Ms.Rose is indifferent between investing all her wealth (which is $5 million) in the risky asset and the risk-free asset. The risky asset has an expected rate of return of 12% per year and a standard deviation of 20% per year. The risk-free lending rate is 6% per year. The risk-free borrowing rate is 8%. Answer the following questions.

(a). What does it mean by Ms.Rose is indifferent between investing all her wealth (which is $5 million) in the risky asset and the risk-free asset.?

(b). What would be the optimal mix of the risky and the risk-free asset?

(c). Mr.Sparkle, a personal friend of Rose, manages an investment fund. He offers a risk-free investment opportunity of 7% per year to Rose, provided she can invest a minimum of $5 million. Suppose the investment opportunity is truly risk-free. Rose realises that in order to take advantage of this opportunity, she has to invest all her wealth with Mr. Sparkle. Should she invest all her wealth with Mr. Sparkle earning a risk-free rate of 7% instead of holding the optimal mix you computed in part (b) above? Support your answer with calculations.