Suppose you are deciding how to allocate your wealth among three assets: an equity portfolio, E, with E|rE| = 0.18 and E = 0.30, a bond portfolio, B, with ElrB| = 0.08 and B = 0.15, and a risk-free asset, F, with rf = 0.05. The correlation between the equity and bond portfolios is = 0.15.

a. Suppose you decide you want a specific return p1 by choosing a portfolio P1, using only the two risky assets. Derive an expression for the portfolio weight of asset E, p1. What will the weight be if you desire a return of 0.11? What is the standard deviation of P1 in this case?

b. Suppose you decide its better to consider investing in the risk-free asset in addition to the two risky assets. Setup, but do not solve, the optimization problem that will determine the weights of the tangency portfolio. Be sure to include all relevant constraints.