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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited
Corporate Finance Ross Westerfield Jaffe Sixth Edition
25Chapter Twenty Five
Derivatives and Hedging Risk
Prepared by
Gady JacobyUniversity of Manitoba
and
Sebouh AintablianAmerican University of Beirut
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McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited
Chapter Outline
25.1 Forward Contracts25.2 Futures Contracts25.3 Hedging25.4 Interest Rate Futures Contracts25.5 Duration Hedging25.6 Swap Contracts25.7 Actual Use of Derivatives25.8 Summary & Conclusions
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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).
Currently US$1 = ¥140.
Currency per U.S. $ equivalent U.S. $
Wed Tue Wed TueJapan (yen) 0.007142857 0.007194245 140 1391-month forward 0.006993007 0.007042254 143 1423-months forward 0.006666667 0.006711409 150 1496-months forward 0.00625 0.006289308 160 159
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:
¥150
US$10¥12,500,00.04 33 US$3,333.
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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:
¥149
US$10¥12,500,0062.892,83$US
You have lost US$559.28 overnight.
But ¥12,500,000 is now worth US$83,892.62:
¥150
US$10¥12,500,00 .33 US$83,333
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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.
¥149
US$10¥12,500,00.04 0US$3,355.7
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 Contract Size ExchangeAgricultural
Corn 5,000 bushels CBOTWheat 5,000 bushels CBOT, KBOT,
MPLSWestern Barley 20 metric tons WCE
Orange Juice 15,000 lbs. NYCEMetals & Petroleum
Gold 100 troy oz. COMEXSilver 5,000 troy oz. COMEX
Unleaded gasoline 42,000 gal. NYMEFinancial
British Pound £62,500 IMMJapanese Yen ¥12.5 million IMM
Australian Dollar A$100,000 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
PrevHigh Low Mth Open High Low Settle Chg Op. int
Corn (CBT)5,000 bushels, US cents per contract; 1/4 cent = $12.5 per contract
270.000 198.500 Mar02 202.500 202.500 199.750 201.500 -1.000 4,709266.500 205.250 May02 209.250 209.250 206.750 208.250 -1.250 199,466
Canadian Govt. Bonds 10 Year (ME)$100,000, points of 100%, 0.01 = $10 per contract
105.33 100.71 Mar02 103.65 103.68 103.35 103.19 -0.24 12,448
S&P 500 Composite Index (CME)250 × index points; 0.10 pt. = $25 per contract1,705.50 950.30 June02 1,148.50 1,168.50 1,148.50 1,165.00 +13.50 171,082
-Lifetime- -Daily-
Expiry month
Opening price
Highest price that day
Lowest price that day
Closing price
Daily Change
Highest and lowest prices over the lifetime of the contract.
Number of open contracts
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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:
Now you can quit worrying about the price of corn and get back to worrying about the weather.
contracts 10contractper bushels 000,5
bushels 000,50
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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
TT rr
C
r
FPV
)1(
11
)1(
Value of the bond under a flat term structure= PV of face value + PV of coupon payments
C…
0 1 2 3 2T
C FC C
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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
TTr
FC
r
C
r
C
r
CPV
)1()1()1()1( 23
32
21
= PV of face value + PV of coupon payments
C…
0 1 2 3 2T
C FC C
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Pricing of Forward ContractsAn N-period forward contract on that Government of
Canada Bond
C…
0 N N+1 N+2 N+3 N+2T
C FC CforwardP
Can be valued as the present value of the forward price.
NN
TTNNNN
r
rFC
rC
rC
rC
PV)1(
)1()1()1()1( 23
32
21
NN
forward
r
PPV
)1(
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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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• 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
25.5 Duration Hedging
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Duration Formula
N
tt
t
N
tt
t
T
r
Cr
tC
D
PV
TCPVCPVCPVD
1
1
21
)1(
)1(
)(2)(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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Discount Present Years x PVYears Cash flow factor value / Bond price
0.5 $40.00 0.96154 $38.46 0.01921 $40.00 0.92456 $36.98 0.0370
1.5 $40.00 0.88900 $35.56 0.05332 $40.00 0.85480 $34.19 0.0684
2.5 $40.00 0.82193 $32.88 0.08223 $1,040.00 0.79031 $821.93 2.4658
$1,000.00 2.7259 yearsBond price Bond duration
Calculating 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 five-year 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 B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
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An Example of an Interest Rate Swap
Bank
A
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
COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
Swap
Bank
LIBOR – 0.125%
10.375%
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COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
An Example of an Interest Rate Swap
Here’s what’s in it for Bank A: They can borrow externally at 10% fixed and have a net borrowing position of
-10.375% + 10% + (LIBOR – 0.125%) = LIBOR – 0.5% which is 0.5% better than they can borrow floating without a swap. 10%
0.5% of US$10,000,000 = US$50,000. That’s quite a cost savings per year for five years.
Swap
Bank
LIBOR – 0.125%
10.375%
Bank
A
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An Example of an Interest Rate Swap
Company
B
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.
Swap
Bank10.5%
LIBOR – 0.25%
COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
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COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
An Example of an Interest Rate Swap
They can borrow externally at
LIBOR + 0.5 % and have a net
borrowing position of
10.5 + (LIBOR + 0.5 ) - (LIBOR – 0.25 ) = 11.25% which is 0.5% better than they can borrow floating.
LIBOR + 0.5%
Here’s what’s in it for B:0.5 % of US$10,000,000 = US$50,000 that’s quite
a cost savings per year for five years.
Swap
Bank
Company
B
10.5%
LIBOR – 0.25%
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An Example of an Interest Rate Swap
The swap bank makes money too. 0.25% of US$10 million = US$25,000
per year for five years.
LIBOR – 0.125 – [LIBOR – 0.25]= 0.125
10.5 – 10.375 = 0.125
0.250
Swap
Bank
Company
B
10.5%
LIBOR – 0.24%LIBOR – 0.125%
10.375%
Bank
A
COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
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An Example of an Interest Rate Swap
Swap
Bank
Company
B
10.5%
LIBOR – 0.25%LIBOR – 0.125%
10.375%
Bank
A
B saves 0.5%A saves 0.5%
The swap bank makes 0.25%
COMPANY B BANK A
Fixed rate 11.75% 10%
Floating rate LIBOR + .5% LIBOR
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An Example of a Currency Swap
• Suppose a U.S. MNC wants to finance a £10,000,000 expansion of a British plant.
• They could borrow dollars in the U.S. where they are well known and exchange dollars for pounds.
– This will give them exchange rate risk: financing a sterling project with dollars.
• They could borrow pounds in the international bond market, but pay a premium since they are not as well known abroad.
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An Example of a Currency Swap
• If they can find a British MNC with a mirror-image financing need they may both benefit from a swap.
• If the spot exchange rate is S0($/£) = US$1.60/£, the U.S. firm needs to find a British firm wanting to finance dollar borrowing in the amount of US$16,000,000.
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An Example of a Currency Swap
Consider two firms A and B: firm A is a U.S.-based multinational and firm B is a U.K.-based multinational.
Both firms wish to finance a project in each other’s country of the same size. Their borrowing opportunities are given in the table below.
US$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
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US$9.4%
An Example of a Currency Swap
US$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Firm
B
US$8% £12%
Swap
Bank
Firm
A
£11%
US$8%
£12%
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An Example of a Currency Swap
US$8% £12%
US$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Firm
B
Swap
Bank
Firm
A
£11%
US$8% US$9.4%
£12%
A’s net position is to borrow at £11%
A saves £.6%
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An Example of a Currency Swap
US$8% £12%
US$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Firm
B
Swap
Bank
Firm
A
£11%
US$8% US$9.4%
£12%
B’s net position is to borrow at US$9.4%
B saves $.6%
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An Example of a Currency Swap
US$8% £12%
US$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Firm
B
The swap bank makes money too:
At S0($/£) = $1.60/£, that is a gain of US$124,000
per year for 5 years. The swap bank faces exchange rate risk, but maybe they can lay it off (in another swap).
1.4% of US$16 million financed with 1% of
£10 million per year for five years.
Swap
Bank
Firm
A
£11%
US$8% US$9.4%
£12%
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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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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.