1. (30 points) Suppose you can only invest in a risk-free asset yielding 10%, and a risky asset that has an expected returnE[r] = 20% and standard deviation= 0.30.

Give an explicit formula for the investment opportunities that this investor is facing (in mean-standard deviation space). Assume that the investor can both invest and borrow at the 10% rate. Plot this opportunity set (in mean-standard deviation space).

Now suppose that the investor can invest in the risk-free asset yielding 10%, but her borrowing rate is 12%. Give an explicit formula for the investment opportunities that this investor is facing (in mean-standard deviation space). Plot this opportunity set (in mean-standard deviation space).