOT[0.0179/ (5- 1)]

                                         = UNDROOT[0.0179/ 4]

                                         = UNDROOT[0.0045]

                                         = 0.0671

So standard deviation of numbers is 0.0671

--------------------------------------------------------------------------------------------------------------

Variance of Cherry Jalopies, Inc.

Variance = standard deviation 2

                  = (0.0671)2

                   = .0045

--------------------------------------------------------------------------------------------------------------

Standard deviation of Straw Construction Company

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 = √[∑(X-µ)^2/N-1]

Where,

                X = Value in the data set

                 µ= Sum of all the data sent divided by number of data

               N = Number of data points

Let's find the mean of the numbers

µ = (Sum of numbers in data set)/number of data

   = (0.16 + 0.2 + -0.03 + 0.01 + 0.12)/ 5

   = 0.46/ 5

   = 0.092

Data (X)

(X-µ)

(X-µ)^2

0.16

0.068

0.0046

0.2

0.108

0.0117

-0.03

-0.122

0.0149

0.01

-0.082

0.0067

0.12

0.028

0.0008

Total

0.0387

Let's put the values in the formula to find standard deviation

Standard deviation = UNDROOT[0.0387/ (5- 1)]

                                         = UNDROOT[0.0387/ 4]

                                         = UNDROOT[0.0097]

                                         = 0.0985

So standard deviation of numbers is 0.0985

--------------------------------------------------------------------------------------------------------------

Variance of Straw Construction Company

Variance = (0.0985)2

                 = 0.0097

--------------------------------------------------------------------------------------------------------------

Hope that helps.

Feel free to comment if you need further assistance J


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