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PROBLEMS
1. Grecian Tile Manufacturing of Athens, Georgia, borrows $1,500,000 at LIBOR plus a lending
margin of 1.25 percent per annum on a six-month rollover basis from a London bank. If six-
month LIBOR is 4 ½ percent over the first six-month interval and 5 3/8 percent over the second
six-month interval, how much will Grecian Tile pay in interest over the first year of its Eurodollar
loan?
2. A bank sells a “three against six” $3,000,000 FRA for a three-month period beginning three
months from today and ending six months from today. The purpose of the FRA is to cover the
interest rate risk caused by the maturity mismatch from having made a three-month Eurodollar
loan and having accepted a six-month Eurodollar deposit. The agreement rate with the buyer is
5.5 percent. There are actually 92 days in the three-month FRA period. Assume that three
months from today the settlement rate is 4 7/8 percent. Determine how much the FRA is worth
and who pays who--the buyer pays the seller or the seller pays the buyer.
Solution: Since the settlement rate is less than the agreement rate, the buyer pays the seller
the absolute value of the FRA. The absolute value of the FRA is:
3. Assume the settlement rate in problem 2 is 6 1/8 percent. What is the solution now?
Solution: Since the settlement rate is greater than the agreement rate, the seller pays the buyer
the absolute value of the FRA. The absolute value of the FRA is:
4. A “three-against-nine” FRA has an agreement rate of 4.75 percent. You believe six-month
LIBOR in three months will be 5.125 percent. You decide to take a speculative position in a
FRA with a $1,000,000 notional value. There are 183 days in the FRA period. Determine
whether you should buy or sell the FRA and what your expected profit will be if your forecast is
correct about the six-month LIBOR rate.
Solution: Since the agreement rate is less than your forecast, you should buy a FRA. If your
forecast is correct your expected profit will be:
5. Recall the FRA problem presented as Example 11.2. Show how the bank can alternatively
use a position in Eurodollar futures contracts (Chapter 7) to hedge the interest rate risk created
by the maturity mismatch it has with the $3,000,000 six-month Eurodollar deposit and rollover
Eurocredit position indexed to three-month LIBOR. Assume that the bank can take a position in
Eurodollar futures contracts that mature in three months and have a futures price of 94.00.
Solution: To hedge the interest rate risk created by the maturity mismatch, the bank would need
to buy (go long) three Eurodollar futures contracts. If on the last day of trading, three-month
Note that this sum differs slightly from the $6,550.59 profit that the bank will earn from the FRA
for two reasons. First, the Eurodollar futures contract assumes an arbitrary 90 days in a three-
6. The Fisher effect (Chapter 6) suggests that nominal interest rates differ between countries
because of differences in the respective rates of inflation. According to the Fisher effect and
your examination of the one-year Eurocurrency interest rates presented in Exhibit 11.3, order
the currencies from the eight countries from highest to lowest in terms of the size of the inflation
premium embedded in the nominal ask interest rates for June 5, 2013.
Solution: According to the Fisher effect, the one-year Eurocurrency interest rates suggest that
the inflation premiums for the countries representing the eight currencies ordered from highest
7. George Johnson is considering a possible six-month $100 million LIBOR-based, floating-rate
bank loan to fund a project at terms shown in the table below. Johnson fears a possible rise in
the LIBOR rate by December and wants to use the December Eurodollar futures contract to
hedge this risk. The contract expires December 20, 2009, has a US$ 1 million contract size,
and a discount yield of 7.3 percent.
Johnson will ignore the cash flow implications of marking to market, initial margin requirements,
and any timing mismatch between exchange-traded futures contract cash flows and the interest
payments due in March.
Loan Terms
September 20, 2009 December 20, 2009 March 20, 2010
Borrow $100 million at Pay interest for first three Pay back principal
September 20 LIBOR + 200 months plus interest
basis points (bps) Roll loan over at
September 20 LIBOR = 7% December 20 LIBOR +
200 bps
Loan First loan payment (9%) Second payment
initiated and futures contract expires and principal
9/20/09 12/20/09 3/20/10
a. Formulate Johnson’s September 20 floating-to-fixed-rate strategy using the Eurodollar future
contracts discussed in the text above. Show that this strategy would result in a fixed-rate loan,
assuming an increase in the LIBOR rate to 7.8 percent by December 20, which remains at 7.8
percent through March 20. Show all calculations.
Johnson is considering a 12-month loan as an alternative. This approach will result in two
additional uncertain cash flows, as follows:
Loan First Second Third Fourth
initiated payment (9%) payment payment payment
and
principal
9/20/09 12/20/09 3/20/10 6/20/10 9/20/10
b. Describe the strip hedge that Johnson could use and explain how it hedges the 12-month
loan (specify number of contracts). No calculations are needed.
CFA Guideline Answer
a. The basis point value (BPV) of a Eurodollar futures contract can be found by substituting the
contract specifications into the following money market relationship:
The number of contract, N, can be found by:
N = (BPV spot) / (BPV futures)
OR
N = (value of spot position) / (face value of each futures contract)
OR
N = (value of spot position) / (value of futures position)
Therefore on September 20, Johnson would sell 100 (or 102) December Eurodollar futures
contracts at the 7.3 percent yield. The implied LIBOR rate in December is 7.3 percent as
A rise in the rate to 7.8 percent represents a 50 basis point (bp) increase over the implied
LIBOR rate. For a 50 basis point increase in LIBOR, the cash flow on the short futures position
is:
However, the cash flow on the floating rate liability is:
Combining the cash flow from the hedge with the cash flow from the loan results in a net outflow
of $2,325,000, which translates into an annual rate of 9.3 percent:
= ($2,325,000 x 4) / $100,000,000 = 0.093
This is precisely the implied borrowing rate that Johnson locked in on September 20.
Regardless of the LIBOR rate on December 20, the net cash outflow will be $2,325,000, which
b. In a strip hedge, Johnson would sell 100 December futures (for the March payment), 100
March futures (for the June payment), and 100 June futures (for the September payment). The
objective is to hedge each interest rate payment separately using the appropriate number of
contracts. The problem is the same as in Part A except here three cash flows are subject to
rising rates and a strip of futures is used to hedge this interest rate risk. This problem is
8. Jacob Bower has a liability that:
has a principal balance of $100 million on June 30, 2008,
accrues interest quarterly starting on June 30, 2008,
Rate).
Bower wishes to hedge his remaining interest payments against changes in interest rates.
Bower has correctly calculated that he needs to sell (short) 300 Eurodollar futures contracts to
Initial Position (6/30/08) in
90-Day LIBOR Eurodollar Contracts
Strategy A Strategy B
Contract Month (contracts) (contracts)
September 2008 300 100
December 2008 0 100
March 2009 0 100
a. Explain why strategy B is a more effective hedge than strategy A when the yield curve
undergoes an instantaneous nonparallel shift.
b. Discuss an interest rate scenario in which strategy A would be superior to strategy B.
CFA Guideline Answer
a. Strategy B’s Superiority
Strategy B is a strip hedge that is constructed by selling (shorting) 100 futures contracts
maturing in each of the next three quarters. With the strip hedge in place, each quarter of the
coming year is hedged against shifts in interest rates for that quarter. The reason Strategy B
will be a more effective hedge than Strategy A for Jacob Bower is that Strategy B is likely to
b. Scenario in Which Strategy A is Superior
Strategy A is a stack hedge strategy that initially involves selling (shorting) 300 September
contracts. Strategy A is rarely better than Strategy B as a hedging or risk-reduction strategy.
Only from the perspective of favorable cash flows is Strategy A better than Strategy B. Such
cash flows occur only in certain interest rate scenarios. For example Strategy A will work as
well as Strategy B for Bower’s liability if interest rates (instantaneously) change in parallel
fashion. Another interest rate scenario where Strategy A outperforms Strategy B is one in which
the yield curve rises but with a twist so that futures yields rise more for near expirations than for
MINI CASE: DETROIT MOTORS’ LATIN AMERICAN EXPANSION
It is September 1990 and Detroit Motors of Detroit, Michigan, is considering establishing an
assembly plant in Latin America for a new utility vehicle it has just designed. The cost of the
capital expenditures has been estimated at $65,000,000. There is not much of a sales market
in Latin America, and virtually all output would be exported to the United States for sale.
Nevertheless, an assembly plant in Latin America is attractive for at least two reasons. First,
labor costs are expected to be half what Detroit Motors would have to pay in the United States
to union workers. Since the assembly plant will be a new facility for a newly designed vehicle,
Detroit Motors expects minimal resistance from its U.S. union in establishing the plant in Latin
America. Secondly, the chief financial officer (CFO) of Detroit Motors believes that a debt-for-
equity swap can be arranged with at least one of the Latin American countries that has not been
able to meet its debt service on its sovereign debt with some of the major U.S. banks.
The September 10, 1990, issue of Barron’s indicated the following prices (cents on
the dollar) on Latin American bank debt:
Brazil 21.75
Mexico 43.12
Argentina 14.25
Venezuela 46.25
Chile 70.25
The CFO is not comfortable with the level of political risk in Brazil and Argentina, and has
decided to eliminate them from consideration. After some preliminary discussions with the
central banks of Mexico, Venezuela, and Chile, the CFO has learned that all three countries
would be interested in hearing a detailed presentation about the type of facility Detroit Motors
would construct, how long it would take, the number of locals that would be employed, and the
number of units that would be manufactured per year. Since it is time-consuming to prepare
and make these presentations, the CFO would like to approach the most attractive candidate
first. He has learned that the central bank of Mexico will redeem its debt at 80 percent of face
value in a debt-for-equity swap, Venezuela at 75 percent, and Chile 100 percent. As a first step,
the CFO decides an analysis based purely on financial considerations is necessary to determine
which country looks like the most viable candidate. You are asked to assist in the analysis.
What do you advise?
Suggested Solution for Detroit Motors’ Latin American Expansion
Regardless in which LDC Detroit Motors establishes the new facility, it will need
$65,000,000 in the local currency of the country to build the plant. The analysis involves a
If Detroit Motors builds in Mexico, it will need to purchase $81,250,000 (= $65,000,000/.80)
If Detroit Motors builds in Venezuela, it will need to purchase $86,666,667 (=
$65,000,000/.75) in Venezuelan sovereign debt in order to have $65,000,000 in bolivars after
If Detroit Motors builds in Chile, it will need to purchase $65,000,000 (= $65,000,000/1.00)
Based on the above analysis, Detroit Motors should consider approaching Mexico about
the possibility of a debt-for-equity swap to build an assembly facility. Of course, there are many
APPENDIX 11A QUESTION
1. Explain how Eurocurrency is created.
Answer: The core of the international money market is the Eurocurrency market. A
Eurocurrency is a time deposit of money in an international bank located in a country different
from the country that issues the currency. For example, Eurodollars are deposits of U.S. dollars
in banks located outside of the United States. As an illustration, assume a U.S. Importer
purchases $100 of merchandise from a German Exporter and pays for the purchase by drawing
a $100 check on his U.S. checking account (demand deposit). If the funds are not needed for
the operation of the business, the German Exporter can deposit the $100 in a time deposit in a
