1. Three independent risky assets are traded in the market. Their characteristics are described in the table below. Asset Expected rate of return (E(r)) Standard Deviation (0) 0.1 1 B 0.2 2 0.3 3 Lucy is a risk-averse investor. She is considering to construct a portfolio P1 = WAO A + wc o C. (a) Is there a portfolio P1, such that Lucy strictly prefers P, to B? If so, characterize the portfolio. If not, why? (b) Lucy of course can use all three traded assets to construct her optimal portfolio. Write down the formal optimization program that can characterize the minimum variance portfolio set. (Hint: you don't need to set the Lagrangian function or solve the equation system from the first-order conditions.] (c) Suppose that the minimum variance portfolio set can be characterized os = 4.154 - 50.770F + 188.462r2. Find the global minimum variance. (d) An investor, Lucy, is risk-averse. Can she choose a portfolio with the variance o