Options, Futures, and Derivatives PDF

1 C H A P T E R Introduction In the last 40 years, derivatives have become increasingly important in ﬁnance. Futures and options are actively traded on many exchanges throughout the world. Many diﬀerent types of forward contracts, swaps, options, and other derivatives are entered into by ﬁnancial institutions, fund managers, and corporate treasurers in the over-the- counter market. Derivatives are added to bond issues, used in executive compensation plans, embedded in capital investment opportunities, used to transfer risks in mortgages from the original lenders to investors, and so on. We have now reached the stage where those who work in ﬁnance, and many who work outside ﬁnance, need to understand how derivatives work, how they are used, and how they are priced. Whether you love derivatives or hate them, you cannot ignore them! The derivatives market is huge—much bigger than the stock market when measured in terms of underlying assets. The value of the assets underlying outstanding derivatives trans- actions is several times the world gross domestic product. As we shall see in this chapter, derivatives can be used for hedging or speculation or arbitrage. They can be used to transfer a wide range of risks in the economy from one entity to another. A derivative can be deﬁned as a ﬁnancial instrument whose value depends on (or derives from) the values of other, more basic, underlying variables. Very often the variables underlying derivatives are the prices of traded assets. A stock option, for example, is a derivative whose value is dependent on the price of a stock. However, derivatives can be dependent on almost any variable, from the price of hogs to the amount of snow falling at a certain ski resort. Since the ﬁrst edition of this book was published in 1988 there have been many developments in derivatives markets. There is now active trading in credit derivatives, electricity derivatives, weather derivatives, and insurance derivatives. Many new types of interest rate, foreign exchange, and equity derivative products have been created. There have been many new ideas in risk management and risk measurement. Capital investment appraisal now often involves the evaluation of what are known as real options. Many new regulations have been introduced covering over-the-counter deriva- tives markets. The book has kept up with all these developments. Derivatives markets have come under a great deal of criticism because of their role in the credit crisis that started in 2007. Derivative products were created from portfolios of risky mortgages in the United States using a procedure known as securitization. Many of the products that were created became worthless when house prices declined. Financial 1 2 CHAPTER 1 institutions, and investors throughout the world, lost a huge amount of money and the world was plunged into the worst recession it had experienced in 75 years. Chapter 8 explains how securitization works and why such big losses occurred. The way market participants trade and value derivatives has evolved through time. Regulatory requirements introduced since the crisis have had a huge eﬀect on the over- the-counter market. Collateral and credit issues are now given much more attention than in the past. Market participants have changed the proxy they use for the risk-free rate. They also now calculate a number of valuation adjustments to reﬂect funding costs and capital requirements, as well as credit risk. This edition has been changed to keep up to date with these developments. Chapter 9 is now devoted to a discussion of how valuation adjustments work and the extent to which they are theoretically valid. In this opening chapter, we take a ﬁrst look at derivatives markets and how they are changing. We describe forward, futures, and options markets and provide an overview of how they are used by hedgers, speculators, and arbitrageurs. Later chapters will give more details and elaborate on many of the points made here. 1.1 EXCHANGE-TRADED MARKETS A derivatives exchange is a market where individuals trade standardized contracts that have been deﬁned by the exchange. Derivatives exchanges have existed for a long time. 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. A rival futures exchange, the Chicago Mercantile Exchange (CME), was established in 1919. Now futures exchanges exist all over the world. (See table at the end of the book.) The CME and CBOT have merged to form the CME Group (www.cmegroup.com), which also includes the New York Mercantile Exchange (NYMEX), and the Kansas City Board of Trade (KCBT). The Chicago Board Options Exchange (CBOE, www.cboe.com) started trading call option contracts on 16 stocks in 1973. Options had traded prior to 1973, but the CBOE succeeded in creating an orderly market with well-deﬁned contracts. Put option contracts started trading on the exchange in 1977. The CBOE now trades options on thousands of stocks and many diﬀerent stock indices. Like futures, options have proved to be very popular contracts. Many other exchanges throughout the world now trade options. (See table at the end of the book.) The underlying assets include foreign currencies and futures contracts as well as stocks and stock indices. Once two traders have agreed on a trade, it is handled by the exchange clearing house. This stands between the two traders and manages the risks. Suppose, for example, that trader A agrees to buy 100 ounces of gold from trader B at a future time for $1,250 per ounce. The result of this trade will be that A has a contract to buy 100 ounces of gold from the clearing house at $1,250 per ounce and B has a contract to sell 100 ounces of gold to the clearing house for $1,250 per ounce. The advantage of this arrangement is that traders do not have to worry about the creditworthiness of the people they are trading with. The clearing house takes care of credit risk by requiring Introduction 3 each of the two traders to deposit funds (known as margin) with the clearing house to ensure that they will live up to their obligations. Margin requirements and the operation of clearing houses are discussed in more detail in Chapter 2. Electronic Markets Traditionally derivatives exchanges have used what is known as the open outcry system. This involves traders physically meeting on the ﬂoor of the exchange, shouting, and using a complicated set of hand signals to indicate the trades they would like to carry out. Exchanges have largely replaced the open outcry system by electronic trading. This involves traders entering their desired trades at a keyboard and a computer being used to match buyers and sellers. The open outcry system has its advocates, but, as time passes, it is becoming less and less used. Electronic trading has led to a growth in high-frequency and algorithmic trading. This involves the use of computer programs to initiate trades, often without human intervention, and has become an important feature of derivatives markets. 1.2 OVER-THE-COUNTER MARKETS Not all derivatives trading is on exchanges. Many trades take place in the over-the- counter (OTC) market. Banks, other large ﬁnancial institutions, fund managers, and corporations are the main participants in OTC derivatives markets. Once an OTC trade has been agreed, the two parties can either present it to a central counterparty (CCP) or clear the trade bilaterally. A CCP is like an exchange clearing house. It stands between the two parties to the derivatives transaction so that one party does not have to bear the risk that the other party will default. When trades are cleared bilaterally, the two parties have usually signed an agreement covering all their trans- actions with each other. The issues covered in the agreement include the circumstances under which outstanding transactions can be terminated, how settlement amounts are calculated in the event of a termination, and how the collateral (if any) that must be posted by each side is calculated. CCPs and bilateral clearing are discussed in more detail in Chapter 2. Large 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). 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 of many new regulations aﬀecting the operation of OTC markets. The main objectives of the regulations are to improve the transparency of OTC markets and reduce systemic risk (see Business Snapshot 1.2). 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 between two ﬁnancial institutions in the United States must, whenever possible, be traded on what are referred to a swap execution 4 CHAPTER 1 Business Snapshot 1.1 The Lehman Bankruptcy On September 15, 2008, Lehman Brothers ﬁled for bankruptcy. This was the largest bankruptcy in U.S. history and its ramiﬁcations were felt throughout derivatives markets. Almost until the end, it seemed as though there was a good chance that Lehman would survive. A number of companies (e.g., the Korean Development Bank, Barclays Bank in the United Kingdom, 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 U.S. 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 Oﬃcer, 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 renew this funding, forcing it into bankruptcy. Lehman was very active in the over-the-counter derivatives markets. It had over a million 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. Litigation aimed at determining who owes what to whom continued for many years after the bank- ruptcy ﬁling. facilities (SEFs). These are platforms similar to exchanges where market participants can post bid and oﬀer quotes and where market participants can trade by accepting the quotes of other market participants. 2. There is a requirement in most parts of the world that a CCP be used for most standardized derivatives transactions between ﬁnancial institutions. 3. All trades must be reported to a central repository. Market Size Both the over-the-counter and the exchange-traded market for derivatives are huge. 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. Although the statistics that are collected for the two markets are not exactly comparable, it is clear that the volume of business in the over-the-counter market is much larger than in the exchange-traded market. The Bank for International Settlements (www.bis.org) started collecting statistics on the markets in 1998. Figure 1.1 compares (a) the estimated total Introduction 5 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 huge 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. principal amounts underlying transactions that were outstanding in the over-the counter markets between June 1998 and December 2015 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 in December 2015 was $492.9 trillion and the size of the exchange-traded market was $63.3 trillion.1 Figure 1.1 shows that the OTC market grew rapidly up to 2007, but has seen very little net growth since then. One reason for the lack of growth is the popularity of compression. This is a procedure where two or more counterparties restructure transactions with each other with the result that the underlying principal is reduced. In interpreting Figure 1.1, we should bear in mind that the principal underlying an over-the-counter transaction is not the same as its value. An example of an over-the- counter transaction is an agreement to buy 100 million U.S. dollars with British pounds Figure 1.1 Size of over-the-counter and exchange-traded derivatives markets. 800 Size of market 700 ($ trillion) 600 500 400 300 OTC 200 Exchange 100 0 Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun Jun 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 1 When a CCP stands between two sides in an OTC transaction, two transactions are considered to have been created for the purposes of the BIS statistics. 6 CHAPTER 1 at a predetermined exchange rate in 1 year. The total principal amount underlying this transaction is $100 million. However, the value of the transaction might be only $1 million. The Bank for International Settlements estimates the gross market value of all over-the-counter transactions outstanding in December 2015 to be about $14.5 trillion.2 1.3 FORWARD CONTRACTS A relatively simple derivative is a forward contract. It is an agreement to buy or sell an asset at a certain future time for a certain price. It can be contrasted with a spot contract, which is an agreement to buy or sell an asset almost immediately. A forward contract is traded in the over-the-counter market—usually between two ﬁnancial institutions or between 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 underlying asset on a certain speciﬁed future date for a certain speciﬁed price. The other party assumes a short position and agrees to sell the asset on the same date for the same price. Forward contracts on foreign exchange are very popular. Most large banks employ both spot and forward foreign-exchange traders. As we shall see in a later chapter, there is a relationship between forward prices, spot prices, and interest rates in the two currencies. Table 1.1 provides 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 May 3, 2016. 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 $1.4542 per GBP and sell sterling in the spot market at $1.4546 per GBP. The second, third, and fourth rows indicate that the bank is prepared to buy sterling in 1, 3, and 6 months at $1.4544, $1.4547, and $1.4556 per GBP, respectively, and to sell sterling in 1, 3, and 6 months at $1.4548, $1.4551, and $1.4561 per GBP, respectively. Forward contracts can be used to hedge foreign currency risk. Suppose that, on May 3, 2016, the treasurer of a U.S. corporation knows that the corporation will pay £1 million in 6 months (i.e., on November 3, 2016) and wants to hedge against exchange rate moves. Using the quotes in Table 1.1, the treasurer can agree to buy £1 million Table 1.1 Spot and forward quotes for the USD/GBP exchange rate, May 3, 2016 (GBP ¼ British pound; USD ¼ U.S. dollar; quote is number of USD per GBP). Bid Oﬀer Spot 1.4542 1.4546 1-month forward 1.4544 1.4548 3-month forward 1.4547 1.4551 6-month forward 1.4556 1.4561 2 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. Introduction 7 6 months forward at an exchange rate of 1.4561. The corporation then has a long forward contract on GBP. It has agreed that on November 3, 2016, it will buy £1 million from the bank for $1.4561 million. The bank has a short forward contract on GBP. It has agreed that on November 3, 2016, it will sell £1 million for $1.4561 million. Both sides have made a binding commitment. Payoffs from Forward Contracts Consider the position of the corporation in the trade we have just described. What are the possible outcomes? The forward contract obligates the corporation to buy £1 million for $1,456,100. If the spot exchange rate rose to, say, 1.5000, at the end of the 6 months, the forward contract would be worth $43,900 (¼ $1,500,000 $1,456,100) to the corporation. It would enable £1 million to be purchased at an exchange rate of 1.4561 rather than 1.5000. Similarly, if the spot exchange rate fell to 1.4000 at the end of the 6 months, the forward contract would have a negative value to the corporation of $56,100 because it would lead to the corporation paying $56,100 more than the market price for the sterling. In general, the payoﬀ from a long position in a forward contract on one unit of an asset is ST K where K is the delivery price and ST is the spot price of the asset at maturity of the contract. This is because the holder of the contract is obligated to buy an asset worth ST for K. Similarly, the payoﬀ from a short position in a forward contract on one unit of an asset is K ST These payoﬀs can be positive or negative. They are illustrated in Figure 1.2. Because it costs nothing to enter into a forward contract, the payoﬀ from the contract is also the trader’s total gain or loss from the contract. Figure 1.2 Payoﬀs from forward contracts: (a) long position, (b) short position. Delivery price ¼ K; price of asset at contract maturity ¼ ST. Payoff Payoff 0 0 K ST K ST (a) (b) 8 CHAPTER 1 In the example just considered, K ¼ 1:4561 and the corporation has a long contract. When ST ¼ 1:5000, the payoﬀ is $0.0439 per £1; when ST ¼ 1:4000, it is $0.0561 per £1. Forward Prices and Spot Prices We shall be discussing in some detail the relationship between spot and forward prices in Chapter 5. For a quick preview of why the two are related, consider a stock that pays no dividend and is worth $60. You can borrow or lend money for 1 year at 5%. What should the 1-year forward price of the stock be? The answer is $60 grossed up at 5% for 1 year, or $63. If the forward price is more than this, say $67, you could borrow $60, buy one share of the stock, and sell it forward for $67. After paying oﬀ the loan, you would net a proﬁt of $4 in 1 year. If the forward price is less than $63, say $58, an investor owning the stock as part of a portfolio would sell the stock for $60 and enter into a forward contract to buy it back for $58 in 1 year. The proceeds of investment would be invested at 5% to earn $3. The investor would end up $5 better oﬀ than if the stock were kept in the portfolio for the year. 1.4 FUTURES CONTRACTS Like a forward contract, a futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price. Unlike forward contracts, futures contracts are normally traded on an exchange. To make trading possible, the exchange speciﬁes certain standardized features of the contract. As the two parties to the contract do not necessarily know each other, the exchange also provides a mechanism that gives the two parties a guarantee that the contract will be honored. Two large exchanges on which futures contracts are traded are the Chicago Board of Trade (CBOT) and the Chicago Mercantile Exchange (CME), which have now merged to form the CME Group. On these and other exchanges throughout the world, a very wide range of commodities and ﬁnancial assets form the underlying assets in the various contracts. The commodities include pork bellies, live cattle, sugar, wool, lumber, copper, aluminum, gold, and tin. The ﬁnancial assets include stock indices, currencies, and Treasury bonds. Futures prices are regularly reported in the ﬁnancial press. Suppose that, on September 1, the December futures price of gold is quoted as $1,380. This is the price, exclusive of commissions, at which traders can agree to buy or sell gold for December delivery. It is determined in the same way as other prices (i.e., by the laws of supply and demand). If more traders want to go long than to go short, the price goes up; if the reverse is true, then the price goes down. Further details on issues such as margin requirements, daily settlement procedures, delivery procedures, bid–oﬀer spreads, and the role of the exchange clearing house are given in Chapter 2. 1.5 OPTIONS Options are traded both on exchanges and in the over-the-counter market. There are two types of option. A call option gives the holder the right to buy the underlying asset by a certain date for a certain price. A put option gives the holder the right to sell the Introduction 9 Table 1.2 Prices of call options on Alphabet Inc. (Google), May 3, 2016; stock price: bid $695.86, oﬀer $696.25 (Source: CBOE). Strike price June 2016 September 2016 December 2016 ($) Bid Oﬀer Bid Oﬀer Bid Oﬀer 660 43.40 45.10 60.80 62.70 72.70 76.70 680 29.20 30.60 47.70 50.70 60.90 64.70 700 18.30 18.90 37.00 39.20 49.70 52.50 720 9.90 10.50 27.50 29.50 40.10 42.80 740 4.70 5.20 19.80 21.60 31.40 34.40 underlying asset by a certain date for a certain price. The price in the contract is known as the exercise price or strike price; the date in the contract is known as the expiration date or maturity. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date itself.3 Most of the options that are traded on exchanges are American. In the exchange-traded equity option market, one contract is usually an agreement to buy or sell 100 shares. European options are generally easier to analyze than American options, and some of the properties of an American option are frequently deduced from those of its European counterpart. 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 is what distinguishes options from forwards and futures, where the holder is obligated to buy or sell the underlying asset. Whereas it costs nothing to enter into a forward or futures contract, except for margin requirements which will be discussed in Chapter 2, there is a cost to acquiring an option. 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), which is now Alphabet Inc. Class C, on May 3, 2016. Table 1.3 does the same for put options trading Table 1.3 Prices of put options on Alphabet Inc. (Google), May 3, 2016; stock price: bid $695.86, oﬀer $696.25 (Source: CBOE). Strike price June 2016 September 2016 December 2016 ($) Bid Oﬀer Bid Oﬀer Bid Oﬀer 660 7.50 8.20 24.20 26.20 35.60 38.10 680 13.30 14.00 31.90 33.80 43.40 46.00 700 21.70 23.00 40.80 42.70 52.40 55.20 720 33.10 34.80 51.10 53.20 62.60 65.20 740 47.70 49.60 63.10 65.20 74.10 76.70 3 Note that the terms American and European do not refer to the location of the option or the exchange. Some options trading on North American exchanges are European. 10 CHAPTER 1 on Google on that date. The quotes are taken from the CBOE website. The Google stock price at the time of the quotes was bid 695.86, oﬀer 696.25. The bid–oﬀer spread for an option (as a percent of the price) is usually greater than that for the underlying stock and depends on the volume of trading. The option strike prices in Tables 1.2 and 1.3 are $660, $680, $700, $720, and $740. The maturities are June 2016, September 2016, and December 2016. The actual expiration day is the third Friday of the expiration month. The June options expire on June 17, 2016, the September options on September 16, 2016, and the December options on December 16, 2016. The tables illustrate a number of properties of options. The price of a call option decreases as the strike price increases, while the price of a put option increases as the strike price increases. Both types of option tend to become more valuable as their time to maturity increases. These properties of options will be discussed further in Chapter 11. Suppose a trader instructs a broker to buy one December call option contract on Google with a strike price of $700. The broker will relay these instructions to a trader at the CBOE and the deal will be done. The (oﬀer) price indicated in Table 1.2 is $52.50. This is the price for an option to buy one share. In the United States, an option contract is a contract to buy or sell 100 shares. Therefore, the trader must arrange for $5,250 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 trader has obtained at a cost of $5,250 the right to buy 100 Google shares for $700 each. If the price of Google does not rise above $700 by December 16, 2016, the option is not exercised and the trader loses $5,250.4 But if Google does well and the option is exercised when the bid price for the stock is $900, the trader is able to buy 100 shares at $700 and immediately sell them for $900 for a proﬁt of $20,000, or $14,750 when the initial cost of the options is taken into account.5 An alternative trade would be to sell one September put option contract with a strike price of $660 at the bid price of $24.20. The trader receives 100 24:20 ¼ $2,420. If the Google stock price stays above $660, the option is not exercised and the trader makes a $2,420 proﬁt. However, if stock price falls and the option is exercised when the stock price is $600, there is a loss. The trader must buy 100 shares at $660 when they are worth only $600. This leads to a loss of $6,000, or $3,580 when the initial amount received for the option contract is taken into account. The stock options trading on the CBOE are American. If we assume for simplicity that they are European, so that they can be exercised only at maturity, the trader’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 3. Buyers of puts 4. Sellers of puts. 4 The calculations here ignore any commissions paid by the trader. 5 The calculations here ignore the eﬀect of discounting. Theoretically, the $20,000 should be discounted from the time of exercise to the purchase date, when calculating the proﬁt. Introduction 11 Figure 1.3 Net proﬁt from (a) purchasing a contract consisting of 100 Google December call options with a strike price of $700 and (b) selling a contract consisting of 100 Google September put options with a strike price of $660. 25,000 Profit ($) 25,000 Profit ($) 20,000 20,000 15,000 15,000 10,000 10,000 5,000 5,000 0 0 500 600 700 800 900 1,000 500 600 700 800 900 1,000 -5,000 Stock price ($) -5,000 Stock price ($) -10,000 -10,000 -15,000 -15,000 (a) (b) 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 TYPES OF TRADERS Derivatives markets have been outstandingly successful. The main reason is that they have attracted many diﬀerent types of traders and have a great deal of liquidity. When a trader wants to take one side of a contract, there is usually no problem in ﬁnding someone who is prepared to take the other side. Three broad categories of traders can be identiﬁed: hedgers, speculators, and arbitrageurs. Hedgers use derivatives 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 will consider the activities of each type of trader in more detail. 1.7 HEDGERS In this section we illustrate how hedgers can reduce their risks with forward contracts and options. Hedging Using Forward Contracts Suppose that it is May 3, 2016, and ImportCo, a company based in the United States, knows that it will have to pay £10 million on August 3, 2016, 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 3-month forward market 12 CHAPTER 1 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 professional fund managers or ﬁnan- cially 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 1 to 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 securities issued by companies 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. at 1.4551. This would have the eﬀect of ﬁxing the price to be paid to the British exporter at $14,551,000. Consider next another U.S. company, which we will refer to as ExportCo, that is exporting goods to the United Kingdom and, on May 3, 2016, knows that it will receive £30 million 3 months later. ExportCo can hedge its foreign exchange risk by selling £30 million in the 3-month forward market at an exchange rate of 1.4547. This would have the eﬀect of locking in the U.S. dollars to be realized for the sterling at $43,641,000. 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 Introduction 13 1.4000 on August 3 and the company has not hedged, the £10 million that it has to pay will cost $14,000,000, which is less than $14,551,000. On the other hand, if the exchange rate is 1.5000, the £10 million will cost $15,000,000—and the company will wish that it had hedged! The position of ExportCo if it does not hedge is the reverse. If the exchange rate in August proves to be less than 1.4547, the company will wish that it had hedged; if the rate is greater than 1.4547, it will be pleased that it has not done so. This example illustrates a key aspect of hedging. The purpose of hedging is to reduce risk. There is no guarantee that the outcome with hedging will be better than the outcome without hedging. Hedging Using Options Options can also be used for hedging. Consider an investor who in May of a particular year owns 1,000 shares of a particular company. The share price is $28 per share. The investor is concerned about a possible share price decline in the next 2 months and wants protection. The investor could buy ten July put option contracts on the company’s stock with a strike price of $27.50. Each contract is on 100 shares, so 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, then 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 $26,500 when the cost of the options is taken into account). Figure 1.4 shows the net value of the portfolio (after taking the cost of the options into account) as a function of the stock price in 2 months. The dotted line shows the value of the portfolio assuming no hedging. Figure 1.4 Value of the stock holding in 2 months with and without hedging. 40,000 Value of holding ($) 35,000 30,000 Hedging No hedging 25,000 Stock price ($) 20,000 20 25 30 35 40 14 CHAPTER 1 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. 1.8 SPECULATORS We now move on to consider how futures and options markets can be used by speculators. Whereas hedgers want to avoid 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 2 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 a higher price. (The sterling once 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 in April.) Table 1.4 summarizes the two alternatives on the assumption that the current exchange rate is 1.4540 dollars per pound and the April futures price is 1.4543 dollars per pound. If the exchange rate turns out to be 1.5000 dollars per pound in April, the futures contract alternative enables the speculator to realize a proﬁt of ð1:5000 1:4543Þ 250,000 ¼ $11,425. The spot market alternative leads to 250,000 units of an asset being purchased for $1.4540 in February and sold for $1.5000 in April, so that a proﬁt of ð1:5000 1:4540Þ 250,000 ¼ $11,500 is made. If the exchange rate falls to 1.4000 dollars per pound, the futures contract gives rise to a ð1:4543 1:4000Þ 250,000 ¼ $13,575 loss, whereas the spot market alternative gives rise to a loss of ð1:4540 1:4000Þ 250,000 ¼ $13,500. The futures market alternative Table 1.4 Speculation using spot and futures contracts. One futures contract is on £62,500. Initial margin on four futures contracts ¼ $20,000. Possible trades Buy £250,000 Buy 4 futures contracts Spot price ¼ 1.4540 Futures price ¼ 1.4543 Investment $363,500 $20,000 Proﬁt if April spot ¼ 1.5000 $11,500 $11,425 Proﬁt if April spot ¼ 1.4000 $13,500 $13,575 Introduction 15 appears to give rise to slightly worse outcomes for both scenarios. But this is because the 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 250,000 1:4540 ¼ $363; 500. In contrast, the second alternative requires only a small amount of cash to be deposited by the speculator in what is termed a ‘‘margin account’’. (The operation of margin accounts is explained in Chapter 2.) In Table 1.4, the initial margin requirement is assumed to be $5,000 per contract, or $20,000 in total. The futures market allows the speculator to obtain leverage. With a relatively small initial outlay, a large speculative position can be taken. 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 2 months. The stock price is currently $20, and a 2-month call option with a $22.50 strike price is currently selling for $1. Table 1.5 illustrates two possible alternatives, assuming that the spec- ulator is willing to invest $2,000. One alternative is to purchase 100 shares; the other 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 $20Þ ¼ $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, 10 times more proﬁtable than directly 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 $15Þ ¼ $500 Table 1.5 Comparison of proﬁts from two alternative strategies for using $2,000 to speculate on a stock worth $20 in October. December stock price Speculator’s strategy $15 $27 Buy 100 shares $500 $700 Buy 2,000 call options $2,000 $7,000 16 CHAPTER 1 Figure 1.5 Proﬁt or loss from two alternative strategies for speculating on a stock currently worth $20. 10000 Profit ($) 8000 6000 4000 Buy shares Buy options 2000 0 15 20 25 30 –2000 Stock price ($) –4000 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 stock price in 2 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. 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. 1.9 ARBITRAGEURS Arbitrageurs are a third important 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 possible 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. Let us consider a stock that is traded on both the New York Stock Exchange (www.nyse.com) and the London Stock Exchange (www.londonstockexchange.com). Suppose that the stock price is $140 in New York and £100 in London at a time when Introduction 17 the exchange rate is $1.4300 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$1:43 100Þ $140 or $300 in the absence of transactions costs. Transactions costs would probably eliminate the proﬁt for a small trader. 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 just described cannot last for long. As arbitrageurs buy the stock in New York, the forces of supply and demand will cause the 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 no arbitrage opportunities exist. 1.10 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 unconsciously) speculators. The results can be disastrous. One example of this is provided by the activities of Jérôme Kerviel at Société Général (see Business Snapshot 1.4). To avoid the sort of problems Société Général encountered, it is very important for both ﬁnancial and nonﬁnancial corporations to set up controls to ensure that deriva- tives are being used for their intended purpose. Risk limits should be set and the activities of traders should be monitored daily to ensure that these 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 U.S. 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 18 CHAPTER 1 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. Jérôme Kerviel joined Société Général (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 Jérôme 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. ﬁnancial institutions during the 2006–2007 period. The key lesson 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 One of the exciting developments in ﬁnance over the last 40 years has been the growth of derivatives markets. In many situations, both hedgers and speculators ﬁnd it more attractive to trade a derivative on an asset than to trade the asset itself. Some derivatives are traded on exchanges; others are traded by ﬁnancial institutions, fund managers, and corporations in the over-the-counter market, or added to new issues of debt and equity securities. Much of this book is concerned with the valuation of derivatives. The aim is

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