Assume that the variance of the returns of stocks A and B is, respectively, 16% and25%. If the covariance between the returns of stocks A and B is 0.06, calculate the correlation coefficient.

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Assume that the variance of the returns of stocks A and B is, respectively, 16% and25%. If the covariance between the returns of stocks A and B is 0.06, calculate the correlation coefficient.

Answer 1

## Answer The correlation coefficient, often denoted by `ρ` (rho), is a measure that determines the degree to which two variables' movements are associated. It is calculated using the formula: ``` ρ = Covariance(A, B) / (Standard Deviation(A) * Standard Deviation(B)) ``` Given that the variance of the returns of stocks A and B is 16% and 25% respectively, and the covariance between the returns of stocks A and B is 0.06, we first need to calculate the standard deviation of each stock. The standard deviation is the square root of the variance. So, * Standard Deviation(A) = sqrt(Variance(A)) = sqrt(0.16) = 0.4 * Standard Deviation(B) = sqrt(Variance(B)) = sqrt(0.25) = 0.5 Substituting these values into the formula for the correlation coefficient, we get: ``` ρ = 0.06 / (0.4 * 0.5) = 0.3 ``` So, the correlation coefficient between the returns of stocks A and B is 0.3. This indicates a positive but relatively weak linear relationship between the returns of the two stocks.

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Assume that the variance of the returns of stocks A and B is, respectively, 16% and25%. If the covariance between the returns of stocks A and B is 0.06, calculate the correlation coefficient.

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