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

Question

Quizplus · Accepted Answer

To calculate the correlation coefficient between the returns of FC and MC, we need to use the formula:

r = [ Σ (x - x̄)(y - ȳ) ] / [ √{Σ(x - x̄)²} √{Σ(y - ȳ)²} ]

where x and y represent the returns of FC and MC, respectively.

Calculating the means and standard deviations of both FC and MC yields:

FC: x̄ = 10 percent, s_x = 11.83 percent
MC: ȳ = 12 percent, s_y = 6.80 percent

Using these values and the formula above, we get:

r = [ (-5 - 10)(8 - 12) + (15 - 10)(8 - 12) + (20 - 10)(20 - 12) ] / [ √{(-5 - 10)² + (15 - 10)² + (20 - 10)²} √{(8-12)² + (8-12)² + (20-12)²} ]
r = 0.655

Therefore, the answer is C (+0.655), indicating a positive correlation between the returns of FC and MC.

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