Question

Stock A ‘s returns have a standard deviation of 0.5, and stock B’s returns have standard deviation of 0.6.The correlation coefficient between A and B equals 0.5. What is the variance of a portfolio composed of 70 percent Stock A and 30 percent Stock B?

Answer 1

Answer:

The variance of the profile is 0.2179.

Step-by-step explanation:

We are given the following in the question:

$\sigma_A = 0.5\\\sigma_B = 0.6\\\rho_{A,B} = 0.5\\w_A = 70\% = 0.7\\w_B = 30\% = 0.3$

Variance of portfolio is given by:

$w_A^2\sigma_A^2 +w_B^2\sigma_B^2 + 2w_Aw_BCov_{A,B}$

$Cov_{A,B} = \rho_{A,B} \times \sigma_A \times \sigma_B \\=0.5\times 0.5 \times 0.6\\=0.15$

Putting values, we get,

$w_A^2\sigma_A^2 +w_B^2\sigma_B^2 + 2w_Aw_BCov_{A,B}\\=(0.7)^2(0.5)^2 + (.3)^2(0.6)^2 + 2(0.7)(0.3)(0.15)\\=0.2179$

Thus, the variance of the profile is 0.2179.