In a two-security portfolio,25% is invested in Security A and the remainder in Security B.If the portfolio standard deviation is 12%,and the individual standard deviations for Security A and Security B are 22% and 7%,respectively,what is the covariance of the returns on Securities A and B?
A) 0.017
B) 0.023
C) 0.0375
D) 0.0469

Question

Quizplus · Accepted Answer

COV_AB = [σ²-(w²_A)(σ²_A)- (w²_B)(σ²_B)]/[2(w_A)(w_B)] = [0.12²-(0.25)²(0.22)²-(0.75)²(0.07)²]/[2(0.25)(0.75)] = (0.0144 - 0.003025 - 0.00275625)/(0.375)= 0.023

In a Two-Security Portfolio,25% Is Invested in Security a and the Remainder