Let w0 be the portfolio (weights) of risky assets corresponding the minimum-variance point in the feasible region. Let w1 be any ohther portfolio on the efficient frontier. Define r0 and r1 to be the corresponding returns. Answer ALL PARTS of the following questions to get FULL points.

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There is a formula of the form sigma 01 = A Find A. [Hint: Consider the portfolios (1 - alpha) w0 + alpha w1, and consider small variations of the variance of such portfolios near alpha = 0.] Corresponding to the portfolio wz on the minimum-variance set that has zero beta with respect to w1; that is sigma1,z = 0. This portfolio can be expressed as wz = (1 - alpha) w0 + alpha w1. Find the proper value of alpha. Show the relation of the three portfolios on a diagram that includes the feasible region. If there is no risk-free asset, it can be shown that other assets can be priced according to the formula where the subscript M denotes the market portfolio and is the expected rate of return on the portfolio that has zero beta with the market portfolio. Suppose that the expected returns on the market and the zero-beta portfolio are 15% and 9%, respectively. Suppose that a stock i has a correlation coefficient with the market of .5. Assume also that the standard deviation of the returns of the market and stock i are 15% and 5%, respectively. Find the expected return of stock