Question

Question 8 4 pts You are the financial advisor of Mr. Smith. There are two stocks, A and B, available for investment E (Ra) = 8% o(Ra) = 5% E (R6) = 13% o(Rb) = 9% The correlation between A and B is given by P(A,B) = 0.5 Beta of A=0.8 Beta of B is 1.2 Beta of minimum variance portfolio, consisting of stocks A and B, is given by O 0.8164 1.1836 0.844 0.865 None of the above

Answer 1

Given about 2 stocks,

Standard deviation of Stock A SD(A) = 5%

Standard deviation on stock B SD(B) = 9%

Correlation between two stock Corr(A,B) = 0.5

So, Covariance between stock Cov(A,B) = SD(A)*SD(B)*Corr(A,B) = 5*9*0.5 = 22.5

For a minimum variance portfolio, weight of stock A is calculated as follow:

Wa = ((SD(B)^2) - Cov(A,B))/((SD(A)^2) + (SD(B)^2) - 2*Cov(A,B))

=> Wa = (9^2 - 22.5 )/(5^2 + 9^2 - 2*22.5) = 0.9590

So, weight of stock B = 1 - Wa = 1 - 0.9590 = 0.0410

Beta of stock A Ba = 0.8

Beta of stock B Bb = 1.2

So, beta of portfolio is weighted average beta of its assets

=> Beta of portfolio = Wa*Ba + Wb*Ba = 0.959*0.8 + 0.041*1.2 = 0.8164

So, Beta of minimum variance portfolio is 0.8164

Option A is correct.