Stock X has a standard deviation of σ_X = 12%, Stock Y has a standard deviation of σ_Y = 20%, and the correlation coefficient between their returns is r_XY = 0.65. What is the covariance between Stock X and Stock Y (express returns as decimals)?

The correlation coefficient is defined as r = Cov(X, Y)/(σ_X × σ_Y), so Cov(X, Y) = r × σ_X × σ_Y Returns are expressed in decimals, so σ_X = 0.12 and σ_Y = 0.20. Cov(X, Y) = 0.65 × 0.12 × 0.20 = 0.65 × 0.024 = 0.0156 If the standard deviations are used as 12 and 20 (in percent), the product is 0.65 × 12 × 20 = 156, which is the same quantity in “percent-squared” units. This is why the question asks for returns as decimals. Option (C), 0.0240, is σ_X × σ_Y with the correlation left out, and option (A) is half of the correct value and has no basis. Hence the correct option is (B).