Hi. Can anyone please help with this? No one has gotten it correct yet. Thank yo

Question

Hi. Can anyone please help with this? No one has gotten it correct yet. Thank you!

You've observed the following returns on Doyscher Corporation's stock over the past five years: -26.7 percent, 14.8 percent, 32.6 percent, 2.9 percent, and 21.9 percent. Requirement 1: What was the arithmetic average return on the stock over this five-year period? Arithmetic average return 9.1 % Requirement 2: (a) What was the variance of the returns over this period? Variance (b)What was the standard deviation of the returns over this period? Standard deviation %

Explanation / Answer

First we will calculate the arithmetic average return of stock by adding the return per year and dividing by number of year. The calculation is given below

Arithmetic average return = -26.7+14.8+32.6+2.9+21.9 /5

Arithmetic average return = 9.10

Now to calculate the variance, following steps are done

To find out the mean which is 9.1

Each year return will be subtracted from mean and its square will be calculated

The total of all squared return will be divided with number of year to find out the variance

The calculation of variance is given below

Variance = (-26.7-9.1)^2 + (14.8-9.1)^2+(32.6-9.1)^2+(2.9-9.1)^2+(21.9-9.1)^2 / 5

Variance = 1281.64 +32.49+552.25+38.44+163.84 /5

Variance = 2068.66 /5

Variance = 413.732

The variance is 413.732

The standard deviation is calculated by taking square root of variance, the standard deviation would be

Standard deviation =

Standard deviation = 20.34

The relative standard deviation is expressed in percent and is obtained by

Multiplying the standard deviation by 100 and dividing this product by the average.

The formula of relative standard deviation,

RSD = 100S/x

Where

S= standard deviation

X = average return mean

Putting values in formula to calculate percentage of SD

= 20.34 /9.1 *100

= 223.516%

The standard deviation is 223.52% rounding of 2 decimals

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