Consider a portfolio choice problem in a world with risk free rate rf and two risky assets i = 1, 2. Assume that one asset has both a higher expected return and volatility than the other, so that Mu1 > Mu2 and sigma1 > sigma2, and that the returns to each are uncorrelated P12 = 0. Let lambda denote the portfolio weight on stock 1. (a) Find the weight lambda that yields the minimum variance portfolio. (b) Let lambda * be the weight that defines the tangency portfolio. Write the condition that defines lambda* and, without solving for it, determine how it compares to A. (c) We now wish to consider how the composition of the tangency portfolio shifts as the risk free rate increases. Without solving the optimization problem, how do you expect to change lambda * to change as rf increases? (d) Using the envelope theorem, determine how the slope of the tangent line changes as the risk free rate increases. Once again, do not solve the optimization