There are only two risky assets $($stocks$)$ A and B in the market.

Now assume that there is a risk free asset. The risk$-$free rate $($for borrowing and for lending$)$ is

$4\%.$ The expected return of the market portfolio $(=$ tangency portfolio, optimal risky portfolio$)$ is

$14\%.$

$($i$)$ What is the standard deviation of the market portfolio?

$($ii$)$ Plot $($sketch$)$ the efficiency frontier $($the optimal investment opportunity set$).$

$($iii$)$ What is the minimal standard deviation of a portfolio that has expected return of $12\%?$

$($iv$)$ What is the minimal standard deviation of a portfolio that has expected return of $18\%?$The returns on the two assets have zero correlation.