Options Markets: Introduction PDF

20 0 Confirming Pages CHAPTER TWENTY Options Markets: Introduction...

20 0 Confirming Pages CHAPTER TWENTY Options Markets: Introduction DERIVATIVE SECURITIES, OR more simply were almost immediately a great success, derivatives, play a large and increasingly crowding out the previously existing over-the- important role in financial markets. These are counter trading in stock options. Option con- securities whose prices are determined by, tracts are traded now on several exchanges. or “derive from,” the prices of other securi- They are written on common stock, stock ties. These assets are also called contingent indexes, foreign exchange, agricultural com- claims because their payoffs are contingent modities, precious metals, and interest rate on the prices of other securities. Options and futures. In addition, the over-the-counter futures contracts are both derivative securi- market has enjoyed a tremendous resurgence ties. We will see that their payoffs depend on in recent years as trading in custom-tailored the value of other securities. Swaps, which we options has exploded. Popular and potent will discuss in Chapter 23, also are derivatives. tools in modifying portfolio characteristics, Because the value of derivatives depends options have become essential tools a portfo- on the value of other securities, they can be lio manager must understand. powerful tools for both hedging and specula- This chapter is an introduction to options tion. We will investigate these applications in markets. It explains how puts and calls work the next four chapters, starting in this chapter and examines their investment characteris- with options. tics. Popular option strategies are considered Trading of standardized options contracts next. Finally, we examine a range of securities on a national exchange started in 1973 when with embedded options such as callable or the Chicago Board Options Exchange (CBOE) convertible bonds, and we take a quick look began listing call options. These contracts at some so-called exotic options. PART VI bod30700_ch20_667-710.indd 667 7/20/10 8:54 PM  Confirming Pages 668 PART VI Options, Futures, and Other Derivatives 20.1 The Option Contract A call option gives its holder the right to purchase an asset for a specified price, called the exercise, or strike, price, on or before some specified expiration date. For example, a January call option on IBM stock with exercise price $130 entitles its owner to purchase IBM stock for a price of $130 at any time up to and including the expiration date in January. The holder of the call is not required to exercise the option. The holder will choose to exer- cise only if the market value of the underlying asset exceeds the exercise price. In that case, the option holder may “call away” the asset for the exercise price. Otherwise, the option may be left unexercised. If it is not exercised before the expiration date of the contract, a call option simply expires and no longer has value. Therefore, if the stock price is greater than the exercise price on the expiration date, the value of the call option equals the differ- ence between the stock price and the exercise price; but if the stock price is less than the exercise price at expiration, the call will be worthless. The net profit on the call is the value of the option minus the price originally paid to purchase it. The purchase price of the option is called the premium. It represents the compensation the purchaser of the call must pay for the right to exercise the option if exercise becomes profitable. Sellers of call options, who are said to write calls, receive premium income now as pay- ment against the possibility they will be required at some later date to deliver the asset in return for an exercise price less than the market value of the asset. If the option is left to expire worthless, however, then the writer of the call clears a profit equal to the premium income derived from the initial sale of the option. But if the call is exercised, the profit to the option writer is the premium income derived when the option was initially sold minus the difference between the value of the stock that must be delivered and the exercise price that is paid for those shares. If that difference is larger than the initial premium, the writer will incur a loss. Example 20.1 Profits and Losses on a Call Option Consider the January 2010 expiration call option on a share of IBM with an exercise price of $130 that was selling on December 2, 2009, for $2.18. Exchange-traded options expire on the third Friday of the expiration month, which for this option was January 15, 2010. Until the expiration date, the purchaser of the calls may buy shares of IBM for $130. On December 2, IBM sells for $127.21. Because the stock price is currently less than $130 a share, exercising the option to buy at $130 clearly would make no sense at that moment. Indeed, if IBM remains below $130 by the expiration date, the call will be left to expire worthless. On the other hand, if IBM is selling above $130 at expiration, the call holder will find it optimal to exercise. For example, if IBM sells for $132 on January 15, the option will be exercised, as it will give its holder the right to pay $130 for a stock worth $132. The value of the option on the expiration date would then be Value at expiration 5 Stock price 2 Exercise price 5 $132 2 $130 5 $2 Despite the $2 payoff at expiration, the call holder still realizes a loss of $.18 on the invest- ment because the initial purchase price was $2.18: Profit 5 Final value 2 Original investment 5 $2.00 2 $2.18 5 2$.18 bod30700_ch20_667-710.indd 668 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 669 Nevertheless, exercise of the call is optimal at expiration if the stock price exceeds the exercise price because the exercise proceeds will offset at least part of the cost of the option. The investor in the call will clear a profit if IBM is selling above $132.18 at the expiration date. At that stock price, the proceeds from exercise will just cover the origi- nal cost of the call. A put option gives its holder the right to sell an asset for a specified exercise or strike price on or before some expiration date. A January expiration put on IBM with exercise price $130 entitles its owner to sell IBM stock to the put writer at a price of $130 at any time before expiration in January even if the market price of IBM is less than $130. While profits on call options increase when the asset increases in value, profits on put options increase when the asset value falls. A put will be exercised only if the exercise price is greater than the price of the underlying asset, that is, only if its holder can deliver for the exercise price an asset with market value less than the exercise price. (One doesn’t need to own the shares of IBM to exercise the IBM put option. Upon exercise, the investor’s broker purchases the necessary shares of IBM at the market price and immediately delivers, or “puts them,” to an option writer for the exercise price. The owner of the put profits by the difference between the exercise price and market price.) Example 20.2 Profits and Losses on a Put Option Now consider the January 2010 expiration put option on IBM with an exercise price of $130, selling on December 2, 2009, for $4.79. It entitled its owner to sell a share of IBM for $130 at any time until January 15. If the holder of the put buys a share of IBM and imme- diately exercises the right to sell at $130, net proceeds will be $130 2 $127.21 5 $2.79. Obviously, an investor who pays $4.79 for the put has no intention of exercising it imme- diately. If, on the other hand, IBM sells for $123 at expiration, the put turns out to be a profitable investment. Its value at expiration would be Value at expiration 5 Exercise price 2 Stock price 5 $130 2 $123 5 $7 and the investor’s profit would be $7.00 2 $4.79 5 $2.21. This is a holding period return of $2.21/$4.79 5.461, or 46.1%—over only 44 days! Apparently, put option sellers on December 2 (who were on the other side of the transaction) did not consider this outcome very likely. An option is described as in the money when its exercise would produce profits for its holder. An option is out of the money when exercise would be unprofitable. Therefore, a call option is in the money when the asset price is greater than the exercise price. It is out of the money when the asset price is less than the exercise price; no one would exercise the right to purchase for the strike price an asset worth less than that price. Conversely, put options are in the money when the exercise price exceeds the asset’s value, because delivery of the lower-valued asset in exchange for the exercise price is profitable for the holder. Options are at the money when the exercise price and asset price are equal. bod30700_ch20_667-710.indd 669 7/20/10 8:54 PM  Confirming Pages 670 PART VI Options, Futures, and Other Derivatives Options Trading Some options trade on over-the-counter markets. PRICES AT CLOSE DECEMBER 02, 2009 The OTC market offers the advantage that the terms I B M (IBM) Underlying Stock Price: 127.21 of the option contract—the exercise price, expiration Call Put date, and number of shares committed—can be tai- Open Open Expiration Strike Last Volume Interest Last Volume Interest lored to the needs of the traders. The costs of estab- Dec 2009 120 7.75 197 2370 0.26 644 8806 lishing an OTC option contract, however, are higher Jan 2010 120 8.63 130 21884 1.18 1267 8871 Apr 2010 120 11.25 43 1705 4.20 33 1903 than for exchange-traded options. Jul 2010 120 13.30 34 108 6.70 1 34 Options contracts traded on exchanges are stan- Dec 2009 125 3.25 416 14419 1.02 1872 9203 Jan 2010 125 4.75 278 14180 2.44 1060 9094 dardized by allowable expiration dates and exercise Apr 2010 125 7.90 69 3652 6.05 82 1122 Jul 2010 125 10.05 7 150 8.85 15 215 prices for each listed option. Each stock option con- Dec 2009 Jan 2010 130 130 0.77 2.18 2108 3489 11033 19278 3.55 4.79 844 198 4233 3273 tract provides for the right to buy or sell 100 shares Apr 2010 130 5.49 29 2773 8.50 66 1312 of stock (except when stock splits occur after the Jul 2010 130 7.75 31 111 11.30 85 228 Dec 2009 135 0.11 214 8955 7.65 86 631 contract is listed and the contract is adjusted for the Jan 2010 135 0.84 176 24556 7.75 24 776 Apr 2010 135 3.45 126 3798 11.50 45 433 terms of the split). Jul 2010 135 5.67 6 140 13.80 1 113 Standardization of the terms of listed option con- tracts means all market participants trade in a lim- ited and uniform set of securities. This increases the Figure 20.1 Stock options on IBM Closing prices depth of trading in any particular option, which low- as of December 2, 2009 ers trading costs and results in a more competitive Source: The Wall Street Journal Online, December 3, 2009. market. Exchanges, therefore, offer two important benefits: ease of trading, which flows from a central marketplace where buyers and sellers or their repre- sentatives congregate; and a liquid secondary market where buyers and sellers of options can transact quickly and cheaply. Until recently, most options trading in the United States took place on the Chicago Board Options Exchange. However, by 2003 the International Securities Exchange, an electronic exchange based in New York, displaced the CBOE as the largest options market. Options trading in Europe is uniformly transacted in electronic exchanges. Figure 20.1 is a selection of listed stock option quotations for IBM. The last recorded price on the New York Stock Exchange for IBM shares was $127.21 per share.1 Options are reported on IBM at exercise prices of $120 through $135. The exercise (or strike) prices bracket the stock price. While exercise prices generally are set at five-point intervals, larger intervals sometimes are set for stocks selling above $100, and intervals of $2.50 may be used for stocks selling at low prices. If the stock price moves outside the range of exercise prices of the existing set of options, new options with appropriate exercise prices may be offered. Therefore, at any time, both in-the-money and out-of-the-money options will be listed, as in this example. Figure 20.1 shows both call and put options listed for each expiration date and exercise price. The three sets of columns for each option report closing price, trading volume in contracts, and open interest (number of outstanding contracts). When we compare prices of call options with the same expiration date but different exercise prices in Figure 20.1, we see that the value of a call is lower when the exercise price is higher. This makes sense, because the right to purchase a share at a lower exercise price is more valuable than the right to purchase at a higher price. Thus the January expiration IBM call option with strike 1 Occasionally, this price may not match the closing price listed for the stock on the stock market page. This is because some NYSE stocks also trade on exchanges that close after the NYSE, and the stock pages may reflect the more recent closing price. The options exchanges, however, close with the NYSE, so the closing NYSE stock price is appropriate for comparison with the closing option price. bod30700_ch20_667-710.indd 670 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 671 price $130 sells for $2.18 whereas the $135 exercise price January call sells for only $.84. Conversely, put options are worth more when the exercise price is higher: You would rather have the right to sell shares for $135 than for $130, and this is reflected in the prices of the puts. The January expiration put option with strike price $135 sells for $7.75, whereas the $130 exercise price January put sells for only $4.79. If an option does not trade on a given day, three dots will appear in the volume and price columns. Because trading is infrequent, it is not unusual to find option prices that appear out of line with other prices. You might see, for example, two calls with different exercise prices that seem to sell for the same price. This discrepancy arises because the last trades for these options may have occurred at different times during the day. At any moment, the call with the lower exercise price must be worth more than an otherwise-identical call with a higher exercise price. Expirations of most exchange-traded options tend to be fairly short, ranging up to only several months. For larger firms and several stock indexes, however, longer-term options are traded with expirations ranging up to several years. These options are called LEAPS (for Long-Term Equity AnticiPation Securities). a. What will be the proceeds and net profits to an investor who purchases the January CONCEPT expiration IBM calls with exercise price $125 if the stock price at expiration is $135? CHECK What if the stock price at expiration is $115? 1 b. Now answer part (a) for an investor who purchases a January expiration IBM put option with exercise price $125. American and European Options An American option allows its holder to exercise the right to purchase (if a call) or sell (if a put) the underlying asset on or before the expiration date. European options allow for exercise of the option only on the expiration date. American options, because they allow more leeway than their European counterparts, generally will be more valuable. Virtually all traded options in the United States are American style. Foreign currency options and stock index options are notable exceptions to this rule, however. Adjustments in Option Contract Terms Because options convey the right to buy or sell shares at a stated price, stock splits would radically alter their value if the terms of the options contract were not adjusted to account for the stock split. For example, reconsider the IBM call options in Figure 20.1. If IBM were to announce a 2-for-1 split, its share price would fall from about $127 to about $63.50. A call option with exercise price $130 would be just about worthless, with virtually no possibility that the stock would sell at more than $130 before the options expired. To account for a stock split, the exercise price is reduced by a factor of the split, and the number of options held is increased by that factor. For example, each original call option with exercise price of $130 would be altered after a 2-for-1 split to 2 new options, with each new option carrying an exercise price of $65. A similar adjustment is made for stock dividends of more than 10%; the number of shares covered by each option is increased in proportion to the stock dividend, and the exercise price is reduced by that proportion. bod30700_ch20_667-710.indd 671 7/20/10 8:54 PM  Confirming Pages 672 PART VI Options, Futures, and Other Derivatives In contrast to stock dividends, cash dividends do not affect the terms of an option con- tract. Because payment of a cash dividend reduces the selling price of the stock without inducing offsetting adjustments in the option contract, the value of the option is affected by dividend policy. Other things being equal, call option values are lower for high-dividend payout policies, because such policies slow the rate of increase of stock prices; conversely, put values are higher for high-dividend payouts. (Of course, the option values do not nec- essarily rise or fall on the dividend payment or ex-dividend dates. Dividend payments are anticipated, so the effect of the payment already is built into the original option price.) CONCEPT Suppose that IBM’s stock price at the exercise date is $140, and the exercise price of the call CHECK is $130. What is the payoff on one option contract? After a 2-for-1 split, the stock price is $70, the exercise price is $65, and the option holder now can purchase 200 shares. Show that 2 the split leaves the payoff from the option unaffected. The Options Clearing Corporation The Options Clearing Corporation (OCC), the clearinghouse for options trading, is jointly owned by the exchanges on which stock options are traded. Buyers and sellers of options who agree on a price will strike a deal. At this point, the OCC steps in. The OCC places itself between the two traders, becoming the effective buyer of the option from the writer and the effective writer of the option to the buyer. All individuals, therefore, deal only with the OCC, which effectively guarantees contract performance. When an option holder exercises an option, the OCC arranges for a member firm with clients who have written that option to make good on the option obligation. The mem- ber firm selects from its clients who have written that option to fulfill the contract. The selected client must deliver 100 shares of stock at a price equal to the exercise price for each call option contract written or must purchase 100 shares at the exercise price for each put option contract written. Because the OCC guarantees contract performance, option writers are required to post margin to guarantee that they can fulfill their contract obligations. The margin required is determined in part by the amount by which the option is in the money, because that value is an indicator of the potential obligation of the option writer. When the required margin exceeds the posted margin, the writer will receive a margin call. In contrast, the holder of the option need not post margin because the holder will exercise the option only if it is profitable to do so. After purchase of the option, no further money is at risk. Margin requirements are determined in part by the other securities held in the investor’s portfolio. For example, a call option writer owning the stock against which the option is written can satisfy the margin requirement simply by allowing a broker to hold that stock in the brokerage account. The stock is then guaranteed to be available for delivery should the call option be exercised. If the underlying security is not owned, however, the margin requirement is determined by the value of the underlying security as well as by the amount by which the option is in or out of the money. Out-of-the-money options require less mar- gin from the writer, for expected payouts are lower. Other Listed Options Options on assets other than stocks are also widely traded. These include options on mar- ket indexes and industry indexes, on foreign currency, and even on the futures prices of agricultural products, gold, silver, fixed-income securities, and stock indexes. We will dis- cuss these in turn. bod30700_ch20_667-710.indd 672 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 673 Index Options An index option is a call or put based on a stock market index such as the S&P 500 or the NASDAQ 100. Index options are traded on several broad-based indexes as well as on several industry-specific indexes and even commodity price indexes. We discussed many of these indexes in Chapter 2. The construction of the indexes can vary across contracts or exchanges. For example, the S&P 100 index is a value-weighted average of the 100 stocks in the Standard & Poor’s 100 stock group. The weights are proportional to the market value of outstanding equity for each stock. The Dow Jones Industrial Index, by contrast, is a price-weighted average of 30 stocks. Option contracts on many foreign stock indexes also trade. For example, options on the (Japanese) Nikkei Stock Index trade on the Chicago Mercantile Exchange, and options on the Eurotop 100 and Japan indexes trade on the American Stock Exchange. The Chicago Board Options Exchange, as well as the Amex, lists options on industry indexes such as the biotech or financial industries. In contrast to stock options, index options do not require that the call writer actually “deliver the index” upon exercise or that the put writer “purchase the index.” Instead, a cash settlement procedure is used. The payoff that would accrue upon exercise of the option is calculated, and the option writer simply pays that amount to the option holder. The payoff is equal to the difference between the exercise price of the option and the value of the index. For example, if the S&P index is at 1100 when a call option on the index with exercise price 1090 is exercised, the holder of the call receives a cash payment of the dif- ference, 110021090, times the contract multiplier of $100, or $1,000 per contract. Options on the major indexes, that is, the S&P 100 (often called the OEX after its ticker symbol), the S&P 500 (the SPX), the NASDAQ 100 (the NDX), and the Dow Jones Industrials (the DJX), are the most actively traded contracts on the CBOE. Together, these contracts dominate CBOE volume. Futures Options Futures options give their holders the right to buy or sell a speci- fied futures contract, using as a futures price the exercise price of the option. Although the delivery process is slightly complicated, the terms of futures options contracts are designed in effect to allow the option to be written on the futures price itself. The option holder receives upon exercise a net payoff equal to the difference between the current futures price on the specified asset and the exercise price of the option. Thus if the futures price is, say, $37, and the call has an exercise price of $35, the holder who exercises the call option on the futures gets a payoff of $2. Foreign Currency Options A currency option offers the right to buy or sell a quan- tity of foreign currency for a specified amount of domestic currency. Currency option con- tracts call for purchase or sale of the currency in exchange for a specified number of U.S. dollars. Contracts are quoted in cents or fractions of a cent per unit of foreign currency. There is an important difference between currency options and currency futures options. The former provide payoffs that depend on the difference between the exercise price and the exchange rate at maturity. The latter are foreign exchange futures options that provide payoffs that depend on the difference between the exercise price and the exchange rate futures price at maturity. Because exchange rates and exchange rate futures prices gener- ally are not equal, the options and futures-options contracts will have different values, even with identical expiration dates and exercise prices. Trading volume in currency futures options dominates by far trading in currency options. Interest Rate Options Options are traded on Treasury notes and bonds, Treasury bills, certificates of deposit, GNMA pass-through certificates, and yields on Treasury and Eurodollar securities of various maturities. Options on several interest rate futures bod30700_ch20_667-710.indd 673 7/20/10 8:54 PM  Confirming Pages 674 PART VI Options, Futures, and Other Derivatives also trade. Among these are contracts on Treasury bond, Treasury note, municipal bond, LIBOR, Euribor,2 and Eurodollar futures. 20.2 Values of Options at Expiration Call Options Recall that a call option gives the right to purchase a security at the exercise price. Suppose you hold a call option on FinCorp stock with an exercise price of $100, and FinCorp is now selling at $110. You can exercise your option to purchase the stock at $100 and simultane- ously sell the shares at the market price of $110, clearing $10 per share. Yet if the shares sell below $100, you can sit on the option and do nothing, realizing no further gain or loss. The value of the call option at expiration equals2 ST 2 X if ST. X Payoff to call holder 5 0 if ST # X where ST is the value of the stock at expiration and X is the exercise price. This formula emphasizes the option property because the payoff cannot be negative. That is, the option is exercised only if ST exceeds X. If ST is less than X, exercise does not occur, and the option expires with zero value. The loss to the option holder in this case equals the price originally paid for the option. More generally, the profit to the option holder is the value of the option at expiration minus the original purchase price. The value at expiration of the call with exercise price $100 is given by the schedule: Stock price: $90 $100 $110 $120 $130 Option value: 0 0 10 20 30 For stock prices at or below $100, the option is worthless. Above $100, the option is worth the excess of the stock price over $100. The option’s value increases by $1 for each dollar increase in the stock price. This relationship can be depicted graphically as in Figure 20.2. The solid line in Figure 20.2 depicts the value of the call at expiration. The net profit to the holder of the call equals the gross payoff less the initial investment in the call. Suppose the call cost $14. Then the profit to the call holder would be given by the dashed (bottom) line of Figure 20.2. At option expiration, the investor suffers a loss of $14 if the stock price is less than or equal to $100. Profits do not become positive unless the stock price at expiration exceeds $114. The break-even point is $114, because at that price the payoff to the call, ST 2 X 5 $114 2 $100 5 $14, equals the initial cost of the call. Conversely, the writer of the call incurs losses if the stock price is high. In that scenario, the writer will receive a call and will be obligated to deliver a stock worth ST for only X dollars: 2(ST 2 X) if ST. X Payoff to call writer 5 0 if ST # X 2 The Euribor market is similar to the LIBOR market (see Chapter 2), but the interest rate charged in the Euribor market is the interbank rate for euro-denominated deposits. bod30700_ch20_667-710.indd 674 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 675 The call writer, who is exposed to losses if the stock price increases, is willing to bear $30 this risk in return for the option premium. Figure 20.3 depicts the payoff and profit Payoff = Value at Expiration $20 diagrams for the call writer. These are the mirror images of the corresponding dia- grams for call holders. The break-even $10 point for the option writer also is $114. The (negative) payoff at that point just offsets 0 ST the premium originally received when the 80 90 100 110 120 option was written. Cost of Option Profit −$10 −$14 Put Options A put option is the right to sell an asset at the exercise price. In this case, the holder will not exercise the option unless the asset Figure 20.2 Payoff and profit to call option at expiration is worth less than the exercise price. For example, if FinCorp shares were to fall to $90, a put option with exercise price $100 could be exercised to clear $10 for its holder. The holder would purchase a share for $90 and simultaneously deliver it to the put option writer for the exercise price of $100. The value of a put option at expiration is 0 if ST $ X Payoff to put holder 5 X 2 ST if ST , X The solid line in Figure 20.4 illustrates the payoff at expiration to the holder of a put option on FinCorp stock with an exercise price of $100. If the stock price at expiration is above $100, the put has no value, as the right to sell the shares at $100 would not be exercised. Below a price of $100, the put value at expiration increases by $1 for each dollar the stock price falls. The dashed line in Figure 20.4 is a graph of the put option owner’s profit at expiration, net of the initial cost of the put. Writing puts naked (i.e., writing a put without an offsetting short position in the stock for hedging purposes) exposes the writer to losses if the market falls. Writing $14 naked out-of-the-money puts was once con- sidered an attractive way to generate income, ST 0 as it was believed that as long as the market $100 $114 did not fall sharply before the option expira- Profit tion, the option premium could be collected without the put holder ever exercising the option against the writer. Because only sharp drops in the market could result in losses to Payoff the put writer, the strategy was not viewed as overly risky. However, in the wake of the market crash of October 1987, such put writ- ers suffered huge losses. Participants now Figure 20.3 Payoff and profit to call writers at expiration perceive much greater risk to this strategy. bod30700_ch20_667-710.indd 675 7/20/10 8:54 PM  Confirming Pages 676 PART VI Options, Futures, and Other Derivatives $100 Payoff = Value of Put at Expiration Profit Price of Put 0 ST $100 Figure 20.4 Payoff and profit to put option at expiration Consider these four option strategies: (i) buy a call; (ii) write a call; (iii) buy a put; (iv) write a put. CONCEPT a. For each strategy, plot both the payoff and profit diagrams as a function of the final CHECK stock price. 3 b. Why might one characterize both buying calls and writing puts as “bullish” strategies? What is the difference between them? c. Why might one characterize both buying puts and writing calls as “bearish” strategies? What is the difference between them? Option versus Stock Investments Purchasing call options is a bullish strategy; that is, the calls provide profits when stock prices increase. Purchasing puts, in contrast, is a bearish strategy. Symmetrically, writing calls is bearish, whereas writing puts is bullish. Because option values depend on the price of the underlying stock, purchase of options may be viewed as a substitute for direct purchase or sale of a stock. Why might an option strategy be preferable to direct stock transactions? For example, why would you purchase a call option rather than buy shares of stock directly? Maybe you have some information that leads you to believe the stock will increase in value from its current level, which in our examples we will take to be $100. You know your analysis could be incorrect, however, and that shares also could fall in price. Suppose a 6-month maturity call option with exercise price $100 currently sells for $10, and the interest rate for the period is 3%. Consider these three strategies for investing a sum of money, say, $10,000. For simplicity, suppose the firm will not pay any dividends until after the 6-month period. Strategy A: Invest entirely in stock. Buy 100 shares, each selling for $100. Strategy B: Invest entirely in at-the-money call options. Buy 1,000 calls, each selling for $10. (This would require 10 contracts, each for 100 shares.) Strategy C: Purchase 100 call options for $1,000. Invest your remaining $9,000 in 6-month T-bills, to earn 3% interest. The bills will grow in value from $9,000 to $9,000 3 1.03 5 $9,270. bod30700_ch20_667-710.indd 676 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 677 Let us trace the possible values of these three portfolios when the options expire in 6 months as a function of the stock price at that time: Stock Price Portfolio $95 $100 $105 $110 $115 $120 Portfolio A: All stock $9,500 $10,000 $10,500 $11,000 $11,500 $12,000 Portfolio B: All options 0 0 5,000 10,000 15,000 20,000 Portfolio C: Call plus bills 9,270 9,270 9,770 10,270 10,770 11,270 Portfolio A will be worth 100 times the share price. Portfolio B is worthless unless shares sell for more than the exercise price of the call. Once that point is reached, the portfolio is worth 1,000 times the excess of the stock price over the exercise price. Finally, portfolio C is worth $9,270 from the investment in T-bills plus any profits from the 100 call options. Remember that each of these portfolios involves the same $10,000 initial investment. The rates of return on these three portfolios are as follows: Stock Price Portfolio $95 $100 $105 $110 $115 $120 Portfolio A: All stock 25.0% 0.0% 5.0% 10.0% 15.0% 20.0% Portfolio B: All options 2100.0 2100.0 250.0 0.0 50.0 100.0 Portfolio C: Call plus bills 27.3 27.3 22.3 2.7 7.7 12.7 These rates of return are graphed in Figure 20.5. Comparing the returns of portfolios B and C to those of the simple investment in stock represented by portfolio A, we see that options offer two interesting features. First, an option offers leverage. Compare the returns of portfolios B and A. Unless the stock increases from its initial value of $100, the value of portfolio B falls precipitously to zero—a rate of return of negative 100%. 100 Conversely, modest increases in the rate 80 of return on the stock result in dispro- portionate increases in the option rate of 60 return. For example, a 4.3% increase in 40 the stock price from $115 to $120 would Rate of Return (%) increase the rate of return on the call 20 from 50% to 100%. In this sense, calls 0 ST are a levered investment on the stock. 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 Their values respond more than propor- −20 tionately to changes in the stock value. −40 Figure 20.5 vividly illustrates this point. The slope of the all-option port- −60 folio is far steeper than that of the all- A: All Stocks −80 stock portfolio, reflecting its greater B: All Options proportional sensitivity to the value of −100 C: Call Plus Bills the underlying security. The leverage −120 factor is the reason investors (illegally) exploiting inside information com- monly choose options as their invest- Figure 20.5 Rate of return to three strategies ment vehicle. bod30700_ch20_667-710.indd 677 7/20/10 8:54 PM  Confirming Pages 678 PART VI Options, Futures, and Other Derivatives The potential insurance value of options is the second interesting feature, as portfolio C shows. The T-bill-plus-option portfolio cannot be worth less than $9,270 after 6 months, as the option can always be left to expire worthless. The worst possible rate of return on portfolio C is 27.3%, compared to a (theoretically) worst possible rate of return on the stock of 2100% if the company were to go bankrupt. Of course, this insurance comes at a price: When the share price increases, portfolio C, the option-plus-bills portfolio, does not perform as well as portfolio A, the all-stock portfolio. This simple example makes an important point. Although options can be used by specu- lators as effectively leveraged stock positions, as in portfolio B, they also can be used by investors who desire to tailor their risk exposures in creative ways, as in portfolio C. For example, the call-plus-bills strategy of portfolio C provides a rate of return profile quite unlike that of the stock alone. The absolute limitation on downside risk is a novel and attractive feature of this strategy. We next discuss several option strategies that provide other novel risk profiles that might be attractive to hedgers and other investors. 20.3 Option Strategies An unlimited variety of payoff patterns can be achieved by combining puts and calls with various exercise prices. We explain in this section the motivation and structure of some of the more popular ones. Protective Put Imagine you would like to invest in a stock, but you are unwilling to bear potential losses beyond some given level. Investing in the stock alone seems risky to you because in prin- ciple you could lose all the money you invest. You might consider instead investing in stock and purchasing a put option on the stock. Table 20.1 shows the total value of your portfolio at option expiration: Whatever happens to the stock price, you are guaranteed a payoff at least equal to the put option’s exercise price because the put gives you the right to sell your shares for that price. Example 20.3 Protective Put Suppose the strike price is X 5 $100 and the stock is selling at $97 at option expiration. Then the value of your total portfolio is $100. The stock is worth $97 and the value of the expiring put option is X 2 ST 5 $100 2 $97 5 $3 Another way to look at it is that you are holding the stock and a put contract giving you the right to sell the stock for $100. The right to sell locks in a minimum portfolio value of $100. On the other hand, if the stock price is above $100, say, $104, then the right to sell a share at $100 is worthless. You allow the put to expire unexercised, ending up with a share of stock worth ST 5 $104. Figure 20.6 illustrates the payoff and profit to this protective put strategy. The solid line in Figure 20.6C is the total payoff. The dashed line is displaced downward by the cost of establishing the position, S0 1 P. Notice that potential losses are limited. bod30700_ch20_667-710.indd 678 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 679 Table 20.1 ST # X ST. X Value of a protective put Stock ST ST portfolio at option 1 Put X 2 ST 0 expiration 5 TOTAL X ST Payoff of Stock A: Stock ST X Payoff of Option + B: Put ST X Payoff of Protective Put Payoff Profit = C: Protective Put X ST X X − (S0 + P) Figure 20.6 Value of a protective put position at option expiration bod30700_ch20_667-710.indd 679 7/20/10 8:54 PM  Confirming Pages 680 PART VI Options, Futures, and Other Derivatives It is instructive to compare the profit on the protective put strategy with that Profits of the stock investment. For simplicity, Profit on Stock consider an at-the-money protective put, Profit on Protective Put so that X 5 S0. Figure 20.7 compares Portfolio the profits for the two strategies. The profit on the stock is zero if the stock price remains unchanged and ST 5 S0. It rises or falls by $1 for every dollar ST swing in the ultimate stock price. The S0 = X profit on the protective put is negative −P and equal to the cost of the put if ST is below S0. The profit on the protective put increases one for one with increases in the stock price once ST exceeds S0. −S0 Figure 20.7 makes it clear that the protective put offers some insurance against stock price declines in that it limits losses. Therefore, protective put strategies provide a form of portfolio Figure 20.7 Protective put versus stock investment insurance. The cost of the protection is (at-the-money option) that, in the case of stock price increases, your profit is reduced by the cost of the put, which turned out to be unneeded. This example also shows that despite the common perception that derivatives mean risk, derivative securities can be used effec- tively for risk management. In fact, such risk management is becoming accepted as part of the fiduciary responsibility of financial managers. Indeed, in one often-cited court case, Brane v. Roth, a company’s board of directors was successfully sued for failing to use derivatives to hedge the price risk of grain held in storage. Such hedging might have been accomplished using protective puts. The claim that derivatives are best viewed as risk management tools may seem surpris- ing in light of the credit crisis of the last few years. The crisis was immediately precipi- tated when the highly risky positions that many financial institutions had established in credit derivatives blew up 2007–2008, resulting in large losses and government bailouts. Still, the same characteristics that make derivatives potent tools to increase risk also make them highly effective in managing risk, at least when used properly. Derivatives have aptly been compared to power tools: very useful in skilled hands, but also very dangerous when not handled with care. The nearby box makes the case for derivatives as central to risk management. Covered Calls A covered call position is the purchase of a share of stock with a simultaneous sale of a call on that stock. The call is “covered” because the potential obligation to deliver the stock is covered by the stock held in the portfolio. Writing an option without an offsetting stock position is called by contrast naked option writing. The value of a covered call position at the expiration of the call, presented in Table 20.2, equals the stock value minus the value of the call. The call value is subtracted because the covered call position involves writing a call to another investor who may exercise it at your expense. bod30700_ch20_667-710.indd 680 7/20/10 8:54 PM  Confirming Pages The Case for Derivatives WORDS FROM THE STREET They’ve been dubbed financial weapons of mass destruc- houses in your area declined, the financial instrument tion, attacked for causing the financial turmoil sweeping would increase in value, offsetting the loss. Lenders could the nation and identified as the kryptonite that brought do the same thing, which would help them hedge against down the global economy. Yet few Main Streeters really foreclosures. The idea is to make the housing market more know what derivatives are—namely, financial contracts liquid. More buyers and sellers mean that markets stay between a buyer and a seller that derive value from an liquid and functional even under pressure. underlying asset, such as a mortgage or a stock. There Some critics dismiss Shiller’s basic premise that more seems to be near consensus that derivatives were a source derivatives would make the housing market more liquid of undue risk. and more stable. They point out that futures contracts And then there’s Robert Shiller. The Yale economist haven’t made equity markets or commodity markets believes just the opposite is true. A champion of financial immune from massive moves up and down. They add that innovation and an expert in management of risk, Shiller a ballooning world of home-based derivatives wouldn’t contends that derivatives, far from being a problem, are lead to homeowners’ insurance: it would lead to a new actually the solution. Derivatives, Shiller says, are merely playground for speculators. a risk-management tool the same way insurance is. “You In essence, Shiller is laying the intellectual ground- pay a premium and if an event happens, you get a pay- work for the next financial revolution. We are now suffer- ment.” That tool can be used well or, as happened recently, ing through the first major crisis of the Information Age used badly. Shiller warns that banishing the tool gets us economy. Shiller’s answers may be counterintuitive, but no nowhere. more so than those of doctors and scientists who centu- For all the trillions in derivative trading, there were very ries ago recognized that the cure for infectious diseases few traders. Almost all the subprime mortgages that were was not flight or quarantine, but purposely infecting more bundled and turned into derivatives were sold by a hand- people through vaccinations. “We’ve had a major glitch ful of Wall Street institutions, working with a small num- in derivatives and securitization,” says Shiller. “The Titanic ber of large institutional buyers. It was a huge but illiquid sank almost a century ago, but we didn’t stop sailing across and opaque market. the Atlantic.” Meanwhile, the system was built on the myriad deci- Of course, people did think twice about getting on a sions of individual homeowners and lenders around the ship, at least for a while. But if we listen only to our fears, world. None of them, however, could hedge their bets the we lose the very dynamism that has propelled us this far. way large institutions can. Those buying a condo in Miami That is the nub of Shiller’s call for more derivatives and had no way to protect themselves if the market went more innovation. Shiller’s appeal is a tough sell at a time down. when derivatives have produced so much havoc. But he Derivatives, according to Shiller, could be used by reminds us that the tools that got us here are not to blame; homeowners—and, by extension, lenders—to insure they can be used badly and they can be used well. And themselves against falling prices. In Shiller’s scenario, you trying to stem the ineffable tide of human creativity is a would be able to go to your broker and buy a new type of fool’s errand. financial instrument, perhaps a derivative that is inversely Source: Zachary Karabell, “The Case for Derivatives,” Newsweek, related to a regional home-price index. If the value of February 2, 2009. The solid line in Figure 20.8C illustrates the payoff pattern. You see that the total posi- tion is worth ST when the stock price at time T is below X and rises to a maximum of X when ST exceeds X. In essence, the sale of the call options means the call writer has sold the claim to any stock value above X in return for the initial premium (the call price). Therefore, at expiration, the position is worth at most X. The dashed line of Figure 20.8C is the net profit to the covered call. Writing covered call options has been a popular investment strategy among institutional investors. Consider the managers of a fund invested largely in stocks. They might find it appealing to write calls on some or all of the stock in order to boost income by the premi- ums collected. Although they thereby forfeit potential capital gains should the stock price rise above the exercise price, if they view X as the price at which they plan to sell the stock anyway, then the call may be viewed as a kind of “sell discipline.” The written call guaran- tees the stock sale will occur as planned. 681 bod30700_ch20_667-710.indd 681 7/20/10 8:54 PM  Confirming Pages 682 PART VI Options, Futures, and Other Derivatives Table 20.2 ST # X ST. X Value of a covered call position at Payoff of stock ST ST option expiration 1 Payoff of written call 20 2(ST 2 X) 5 TOTAL ST X Payoff of Stock A: Stock ST X Payoff of Written Call ST + B: Write Call X Payoff of Covered Call X Payoff = C: Covered Call Profit ST X – (S0 – C) Figure 20.8 Value of a covered call position at expiration bod30700_ch20_667-710.indd 682 7/20/10 8:54 PM  Confirming Pages eXcel APPLICATIONS: Spreads and Straddles U sing spreadsheets to analyze combinations of options is very helpful. Once the basic models are built, it is easy to extend the analysis to different bundles of options. be used to evaluate the profitability of different strate- gies. You can find a link to this spreadsheet at www.mhhe. com/bkm. The Excel model “Spreads and Straddles” shown below can A B C D E F G H I J K L 1 Spreads and Straddles 2 3 Stock Prices 4 Beginning Market Price 116.5 5 Ending Market Price 130 X 110 Straddle X 120 Straddle 6 Ending Profit Ending Profit 7 Buying Options: Stock Price −15.40 Stock Price −24.00 8 Call Options Strike Price Payoff Profit Return % 50 24.60 50 36.00 9 110 22.80 20.00 −2.80 −12.28% 60 14.60 60 26.00 10 120 16.80 10.00 −6.80 −40.48% 70 4.60 70 16.00 11 130 13.60 0.00 −13.60 −100.00% 80 −5.40 80 6.00 12 140 10.30 0.00 −10.30 −100.00% 90 −15.40 90 −4.00 13 100 −25.40 100 −14.00 14 Put Options Strike Price Payoff Profit Return % 110 −35.40 110 −24.00 15 110 12.60 0.00 −12.60 −100.00% 120 −25.40 120 −34.00 16 120 17.20 0.00 −17.20 −100.00% 130 −15.40 130 −24.00 17 130 23.60 0.00 −23.60 −100.00% 140 −5.40 140 −14.00 18 140 30.50 10.00 −20.50 −67.21% 150 4.60 150 −4.00 19 160 14.60 160 6.00 20 Straddle Price Payoff Profit Return % 170 24.60 170 16.00 21 110 35.40 20.00 −15.40 −43.50% 180 34.60 180 26.00 22 120 34.00 10.00 −24.00 −70.59% 190 44.60 190 36.00 23 130 37.20 0.00 −37.20 −100.00% 200 54.60 200 46.00 24 140 40.80 10.00 −30.80 −75.49% 210 64.60 210 56.00 25 Example 20.4 Covered Call Assume a pension fund holds 1,000 shares of stock, with a current price of $100 per share. Suppose the portfolio manager intends to sell all 1,000 shares if the share price hits $110, and a call expiring in 60 days with an exercise price of $110 currently sells for $5. By writ- ing 10 call contracts (for 100 shares each) the fund can pick up $5,000 in extra income. The fund would lose its share of profits from any movement of the stock price above $110 per share, but given that it would have sold its shares at $110, it would not have realized those profits anyway. Straddle A long straddle is established by buying both a call and a put on a stock, each with the same exercise price, X, and the same expiration date, T. Straddles are useful strategies for investors who believe a stock will move a lot in price but are uncertain about the direction of the move. For example, suppose you believe an important court case that will make or break a company is about to be settled, and the market is not yet aware of the situation. The stock will either double in value if the case is settled favorably or will drop by half if the settlement goes against the company. The straddle position will do well regardless of the outcome because its value is highest when the stock price makes extreme upward or downward moves from X. The worst-case scenario for a straddle is no movement in the stock price. If ST equals X, both the call and the put expire worthless, and the investor’s outlay for the purchase of both options is lost. Straddle positions, therefore, are bets on volatility. An investor 683 bod30700_ch20_667-710.indd 683 7/20/10 8:54 PM  Confirming Pages 684 PART VI Options, Futures, and Other Derivatives who establishes a straddle must view the stock as more volatile than the market does. Conversely, investors who write straddles—selling both a call and a put—must believe the stock is less volatile. They accept the option premiums now, hoping the stock price will not change much before option expiration. The payoff to a straddle is presented in Table 20.3. The solid line of Figure 20.9C illus- trates this payoff. Notice the portfolio payoff is always positive, except at the one point where the portfolio has zero value, ST 5 X. You might wonder why all investors don’t pursue such a seemingly “no-lose” strategy. The reason is that the straddle requires that both the put and call be purchased. The value of the portfolio at expiration, while never negative, still must exceed the initial cash outlay for a straddle investor to clear a profit. The dashed line of Figure 20.9C is the profit to the straddle. The profit line lies below the payoff line by the cost of purchasing the straddle, P 1 C. It is clear from the diagram that the straddle position generates a loss unless the stock price deviates substantially from X. The stock price must depart from X by the total amount expended to purchase the call and the put for the straddle to clear a profit. Strips and straps are variations CONCEPT of straddles. A strip is two puts and CHECK Graph the profit and payoff diagrams for strips and one call on a security with the same straps. 4 exercise price and maturity date. A strap is two calls and one put. Spreads A spread is a combination of two or more call options (or two or more puts) on the same stock with differing exercise prices or times to maturity. Some options are bought, whereas others are sold, or written. A money spread involves the purchase of one option and the simultaneous sale of another with a different exercise price. A time spread refers to the sale and purchase of options with differing expiration dates. Consider a money spread in which one call option is bought at an exercise price X1, whereas another call with identical expiration date, but higher exercise price, X2, is written. The payoff to this position will be the difference in the value of the call held and the value of the call written, as in Table 20.4. There are now three instead of two outcomes to distinguish: the lowest-price region where ST is below both exercise prices, a middle region where ST is between the two exer- cise prices, and a high-price region where ST exceeds both exercise prices. Figure 20.10 illustrates the payoff and profit to this strategy, which is called a bullish spread because the payoff either increases or is unaffected by stock price increases. Holders of bullish spreads benefit from stock price increases. One motivation for a bullish spread might be that the investor thinks one option is over- priced relative to another. For example, an investor who believes an X 5 $100 call is cheap compared to an X 5 $110 call might establish the spread, even without a strong desire to take a bullish position in the stock. Collars A collar is an options strategy that brackets the value of a portfolio between two bounds. Suppose that an investor currently is holding a large position in FinCorp stock, which is currently selling at $100 per share. A lower bound of $90 can be placed on the value of the portfolio by buying a protective put with exercise price $90. This protection, however, requires that the investor pay the put premium. To raise the money to pay for the put, the investor might write a call option, say, with exercise price $110. The call might sell for bod30700_ch20_667-710.indd 684 7/20/10 8:54 PM  Confirming Pages CHAPTER 20 Options Markets: Introduction 685 Table 20.3 ST , X ST $ X Value of a straddle Payoff of call 0 ST 2 X position at option 1 Payoff of put X 2 ST 0 expiration 5 TOTAL X 2 ST ST 2 X Payoff of Call Payoff Profit A: Call 0 ST X −C Payoff of Put X X−P Payoff + B: Put X 0 ST −P Profit Payoff of Straddle X Payoff = C : Straddle X−P−C Profit P+C 0 ST X − (P + C) Figure 20.9 Value of a straddle at expiration bod30700_ch20_667-710.indd 685 7/20/10 8:54 PM  Confirming Pages 686 PART VI Options, Futures, and Other Derivatives Table 20.4 ST # X1 X1 , ST # X2 ST $ X2 Value of a bullish spread position at Payoff of purchased call, exercise price 5 X1 0 ST 2 X1 ST 2 X 1 expiration 1 Payoff of written call, exercise price 5 X2 20 20 2(ST 2 X2) 5 TOTAL 0 ST 2 X 1 X2 2 X 1 Payoff Payoff Profit A: Call Held (Call 1) 0 ST X1 X2 − C1 Payoff C2 0 ST B: Call X1 X2 Written (Call 2) Profit Payoff Payoff and Profit C: Bullish Spread X2 − X1 Payoff Profit 0 ST