1. This problem will guide you to derive the mean-variance frontier with a risk-free bond, and three risky stocks. The gross returns of the three stocks are normally distributed, with expected values E[R1]=2;E[R2]=3;E[R3]=4, respectively. The standard deviations are all equal to 1 . For simplicity, assume that the stock returns are not correlated. The risk-free rate is Rf=3/2. (a) Write down the problem of minimizing a portfolio return's variance, given a certain level of expected return. (b) Prove that for a given expected portfolio return , the weights for the risky stocks in the optimal portfolio are (Hint: see the Appendix in the lecture notes of Module 8 for how to solve the optimization problem.): w1=352(23),w2=356(23),w3=3510(23) (c) Show that the efficient frontier is an upward sloping straight line