INTERNATIONAL
FINANCIAL
MANAGEMENT
Fifth Edition
EUN / RESNICK
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Rate and
Currency Swaps
14
Chapter Fourteen
Chapter Objective:
This chapter discusses currency and interest rate
swaps, which are relatively new instruments for
hedging long-term interest rate risk and foreign
exchange risk.
14-1
Chapter Outline









Types of Swaps
Size of the Swap Market
The Swap Bank
Swap Market Quotations
Interest Rate Swaps
Currency Swaps
Variations of Basic Interest Rate and Currency Swaps
Risks of Interest Rate and Currency Swaps
Is the Swap Market Efficient?
14-2
Definitions


In a swap, two counterparties agree to a
contractual arrangement wherein they agree to
exchange cash flows at periodic intervals.
There are two types of interest rate swaps:

Single currency interest rate swap


Cross-Currency interest rate swap

14-3
“Plain vanilla” fixed-for-floating swaps are often just called
interest rate swaps.
This is often called a currency swap; fixed for fixed rate debt
service in two (or more) currencies.
Size of the Swap Market

In 2007 the notational principal of:
Interest rate swaps was $271.9 trillion USD.
Currency swaps was $12 trillion USD

The most popular currencies are:





14-4
U.S. dollar
Japanese yen
Euro
Swiss franc
British pound sterling
The Swap Bank
A swap bank is a generic term to describe
a financial institution that facilitates
swaps between counterparties.
 The swap bank can serve as either a
broker or a dealer.



14-5
As a broker, the swap bank matches counterparties but
does not assume any of the risks of the swap.
As a dealer, the swap bank stands ready to accept either
side of a currency swap, and then later lay off their risk,
or match it with a counterparty.
Swap Market Quotations


Swap banks will tailor the terms of interest rate
and currency swaps to customers’ needs
They also make a market in “plain vanilla” swaps
and provide quotes for these. Since the swap
banks are dealers for these swaps, there is a bidask spread.
14-6
The convention is to quote against U.S. dollar LIBOR.
Interest Rate Swap Quotations
Euro-€
Bid
Ask
£ Sterling
Swiss franc
Bid
Bid
Ask
Bid
Ask
Ask
U.S. $
1 year
2.34
2.37
5.21
5.22
0.92
0.98
3.54
3.57
2 year
2.62
2.65
5.14
5.18
1.23
1.31
3.90
3.94
3 year
2.86
2.89 3.82–3.85
5.13
5.17
means1.50
the
4 year
3.06
5 year
3.23
6 year
3.38
7 year
3.52
1.58bank4.11
4.13
swap
will pay
3.09 fixed-rate
5.12
5.17
1.73
1.81
4.25
4.28
euro payments
at 3.82%
3.26 against
5.11 receiving
5.16
1.93
2.01
4.37
euro LIBOR
or
it will4.39
3.41 receive
5.11 fixed-rate
5.16
2.10
2.18
4.46
euro payments
at 4.50
3.55 3.85%
5.10 against
5.15 receiving
2.25
2.33
4.55
4.58
euro LIBOR
8 year
3.63
3.66
5.10
5.15
2.37
2.45
4.62
4.66
9 year
3.74
3.77
5.09
5.14
4.48
2.56
4.70
4.72
10 year
3.82
3.85
5.08
5.13
2.56
2.64
4.75
4.79
14-7
Swap Quotations
3.82–3.85 means the swap bank will pay fixed-rate
euro payments at 3.82% against receiving dollar
LIBOR or it will receive fixed-rate euro payments at
3.85% against paying dollar LIBOR
Firm
B
€3.85%
$LIBOR
Swap
Bank
€3.82%
$LIBOR
Firm
A
While most swaps are quoted against “flat” dollar
LIBOR, “off-market” swaps are available where
one party pays LIBOR plus or minus some number.
14-8
Example of an Interest Rate Swap
Consider firms A and B;
each firm wants to borrow
$40 million for 3 years.
Fixed
Floating
A
5%
LIBOR
B
5.50% LIBOR + .20%
Firm A wants finance an interest-rate-sensitive asset and
therefore wants to borrow at a floating rate.
A has good credit and can borrow at LIBOR
Firm B wants finance an interest-rate-insensitive asset and
therefore wants to borrow at a fixed rate.
B has less-than-perfect credit and can borrow at 5.5%
The swap bank quotes 5.1—5.2 against dollar LIBOR for a
3-year swap.
14-9
Example of an Interest Rate Swap
Firm 5.10%
A
LIBOR
Swap
Bank
If Firm A borrows from their bank at 5.0% fixed
and takes up the swap bank on their offer of
5.1—5.2 they can convert their fixed rate 5%
debt into a floating rate debt at LIBOR – 0.10%
Bank
X
14-10
A’s all-in-cost:
= 5.0% + LIBOR – 5.10% = LIBOR – 0.10%
Example of an Interest Rate Swap
Swap
Bank
Firm
B
LIBOR
5.20%
If Firm B borrows floating from their bank at
LIBOR + 0.20% and takes up the swap bank on
their offer of 5.1—5.2 they can convert their
floating rate debt into a fixed rate debt at 5.40%
B’s all-in-cost:
= –LIBOR + LIBOR + 0.20% + 5.20% = 5.40%
14-11
Bank
Y
Example of an Interest Rate Swap
Firm 5.10%
A
LIBOR
Swap
Bank
Firm
B
LIBOR
5.20%
The Swap Bank makes 10 basis points on the deal:
The Swap Bank’s all-in-cost:
= –LIBOR + LIBOR – 5.20% + 5.10% = –0.10%
14-12
Example of an Interest Rate Swap
Firm 5.10%
A
LIBOR
Swap
Bank
Firm
B
LIBOR
5.20%
The notional size is $40 million.
The tenor is for 3 years.
Bank
X
14-13
A earns $40,000 per year on the swap.
B earns $40,000 per year on the swap.
Swap Bank earns $40,000 per year.
Bank
Y
Using a Swap to Transform a Liability

Firm A has transformed a fixed rate liability
into a floater.



A is borrowing at LIBOR – .10%
A savings of 10 bp
Firm B has transformed a floating rate liability
into a fixed rate liability.


14-14
B is borrowing at 5.40%
A savings of 10 bp
What about the Principal?
In our “plain vanilla” interest-only interest
rate swap just given, we did not mention
swapping the Notational Principal.
 It could be the case that firm A exchanged
principal with their lender (Bank X) and
firm B exchanged principal with their
outside lender, Bank Y.

14-15
Cash Flows of an Interest-Only Swap: T = 0
Firm
A
Bank
X
14-16
Swap
Bank
Firm
B
Bank
Y
Cash Flows of an Interest-Only Swap: T = 1
Assume LIBOR = 3%
Firm
A
$2,040,000
$1,200,000
Swap
Bank
Firm
B
$1,200,000
$2,080,000
Swap Bank earns $40,000 per year.
A saves $40,000 per year relative to
borrowing at LIBOR = 3%.
Bank
X
14-17
B saves $40,000 per year relative to
borrowing at 5.5%.
Bank
Y
Cash Flows of an Interest-Only Swap: T = 2
Assume LIBOR = 4%
Firm
A
$2,040,000
$1,600,000
Swap
Bank
Firm
B
$1,600,000
$2,080,000
Swap Bank earns $40,000 per year.
A saves $40,000 per year relative to
borrowing at LIBOR = 4%.
Bank
X
14-18
B saves $40,000 per year relative to
borrowing at 5.5%.
Bank
Y
Cash Flows of an Interest-Only Swap: T = 3
Assume LIBOR = 5%
Firm
A
$2,040,000
$2,000,000
Swap
Bank
Firm
B
$2,000,000
$2,080,000
Swap Bank earns $40,000 per year.
A saves $40,000 per year relative to
borrowing at LIBOR = 4%.
Bank
X
14-19
B saves $40,000 per year relative to
borrowing at 5.5%.
Bank
Y
Example of an Currency Swap
$
€
Firm A is a U.S. MNC and wants to
borrow €40 million for 3 years.
A $7% €6%
Firm B is a French MNC and wants to
B $8% €5%
borrow $60 million for 3 years
Firm A wants finance euro denominated asset in Italy and
therefore wants to borrow euro.
A can borrow euro at 6%
Firm B wants finance a dollar denominated asset and
therefore wants to borrow dollars.
B can borrow dollars at 8%
The current exchange rate is $1.50 = €1.00
14-20
Example of a Currency Swap
 Suppose
that the Swap Bank publishes these quotes.
The convention is to quote against U.S. dollar LIBOR.
Euro-€
Bid Ask
3 year 5.00 5.20
U.S. $
Bid
Ask
7.00
7.20
Firm A wants finance euro-denominated
asset in Italy and wants to borrow euro.
A can borrow euro at 6% or they can
borrow euro at 5.2% by using a
currency swap.
14-21
$
€
A $7%
€6%
B $8%
€5%
Example of a Currency Swap
(The convention is to quote against U.S. dollar LIBOR.)
Euro-€
Bid Ask
5.00 5.20
$
U.S. $
Bid
Ask
7.00
7.20
€
A $7%
€6%
B $8%
€5%
LIBOR
$7.0%
$60m
Firm A then enters in to 2
fixed14-22for floating swaps.
$60m
Suppose that Firm A borrows
$60m at $7%; trades for € at spot.
Firm
A
€40m
Bank
X
$7.0%
€5.2%
LIBOR
FOREX Market
Swap
Bank
Example of a Currency Swap
(The convention is to quote against U.S. dollar LIBOR.)
Euro-€
Bid Ask
5.00 5.20
€
$
U.S. $
Bid
Ask
7.00
7.20
A $7%
€6%
B $8%
€5%
LIBOR
$7.2%
€40m
€5.0%
LIBOR
Firm
B
$60m
Swap
Bank
€40m
€5%
Bank
Y
Suppose that Firm B borrows
€40m at €5%, trades for $.
FOREX Market Firm B then enters in to 2
14-23
fixed for floating swaps.
Example of a Currency Swap
Swap Bank earns 40 bp per year (20bp in $ and 20bp in €).
Firm
A
$7.0%
€5.2%
Swap
Bank
Firm
B
€5.0%
$7.2%
The notional size is $60m.
The tenor is for 3 years.
Bank
X
14-24
Firm A earns 80 bp per year on the swap and
hedges exchange rate risk.
Firm B earns 80 bp per year on the swap
and hedges exchange rate risk.
Bank
Y
Cash Flows of the Swaps: T = 0
Firm
A
Bank
X
14-25
Swap
Bank
Foreign Exchange
Spot Market
Firm
B
Bank
Y
Cash Flows of the Swaps: T = 1
Assume LIBOR = 3%
$1.8m
Firm
A
Bank
X
14-26
$4.2m
€2.08m
$1.8m
$1.8m
Swap
Bank
$4.32m
€2m
$1.8m
Firm
B
Swap bank earns €80,000 + $120,000
or .002×€40m + .002×$60m per year.
Firm A’s all-in-cost
€2.08m or
5.2% of €40m
Firm B’s all-in-cost
$4.32 or
7.2% of $60m
Bank
Y
Cash Flows of the Swaps: T = 2
Assume LIBOR = 4%
$2.4m
Firm
A
Bank
X
14-27
$4.2m
€2.08m
$2.4m
$2.4m
Swap
Bank
$4.32m
€2m
$2.4m
Firm
B
Bank
Y
Cash Flows of the Swaps: T = 3
Assume LIBOR = 5%
$3m
Firm
A
$4.2m
€2.08m
$3m
$3m
Swap
Bank
$4.32m
€2m
$3m
Bank
X
14-28
Firm
B
Bank
Y
Foreign Exchange
Forward Market
Example of a Direct Currency Swap
If firms A and B knew and trusted each
other, they could theoretically cut out the
swap bank:
$7.0%
Firm
Firm
A
Bank
X
14-29
€5.0%
$
€
A $7%
€6%
B $8%
€5%
B
The problem is of course that the swap
bank is acting as a broker (or even a
dealer) and providing a service—that’s
why they get paid.
Signing 1 contract is less work than 4.
Bank
Y
Equivalency of Currency Swap
A
Debt Service Obligations

$
€
$7%
€6%
B $8%
€5%
We can assume that IRP holds between the €5%
euro rate and the $7% dollar rate.


This is reasonable since these rates are, respectively, the
best rates available for each counterparty who is well
known in its national market.
(1 + i$)t
According to IRP: St($/€) = S0($/€) ×
(1 + i€)t
$1.50×(1.07)1 $1.5286
S1($/€) = €1.00×(1.05)1 = €1.00
14-30
IRR
0
1
2
3
7.00%
–$60.00
$4.20
$4.20
$64.20
5.00%
–€40.00
€2.75
€2.70
€40.44
The swap bank could borrow $60m at 7% and use a set of 3
forward contracts to redenominate their bond as a 5% euro
bond.
€1.00
€1.00×(1.05)
–€40m = –$60m×
€2.7477m = $4.20m×
$1.50
$1.50×(1.07)
€1.00×(1.05)2
€2.6963m = $4.20m×
$1.50×(1.07)2
€1.00×(1.05)3
€40.4446m = $64.20m×
$1.50×(1.07)3
14-31
IRR
0
1
2
3
5.00%
–€40.00
€2.00
€2.00
€42.00
7.00%
–$60.00
$3.06
$3.12
$66.67
The swap bank could borrow €40m at 5% and use a set of 3
forward contracts to redenominate their bond as a 7% dollar
bond.
$1.50
$1.50×(1.07)
–$60m = –€40m×
$3.06m = €2m × ×
€1.00
€1.00×(1.05)
$1.50×(1.07)2
$3.12m = €2m ××
€1.00×(1.05)2
$1.50×(1.07)3
$66.67m = €42m×
€1.00×(1.05)3
14-32
Equivalency of Currency Swap Debt
Service Obligations

The ability to hedge with covered interest arbitrage
is where the swap bank found the €5% and $7%
rates
Euro-€
Bid Ask
5.00 5.20
U.S. $
Bid
Ask
7.00
7.20
Competition from other swap banks will keep their
spreads from getting too wide—the theoretical
limit is 200 basis points total. (See QSD on next
14-33
slide.)

The QSD


The Quality Spread Differential represents the
potential gains from the swap that can be shared
between the counterparties and the swap bank.
There is no reason to presume that the gains will
be shared equally.
$
€
The QSD is calculated
as the difference
A
$7%
€6%
B
$8%
€5% between the differences.
QSD
14-34
1%
–
–1%
= 2%
Comparative Advantage
as the Basis for Swaps


A has a comparative advantage in borrowing in
dollars.
B has a comparative advantage in borrowing in
euro.
$
€
14-35
A $7%
€6%
B $8%
€5%
Variations of Basic Currency and
Interest Rate Swaps

Currency Swaps





Interest Rate Swaps



fixed for fixed
fixed for floating
floating for floating
amortizing
zero-for floating
floating for floating
For a swap to be possible, a QSD must exist.
Beyond that, creativity is the only limit.
14-36
Risks of Interest Rate
and Currency Swaps

Interest Rate Risk


Basis Risk


Interest rates might move against the swap bank after it
has only gotten half of a swap on the books, or if it has
an unhedged position.
If the floating rates of the two counterparties are not
pegged to the same index.
Exchange rate Risk

14-37
In the example of a currency swap given earlier, the
swap bank would be worse off if the pound appreciated.
Risks of Interest Rate
and Currency Swaps (continued)

Credit Risk


Mismatch Risk


This is the major risk faced by a swap dealer—the risk
that a counter party will default on its end of the swap.
It’s hard to find a counterparty that wants to borrow the
right amount of money for the right amount of time.
Sovereign Risk

14-38
The risk that a country will impose exchange rate
restrictions that will interfere with performance on the
swap.
Pricing a Swap


A swap is a derivative security so it can be priced
in terms of the underlying assets:
How to:



14-39
Any swap’s value is the difference in the present values
of the payment streams that are incoming and outgoing.
Plain vanilla fixed for floating swaps get valued just like
a pair of bonds.
Currency swap gets valued just like two nests of
currency forward contracts.
Swap Pricing Example
A currency swap has a remaining life of 18 months.
It involves exchanging interest at 14% on £20
million for interest at 10% on $30 million once a
year. The term structure of interest rates is currently
flat in both the US. And the U.K. and if the swap
were negotiated today the interest rates exchanged
would be $8% and £11%. All rates were quoted with
annual compounding. The current exchange rate is
$1.65 = £1. What is the value of the swap to the
party paying dollars?
14-40
Answer
18
6
£2.8m
£2.8m
–$3m
–$3m
Value of the swap to the party paying dollars:
0
£2.8m
£2.8m
$1.65
$8,335,659 = (1.11)½ + (1.11)3/2 × £1
–$5,559,669 = –$3m ½ + –$3m 3/2
(1.08)
(1.08)
$2,775,990
14-41
Swap Market Efficiency


Swaps offer market completeness and that has
accounted for their existence and growth.
Swaps assist in tailoring financing to the type
desired by a particular borrower. Since not all
types of debt instruments are available to all types
of borrowers, both counterparties can benefit (as
well as the swap dealer) through financing that is
more suitable for their asset maturity structures.
14-42
Concluding Remarks



The growth of the swap market has been
astounding.
Swaps are off-the-books transactions.
Swaps have become an important source of
revenue and risk for banks
14-43
End Chapter Fourteen
But here’s a couple of sample problems…
14-44
Sample Interest Rate Swap Problem

A is a credit-worthy firm




B is a less-credit-worthy firm





A can borrow at 8% fixed
A can borrow at flat LIBOR
A prefers to borrow floating
B can borrow at 9% fixed
B can borrow at LIBOR + ½%
B prefers to borrow fixed
Fixed Floating
A 8% LIBOR
B 9% LIBOR + ½
Both firms want a 10-year maturity
Devise a swap that is mutually beneficial for A and B.

14-45
Follow the convention of pricing against “flat” LIBOR.
Step 2: We are to quote the swap against flat LIBOR
Step 4: check our work
Step 3: The QSD = ½
so we have 50 bp to
A’s all-in-cost:
distribute among 3
LIBOR – 0.2
players. Let’s try 20 forLIBOR
LIBOR
B’s all-in-cost:
(Step
2)
A and B,
(Step 2)
8.8%
(this leaves 10 bp
Swap Bank Profit:
for the swap bank)
8.2% 8.3%
10 basis points
(Step 3)
Swap
Bank
A
(Step 1)
8%
Outside
Lender
X
14-46
B
(Step 1)
LIBOR + ½
Step 1: A is better at borrowing fixed; B is better at
borrowing floating so have them borrow externally
according to their comparative advantage
Fixed
Floating
A 8%
LIBOR
B 9%
LIBOR + ½
QSD = 1% –
½%
= ½%
Outside
Lender
Y
Sample Currency Swap Problem

A is an Italian firm



B is an American firm





A can borrow in euro at €5% fixed
A prefers to borrow in dollars but faces $8% cost
B has already borrowed in dollars at $8½%
5 years ago they issued a 15-year bond
B now prefers to borrow in euro but faces €6% cost
Both firms want a 10-year maturity
Devise a feasible swap that eliminates exchange
rate risk for A and B
Step 2: We are to eliminate exchange rate risk for A and B
Step 4: check our work
Step 3: The QSD = ½ so
A’s all-in-cost:
we have 50 bp to distribute
$7.8%
among 3 players. Let’s try
B’s all-in-cost:
$8½%
€5%
20 for A and B,
€5.8%
(Step 2)
(Step 2)
Swap Bank Profit:
10 basis points at
(this leaves 10 bp
$7.8%
€5.8%
current exchange rate
for the swap bank)
(Step 3)
Swap
Bank
A
(Step 1)
B
€5%
Outside
LenderX
(Step 1)
$8½%
Step 1: A is better at borrowing €;
B is better at borrowing $
so have them borrow externally according to their
comparative advantage
Outside
LenderY
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.