25-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield ...

25-1

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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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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• 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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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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• 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

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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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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• 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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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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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



Swap

Bank

LIBOR – 0.125%

10.375%

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COMPANY B BANK A




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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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



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COMPANY B BANK A




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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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



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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



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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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• 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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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%


US$ £


Company B 10.0% 12.0%

Firm

B

US$8% £12%

Swap

Bank

Firm

A

£11%

US$8%

£12%

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US$8% £12%

US$ £


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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US$8% £12%

US$ £


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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US$8% £12%

US$ £


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.

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Transcript of 25-0 McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited Corporate Finance Ross Westerfield ...