Q$2.$ Consider three zero coupon bonds:$5$Y yielding $4\mathrm{.}00\%,10$Y yielding $4\mathrm{.}50\%,$ and $30$Y yielding $5\mathrm{.}00\%.$Q$2$a Calculate duration and convexity for all three $(3$ points$)$Q$2$b If you want to construct a $100$M portfolio of $5$Y and $30$Y to match the dollar duration of $100$M position in $10$Y$,$what are the weights in $5$Y and $30$Y respectively? $(3$ points$)$Q$2$c What is the $convexity for a short $100$M of $10$Y zero? What is $convexity for LONG $100$M portfolio of $5$Y and$30$Y as constructed in Q$2$b$?(3$ points$)$Page $3$Q$2$d$.$ What is the $1-$day net interest payment $($ie carry$)$ for the long$-$short duration$-$neutral portfolio above in Q$2$c$?$ Isit positive or negative $(3$ points$)$Q$2$e$.$ What is the break$-$even amount of parallel movement in yield curve in a single day $($breakeven means theconvexity pnl will offset daily interest payment$)(3$ points$)$