Question $2$

Matteo is a mean$-$variance investor whose utility function is $u=$min$\{r_x,30-4{}_x\}.$ If he invests in a market portfolio, he expects to receive a return of $13\%$ with the standard deviation of $9\%.$ The riskfree rate is $2\%$

$2\mathrm{.}1$ Draw the budget line $($the CML line$).$

$2\mathrm{.}2$ is it possible for him to achieve a portfolio whose return is $13\%$ and standard deviation is $4\%?$

$2\mathrm{.}3$ Is it possible for him to achieve a portfolio whose standard deviation is $4\mathrm{.}5\%$ and the expected return is $11\%.$

$2\mathrm{.}4$ From your answer in $2\mathrm{.}3,$ do you think this is his best choice possible? Can you recommend any portfolio that is better? $($hint: find his utility$-$maximizing portfolio$)$