Question

Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.

a. What are the weights of A and B in the global minimum variance portfolio respectively?
b. What is the rate of return on the risk-free portfolio that can be formed with the two securities ?

Answer 1

a. The weights of A and B in the global minimum variance portfolio are 0.4436 and 0.5564 respectively. b. The rate of return on the risk-free portfolio formed with the two securities is 10.08%.

Step-by-step explanation:

a. In the global minimum variance portfolio, the weights of A and B can be found using the formula:

Weight of A = (Standard deviation of B)^2 / ((Standard deviation of A)^2 + (Standard deviation of B)^2)

Weight of B = 1 - Weight of A

Using the given standard deviations, the weights of A and B are:

Weight of A = (14^2) / (17^2 + 14^2) = 0.4436

Weight of B = 1 - 0.4436 = 0.5564

b. The rate of return on the risk-free portfolio that can be formed with the two securities can be found using the formula:

Rate of return on risk-free portfolio = (Expected rate of return of A) * (Weight of A) + (Expected rate of return of B) * (Weight of B)

Using the given expected rates of return and the calculated weights, the rate of return on the risk-free portfolio is:

Rate of return on risk-free portfolio = (0.12) * (0.4436) + (0.09) * (0.5564) = 0.1008 or 10.08%