A portfolio that has an expected outcome of $115 is formed by

Question

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.

A. investing $100 in the risky asset.
B. investing $80 in the risky asset and $20 in the risk-free asset.
C. borrowing $43 at the risk-free rate and investing the total amount ($143) in the risky asset.
D. investing $43 in the risky asset and $57 in the riskless asset.
E. Such a portfolio cannot be formed.

Answer 1

C. borrowing $43 at the risk-free rate and investing the total amount ($143) in the risky asset.

For $100: (115 – 100)/100 = 15%; .15 = w1(0.12) + (1 w1)(0.05); .15 = 0.12w1 + 0.05 – 0.05w1; 0.10 = 0.07w1; w1 = 1.43($100) = $143; (1 – w1)$100 = –$43.