Florida Company (FC)and Minnesota Company (MC)are both service companies.Their stock returns for the past three years were: FC: -5%,15%,20%; MC: 8%,8%,20%.
Calculate the correlation coefficient between the returns of FC and MC.

Question

Quizplus · Accepted Answer

We can use the formula for calculating the correlation coefficient between two sets of returns:

r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]

where:
n = number of observations
Σxy = sum of the products of the corresponding values in the two sets of returns
Σx = sum of the values in the first set of returns
Σy = sum of the values in the second set of returns
Σx^2 = sum of the squared values in the first set of returns
Σy^2 = sum of the squared values in the second set of returns

Using this formula, we can calculate:

n = 3
Σxy = (-5% * 8%) + (15% * 8%) + (20% * 20%) = 3.1%
Σx = -5% + 15% + 20% = 30%
Σy = 8% + 8% + 20% = 36%
Σx^2 = (-5%)^2 + (15%)^2 + (20%)^2 = 6500 bps^2
Σy^2 = (8%)^2 + (8%)^2 + (20%)^2 = 784 bps^2

Plugging these values into the formula, we get:

r = (3*3.1% - 30%*36%) / sqrt[(3*6500 bps^2 - (30%)^2)(3*784 bps^2 - (36%)^2)]
r = -0.655

So the correlation coefficient between the returns of FC and MC is -0.655, which suggests a strong negative relationship between the two. Choice C is the best answer.

Florida Company (FC)and Minnesota Company (MC)are Both Service Companies