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25-0
Chapter Twenty Five
Derivatives and
Hedging
Corporate
Finance
Ross Westerfield Jaffe
Risk


25
Sixth Edition
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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25-1
Chapter Outline
25.1 Forward Contracts
25.2 Futures Contracts
25.3 Hedging
25.4 Interest Rate Futures Contracts
25.5 Duration Hedging
25.6 Swap Contracts
25.7 Actual Use of Derivatives
25.8 Summary & Conclusions
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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.
– It’s 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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25.2 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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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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Daily Resettlement: An Example
Suppose you want to speculate on a rise in the US$/¥
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 US$1 = ¥140.
The 3-month forward price is US$1=¥150.
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Daily Resettlement: An Example
• Currently US$1 = ¥140 and it appears that the
dollar is strengthening.
• If you enter into a three-month futures contract to
sell ¥ at the rate of US$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:
US$1
US$3,333.33  .04  ¥12,500,000 
¥150
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Daily Resettlement: An Example
If tomorrow, the futures rate closes at US$1 =
¥149, then your position’s value drops.
Your original agreement was to sell
¥12,500,000 and receive US$83,333.33:
US$1
US$83,333.33  ¥12,500,000 
¥150
But ¥12,500,000 is now worth US$83,892.62:
US$1
US$83,892.62  ¥12,500,000 
¥149
You have lost US$559.28 overnight.
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Daily Resettlement: An Example
• The US$559.28 comes out of your US$3,333.33
margin account, leaving US$2,774.05
• This is short of the US$3,355.70 required for a new
position.
US$1
US$3,355.70  .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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Selected Futures Contracts
Contract
Agricultural
Contract Size
Exchange
Corn
Wheat
5,000 bushels
5,000 bushels
Western Barley
Orange Juice
Metals & Petroleum
Gold
Silver
Unleaded gasoline
Financial
British Pound
Japanese Yen
Australian Dollar
20 metric tons
15,000 lbs.
CBOT
CBOT, KBOT,
MPLS
WCE
NYCE
100 troy oz.
5,000 troy oz.
42,000 gal.
COMEX
COMEX
NYME
£62,500
¥12.5 million
A$100,000
IMM
IMM
IMM
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Futures Markets
• The Chicago Mercantile Exchange (CME) is by far
the largest.
• In Canada:
– Montreal Futures Exchange (MFE)
– Winnipeg Commodity Exchange (WCE)
• 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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The Winnipeg Commodity Exchange
Canola Futures
• Expiry cycle: January, March, May, July,
September, November.
• First delivery day is the first business day of the
delivery month.
• Last trading day is seven clear business days prior
to the end of the delivery month.
• Trading hours 9:30 a.m. to 1:15 p.m. CT.
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The Chicago Mercantile Exchange
• Expiry cycle: March, June, September, December.
• Delivery date third 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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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) offers interchangeable contracts.
• There are other markets, but none are close to CME
and SIMEX trading volume.
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National Post Futures Price Quotes
Highest and lowest prices over the lifetime of the contract.
-LifetimeLow
High
Mth
Open
High
-DailyLow
Settle
Prev
Chg Op. int
Highest price that day
Corn (CBT)
5,000 bushels, US cents per contract; 1/4 cent = $12.5 per contract
4,709
201.500 -1.000
199.750
202.500
270.000 198.500 Mar02 202.500
208.250 -1.250 199,466
206.750
209.250
266.500 205.250 May02 209.250
Canadian Govt. Bonds 10 Year (ME)
$100,000, points of 100%, 0.01 = $10 per contract
103.68
105.33 100.71 Mar02 103.65
Opening price
S&P 500 Composite Index (CME)
250 × index points; 0.10 pt. = $25 per contract
1,705.50 950.30 June02 1,148.50 1,168.50
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Closing price
103.35
103.19
-0.24
12,448
Daily Change
1,148.50
1,165.00 +13.50 171,082
Lowest price that day
Number of open contracts
Expiry month
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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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25.3 Hedging
• Two counterparties with offsetting risks can
eliminate risk.
– For example, if a wheat farmer and a flour mill operator
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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Hedging and Speculating Example
You speculate that copper will go up in price, so you
go long 10 copper contracts for delivery in three
months. A contract is 25,000 pounds in cents per
pound and is at US$0.70 per pound or US$17,500
per contract.
If futures prices rise by 5 cents, you will gain:
Gain = 25,000 × .05 × 10 = US$12,500
If prices decrease by 5 cents, your loss is:
Loss = 25,000 × -.05 × 10 = -US$12,500
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Hedging: How many contacts?
You are a farmer and you will harvest 50,000 bushels
of corn in three months. You want to hedge against a
price decrease. Corn is quoted in U.S. cents per
bushel at 5,000 bushels per contract. It is currently
at 230 cents for a contract three months out and the
spot price is US$2.05.
To hedge you will sell 10 corn futures contracts:
50,000 bushels
 10 contracts
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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25.4 Interest Rate Futures Contracts
•
•
•
•
Pricing of Treasury Bonds
Pricing of Forward Contracts
Futures Contracts
Hedging in Interest Rate Futures
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Pricing of Government of Canada Bonds
Consider a Government of Canada 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 bond under a flat term structure
= PV of face value + PV of coupon payments
F
C
1 
PV 
 1 
T
T 
(1  r )
r  (1  r ) 
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Pricing of Government of Canada 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
PV 



2
3
T
(1  r1 ) (1  r2 ) (1  r3 )
(1  r2T )
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Pricing of Forward Contracts
An N-period forward contract on that Government of
Canada 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.
PV 
Pforward
(1  rN )
N
C
C
C
CF



2
3
(1  rN 1 ) (1  rN  2 ) (1  rN 3 )
(1  rN  2T )T
PV 
(1  rN ) N
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Futures Contracts
• The pricing equation given above will be a good
approximation.
• The only real difference is the daily resettlement.
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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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25.5 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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25.5 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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Duration Formula
PV (C1 ) 1  PV (C2 )  2    PV (CT )  T
D
PV
N
Ct  t

t
(
1

r
)
D  tN1
Ct

t
(
1

r
)
t 1
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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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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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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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25.6 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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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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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 US$10,000,000 to
finance floating-rate eurodollar loans.
– Bank A is considering issuing five-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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An Example of an Interest Rate Swap
• Firm B is a BBB-rated U.S. company. It needs
US$10,000,000 to finance an investment with a
five-year economic life.
– Firm B is considering issuing five-year fixed-rate
eurodollar bonds at 11.75-percent.
– Alternatively, firm B can raise the money by issuing fiveyear floating-rate notes at LIBOR + 0.5-percent.
– Firm B would prefer to borrow at a fixed rate.
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An Example of an Interest Rate Swap
The borrowing opportunities of the two firms are:
COMPANY
Fixed rate
Floating rate
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B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of an Interest Rate Swap
The swap bank makes this
offer to Bank A: You pay
LIBOR – 0.125% per year
on US$10 million for five
years and we will pay you
10.375% on US$10
million for five years
Swap
10.375%
Bank
LIBOR – 0.125%
Bank
A
COMPANY
Fixed rate
Floating rate
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B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of an Interest Rate Swap
0.5% of US$10,000,000 =
US$50,000. That’s quite a
cost savings per year for
five years.
10.375%
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
-10.375% + 10% + (LIBOR –
0.125%) = LIBOR – 0.5% which
is 0.5% better than they can
borrow floating without a swap.
LIBOR – 0.125%
Bank
10%
A
COMPANY
Fixed rate
Floating rate
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B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of an Interest Rate Swap
The swap bank
makes this offer to
company B: You
pay us 10.5% per
year on US$10
million for five
years and we will
pay you LIBOR –
0.25% per year on
US$10 million for
five years.
Fixed rate
Floating rate
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Swap
Bank
10.5%
LIBOR – 0.25%
Company
B
COMPANY
B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of an Interest Rate Swap
Here’s what’s in it for B:
Swap
Bank
10.5%
They can borrow externally at
LIBOR + 0.5 % and have a net
0.5 % of US$10,000,000
= US$50,000 that’s quite
a cost savings per year for
five years.
LIBOR – 0.25%
Company
borrowing position of
10.5 + (LIBOR + 0.5 ) - (LIBOR – 0.25 ) =
11.25% which is 0.5% better than they can borrow
floating.
COMPANY B
BANK A
Fixed rate
Floating rate
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11.75%
10%
LIBOR + .5%
LIBOR
B
LIBOR
+ 0.5%
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An Example of an Interest Rate Swap
The swap bank makes money too.
0.25% of US$10
million = US$25,000
per year for five years.
Swap
10.375%
Bank
10.5%
LIBOR – 0.125%
Bank
LIBOR – 0.24%
LIBOR – 0.125 – [LIBOR – 0.25]= 0.125
Company
10.5 – 10.375 = 0.125
A
B
0.250
COMPANY
Fixed rate
Floating rate
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B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of an Interest Rate Swap
The swap bank makes 0.25%
Swap
10.375%
Bank
10.5%
LIBOR – 0.125%
LIBOR – 0.25%
Bank
Company
A
B
A saves 0.5%
B saves 0.5%
COMPANY
Fixed rate
Floating rate
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B
BANK A
11.75%
10%
LIBOR + .5%
LIBOR
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An Example of a Currency Swap
• Suppose a U.S. MNC wants to finance a £10,000,000
expansion of a British plant.
• They could borrow dollars in the U.S. where they are well
known and exchange dollars for pounds.
– This will give them exchange rate risk: financing a
sterling project with dollars.
• They could borrow pounds in the international bond market,
but pay a premium since they are not as well known abroad.
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An Example of a Currency Swap
• If they can find a British MNC with a mirror-image
financing need they may both benefit from a swap.
• If the spot exchange rate is S0($/£) = US$1.60/£, the U.S.
firm needs to find a British firm wanting to finance dollar
borrowing in the amount of US$16,000,000.
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An Example of a Currency Swap
Consider two firms A and B: firm A is a U.S.-based
multinational and firm B is a U.K.-based multinational.
Both firms wish to finance a project in each other’s country of
the same size. Their borrowing opportunities are given in the
table below.
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US$
£
Company A
8.0%
11.6%
Company B
10.0% 12.0%
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An Example of a Currency Swap
Swap
Bank
US$9.4%
US$8%
£12%
£11%
US$8%
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Firm
Firm
A
B
US$
£
Company A
8.0%
11.6%
Company B
10.0% 12.0%
£12%
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An Example of a Currency Swap
A’s net position is to borrow at £11%
Swap
Bank
US$8%
US$9.4%
£11%
US$8%
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£12%
Firm
Firm
A
B
A saves £.6%
US$
£
Company A
8.0%
11.6%
Company B
10.0% 12.0%
£12%
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25-47
An Example of a Currency Swap
B’s net position is to borrow at US$9.4%
Swap
Bank
US$8%
US$9.4%
£11%
US$8%
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£12%
Firm
Firm
A
B
US$
£
Company A
8.0%
11.6%
Company B
10.0% 12.0%
£12%
B saves $.6%
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An Example of a Currency Swap
The swap bank makes money too:
Swap
Bank
US$8%
£11%
US$8%
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1.4% of US$16 million
financed with 1% of
£10 million per year for
five years.
US$9.4%
£12%
Firm
Firm £12%
At S0($/£) = $1.60/£, that
is a gain of US$124,000
A
B
per year for 5 years.
The swap bank
US$
£
faces exchange rate
Company A 8.0% 11.6% risk, but maybe
Company B 10.0% 12.0% they can lay it off
(in another swap).
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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
present a challenge to financial economists who wish to
observe their use.
• Survey results appear to support the notion of widespread
use of derivatives among:
–
–
–
–
large publicly traded firms,
Canadian multinational companies,
nonregulated companies,
gold and silver, paper and forest, pipelines, and agricultural
companies.
• Foreign currency and interest rate derivatives are the most
frequently used.
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© 2003 McGraw–Hill Ryerson Limited
25-54
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.
McGraw-Hill Ryerson
© 2003 McGraw–Hill Ryerson Limited