Question 3: (15 pts] Suppose a 2-asset portfolio has parameters a r= = (2) s=(21), x=(1-2) . S X = for some a > 0. a. Use the portfolio equations to find y(x) and (x), and hence show that u=+(a-2) + 4-a, o > 0 in the ou-plane. b. Sketch the feasible set in the ou-plane for a = 1, a = 2 and a = 3 showing the locations of the two cases, where all initial wealth is invested in Asset 1 and in Asset 2, respectively. Show as well the minimum risk portfolio Po for a = 1. a = 2 and a = 3. c. Show that if no short-selling is allowed, optimal portfolios only exist for a > 2. d. Write down the allocation vector x for Po, for a > 0. e. Let a = 4. i. In a new sketch, indicate the regions of the feasible set that correspond to the short-selling of Asset 1, short-selling of Asset 2, and no short-selling of either. ii. What is the optimal portfolio of an investor with risk-aversion parametert = 1? iii. For what values of t is Asset 1 short-sold at optimality? ants Question 3: (15 pts] Suppose a 2-asset portfolio has parameters a r= = (2) s=(21), x=(1-2) . S X = for some a > 0. a. Use the portfolio equations to find y(x) and (x), and hence show that u=+(a-2) + 4-a, o > 0 in the ou-plane. b. Sketch the feasible set in the ou-plane for a = 1, a = 2 and a = 3 showing the locations of the two cases, where all initial wealth is invested in Asset 1 and in Asset 2, respectively. Show as well the minimum risk portfolio Po for a = 1. a = 2 and a = 3. c. Show that if no short-selling is allowed, optimal portfolios only exist for a > 2. d. Write down the allocation vector x for Po, for a > 0. e. Let a = 4. i. In a new sketch, indicate the regions of the feasible set that correspond to the short-selling of Asset 1, short-selling of Asset 2, and no short-selling of either. ii. What is the optimal portfolio of an investor with risk-aversion parametert = 1? iii. For what values of t is Asset 1 short-sold at optimality? ants