Добавил:
Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:

economics_of_money_banking__financial_markets

.pdf
Скачиваний:
179
Добавлен:
10.06.2015
Размер:
27 Мб
Скачать
☆

316 P A R T I I I Financial Institutions

Table 1 Widely Traded Financial Futures Contracts

 

 

 

Open Interest

 

 

 

January 30, 2003

Type of Contract

Contract Size

Exchange*

Reflects March 2003 Futures

Treasury Rate Contracts

 

 

 

Treasury bonds

$100,000

CBT

393,546

Treasury notes

$100,000

CBT

746,015

Five-year Treasury notes

$100,000

CBT

683,499

Two-year Treasury notes

$200,000

CBT

106,184

Thirty-day Fed levels

$5 million

CBT

49,069

Treasury bills

$1 million

CME

292

One-month LIBOR

$3 million

CME

6,389

Municipal Bond Index

$1,000

CBT

2,683

Eurodollar

$4 million

CME

747,691

Euroyen

$100 million

CME

10,765

Sterling

£500,000

LIFFE

159,800

Long Gilt

£100,000

LIFFE

90,093

Three-month Euribor

€€1 million

LIFFE

497,688

Euroswiss franc

SF 1 million

LIFFE

85,366

Ten-year Euronational bonds

€€100,000

EUREX

812,029

Canadian bankerÕs acceptance

C$1 million

ME

64,333

Stock Index Contracts

 

 

 

Standard & PoorÕs 500 Index

$250 index

CME

577,661

Standard & PoorÕs MIDCAP 400

$500 index

CME

13,652

NASDAQ 100

$100 index

CME

71,233

Nikkei 225 Stock Average

$5 index

CME

16,193

Financial TimesÐStock Exchange

 

 

 

100-Share Index

£10 per index point

LIFFE

460,997

Currency Contracts

 

 

 

Yen

12,500,000 yen

CME

90,508

Euro

125,000 euros

CME

102,536

Canadian dollar

100,000 Canadian $

CME

89,651

British pound

100,000 pounds

CME

102,536

Swiss franc

125,000 francs

CME

55,402

Mexican peso

500,000 new pesos

CME

29,774

*Exchange abbreviations: CBT, Chicago Board of Trade; CME, Chicago Mercantile Exchange; LIFFE, London International Financial Futures Exchange; EUREX, European Exchange; ME, Montreal Exchange.

Source: Wall Street Journal, January 31, 2003, p. C21.

The Globalization

of Financial

Futures Markets

Explaining the

Success of

Futures Markets

C H A P T E R 1 3 Financial Derivatives 317

Because American futures exchanges were the first to develop financial futures, they dominated the trading of financial futures in the early 1980s. For example, in 1985, all of the top ten futures contracts were traded on exchanges in the United States. With the rapid growth of financial futures markets and the resulting high profits made by the American exchanges, foreign exchanges saw a profit opportunity and began to enter this business. By the 1990s, Eurodollar contracts traded on the London International Financial Futures Exchange, Japanese government bond contracts and Euroyen contracts traded on the Tokyo Stock Exchange, French government bond contracts traded on the MarchŽ ˆ Terme International de France, and Nikkei 225 contracts traded on the Osaka Securities Exchange all became among the most widely traded futures contracts in the world.

Foreign competition has also spurred knockoffs of the most popular financial futures contracts initially developed in the United States. These contracts traded on foreign exchanges are virtually identical to those traded in the United States and have the advantage that they can be traded when the American exchanges are closed. The movement to 24-hour-a-day trading in financial futures has been further stimulated by the development of the Globex electronic trading system, which allows traders throughout the world to trade futures even when the exchanges are not officially open. Financial futures trading has thus become completely internationalized, and competition between U.S. and foreign exchanges will be intense in the future.

The tremendous success of the financial futures market in Treasury bonds is evident from the fact that the total open interest of Treasury bond contracts was over 393,000 on January 30, 2003, for a total value of over $39 billion (393,000 $100,000). There are several differences between financial futures and forward contracts and in the organization of their markets that help explain why financial futures markets like those for Treasury bonds have been so successful.

Several features of futures contracts were designed to overcome the liquidity problem inherent in forward contracts. The first feature is that, in contrast to forward contracts, the quantities delivered and the delivery dates of futures contracts are standardized, making it more likely that different parties can be matched up in the futures market, thereby increasing the liquidity of the market. In the case of the Treasury bond contract, the quantity delivered is $100,000 face value of bonds, and the delivery dates are set to be the last business day of March, June, September, and December. The second feature is that after the futures contract has been bought or sold, it can be traded (bought or sold) again at any time until the delivery date. In contrast, once a forward contract is agreed on, it typically cannot be traded. The third feature is that in a futures contract, not just one specific type of Treasury bond is deliverable on the delivery date, as in a forward contract. Instead, any Treasury bond that matures in more than 15 years and is not callable for 15 years is eligible for delivery. Allowing continuous trading also increases the liquidity of the futures market, as does the ability to deliver a range of Treasury bonds rather than one specific bond.

Another reason why futures contracts specify that more than one bond is eligible for delivery is to limit the possibility that someone might corner the market and ÒsqueezeÓ traders who have sold contracts. To corner the market, someone buys up all the deliverable securities so that investors with a short position cannot obtain from anyone else the securities that they contractually must deliver on the delivery date. As

318 P A R T I I I

Financial Institutions

a result, the person who has cornered the market can set exorbitant prices for the securities that investors with a short position must buy to fulfill their obligations under the futures contract. The person who has cornered the market makes a fortune, but investors with a short position take a terrific loss. Clearly, the possibility that corners might occur in the market will discourage people from taking a short position and might therefore decrease the size of the market. By allowing many different securities to be delivered, the futures contract makes it harder for anyone to corner the market, because a much larger amount of securities would have to be purchased to establish the corner. Corners are a concern to both regulators and the organized exchanges that design futures contracts.

Trading in the futures market has been organized differently from trading in forward markets to overcome the default risk problems arising in forward contracts. In both types, for every contract, there must be a buyer who is taking a long position and a seller who is taking a short position. However, the buyer and seller of a futures contract make their contract not with each other but with the clearinghouse associated with the futures exchange. This setup means that the buyer of the futures contract does not need to worry about the financial health or trustworthiness of the seller, or vice versa, as in the forward market. As long as the clearinghouse is financially solid, buyers and sellers of futures contracts do not have to worry about default risk.

To make sure that the clearinghouse is financially sound and does not run into financial difficulties that might jeopardize its contracts, buyers or sellers of futures contracts must put an initial deposit, called a margin requirement, of perhaps $2,000 per Treasury bond contract into a margin account kept at their brokerage firm. Futures contracts are then marked to market every day. What this means is that at the end of every trading day, the change in the value of the futures contract is added to or subtracted from the margin account. Suppose that after you buy the Treasury bond contract at a price of 115 on Wednesday morning, its closing price at the end of the day, the settlement price, falls to 114. You now have a loss of 1 point, or $1,000, on the contract, and the seller who sold you the contract has a gain of 1 point, or $1,000. The $1,000 gain is added to the sellerÕs margin account, making a total of $3,000 in that account, and the $1,000 loss is subtracted from your account, so you now only have $1,000 in your account. If the amount in this margin account falls below the maintenance margin requirement (which can be the same as the initial requirement but is usually a little less), the trader is required to add money to the account. For example, if the maintenance margin requirement is also $2,000, you would have to add $1,000 to your account to bring it up to $2,000. Margin requirements and marking to market make it far less likely that a trader will default on a contract, thus protecting the futures exchange from losses.

A final advantage that futures markets have over forward markets is that most futures contracts do not result in delivery of the underlying asset on the expiration date, whereas forward contracts do. A trader who sold a futures contract is allowed to avoid delivery on the expiration date by making an offsetting purchase of a futures contract. Because the simultaneous holding of the long and short positions means that the trader would in effect be delivering the bonds to itself, under the exchange rules the trader is allowed to cancel both contracts. Allowing traders to cancel their contracts in this way lowers the cost of conducting trades in the futures market relative to the forward market in that a futures trader can avoid the costs of physical delivery, which is not so easy with forward contracts.

C H A P T E R 1 3 Financial Derivatives 319

Application

Hedging Foreign Exchange Risk with Forward Contracts

Hedging Foreign Exchange Risk

As we discussed in Chapter 1, foreign exchange rates have been highly volatile in recent years. The large fluctuations in exchange rates subject financial institutions and other businesses to significant foreign exchange risk because they generate substantial gains and losses. Luckily for financial institution managers, the financial derivatives discussed in this chapterÑ forward and financial futures contractsÑcan be used to hedge foreign exchange risk.

To understand how financial institution managers manage foreign exchange risk, letÕs suppose that in January, the First National BankÕs customer Frivolous Luxuries, Inc. is due a payment of 10 million euros in two months for $10 million worth of goods it has just sold in Germany. Frivolous Luxuries is concerned that if the value of the euro falls substantially from its current value of $1, the company might suffer a large loss because the 10 million euro payment will no longer be worth $10 million. So Sam, the CEO of Frivolous Luxuries, calls up his friend Mona, the manager of the First National Bank, and asks her to hedge this foreign exchange risk for his company. LetÕs see how the bank manager does this using forward and financial futures contracts.

Forward markets in foreign exchange have been highly developed by commercial banks and investment banking operations that engage in extensive foreign exchange trading and so are widely used to hedge foreign exchange risk. Mona knows that she can use this market to hedge the foreign exchange risk for Frivolous Luxuries. Such a hedge is quite straightforward for her to execute. Because the payment of euros in two months means that at that time Sam would hold a long position in euros, Mona knows that the basic principle of hedging indicates that she should offset this long position by a short position. Thus, she just enters a forward contract that obligates her to sell 10 million euros two months from now in exchange for dollars at the current forward rate of $1 per euro.4

In two months, when her customer receives the 10 million euros, the forward contract ensures that it is exchanged for dollars at an exchange rate of $1 per euro, thus yielding $10 million. No matter what happens to future exchange rates, Frivolous Luxuries will be guaranteed $10 million for the goods it sold in Germany. Mona calls up her friend Sam to let him know that his company is now protected from any foreign exchange movements, and he thanks her for her help.

4The forward exchange rate will probably differ slightly from the current spot rate of $1 per euro because the interest rates in Germany and the United States may not be equal. In that case, as we will see in Equation 2 in Chapter 19, the future expected exchange rate will not equal the current spot rate and neither will the forward rate. However, since interest differentials have typically been less than 6% at an annual rate (1% bimonthly), the expected appreciation or depreciation of the euro over a two-month period has always been less than 1%. Thus the forward rate is always close to the current spot rate, and so our assumption in the example that the forward rate and the spot rate are the same is a reasonable one.

320 P A R T I I I

Hedging Foreign Exchange Risk with Futures Contracts

Financial Institutions

As an alternative, Mona could have used the currency futures market to hedge the foreign exchange risk. In this case, she would see that the Chicago Mercantile Exchange has a euro contract with a contract amount of 125,000 euros and a price of $1 per euro. To do the hedge, Mona must sell euros as with the forward contract, to the tune of 10 million euros of the March futures. How many of the Chicago Mercantile Exchange March euro contracts must Mona sell in order to hedge the 10 million euro payment due in March?

Using Equation 1 with VA 10 million euros and VC 125,000 euros:

NC 10 million/125,000 40

Thus Mona does the hedge by selling 40 of the CME euro contracts. Given the $1-per-euro price, the sale of the contract yields 40 125, 000 euros $10 million. The futures hedge thus again enables her to lock in the exchange rate for Frivolous Luxuries so that it gets its payment of $10 million.

One advantage of using the futures market is that the contract size of 125,000 euros, worth $125,000, is quite a bit smaller than the minimum size of a forward contract, which is usually $1 million or more. However, in this case, the bank manager is making a large enough transaction that she can use either the forward or the futures market. Her choice depends on whether the transaction costs are lower in one market than in the other. If the First National Bank is active in the forward market, that market would probably have the lower transaction costs, but if First National rarely deals in foreign exchange forward contracts, the bank manager may do better by sticking with the futures market.

Options

Another vehicle for hedging interest-rate and stock market risk involves the use of options on financial instruments. Options are contracts that give the purchaser the option, or right, to buy or sell the underlying financial instrument at a specified price, called the exercise price or strike price, within a specific period of time (the term to expiration) . The seller (sometimes called the writer) of the option is obligated to buy or sell the financial instrument to the purchaser if the owner of the option exercises the right to sell or buy. These option contract features are important enough to be emphasized: The owner or buyer of an option does not have to exercise the option; he or she can let the option expire without using it. Hence the owner of an option is not obligated to take any action, but rather has the right to exercise the contract if he or she so chooses. The seller of an option, by contrast, has no choice in the matter; he or she must buy or sell the financial instrument if the owner exercises the option.

Because the right to buy or sell a financial instrument at a specified price has value, the owner of an option is willing to pay an amount for it called a premium. There are two types of option contracts: American options can be exercised at any time up to the expiration date of the contract, and European options can be exercised only on the expiration date.

Option contracts are written on a number of financial instruments (an example of which is shown in the ÒFollowing the Financial NewsÓ box). Options on individ-

C H A P T E R 1 3 Financial Derivatives 321

Following the Financial News

Futures Options

The prices for financial futures options are published daily. In the Wall Street Journal, they are found in the section ÒFutures Options PricesÓ under the ÒInterest RateÓ heading. An excerpt from this listing is reproduced here.

INTEREST RATE

T-BONDS (CBT)

 

 

 

 

$100,000; points and 64ths of 100%

 

Strike

Calls-Settle

Puts-Settle

Price

Mar

Apr

May

Mar

Apr

May

111

2-34 2-21

2-62

0-08 1-15

1-57

112

1-45 1-50

2-28

0-19

1-43

2-22

113

1-01 1-20

1-61

0-39

2-14 ...

114

0-34

0-59

1-36

1-08

2-52 ...

115

0-16

0-41

1-14

1-54 ...

...

116

0-07

0-28

0-60

2-45 ...

...

Est vol 78,455;

Wd vol 51,578 calls 17,896 puts

Op int Wed 252,705 calls 282,711 puts

Information for each contract is reported in columns, as follows. (The Chicago Board of TradeÕs option on its Treasury bonds futures contract is used as an example.)

Source: Wall Street Journal, February 14, 2003, p. C10.

Strike Price: Strike (exercise) price of each contract, which runs from 111 to 116

Calls-Settle: Premium (price) at settlement for call options on the Treasury bond futures expiring in the month listed, with each full point representing $1,000 and 64ths of a point listed to the right of the hyphen; at a strike price of 112, the March call optionÕs premium is 1 45/64, or $1,703.10 per contract

Puts-Settle: Premium (price) at settlement for put options on the Treasury bond futures expiring in the month listed, with each full point representing $1,000 and 64ths of a point listed to the right of the hyphen; at a strike price of 112, the March put optionÕs premium is 19/64, or $296.90 per contract

ual stocks are called stock options, and such options have existed for a long time. Option contracts on financial futures called financial futures options or, more commonly, futures options, were developed in 1982 and have become the most widely traded option contracts.

You might wonder why option contracts are more likely to be written on financial futures than on underlying debt instruments such as bonds or certificates of deposit. As you saw earlier in the chapter, at the expiration date, the price of the futures contract and of the deliverable debt instrument will be the same because of arbitrage. So it would seem that investors should be indifferent about having the option written on the debt instrument or on the futures contract. However, financial futures contracts have been so well designed that their markets are often more liquid than the markets in the underlying debt instruments. So investors would rather have the option contract written on the more liquid instrument, in this case the futures contract. That explains why the most popular futures options are written on many of the same futures contracts listed in Table 1.

The regulation of option markets is split between the Securities and Exchange Commission (SEC), which regulates stock options, and the Commodity Futures Trading Commission (CFTC), which regulates futures options. Regulation focuses on ensuring that writers of options have enough capital to make good on their contractual obligations and on overseeing traders and exchanges to prevent fraud and ensure that the market is not being manipulated.

322 P A R T I I I

Financial Institutions

 

Option Contracts

A call option is a contract that gives the owner the right to buy a financial instrument

 

 

at the exercise price within a specific period of time. A put option is a contract that

 

 

gives the owner the right to sell a financial instrument at the exercise price within a

 

 

specific period of time.

 

Study Guide

 

 

Remembering which is a call option and which is a put option is not always easy. To

 

 

 

keep them straight, just remember that having a call option to buy a financial instru-

 

 

 

ment is the same as having the option to call in the instrument for delivery at a spec-

 

 

 

ified price. Having a put option to sell a financial instrument is the same as having the

 

 

 

option to put up an instrument for the other party to buy.

 

 

 

 

 

 

 

 

 

 

Profits and Losses on Option and Futures Contracts

To understand option contracts more fully, letÕs first examine the option on the same June Treasury bond futures contract that we looked at earlier in the chapter. Recall that if you buy this futures contract at a price of 115 (that is, $115,000), you have agreed to pay $115,000 for $100,000 face value of long-term Treasury bonds when they are delivered to you at the end of June. If you sold this futures contract at a price of 115, you agreed, in exchange for $115,000, to deliver $100,000 face value of the long-term Treasury bonds at the end of June. An option contract on the Treasury bond futures contract has several key features: (1) It has the same expiration date as the underlying futures contract, (2) it is an American option and so can be exercised at any time before the expiration date, and (3) the premium (price) of the option is quoted in points that are the same as in the futures contract, so each point corresponds to $1,000. If, for a premium of $2,000, you buy one call option contract on the June Treasury bond contract with an exercise price of 115, you have purchased the right to buy (call in) the June Treasury bond futures contract for a price of 115 ($115,000 per contract) at any time through the expiration date of this contract at the end of June. Similarly, when for $2,000 you buy a put option on the June Treasury bond contract with an exercise price of 115, you have the right to sell (put up) the June Treasury bond futures contract for a price of 115 ($115,000 per contract) at any time until the end of June.

Futures option contracts are somewhat complicated, so to explore how they work and how they can be used to hedge risk, letÕs first examine how profits and losses on the call option on the June Treasury bond futures contract occur. In February, our old friend Irving the Investor buys, for a $2,000 premium, a call option on the $100,000 June Treasury bond futures contract with a strike price of 115. (We assume that if Irving exercises the option, it is on the expiration date at the end of June and not before.) On the expiration date at the end of June, suppose that the underlying Treasury bond for the futures contract has a price of 110. Recall that on the expiration date, arbitrage forces the price of the futures contract to be the same as the price of the underlying bond, so it too has a price of 110 on the expiration date at the end of June. If Irving exercises the call option and buys the futures contract at an exercise price of 115, he will lose money by buying at 115 and selling at the lower market price of 110. Because Irving is smart, he will not exercise the option, but he will be out the $2,000 premium he paid. In such a situation, in which the price of the underlying financial instrument is below the exercise price, a call option is said to be Òout of the money.Ó At the price of 110 (less than the exercise price), Irving thus suffers a

C H A P T E R 1 3 Financial Derivatives 323

loss on the option contract of the $2,000 premium he paid. This loss is plotted as point A in panel (a) of Figure 1.

On the expiration date, if the price of the futures contract is 115, the call option is Òat the money,Ó and Irving is indifferent whether he exercises his option to buy the futures contract or not, since exercising the option at 115 when the market price is also at 115 produces no gain or loss. Because he has paid the $2,000 premium, at the price of 115 his contract again has a net loss of $2,000, plotted as point B.

If the futures contract instead has a price of 120 on the expiration day, the option is Òin the money,Ó and Irving benefits from exercising the option: He would buy the futures contract at the exercise price of 115 and then sell it for 120, thereby earning a 5-point gain ($5,000 profit) on the $100,000 Treasury bond contract. Because Irving paid a $2,000 premium for the option contract, however, his net profit is

Profit ($)

 

 

 

 

12,000

 

 

 

Buyer of

 

 

 

 

Futures

10,000

 

 

D

Buyer of

 

 

 

 

 

 

 

Call Option

8,000

 

 

 

D

 

 

 

 

6,000

 

C

 

 

 

 

 

 

4,000

 

 

 

 

 

 

 

C

 

2,000

 

 

 

Price of

 

 

 

 

0

B

 

 

Futures

 

 

125

Contract

110

115

120

at Expiration

A

 

 

 

B

 

($)

– 2,000

 

– 4,000

 

 

 

 

A

 

 

 

 

– 6,000

 

 

 

 

– 8,000

 

 

 

 

– 10,000

 

 

 

 

–12,000

 

 

 

 

Loss ($)

 

 

 

 

Profit ($)

 

 

 

 

 

 

12,000

 

 

 

 

 

 

10,000

 

 

 

 

 

 

8,000

 

 

 

 

 

 

6,000

A

 

 

 

 

 

 

 

 

 

 

 

4,000

 

 

 

 

 

 

2,000

A

 

 

 

 

 

 

 

 

 

 

Price of Futures

 

 

 

 

 

 

0

 

B

 

 

Contract at

110

115

120

125

Expiration ($)

 

 

 

– 2,000

 

 

 

 

 

Buyer of

 

 

B

C

 

D Put Option

– 4,000

 

 

 

 

 

 

– 6,000

 

 

C

 

 

 

 

 

 

 

 

 

– 8,000

 

 

 

 

 

 

– 10,000

 

 

 

D

 

Seller of

 

 

 

 

 

 

–12,000

 

 

 

 

 

Futures

 

 

 

 

 

 

Loss ($)

 

 

 

 

 

 

(a)Profit or loss for buyer of call option and buyer of futures

(b)Profit or loss for buyer of put option and seller of futures

F I G U R E 1 Profits and Losses on Options Versus Futures Contracts

The futures contract is the $100,000 June Treasury bond contract, and the option contracts are written on this futures contract with an exercise price of 115. Panel (a) shows the profits and losses for the buyer of the call option and the buyer of the futures contract, and panel (b) shows the profits and losses for the buyer of the put option and the seller of the futures contract.

324 P A R T I I I

Financial Institutions

$3,000 ($5,000 $2,000). The $3,000 profit at a price of 120 is plotted as point C. Similarly, if the price of the futures contract rose to 125, the option contract would yield a net profit of $8,000 ($10,000 from exercising the option minus the $2,000 premium), plotted as point D. Plotting these points, we get the kinked profit curve for the call option that we see in panel (a).

Suppose that instead of purchasing the futures option contract in February, Irving decides instead to buy the $100,000 June Treasury bond futures contract at the price of 115. If the price of the bond on the expiration day at the end of June declines to 110, meaning that the price of the futures contract also falls to 110, Irving suffers a loss of 5 points, or $5,000. The loss of $5,000 on the futures contract at a price of 110 is plotted as point A in panel (a). At a price of 115 on the expiration date, Irving would have a zero profit on the futures contract, plotted as point B . At a price of 120, Irving would have a profit on the contract of 5 points, or $5,000 (point C ), and at a price of 125, the profit would be 10 percentage points, or $10,000 (point D ). Plotting these points, we get the linear (straight-line) profit curve for the futures contract that appears in panel (a).

Now we can see the major difference between a futures contract and an option contract. As the profit curve for the futures contract in panel (a) indicates, the futures contract has a linear profit function: Profits grow by an equal dollar amount for every point increase in the price of the underlying financial instrument. By contrast, the kinked profit curve for the option contract is nonlinear, meaning that profits do not always grow by the same amount for a given change in the price of the underlying financial instrument. The reason for this nonlinearity is that the call option protects Irving from having losses that are greater than the amount of the $2,000 premium. In contrast, IrvingÕs loss on the futures contract is $5,000 if the price on the expiration day falls to 110, and if the price falls even further, IrvingÕs loss will be even greater. This insurance-like feature of option contracts explains why their purchase price is referred to as a premium. Once the underlying financial instrumentÕs price rises above the exercise price, however, IrvingÕs profits grow linearly. Irving has given up something by buying an option rather than a futures contract. As we see in panel (a), when the price of the underlying financial instrument rises above the exercise price, IrvingÕs profits are always less than that on the futures contract by exactly the $2,000 premium he paid.

Panel (b) plots the results of the same profit calculations if Irving buys not a call but a put option (an option to sell) with an exercise price of 115 for a premium of $2,000 and if he sells the futures contract rather than buying one. In this case, if on the expiration date the Treasury bond futures have a price above the 115 exercise price, the put option is Òout of the money.Ó Irving would not want to exercise the put option and then have to sell the futures contract he owns as a result at a price below the market price and lose money. He would not exercise his option, and he would be out only the $2,000 premium he paid. Once the price of the futures contract falls below the 115 exercise price, Irving benefits from exercising the put option because he can sell the futures contract at a price of 115 but can buy it at a price below this. In such a situation, in which the price of the underlying instrument is below the exercise price, the put option is Òin the money,Ó and profits rise linearly as the price of the futures contract falls. The profit function for the put option illustrated in panel (b) of Figure 1 is kinked, indicating that Irving is protected from losses greater than the amount of the premium he paid. The profit curve for the sale of the futures contract is just the negative of the profit for the futures contract in panel (a) and is therefore linear.

Panel (b) of Figure 1 confirms the conclusion from panel (a) that profits on option contracts are nonlinear but profits on futures contracts are linear.

 

 

C H A P T E R 1 3 Financial Derivatives 325

 

 

Study Guide

 

 

 

 

 

To make sure you understand how profits and losses on option and futures contracts

 

 

 

 

 

are generated, calculate the net profits on the put option and the short position in the

 

 

 

 

 

futures contract at prices on the expiration day of 110, 115, 120, and 125. Then ver-

 

 

 

 

 

ify that your calculations correspond to the points plotted in panel (b) of Figure 1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Two other differences between futures and option contracts must be mentioned.

 

 

 

The first is that the initial investment on the contracts differs. As we saw earlier in the

 

 

 

chapter, when a futures contract is purchased, the investor must put up a fixed

 

 

 

amount, the margin requirement, in a margin account. But when an option contract is

 

 

 

purchased, the initial investment is the premium that must be paid for the contract.

 

 

 

The second important difference between the contracts is that the futures contract

 

 

 

requires money to change hands daily when the contract is marked to market, whereas

 

 

 

the option contract requires money to change hands only when it is exercised.

 

 

 

 

 

 

 

Application

Hedging with Futures Options

 

 

 

 

 

Earlier in the chapter, we saw how the First National Bank could hedge the

 

 

 

 

 

interest-rate risk on its $5 million holdings of 8s of 2023 by selling $5 mil-

 

 

 

 

 

lion of T-bond futures. A rise in interest rates and the resulting fall in bond

 

 

 

 

 

prices and bond futures contracts would lead to profits on the bankÕs sale of

 

 

 

 

 

the futures contracts that would exactly offset the losses on the 8s of 2023

 

 

 

 

 

the bank is holding.

 

 

 

 

 

As panel (b) of Figure 1 suggests, an alternative way for the manager to

 

 

 

 

 

protect against a rise in interest rates and hence a decline in bond prices is to

 

 

 

 

 

buy $5 million of put options written on the same Treasury bond futures. As

 

 

 

 

 

long as the exercise price is not too far from the current price as in panel (b),

 

 

 

 

 

the rise in interest rates and decline in bond prices will lead to profits on the

 

 

 

 

 

futures and the futures put options, profits that will offset any losses on the

 

 

 

 

 

$5 million of Treasury bonds.

 

 

 

 

 

The one problem with using options rather than futures is that the First

 

 

 

 

 

National Bank will have to pay premiums on the options contracts, thereby

 

 

 

 

 

lowering the bankÕs profits in order to hedge the interest-rate risk. Why might

 

 

 

 

 

the bank manager be willing to use options rather than futures to conduct the

 

 

 

 

 

hedge? The answer is that the option contract, unlike the futures contract,

 

 

 

 

 

allows the First National Bank to gain if interest rates decline and bond prices

 

 

 

 

 

rise. With the hedge using futures contracts, the First National Bank does not

 

 

 

 

 

gain from increases in bond prices because the profits on the bonds it is hold-

 

 

 

 

 

ing are offset by the losses from the futures contracts it has sold. However, as

 

 

 

 

 

panel (b) of Figure 1 indicates, the situation when the hedge is conducted

 

 

 

 

 

with put options is quite different: Once bond prices rise above the exercise

 

 

 

 

 

price, the bank does not suffer additional losses on the option contracts. At

 

 

 

 

 

the same time, the value of the Treasury bonds the bank is holding will

 

 

 

 

 

increase, thereby leading to a profit for the bank. Thus using options rather

 

 

 

 

 

than futures to conduct the micro hedge allows the bank to protect itself from

 

 

 

 

 

rises in interest rates but still allows the bank to benefit from interest-rate

 

 

 

 

 

declines (although the profit is reduced by the amount of the premium).

 

 

 

 

 

 

 

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]