What is the optimal portfolio that includes the risk free asset?

Economics

Learning Goal: I’m working on a economics multi-part question and need an explanation and answer to help me learn.(example problem, please see pdf below). Based on this data, what is the Mean-Variance E¢ cient portfolio?
2. What is the optimal portfolio that includes the risk free asset?
3. Calculate the Sharpe ratio of the MVE portfolio and compare it with the Sharpe
ratio of the individual assets.
4. Suppose that you have to make an investment recommendation to a less risk averse
investor with = 2. What Sharpe ratio will the new portfolio have?
5. Suppose the manager has the opportunity to invest in a new asset CITI, which has
an expected return E(rC) = 10% and a Sharpe ratio of 26%. Moreover, XC = 0:7
and T C = 0:1 (where represents to correlation coe¢ cient). Which portfolio of
risky assets will the manager hold? Why?
6. (a) Redo (5) assuming that short-selling is not allowed. How does the Sharpe ratio
of the new portfolio compares with the ones obtained in (5)?
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