3. (30) Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return ji = 0.12 and standard deviation 01 = 0.4 and the second with mean M2 = 0.08 and standard deviation 02 = 0.3, with correlation P12 = 0. For any stock portfolio let | denote the proportion invested in stock 1. (a) (10) Find the weight that minimizes portfolio standard deviation Op. (b) (5) Consider the tangency portfolio and let 1* denote the weight it places on stock 1. Find the condition that defines this value, but do not solve for it, and explain how it would compare to . (c) (5) Now consider varying the risk-free rate rf. Again without solving anything, explain how you would expect \* to vary as rf increases. (d) (10) Show how the slope of the tangent line changes with rf. Recall a useful theorem that allows you to do this without ever actually solving for \*. 3. (30) Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return ji = 0.12 and standard deviation 01 = 0.4 and the second with mean M2 = 0.08 and standard deviation 02 = 0.3, with correlation P12 = 0. For any stock portfolio let | denote the proportion invested in stock 1. (a) (10) Find the weight that minimizes portfolio standard deviation Op. (b) (5) Consider the tangency portfolio and let 1* denote the weight it places on stock 1. Find the condition that defines this value, but do not solve for it, and explain how it would compare to . (c) (5) Now consider varying the risk-free rate rf. Again without solving anything, explain how you would expect \* to vary as rf increases. (d) (10) Show how the slope of the tangent line changes with rf. Recall a useful theorem that allows you to do this without ever actually solving for \*