Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 70%. B has an expected rate of return of 8% and a standard deviation of 40%. The global minimum variance portfolio that can be formed with the two securities will earn rate of return.

9.45%

Explanation:

To solve this question, we need to know the weights of securities A and B and this will be:

Weight of A = STD of B / (STD of A + STD of B)

= 40% / (70% + 40%)

= 40% / 110%

= 0.4/1.1

= 0.3636

Weight of security A = 0.3636

Weight of security B = 1 - 0.3636 = 0.6364

Then, the rate of return of risk free portfolio will be:

= (Return of A × Weight of A) + (Return of B × Weight of B)

= (12% × 0.3636) + (8% × 0.6364)

= 0.043632 + 0.050912

= 0.094544

= 9.45%

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