1. [L] Chapter 6: Exercise 7 (Markowitz fun) There are just three assets with rates of return1, 72, and r3, respectively. The covariance matrix and the expected rates of return are E= 00 00 is (a) Find the global minimum-variance portfolio. (b) Find another efficient portfolio by setting) = 1, A = 0. (c) If the risk-free rate isry = .2, find the efficient portfolio of risky assets. 2. [L] Chapter 6: Exercise 8 (Tracking) Suppose that it is impractical to use all the assets that are incorpo rated into a specified portfolio (such as a given efficient portfolio). One alter- native is to find the portfolio, made up of a given set of stocks, that tracks the specified portfolio most closely-in the sense of minimizing the variance of the difference in returns. Specifically, suppose that the target portfolio has (random) rate of returnM. Suppose that there aren assets with (random) rates of returnri, r2, . .., m. We wish to find the portfolio rate of return r = air1+ azr2 + . . . + ann (with _10; = 1) minimizing var(r - TM). (a) Find a set of equations for thei's. (b) Although this portfolio tracks the desired portfolio most closely in terms of variance, it may sacrifice the mean. Hence a logical approach is to minimize the variance of the tracking error subject to achieving a given mean return. As the mean is varied, this results in a family of portfolios that are efficient in a new sense say, tracking efficient. Find the equation for the o's that are tracking efficient. 3. [L] Chapter 7: Exercise 1 (Capital market line) Assume that the expected rate of return on the market portfolio is 23% and the rate of return on T-bills (the risk-free rate) is 7%. The standard deviation of the market is 32%. Assume that the market portfolio is efficient