problem: Identify a linear regression model consistent with CAPM in the following way:
ri = ai + birM + Ei (3)
Where ri = Ri - Rf is security i's excess return, rM= RM - Rf is market M's excess return. Under standard linear regression assumptions, that is, when Ei are independent & their means are equal to zero, it is the case that bi = βi. The forecast of CAPM is that, in equilibrium, ai = 0.
The expected value and standard deviation of the market portfolio are 8 percent and 12 percent, respectively. The expected return of security A is 6%. The standard deviation of security B is 18%, & its specific risk is (10%)2. A portfolio that invests 1/3 of value in A & 2/3 in B has a beta of 1. find out the risk-free rate and the expected return of B according to CAPM?
Suggestion: using (3) consider the covariance of ri with rM and the variance of ri. Decompose the latter one into systematic and firm specific risk.