6. The market has three assets. F A B E(r) 0.04 0.25 0.16 00 3 1 In addition, PAB = 0. (a) If the investor can choose EITHER security A OR security B (but not a portfolio consisting of A and B) to form a portfolio with F. Which one will the investor choose? Why? [4 points] (b) Now suppose the investor can invest in a portfolio consisting of security A and security B. The investor wants to identify the portfolio P* consisting of risky assets, such that by choosing a portfolio as a combination of P* and F, her utility level can be maximized. Write down the investor's objective function. Let the weight on security A be w. The objective function you write down must be in terms of w. (Hint: you don't need to solve it.] [4 points) Suppose the optimal risky portfolio derived from Question 6(b) is P* = 0.40 A +0.6 0 B. (Hint: please take this as given. Don't try to verify it.] (c) Suppose the investor's optimal portfolio is P= -0.50 F +1.5 0 P*. Also assume that P' = ho A+(1 h)o B is the optimal risky portfolio when the risk-free asset is not available. Then is h greater than, equal to, or less than 0.4? Why? (Hint: you can use a graph to make your argument.] [2 points) (d) Now, suppose the rate of return of the risk-free asset rf decreases to 0.02, then the investor will form new P* and P. Is the investor better off now? Why? (Hint: you can use a graph to make your argument. You can also use your intuition. The key is to determine whether the investor's utility increases or decrease at the new optimum.] [2 points) 6. The market has three assets. F A B E(r) 0.04 0.25 0.16 00 3 1 In addition, PAB = 0. (a) If the investor can choose EITHER security A OR security B (but not a portfolio consisting of A and B) to form a portfolio with F. Which one will the investor choose? Why? [4 points] (b) Now suppose the investor can invest in a portfolio consisting of security A and security B. The investor wants to identify the portfolio P* consisting of risky assets, such that by choosing a portfolio as a combination of P* and F, her utility level can be maximized. Write down the investor's objective function. Let the weight on security A be w. The objective function you write down must be in terms of w. (Hint: you don't need to solve it.] [4 points) Suppose the optimal risky portfolio derived from Question 6(b) is P* = 0.40 A +0.6 0 B. (Hint: please take this as given. Don't try to verify it.] (c) Suppose the investor's optimal portfolio is P= -0.50 F +1.5 0 P*. Also assume that P' = ho A+(1 h)o B is the optimal risky portfolio when the risk-free asset is not available. Then is h greater than, equal to, or less than 0.4? Why? (Hint: you can use a graph to make your argument.] [2 points) (d) Now, suppose the rate of return of the risk-free asset rf decreases to 0.02, then the investor will form new P* and P. Is the investor better off now? Why? (Hint: you can use a graph to make your argument. You can also use your intuition. The key is to determine whether the investor's utility increases or decrease at the new optimum.] [2 points)