Consider $2$ different EN $6$ pass$-$throughs backed by new $30$ yr mortgages $(360mo$ to maturity$).$ with two different groups of underlying borrowers, group $x$ and group $Y.$ We will refer to the pass$-$through backed by bonrower group $x$ as bond $x$ and the pass$-$through backed by bonower group $Y$ as bond $Y$ :

Group X

$\backslash$table$[[$# of borrowers,Note Rate,Loan Size$],[25,6\mathrm{.}99,600,000],[25,6\mathrm{.}73,500,000],[25,6\mathrm{.}7,400,000],[25,6\mathrm{.}55,100,000]]$

Group Y

$\backslash$table$[[$# of bomrowers,Note Rate,Loan Size$],[25,6\mathrm{.}5,400,000],[25,6\mathrm{.}45,350,000],[25,6\mathrm{.}63,325,000],[25,6\mathrm{.}9,225,000]]$

Assume all other characteristics are the same.

I$)$ What is the weighted average coupon $($WAC$)$ and weighted average loan size $($WAOLS$)$ of group X

II$)$ What is the weighted average coupon $($WAC$)$ and weighted average loan size $($WAOLS$)$ of group $Y?$

III$)$ Assume IN $65$ trade above par and prevailing primary mortgage rates are $5\mathrm{.}5\%($note rates available to borrowers$).$ Which bond $(x$ or $Y)$ would you expect investors to prefer and why?

IV$)$ On the chart below, draw how you expect the s$-$curves to look on these fivo borrower groups $($hint: the important part is how they are positioned$/$shaped relative to each other, be sure to label each one$)$

V$)$ Which bond is less negatively convex? How is this related to the shape of the s$-$curves you drew in part $($IV$)?$