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C h a p t e r 1Introduction to Derivatives

Risk is the central element that influences financial behavior.

—Robert C. Merton (1999)

The world of finance and capital markets has undergone a stunning transformationin the last 30 years. Simple stocks and bonds now seem almost quaint alongside thedazzling, fast-paced, and seemingly arcane world of futures, options, swaps, and other“new” financial products. (The word “new” is in quotes because it turns out that someof these products have been around for hundreds of years.)

Frequently this world pops up in the popular press: Procter & Gamble lost$150 million in 1994, Barings bank lost $1.3 billion in 1995, Long-Term Capital Man-agement lost $3.5 billion in 1998 and (according to some press accounts) almost broughtthe world financial system to its knees.1 What is not in the headlines is that, most of thetime, for most companies and most users, these financial products are an everyday partof business. Just as companies routinely issue debt and equity, they also routinely useswaps to fix the cost of production inputs, futures contracts to hedge foreign exchangerisk, and options to compensate employees, to mention just a few examples.

1.1 WHAT IS A DERIVATIVE?

Options, futures, and swaps are examples of derivatives. A derivative is simply afinancial instrument (or even more simply, an agreement between two people) whichhas a value determined by the price of something else. For example, a bushel of cornis not a derivative; it is a commodity with a value determined by the price of corn.However, you could enter into an agreement with a friend that says: If the price of abushel of corn in one year is greater than $3, you will pay the friend $1. If the price ofcorn is less than $3, the friend will pay you $1. This is a derivative in the sense that youhave an agreement with a value depending on the price of something else (corn, in thiscase).

You might be tempted to say: “That’s not a derivative; that’s just a bet on the priceof corn.” So it is: Derivatives can be thought of as bets on the price of something. But

.................................1A readable summary of these and other infamous derivatives-related losses is in Jorion (2001).


2 w Introduction to Derivatives

don’t automatically think the term “bet” is pejorative. Suppose your family grows cornand your friend’s family buys corn to mill into cornmeal. The bet provides insurance:You earn $1 if your family’s corn sells for a low price; this supplements your income.Your friend earns $1 if the corn his family buys is expensive; this offsets the high cost ofcorn. Viewed in this light, the bet hedges you both against unfavorable outcomes. Thecontract has reduced risk for both of you.

Investors could also use this kind of contract simply to speculate on the price ofcorn. In this case the contract is not insurance. And that is a key point: It is not thecontract itself, but how it is used, and who uses it, that determines whether or not it isrisk-reducing. Context is everything.

Although we’ve just defined a derivative, if you are new to the subject the impli-cations of the definition will probably not be obvious right away. You will come to adeeper understanding of derivatives as we progress through the book, studying differentproducts and their underlying economics.

Uses of Derivatives

What are reasons someone might use derivatives? Here are some motives:

Risk management Derivatives are a tool for companies and other users to reducerisks. The corn example above illustrates this in a simple way: The farmer—a sellerof corn—enters into a contract which makes a payment when the price of corn is low.This contract reduces the risk of loss for the farmer, who we therefore say is hedging.It is common to think of derivatives as forbiddingly complex but many derivatives aresimple and familiar. Every form of insurance is a derivative, for example. Automobileinsurance is a bet on whether you will have an accident. If you wrap your car around atree, your insurance is valuable; if the car remains intact, it is not.

Speculation Derivatives can serve as investment vehicles. As you will see later inthe book, derivatives can provide a way to make bets that are highly leveraged (that is,the potential gain or loss on the bet can be large relative to the initial cost of makingthe bet) and tailored to a specific view. For example, if you want to bet that the S&P500 stock index will be between 1300 and 1400 one year from today, derivatives can beconstructed to let you do just that.

Reduced transaction costs Sometimes derivatives provide a lower-cost way to effecta particular financial transaction. For example, the manager of a mutual fund may wishto sell stocks and buy bonds. Doing this entails paying fees to brokers and paying othertrading costs, such as the bid-ask spread, which we will discuss later. It is possible totrade derivatives instead and achieve the same economic effect as if stocks had actuallybeen sold and replaced by bonds. Using the derivative might result in lower transactioncosts than actually selling stocks and buying bonds.

Regulatory arbitrage It is sometimes possible to circumvent regulatory restrictions,taxes, and accounting rules by trading derivatives. Derivatives are often used, for exam-ple, to achieve the economic sale of stock (receive cash for it and eliminate the risk of


What Is a Derivative? w 3

holding it) while still maintaining physical possession of the stock. This transaction mayallow the owner to defer taxes on the sale of the stock, or retain voting rights, withoutthe risk of holding the stock.

These are common reasons for using derivatives. The general point is that deriva-tives provide an alternative to a simple sale or purchase, and thus increase the range ofpossibilities for an investor or manager seeking to accomplish some goal.

Perspectives on Derivatives

How you think about derivatives depends on who you are. In this book we will thinkabout three distinct perspectives on derivatives:

The end-user perspective End-users are the corporations, investment managers, andinvestors who enter into derivative contracts for the reasons listed in the previous section:To manage risk, speculate, reduce costs, or avoid a rule or regulation. End-users have agoal (for example, risk reduction) and care about how a derivative helps to meet that goal.

The market-maker perspective Market-makers are intermediaries, traders who willbuy derivatives from customers who wish to sell, and sell derivatives to customerswho wish to buy. In order to make money, market-makers charge a spread: Theybuy at a low price and sell at a high price. In this respect market-makers are likegrocers who buy at the low wholesale price and sell at the higher retail price. Market-makers are also like grocers in that their inventory reflects customer demands rather thantheir own preferences: As long as shoppers buy paper towels, the grocer doesn’t carewhether they buy the decorative or super-absorbent style. After dealing with customers,market-makers are left with whatever position results from accommodating customerdemands. Market-makers typically hedge this risk and thus are deeply concerned aboutthe mathematical details of pricing and hedging.

The economic observer Finally, we can look at the use of derivatives, the activities ofthe market-makers, the organization of the markets, the logic of the pricing models, andtry to make sense of everything. This is the activity of the economic observer. Regulatorsmust often don their economic observer hats when deciding whether and how to regulatea certain activity or market participant.

These three perspectives are intertwined throughout the book, but as a generalpoint, in the early chapters the book emphasizes the end-user perspective. In the latechapters, the book emphasizes the market-maker perspective. At all times, however, theeconomic observer is interested in making sense of everything.

Financial Engineering and Security Design

One of the major ideas in derivatives—perhaps the major idea—is that it is generallypossible to create a given payoff in multiple ways. The construction of a given financialproduct from other products is sometimes called financial engineering. The fact thatthis is possible has several implications. First, since market-makers need to hedge their



positions, this idea is central in understanding how market-making works. The market-maker sells a contract to an end-user, and then creates an offsetting position which payshim if it is necessary to pay the customer. This creates a hedged position.

Second, the idea that a given contract can be replicated often suggests how it canbe customized. The market-maker can, in effect, turn dials to change the risk, initialpremium, and payment characteristics of a derivative. These changes permit the creationof a product that is more appropriate for a given situation.

Third, it is often possible to improve intuition about a given derivative by realizingthat it is equivalent to something we already understand.

Finally, because there are multiple ways to create a payoff, the regulatory arbitragediscussed above can be difficult to stop. Distinctions existing in the tax code, or inregulations, may not be enforceable, since a particular security or derivative that isregulated or taxed may be easily replaced by one which is treated differently but has thesame economic profile.

A theme running throughout the book is that derivative products can generally beconstructed from other products.

1.2 THE ROLE OF FINANCIAL MARKETS

We take for granted headlines saying that the Dow Jones Industrial Average has gone up100 points, the dollar has fallen against the Yen, and interest rates have risen. But whydo we care about these things? Is the rise and fall of a particular financial index (suchas the Dow Jones Industrial Average) simply a way to keep score, to track winners andlosers in the economy? Is watching the stock market like watching sports, where weroot for certain players and teams—a tale told by journalists, full of sound and fury, butsignifying nothing?

Financial markets in fact have an enormous, often underappreciated, impact oneveryday life. To help us understand the role of financial markets we will consider theAverage family, living in Anytown. Joe and Sarah Average have 2.3 children and bothwork for the XYZ Co., the dominant employer in Anytown. Their income pays fortheir mortgage, transportation, food, clothing, and medical care. What is left over goestoward savings earmarked for their children’s college tuition and their own retirement.

What role do global financial markets and derivatives play in the lives of theAverages?

Financial Markets and the Averages

The Averages are largely unaware of the ways in which financial markets affect theirlives. Here are a few:

• The Average’s employer, XYZ Co., has an ongoing need for money to financeoperations and investments. It is not dependent on the local bank for funds becauseit can raise the money it needs by issuing stocks and bonds in global markets.


The Role of Financial Markets w 5

• XYZ Co. insures itself against certains risks. In addition to having property andcasualty insurance for its buildings, it uses global derivatives markets to protectitself against adverse currency, interest rate, and commodity price changes. Bybeing able to manage these risks, XYZ is less likely to go into bankruptcy, and lesslikely to throw the Averages into unemployment.

• The Averages invest in mutual funds. As a result they pay lower transaction coststhan if they tried to achieve comparable diversification by buying individual stocks.

• Since both Averages work at XYZ, they run the risk that if XYZ does fall on hardtimes they will lose their jobs. The mutual funds in which they invest own stocksin a broad array of companies, ensuring that the failure of any one company willnot wipe out their savings.

• The Averages live in an area susceptible to tornadoes and insure their home. Iftheir insurance company were completely local, it could not offer tornado insurancebecause one disaster would leave it unable to pay claims. By selling tornado riskin global markets, the insurance company can in effect pool Anytown tornadorisk with Japan earthquake risk and Florida hurricane risk. This pooling makesinsurance available at lower rates.

• The Averages borrowed money from Anytown bank to buy their house. The banksold the mortgage to other investors, freeing itself from interest rate and defaultrisk associated with the mortgage, leaving that to others. Because the risk of theirmortgage is borne by those willing to pay the highest price for it, the Averages getthe lowest possible mortgage rate.

In all of these examples, particular financial functions and risks have been splitup and parceled out to others. A bank that sells a mortgage does not have to bear therisk of the mortgage. An insurance company does not bear all the risk of a disaster.Risk-sharing is one of the most important functions of financial markets.

Risk-Sharing

Risk is an inevitable part of all lives and all economic activity. As we’ve seen in theexample of the Averages, financial markets enable this risk to be shared. To demonstratehow risk may be shared, let’s examine one brief time period. Within the span of afew weeks in 1999 earthquakes devastated Turkey and Taiwan, floods ravaged NorthCarolina, and war loomed in the former Soviet Union, as well as in India and Pakistan.Drought and pestilence destroy agriculture every year in some part of the world. Someeconomies surge as others falter. On a more personal scale, people are born, die, retire,find jobs, lose jobs, marry, divorce, and become ill.

In the face of this risk, it seems natural to have arrangements where the lucky sharewith the unlucky. Risk-sharing occurs informally in families and communities. Theinsurance market makes formal risk-sharing possible. Buyers pay a premium to obtainvarious kinds of insurance, such as homeowner’s insurance. Total collected premiumsare then available to help those whose houses burn down. The lucky, meanwhile, did



not need insurance and have lost their premium. The market makes it possible for thelucky to help the unlucky.

In the business world, changes in commodity prices, exchange rates, and interestrates can be the financial equivalent of a house burning down. If the dollar becomesexpensive relative to the Yen, some companies are helped and others are hurt. It makessense for there to be a mechanism enabling companies to exchange this risk, so that thelucky can, in effect, help the unlucky.

You might be wondering what this discussion has to do with the notions of diver-sifiable and nondiversifiable risk familiar from portfolio theory. Risk is diversifiablerisk if it is unrelated to other risks. The risk that a lightning strike will cause a factoryto burn down, for example, is idiosyncratic and hence diversifiable. If many investorsshare a small piece of this risk, it has no significant effect on anyone. Risk that does notvanish when spread across many investors is nondiversifiable risk. The risk of a stockmarket crash, for example, is nondiversifiable.

Financial markets in theory serve two purposes. Markets permit diversifiable riskto be widely shared. This is efficient: By definition, diversifiable risk vanishes whenit is widely shared. At the same time, financial markets permit nondiversifiable risk,which does not vanish when shared, to be held by those most willing to hold it. Thus,the fundamental economic idea underlying the concepts and markets discussed in thisbook is that the existence of risk-sharing mechanisms benefits everyone.

A risk-management problem faced by Tokyo Disneyland illustrates how it wasable to diversify risk using capital markets. Disney decided that it would profit byopening a theme park in Japan. However, Japan is in a high-earthquake region. Thislocation creates unavoidable risk for a theme park, or any business. Disney had severalalternatives. First, it could have self-insured. In this case, Disney shareholders wouldhave absorbed the earthquake risk. Second, Disney could have bought earthquake in-surance from an insurance company. Because the insurance company’s payout wouldbe large if an earthquake did occur, that insurance company would likely have boughtinsurance for itself from other insurance companies, in what is called the reinsurancemarket. (Reinsurance is insurance for insurance companies, and it is one way for insur-ance risks to become more widely held.) In the end, the shareholders and bondholdersof the reinsurance companies would have held the risk.

Disney took a third alternative, essentially bypassing intermediaries by issuingearthquake bonds, held directly by investors. The box on page 7 discusses thesebonds.

All three alternatives—self-insurance, conventional insurance, and earthquakebonds—would have resulted in risk being held by numerous investors. The earthquakebond allowed earthquake risk to be borne by exactly those investors who wished tobear it.

1.3 DERIVATIVES IN PRACTICE

Derivatives use and the variety of derivatives have grown over the last 30 years.


Derivatives in Practice w 7

The Tokyo Disneyland Bond

Oriental Land Co. Ltd. is licensed by theWalt Disney Co. to operate theme parks inJapan, including Tokyo Disneyland. InMay 1999, the company issued a $100m5-year earthquake bond, designed both toraise money and to provide earthquakeinsurance. The bond is structured so that inthe event of a severe earthquake, TokyoDisneyland is not obligated to repay the entirebond. Bondholders thus suffer a loss if anearthquake occurs.

Damage to Tokyo Disneyland wouldincrease with the severity and proximity ofthe earthquake. The bond was structured toaccount for this, with the forgiveness ofprincipal linked to the magnitude and locationof the earthquake. If an earthquake ratedabove Richter 7.5 occurs within a 10kmradius of the park, the entire bond is forgiven.

There is then a sliding scale down to Richter6.5, at which point only 25% of the bond’sprincipal is forgiven. The bond also specifiesa middle and outer ring, extending to 75kmfrom the park, with increasingly severeearthquakes necessary to trigger nonpaymentof principal. The bond coupon was set toequal the London Interbank interest rate(LIBOR) plus 310 basis points.

This deal was the first in which a privatecompany, rather than a reinsurer, issued acatastrophe bond. The bond is not perfectinsurance for Oriental Land Co. since thebond payout is related to the severity of theearthquake, not specifically to damage to thepark. A second $100m bond called fortemporary nonpayment of interest in the eventof an earthquake.

Growth in Derivatives Trading

If we examine recent history, the introduction of derivatives has coincided with increasesin price risk in various markets. Currencies were officially permitted to float in 1971when the gold standard was officially abandoned. OPEC’s 1973 reduction in the supplyof oil was followed by high and variable oil prices. U.S. interest rates became morevolatile following inflation and recessions in the 1970s. The market for natural gas hasbeen deregulated gradually since 1978, resulting in a volatile market in recent years.The deregulation of electricity began during the 1990s. Figures 1.1, 1.2, and 1.3 showthe changes for oil prices, exchange rates, and interest rates. The link between pricevariability and the development of derivatives markets is natural—there is no need tomanage risk when there is no risk.2 When risk does exist, we would expect that marketswill develop to permit efficient risk-sharing. Investors who have the most tolerance forrisk will bear more of it, and risk-bearing will be widely spread among investors.

.................................2It is sometimes argued that the existence of derivatives markets can increase the price variability ofthe underlying asset or commodity. Without some price risk in the first place, however, the derivativesmarket is unlikely to exist.



FIGURE 1.1

Monthly percentagechange in the producerprice index for oil,1951–1999.

1960 1970 1980 1990 2000

–30

–20

–10

0

10

20

30

40

% c

han

ge

FIGURE 1.2

Monthly percentagechange in theDeutschemark/dollarexchange rate,1951–1999.

1960 1970 1980 1990 2000

–8

–6

–4

–2

0

2

4

6

8

% c

han

ge

Figure 1.4 depicts contract volume for the three largest U.S. futures exchangesover the last 25 years. Table 1.1 illustrates the kinds of futures contracts traded at theseexchanges.3 Futures exchanges are an organized and regulated marketplace for trading

.................................3The table lists only a fraction of the contracts traded at these exchanges. For example, in January 2002,the Chicago Mercantile Exchange Web page listed futures contracts on over 75 different underlyingassets ranging from butter to a bankruptcy index.


Derivatives in Practice w 9

FIGURE 1.3

Monthly change in3-month Treasury billrate, 1951–1999.

1960 1970 1980 1990 2000

–4

–3

–2

–1

0

1

2

Ch

ange

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rat

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erce

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FIGURE 1.4

Millions of contractstraded annually at theChicago Board of Trade(CBT), ChicagoMercantile Exchange(CME), and the NewYork MercantileExchange (NYMEX).

1970 1975 1980 1985 1990 1995 20000

20

40

60

80

100

120

140

160

180

200

An

nu

al v

olu

me,

mil

lion

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CBTCMENYMEX

Source: CRB Commodity Yearbook.

futures contracts, a kind of derivative, but much commercial derivatives trading occurs inthe over-the-counter market, where buyers and sellers transact with banks and dealersrather than on an exchange. It is difficult to obtain statistics for over-the-counter volume.However, in some markets, such as currencies, it is clear that the over-the-counter marketis significantly larger than the exchange-traded market.



TABLE 1.1 Examples of futures contracts traded on the Chicago Board ofTrade (CBT), Chicago Mercantile Exchange (CME), and theNew York Mercantile Exchange (NYMEX).

CBT CME NYMEX

30-year U.S. Treasury S&P 500 Index Crude Oil

Bonds

10-year U.S. Treasury NASDAQ 100 Index Natural Gas

Bonds

Municipal Bond Index Eurodollars Heating Oil

Corn Nikkei 225 Gasoline

Soybeans Pork Bellies Gold

Wheat Heating and Cooling Degree-Days Copper

Oats Japanese Yen Electricity

How Are Derivatives Used?

In recent years the U.S. Securities and Exchange Commission (SEC) and Financial Ac-counting Standards Board (FASB) have increased the requirements for corporations toreport on their use of derivatives. Nevertheless, surprisingly little is known about howcompanies actually use derivatives to manage risk. The basic strategies companies useare well-understood—and will be described in this book—but it is not known, for exam-ple, what fraction of perceived risk is hedged by a given company, or by all companiesin the aggregate. We frequently do not know a company’s specific rationale for hedgingor not hedging.

We would expect the use of derivatives to vary by type of firm. For example,financial firms, such as banks, are highly regulated and have capital requirements. Theymay have assets and liabilities in different currencies, with different maturities, and withdifferent credit risks. Hence banks could be expected to use interest rate derivatives,currency derivatives, and credit derivatives to manage risks in those areas. Manufac-turing firms that buy raw materials and sell in global markets might use commodity andcurrency derivatives, but their incentives to manage risk are less clear-cut because theyare not regulated in the same ways as financial firms.

1.4 BUYING AND SHORT-SELLINGFINANCIAL ASSETS

Throughout this book we will talk about buying and selling—and short-selling—assetssuch as stocks. These basic transactions are so important that it is worth describingthe details. First, it is important to understand the costs associated with buying and


Buying and Short-Selling Financial Assets w 11

selling. Second, a very important idea used throughout the book is that of short-sales.The concept of short-selling should be intuitive—a short-sale is just the opposite of apurchase—but for almost everyone it is hard to grasp at first. Even if you are familiarwith short sales, spend a few minutes reading this section.

Buying an Asset

Suppose we want to buy 100 shares of XYZ stock. This seems simple: If the stockprice is $50, 100 shares will cost $50×100 = $5000. However, this calculation ignorestransaction costs.

First, there is a commission, which is a transaction fee you pay your broker. Acommission for the above order could be $15, or .3% of the purchase price.

Second, the term “stock price” is, surprisingly, imprecise. There are in fact twoprices, a price at which you can buy, and a price at which you can sell. The price atwhich you can buy is called the offer price or ask price, and the price at which you cansell is called the bid price. Where do these terms come from?

If you want to buy stock, you pick up the phone and call a broker. If the stock is nottoo obscure and your order is not too large, your purchase will probably be completed ina matter of seconds. Have you ever wondered where the stock comes from that you havejust bought? It is possible that at the exact same moment, another customer called thebroker and put in an order to sell. More likely, however, a market-maker sold you thestock. Market-makers do what their name implies: They make markets. If you want tobuy, they sell, and if you want to sell, they buy. In order to earn a living, market-makerssell for a high price and buy for a low price. If you deal with a market-maker, therefore,you buy for a high price and sell for a low price. This difference between the price atwhich you can buy and the price at which you can sell is called the bid-ask spread.4

In practice the bid-ask spread on the stock you are buying may be $49.75 to $50. Thismeans that you can buy for $50/share and sell for $49.75/share. If you were to buyimmediately and then sell, you would pay the commission twice, and you would pay thebid-ask spread.

Note that when you observe prices in the real world, you will often see thembounce up and down a bit. This can reflect bid-ask bounce. If the bid is $49.75 and theask is $50, a series of buy and sell orders will cause the price at which the stock was lasttraded to move between $49.75 and $50. The “true” price has not changed, however,because the bid and ask have not changed.

Example 1.1 Suppose XYZ is bid at $49.75 and offered at $50, and the commissionis $15. If you buy 100 shares of the stock you pay ($50 × 100) + $15 = $5015. If you

.................................4If you think a bid-ask spread is unreasonable, ask what a world without dealers would be like. Everybuyer would have to find a seller, and vice versa. The search would be costly and take time. Dealers,because they maintain inventory, offer an immediate transaction, a service called immediacy.



immediately sell them again, you receive ($49.75 × 100) − $15 = $4960. Your roundtrip transaction cost—the difference between what you pay and what you receive froma sale, not counting changes in the bid and ask prices—is $5015 − $4960 = $55. w

Incidentally, this discussion reveals where the terms “bid” and “ask” come from.Your first thought might have been that the terminology is backward. The bid pricesounds like it should be what you pay. It is in fact what the market-maker pays; henceit is the price at which you sell. The offer price is what the market-maker will sellfor, hence it is what you have to pay. The terminology reflects the perspective of themarket-maker.

One last point: What happens to your shares after you buy them? Generally theyare held by your broker. If you read the fine print on your brokerage contract carefully,your broker typically has the right to lend your shares to another investor. Why wouldanyone want to borrow your shares? The answer to that brings us to the next topic,short-sales.

Although we have focused here on shares of stock, there are similar issues associ-ated with buying any asset.

Short-Selling

When we buy something, we are said to have a long position in that thing. For example,if we buy the stock of XYZ, we pay cash and receive the stock. Some time later, we sellthe stock and receive cash. This transaction is lending, in the sense that we pay moneytoday and receive money back in the future. The rate of return we receive may not beknown in advance (if the stock price goes up a lot, we get a high return; if the stock pricegoes down, we get a negative return), but it is a kind of loan nonetheless.

The opposite of a long position is a short position. A short-sale of XYZ entailsborrowing shares of XYZ and then selling them, receiving the cash. Some time later, webuy back the XYZ stock, paying cash for it, and return it to the lender. The idea is to firstsell high and then buy low. (With a long position, the idea is to first buy low and thensell high.) A short-sale can be viewed, then, as just a way of borrowing money. Whenyou borrow money from a bank, you receive money today and repay it later, paying arate of interest set in advance. This is also what happens with a short-sale, except thatyou don’t necessarily know the rate you pay to borrow.

There are at least three reasons to short-sell:

1. Speculation A short-sale, considered by itself, makes money if the price of the stockgoes down.

2. Financing A short-sale is a way to borrow money, and it is frequently used as aform of financing. This is very common in the bond market, for example.

3. Hedging You can undertake a short-sale to offset the risk of owning the stock or aderivative on the stock. This is frequently done by market-makers and traders.



These reasons are not mutually exclusive. For example, a market-maker mightuse a short-sale to simultaneously hedge and finance a position.

Because short-sales can seem confusing, here is a detailed example that illustrateshow short-sales work.

Example: Short-selling pokey babies Consider the (hypothetical) “pokey-baby”phenomenon, in which small dolls representing Japanese cartoon characters becomeexpensive collectors items that are bought and sold worldwide. Suppose, however, thatyou believe the pokey-baby phenomenon is over and that prices of pokey babies aregoing to fall. How could you speculate based on this belief?

If you believed prices would rise, you would buy pokey babies today and sell later.However, if you believed prices would fall, you would like to do the opposite: Sell today(at the high price) and buy tomorrow (at the low price). How do you actually accomplishthis?

In order to sell today, you must first obtain pokey babies to sell. You can do thisby borrowing them from a collector. The collector, of course, will want a promise thatthe pokey babies will be returned at some point, so suppose you agree to return them inone week. Thus, you borrow them and sell them at the market price. After one week,you acquire replacement pokey babies on the market, then return them to the collectorfrom whom you borrowed them. If the price has fallen, you have made money, while ifthe price has risen you have lost money. Whatever happens to the price, you have justcompleted a short-sale of pokey babies. The act of buying the pokey baby and returningit to the lender is said to be closing or covering the short position.

Note that you really have borrowed money. Initially, you received money fromselling the pokey babies, and a week later you pay the money back (you had to buythe pokey babies back to return them). The rate of interest you paid was low if thepokey-baby price was low, and high if the pokey-baby price was high.

This example is obviously simplified. We have assumed that

• It is easy to find a pokey-baby lender.

• It is easy to buy, at a fair price, a satisfactory pokey baby to return to the lender.The pokey babies you buy after one week are a perfect substitute for the pokeybabies you borrowed.

• The collector from whom you borrowed is not concerned that you will fail to returnthe borrowed toy.

Example: Short-selling stock Now consider a short-sale of stock. As with the previ-ous example, when you short-sell stock you borrow the stock and sell it, receiving cashtoday. At some future date you buy the stock in the market and return it to the originalowner. You have cash coming in today, equal to the market value of the stock you short-sell. In the future, you repay the borrowing by buying the asset at its then-current marketprice and returning the asset—this is like the repayment of a loan. Thus, short-sellinga stock is equivalent to borrowing money, except that the interest rate you pay is notknown in advance. Rather, it is determined by the change in the stock price. The rate of



TABLE 1.2 Cash flows associated with short-selling a share of IBM for 90days. Note that the short-seller must pay the dividend, D, tothe share-lender.

Day 0 Dividend Ex-Day Day 90

Action Borrow Shares — Return Shares

Security Sell Shares — Purchase Shares

Cash +S0 −D −S90

interest is high if the security rises in price and low if the security falls in price. In effect,the rate of return on the security is the rate at which you borrow. With a short-sale, youare like the issuer of a security rather than the buyer of a security.

Suppose you want to short-sell IBM stock for 90 days. Table 1.2 depicts the cashflows. Observe in particular that if the share pays dividends, the short-seller must in turnmake dividend payments to the share-lender. This issue did not arise with pokey babies!This dividend payment is taxed to the recipient, just like an ordinary dividend payment,and it is tax-deductible to the short-seller.

Notice that the cash flows in Table 1.2 are exactly the opposite of the cash flowsfrom purchasing the stock. Thus, short-selling is literally the opposite of buying.

The Lease Rate of an Asset

We have seen that when you borrow an asset it may be necessary to make payments tothe lender. Dividends on short-sold stock are an example of this. We will refer to thepayment required by the lender as the lease rate of the asset. This concept will arisefrequently, and, as we will see, provides a unifying concept for our later discussions ofderivatives.

The pokey-baby example did not have a lease payment. But under some circum-stances it might be necessary to make a payment to borrow a pokey baby. Pokey babiesdo not pay an explicit dividend, but they do pay an implicit dividend if the owner enjoysseeing them on the shelf. The owner might thus require a payment in order to lend apokey baby. This would be a lease rate for pokey babies.

Risk and Scarcity in Short-Selling

The preceding examples were simple illustrations of the mechanics and economics ofshort-selling, and demonstrate the ideas you will need to understand our discussionsof derivatives. It turns out, however, that some of the complexities we skipped overare easy to understand and are important in practice. In this section we return to thepokey-baby example to illustrate some of these practical issues.



Credit risk As the short-seller, you have an obligation to the pokey-baby lender toreturn the toys. The pokey-baby lender fears that you will renege on this obligation.This concern can be addressed with collateral: After you sell the pokey babies, thepokey-baby lender can hold the money you received from selling the pokey babies. Youhave an obligation to return the toy; the lender keeps the money in the event that youdon’t.

Holding on to the money will help the lender feel more secure, but after thinkingthe matter over, the lender will likely want more from you than just the value of thepokey babies. Suppose you borrow $5000 worth of pokey babies. What happens, thelender will think, if the price of the pokey babies rises to $6000 one week later? This isa $1000 loss on your short-sale. In order to return the toys, you will have to pay $6000for toys you just sold for $5000. Perhaps you cannot afford the extra $1000 and youwill fail to return the borrowed toys. The lender, thinking ahead, will be worried at theoutset about this possibility and will ask you to provide more than the $5000 the pokeybabies are worth, say an extra $1000. This extra amount is called a haircut, and servesto protect the lender against your failure to return the toys when the price rises.5 Inpractice, short-sellers must have funds—called capital—to be able to pay haircuts. Theamount of capital places a limit on their ability to short-sell.

Scarcity As the short-seller, do you need to worry about the short-sale proceeds? Thelender is going to have $6000 of your money. Most of this, however, simply reflectsyour obligation, and we could imagine asking a trustworthy third party, such as a bank,to hold the money so the lender cannot abscond with it. However, when you return thetoys, you are going to want your money back, plus interest. This raises the question:What rate of interest will the lender pay you? Over the course of the short-sale, thelender can invest your money, earning, say, 6%. The lender could offer to pay you 4%on the funds, thinking to keep as a fee the 2% difference between the 6% earned on themoney and the 4% paid to you. What happens if the lender and borrower negotiate?

Here is the interesting point: The rate of interest the lender pays on the collateralis going to depend on how many people want to borrow pokey babies and how many arewilling to lend them! As a practical matter, it may not be easy to find a lender. If thereis high demand for borrowed pokey babies, the lender will offer a low rate of interest,essentially earning a fee for being willing to lend something that is scarce. However, ifno one else wants to borrow the toys, the lender might conclude that a small fee is betterthan nothing and offer you a rate of interest close to the market rate.

The rate paid on collateral is called different things in different markets, the reporate in bond markets and the short rebate in the stock market. Whatever it is called,the difference between this rate and the market rate of interest is another cost to yourshort-sale.

.................................5Note that the lender is not concerned about your failure to perform when the price goes down becausethe lender has the money!



CHAPTER SUMMARY

Derivatives are financial instruments with a payoff determined by the price of some-thing else. They can be used as a tool for risk management, for speculation, to reducetransaction costs, or to avoid taxes or regulation.

One important function of financial markets is to facilitate optimal risk-sharing.The growth of derivatives markets over the last 50 years has coincided with an increase inthe risks evident in various markets. Events such as the 1973 oil shock, the abandonmentof fixed exchange rates, and the deregulation of energy markets have created a new rolefor derivatives.

Ashort-sale entails borrowing a security, selling it, making dividend (or other cash)payments to the security lender, and then returning it. A short-sale is conceptually theopposite of a purchase. Short-sales can be used for speculation, as a form of financing,or as a way to hedge. Many of the details of short-selling in practice can be understoodas a response to credit risk of the short-seller and scarcity of shares that can be borrowed.Short-sellers typically leave the short-sale proceeds on deposit with lenders, along withadditional capital called a haircut. The rate paid on this collateral is called the shortrebate, and is less than the interest rate.

FURTHER READING

The rest of this book provides an elaboration of themes discussed in this chapter. How-ever, certain chapters are directly related to the discussion. Chapters 2, 3, and 4 introduceforward and option contracts, which are the basic contracts in derivatives, and show howthey are used in risk management. Chapter 13 discusses in detail how derivatives market-makers manage their risk, and Chapter 15 explains how derivatives can be combinedwith instruments such as bonds to create customized risk-management products.

The various derivatives exchanges have websites which list their contracts. Thewebsites for the exchanges in Figure 1.4 are www.cbot.com (Chicago Board of Trade),www.cme.com (Chicago Mercantile Exchange), and www.nymex.com (New YorkMercantile Exchange).

Jorion (1995) examines in detail one famous “derivatives disaster”: OrangeCounty in California. Bernstein (1992) is a history of the development of financialmarkets, and Bernstein (1996) discusses the concept of risk measurement and how itevolved over the last 800 years. Miller (1986) discusses origins of past financial innova-tion, and Merton (1999) provides a fascinating academic perspective on possible futuredevelopments in financial markets. Froot and O’Connell (1999) and Froot (2001) exam-ine the market for catastrophe reinsurance. D’Avolio (2001) explains the economics andpractices associated with short-sales. Finally, Lewis (1989) is a classic, funny, insider’saccount of investment banking, offering a different (to say the least) perspective on themechanics of global risk-sharing.


Problems w 17

PROBLEMS

1.1. Heating degree-day and cooling degree-day futures contracts make paymentsbased on whether the temperature is abnormally hot or cold. Explain why thefollowing businesses might be interested in such a contract:

a. Soft-drink manufacturers.

b. Ski-resort operators.

c. Electric utilities.

d. Amusement park operators.

1.2. Suppose the businesses in the previous problem use futures contracts to hedgetheir temperature-related risk. Who do you think might accept the opposite risk?

1.3. ABC stock has a bid price of $40.95 and an ask price of $41.05. Assume there isa $20 brokerage commission.

a. What amount will you pay to buy 100 shares?

b. What amount will you receive for selling 100 shares?

c. Suppose you buy 100 shares, then immediately sell 100 shares with thebid and ask prices being the same in both cases. What is your round-triptransaction cost?

1.4. Repeat the previous problem supposing that the brokerage fee is quoted as 0.3%of the bid or ask price.

1.5. Suppose a security has a bid price of $100 and an ask price of $100.12. At whatprice can the market-maker purchase a security? At what price can a market-maker sell a security? What is the spread in dollar terms when 100 shares aretraded?

1.6. Suppose you short-sell 300 shares of XYZ stock at $30.19 with a commissioncharge of 0.5%. Supposing you pay commission charges for purchasing the se-curity to cover the short-sale, how much profit have you made if you close theshort-sale at a price of $29.87?

1.7. Suppose you desire to short-sell 400 shares of JKI stock, which has a bid priceof $25.12 and an ask price of $25.31. You cover the short position 180 days laterwhen the bid price is $22.87 and the ask price is $23.06.

a. Taking into account only the bid and ask prices (ignoring commissionsand interest), what profit did you earn?

b. Suppose that there is a 0.3% commission to engage in the short-sale (thisis the commission to sell the stock) and a 0.3% commission to close theshort-sale (this is the commission to buy the stock back). How do thesecommissions change the profit in the previous answer?



c. Suppose the 6-month interest rate is 3% and that you are paid nothingon the short-sale proceeds. How much interest do you lose during the 6months in which you have the short position?

1.8. When you open a brokerage account, you typically sign an agreement giving thebroker the right to lend your shares without notifying or compensating you. Whydo brokers want you to sign this agreement?

1.9. Suppose a stock pays a quarterly dividend of $3. You plan to hold a short positionin the stock across the dividend ex-date. What is your obligation on that date? Ifyou are a taxable investor, what would you guess is the tax consequence of thepayment? (In particular, would you expect the dividend to be tax deductible?)Suppose the company announces instead that the dividend is $5. Should you carethat the dividend is different from what you expected?

1.10. Short interest is a measure of the aggregate short positions on a stock. Check anonline brokerage or other financial service for the short interest on several stocksof your choice. Can you guess which stocks have high short interest and whichhave low? Is it theoretically possible for short interest to exceed 100% of sharesoutstanding?

1.11. Suppose that you go to a bank and borrow $100. You promise to repay the loan in90 days for $102. Explain this transaction using the terminology of short-sales.

1.12. Suppose your bank’s loan officer tells you that if you take out a mortgage (i.e.,you borrow money to buy a house) you will be permitted to borrow no more than80% of the value of the house. Describe this transaction using the terminology ofshort-sales.

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