Consider a portfolio choice problem with a risk-free asset with return rf and two risky assets, the first with mean return 1 = 0.12 and standard deviation 1 = 0.4 and the second with mean 2 = 0.08 and standard deviation 2 = 0.3, with correlation 12 = 0. For any stock portfolio let denote the proportion invested in stock 1.

1. (a) (10) Find the weight that minimizes portfolio standard deviation p.

2. (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 .

3. (c) (5) Now consider varying the risk-free rate rf . Again without solving anything, explain how you would

   expect to vary as rf increases.

4. (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 .