Question $2(10$ Marks$)$

In mid$-$July, JK Ltd $($a US firm$)$ holds a pay$-$fixed, receive$-$floating $69$ FRA contract which

was entered into $6$ months ago $($i$.$e$.$ in mid$-$January$).$ The FRA rate is $0\mathrm{.}70\%$ per annum and the

notional amount is $$20,000,000.$

The $69$ FRA reaches expiration now $($in mid$-$July$),$ and the following LIBOR rates are

observed from the market:

Note: The FRA contracts follow the standard US FRA settlement terms and adopt the

Actual $\frac{?}{360}$ day count convention. All interest rates are measured with a compounding

frequency reflecting the length of the period they apply to$.$

Required:

$($a$)$ Based on the information above, explain whether JK Ltd makes a gain or loss by showing

the settlement amount for JK Ltd to settle the $69$ FRA at expiration. Report your answer

in $2$ decimal places $(dps).$

$(4$ marks$)$

$($b$)$ Suppose that JK Ltd plans to take a $20-$million $90-$day floating$-$rate loan in mid$-$October

from a local bank. The firm wants to hedge the interest rate risk involved in the floating$-$

rate loan by entering into another FRA contract in mid$-$July. Based on the LIBOR rate

information in mid$-$July, explain what type of FRA contracts it should use.

Hint: You need to specify what the values of $M$ and $N$ are for such a $MN$ FRA contract,

and whether the firm should buy $($long$)$ or sell $($short$)$ such a contract.

$(3$ marks$)$

$($c$)$ What should be the FRA rate of the contract specified in part $($b$).$ Report your answer in

percentage $(\%)$ with $4$ dps i$.$e$..\%.$