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25-0
CHAPTER
25
Derivatives
and Hedging Risk
McGraw-Hill/Irwin
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© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-1
Chapter Outline
25.1
25.2
25.3
25.4
25.5
25.6
25.7
25.8
McGraw-Hill/Irwin
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Forward Contracts
Futures Contracts
Hedging
Interest Rate Futures Contracts
Duration Hedging
Swap Contracts
Actual Use of Derivatives
Summary & Conclusions
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-2
25.1 Forward Contracts
A forward contract specifies that a certain
commodity will be exchanged for another
at a specified time in the future at prices
specified today.
Its not an option: both parties are expected to hold up
their end of the deal.
If you have ever ordered a textbook that was not in
stock, you have entered into a forward contract.
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25-3
25.2 Futures Contracts: Preliminaries
A futures contract is like a forward contract:
It specifies that a certain commodity will be
exchanged for another at a specified time in the future
at prices specified today.
A futures contract is different from a
forward:
Futures are standardized contracts trading on
organized exchanges with daily resettlement
(“marking to market”) through a clearinghouse.
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25-4
Futures Contracts: Preliminaries
Standardizing Features:
Contract Size
Delivery Month
Daily resettlement
Minimizes the chance of default
Initial Margin
About 4% of contract value, cash or T-bills held in a
street name at your brokerage.
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25-5
Daily Resettlement: An Example
Suppose you want to speculate on a rise in the $/¥ exchange
rate (specifically you think that the dollar will appreciate).
Japan (yen)
1-month forward
3-months forward
6-months forward
U.S. $ equivalent
Wed
Tue
0.007142857 0.007194245
0.006993007 0.007042254
0.006666667 0.006711409
0.00625 0.006289308
Currency per
U.S. $
Wed
Tue
140
139
143
142
150
149
160
159
Currently $1 = ¥140.
The 3-month forward price is $1=¥150.
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25-6
Daily Resettlement: An Example
Currently $1 = ¥140 and it appears that the dollar is
strengthening.
If you enter into a 3-month futures contract to sell ¥ at
the rate of $1 = ¥150 you will make money if the yen
depreciates. The contract size is ¥12,500,000
Your initial margin is 4% of the contract value:
$3,333.33 = 0.04 × ¥12,500,000 ×
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$1
¥150
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-7
Daily Resettlement: An Example
If tomorrow, the futures rate closes at $1 = ¥149, then your position’s
value drops.
Your original agreement was to sell ¥12,500,000 and receive
$83,333.33:
$1
$83,333.33 = ¥12,500,000 ×
¥150
But ¥12,500,000 is now worth $83,892.62:
$83,892.62 = ¥12,500,000 ×
$1
¥149
You have lost $559.28 overnight.
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25-8
Daily Resettlement: An Example
The $559.28 comes out of your $3,333.33 margin
account, leaving $2,774.05
This is short of the $3,355.70 required for a new
position.
$1
$3,355.70 = 0.04 × ¥12,500,000 ×
¥149
Your broker will let you slide until you run through
your maintenance margin. Then you must post
additional funds or your position will be closed out.
This is usually done with a reversing trade.
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25-9
Selected Futures Contracts
Contract
Agricultural
Contract Size
Exchange
Corn
Wheat
Cocoa
OJ
Metals & Petroleum
Copper
Gold
Unleaded gasoline
Financial
British Pound
Japanese Yen
Eurodollar
5,000 bushels
5,000 bushels
10 metric tons
15,000 lbs.
Chicago BOT
Chicago & KC
CSCE
CTN
McGraw-Hill/Irwin
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25,000 lbs.
100 troy oz.
42,000 gal.
CMX
CMX
NYM
£62,500
¥12.5 million
$1 million
IMM
IMM
LIFFE
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-10
Futures Markets
The Chicago Mercantile Exchange (CME)
is by far the largest.
Others include:
The Philadelphia Board of Trade (PBOT)
The MidAmerica Commodities Exchange
The Tokyo International Financial Futures Exchange
The London International Financial Futures
Exchange
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25-11
The Chicago Mercantile Exchange
Expiry cycle: March, June, September,
December.
Delivery date 3rd Wednesday of delivery
month.
Last trading day is the second business day
preceding the delivery day.
CME hours 7:20 a.m. to 2:00 p.m. CST.
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25-12
CME After Hours
Extended-hours trading on GLOBEX runs from
2:30 p.m. to 4:00 p.m dinner break and then back
at it from 6:00 p.m. to 6:00 a.m. CST.
Singapore International Monetary Exchange
(SIMEX) offer interchangeable contracts.
There’s other markets, but none are close to
CME and SIMEX trading volume.
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25-13
Wall Street Journal Futures Price Quotes
Highest price that day
Open
High
Low
Settle
Change
Lifetime
High
Low
Open
Interest
Highest and lowest prices over the lifetime of the contract.
July
Sept
Dec
Corn (CBT) 5,000 bu.; cents per bu.
179
180
178¼
178½
-1½
186
186½
184
186
-¾
196
197
194
196½
-¼
Sept
Dec
TREASURY BONDS (CBT) - $1,000,000; pts. 32nds of 100%
117-05 117-21 116-27 117-05
+5
131-06 111-15 647,560
116-19 117-05 116-12 116-21
+5
128-28 111-06
13,857
Opening price
Sept
Dec
Closing price
312
280
291¼
177
184
194
2,837
104,900
175,187
Daily Change
DJ INDUSTRIAL AVERAGE (CBOT) - $10 times average
11200
11285 11145
11241
-17
11324
7875
11287
11385 11255
11349
-17
11430
7987
18,530
1,599
Lowest price that day
Number of open contracts
Expiry month
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25-14
Basic Currency Futures Relationships
Open Interest refers to the number of contracts
outstanding for a particular delivery month.
Open interest is a good proxy for demand for a
contract.
Some refer to open interest as the depth of the
market. The breadth of the market would be how
many different contracts (expiry month,
currency) are outstanding.
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25-15
25.3 Hedging
Two counterparties with offsetting risks can
eliminate risk.
For example, if a wheat farmer and a flour mill enter into a
forward contract, they can eliminate the risk each other faces
regarding the future price of wheat.
Hedgers can also transfer price risk to
speculators and speculators absorb price risk
from hedgers.
Speculating: Long vs. Short
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25-16
Hedging and Speculating Example
You speculate that copper will go up in price, so you go
long 10 copper contracts for delivery in 3 months. A
contract is 25,000 pounds in cents per pound and is at
$0.70 per pound or $17,500 per contract.
If futures prices rise by 5 cents, you will gain:
Gain = 25,000 × .05 × 10 = $12,500
If prices decrease by 5 cents, your loss is:
Loss = 25,000 ×( –.05) × 10 = –$12,500
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25-17
Hedging: How many contacts?
You are a farmer and you will harvest 50,000 bushels of
corn in 3 months. You want to hedge against a price
decrease. Corn is quoted in cents per bushel at 5,000
bushels per contract. It is currently at $2.30 cents for a
contract 3 months out and the spot price is $2.05.
To hedge you will sell 10 corn futures contracts:
10 contracts =
50,000 bushels
5,000 bushels per contract
Now you can quit worrying about the price of corn
and get back to worrying about the weather.
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25-18
25.4 Interest Rate Futures Contracts
Pricing of Treasury Bonds
Pricing of Forward Contracts
Futures Contracts
Hedging in Interest Rate Futures
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25-19
Pricing of Treasury Bonds
Consider a Treasury bond that pays a semiannual coupon of
$C for the next T years:
The yield to maturity is r
0
C
C
C
1
2
3
…
C +F
2T
Value of the T-bond under a flat term structure
= PV of face value + PV of coupon payments
F
C
+
PV =
T
+
(1 r )
r
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
1 
1 - + T 
 (1 r ) 
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25-20
Pricing of Treasury Bonds
If the term structure of interest rates is not flat, then we need to
discount the payments at different rates depending upon maturity
0
C
C
C
1
2
3
…
C +F
2T
= PV of face value + PV of coupon payments
+
C
C
C
C
F
L
+
+
+
+
PV =
2
3
T
+
+
+
+
(1 r1 ) (1 r2 )
(1 r3 )
(1 r2T )
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25-21
Pricing of Forward Contracts
An N-period forward contract on that T-Bond
- Pforward C
0
N
N+1
C
C
N+2 N+3
…
C +F
N+2T
Can be valued as the present value of the forward price.
Pforward
PV =
(1 + rN )N
C
C
C
C +F
L
+
+
+ +
2
3
(1 + rN +1 ) (1 + rN +2 ) (1 + rN +3 )
(1 + rN +2T )T
PV =
(1 + rN )N
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25-22
Pricing of Forward Contracts: Example
Find the value of a 5-year forward contract on a 20-year T-bond.
The coupon rate is 6 percent per annum and payments are made
semiannually on a par value of $1,000.
40 = 20 × 2
The Yield to Maturity is 5
percent.
I/Y
5
PV
–1,125.51
First, set your calculator to 2
payments per year.
N
PMT
FV
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30 =
1,000
1,000 × .06
2
Then enter what you know
and solve for the value of a
20-year Treasury bond at the
maturity of the forward
contract.
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-23
Pricing of Forward Contracts: Example
First, set your calculator to 1 payment per year.
Then, use the cash flow menu:
CF0
0
I
CF1
0
NPV
F1
5
CF2
F2
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5
881.86
–1,125.51
1
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-24
Pricing of Futures Contracts
The pricing equation given above will be a
good approximation.
The only real difference is the daily
resettlement.
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25-25
Hedging in Interest Rate Futures
A mortgage lender who has agreed to loan
money in the future at prices set today can hedge
by selling those mortgages forward.
It may be difficult to find a counterparty in the
forward who wants the precise mix of risk,
maturity, and size.
It’s likely to be easier and cheaper to use interest
rate futures contracts however.
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25-26
25.5 Duration Hedging
As an alternative to hedging with futures or
forwards, one can hedge by matching the
interest rate risk of assets with the interest
rate risk of liabilities.
Duration is the key to measuring interest
rate risk.
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25-27
25.5 Duration Hedging
Duration measures the combined effect of
maturity, coupon rate, and YTM on bond’s
price sensitivity
Measure of the bond’s effective maturity
Measure of the average life of the security
Weighted average maturity of the bond’s cash
flows
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25-28
Duration Formula
PV (C1 ) 1 + PV (C2 )  2 + L + PV (CT ) T
D=
PV
N
Ct t

t
+
(
1
r
)
t =1
=
D N
Ct

t
+
t =1 (1 r )
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25-29
Calculating Duration
Calculate the duration of a three-year bond
that pays a semi-annual coupon of $40, has a
$1,000 par value when the YTM is 8%
semiannually?
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25-30
Calculating Duration
Years
Discount
Cash flow factor
0.5
$40.00
1
$40.00
1.5
$40.00
2
$40.00
2.5
$40.00
3 $1,040.00
0.96154
0.92456
0.88900
0.85480
0.82193
0.79031
Present Years x PV
value / Bond price
$38.46
0.0192
$36.98
0.0370
$35.56
0.0533
$34.19
0.0684
$32.88
0.0822
$821.93
2.4658
$1,000.00
2.7259 years
Bond price Bond duration
Duration is expressed in units of time; usually years.
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25-31
Duration
The key to bond portfolio management
Properties:
Longer maturity, longer duration
Duration increases at a decreasing rate
Higher coupon, shorter duration
Higher yield, shorter duration
Zero coupon bond: duration = maturity
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25-32
25.6 Swaps Contracts: 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
“Plain vanilla” fixed-for-floating swaps are often just called interest
rate swaps.
Cross-Currency interest rate swap
This is often called a currency swap; fixed for fixed rate debt service in
two (or more) currencies.
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25-33
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.
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.
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25-34
An Example of an Interest Rate Swap
Consider this example of a “plain vanilla” interest rate
swap.
Bank A is a AAA-rated international bank located in the
U.K. and wishes to raise $10,000,000 to finance
floating-rate Eurodollar loans.
Bank A is considering issuing 5-year fixed-rate Eurodollar bonds at
10 percent.
It would make more sense to for the bank to issue floating-rate notes
at LIBOR to finance floating-rate Eurodollar loans.
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25-35
An Example of an Interest Rate Swap
Firm B is a BBB-rated U.S. company. It
needs $10,000,000 to finance an investment
with a five-year economic life.
Firm B is considering issuing 5-year fixed-rate
Eurodollar bonds at 11.75 percent.
Alternatively, firm B can raise the money by issuing
5-year floating-rate notes at LIBOR + ½ percent.
Firm B would prefer to borrow at a fixed rate.
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25-36
An Example of an Interest Rate Swap
The borrowing opportunities of the two firms
are:
COM PANY
F ix ed ra te
F lo a tin g ra te
McGraw-Hill/Irwin
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B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-37
An Example of an Interest Rate Swap
The swap bank makes
this offer to Bank A: You
pay LIBOR – 1/8 % per
year on $10 million for 5
years and we will pay
you 10 3/8% on $10
million for 5 years
Swap
10 3/8%
Bank
LIBOR – 1/8%
Bank
A
COM PANY
F ix e d ra te
F lo a tin g ra te
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B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-38
An Example of an Interest Rate Swap
½% of $10,000,000 =
$50,000. That’s quite
a cost savings per year
10 3/8%
for 5 years.
Here’s what’s in it for Bank A:
They can borrow externally at
10% fixed and have a net
borrowing position of
Swap
Bank
-10 3/8 + 10 + (LIBOR – 1/8) =
LIBOR – 1/8%
LIBOR – ½ % which is ½ %
better than they can borrow
floating without a swap.
Bank
10%
A
COM PANY
F ix e d ra te
F lo a tin g ra te
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B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-39
An Example of an Interest Rate Swap
The swap bank
makes this offer to
company B: You
pay us 10½% per
year on $10 million
for 5 years and we
will pay you
LIBOR – ¼ % per
year on $10 million
for 5 years.
F ix e d ra te
F lo a tin g ra te
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Swap
Bank
10 ½%
LIBOR – ¼%
Company
B
COM PANY
B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
© 2005 The McGraw-Hill Companies, Inc. All Rights Reserved.
25-40
An Example of an Interest Rate Swap
Here’s what’s in it for B:
Swap
½ % of $10,000,000 =
$50,000 that’s quite a cost
savings per year for 5
years.
Bank
10 ½%
They can borrow externally at
LIBOR + ½ % and have a net
LIBOR – ¼%
Company
borrowing position of
B
10½ + (LIBOR + ½ ) - (LIBOR - ¼ ) = 11.25%
which is ½% better than they can borrow floating.
COM PANY
F ix e d ra te
F lo a tin g ra te
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B
LIBOR
+ ½%
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-41
An Example of an Interest Rate Swap
The swap bank makes money too.
¼% of $10 million
= $25,000 per year
for 5 years.
Swap
10 3/8%
Bank
10 ½%
LIBOR – 1/8%
Bank
LIBOR – ¼%
LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8
A
10 ½ - 10 3/8 = 1/8
Company
B
¼
COM PANY
F ix e d ra te
F lo a tin g ra te
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B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-42
An Example of an Interest Rate Swap
The swap bank makes ¼%
Swap
10 3/8%
Bank
10 ½%
LIBOR – 1/8%
LIBOR – ¼%
Bank
Company
A
B
A saves ½%
B saves ½%
COM PANY
F ix e d ra te
F lo a tin g ra te
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B
BANK A
1 1 .7 5 %
10%
L IB O R + .5 %
L IB O R
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25-43
An Example of a Currency Swap
Suppose a U.S. MNC wants to finance a £10,000,000
expansion of a British plant.
They could borrow dollars in the U.S. where they are
well known and exchange for dollars for pounds.
This will give them exchange rate risk: financing a sterling
project with dollars.
They could borrow pounds in the international bond
market, but pay a premium since they are not as well
known abroad.
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25-44
An Example of a Currency Swap
If they can find a British MNC with a mirrorimage financing need they may both benefit from
a swap.
If the spot exchange rate is S0($/£) = $1.60/£, the
U.S. firm needs to find a British firm wanting to
finance dollar borrowing in the amount of
$16,000,000.
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25-45
An Example of a Currency Swap
Consider two firms A and B: firm A is a U.S.–based
multinational and firm B is a U.K.–based multinational.
Both firms wish to finance a project in each other’s
country of the same size. Their borrowing opportunities
are given in the table below.
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$
£
Com pany A
8 .0 %
1 1 .6 %
Com pany B
1 0 .0 %
1 2 .0 %
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25-46
An Example of a Currency Swap
Swap
Bank
$8%
$9.4%
£11%
$8%
£12%
Firm
Firm
A
B
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$
£
Com pany A
8 .0 %
1 1 .6 %
Com pany B
1 0 .0 %
1 2 .0 %
£12%
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25-47
An Example of a Currency Swap
A’s net position is to borrow at £11%
Swap
Bank
$8%
$9.4%
£11%
$8%
£12%
Firm
Firm
A
B
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A saves £.6%
$
£
Com pany A
8 .0 %
1 1 .6 %
Com pany B
1 0 .0 %
1 2 .0 %
£12%
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25-48
An Example of a Currency Swap
B’s net position is to borrow at $9.4%
Swap
Bank
$8%
$9.4%
£11%
$8%
£12%
Firm
Firm
A
B
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$
£
Com pany A
8 .0 %
1 1 .6 %
Com pany B
1 0 .0 %
1 2 .0 %
£12%
B saves $.6%
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25-49
An Example of a Currency Swap
The swap bank makes money too:
Swap
Bank
$8%
£11%
$8%
1.4% of $16 million
financed with 1% of
£10 million per year
for 5 years.
$9.4%
£12%
Firm
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Firm £12%
At S0($/£) = $1.60/£, that
is a gain of $64,000 per
A
B
year for 5 years.
The swap bank faces
$
£
exchange rate risk, but
8 .0 %
1 1 .6 % maybe they can lay it
Com pany A
1 0 .0 % 1 2 .0 % off (in another swap).
Com pany B
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25-50
Variations of Basic Swaps
Currency Swaps
fixed for fixed
fixed for floating
floating for floating
amortizing
Interest Rate Swaps
zero-for floating
floating for floating
Exotica
For a swap to be possible, two humans must like the idea. Beyond that,
creativity is the only limit.
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Risks of Interest Rate and Currency Swaps
Interest Rate 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.
Basis Risk
If the floating rates of the two counterparties are not pegged to
the same index.
Exchange Rate Risk
In the example of a currency swap given earlier, the swap bank
would be worse off if the pound appreciated.
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Risks of Interest Rate and Currency Swaps
Credit 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.
Mismatch Risk
It’s hard to find a counterparty that wants to borrow the right
amount of money for the right amount of time.
Sovereign Risk
The risk that a country will impose exchange rate restrictions
that will interfere with performance on the swap.
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Pricing a Swap
A swap is a derivative security so it can be
priced in terms of the underlying assets:
How to:
Plain vanilla fixed for floating swap gets valued just
like a bond.
Currency swap gets valued just like a nest of currency
futures.
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25.7 Actual Use of Derivatives
Because derivatives don’t appear on the balance
sheet, they are present a challenge to financial
economists who which to observe their use.
Survey results appear to support the notion of
widespread use of derivatives among large
publicly traded firms.
Foreign currency and interest rate derivatives are
the most frequently used.
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25.8 Summary & Conclusions
This chapter shows a number of hedging
strategies.
A short hedge involves an agreement to sell
the underlying asset in the future.
A long hedge involves an agreement to buy
the underlying asset in the future.
Swaps can also be used to hedge; a swap
can be viewed as a portfolio of futures with
different maturities.
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