Asset $1$ has an expected return of $10\%$ with a standard deviation of $25\%,$ and asset $2$ has an

expected return of $15\%$ and a standard deviation of $35\%.$ The covariance between the returns

is $0\mathrm{.}0175$ and the risk$-$free rate is $8\%.$

$($a$)$ What is the optimal portfolio consisting of risky assets and risk$-$free asset if you want

an average return of $0\mathrm{.}10?$ Answer.

$($b$)$ Can you find a portfolio consisting of risky and risk$-$free assets with average return of

$0\mathrm{.}10$ and variance of return $0\mathrm{.}009?$ Why or why not? Answer.