Please solve the following questions.The following table is the daily variance$-$covariance matrix of Assets $1,2$ and $3.$

$(1)$ Consider a portfolio consisting of a $$450$ position in Asset $1$ and a $$450$ position in Asset $2.$ The $10-$day $99\mathrm{.}9\%$ VaR for

the portfolio is

The benefits of diversification are

$.$ The $10-$day $99\mathrm{.}9\%$ ES for the portfolio is

$(2)$ Consider a portfolio consisting of a $$450$ position in Asset $1$ and a $$450$ position in Asset $3.$ The $10-$day $99\mathrm{.}9\%$ VaR

for the portfolio is

$.$ The benefits of diversification are

$.$ The $10-$day $99\mathrm{.}9\%$ ES for the portfolio is

$(3)$ Consider a portfolio consisting of a $$300$ position in Asset $1,$ a $$300$ in Asset $2$ and a $$300$ position in Asset $3.$ The $10$

$-$day $99\mathrm{.}9\%$ VaR for the portfolio is

$.$ The benefits of diversification are

The $10-$day $99\mathrm{.}9\%$ ES

for the portfolio is

$(4)$ Suppose that short selling is permitted. Find the weight $w=(w_1,w_2,w_3)$ of Assets $1,2$ and $3$ in portfolio which

minimizes the variance of the portfolio.

$w_1=,w_2=,w_3=$

$(5)$ Consider a portfolio worth $$900$ consisting of Asset $1,$ Asset $2$ and Asset $3.$ The minimum value of the $10-$day $99\mathrm{.}9\%$

VaR for the portfolio is

$.$ The minimum value of the $10-$day $99\mathrm{.}9\%$ ES for the portfolio is