3. (30) Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return Mi 0.12 and standard deviation 01 0.4 and the second with mean up = 0.08 and standard deviation 02 0.3, with correlation P12 = 0. For any stock portfolio let i 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 \* 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 A. (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 1*. 3. (30) Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return Mi 0.12 and standard deviation 01 0.4 and the second with mean up = 0.08 and standard deviation 02 0.3, with correlation P12 = 0. For any stock portfolio let i 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 \* 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 A. (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 1*