$1.$ Consider a $5-$year bond with $$1,000$ face value with a $9\mathrm{.}5\%$ coupon rate paid semiannually. This

face value is split evenly to create a floating rate bond which pays a coupon equal to the LIBOR

reference rate $($L$)$ and an inverse floater. What is the coupon payment of the inverse floater?

$2.$ There is a $10-$year $$1,000$ face value bond with a $5\mathrm{.}5\%$ coupon paid semiannually. From this bond

you are going to create a floating rate bond, and an inverse floating rate bond. The floater will have a

face value of $$600$ and pay the SOFR reference rate $($call this rate S$,$ similar to how we called the

LIBOR rate L$).$ What is the coupon rate of the inverse floater?

$3.$ A $$5-$year bond that pays a $6\%$ coupon annually has a face value of $$1,000.$ You use this face

value as collateral to create a $$500$ floater $($paying SOFR, call this rate S$)$ and a $$500$ inverse floater.

The collateral bond currently sells for $$1,234.$

a$)$ What are the coupon payments for the floater and the inverse floater?

b$)$ What is the duration of the collateral bond? $($Hint: solve for ytm first$)$

c$)$ Given your answer to part b$,$ what is the duration of the inverse floater? $($hint: construct a weighted portfolio$)$

$4.$ You know that in $1$ year you will need to borrow money for a year. You are given the following

annual spot rates from zero coupon bonds:

S$1=3\%,$ S$2=3\mathrm{.}5\%,$ S$3=4\%,$ S$4=5\%.$

a$)$ What is the forward rate that would be offered to you between years $2$ and $3($ f$(2,3))?$

b$)$ What is the forward rate that would be offered to you between years $3$ and $4($ f$(3,4))?$

$5.$ You are given the following annual spot rates from zero coupon bonds: S$1=5\%,$ S$2=5\mathrm{.}25\%,$ S$3=$

$6\mathrm{.}1\%,$ S$4=6\mathrm{.}6\%.$

a$)$ What is the forward discount factor that would price a cashflow from year $3$ to year $2?($F$(2,3))$

b$)$ What is the forward discount factor that would price a cashflow from year $4$ to year $2?($F$(2,4))$