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ANSWERS TO END OF CHAPTER QUESTIONS

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									ANSWERS TO END OF CHAPTER QUESTIONS
QUESTIONS
1. Consider an interest-rate swap with these features: maturity is five years, notional principal is
$100 million, payments occur every six months, the fixed-rate payer pays a rate of 9.05% and
receives LIBOR, while the floating-rate payer pays LIBOR and receives 9%. Now suppose that at
a payment date, LIBOR is at 6.5%. What is each party's payment and receipt at that date?
NOTE. The below answers assume the time period of six months is from January 1st to June 30th
which is a period of 181 days. The answer will vary if the number of days per six-month period
changes based upon if the first month is a month other than January.
Fixed-rate payer pays: (notional amount)(fixed-rate)(number of days in period / 360) =
($100,000,000)(0.0905)(181 / 360) = $4,550,138.89.
Fixed-party receives: (notional amount)(three-month LIBOR)(days in period / 360) =
($100,000,000)(0.065X181/360) = $3,268,055.56.
Floating-rate payer pays: (notional amount)(three-month LIBOR)(days in period / 360) =
($100,000,000)(0.065)(181 / 360) = $$3,268,055.56.
Floating-rate payer receives: (notional amount)(fixed-rate)(number of days in period / 360) =
($100,000,000)(0.0905X181 / 360) = $4,550,138.89.
2. Suppose that a dealer quotes these terms on a five-year swap: fixed-rate payer to pay 9.5% for
LIBOR and floating-rate payer to pay LIBOR for 9.2%.
Answer the below questions.
(a) What is the dealer's bid-asked spread?
Dealer's bid-asked spread =
(offer price dealer quotes fixed-rate payer) - (bid price dealer quotes floating-rate payer)
rb Dealer's bid-asked spread = 9.50% - 9.20% = 0.03% or 0.0003 or 30 baas points.
(b) How would the dealer quote the terms by reference to the yield on five-year Treasury notes?
The fixed rate is some spread above the Treasury yield curve with the same term to maturity as
the swap. Suppose the 5-year Treasury yield is 9.0%. Then the offer price that the dealer would
quote to the fixed-rate payer is the 10-year Treasury rate plus 60 basis points versus receiving
LIBOR flat. For the floating-rate payor, the bid price quoted would be LIBOR flat versus the 5-
year Treasury rate plus 30 basis points. The dealer would quote such a swap as 30-60, meaning
that the dealer is willing to enter into a swap to receive LIBOR and pay a fixed rate equal to the
5-year Treasury rate plus 30 basis points; and it would be willing to enter into a swap to pay
LIBOR and receive a fixed rate equal to the 5-year Treasury rate plus 60 basis points. The
difference between the Treasury rate paid and received is the bid-offer spread.
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3.	Give two interpretations of an interest-rate swap.
There are two ways that a swap position can be interpreted: (i) as a package of forward/ futures
contracts, and (ii) as a package of cash flows from buying and selling cash market instruments.
4.	In determining the cash flow for the floating-rate side of a LIBOR swap, explain how the cash
flow is determined.
Assume a swap of 12 quarterly floating-rate payments for three years with the first quarter
consisting of 90 days from January 1st of year 1 to March 31st of year 1. The cash flow for this
period is: (notional amount)(current LIBOR)(90 / 360).
Let's assume $100 million notional amount and a LIBOR of 5%. The cash flow for period 1 is:
($100 million)(0.05)(0.25) = $1.25 million. While this first quarterly payment is known, the next
11 are not The second quarterly payment from April 1 of year 1 to June 30 of year 1, has 91
days. The floating-rate payment is determined by three-month LIBOR on April 1 of year 1 and
paid on June 30 of year 1. This is achieved by looking at the three-month Eurodollar CD futures
contract for settlement on June 30 of year 1. That futures contract provides the rate that can be
locked in for three-month LIBOR on April 1 of year 1. We refer to that rate for three-month
LIBOR as the forward rate. Therefore, if the fixed-rate payer bought 100 contract of these three-
month Eurodollar CD futures contracts on January 1 of year 1 (the inception of the swap) that
settle on June 30 of year 1, then the payment that will be locked in for the quarter (April 1 to June
30 of year 1) is
(notional amount)(period forward rate)
where period forward rate = (annual forward rate)(91 / 360)
If the annual forward rate is 5.2%, then the payment is: ($100 million)(0.052X91 / 360) =
$1,314,444.44. Note that each futures contract is for $1 million and hence 100 contracts have a
notional amount of $100 million. Similarly, the Eurodollar CD futures contract can be used to
lock in a floating-rate payment for each of the next 10 quarters. It is important to emphasize that
the reference rate at the beginning of period t determines the floating rate that will be paid for the
period. However, the floating-rate payment is not made until the end of period t.
5. How is the swap rate calculated?
To compute the swap rate, we begin with the basic relationship for no arbitrage to exist:
PV of fixed-rate payments = PV of floating-rate payments.
The fixed-rate payment for period t is equal to
(notional amount)(swap rate)(days in period t / 360)
The present value of the fixed-rate payment for period t is found by multiplying the fixed-rate
payment expression by the forward discount factor for period t. That is, the present value of the
fixed-rate payment for period t is equal to
(notional amount)(swap rate)(days in period t / 360)(forward discount factor for period t)
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