The market has three assets. In addition, ρAB = −1. F A B

E(r) 0.08 0.25 0.16

σ 0 0.3 0.1

(a) If a risk-averse investor can only choose to invest in ONE asset, which asset would he choose? Why? [2 points] (b) If a risk-averse investor can only choose EITHER A or B (but not a portfolio consisting of A and B) to form a portfolio with F, which one would the investor choose? Why? [2 points] (c) Suppose that P∗ is the tangent portfolio consisting of risky assets A and B. Let the weight on A be ω. How do you solve for P∗? Write down the objective function. [Hint: you do not have to solve it. ] [2 points] (d) The investor forms a new portfolio ˜ P which combines P∗ and F to maximize his mean-variance utility. The investor’s utility at ˜ P is U1. Now suppose that the rate of risk-free asset rf increases to 10%. The investors will recalculate P∗, form a new ˜ P, and achieve a new utility level of U2. If the investor is extremely risk averse, which utility level is greater, U1 or U2? Would your answer change if the investor is less risk averse?

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