Three securities $(1,2$ and $3)$ are listed on a capital market. A certain investor, according to his expectations, has the following vector of returns and covariance matrix:

Vector of returns:$($s$1=5,$ s$2=4,$ s$3=6)$

Covariance matrix: $(\backslash$sigma $11=20,\backslash$sigma $22=20,\backslash$sigma $33=30,\backslash$sigma $12=10,\backslash$sigma $21=10,\backslash$sigma $13=0,\backslash$sigma $31=0,\backslash$sigma $23=0,\backslash$sigma $32=0.)$

The value of all the securities listed on the market is $100$ million, of which $50$ million corresponds to security $1,20$ million to security $2$ and the rest to security $3.$

According to this investor's expectations, we want to know:

$1.$ The expected return of the market portfolio.

$2.$ The total risk of the market portfolio and the contribution of each security

$3.$ The market model of each security

$4.$ The market model of a portfolio p$,$ formed by investing $20\%$in s$1,30\%$ in s$2$ and the rest in s$3.$

$5.$ The coefficients of the market model of the market portfolio