You have been provided the following summary of the performance of stocks A and B; of the market index; and the risk free rate.

A B Market Index Risk Free Asset

Average annual return $22\%14\%9\%5\%$

Standard deviation of annual returns $18\%8\%4\%$

Correlation coefficient A and B $0\mathrm{.}75$

Correlation coefficient A and Market $0\mathrm{.}35$

Correlation coefficient B and Market $0\mathrm{.}25$

a$.$ What is the lowest risk possible in a portfolio consisting only of A and B$?$ What is the composition of such a portfolio?

b$.$ You wish to replicate the risk of the portfolio above by using only the Market Index and Risk Free Asset. What would be the weights of the Market Index and Risk Free Asset in the new portfolio to achieve the same risk? What would be the expected return of this portfolio?

c$.$ Apply Capital Asset Pricing Model $($CAPM$)$ to estimate the expected returns of A and B$.$ Compare it to the actual expected returns to decide if A and B are over or under priced by the stock market