CHAPTER 14 INTEREST RATE AND CURRENCY SWAPS
ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS
QUESTIONS
1. Describe the difference between a swap broker and a swap dealer.
Answer: A swap broker arranges a swap between two counterparties for a fee without taking a
risk position in the swap. A swap dealer is a market maker of swaps and assumes a risk
2. What is the necessary condition for a fixed-for-floating interest rate swap to be possible?
Answer: For a fixed-for-floating interest rate swap to be possible it is necessary for a quality
3. Discuss the basic motivations for a counterparty to enter into a currency swap.
Answer: One basic reason for a counterparty to enter into a currency swap is to exploit the
comparative advantage of the other in obtaining debt financing at a lower interest rate than
4. How does the theory of comparative advantage relate to the currency swap market?
Answer: Name recognition is extremely important in the international bond market. Without it,
even a creditworthy corporation will find itself paying a higher interest rate for foreign
denominated funds than a local borrower of equivalent creditworthiness. Consequently, two
5. Discuss the risks confronting an interest rate and currency swap dealer.
Answer: An interest rate and currency swap dealer confronts many different types of risk.
Interest rate risk refers to the risk of interest rates changing unfavorably before the swap dealer
can lay off on an opposing counterparty the unplaced side of a swap with another counterparty.
Basis risk refers to the floating rates of two counterparties being pegged to two different indices.
In this situation, since the indexes are not perfectly positively correlated, the swap bank may not
always receive enough floating rate funds from one counterparty to pass through to satisfy the
6. Briefly discuss some variants of the basic interest rate and currency swaps diagramed in the
chapter.
Answer: Instead of the basic fixed-for-floating interest rate swap, there are also zero-coupon-
for-floating rate swaps where the fixed rate payer makes only one zero-coupon payment at
maturity on the notional value. There are also floating-for-floating rate swaps where each side
7. If the cost advantage of interest rate swaps would likely be arbitraged away in competitive
markets, what other explanations exist to explain the rapid development of the interest rate
swap market?
Answer: All types of debt instruments are not always available to all borrowers. Interest rate
swaps can assist in market completeness. That is, a borrower may use a swap to get out of
8. Suppose Morgan Guaranty, Ltd. is quoting swap rates as follows: 7.75 – 8.10 percent
annually against six-month dollar LIBOR for dollars and 11.25 – 11.65 percent annually against
six-month dollar LIBOR for British pound sterling. At what rates will Morgan Guaranty enter into
a $/£ currency swap?
Answer: Morgan Guaranty will pay annual fixed-rate dollar payments of 7.75 percent against
receiving six-month dollar LIBOR flat, or it will receive fixed-rate annual dollar payments at 8.10
percent against paying six-month dollar LIBOR flat. Morgan Guaranty will make annual fixed-
rate £ payments at 11.25 percent against receiving six-month dollar LIBOR flat, or it will receive
9. A U.S. company needs to raise €50,000,000. It plans to raise this money by issuing dollar-
denominated bonds and using a currency swap to convert the dollars to euros. The company
expects interest rates in both the United States and the euro zone to fall.
a. Should the swap be structured with interest paid at a fixed or a floating rate?
b. Should the swap be structured with interest received at a fixed or a floating rate?
CFA Guideline Answer:
a. The U.S. company would pay the interest rate in euros. Because it expects that the interest
b. The U.S. company would receive the interest rate in dollars. Because it expects that the
*10. Assume a currency swap in which two counterparties of comparable credit risk each
borrow at the best rate available, yet the nominal rate of one counterparty is higher than the
other. After the initial principal exchange, is the counterparty that is required to make interest
payments at the higher nominal rate at a financial disadvantage to the other in the swap
agreement? Explain your thinking.
Answer: Superficially, it may appear that the counterparty paying the higher nominal rate is at a
disadvantage since it has borrowed at a lower rate. However, if the forward rate is an unbiased
predictor of the expected spot rate and if IRP holds, then the currency with the higher nominal
PROBLEMS
1. Alpha and Beta Companies can borrow for a five-year term at the following rates:
Alpha Beta
Moody’s credit rating Aa Baa
Fixed-rate borrowing cost 10.5% 12.0%
Floating-rate borrowing cost LIBOR LIBOR + 1%
a. Calculate the quality spread differential (QSD).
b. Develop an interest rate swap in which both Alpha and Beta have an equal cost savings in
their borrowing costs. Assume Alpha desires floating-rate debt and Beta desires fixed-rate debt.
No swap bank is involved in this transaction.
Solution:
b. Alpha needs to issue fixed-rate debt at 10.5% and Beta needs to issue floating rate-debt at
LIBOR + 1%. Alpha needs to pay LIBOR to Beta. Beta needs to pay 10.75% to Alpha. If this is
2. Do problem 1 over again, this time assuming more realistically that a swap bank is involved
as an intermediary. Assume the swap bank is quoting five-year dollar interest rate swaps at
10.7% – 10.8% against LIBOR flat.
Solution: Alpha will issue fixed-rate debt at 10.5% and Beta will issue floating rate-debt at
LIBOR + 1%. Alpha will receive 10.7% from the swap bank and pay it LIBOR. Beta will pay
10.8% to the swap bank and receive from it LIBOR. If this is done, Alpha’s floating-rate all-in-
3. Company A is a AAA-rated firm desiring to issue five-year FRNs. It finds that it can issue
FRNs at six-month LIBOR + .125 percent or at three-month LIBOR + .125 percent. Given its
asset structure, three-month LIBOR is the preferred index. Company B is an A-rated firm that
also desires to issue five-year FRNs. It finds it can issue at six-month LIBOR + 1.0 percent or at
three-month LIBOR + .625 percent. Given its asset structure, six-month LIBOR is the preferred
index. Assume a notional principal of $15,000,000. Determine the QSD and set up a floating-
for-floating rate swap where the swap bank receives .125 percent and the two counterparties
share the remaining savings equally.
Solution: The quality spread differential is [(Six-month LIBOR + 1.0 percent) minus (Six-month
LIBOR + .125 percent) =] .875 percent minus [(Three-month LIBOR + .625 percent) minus
(Three-month LIBOR + .125 percent) =] .50 percent, which equals .375 percent. If the swap
bank receives .125 percent, each counterparty is to save .125 percent. To affect the swap,
Company A would issue FRNs indexed to six-month LIBOR and Company B would issue FRNs
indexed three-month LIBOR. Company B might make semi-annual payments of six-month
LIBOR + .125 percent to the swap bank, which would pass all of it through to Company A.
*4. A corporation enters into a five-year interest rate swap with a swap bank in which it agrees
to pay the swap bank a fixed rate of 9.75 percent annually on a notional amount of €15,000,000
and receive LIBOR. As of the second reset date, determine the price of the swap from the
corporation’s viewpoint assuming that the fixed-rate side of the swap has increased to 10.25
percent.
Solution: On the reset date, the present value of the future floating-rate payments the
corporation will receive from the swap bank based on the notional value will be €15,000,000.
The present value of a hypothetical bond issue of €15,000,000 with three remaining 9.75
5. DVR, Inc. can borrow dollars for five years at a coupon rate of 2.75 percent. Alternatively, it
can borrow yen for five years at a rate of .85 percent. The five-year yen swap rates are .64–.70
percent and the dollar swap rates are 2.41–2.44 percent. The current ¥/$ exchange rate is
87.575. Determine the dollar AIC and the dollar cash flow that DVR would have to pay under a
currency swap where it borrows ¥1,750,000,000 and swaps the debt service into dollars. This
problem can be solved using the excel spreadsheet CURSWAP.xls.
Solution: Since the dollar AIC is 2.66% and the DVR’s dollar borrowing rate is 2.75%, it should
Cross-Currency Swap Analyzer
FC Bond FC $ Actual
Year Cashflow Received Paid $ Cashflow
0 1,750,000,000 -1,768,027,402 20,188,723 19,982,872
1 -14,875,000 14,875,000 -492,605 -492,605
–
–
AIC 0.85% 0.64% 2.44% 2.66%
Face Value: 1,750,000,000 Bid Ask
Coupon Rate: 0.850% Spot FX Rate: 87.57500 87.57500
6. Karla Ferris, a fixed income manager at Mangus Capital Management, expects the current
positively sloped U.S. Treasury yield curve to shift parallel upward.
Ferris owns two $1,000,000 corporate bonds maturing on June 15, 2014, one with a
variable rate based on 6-month U.S. dollar LIBOR and one with a fixed rate. Both yield 50 basis
points over comparable U.S. Treasury market rates, have very similar credit quality, and pay
interest semi-annually.
Ferris wished to execute a swap to take advantage of her expectation of a yield curve shift
and believes that any difference in credit spread between LIBOR and U.S. Treasury market
rates will remain constant.
a. Describe a six-month U.S. dollar LIBOR-based swap that would allow Ferris to take
advantage of her expectation. Discuss, assuming Ferris’ expectation is correct, the change in
the swap’s value and how that change would affect the value of her portfolio. [No calculations
required to answer part a.]
Instead of the swap described in part a, Ferris would use the following alternative derivative
strategy to achieve the same result.
b. Explain, assuming Ferris’ expectation is correct, how the following strategy achieves the
same result in response to the yield curve shift. [No calculations required to answer part b.]
Settlement Date Nominal Eurodollar Futures Contract Value
12-15-12 $1,000,000
03-15-13 1,000,000
06-15-13 1,000,000
09-15-13 1,000,000
12-15-13 1,000,000
03-15-14 1,000,000
c. Discuss one reason why these two derivative strategies provide the same result.