Q$2.$ Consider three zero coupon bonds:

$10$Y yielding $4\mathrm{.}40\%,20Y$ yielding $4\mathrm{.}60\%,$ and $30Y$ yielding $4\mathrm{.}50\%.$

Q$2$a Calculate duration and convexity for all three $(4$ points$)$

Q$2$b If you want to construct a $100M$ portfolio of $10Y$ and $30Y$ to match the dollar duration of $100M$ position in $20Y,$ what is the weight in $5Y$ and $30Y$ respectively? $(4$ points$)$

Q$2$c What is the $convexity for LONG $100$M of $20$Y zero? What is $convexity for short $100M$ portfolio of $10Y$ and $30Y$ as constructed in Q$2$b$?(4$ points$)$