Assume that security returns are generated by the single-index model, R_i = alpha_i + beta_iR_M + e_i where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: a. If sigmaM= 20%, calculate the variance of returns of securities A, B and C. b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B and C, respectively. If one forms a well-diversified portfolio of type A securities, what will be the mean and variance of the portfolio's excess returns? What about portfolios composed only of type B or C stocks? c. Is there an arbitrage opportunity in this market? What is it? Analyze the opportunity graphically. For c. according to the solutions manual: "There is no arbitrage opportunity because the well-diversified portfolios all plot on the SML. Because they are fairly priced there is no arbitrage". How is this possible since the E(R_i)/beta_i are not all equal? Should not E(R_i) = E(r_i) - r_f, and that over beta_i be equal for all the portfolios if there is no arbitrage