Use the following information to calculate the covariance of asset A with an equally weighted portfolio of assets B and C.
Asset Standard Deviation
A 20%
B 30%
C 40%
The correlation coefficient between A and B is 0.6.
The correlation coefficient between A and C is 0.5.
The correlation coefficient between B and C is 0.4.
To calculate the covariance of asset A with an equally weighted portfolio of assets B and C, we can use the formula:
Cov(A, Portfolio) = wB * Cov(A, B) + wC * Cov(A, C)
where wB and wC are the weights of assets B and C in the portfolio, and Cov(A, B) and Cov(A, C) are the covariances between asset A and assets B and C, respectively.
Since the portfolio is equally weighted, the weights of assets B and C are both 0.5.
Now let's calculate the covariances:
Cov(A, B) = correlation coefficient (A, B) * standard deviation of A * standard deviation of B
= 0.6 * 20% * 30% = 0.12
Cov(A, C) = correlation coefficient (A, C) * standard deviation of A * standard deviation of C
= 0.5 * 20% * 40% = 0.4
Substituting the values into the formula:
Cov(A, Portfolio) = 0.5 * 0.12 + 0.5 * 0.4
= 0.06 + 0.2
= 0.26
Therefore, the covariance of asset A with an equally weighted portfolio of assets B and C is 0.26.