Assume today is t$=0.$ A $10-$year fixed rate bond with a $5\%$ coupon rate is selling at par $($annual coupons$).$ From $$200$ FV of this bond, we form a floater and an inverse floater by equally splitting its face value. The floater$$s coupon rate is LIBOR. At t$=0,$ duration of the fixed rate bond is $8\mathrm{.}11.$

a$)$ What is the duration of the floater at t$=0?$

b$)$ What is the price of the inverse floater at$=0?$

c$)$ What is the duration of the inverse floater?

d$)$ Now consider the range of YTMs the fixed rate bond can have one year from now. Create a table

by calculating the potential prices by varying the YTM between $1\%$ and $10\%$ and fill in the table.

Yield Price per $100$ FV Price per $200$ FV P$($Floater$)$ P$($IF$)$

$1\%$

$2\%$

$3\%$

$4\%$

$5\%$

$6\%$

$7\%$

$8\%$

$9\%$

$10\%$

e$)$ Plot the price$-$yield curve for the fixed rate bond $(100$ FV$)$ and inverse floater on the same graph.

Comment on their price sensitivity to changing yields.