Assume that an economy has $2$ stocks: A and B$.$ Additionally, there is a

risk$-$free asset with an expected return of $5\%.$ The expected return of stock

A is $10\%,$ with a standard deviation of $20\%.$ The expected return of stock B

is $15\%,$ with a standard deviation of $25\%.$ The correlation between both

stocks is $0\mathrm{.}135.$ The market capitalization of $A$ is $$240,000,000,$ and the

market capitalization of $B$ is $$360,000,000.(10$ points$)$

a$.$ Is a portfolio that invests $40\%$ in $A,60\%$ in $B,$ and $0\%$ in the risk$-$free

asset efficient?

b$.$ Is a portfolio that invests $20\%$ in $A,80\%$ in $B,$ and $0\%$ in the risk$-$free

asset efficient?

c$.$ If any of the portfolios in the previous two points are inefficient, how

much more expected return would we be able to obtain in an efficient

portfolio with the same risk as the portfolio in question? What would be

the weights in A$,$ B$,$ and the risk$-$free asset of this efficient portfolio?

$($hint: Use the capital market line$)$