4. In a CAPM market, define the excess of market returns rMRM r and the excess of returns of security i by Ti-Ri-r. We postulate a linear regression model for the relationship between rM and Ti given by where (ai, bi-1, M are constants and the 's are independent random variables with zero mean () (2 points) Find the values of ay and b, predicted by the CAPM theory, when all its assumptions hold (b) (2 points) Prove that Cov(Ei,TM)-0 for every i-1,...,N (c) (2 points) Denote by ? = Var(-), which is called the specific risk of security i. Deduce from the previous parts that the following equality holds for every i We will say that the risk of security i has two components, the market risk and the specific risk. (d) (4 points) Consider a market with two securities, A and B. The expected return and standard deviation of the market portfolio are 8% and 12%, respectively. The expected return of security A is 6%. The standard deviation of security B is 18%, and its specific risk is given by ,-(10%)2 . A portfolio that invests of its value in A and in B has a beta of 1 . What are the risk-free rate and the expected return of B