CHAPTER 10 INTEREST RATE & CURRENCY SWAPS
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
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 position in matching
opposite sides of a swap and in assuring that each counterparty fulfills its contractual obligation to the
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 spread
differential to exist. In general, the default-risk premium of the fixed-rate debt will be larger than the
default-risk premium of the floating-rate debt.
4. 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 could be obtained on its
own. A second basic reason is to lock in long-term exchange rates in the repayment of debt service
obligations denominated in a foreign currency.
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 firms of equivalent creditworthiness
can each exploit their, respective, name recognition by borrowing in their local capital market at a
favorable rate and then re-lending at the same rate to the other.
IM-10 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 with 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 other side, while still covering its desired
spread, or avoiding a loss. Exchange-rate risk refers to the risk the swap bank faces from fluctuating
exchange rates during the time it takes the bank to lay off a swap it undertakes on an opposing
counterparty before exchange rates change. Additionally, the dealer confronts credit risk from one
counterparty defaulting and its having to fulfill the defaulting party’s obligation to the other counterparty.
Mismatch risk refers to the difficulty of the dealer finding an exact opposite match for a swap it has
agreed to take. Sovereign risk refers to a country imposing exchange restrictions on a currency involved
in a swap making it costly, or impossible, for a counterparty to honor its swap obligations to the dealer.
In this event, provisions exist for the early termination of a swap, which means a loss of revenue to the
6. Briefly discuss some variants of the basic interest rate and currency swaps diagrammed 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 is tied to a different
floating rate index or a different frequency of the same index. Currency swaps need not be fixed-for-
fixed; fixed-for-floating and floating-for-floating rate currency swaps are frequently arranged. Moreover,
both currency and interest rate swaps can be amortizing as well as non-amortizing.
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 one type of financing and
to obtain a more desirable type of credit that is more suitable for its asset maturity structure.
IM-10 8. Assume you are the swap bank in the Eli Lilly swap discussed in the chapter. Develop an example
of how you might lay off the swap to an opposing counterparty.
Answer: The swap bank may try to lay off the swap on a Japanese MNC that has issued yen
denominated debt to finance a capital expenditure of a U.S. subsidiary. The subsidiary is earning U.S.
dollar revenues which are to be used to service the yen debt. A currency swap would allow the Japanese
MNC to avoid the foreign exchange risk of an appreciating yen; the swap could serve as a ready means
for disposing of dollars and receiving yen to service the debt.
9. Discuss the motivational difference in the currency swap presented as Exhibit 10.5 and the Eli Lilly
and Company swap discussed in the chapter.
Answer: The currency swap presented as Exhibit 10.5 can be classified as a liability swap. The
motivation of a counterparty to enter into a liability swap is to obtain the cost-saving advantage of the
other counterparty. Each has a comparative advantage in raising funds in a particular currency. When the
proceeds are swapped and each counterparty pays the other’s debt service, a cost-savings is obtained.
The Eli Lilly currency swap was motivated by Lilly’s desire to find a use for its yen cash inflows. What
it desired to do was to convert yen cash flow into dollar cash flow at a stable exchange rate. The swap
allowed Lilly to do this. Currency swaps that transform cash flows are referred to as asset swaps.
10. Assume a currency swap between two counterparties of comparable credit risk; each borrows at the
best rate available, and 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: At first glance 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 rate is expected to
depreciate versus the other. In this case, the counterparty making the interest payments at the higher
nominal rate is in effect making interest payments at the lower interest rate because the payment currency
is depreciating in value versus the borrowing currency.
1. Develop a different arrangement of interest payments among the counterparties and the swap bank in
Section 10.5 (with detail in Exhibit 10.5) that still leaves each counterparty with an all-in cost 0.50
percent below their best rate and the swap bank with a 0.25 percent inflow.
Solution: Company B could pay a fixed-rate of 5.75 percent to the swap bank, which would pass through
5.50 percent to Bank A. Bank A could pay LIBOR, which the swap bank would pass in its entirety
through to Company B. In fact, generic plain vanilla interest rate swaps, such as this one, are quoted by
swap banks against LIBOR flat. The swap bank would pay dollar LIBOR flat in return for receiving
dollar payments at 5.75 percent or the bank would make dollar payments at 5.50 percent in return for
receiving dollar LIBOR flat. Hence, the bank is charging a fixed-rate spread of 0.25 percent for the swap.
2. Alpha and Beta Companies can borrow at the following rates:
Moody’s credit rating Aa Baa
Fixed-rate borrowing cost 5.5% 7.0%
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.
a. QSD = (7.0% - 5.5%) minus (LIBOR + 1% - LIBOR) = 0.5%.
b. Alpha needs to issue fixed-rate debt at 5.5% .
Beta needs to issue floating rate-debt at LIBOR + 1%.
Alpha pays LIBOR to Beta. Beta pays 5.75% to Alpha.
Under these arrangements …
Alpha’s floating-rate all-in-cost is: 5.5% + LIBOR - 5.75% = LIBOR - 0.25%
For Alpha this represents a 0.25% savings over issuing floating-rate debt on its own.
Beta’s fixed-rate all-in-cost is: LIBOR+ 1% + 5.75% - LIBOR = 6.75%.
For Beta this represents a saving of 0.25% over issuing fixed-rate debt.
IM-10 3. Company A is an AAA-rated firm desiring to issue five-year FRNs. It finds that it can issue FRNs at six-
month LIBOR + 0.125 percent or at three-month LIBOR + 0.125 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 + 0.625 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 0.125 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
+ 0.125 percent) = ] 0.875 percent minus [(Three-month LIBOR + 0.625 percent) minus (Three-month
LIBOR + .125 percent) =] 0.50 percent, which equals 0.375 percent. If the swap bank receives 0.125
percent, each counterparty saves 0.125 percent.
To construct the swap, Company A issues FRNs indexed to six-month LIBOR and Company B issues
FRNs indexed three-month LIBOR. Company B might make semi-annual payments of six-month
LIBOR + 0.125 percent to the swap bank, which would pass all of it through to Company A. Company
A, in turn, might make quarterly payments of three-month LIBOR to the swap bank, which would pass
through three-month LIBOR - 0.125 percent to Company B. On an annualized basis, Company B remits
to the swap bank six-month LIBOR + 0.125 percent and pays three-month LIBOR + 0.0625 percent on its
FRNs. B receives three-month LIBOR - 0.125 percent from the swap bank.
This arrangement results in an all-in cost of the six-month LIBOR + 0.825 percent, which is a 0.125
percent below the FRNs indexed to six-month LIBOR + 1.0 percent Company B could issue on its own.
Company A remits three-month LIBOR to the swap bank and pays six-month LIBOR + 0.125 percent on
its FRNs. It will receive six-month LIBOR + .125 percent from the swap bank. This arrangement results
in an all-in cost of three-month LIBOR for Company A, which is 0.125 percent less than the FRNs
indexed to three-month LIBOR + 0.125 percent it could issue on its own. Theses arrangements with the
two counterparties net the swap bank 0.125 percent per annum, received quarterly.
4. 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?
Solution: Morgan Guaranty will pay annual fixed-rate dollar payments of 7.75 percent against receiving
IM-10 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 annual fixed-rate £ payments at
11.65 percent against paying six-month dollar LIBOR flat. Thus, Morgan Guaranty will enter into a
currency swap in which it would pay annual fixed-rate dollar payments of 7.75 percent in return for
receiving semi-annual fixed-rate £ payments at 11.65 percent, or it will receive annual fixed-rate dollar
payments at 8.10 percent against paying annual fixed-rate £ payments at 11.25 percent.
5. 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 percent coupon payments at the new
fixed-rate of 10.25 percent is €14,814,304. This sum represents the present value of the remaining
payments the swap bank will receive from the corporation. Thus, the swap bank should be willing to buy
and the corporation should be willing to sell the swap for €15,000,000 - €14,814,304 = €185,696.
6. Karla Ferris, a fixed income manager at Mangus Capital Management, expects the current
positively sloped Treasury yield curve to shift parallel upward.
Ferris owns two $1,000,000 corporate bonds maturing on June 15, 2009, one with a variable
rate based on six-month dollar LIBOR and one with a fixed rate. Both yield 50 basis points
over comparable Treasury market rates, have similar credit quality, and pay interest semi-
Ferris wants 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 Treasury market rates will
IM-10 a. Describe a six-month dollar LIBOR-based swap that would