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

		Investing $100 in the risky asset.
		Investing $80 in the risky asset and $20 in the risk-free asset.
		Borrowing $43 at the risk-free rate and investing the total amount ($143) in the risky asset.
		Investing $43 in the risky asset and $57 in the riskless asset.

Answer 1

For $100,

(115 - 100)/100=15%;

0.15 = w1(0.12) + (1 - w1)(0.05)

0.15 = 0.12w1 + 0.05 - 0.05w1

0.10 = 0.07w1

w1 = 1.43($100) = $143;

(1 - w1)$100 = -$43

Hence, Option "C" is correct, i.e., Borrowing $43 at the risk-free rate and investing the total amount ($143) in the risky asset.