Please provide full answer with complete calculations, explanations and proofs:

3. Portfolio optimization with risk free asset: Now asstune that in addition to the risky assets described above with expected return vector and positive definite variance-covariance matrix E, there is a risk-free asset with deterministic return R > 0. We can think of this asset as a one-year treasury bond, or alternatively as a certificate of deposit (CD) in a bauk. Consider a portfolio of her in the risky assets, and the remaining 1-h71 in the risk frce asset. You can verify that the expected return on this portfolio is R+h"(- RI), (8) and that the variance is (as before) (9) The case when h+1 > 1 corresponds to a situation when money is borrowed from the bank to invest in the inarket. The case when h+1 0. We can think of this asset as a one-year treasury bond, or alternatively as a certificate of deposit (CD) in a bauk. Consider a portfolio of her in the risky assets, and the remaining 1-h71 in the risk frce asset. You can verify that the expected return on this portfolio is R+h"(- RI), (8) and that the variance is (as before) (9) The case when h+1 > 1 corresponds to a situation when money is borrowed from the bank to invest in the inarket. The case when h+1