Suppose that the market is efficient. Its risk-free rate of return is mu_f > 0 and its tangency portfolio, R_M, has mean and standard deviation mu_M and sigma_M. Show that for a risky asset in the market, if its beta is 0, then its mean must be equal to mu_f, the risk-free rate. Suppose that a market consists of one risk-free asset with rate of return mu_f = 1%, and two risky assets with means and standard deviations of returns being mu_1 = 3%, mu_2 = 6%, sigma_1 = 20% and sigma_2 = 30%. The correlation between the two returns is rho = 0.2, 0.4, 0.8. Find the Sharpe ratios of the tangency portfolios for different rho's and write down the equations for the capital market lines. Do problem ii again with sigma_1 = 40% and sigma_2 = 60%. How do Sharpe ratios change and the portfolio weights change with the changes in sigma's