The rates of return of two financial securities have the following vector of expected returns and matrix V of variances$-$covariances:

$=\frac{1}{100}\left[\begin{array}{c}5\\ 10\end{array}\right],$ V$=\frac{1}{100}\left[\begin{array}{cc}2& 1\\ 1& 4\end{array}\right]$

$($i$)$ Compute the ecient frontier of the Markowitzs model.

$($ii$)$ Compute the expected return, the variance and the proportions invested in the two securities of the ecientportfolio with the minimum variance

$.($iii$)$ Suppose that short sales are not allowed. Say if the ecient frontier exibits risk reduction and why this happens or does not happen.