Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return u1 = 0.12 and standard deviation sd1 = 0.4 and the second with mean u2 = 0.08 and standard deviation sd2 = 0.3, with correlation p12 = 0. For any stock portfolio let denote the proportion invested in stock 1. (a) Find the weight that minimizes portfolio standard deviation portofolio. (b) Consider the tangency portfolio and let * denote the weight it places on stock 1. Find the condition that de nes this value, but do not solve for it, and explain how it would compare to in part a. (c) Now consider varying the risk-free rate rf . Again without solving anything, explain how you would expect * to vary as rf increases. (d) 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 *.