Answer :
Answer:
The variance of the profile is 0.2179.
Step-by-step explanation:
We are given the following in the question:
[tex]\sigma_A = 0.5\\\sigma_B = 0.6\\\rho_{A,B} = 0.5\\w_A = 70\% = 0.7\\w_B = 30\% = 0.3[/tex]
Variance of portfolio is given by:
[tex]w_A^2\sigma_A^2 +w_B^2\sigma_B^2 + 2w_Aw_BCov_{A,B}[/tex]
[tex]Cov_{A,B} = \rho_{A,B} \times \sigma_A \times \sigma_B \\=0.5\times 0.5 \times 0.6\\=0.15[/tex]
Putting values, we get,
[tex]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[/tex]
Thus, the variance of the profile is 0.2179.