Question $7$: Efficient Portfolios

Consider the following investment opportunity set:

Mixing among portfolios is not allowed, but a risk$-$free asset exists permitting lending$/$borrowing at a rate

of $2\%.$ Show your work.

a$.$ What is the equation of the capital market line in this context? Be specific.

b$.$ A specific investor approaches you with the goal to invest $$1$ million in a very risky portfolio with a

$20\%$ standard deviation. What is the highest expected return you can offer her? In your answer please

also state the portfolio weights needed to achieve the investor's goal.

c$.$ What is the maximum expected return an investor can achieve without borrowing? Specify the

strategy to achieve it$.$