3. (2) The capital asset pricing model (CAPM) is an important model in the field of finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publicly traded stocks, which is call the market portfolio. The resulting difference is called the risk premium since it is the reward or punishment for making a risky investment. The CAPM says that the risk premium on security j is proportional to the risk premium on the market portfolio. The CAPM is traditionally modeled as R-R, =a +BR.-R)+e, where R, is the return on stock), R, is the risk-free rate, R. is the return on the market portfolio, e is a random error, and a, is the firm's interceptor "alpha". Theory says that alpha" should be zero, so consider the model R-R, PR - R)+e. a) Suppose that the value of B is greater than I for a particular stock. Show that the variance of (R-R) for this stock is greater than the variance of (R - R). (Hint: Var(e) = and we may assume that cover -Re)=0. b) Suppose that the value of B is less than I for a particular stock. Is it possible that the variance of (R-R) for this stock is greater than the variance of (R.-R)? Explain. c) In a given year, the rate of return on 3-month Treasury bills, R,, is 3% and the rate of return on a large diversified portfolio of stocks, R. (the S&P 500) is 9% Calculate the estimated retum. R. for a stock with (recall that E(e) - 0): i) -03 ii) B=0.9 -1.2 -17 iii) iv)