Question 1
Multiple ChoiceThe correlation between the historical returns of Stock X and Stock Y is 0.50. The variance of Stock X is 0.36 and the variance of Stock Y is 0.16. The covariance of returns between Stock X and Stock Y is closest to:
Explanation
To calculate the covariance between the returns of two assets, we use the formula:
COV(A,B) = P_{AB} σ_{A} σ_{B}
Why this formula?
Covariance measures how two variables move together. When we have the correlation coefficient (ρ) and standard deviations (σ) of the two assets, this formula helps us find the linear relationship between their returns over time. Correlation standardizes the direction and strength of the relationship, while standard deviations scale it back into actual units.
Step-by-step:
Identify the inputs:
Correlation (ρXY) = 0.50
Variance of Stock X = 0.36 → Standard deviation (σX) = √0.36 = 0.6
Variance of Stock Y = 0.16 → Standard deviation (σY) = √0.16 = 0.4
Plug values into the formula:
Cov(X, Y) = 0.50 × 0.6 × 0.4
Cov(X, Y) = 0.50 × 0.24
Cov(X, Y) = 0.12
So, the correct answer is 0.12.