Fundamentals of Futures and Options Markets John C. Hull Eighth

9 781292 041902

ISBN 978-1-29204-190-2

Fundamentals of Futures

and Options Markets

John C. Hull

Eighth Edition

Fundamentals of Futures and Options Markets Hull 8e

Pearson New International Edition

International_PCL_TP.indd 1 7/29/13 11:23 AM

Fundamentals of Futures

and Options Markets

John C. Hull

Eighth Edition

Pearson Education Limited

Edinburgh Gate

Harlow

Essex CM20 2JE

England and Associated Companies throughout the world

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ISBN 13: 978-1-269-37450-7

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ISBN 10: 1-292-04190-0

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ISBN 10: 1-292-04190-0

ISBN 13: 978-1-292-04190-2

Table of Contents

PEARSON C U S T OM LIBRAR Y

. Introduction

1John C. Hull

. Mechanics of Futures Markets

24John C. Hull

. Hedging Strategies Using Futures

49John C. Hull

. Interest Rates

81John C. Hull

. Determination of Forward and Future Prices

104

104John C. Hull

. Interest Rate Futures

133

133John C. Hull

. Swaps

158

158John C. Hull

. Securitization and the Credit Crisis of 2007

195

195John C. Hull

. Mechanics of Options Markets

210

210John C. Hull

. Properties of Stock Options

232

232John C. Hull

. Trading Strategies Involving Options

254

254John C. Hull

. Introduction to Binomial Trees

273

273John C. Hull

. Valuing Stock Options: The Black-Scholes-Merton Model

298

298John C. Hull

. Employee Stock Options

323

323John C. Hull

. Options on Stock Indices and Currencies

334

334John C. Hull

. Futures Options

350

350John C. Hull

. The Greek Letters

365

365John C. Hull

. Binomial Trees in Practice

396

396John C. Hull

. Volatility Smiles

418

418John C. Hull

. Value at Risk

433

433John C. Hull

. Interest Rate Options

463

463John C. Hull

. Exotic Options and Other Nonstandard Products

483

483John C. Hull

. Credit Derivatives

503

503John C. Hull

Answers to Quiz Questions

522

522John C. Hull

Glossary of Terms

546

546John C. Hull

DerivaGem Software

564

564John C. Hull

Major Exchanges for Trading Futures and Options

569

569John C. Hull

Tables for N(x)

570

570John C. Hull

573

573Index

Introduction

Derivatives markets have become increasingly important in the world of ﬁnance and

investments. It is now essential for all ﬁnance professionals to understand how these

markets work, how they can be used, and what determines prices in them. This book

addresses these issues.

Derivatives are traded on exchanges and in what are termed ‘‘over-the-counter’’

(OTC) markets. The two main products trading on exchanges are futures and options.

In the over-the counter markets forwards, swaps, options, and a wide range of other

derivatives transactions are agreed to. Prior to the crisis which started in 2007, the OTC

derivatives market was relatively free from regulation. This has now changed. As we will

explain, OTC market participants are now subject to rules specifying how trading must

be done, how trades must be reported, and the collateral that must be provided.

This opening chapter starts by providing an introduction to futures markets and

futures exchanges. It then compares exchange-traded derivatives markets with OTC

derivatives markets and discusses forward contracts, which are the OTC counterpart of

futures contracts. After that, it introduces options and outlin es the activities of hedgers,

speculators, and arbitrageurs in derivatives markets.

1.1 FUTURES CONTRACTS

A futures contract is an agreement to buy or sell an asset at a certain time in the future

for a certain price. There are many exchanges throughout the world trading futures

contracts. The Chicago Boar d of Trade, the Chicago Mercantile Exchange, and the New

York Mercantile Exchange have merged to form the CME Group (www.cmegroup.

com). Other large exchanges include NYSE Euronext (www.euronext.c om), Eurex

(www.eurexchange.com), BM&FBOVESPA (www.bmfbovespa.com.br), and the

Tokyo Financial Exchange (www.tfx.co.jp). A table at the end of this book gives a

more complete list.

Futures exchanges allow people who want to buy or sell assets in the future to trade

with each other. In June a trader in New York might contact a broker with instructions

to buy 5,000 bushels of corn for September delivery. The broker would immediately

communicate the client’s instructions to the CME Group. At about the same time,

CHAPTER

From Chapter 1 of Fundamentals of Futures and Options Markets, Eighth Edition. John C. Hull.

another trader in Kansas might instruct a broker to sell 5,000 bushels of corn for

September delivery. These instructions would also be passed on to the CME Group.

A price would be determined and the deal would be done.

The trader in New York who agreed to buy has what is termed a long futures position;

the trader in Kansas who agreed to sell has what is termed a short futures position. The

price is known as the futures price. We will suppose the price is 600 cents per bushel.

This price, like any other price, is determined by the laws of supply and demand. If at a

particular time more people wish to sell September corn than to buy September corn,

the price goes down. New buyers will then enter the market so that a balance between

buyers and sellers is maintained. If more people wish to buy September corn than to sell

September corn, the price goes up—for similar reasons.

Issues such as margin requirements, daily settlement procedures, trading practices,

commissions, bid–oﬀer spreads, and the role of the exchange clearing house will be

discussed in Chapter 2. For the time being, we can assume that the end result of the

events just described is that the trader in New York has agreed to buy 5,000 bushels of

corn for 600 cents per bushel in September and the trader in Kansas has agreed to sell

5,000 bushels of corn for 600 cents per bushel in September. Both sides have entered

into a binding contract. The contract is illustrated in Figure 1.1.

A futures price can be contrasted with the spot price. The spot price is for immediate,

or almost immediate, delivery. The futures price is the price for delivery at some time in

the future. The two are not usually equal. As we will see in later chapter s, the futures

price may be greater than or less than the spot price.

1.2 HISTORY OF FUTURES MARKETS

Futures markets can be traced back to the Middle Ages. They were originally developed

to meet the needs of farmers and merchants. Consider the position of a farmer in June of

a certain year who will harvest a known amount of corn in September. There is

uncertainty about the price the farmer will receive for the corn. In years of scarcity it

might be possible to obtain relatively high prices, particularly if the farmer is not in a

hurry to sell. On the other hand, in years of oversupply the corn might have to be

disposed of at ﬁre-sale prices. The farmer and the farmer’s family are clearly exposed to a

great deal of risk.

Consider next a company that has an ongoing requirement for corn. The company is

also exposed to price risk. In some years an oversupply situation may create favorable

prices; in other years scarcity may cause the prices to be exorbitant. It can make sense

for the farmer and the company to get together in June (or even earlier) and agree on a

June:

September:

Trader must buy 5,000 bushels of corn

for $30,000

Trader takes a long position in a September

futures contract on corn at 600 cents per bushel

Figure 1.1 A futures contract (assuming it is held to maturity)

2 CHAPTER 1

price for the farmer’s production of corn in September. This involves them negotiating

a type of futures contract. The contract provides a way for each side to eliminate the

risk it faces because of the uncertain future price of corn.

We might ask what happens to the company’s requirements for corn during the rest

of the year. Once the harvest season is over, the corn must be stored until the next

season. In undertaking this storage, the company does not bear any price risk, but does

incur the costs of storage. If the farmer or some other person stores the corn, the

company and the storer both face risks associated with the future corn price, and again

there is a clear role for futures contracts.

The C hicago Board of Trade

The Chicago Board of Trade (CBOT) was established in 1848 to bring farmers and

merchants together. Initially, its main task was to standardize the quantities and

qualities of the grains that were traded. Within a few years, the ﬁrst futures-type

contract was developed. It was known as a to-arrive contract. Speculators soon became

interested in the contract and found trading the contract to be an attractive alternative

to trading the grain itself. The CBOT developed futures contracts on many diﬀerent

underlying assets, including corn, oats, soybeans, soybean meal, soybean oil, wheat,

Treasury bonds, and Treasury notes. It is now part of the CME Group.

The Chicago Mercantile Exchange

In 1874 the Chicago Produce Exchange was established, providing a market for butter,

eggs, poultry, and other perishable agricultural products. In 1898 the butter and egg

dealers withdrew from the exchange to form the Chicago Butter and Egg Board. In 1919,

this was renamed the Chicago Mercantile Exchange (CME) and was reorganized for

futures trading. Since then, the exchange has provided a futures market for many

commodities, including pork bellies (1961), live cattle (1964), live hogs (1966), and feeder

cattle (1971). In 1982 it introduced a futures contract on the Standard & Poor’s (S&P)

500 Stock Index.

The Chicago Mercantile Exchange started futures trading in foreign currencies

in 1972. The currency futures traded now include the euro, British pound, Canadian

dollar, Japanese yen, Swiss franc, Australian dollar, Mexican peso, Brazilian real,

South African rand, New Zealand dollar, Russian rouble, Chinese renminbi, Swedish

krona, Czech koruna, Hungarian forint, Israeli shekel, Korean won, Polish złoty, and

Turkish lira. The Chicago Mercantile Exchange developed the very popular Eurodollar

futures contract. (As later chapters will explain, this is a contract on the future value of

a short-term interest rate.) It has also introduced futures contracts on weather and real

estate.

Electronic T rading

Traditionally futures have been traded using what is known as the open-outcry system.

This involves traders physically meeting on the ﬂoor of the exchange, known as the

‘‘trading pit,’’ and using a complicated set of hand signals to indicate the trades they

would like to carry out. In the example we considered earlier, one ﬂoor trader would

represent the investor in New York who wanted to buy September corn and another

ﬂoor trader would represent the investor in Kansas who wanted to sell September corn.

Introduction

Exchanges have largely replaced the open outcry system by electronic trading. This

involves traders entering their required trades at a keyboard and a computer being used

to match buyers and sellers. Most futures exch anges throughout the world are entirely

electronic. Electronic trading has led to a growth in algorithmic trading, also known as

black-box, automated, high-frequency, or robo trading. This involves the use of

computer programs to initiate trades, often without human intervention.

1.3 THE OVER-THE-COUNTER MARKET

Futures contracts are very popular exchange-traded contracts. Options, which are

introduced later in this chapter, also trade very actively on exchanges. But not all

trading of derivatives is on exchanges. Many trades take place in the over-the-counter

(OTC) market. Banks, other large ﬁnancial institutions, fund managers, and corpora-

tions are the main participants in OTC derivatives markets. The number of derivatives

transactions per year in OTC markets is smaller than in exchange-traded markets, but

the average size of the transactions is much greater.

Traditionally, participants in the OTC derivatives markets have contacted each other

Business Snapshot 1.1 The Lehman Bankruptcy

On September 15, 2008, Lehman Brothers ﬁled for bankruptcy. This was the largest

bankruptcy ﬁling in US history and its ramiﬁcations were felt throughout derivatives

markets. Almost until the end, it seemed as though there was a good chance that

Lehman woul d survive. A number of companies (e.g., the Korean Development

Bank, Barclays Bank in the UK, and Bank of America) expressed interest in buying

it, but none of these was able to close a deal. Many people thought that Lehman was

‘‘too big to fail’’ and that the US government would have to bail it out if no purchaser

could be found. This proved not to be the case.

How did this happen? It was a combination of high leverage, risky investments, and

liquidity problems. Commercial banks that take deposits are subject to regulations on

the amount of capital they must keep. Lehman was an investment bank and not subject

to these regulations. By 2007, its leverage ratio had increased to 31:1, which means that

a 3–4% decline in the value of its assets would wipe out its capital. Dick Fuld,

Lehman’s Chairman and Chief Executive, encouraged an aggressive deal-making,

risk-taking culture. He is reported to have told his executives: ‘‘Every day is a battle.

You have to kill the enemy.’’ The Chief Risk Oﬃcer at Lehman was competent, but did

not have much inﬂuence and was even removed from the executive committee in 2007.

The risks taken by Lehman included large positions in the instruments created from

subprime mortgages, which will be described in Chapter 8. Lehman funded much of its

operations with short-term debt. When there was a loss of conﬁdence in the company,

lenders refused to roll over this funding, forcing it into bankruptcy.

Lehman was very active in the over-the-counter derivatives markets. It had hundreds

of thousands of transactions outstanding with about 8,000 diﬀerent counterparties.

Lehman’s counterparties were often required to post collateral and this collateral had

in many cases been used by Lehman for various purposes. It is easy to see that sorting

out who owes what to whom in this type of situation is a nightmare!

4 CHAPTER 1

directly or have found counterparties for their trades using an interdealer broker. Banks

often act as market makers for the more commonly traded instruments. This means that

they are always prepared to quote a bid price (at which they are prepared to take one side

of a derivatives transaction) and an oﬀer price (at which they are prepared to take the

other side). When they start trading with each other, two market participants often sign

an agreement covering all transactions they might enter into in the future. The issues

covered in the agreement include the circumstances under which outstanding trans-

actions can be terminated, how settlement amounts are calculated in the event of a

termination, and how the collateral (if an y) that must be posted by each side is calculated.

Prior to the credit crisis, which started in 2007 and is discussed in some detail in

Chapter 8, OTC derivatives markets were largely unregulated. Following the credit

crisis and the failure of Lehman Brothers (see Business Snapshot 1.1), we have seen the

development many new regulations aﬀecting the operation of OTC markets. The

purpose of the regulations is to improve the transparency of OTC markets, improve

market eﬃciency, and reduce systemic risk (see Business Snapshot 1.2 for a discussion

of systemic risk). The over-the-counter market in some respects is being forced to

become more like the exchange-traded market. Three important changes are:

1. Standardized OTC derivatives in the United States must whenever possible be

traded on what are referred to as swap execution facilities (SEFs). These are

platforms where market participants can post bid and oﬀer quotes and where they

can choose to trade by accepting the quotes of other market participants.

2. There is a requirement in most parts of the world that a central clearing party

(CCP) be used for most standardized derivatives transactions. The CCP’s role is

to stand between the two sides in an over-the-counter derivatives transaction in

much the same way that an exchange does in the exchange-traded derivatives

market. CCPs are discussed in more detail in Chapter 2.

3. All trades must be reported to a central registry.

Market Size

Both the over-the-counter and the exchange-traded market for derivatives are huge.

Although the statistics that are co llected for the two markets are not exactly comparable,

Business Snapshot 1.2 Systemic risk

Systemic risk is the risk that a default by one ﬁnancial institution will create a ‘‘ripple

eﬀect’’ that leads to defaults by other ﬁnancial institutions and threatens the stability

of the ﬁnancial system. There are hug e numbers of over-the-counter transactions

between banks. If Bank A fails, Bank B may take a huge loss on the transactions it

has with Bank A. This in turn could lead to Bank B failing. Bank C that has many

outstanding transactions with both Bank A and Bank B might then take a large loss

and experience severe ﬁnancial diﬃculties; and so on.

The ﬁnancial system has survived defaults such as Drexel in 1990 and Lehman

Brothers in 2008, but regulators continue to be concerned. During the market turmoil

of 2007 and 2008, many large ﬁnancial institutions were bailed out, rather than being

allowed to fail, because governments were concerned about systemic risk.

Introduction

it is clear that the over-the-counter market is much larger than the exchange-traded

market. The Bank for International Settlement s (www.bis.org) started collecting

statistics on the markets in 1998. Figure 1.2 compares (a) the estimated total principal

amounts underlying transactions that were outstanding in the over-the-counter markets

between 1998 and 2011 and (b) the estimated total value of the assets underlying

exchange-traded contracts during the same period. Using these measures, the size of

the over-the-counter market was $648 trillion in December 2011 and that of the

exchange-traded market was $64 trillion at this time.

In interpreting these numbers we should bear in mind that the principal underlying

an over-the-counter transaction is not the same as its value. An example of an over-the-

counter transaction is an agreement to buy 100 million U.S. dollars with British pounds

at a predetermined exchange rate in one year. The total principal amount underlying

this transaction is $100 million. However, the value of the transaction at a particular

point in time might be only $1 million. The Bank for International Settlements

estimates the gross market value of all OTC contracts outstanding in Decem ber 2011

to be about $27 trillion.

1.4 FORWARD CONTRACTS

A forward contract is similar to a futures contracts in that it is an agreement to buy or sell

an asset at a certain time in the future for a certain price. But, whereas futures contracts

are traded on exchanges, forward contracts trade in the over-the-counter market.

Forward contracts on foreign exchange are very popular. Most large banks employ

both spot and forward foreign exchange traders. Spot traders are trading a foreign

currency for almost immediate delivery. Forward traders are trading for delivery at a

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

100

200

300

400

500

600

700

1998

OTC

Exchange

Size of market

($ trillion)

Figure 1.2 Size of over-the-counter and exchange-traded derivatives markets

A contract that is worth $1 million to one side and $1 million to the other side would be counted as

having a gross market value of $1 million.

6 CHAPTER 1

future time. Table 1 .1 provides the quotes for the exchange rate between the British

pound (GBP) and the U.S. dollar (USD) that might be made by a large international

bank on June 22, 2012. The quote is for the number of USD per GBP. The ﬁrst row

indicates that the bank is prepared to buy GBP (also known as sterling) in the spot market

(i.e., for virtually immediate delivery) at the rate of $1.5585 per GBP and sell sterling in

the spot market at $1.5589 per GBP. The second row indicates that the bank is prepared

to buy sterling in one month at $1.5582 per GBP and sell sterling in one month at $1.5587

per GBP; the third row indicates that it is prepared to buy sterling in three months at

$1.5579 per GBP and sell sterling in three months at $1.5585 per GBP; and so on.

The quotes are for very large transactions. (As anyone who has traveled abroad

knows, retail customers face much larger spreads between bid and oﬀer quotes than

those in Table 1.1.) After examining the quotes in Table 1.1, a large corporation might

agree to sell £100 million in six months for $155.73 million to the bank as part of its

hedging program.

There is a relationship between the forward price of a foreign currency, the spot price

of the foreign currency, domestic interest rates, an d foreign interest rates. This is

explained in Chapt er 5.

1.5 OPTIONS

Options are traded both on exchanges and in the over-the-counter markets. There are

two types of option: calls and puts. A call option gives the holder the right to buy an

asset by a certain date for a certain price. A put option gives the holder the right to sell

an asset by a certain date for a certain price. The price in the contract is known as the

exercise price or the strike price; the date in the contract is known as the expiration date

or the maturity date.AEuropean option can be exercised only on the maturity date; an

American option can be exercised at any time during its life.

It should be emphasized that an option gives the holder the right to do something.

The holder does not have to exercise this right. This fact distinguishes options from

futures (or forward) contracts. The holder of a long futures contract is committed to

buying an asset at a certain price at a certain time in the future. By contrast, the

holder of a call option has a choice as to whether to buy the asset at a certain price at

a certain time in the future. It costs nothing (except for margin requirements, which

will be discussed in Chapter 2) to enter into a futures contract. By contrast, an

Table 1.1 Spot and forward quotes for the

USD/GBP exchange rate, June 22, 2012

(GBP ¼ British pound; USD ¼ U.S. dollar;

quote is number of USD per GBP)

Bid Oﬀer

Spot 1.5585 1.5589

1-month forward 1.5582 1.5587

3-month forward 1.5579 1.5585

6-month forward 1.5573 1.5580

Introduction

investor must pay an up-front price, known as the option premium, for an option

contract.

The largest exchange in the world for trading stock options is the Chicago Board

Options Exchange (CBOE; www.cboe.com). Table 1.2 gives the bid and oﬀer quotes

for some of the call options trading on Google (ticker symbol: GOOG) on June 25,

2012. Table 1.3 does the same for put options trading on Google on that date. The

tables have been constructed from data on the CBOE web site. The Google stock price

at the time of the quotes was bid 561.32, oﬀer 561.51. The bid–oﬀer spread on an

option, as a percentage of its price, is greater than that on the underlying stock and

depends on the volume of trading. The option strike prices in the tables are $520, $540,

$560, $580, and $600. The maturities are July 2012, September 2012, and December

2012. The July options have a maturity date of July 21, 2012, the September options

have a maturity date of September 22, 2012, and the Decem ber options have a maturity

date of December 22, 2012.

The tables illustrate a number of properties of options. The price of a call option

decreases as the strike price increases; the price of a put option increases as the strike

price increases. Both types of options tend to become more valuable as their time to

maturity increases. These properties of options will be discussed further in Chapter 10.

Suppose an investor instructs a broker to buy one December call option contract on

Google with a strike price of $580. The broker will relay these instructions to a trader at

the CBOE and the deal will be done. The (oﬀer) price is $35.30, as indicated in

Table 1.2. This is the price for an option to buy one share. In the United States, an

Table 1.2. Prices of call options on Google, June 25, 2012; stock price:

bid $561.32; oﬀer $561.51

Strike price July 2012 Sept. 2012 Dec. 2012

($) Bid Oﬀer Bid Oﬀer Bid Oﬀer

520 46.50 47.20 55.40 56.80 67.70 70.00

540 31.70 32.30 41.60 42.50 55.30 56.20

560 20.00 20.40 30.20 30.70 44.20 45.00

580 11.30 11.60 20.70 21.20 34.50 35.30

600 5.60 5.90 13.50 13.90 26.30 27.10

Table 1.3 Prices of put options on Google, June 25, 2012; stock price:

bid $561.32; oﬀer $561.51

Strike price July 2012 Sept. 2012 Dec. 2012

($) Bid Oﬀer Bid Oﬀer Bid Oﬀer

520 5.00 5.30 13.60 14.00 25.30 26.10

540 10.20 10.50 19.80 20.30 32.80 33.50

560 18.30 18.70 28.10 28.60 41.50 42.30

580 29.60 30.00 38.40 39.10 51.80 52.60

600 43.80 44.40 51.10 52.10 63.50 64.90

8 CHAPTER 1

option contract is an agreement to buy or sell 100 shares. Therefore, the investor must

arrange for $3,530 to be remitted to the exchange through the broker. The exchange will

then arrange for this amount to be passed on to the party on the other side of the

transaction.

In our example, the investor has obtained at a cost of $3,530 the right to buy 100

Google shares for $580 each. If the price of Google does not not rise above $580.00 by

December 22, 2012, the option is not exercised and the investor loses $3,530.

But if

Google does well and the option is exercised when the bid price for the stock is $650,

the investor is able to buy 100 shares at $580 and immediately sell them for $650 for a

proﬁt of $7,000—or $3,470 when the initial cost of the options is taken into account.

An alternative trade would be to sell one September put option contract with a strike

price of $540 at the bid price of $19.80. This would lead to an immediate cash inﬂow of

$100  19 :80 ¼ $1,980. If the Google stock price stays above $540, this option is not

exercised and the investor makes a $1,980 proﬁt. However, if stock price falls and the

option is exercised when the stock price is $500 there is a loss. The investor must buy 100

shares at $540 when they are worth only $500. This leads to a loss of $4,000, or $2,020

when the initial amount received for the option contract is taken into account.

The stock options trading on the CBOE are American (i.e., they can be exercised at

any time). If we assume for simplicity that they are European, so that they can be

exercised only at maturity, the investor’s proﬁt as a function of the ﬁnal stock price for

the two trades we have considered is shown in Figure 1.3.

Further details about the operation of options markets and how prices such as those

in Tables 1.2 and 1.3 are determined by traders are given in later chapters. At this stage

we note that there are four types of participants in options markets:

1. Buyers of calls

2. Sellers of calls

200

400

600 800

1000

200

400

600

800

1000

–50

–40

–30

–20

–10

Stock price ($)

Proﬁt

($ 000)

Proﬁt

($ 000)

(a)

(b)

–10

Figure 1.3 Net proﬁt from (a) purchasing a contract consisting of 100 Google December

call options with a strike price of $580 and (b) selling a contract consisting of 100 Google

September put options with a strike price of $540

The calculations here ignore commissions paid by the investor.

The calculations here ignore the eﬀect of discounting. Theoretically, the $7,000 should be discounted from

the time of exercise to June 25, 2012 when calculating the payoﬀ.

Introduction 9

3. Buyers of puts

4. Sellers of puts

Buyers are referred to as having long positions; sellers are referred to as having short

positions. Selling an option is also known as writing the option.

1.6 HISTORY OF OPTIONS MARKETS

The ﬁrst trading in put and call options began in Europe and in the United States as

early as the eighteenth century. In the early years the market got a bad name because of

certain corrupt practices. One of these involved brokers being given options on a certain

stock as an inducement for them to recommend the stock to their clients.

Put and Call Brokers and Dealers Association

In the early 1900s a group of ﬁrms set up the Put and Call Brokers and Dealers

Association. The aim of this association was to provide a mechan ism for bringing

buyers and sellers together. Investors who wanted to buy an option would contact one

of the member ﬁrms. This ﬁrm would attempt to ﬁnd a seller or writer of the option

from either its own clients or those of other member ﬁrms. If no seller could be found,

the ﬁrm would undertake to write the option itself in return for what was deemed to be

an appropriate price.

The options market of the Put and Call Brokers and Dealers Association suﬀered

from two deﬁciencies. First, there was no secondary market. The buyer of an option did

not have the right to sell it to another party prior to expiration. Second, there was no

mechanism to guarantee that the writer of the option would honor the contract. If the

writer did not live up to the agreement when the option was exercised, the buyer had to

resort to costly lawsuits.

The Formation of Options Exchanges

In April 1973 the Chicago Board of Trade set up a new exchange, the Chicago Board

Options Exchange, speciﬁcally for the purpose of trading stock options. Since then

options markets have become increasingly popular with investors. By the early 1980s

the volume of trading had grown so rapidly that the number of shares underlying the

stock option contracts traded each day in United States exceeded the daily volume of

shares traded on the New York Stock Exchange.

The exchanges trading options in the United States now include the Chicago Board

Options Exchange (www.cboe.com), NASDAQ OMX (www.nasdaqtrader.com),

NYSE Euronext (www.euronext.com), the International Securities Exchange (www.i-

seoptions.com), and the Boston Options Exchange (www.bostonoptions.com).

Options trade on several thousand diﬀerent stocks as well as stock indices, foreign

currencies, and other assets.

Most exchanges oﬀering futures contracts also oﬀer options on these contracts. Thus,

the CME Group oﬀers options on corn futures, live cattle futures, and so on. Options

exchanges exist all over the world (see the table at the end of this book).

10 CHAPTER 1

The O ver-the-Counter Market for Options

The over-t he-counter market for options has grown very rapidly since the early 1980s

and is now bigger than the exchange-traded market. One advantage of options traded

in the over-the-counter market is that they can be tailored to meet the particular needs

of a corporate treasurer or fund manager. For example, a corporate treasurer who wants

a European call option to buy 1.6 milli on British pounds at an exchange rate of 1.5580

may not ﬁnd exactly the right product trading on an exchange. However, it is likely that

many derivatives dealers would be pleased to provide a quote for an over-the-counter

contract that meets the treasurer’s precise needs.

1.7 TYPES OF TRADER

Futures, forward, and options markets have been outstandingly successful. The main

reason is that they have attracted many diﬀerent types of trader and have a great deal of

liquidity. When an investor wants to take one side of a contract, there is usually no

problem in ﬁndi ng someone who is prepared to take the other side.

Three broad categories of trader can be identiﬁed: hedgers, speculators, and

arbitrageurs. Hedgers use futures, forwards, and options to reduce the risk that they

face from potential future movements in a market variable. Speculators use them to

bet on the future direction of a market variable. Arbitrageurs take oﬀsetting positions

in two or more instruments to lock in a proﬁt. As described in Business Snapshot 1.3,

hedge funds have become big users of derivatives for all three purposes.

In the next few sections, we consider the activities of each type of trader in more

detail.

1.8 HEDGERS

In this section we illustrate how hedgers can reduce their risks with forward contracts

and options.

Hedging U sing Forward Contracts

Suppose that it is June 22, 2012, and ImportCo, a company based in the United States,

knows that it will have to pay £10 million on September 22, 2012, for goods it has

purchased from a British supplier. The USD/GBP exchange rate quotes made by a

ﬁnancial institution are shown in Table 1.1. ImportCo could hedge its foreign exchange

risk by buying pounds (GBP) from the ﬁnancial institution in the three-month forward

market at 1.5585. This would have the eﬀect of ﬁxing the price to be paid to the British

exporter at $15,585,000.

Consider next another U.S. company, which we will refer to as ExportCo, that is

exporting goods to the United Kingdom and on June 22, 2012, knows that it will

receive £30 million three months later. ExportCo can hedge its foreign exchange risk by

selling £30 million in the three-month forward market at an exchange rate of 1.5579.

This would have the eﬀect of locking in the U.S. dollars to be realized for the pounds at

$46,737,000.

Introduction

Example 1.1 summarizes the hedging strategies open to ImportCo and ExportCo.

Note that a company might do better if it chooses not to hedge than if it chooses to

hedge. Alternatively, it might do worse. Consider ImportCo. If the exchange rate is

1.5000 on September 22 and the company has not hedged, the £10 million that it has to

pay will cost $15,000,000, which is less than $15,585,000. On the other hand, if the

exchange rate is 1.6000, the £10 million will cost $16,000,000—and the company will

wish it had hedged! The position of ExportCo if it does not hedge is the reverse. If the

exchange rate in September proves to be less than 1.5579, the company will wish it had

hedged; if the rate is greater than 1.5579, it will be pleased it has not done so.

Business Snapshot 1.3 Hedge funds

Hedge funds have become major users of derivatives for hedging, speculation, and

arbitrage. They are similar to mutual funds in that they invest funds on behalf of

clients. However, they accept funds only from ﬁnancially sophisticated individuals

and do not publicly oﬀer their securities. Mutual funds are subject to regulations

requiring that the shares be redeemable at any time, that investment policies be

disclosed, that the use of leverage be limited, and so on. Hedge funds are relatively

free of these regulations. This gives them a great deal of freedom to develop

sophisticated, unconventional, and proprietary investment strategies. The fees

charged by hedge fund managers are dependent on the fund’s performance and are

relatively high—typically 2 plus 20%, i.e., 2% of the amount invested plus 20% of the

proﬁts. Hedge funds have grown in popularity, with about $2 trillion being invested in

them throughout the world. ‘‘Funds of funds’’ have been set up to invest in a portfolio

of hedge funds.

The investment strategy followed by a hedge fund manager often involves using

derivatives to set up a speculative or arbitrage position. Once the strategy has been

deﬁned, the hedge fund manager must:

1. Evaluate the risks to which the fund is exposed

2. Decide which risks are acceptable and which will be hedged

3. Devise strategies (usually involving derivatives) to hedge the unacceptable risks.

Here are some examples of the labels used for hedge funds together with the trading

strategies followed:

Long/Short Equities: Purchase securities considered to be undervalued and short those

considered to be overvalued in such a way that the exposure to the overall direction of

the market is small.

Convertible Arbitrage: Take a long position in a thought-to-be-undervalued convert-

ible bond combined with an actively managed short position in the underlying equity.

Distressed Securities: Buy securitie s issued by comp anies in, or close to, bankruptcy.

Emerging Markets: Invest in debt and equity of companies in developing or emerging

countries and in the debt of the countries themselves.

Global Macro: Carry out trades that reﬂect anticipated global macroeconomic trends.

Merger Arbitrage: Trade after a possible merger or acquisition is announced so that a

proﬁt is made if the announced deal takes place.

12 CHAPTER 1

This example illustrates a key aspect of hedging. Hedging reduces the risk, but it is

not necessarily the case that the outcome with hedging will be better than the outcome

without hedging.

Hedging U sing Options

Options can also be used for hedging. Example 1.2 considers an investor who in May of

a particular year owns 1,000 shares of a company. The share price is $28 per share. The

investor is concerned about a possible share price decline in the next two months and

wants protection. The investor could buy 10 July put option contracts on the company’s

stock on the Chicago Board Options Exchange with a strike price of $27.50. This would

give the investor the right to sell a total of 1,000 shares for a price of $27.50. If the

quoted option price is $1, each option contract would cost 100  $1 ¼ $100 and the

total cost of the hedging strategy would be 10  $100 ¼ $1,000.

The strategy costs $1,000 but guarantees that the shares can be sold for at least $27.50

per share during the life of the option. If the market price of the stock falls below

$27.50, the options will be exercised so that $27,500 is realized for the entire holding.

When the cost of the options is taken into account, the amount realized is $26,500. If

the market price stays above $27.50, the options are not exercised and expire worthless.

However, in this case the value of the holding is always above $27,500 (or above $26,500

when the cost of the options is taken into account). Figure 1.4 shows the net value of

the portfolio (after taking the cost of the options into account) as a function of the

stock price in two months. The dotted line shows the value of the portfolio assuming no

hedging.

Example 1.1 Hedging with forward contracts

It is June 22, 2012. ImportCo must pay £10 million on September 22, 2012, for

goods purchased from Britain. Using the quotes in Table 1.1, it buys £10 million in

the three-month forward market to lock in an exchange rate of 1.5585 for the

pounds it will pay.

ExportCo will receive £30 million on September 22, 2012, from a customer in

Britain. Using quotes in Table 1.1, it sells £30 million in the three-month forward

market to lock in an exchange rate of 1.5579 for the pounds it will receive.

Example 1.2 Hedging with options

It is May. An investor who owns 1,000 shares of a compan y and wants protection

against a possible decline in the share price over the next two months. Market

quotes are as follows:

Current share price: $28

July 27.50 put price: $1

The investor buys 10 put option contracts for a total cost of $1,000. This gives

the investor the right to sell 1,000 shares for $27.50 per share during the next

two months.

Introduction

A Comparison

There is a fundamental diﬀerence between the use of forward contracts and options for

hedging. Forward contracts are designed to neutralize risk by ﬁxing the price that the

hedger will pay or receive for the underlying asset. Option contracts, by contrast,

provide insurance. They oﬀer a way for investors to protect themselves against adverse

price movements in the future while still allowing them to beneﬁt from favorable price

movements. Unlike forwards, options involve the payment of an up-front fee.

1.9 SPECULATORS

We now move on to consider how futures and options markets can be used by

speculators. Whereas hedgers want to avoid an exposure to adverse movements in

the price of an asset, speculators wish to take a position in the market. Either they are

betting that the price of the asset will go up or they are betting that it will go down.

Speculation Using Futures

Consider a U.S. speculator who in February thinks that the British pound will

strengthen relative to the U.S. dollar over the next two months and is prepared to

back that hunch to the tune of £250,000. One thing the speculator can do is purchase

£250,000 in the spot market in the hope that the sterling can be sold later at higher

price. (The sterling onc e purchased would be kept in an interest-bearing account.)

Another possibility is to take a long position in four CME April futures contracts on

sterling. (Each futures contract is for the purchase of £62,500.) Table 1.4 summarizes

the two alternatives on the assumption that the current exchange rate is 1.5470 dollars

20,000

25,000

30,000

35,000

40,000

Value of

holding ($)

Stock price ($)

Hedging

No hedging

Figure 1.4 Value in Example 1.2 of the investor’s holding in two months

14 CHAPTER 1

per pound and the April futures price is 1.5410 dollars per pound. If the exchange rate

turns out to be 1.6000 dollars per pound in April, the futures contract alternative

enables the speculator to realize a proﬁt of ð1:6000  1:5410Þ250,000 ¼ $14,750. The

spot market alternative leads to 250,000 units of an asset being purchased for $1.5470 in

February and sold for $1.6000 in April, so that a proﬁt of ð1:6000  1:5470Þ

250,000 ¼ $13,250 is made. If the exchange rate falls to 1.5000 dollars per pound,

the futures contract gives rise to a ð1:5410  1:5000Þ250,000 ¼ $10,250 loss, whereas

the spot market alternative gives rise to a loss of ð1:5470  1:5000Þ250,000 ¼

$11,750. The alternatives appear to give rise to slightly diﬀerent proﬁts and losses,

but these calculations do not reﬂect the interest that is earned or paid.

What then is the diﬀerence between the two alternatives? The ﬁrst alternative of buying

sterling requires an up-front investment of $386,750 (¼ 250,000  1:5470). By contrast,

the second alternative requires only a small amount of cash—perhaps $20,000—to be

deposited by the speculator in what is termed a margin account (this is explained in

Chapter 2). The futures market allows the speculator to obtain leverage. With a relatively

small initial outlay, the investor is able to take a large speculative position.

Speculation Using Options

Options can also be used for speculation. Suppose that it is October and a speculator

considers that a stock is likely to increase in value over the next two months. The stock

price is currently $20, and a two-month call option with a $22.50 strike price is

currently selling for $1. Table 1.5 illustrates two possible alternatives assuming that

the speculator is willing to invest $2,000. One alternative is to purchase 100 shares.

Table 1.4 Speculation using spot and futures contracts. One futures contract is on

£62,500. Initial margin for four futures contracts ¼ $20,000

Possible Trade

Buy £250,000

Spot price ¼ 1.5470

Buy 4 futures contracts

Futures price ¼ 1.5410

Investment $386,750 $20,000

Proﬁt if April spot ¼ 1.6000 $13,250 $14,750

Proﬁt if April spot ¼ 1.5000 $11,750 $10,250

Table 1.5 Comparison of proﬁts from two alternative

strategies for using $2,000 to speculate on a stock worth

$20 in October

Investor’s strategy December stock price

$15 $27

Buy 100 shares $500 $700

Buy 2,000 call options $2,000 $7,000

Introduction

Another involves the purchase of 2,000 call options (i.e., 20 call option contracts).

Suppose that the speculator’s hunch is correct and the price of the stock rises to $27 by

December. The ﬁrst alternative of buying the stock yields a proﬁt of

100 ð$27  $20 Þ¼$700

However, the second alternative is far more proﬁtable. A call option on the stock with

a strike price of $22.50 gives a payoﬀ of $4.50, because it enables something worth

$27 to be bought for $22.50. The total payoﬀ from the 2,000 options that are

purchased under the second alternative is

2,000  $4:50 ¼ $9,000

Subtracting the original cost of the options yields a net proﬁt of

$9,000  $2; 000 ¼ $7,000

The options strategy is, therefore, ten times more proﬁtable than the strategy of buying

the stock.

Options also give rise to a greater potential loss. Suppose the stock price falls to $15

by December. The ﬁrst alternative of buying stock yields a loss of

100 ð$20  $15 Þ¼$500

Because the call options expire without being exercised, the options strategy would lead

to a loss of $2,000—the original amount paid for the options. Figure 1.5 shows the proﬁt

or loss from the two strategies as a function of the price of the stock in two months.

Options like futures provide a form of leverage. For a given investment, the use of

options magniﬁes the ﬁnancial consequences. Good outcomes become very good, while

bad outcomes result in the whole initial investment being lost.

–

4000

–

2000

4000

6000

8000

10000

Profit ($)

Stock price ($)

Buy shares

Buy options

Figure 1.5 Proﬁt or loss from two alternative strategies for speculating on a stock currently

worth $20

16 CHAPTER 1

A Comparison

Futures and options are similar instruments for speculators in that they both provide a

way in which a type of leverage can be obtained. However, there is an important

diﬀerence between the two. When a speculator uses futures the potential loss as well as

the potential gain is very large. When options are used, no matter how bad things get,

the speculator’s loss is limited to the amount paid for the options.

1.10 ARBITRAGEURS

Arbitrageurs are a third impor tant group of participants in futures, forward, and

options markets. Arbitrage involves locking in a riskless proﬁt by simultaneously

entering into transactions in two or more markets. In later chapters we will see how

arbitrage is sometimes pos sible when the futures price of an asset gets out of line with

its spot price. We will also examine how arbitrage can be used in options markets. This

section illustrates the concept of arbitrage with a very simple example.

Example 1.3 considers a stock that is traded in both New York and London. Suppose

that the stock price is $152 in New York and £100 in London at a time when the

exchange rate is $1.5500 per pound. An arbitrageur could simultaneously buy 100 shares

of the stock in New York and sell them in London to obtain a risk-free proﬁt of

100 ½ð$1:55  100Þ$152

or $300 in the absence of transactions costs. Transactions costs would probably

eliminate the proﬁt for a small investor. However, a large investment bank faces very

low transactions costs in both the stock market and the foreign exchange market. It

would ﬁnd the arbitrage opportunity very attractive and would try to take as much

advantage of it as possible.

Arbitrage opportunities such as the one in Example 1.3 cannot last for long. As

arbitrageurs buy the stock in New York, the forces of supply and demand will cause the

Example 1.3 An arbitrage opportunity

A stock is traded in both New York and London. The following quotes have been

obtained:

New York: $152 per share

London: £100 per share

Value of £1: $1.5500

A trader does the following:

1. Buys 100 shares in New York

2. Sells the shares in London

3. Converts the sale proceeds from pounds to dollars.

This leads to a proﬁt of

100 ½ð$1:55  100Þ$152¼$300

Introduction

dollar price to rise. Similarly, as they sell the stock in London, the sterling price will be

driven down. Very quickly the two prices will become equivalent at the current

exchange rate. Indeed, the existence of proﬁt-hungry arbitrageurs makes it unlikely

that a major disparity between the sterling price and the dollar price could ever exist in

the ﬁrst place. Generalizing from this example, we can say that the very existence of

arbitrageurs means that in practice only very small arbitrage opportunities are observed

in the prices that are quoted in most ﬁnancial markets. In this book most of the

arguments concerning futures prices, forward prices, and the values of option contracts

will be based on the assumption that there are no arbitrage opportunities.

1.11 DANGERS

Derivatives are very versatile instruments. As we have seen they can be used for

hedging, for speculation, and for arbitrage. It is this very versatility that can cause

problems. Sometimes traders who have a mandate to hedge risks or follow an arbitrage

strategy become (consciously or uncon sciously) speculators. The results can be disas-

trous. One example of this is provided by the activities of Je

roˆ me Kerviel at Socie

ral (see Business Snapshot 1.4).

To avoid the type of problems Socie

ral encountered it is very important for

both ﬁnancial and nonﬁnancial corporations to set up controls to ensure that derivatives

are being used for their intended purpose. Risk limits should be set and the activities of

traders should be monitored daily to ensure that the risk limits are adhered to.

Unfortunately, even when traders follow the risk limits that have been speciﬁed, big

mistakes can happen. Some of the activities of traders in the derivatives market during

the period leading up to the start of the credit crisis in July 2007 proved to be much

riskier than they were thought to be by the ﬁnancial institutions they worked for. As

will be discussed in Chapter 8, house prices in the United States had been rising fast.

Most people thought that the increases would continue—or, at worst, that house prices

would simply level oﬀ. Very few were prepared for the steep decline that actually

happened. Furthermore, very few were prepared for the high correlation between

mortgage default rates in diﬀerent parts of the country. Some risk managers did express

reservations about the exposures of the companies for which they worked to the US real

estate market. But, when times are good (or appear to be good), there is an unfortunate

tendency to ignore risk managers and this is what happened at many ﬁnancial

institutions during the 2006–2007 period. The key less on from the credit crisis is that

ﬁnancial institutions should always be dispassionately asking ‘‘What can go wrong?’’,

and they should follow that up with the question ‘‘If it does go wrong, how much will

we lose?’’

SUMMARY

In this chapter we have taken a ﬁrst look at futures, forward, and options markets.

Futures and forward contracts are agreements to buy or sell an asset at a certain time in

the future for a certain price. Futures contracts are traded on an exchange, whereas

forward contracts are traded in the over-the-counter market. There are two types of

18 CHAPTER 1

options: calls and puts. A call option gives the holder the right to buy an asset by a

certain date for a certain price. A put option gives the holder the right to sell an asset by

a certain date for a certain price. Options trade both on exchanges and in the over-the-

counter market.

Futures, forwards, and options have been very successful innovations. Three main

types of participants in the markets can be identiﬁed: hedgers, speculators, and

arbitrageurs. Hedgers are in the position of facing risk associated with the price of

an asset. They use futures, forward, or option contracts to reduce or eliminate this risk.

Speculators wish to bet on future movements in the price of an asset. Futures, forward,

and option contracts can give them extra leverage; that is, the contracts can increase

both the potential gains and potential losses in a speculative investment. Arbitrageurs

are in business to take advantage of a discrepancy between prices in two diﬀerent

markets. If, for example, they see the futures price of an asset getting out of line with

the spot price, they will take oﬀsetting positions in the two markets to lock in a proﬁt.

Business Snapshot 1.4 SocGen’s big loss in 2008

Derivatives are very versatile instruments. They can be used for hedging, speculation,

and arbitrage. One of the risks faced by a company that trades derivatives is that an

employee who has a mandate to hedge or to look for arbitrage opportunities may

become a speculator.

roˆ me Kerviel joined Socie

ral (SocGen) in 2000 to work in the compliance

area. In 2005, he was promoted and became a junior trader in the bank’s Delta One

products team. He traded equity indices such as the German DAX index, the French

CAC 40, and the Euro Stoxx 50. His job was to look for arbitrage opportunities.

These might arise if a futures contract on an equity index was trading for a diﬀerent

price on two diﬀerent exchanges. They might also arise if equity index futures prices

were not consistent with the prices of the shares constituting the index. (This type of

arbitrage is discussed in Chapter 5.)

Kerviel used his knowledge of the bank’s procedures to speculate while giving the

appearance of arbitraging. He took big positions in equity indices and created

ﬁctitious trades to make it appear that he was hedged. In reality, he had large bets

on the direction in which the indices would move. The size of his unhedged position

grew over time to tens of billions of euros.

In January 2008, his unauthorized trading was uncovered by SocGen. Over a three-

day period, the bank unwound his position for a loss of 4.9 billion euros. This was at

the time the biggest loss created by fraudulent activity in the history of ﬁnance. (Later

in the year, a much bigger loss from Bernard Madoﬀ’s Ponzi scheme came to light.)

Rogue trader losses were not unknown at banks prior to 2008. For example, in the

1990s, Nick Leeson, who worked at Barings Bank, had a mandate similar to that of

roˆ me Kerviel. His job was to arbitrage between Nikkei 225 futures quotes in

Singapore and Osaka. Instead he found a way to make big bets on the direction of

the Nikkei 225 using futures and options, losing $1 billion and destroying the 200-year

old bank in the process. In 2002, it was found that John Rusnak at Allied Irish Bank

had lost $700 million from unauthorized foreign exchange trading. The lessons from

these losses are that it is important to deﬁne unambiguous risk limits for traders and

then to monitor what they do very carefully to make sure that the limits are adhered to.

Introduction

FURTHER READING

Chancellor, E. Devil Take the Hindmost—A History of Financial Speculation. New York: Farra

Straus Giroux, 2000.

Merton, R. C. ‘‘Finance Theory and Future Trends: The Shift to Integration,’’ Risk, 12, 7 (July

1999): 48–51.

Miller, M. H. ‘‘Financial Innovation: Achievements and Prospects,’’ Journal of Applied

Corporate Finance, 4 (Winter 1992): 4–11.

Zingales, L. ‘‘Causes and Eﬀects of the Lehman Bankruptcy,’’ Testimony before Committee on

Oversight and Government Reform, United States House of Representatives, October 6, 2008.

Quiz (Answers at End of Book)

1.1. What is the diﬀerence between a long futures position and a short futures position?

1.2. Explain carefully the diﬀerence between (a) hedging, (b) speculation, and (c) arbitrage.

1.3. What is the diﬀerence between (a) entering into a long futures contract when the futures

price is $50 and (b) taking a long position in a call option with a strike price of $50?

1.4. An investor enters into a short forward contract to sell 100,00 0 British pounds for

U.S. dollars at an exchange rate of 1.4000 U.S. dollars per pound. How much does the

investor gain or lose if the exchange rate at the end of the contract is (a) 1.3900

and (b) 1.4200?

1.5. Suppose that you write a put contract with a strike price of $40 and an expiration date

in three months. The current stock price is $41 and one put option contract is on 100

shares. What have you committed yourself to? How much could you gain or lose?

1.6. You would like to speculate on a rise in the price of a certain stock. The current stock

price is $29 and a three-month call wi th a strike price of $30 costs $2.90. You have

$5,800 to invest. Identify two alternative strategies. Brieﬂy outlin e the advantages and

disadvantages of each.

1.7. What is the diﬀerence between the over-the-counter and the exchange-traded market?

What are the bid and oﬀer quotes of a market maker in the over-the-counter market?

Practice Questions (Answers in Solutions Manual/Study Guide)

1.8. Suppose you own 5,000 shares that are worth $25 each. How can put options be used to

provide you with insurance against a decline in the value of your holding over the next

four months?

1.9. A stock when it is ﬁrst issued provides funds for a company. Is the same true of an

exchange-traded stock option? Discuss.

1.10. Explain why a futures contract can be used for either speculation or hedging.

1.11. A cattle farmer expects to have 120,000 pounds of live cattle to sell in three months. The

live-cattle futures contract on the Chicago Mercantile Exchange is for the delivery of

40,000 pounds of cattle. How can the farmer use the contract for hedging? From the

farmer’s viewpoint, what are the pros and cons of hedging?

20 CHAPTER 1

1.12. It is July 2013. A mining company has just discovered a small deposit of gold. It will take

six months to construct the mine. The gold will then be extracted on a more or less

continuous basis for one year. Futures contracts on gold are available on the New York

Mercantile Exchange. There are delivery months every two months from August 2013 to

December 2014. Each contract is for the delivery of 100 ounces. Discuss how the mining

company might use futures markets for hedging.

1.13. Suppose that a March call option on a stock with a strike price of $50 costs $2.50 and is

held until March. Under what circumstances will the holder of the option make a gain?

Under what circumstances will the option be exercised? Draw a diagram showing how the

proﬁt on a long position in the option depends on the stock price at the maturity of the

option.

1.14. Suppose that a June put option on a stock with a strike price of $60 costs $4 and is held

until June. Under what circumstances will the holder of the option make a gain? Under

what circumstances wi ll the option be exercised? Draw a diagram showing how the proﬁt

on a short position in the option depends on the stock price at the maturity of the option.

1.15. It is May and a trader writes a September call option with a strike price of $20. The stock

price is $18 and the option price is $2. Describe the investor’s cash ﬂows if the option is

held until September and the stock price is $25 at this time.

1.16. An investor writes a December put option with a strike price of $30. The price of the

option is $4. Under what circumstances does the investor make a gain?

1.17. The CME Group oﬀers a futures contract on long-term Treasury bonds. Characterize the

investors likely to use this contract.

1.18. An airline executive has argued: ‘‘There is no point in our using oil futures. There is just

as much chance that the price of oil in the future will be less than the futures price as there

is that it will be greater than this price.’’ Discuss the executive’s viewpoint.

1.19. ‘‘Options and futures are zero-sum games.’’ What do you think is meant by this statement?

1.20. A trader enters into a short forward contract on 100 million yen. The forward exchange

rate is $0.0080 per yen. How much does the trader gain or lose if the exchange rate at the

end of the contract is (a) $0.0074 per yen; (b) $0.0091 per yen?

1.21. A trader enters into a short cotton futures contract when the futures price is 50 cents per

pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or

lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents

per pound?

1.22. A company knows that it is due to receive a certain amount of a foreign currency in four

months. What type of option contract is appropriate for hedging?

1.23. A United States company expects to have to pay 1 million Canadian dollars in six

months. Explain how the exchange rate risk can be hedged using (a) a forward contract;

(b) an option.

1.24. A trader buys a call option with a strike price of $30 for $3. Does the trader ever exercise

the option and lose money on the trade. Explain.

1.25. A trader sells a put option with a strike price of $40 for $5. What is the trader’s maximum

gain and maximum loss? How does your answer change if it is a call option?

1.26. ‘‘Buyin g a stock and a put option on the stock is a form of insurance.’’ Explain this

statement.

Introduction

Further Questions

1.27. Trader A enters into a forward contract to buy an asset for $1,000 in one year. Trader B

buys a call option to buy the asset for $1,000 in one year. The cost of the option is $100.

What is the diﬀerence between the positions of the traders? Show the proﬁt as a function

of the price of the asset in one year for the two traders.

1.28. On June 25, 2012, as indicated in Table 1.2, the spot oﬀer price of Google stock is $561.5 1

and the oﬀer price of a call option with a strike price of $560 and a maturity date of

September is $30.70. A trader is considering two alternatives: buy 100 shares of the stock

and buy 100 September call options . For each alternative, what is (a) the upfront cost, (b)

the total gain if the stock price in September is $620, and (c) the total loss if the stock

price in September is $500. Assume that the option is not exercised before September and

if stock is purchased it is sold in September.

1.29. What is arbitrage? Explain the arbitrage opportunity when the price of a dually listed

mining company stock is $50 (USD) on the New York Stock Exchange and $52 (CAD)

on the Toronto Stock Exchange. Assume that the exchange rate is such that 1 USD

equals 1.01 CAD. Explain what is likely to happen to prices as traders take advantage of

this opportunity.

1.30. In March, a U.S. investor instructs a broker to sell one July put option contract on a

stock. The stock price is $42 and the strike price is $40. The option price is $3. Explain

what the investor has agreed to. Under what circumstances will the trade prove to be

proﬁtable? What are the risks?

1.31. A U.S. company knows it will have to pay 3 million euros in three months. The current

exchange rate is 1.4500 dollars per euro. Discuss how forward and options contracts can

be used by the company to hedge its exposure.

1.32. A stock price is $29. An investor buys one call option contract on the stock with a strike

price of $30 and sells a call option contract on the stock with a strike price of $32.50. The

market prices of the options are $2.75 and $1.50, respectively. The options have the same

maturity date. Describe the investor’s position.

1.33. The price of gold is currently $1,800 per ounce. Forward contracts are available to buy or

sell gold at $2,000 per ounce for delivery in one year. An arbitrageur can borrow money at

5% per annum. What should the arbitrageur do? Assume that the cost of storing gold is

zero and that gold provides no income.

1.34. Discuss how foreign currency options can be used for hedging in the situation described in

Example 1.1 so that (a) ImportCo is guaranteed that its exchange rate will be less than

1.5800, and (b) ExportCo is guaranteed that its exchange rate will be at least 1.5400.

1.35. The current price of a stock is $94, and three-month European call options with a strike

price of $95 currently sell for $4.70. An investor who feels that the price of the stock will

increase is trying to decide between buying 100 shares and buying 2,000 call options

(20 contracts). Both strategies involve an investment of $9,400. What advice would you

give? How high does the stock price have to rise for the option strategy to be more

proﬁtable?

1.36. On June 25, 2012, an investor owns 100 Google shares. As indicated in Table 1.3, the bid

share price is $561.32 an d a Decembe r put option with a strike price of $520 costs $26.10.

The investor is comparing two alternatives to limit downside risk. The ﬁrst involves

22 CHAPTER 1

buying one December put option contract with a strike price of $520. The second involves

instructing a broker to sell the 100 shares as soon as Google’s price reaches $520. Discuss

the advantages and disadvantages of the two strategies.

1.37. A trader buys a European call option and sells a European put option. The options have

the same underlying asset, strike price, and maturity. Describe the trader’s position.

Under what circumstances does the price of the call equal the price of the put?

Introduction

Mechanics of

Futures Markets

In Chapter 1 we explained that both futures and forward contracts are agreements to

buy or sell an asset at a future time for a certain price. Futures contracts are traded on

an exchange and the contract terms are standardized by that exchange. Forward

contracts are traded in the over-the-counter market.

This chapter covers the details of how futures markets work. We examine issues such

as the speciﬁcation of contracts, the operation of margin accounts, the organization of

exchanges, the regulation of markets, the way in which quotes are made, and the

treatment of futures transactions for accounting and tax purposes. We explain how

some of the ideas pioneered by futures exchanges are now being adopted by over-the-

counter markets.

2.1 OPENING AND CLOSING FUTURES POSITIONS

A futures contract is an agreement to buy or sell an asset for a certain price at a certain

time in the future. A contract is usually referred to by its delivery month. Thus an

investor could instruct a broker to buy one October oil futures contract. There is a

period of time during the delivery month (often the whole month) when delivery can be

made. Trading in the contract usually ceases some time during the delivery period. The

party with the short position chooses when delivery is made.

The reader may be surprised to learn that the vast majority of the futures contracts

that are initiated do not lead to delivery. The reason is that most investors choose to

close out their posit ions prior to the delivery period speciﬁed in the contract. Making or

taking delivery under the terms of a futures contract is often inconvenient and in some

instances quite expensive. This is true even for a hedger who wants to buy or sell the

asset underlying the futures contract. Such a hedger usually prefers to close out the

futures position and then buy or sell the asset in the usual way.

Closing a position involves entering into an opposite trade to the original one that

opened the position. For example, an investor who buys ﬁve July corn futures contracts

on May 6 can close out the position on June 20 by selling (i.e., shorting) ﬁve July corn

futures contracts. An investor who sells (i.e., shorts) ﬁve July contracts on May 6 can

close out the position on June 20 by buying ﬁve July contracts. In each case, the

CHAPTER

From Chapter 2 of Fundamentals of Futures and Options Markets, Eighth Edition. John C. Hull.

investor’s total gain or loss is determined by the change in the futures price between

May 6 and June 20.

Delivery is so unusual that traders sometimes forget how the delivery process works

(see Business Snapshot 2.1). Nevertheless we will spend part of this chapter reviewing

the delivery arrangements in futures contracts. This is because it is the possibility of

ﬁnal delivery that ties the futures price to the spot price.

2.2 SPECIFICATION OF A FUTURES CONTRACT

When developing a new contract, the exchange must specify in some detail the exact

nature of the agreement between the two parties. In parti cular, it must specify the asset,

the contract size (exactly how much of the asset will be delivered under one contract),

where delivery will be made, and when delivery will be made.

Sometimes alternatives are speciﬁed for the grade of the asset that will be delivered or

for the delivery locations. As a general ru le, it is the party with the sho rt position (the

party that has agreed to sell the asset) that chooses what will happen when alternatives

are speciﬁed by the exchange.

When the party with the short position is ready to

deliver, it ﬁles a notice of intention to deliver with the exchange. This notice indicates

selections it has made with respect to the grade of asset that will be delivered and the

delivery location.

The Asset

When the asset is a commodity, there may be quite a variation in the quality of what is

available in the marketplace. When the asset is speciﬁed, it is therefore important that

the exchange stipulate the grade or grades of the commodity that are acceptable. The

IntercontinentalExchange (ICE) has speciﬁed the asset in its orange juice futures

contract as frozen concentrates that are U.S. Grade A, with Brix value of not less than

62.5 degrees.

For some commodities a range of grades can be delivered, but the price received

depends on the grade chosen. For example, in the CME Group corn futures contract,

the standard grade is ‘‘No. 2 Yellow,’’ but substitutions are allowed with the price being

adjusted in a way established by the exchange. No. 1 Yellow is deliverable for 1.5 cents

per bushel more than No. 2 Yellow. No. 3 Yellow is deliverable for 1.5 cents per bushel

less than No. 2 Yellow.

The ﬁnancial assets in futures contracts are generally well deﬁned and unambiguous .

For example, there is no need to specify the grade of a Japanese yen. However, there are

some interesting features of the Treasury bond and Treasury note futures contracts

traded by the CME Group. The underlying asset in the Treasury bond contract is any

U.S. Treasury bond that has a maturity between 15 and 25 years on the ﬁrst day of the

delivery month. In the 10-year Treasury note futures contract, the underlying asset is

any Treasury note with a maturity between 6.5 and 10 years on the ﬁrst day of the

As mentioned in Chapter 1, the spot price is the price for almost immediate delivery.

There are exceptions. As pointed out by J. E. Newsome, G. H. K. Wang, M. E. Boyd, and M. J. Fuller in

‘‘Contract Modiﬁcations and the Basis Behavior of Live Cattle Futures,’’ Journal of Futures Markets, 24, 6

(2004), 557–90, the CME gave the buyer some options on how delivery could be made in live cattle futures

in 1995.

Mechanics of Futures Markets 25

delivery month.. In both cases, the exchange has a formula for adjusting the price

received according to the coupon and maturity date of the bond delivered. This is

discussed in Chapter 6.

The C ontract Size

The con tract size speciﬁes the amount of the asset that has to be delivered under one

contract. This is an important decision for the exchange. If the contract size is too large,

many investors who wish to hedge relatively small exposures or who wish to take

relatively small speculative positions will be unable to use the exchange. On the other

hand, if the contract size is too small, trading may be expensive as there is a cost

associated with each contract traded.

The correct size for a contract clearly depends on the likely user. Whereas the value of

what is delivered under a futures contract on an agricultural product might be $10,000

to $20,00 0, it is much higher for some ﬁnancial futures. For example, under the

Business Snapshot 2.1 The unanticipated delivery of a futures contract

This story (which may well be apocryphal) was told to the author of this book a long

time ago by a senior executive of a ﬁnancial institution. It concerns a new employee of

the ﬁnancial institution who had not previously worked in the ﬁnancial sector. One of

the clients of the ﬁnancial institution regularly entered into a long futures contract on

live cattle for hedging purposes and issued instructions to close out the position on

the last day of trading. (Live cattle futures contracts are traded by the CME Group

and each contract is on 40,000 pounds of cattle.) The new employee was given

responsibility for handling the account.

When the time came to close out a contract, the employee noted that the client was

long one contract and instructed a trader at the exchange to buy (not sell) one

contract. The result of this mistake was that the ﬁnancial institution ended up with

a long position in two live cattle futures contracts. By the time the mistake was

spotted, trading in the contract had ceased.

The ﬁnancial institution (not the client) was responsible for the mistake. As a result

it started to look into the details of the delivery arrangements for live cattle futures

contracts—something it had never done before. Under the terms of the contract,

cattle could be delivered by the party with the short position to a number of diﬀerent

locations in the United States during the delivery month. Because it was long, the

ﬁnancial institution could do nothing but wait for a party with a short position to

issue a notice of intention to deliver to the exchange and for the exchange to assign

that notice to the ﬁnancial institution.

It eventually received a notice from the exchange and found that it would receive live

cattle at a location 2,000 miles away the following Tuesday. The new employee was sent

to the location to handle things. It turned out that the location had a cattle auction

every Tuesday. The party with the short position that was making delivery bought

cattle at the auction and then immediately delivered them. Unfortunately the cattle

could not be resold until the next cattle auction the following Tuesday. The employee

was therefore faced with the problem of making arrangements for the cattle to be

housed and fed for a week. This was a great start to a ﬁrst job in the ﬁnancial sector!

26 CHAPTER 2

Treasury bond futures contract traded by the CME Group, instruments with a face

value of $100,000 are delivered.

In some cases exchanges have introduced ‘‘mini’’ contracts to attract smaller inves-

tors. For example, the CME Group’s Mini Nasdaq 100 contract is on 20 times the

Nasdaq 100 index whereas the regular contract is on 100 times the index. (We will cover

futures on indices more fully in Chapter 3.)

Delivery Arrangements

The place where delivery will be made must be speciﬁed by the exchange. This is

particularly important for commodities that involve signiﬁcant transportation costs. In

the case of the ICE frozen concentrate orange juice contract, delivery is to exchange-

licensed warehouses in Florida, New Jersey, or Delaware.

When alternative delivery locations are speciﬁed, the price received by the party with

the short position is sometimes adjusted according to the location chosen by that party.

The price tends to be higher for delivery locations that are relatively far from the main

sources of the commodity.

Delivery Months

A futures contract is referred to by its delivery month. The exchange must specify the

precise period during the month when delivery can be made. For many futures

contracts, the delivery period is the whole month.

The delivery months vary from contract to contract and are chosen by the exchange

to meet the needs of market participants. For example, corn futures traded by the CME

Group have delivery months of March, May, July, September, and December. At any

given time, contracts trade for the closest delivery month and a number of subsequent

delivery months. The exchange speciﬁes when trading in a particular month’s contract

will begin. The exchange also speciﬁes the last day on which trading can take place for a

given contract. Trading generally ceases a few days before the last day on which delivery

can be made.

Price Quotes

The exchange deﬁnes how prices will be quoted. For example, in the U.S., crude oil

futures prices are quoted in dollars and cents, but Treasury bond and Treasury note

futures prices are quoted in dollars and thirty-seconds of a dollar.

Price Limits and Position Limits

For most contracts, daily price movement limits are speciﬁed by the exchange. If in a day

the price moves down from the previous day’s close by an amount equal to the daily price

limit, the contract is said to be limit down. If it moves up by the limit, it is said to be limit

up.Alimit move is a move in either direction equal to the daily price limit. Normally,

trading ceases for the day once the contract is limit up or limit down. However, in some

instances the exchange has the authority to step in and change the limits.

The purpose of daily price limits is to prevent large price movements from occurring

because of speculative excesses. However, limits can become an artiﬁcial barrier to

Mechanics of Futures Markets

trading when the price of the underlying commodity is advan cing or declining rapidly.

Whether price limits are, on balance, good for futures markets is controversial.

Position limits are the maximum number of contracts that a speculator may hold.

The purpose of these limits is to prevent speculators from exercising undue inﬂuence on

the market.

2.3 CONVERGENCE OF FUTURES PRICE TO SPOT PRICE

As the delivery period for a futures contract is approached, the futures price converges

to the spot price of the underlying asset. When the delivery period is reached, the

futures price equals, or is very close to the spot price.

To see why this is so, we ﬁrst suppose that the futures price is above the spot price

during the delivery period. Traders then have a clear arbitrage opportunity:

1. Sell (i.e., short) a futures contract

2. Buy the asset

3. Make delivery

These steps are certa in to lead to a proﬁt equal to the amount by which the futures price

exceeds the spot price. As traders exploit this arbitrage opportunity, the futures price

will fall. Suppose next that the futures price is below the spot price during the delivery

period. Companies interested in acquiring the asset will ﬁnd it attractive to buy a futures

contract and then wait for delivery to be made. As they do so, the futures price will tend

to rise.

The result is that the futures price is very close to the spot price during the delivery

period. Figure 2.1 illustrates the convergence of the futures price to the spot price. In

Figure 2.1a the futures price is above the spot price prior to the delivery period, and in

Figure 2.1b the futures price is below the spot price prior to the delivery period. The

circumstances under which these two patterns are observed are discussed in Chapter 5.

Time

(a) (b)

Futures

price

Spot

price

Time

Futures

price

Spot

price

Figure 2.1 Relationship between futures price and spot price as the delivery month is

approached: (a) futures price above spot price; (b) futures price below spot price

28 CHAPTER 2

2.4 THE OPERATION OF MARGIN ACCOUNTS

If two investors get in touch with each other directly and agree to trade an asset in the

future for a certain price, there are obvious risks. One of the investors may regret the

deal and try to back out. Alternatively, the investor simply may not have the ﬁnancial

resources to honor the agreement. One of the key roles of the exchange is to organize

trading so that contract defaults are avoided. This is where margin accounts come in.

Daily Settlement

To illu strate how margin accounts work, we consider an investor who contacts his or her

broker on June 5 to buy two December gold futures contracts. We suppose that the

current futures price is $1,650 per ounce. Because the contract size is 100 ounces, the

investor has contracted to buy a total of 200 ounces at this price. The broker will require

the investor to deposit funds in a margin account. The amount that must be deposited at

the time the contract is entered into is known as the initial margin. We suppose this is

$6,000 per contract, or $12,000 in total. At the end of each trading day, the margin

account is adjusted to reﬂect the investor’s gain or loss. This practice is referred to as daily

settlement or marking to market.

Suppose, for example, that by the end of June 5 the futures price has dropped from

$1,650 to $1,641. The investor has a loss of $1,800 (¼ 200  $9), because the 200

ounces of December gold, which the investor contracted to buy at $1,650, can now be

sold for only $1,641. The balance in the margin account would therefore be reduced by

$1,800 to $10,200. Similarly, if the price of December gold rose to $1,659 by the end of

June 5, the balance in the margi n account would be increased by $1,800 to $13,800. A

trade is ﬁrst settled at the close of the day on which it takes place. It is then settled at the

close of trading on each subsequent day.

Note that daily settlement is not merely an arrangement between broker and client.

When there is a decrease in the futures price so that the margin account of an investor

with a long posit ion is reduced by $1,800, the investor’s broker has to pay the exchange

clearing house $1,800 and this money is passed on to the broker of an investor with a

short position. Similarly, when there is an increase in the futures price, brokers for

parties with short positions pay money to the exchange clearing house and brokers for

parties with long positions receive money from the exchange clearing house. Later we

will examine in more detail the mechanism by which this happens.

The investor is entitled to withdraw any balance in the margin account in excess of the

initial margin. To ensure that the balance in the margin account never becomes negative,

a maintenance margin, which is somewhat lower than the initial margin, is set. If the

balance in the margin account falls below the maintenance margin, the investor receives

a margin call and is expected to top up the margin account to the initial margin level the

next day. The extra funds deposited are known as a variation margin. If the investor does

not provide the variation margin, the broker closes out the position. In the case

considered above, closing out the position would involve neutralizing the existing

contract by selling 200 ounces of gold for delivery in December.

Table 2.1 illustrates the operation of the margin account for one possible sequence of

futures prices in the case of the investor considered earlier. The maintenance margin is

assumed for the purpose of the illustration to be $4,500 per contract, or $9,000 in total.

On Day 7 the balance in the margin account falls $1,020 below the maintenance margin

Mechanics of Futures Markets

level. This drop triggers a margin call from the broker for additional $4,020 to bring the

margin account balance up to $12,000. Table 2.1 assumes that the investor does in fact

provide this margin by the close of trading on Day 8. On Day 11 the balance in the

margin account again falls below the maintenance margin level, and a margin call for

$3,780 is sent out. The investor provides this margin by the close of trading on Day 12.

On Day 16 the investor decides to close out the position by selling two contracts. The

futures price on that day is $1,626.90, and the investor has a cumulative loss of $4,620.

Note that the investor has excess margin on Days 8, 13, 14, and 15. Table 2.1 assumes

that the excess is not withdrawn.

Further Details

Most brokers pay investors interest on the balance in a margin account. The balance in

the account does not, therefore, represent a true cost, providing the interest rate is

competitive with what could be earned elsewhere. To satisfy the initial margi n require-

ments (but not subsequent margin calls), an investor can usually deposit securities with

the broker. Treasury bills are usually accepted in lieu of cash at about 90% of their face

value. Shares are also sometimes accepted in lieu of cash—but at about 50% of their

market value.

Whereas a forward contract is settled at the end of its life, a futures contract is settled

daily. At the end of each day, the investor’s gain (loss) is added to (subtracted from) the

Table 2.1 Operation of margin account for a long position in two gold futures

contracts. The initial margin is $6,000 per contract, or $12,000 in total; the

maintenance margin is $4,500 per contract, or $9,000 in total. The contract

is entered into on Day 1 at $1,650 and closed out on Day 16 at $1,626.90

Day Trade

price ($)

Settlement

price ($)

Daily

gain ($)

Cumulative

gain ($)

Margin account

balance ($)

Margin

call ($)

1 1,650.00 12,000

1 1,641.00 1,800 1,800 10,200

2 1,638.30 540 2,340 9,660

3 1,644.60 1,260 1,080 10,920

4 1,641.30 660 1,740 10,260

5 1,640.10 240 1,980 10,020

6 1,636.20 780 2,760 9,240

7 1,629.90 1,260 4,020 7,980 4,020

8 1,630.80 180 3,840 12,180

9 1,625.40 1,080 4,920 11,100

10 1,628.10 540 4,380 11,640

11 1,611.00 3,420 7,800 8,220 3,780

12 1,611.00 0 7,800 12,000

13 1,614.30 660 7,140 12,660

14 1,616.10 360 6,780 13,020

15 1,623.00 1,380 5,400 14,400

16 1,626.90 780 4,620 15,180

30 CHAPTER 2

margin account, bringing the value of the contract back to zero. A futures contract is in

eﬀect closed out and rewritten at a new price each day.

Minimum levels for the initial and maintenance margin are set by the exchange

clearing house. Individual brokers may require more margin from their clients than the

minimum level speciﬁed by the exchange clearing house. Minimum margin levels are

determined by the variability of the price of the underlying asset and are revised when

necessary. The higher the variability, the higher the margin levels. The maintenance

margin is usually about 75% of the initial margin.

Margin requirements may depend on the objectives of the trader. A bona ﬁde hedger,

such as a company that produces the commod ity on which the futures contract is

written, is often subject to lower margin requirements than a speculator. The reason is

that there is deemed to be less risk of default. Day trades and spread transactions often

give rise to lower margin requirements than do hedge transactions. In a day trade the

trader announces to the broker an intent to close out the position in the same day. In a

spread transaction the trader simultaneously buys (i.e., takes a long position in) a

contract on an asset for one maturity month and sells (i.e., takes a short position in)

a contract on the same asset for another maturity month.

Note that margin requirements are the same on short futures positions as they are on

long futures positions. It is just as easy to take a short futures position as it is to take a

long one. The spot market does not have this symmetry. Taking a long position in the

spot market involves buying the asset for immediate delivery and presents no problems.

Taking a short position involves selling an asset that you do not own. This is a more

complex transaction that may or may not be possible in a particular market. It is

discussed further in Chapter 5.

The Clearing House and Clearing Margin

A clearing house acts as an intermediary in futures transactions. It guarantees the

performance of the parties to each transaction. The clearing house has a number of

members, who must contribute to a default fund. Brokers who are not members

themselves must channel their business through a member. The main task of the clearing

house is to keep track of all the transactions that take place during a day so that it can

calculate the net position of each of its members.

Just as an investor is required to maintain a margin account with a broker, the broker is

required to maintain margin with a clearing house member and the clearing house

member is required to maintain a margin account with the clearing house. The latter

is known as a clearing margin. The margin accounts for clearing house members are

adjusted for gains and losses at the end of each trading day in the same way as are the

margin accounts of investors. However, in the case of the clearing house member, there is

an original margin, but no maintenance margin. Every day the account balance for each

contract must be maintained at an amount equal to the original margin times the number

of contracts outstanding. Thus, depending on transactions during the day and price

movements, the clearing house member may have to add funds to its margin account at

the end of the day, or it may ﬁnd it can remove funds from the account at this time.

Brokers who are not clearing house members must maintain a margin account with a

clearing house member.

In determining a clearing margin, the exchange clearing house calculates the number

of contracts outstanding on either a gross or a net basis. When the gross basis is used,

Mechanics of Futures Markets

the number of contracts equals the sum of long and short positions; when the net basis is

used, these are oﬀset against each other. Suppose a clearing house member has two

clients: one with a long position in 20 contracts, the other with a short position in

15 contracts. Gross margining would calculate the clearing margin on the basis of

35 contracts; net margining would calculate the clearing margin on the basis of

5 contracts. Most exchanges currently use net margining.

Credit Risk

The whole purpose of the margining system is to ensure that funds are available to pay

traders when they make a proﬁt. Overall the system has been very successful. Traders

entering into contracts at major exchanges have always had their contracts honored.

Futures markets were tested on October 19, 1987, when the S&P 500 index declined by

over 20% and traders with long positions in S&P 500 futures found they had negative

margin balances. Traders who did not meet margin calls were closed out but still owed

their brokers money. Some did not pay, and as a result some brokers went bankrupt

because, without their clients’ money, they were unable to meet margin calls on contracts

they had entered into on behalf of their clients. However, the clearing house had suﬃcient

funds to ensure that everyone who had a short futures position on the S&P 500 got paid.

2.5 OTC MARKETS

Over-the-counter (OTC) markets, introduced in Chapter 1, are markets where companies

agree to derivatives transactions without involving an exchange. Credit risk has tradi-

tionally been a feature of OTC derivatives markets. Consider two companies, A and B,

that have entered into a number of derivatives transactions. If A defaults when the net

value of the outstanding transactions to B is positive, a loss is liable to be taken by B.

Similarly, if B defaults when the net value of outstanding transactions to A is positive, a

loss is likely to be taken by A.

In an attempt to reduce credit risk, the OTC market has used some of the procedures

of exchange-traded markets. The agreement between company A and company B may

require A or B, or both, to post margin. (In this case of OTC markets, margin is

referred to as collateral.) Also, as mentioned in Section 1.3, A and B may use a central

clearing party, which is similar to an exchange clearing house, for its transactions. We

will now explain these developments.

Collateral

Consider again two companies, A and B, that have entered into a number of OTC

derivatives transactions. A collateral agreement between the companies is likely to

involve the transactions being valued each day. The agreement may be one-way, where

only one side is liable to have to post collateral, or two-way, where both sides are liable

to have to post collateral. Many diﬀerent types of collateral arrangements can be

negotiated. A simple two-way agreement might work as follows. If from one day to

the next the transactions increase in value to A by $X (and decrease in value to B

by $X), company B is required to provide $X of collateral to A. If the reverse happens

and the transactions increase in value to B by $X (and decrease in value to A by $X),

32 CHAPTER 2

company A is required to provide $X to B. To use the terminology of exchange-traded

markets, in this arrangement the companies would be required to post variation

margin, but no initial margin.

The collateral can be in the form of cash or acceptable marketable securities. Interest

is usually paid on cash collateral. The market value of securities is usually reduced by a

certain percentage amount to determine their value for collateral purposes. This

reduction is known as a haircut.

Collateralization signiﬁcantly reduces the credit risk in over-the-counter contracts.

Collateralization agreements were used by a hedge fund, Long-Term Capital Manage-

ment (LTCM) in the 1990s. They allowed LTCM to be highly levered. The contracts did

provide credit risk protection, but as descri bed in Business Snapshot 2.2 the high

leverage left the hedge fund vulnerable to other risks.

The U se of Clearing Houses in OTC Markets

Prior to the credit crisis that started in 2007, most OTC trades were handled by bilateral

agreements between market participants.

As just described, the agreements often

Business Snapshot 2.2 Long-Term Capital Management’s big loss

Long-Term Capital Management (LTCM), a hedge fund formed in the mid-1990s,

always collateralized its transactions. The hedge fund’s investment strategy was

known as convergence arbitrage. A very simple example of what it might do is the

following. It would ﬁnd two bonds, X and Y, issued by the same company that

promised the same payoﬀs, with X being less liquid (i.e., less actively traded) than Y.

The market places a value on liquidity. As a result the price of X would be less than

the price of Y. LTCM would buy X, short Y, and wait, expecting the prices of the two

bonds to converge at some future time.

When interest rates increased, the company expected both bonds to move down in

price by about the same amount so that the collateral it paid on bond X would be

about the same as the collateral it received on bond Y. Similarly, when interest rates

decreased LTCM expected both bonds to move up in price by about the same amount

so that the collateral it received on bond X would be about the same as the collateral

it paid on bond Y. It therefore expected that there would be no signiﬁcant outﬂow of

funds as a result of its collateralization agreements.

In August 1998, Russia defaulted on its debt and this led to what is termed a

‘‘ﬂight to quality’’ in capital markets. One result was that investors valued liquid

instruments more highly than usual and the spreads between the prices of the liquid

and illiquid instruments in LTCM’s portfolio increased dramatically. The prices of

the bonds LTCM had bought went down and the prices of those it had shorted

increased. It was required to post collateral on both. The company experienced

diﬃculties because it was highly leveraged. Positions had to be closed out and LTCM

lost about $4 billion. If the company had been less highly leveraged, it would

probably have been able to survive the ﬂight to quality and c ould have waited for

the prices of the liquid and illiquid bonds to move back closer to each other.

The most common such agreement was an International Swaps and Derivatives Association (ISDA) Master

Agreement.

Mechanics of Futures Markets 33

involved collateral being posted, but the amount of collateral required was not usually

as great as the amount of margin that would be required for similar transactions in the

exchange-traded market. As a result, whereas exchange-traded markets were almost

completely free of credit risk, OTC markets were not.

Following the credit crisis that started in 2007, regulators have become more

concerned about systemic risk (see Business Snapshot 1.2). This has led them to look

for ways reducing credit risk by making the OTC markets more like exchange-traded

markets. The result has been legislation requiring that standard OTC transactions (with

a few exceptions) be handled by what are known as central clearing parties (CCPs).

CCPs are similar to exchange clearing houses. Once it has been agreed between two

parties A and B, a standard OTC derivative transaction is presented to a CCP.

Assuming the CCP accepts the transaction, it becomes the counterparty to both A

and B. (This is similar to the way the clearing house for a futures exchange becomes the

counterparty to the two sides of a futures trade). For example, if the transaction is a

forward contract where A has agreed to buy an asset from B in one year for a certain

price, the clearing house agrees to

1. Buy the asset from B in one year for the agreed price, and

2. Sell the asset to A in one year for the agreed price.

It takes on the credit risk of both A and B. It manages this risk by requiring an initial

margin and a daily variation margin from each of them.

Figure 2.2 illustrates the way bilateral and central clearing work. (It makes the

simplifying assumption that there are only eight market participants and one CCP.)

Under bilateral clearing there are many diﬀerent agreements between market partici-

pants as indicated in Figure 2.2a. If all OTC contracts were cleared through a single

CCP we would move to the situation shown in Figure 2.2b. In practice, because not all

OTC transaction are routed through CCPs and there is more than one CCP, the market

has elements of both Figure 2.2a and 2.2b.

(a) (b)

Figure 2.2 (a) The traditional way in which OTC markets have operated: a series of

bilateral agreements between market participants; (b) how OTC markets would operate

with a single central clearing house.

34 CHAPTER 2

Table 2.2 Futures quotes for a selection of CME Group contracts on commodities

on July 13, 2012

Open High Low Prior

settlement

Last

trade

Change Volume

Gold, 100 oz, $ per oz

Aug. 2012 1571.2 1596.5 1565.6 1565.3 1589.7 þ24.4 115,296

Sept. 2012 1570.4 1597.5 1567.1 1566.4 1590.2 þ23.8 303

Oct. 2012 1574.0 1598.3 1570.0 1567.6 1593.6 þ26.0 726

Dec. 2012 1576.5 1601.0 1570.7 1570.0 1596.0 þ26.0 11,283

June 2013 1598.0 1604.6 1598.0 1576.1 1604.6 þ28.5 250

Crude Oil, 1,000 barrels, $ per barrel

Aug. 2012 85.86 87.61 85.58 86.08 87.28 þ1.20 223,698

Sept. 2012 86.33 88.00 85.95 86.46 87.68 þ1.22 87,931

Dec. 2012 87.45 89.21 87.39 87.73 88.94 þ1.21 31,701

Dec. 2013 88.85 90.15 88.78 88.92 89.95 þ1.03 11,128

Dec. 2014 87.20 87.74 87.20 86.98 87.74 þ0.76 2,388

Corn, 5,000 bushels, cents per bushel

Sept. 2012 730.00 748.00 726.50 731.25 742.25 þ11.00 78,317

Dec. 2012 731.25 749.00 727.25 732.25 742.25 þ10.00 179,010

Mar. 2013 733.00 748.25 729.00 734.50 743.50 þ9.00 22,588

May 2013 731.00 744.25 726.75 732.75 739.75 þ7.00 4,548

July 2013 728.00 739.00 721.00 728.75 733.50 þ4.75 7,874

Dec. 2013 618.75 626.50 613.75 618.25 626.00 þ7.75 4,260

Soybeans, 5,000 bushels, cents per bushel

Aug. 2012 1572.00 1600.00 1571.50 1572.50 1596.00 þ23.50 19,194

Sept. 2012 1544.50 1574.00 1544.50 1545.50 1570.00 þ24.50 7,024

Nov. 2012 1528.00 1561.50 1526.50 1529.00 1552.75 þ23.75 98,526

Jan. 2013 1527.75 1557.25 1523.75 1526.00 1548.00 þ22.00 11,621

Mar. 2013 1486.25 1508.00 1482.25 1481.25 1500.25 þ19.00 6,226

May 2013 1432.25 1453.25 1428.00 1430.25 1449.00 þ18.75 5,234

Wheat, 5,000 bushels, cents per bushel

Sept. 2012 845.75 865.75 842.00 846.75 846.25 0.50 41,301

Dec. 2012 859.00 877.75 856.00 859.75 861.50 þ1.75 29,450

Mar. 2013 868.00 885.75 865.00 869.00 870.00 þ2.00 6,972

May 2013 865.00 881.00 863.00 864.50 867.00 þ2.50 2,339

July 2013 824.50 840.00 824.25 826.75 832.50 þ5.75 4,118

Live Cattle, 40,000 lbs, cents per lb

Aug. 2012 116.900 117.600 116.300 117.025 117.225 þ0.200 23,117

Oct. 2012 121.450 121.650 120.525 121.650 121.600 0.050 18,427

Dec. 2012 124.900 125.000 124.050 124.975 124.950 0.025 6,561

Feb. 2013 128.500 128.500 127.525 128.550 128.500 0.050 2,450

Apr. 2013 131.225 131.400 130.300 131.375 131.250 0.125 1,615

Mechanics of Futures Markets

2.6 MARKET QUOTES

Futures quotes are available from exchanges and several online sources. Table 2.2 is

constructed from quotes provided by the CME Group for a number of diﬀerent

commodities at a particular time on July 13, 2012. Quotes for index, currency, and

interest rate futures are given in Chapters 3, 5, and 6, respectively.

The asset underlying the futures contract, the contract size, and the way the price is

quoted are shown at the top of each section of Table 2.2. The ﬁrst asset is gold. The

contract size is 100 ounces and the price is quoted as dollars per ounc e. The maturity

month of the co ntract is indicated in the ﬁrst column of the table.

Prices

The ﬁrst three numbers in each row of Table 2.2 show the opening price, the highest

price in trading so far during the day, and the lowest price in trading so far during the

day. The opening price is representative of the prices at which contracts were trading

immediately after the start of trading on July 13, 2012. For the August 2012 gold

contract, the opening price on July 13, 2012 was $1,571.2 per ounce. The highest price

during the day was $1,596.5 per ounce and the lowest price during the day was $1,565.6

per ounce.

Settlement Price

The settlement price is the price used for calculating daily gains and losses and margin

requirements. It is usually calculated as the price at which the contract traded im-

mediately before the end of a day’s trading session. The fourth number in Table 2.2

shows the settlement price the previous day (i.e., July 12, 2012). The ﬁfth number shows

the most recent trading price, and the sixth number shows the price change from the

previous day’s settlement price. In the case of the August 2012 gold contract, the

previous day’s settlem ent price was $1,565.3. The most recent trade was at $1,589.7,

$24.4 higher than the previous day’s settlement price. If $1,589.7 proved to be the

settlement price on July 13, 2012, the margin account of a trader with a long position in

one contract would gain $2,440 on July 13 and the margin account of a trader with a

short position woul d lose this amount on July 13.

Trading Volume and Open Interest

The ﬁnal column of Table 2.2 shows the trading volume. The trading volume is the

number of contracts traded in a day. It can be contrasted with the open interest, which is

the number of contracts outstanding, that is, the number of long positions or, equiva-

lently, the number of short positions.

If there is a large amount of trading by day traders (i.e., traders who enter into a

position and close it out on the same day) the volume of trading in a day can be greater

than either the beginning-of-day or end-of-day open interest.

Patterns of Futures

Futures prices can show a number of diﬀerent patterns. In Table 2.2, gold futures prices

and live cattle futures prices are an increasing function of maturity. This is known as a

36 CHAPTER 2

normal market. Soybean futures prices are a decreasing function of maturity. This is

known as an inverted market. Other commodities such as crude oil, corn, and wheat

showed patterns that were partly normal and partly inverted on July 13, 2012.

2.7 DELIVERY

As mentioned earlier in this chapter, very few of the futures contracts that are entered

into lead to delivery of the underlying asset. Most are closed out early. Nevertheless, it

is the possibility of eventual delivery that determines the futures price. An under-

standing of delivery procedures is therefore important.

The period during which delivery can be made is deﬁned by the exchange and varies

from contract to contract. The decision on when to deliver is made by the party with

the short position, whom we shall refer to as investor A. When investor A decides to

deliver, investor A’s broker issues a notice of intention to deliver to the exchange

clearing house. This notice states how many contracts will be delivered and, in the case

of commodi ties, also speciﬁes where delivery will be made and what grade will be

delivered. The exchange then chooses a party with a long position to accept delivery.

Suppose that investor B was the party on the other side of investor A’s futures

contract when it was entered into. It is important to realize that there is no reason to

expect that it will be investor B who takes delivery. Investor B may well have closed out

his or her position by trading with investor C, investor C may have closed out his or her

position by trading with investor D, and so on. The usual rule chosen by the exchange

is to pass the notice of intention to deliver on to the party with the oldest outstanding

long position. Parties with long positions must accept delivery notices. However, if the

notices are transferable, long investors have a short period of time, usually half an

hour, to ﬁnd another party with a long position that is prepared to accept the notice

from them.

In the case of a commodity, taking delivery usually means accepting a warehouse

receipt in return for immediate payment. The party taking delivery is then responsible

for all warehousing costs. In the case of livestock futures, there may be costs associated

with feeding and looking after the animals (see Business Snapshot 2.1). In the case of

ﬁnancial futures, delivery is usually made by wire transfer. For all contracts, the price

paid is usually the most recent settlement price. If speciﬁed by the exchange, this price is

adjusted for grade, location of delivery, and so on. The whole delivery procedure from

the issuance of the notice of intention to deliver to the delivery itself generally takes two

to three days.

There are three critical days for a contract. These are the ﬁrst notice day, the last

notice day, and the last trading day. The ﬁrst notice day is the ﬁrst day on which a notice

of intention to make delivery can be submitted to the exchange. The last notice day is

the last such day. The last trading day is generally a few days before the last notice day.

To avoid the risk of having to take delivery, an investor with a long position should

close out his or her contracts prior to the ﬁrst notice day.

Cash Settlement

Some ﬁnancial futures, such as those on stock indices discussed in Chapter 3, are settled

in cash because it is inconvenient or impossible to deliver the underlying asset. In the

Mechanics of Futures Markets

case of the futures contract on the S&P 500, for example, delivering the underlying asset

would involve delivering a portfolio of 500 stocks. When a contract is settled in cash, all

outstanding contracts are declared closed on a predetermined day. The ﬁnal settlement

price is set equal to the spot price of the underlying asset at either the open or close of

trading on that day. For example, in the S&P 500 futures contract traded by the CME

Group, the predetermined day is the third Friday of the delivery month and ﬁnal

settlement is at the opening price.

2.8 TYPES OF TRADER AND TYPES OF ORDER

There are two main types of trader executing trades: futures commission merchants

(FCMs) and locals. FCMs are following the instructions of their clients and charge a

commission for doing so; locals are trading on their own account.

Individuals taking positions, whether locals or the clients of FCMs, can be categor-

ized as hedgers, speculators, or arbitrageurs, as discussed in Chapter 1. Speculators can

be classiﬁed as scalpers, day traders, or position traders. Scalpers are watching for very

short term trends and attempt to proﬁt from small changes in the contract price. They

usually hold their positions for only a few minutes. Day traders hold their positions for

less than one trading day. They are unwilling to take the risk that adverse news will

occur overnight. Position traders hold their positions for much longer periods of time.

They hope to make signiﬁcant proﬁts from major movements in the markets.

Orders

The simplest type of order placed with a broker is a market order. It is a request that

a trade be carried out immediately at the best price available in the market. However,

there are many other types of orders. We will consider those that are more

commonly used.

A limit order speciﬁes a pa rticular price. The order can be executed only at this price

or at one more favorable to the investor. Thus, if the limit price is $30 for an investor

wanting to buy, the order will be executed only at a price of $30 or less. There is, of

course, no guarantee that the order will be executed at all, because the limit price may

never be reached.

A stop order or stop-loss order also speciﬁes a particular price. The order is executed

at the best available price once a bid or oﬀer is made at that particular price or a less-

favorable price. Suppose a stop order to sell at $30 is issued when the market price

is $35. It becomes an order to sell when and if the price falls to $30. In eﬀect, a stop

order becomes a market order as soon as the speciﬁed price has been hit. The purpose

of a stop order is usually to close out a position if unfavorable price movements take

place. It limits the loss that can be incurred.

A stop–limit order is a combination of a stop order and a limit order. The order

becomes a limit order as soon as a bid or oﬀer is made at a price equal to or less

favorable than the stop price. Two prices must be speciﬁed in a stop–limit order: the stop

price and the limit price. Suppose that, at the time the market price is $35, a stop–limit

order to buy is issued with a stop price of $40 and a limit price of $41. As soon as there is

a bid or oﬀer at $40, the stop–limit becomes a limit order at $41. If the stop price and the

limit price are the same, the order is sometimes called a stop-and-limit order.

38 CHAPTER 2

A market-if-touched order (MIT) is executed at the best available price after a trade

occurs at a speciﬁed price or at a price more favorable than the speciﬁed price. In eﬀect,

an MIT becomes a market order once the speciﬁed price has been hit. An MIT is also

known as a board order. Consider an investor who has a long position in a futures

contract and is issuing instructions that would lead to closing out the contract. A stop

order is designed to place a limit on the loss that can occur in the event of unfavorable

price movements. By contrast, a market-if-touched order is designed to ensure that

proﬁts are taken if suﬃciently favorable price movements occur.

A discretionary order or market-not-held order is traded as a market order except that

execution may be delayed at the broker’s discretion in an attempt to get a better price.

Some orders specify time conditions. Unless otherwise stated, an order is a day order

and expires at the end of the trading day. A time-of-day order speciﬁes a particular

period of time during the day when the order can be executed. An open order or a good-

till-canceled order is in eﬀect until executed or until the end of trading in the particular

contract. A ﬁll-or-kill order, as its name implies, must be executed immediately on

receipt or not at all.

2.9 REGULATION

Futures markets in the United States are currently regulated federally by the Commodity

Futures Trading Commission (CFTC; www.cftc.gov), which was established in 1974.

The CFTC looks after the public interest. It is responsible for ensuring that prices are

communicated to the public and that futures traders report their outstanding positions if

they are above certain levels. The CFTC also licenses all individuals who oﬀer their

services to the public in futures trading. The backgrounds of these individuals are

investigated, and there are minimum capital requirements. The CFTC deals with

complaints brought by the public and en sures that disciplinary action is taken against

individuals when appropriate. It has the authority to force exchanges to take disciplinary

action against members who are in violation of exchange rules.

With the formation of the National Futures Association (NFA; www.nfa.futures.org)

in 1982, some of responsibilities of the CFTC were shifted to the futures industry itself.

The NFA is an organization of individuals who participate in the futures industry. Its

objective is to prevent fraud and to ensure that the market operates in the best interests of

the general public. It is authorized to monitor trading and take disciplinary action when

appropriate. The agency has set up an eﬃcient system for arbitrating disputes between

individuals and its members.

From time to time other bodies such as the Securities and Exchange Commission

(SEC; www.sec.gov), the Federal Reserve Board (www.federalreserve.gov), and the

U.S. Treasury Department (www.treas.gov) have claimed jurisdictional rights over

some aspects of futures trading. These bodies are concerned with the eﬀects of futures

trading on the spot markets for securities such as stocks, Treasury bills, and Treasury

bonds.

Trading Irregularities

Most of the time futures markets operate eﬃciently and in the public interest. However,

from time to time trading irregularities do come to light. One type of trading irregularity

Mechanics of Futures Markets

occurs when an investor group tries to ‘‘corner the market.’’

The investor group takes a

huge long futures position and also tries to exercise some control over the supply of the

underlying commodity. As the maturity of the futures contracts is approached, the

investor group does not close out its position, so that the number of outstanding futures

contracts may exceed the amount of the commodity available for delivery. The holders

of short positions realize that they will ﬁnd it diﬃcult to deliver and become desperate to

close out their positions. The result is a large rise in both futures and spot prices.

Regulators usually deal with this type of abuse of the market by increasing margin

requirements or imposing stricter position limits or prohibiting trades that increase a

speculator’s open position or requiring market participants to close out their positions.

Other types of trading irregularities can involve the traders on the ﬂoor of the

exchange. These received some publicity early in 1989 when it was announced that

the FBI had carried out a two-year investigation, using undercover agents, of trading on

the Chicago Board of Trade and the Chicago Mercantile Exchange. The investigation

was initiated because of complaints ﬁled by a large agricultural concern. The alleged

oﬀenses included overcharging customer s, not paying customers the full proceeds of

sales, and traders using their knowledge of customer orders to trade ﬁrst for themselves.

(The latter is known as front running.)

2.10 ACCOUNTING AND TAX

The full details of the accounting and tax treatment of futures contracts are beyond the

scope of this book. A trader who wants detailed information on this should obtain

professional advice. This section provides some general background information.

Accounting

Accounting standards require changes in the market value of a futures contract to be

recognized when they occur unless the contract qualiﬁes as a hedge. If the contract does

qualify as a hedge, then gains or losses are generally recognized for accounting purposes

in the same period in which the gains or losses from the item being hedged are

recognized. The latter treatment is referred to as hedge accounting.

Example 2.1 considers a company with a December year end. In September 2013 it

buys a March 2014 corn futures contract and closes out the position at the end of

February 2014. Suppose that the futures prices are 750 cents per bushel when the

contract is entered into, 770 cents per bushel at the end of 2013, and 780 cents per

bushel when the contract is closed out. The contract is for the delivery of 5,000 bushels.

If the contract does not qualify as a hedge, the gains for accounting purposes are

5,000 ð7:70  7:50Þ¼$1,000

in 2013 and

5,000 ð7:80  7 :70Þ¼$ 500

in 2014. If the company is hedging the purchase of 5,000 bushels of corn in February

Possibly the best known example of this involves the activities of the Hunt brothers in the silver market in

1979–80. Between the middle of 1979 and the beginning of 1980, their activities led to a price rise from $6 per

ounce to $50 per ounce.

40 CHAPTER 2

2014 so that the contract qualiﬁes for hedge accounting, the entire gain of $1,500 is

realized in 2014 for accounting purposes.

The treatment of hedging gains and losses is sensible. If the company is hedging the

purchase of 5,000 bushels of corn in February 2014, the eﬀect of the futures contract is

to ensure that the price paid is close to 750 cents per bushel. The accounting treatment

reﬂects that this price is paid in 2014.

In June 1998, the Financial Accounting Standards Board issued Statement No. 133

(FAS 133), Accounting for Derivative Instruments and Hedging Activities. FAS 133

applies to all types of derivatives (including futures, forwards, swaps, and options). It

requires all derivatives to be included on the balance sheet at fair market value.

increases disclosure requirements. It also gives companies far less latitude than previ-

ously in using hedge accounting. For hedge accounting to be used, the hedging

instrument must be highly eﬀective in oﬀsetting exposures and an assessment of this

eﬀectiveness is required every three months. A similar standard IAS 39 has been issued

by the International Accounting Standards Board.

Tax

Under the U.S. tax rules, two key issues are the nature of a taxable gain or loss and the

timing of the recognition of the gain or loss. Gains or losses are either classiﬁed as

capital gains/losses or as part of ordinary income.

For a corporate taxpayer, capital gains are taxed at the same rate as ordinary income,

and the ability to deduct losses is restricted. Capital losses are deductible only to the

extent of capital gains. A corporation may carry back a capital loss for three years and

carry it forward for up to ﬁve years. For a noncorporate taxpayer, short-term capital

gains are taxed at the same rate as ordinary income, but long-term capital gains are

taxed at a lower rate than ordinary income. (Long-term capital gains are gains from the

sale of a capital asset held for longer than one year; short term capital gains are the

gains from the sale of a capital asset held one year or less.) The Taxpayer Relief Act of

1997 widened the rate diﬀerential between ordinary income and long-term capital gains.

For a noncorporate taxpayer, capital losses are deductible to the extent of capital gains

plus ordinary income up to $3,000 and can be carried forward indeﬁnitely.

Example 2.1 Accounting treatment of a futures transaction

A company buys 5,000 bushels of March 2014 corn in September 2013 for

750 cents per bushel and closes out the position in February 2014 for 780 cents

per bushel. The price of March 2014 corn on December 31, 2013, the company’s

year end, is 770 cents per bushel.

If contract is not a hedge, the treatment of these transactions leads to:

Accounting proﬁt in 2013 ¼ 5,000  20 cents ¼ $1,000.

Accounting proﬁt in 2014 ¼ 5,000  10 cents ¼ $500.

If contract is hedging a purchase of corn in 2014, the result is:

Accounting proﬁt in 2013 ¼ $0:

Accounting proﬁt in 2014 ¼ 5,000  30 cents ¼ $1,500.

Previously the attraction of derivatives in some situations was that they were ‘‘oﬀ-balance-sheet’’ items.

Mechanics of Futures Markets 41

Generally, positions in futures contracts are treated as if they are closed out on the

last day of the tax year. For the noncorporate taxpayer this gives rise to capital gains

and losses. These are treated as if they are 60% long term and 40% short term without

regard to the holding period. This is referred to as the ‘‘60/40’’ rule. A noncorporate

taxpayer may elect to ca rry back for three years any net losses from the 60/40 rule to

oﬀset any gains recognized under the rule in the previous three years.

Hedging transactions are exempt from this rule. The deﬁnition of a hedge transaction

for tax purposes is diﬀerent from that for accounting purposes. The tax regulations

deﬁne a hedging transaction as a transaction entered into in the normal course of

business primarily for one of the following reasons:

1. To reduce the risk of price changes or currency ﬂuctuations with respect to

property that is held or to be held by the taxpayer for the purposes of producing

ordinary income

2. To reduce the risk of price or interest rate changes or currency ﬂuctuations with

respect to borrowings made by the taxpayer.

A hedging transaction must be clearly identiﬁed in a timely manner in the company’s

records as a hedge. Gains or losses from hedging transactions are treated as ordinary

income. The timing of the recognition of gains or losses from hedging transactions

generally matches the timing of the recognition of income or expense associated with

the transaction being hedged.

2.11 FORWARD vs. FUTURES CONTRACTS

As explained in Chapter 1, forward contracts are similar to futures contracts in that

they are agreements to buy or sell an asset at a certain time in the future for a certain

price. Whereas futures contracts are traded on an exchange, forward contracts are

traded in the over-the-counter market. They are typically entered into by two ﬁnancial

institutions or by a ﬁnancial institution and one of its clients.

One of the parties to a forward contract assumes a long position and agrees to buy the

asset on a certain speciﬁed date for a certain price. The other party assumes a short

position and agrees to sell the asset on the same date for the same price. Forward

contracts do not have to conform to the standards of a particular exchange. The

contract delivery date can be any date mutually convenient to the two parties. Usually,

in forward contracts a single delivery date is speciﬁed, whereas in futures contracts there

is a range of possible delivery dates.

Unlike futures contracts, forward contracts are not settled daily. The two parties

contract to settle up on the speciﬁed delivery date. Whereas most futures contracts are

closed out prior to delivery, most forward contracts do lead to delivery of the physical

asset or to ﬁnal settlement in cash. Table 2.3 summarizes the main diﬀerences between

forward and futures contracts.

Proﬁts from Forward and Futures Contracts

Suppose that the sterling exchange rate for a 90-day forward contract is 1.6000 dollars

per pound and that this rate is also the futures price for a contract that will be delivered

in exactly 90 days. Under the forward contract, the whole gain or loss is realized at the

42 CHAPTER 2

end of the life of the contract. Under the futures contract, the gain or loss is realized day

by day because of the daily settlement procedures. Figure 2.3 shows the net proﬁt as a

function of the exchange rate for 90-day long and short forward or futures positions on

£1 million.

Example 2.2 considers the situation where investor A is long £1 million in a 90-day

forward contract, and investor B is long £1 million in 90-day futures contracts. (Each

futures contract is for the purchase or sale of £62,500, so investor B has purchased a

total of 16 contracts.) Assume that the spot exchange rate in 90 days proves to be 1.7000

dollars per pound. Investor A makes a gain of $100,000 on the 90th day. Investor B

makes the same gain—but spread out over the 90-day period. On some days investor B

may realize a loss, whereas on other days he or she makes a gain. However, in total,

when losses are netted against gains, there is a gain of $100,000 over the 90-day period.

Foreign Exchange Quotes

Both forward and futures contracts trade actively on foreign currencies. However, there

is sometimes a diﬀerence in the way exchange rates are quoted in the two markets.

Futures prices are always quoted as the number of U.S. dollars per unit of the foreign

Table 2.3 Comparison of forward and futures contracts

Forward Futures

Private contract between two parties Traded on an exchange

Not standardized Standardized contract

Usually one speciﬁed delivery date Range of delivery dates

Settled at end of contract Settled daily

Delivery or ﬁnal cash settlement

usually takes place

Contract is usually closed out

prior to maturity

Some credit risk Virtually no credit risk

(a) Lon

osition

Exchange rate

Profit ($)

(b) Short position

–

200,000

–

100,000

200,000

1.4000 1.5000 1.6000 1.7000 1.8000

Exchange rate

Profit ($)

–200,000

–100,000

100,000

200,000

1.4000 1.5000 1.6000 1.7000 1.8000

Figure 2.3 Proﬁt from (a) long and (b) short forward or futures position on £1 million

Mechanics of Futures Markets 43

currency or as the number of U.S. cents per unit of the foreign currency. Forward prices

are always quoted in the same way as spot prices. This means that for the British pound,

the euro, the Australian dollar, and the New Zealand dollar, the forward quotes show

the number of U.S. dollars per unit of the foreign currency and are directly comparable

with futures quotes. For other major currencies, forward quotes show the number of

units of the foreign currency per U.S. dollar (USD). Consider the Canadian dollar

(CAD). A futures price quote of 0.9500 USD per CAD corresponds to a forward price

quote of 1.0526 CAD per USD (1.0 526 ¼ 1/0.9500).

SUMMARY

A very high proportion of the futures contracts that are traded do not lead to the

delivery of the underlying asset. This is because traders usually enter into oﬀsetting

contracts to close out their positions before the delivery period is reached. However, it is

the possibility of ﬁnal delivery that drives the determination of the futures price. For

each futures contract, there is a range of days during which delivery can be made and a

well-deﬁned delivery procedure. Some contracts, such as those on stock indices, are

settled in cash rather than by delivery of the underlying asset.

The speciﬁcation of contracts is an important activity for a futures exchange. The

two sides to any contract must know what can be delivered, where delivery can take

place, and when delivery can take place. They also need to know details on the trading

hours, how prices will be quoted, maximum daily price movements, and so on. New

contracts must be approved by the Commodity Futures Trading Commission before

trading starts.

Margin requirements are an important aspect of futures markets. An investor keeps a

margin account with his or her broker. The account is adjusted daily to reﬂect gains or

losses, and from time to time the broker may require the account to be topped up if

adverse price movements have taken place. The broker either must be a clearing house

member or must maintain a margin account with a clearing house member. Each

clearing house member maintains a margin account with the exchange clearing house.

The balance in the account is adjusted daily to reﬂect gains and losses on the business

for which the clearing house member is responsible.

Example 2.2 Futures vs. forwards

Investor A takes a long position in a 90-day forward contract on £1 million. The

forward price is 1.6000 dollars per pound. Investor B takes a long position in

90-day futures contracts on £1 million. The futures price is also 1.6000 dollars per

pound. At the end of the 90 days, the exchange rate proves to be 1.7000.

The result of this is that investors A and B each make a total gain equal to

ð1:7000  1 :6000Þ1,000,000 ¼ $100,000

Investor A’s gain is made entirely on the 90th day. Investor B’s gain is realized day

by day over the 90-day period. On some days investor B may realize a loss, whereas

on other days he or she will realize a gain.

44 CHAPTER 2

In over-the-counter derivatives markets, transactions are cleared either bilaterally or

centrally. When bilateral clearing is used, collateral frequently has to be posted by one

or both parties to reduce credit risk. When central clearing is used, a central clearing

party (CCP) stands between the two sides and performs much the same function as an

exchange clearing house.

Forward contracts diﬀer from futures contracts in a number of ways. Forward

contracts are private arrangements between two parties, whereas futures contracts are

traded on exchanges. There is generally a single delivery date in a forward contract,

whereas futures contracts frequently involve a range of such dates. Because they are not

traded on exchanges, forward contracts do not need to be standardized. A forward

contract is not usually settled until the end of its life, and most contracts do in fact lead

to delivery of the underlying asset or a cash settlement at this time.

In the next few chapters we will examine in more detail the ways in which forward

and futures contracts can be used for hedging. We will also look at how forward and

futures prices are determined.