1. Suppose now you can allocate your money in the n risky stocks and in the risk-free asset (so there n + 1 assets). What is the optimization problem that you need to solve? What is the constraint for this problem?

2. What is the shape of the frontier when the investor has access to the risk-free asset? Why are two portfolios on the capital allocation line perfectly correlated?

3. Usually, when there are n risky stocks and one risky free asset we draw the tangent to the efficient frontier and the tangency point is called the optimal portfolio. How do we find the composition of this portfolio?

4. Consider the investing possibilities as in (3). Give the expression that computes the weight of the kth asset of the tangency portfolio.