$($Markowitz fun$)$ There are just three assets with rates of return $r_1,r_2$ and $r_3,$ respec$-$

tively. The covariance matrix and the expected rates of return are

$=\left[\begin{array}{ccc}1& 1& 0\\ 1& 2& 1\\ 0& 1& 2\end{array}\right]\frac{,}{b}ar(r)=\left[\begin{array}{c}0\mathrm{.}4\\ 0\mathrm{.}8\\ 0\mathrm{.}8\end{array}\right].$

$($a$)$ Find the minimum$-$variance portfolio. What is $$ in this case?

$($b$)$ Find the optimal portfolio with $\frac{?}{\text{b}\text{a}\text{r}}(r)=0\mathrm{.}7$ directly $($i$.$e$.,$ without using the Two Fund

Theorem.

$($c$)$ Find another efficient portfolio by setting $=1,=0,$ and thus the optimal

portfolio with an expected rate of return $1$ by the Two Fund Theorem.

$($d$)$ If the risk$-$free rate is $r_f=0\mathrm{.}1,$ then find the efficient portfolio of risky assets that

is required by One$-$Fund Theorem.