Textbook Questions

Call and Put Options

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2. LG 2

When investors buy shares of common or preferred stock, they are entitled to all the rights and privileges of ownership such as receiving dividends or, in the case of common stock, having the right to vote at shareholder meetings. Investors who acquire bonds or convertible issues are also entitled to certain benefits of ownership such as receiving periodic interest payments. Stocks, bonds, and convertibles are all examples of financial assets. They represent financial claims on the issuing organization. In contrast, investors who buy options acquire nothing more than the right to subsequently buy or sell other, related securities. An  option  gives the holder the right to buy or sell an underlying asset (such as common stock) at a fixed price over a limited period of time.

Options are contractual instruments, whereby two parties enter into an agreement to exchange something of value. The option buyer has the right to buy or sell an underlying asset, and in exchange for this right the option buyer makes an up-front payment to the seller. The option seller receives the payment and then stands ready to buy or sell the underlying asset to the option holder according to the terms of the contract. In this chapter we’ll look at two basic kinds of options: calls and puts.

Before we get into the details of call and put options, note that there are two other types of options: rights and warrants. Rights are issued by corporations to their existing shareholders, and they entitle shareholders to buy new shares that the company plans to issue in the near future, usually at a price that is slightly below the stock’s market value. By using their rights to buy new shares, existing stockholders can avoid having their ownership stake diluted when the company issues new shares. If they do not wish to purchase new shares, existing stockholders can sell their rights on the open market. These rights typically expire within 30 to 60 days, so they hold very little investment appeal for the average individual investor.

In contrast, warrants are long-term options that grant the right to buy shares in a certain company for a given period of time (often fairly long—5 to 10 years or more). Warrants are usually created as “sweeteners” to bond issues and are used to make the issues more attractive to investors. That is, some bonds come with warrants attached, which gives bondholders the opportunity to earn higher returns if the underlying stock performs well. In essence, the buyer of one of these bonds also receives one or more warrants, and the additional upside potential that these bonds provide is called an equity kicker.

Basic Features of Calls and Puts

Stock options began trading on the Chicago Board Options Exchange in the early 1970s. Soon the interest in options spilled over to other kinds of financial assets. Today investors can trade puts and calls on common stock, stock indexes, exchange-traded funds, foreign currencies, debt instruments, and commodities and financial futures. For the most part, we will focus on options on common stock, though many of the principles that apply to stock options also apply to options on other kinds of financial assets.

As we will see, although the underlying financial assets may vary, the basic features of different types of options are very similar. Perhaps the most important feature to understand is that options allow investors to benefit from price changes in the underlying asset without investing much capital.

The Option Contract

 Call and put options allow the holder to buy or sell an underlying security at a fixed price known as the strike price or exercise price. We’ll focus our attention on calls and puts that grant the right to buy or sell shares of common stock. A  call  enables the holder to buy the underlying stock at the strike price over a set period of time. A  put , in contrast, gives the holder the right to sell the stock at the strike price within a set period of time. In most cases, calls and puts allow investors to buy or sell 100 shares of the underlying stock. Calls and puts are entitled to no voting rights, no privileges of ownership, and no interest or dividend income. Instead, calls and puts possess value to the extent that they allow the holder to benefit from price movements of the underlying asset.

Because call and put options derive their value from the price of some other underlying asset, they are known as  derivative securities . In other words, call and put options derive their value from the price of the underlying asset. Rights and warrants, as well as futures contracts (which we’ll study later), are also derivative securities. Although certain segments of the derivative market are for big institutional investors only, there’s still ample room for the individual investor. Many of these securities—especially those listed on exchanges—are readily available for individuals to trade.

The price that an investor pays to buy an option is called the  option premium . As we will see, an option’s premium depends on the option’s characteristics such as its strike price and expiration date and on the price and volatility of the underlying asset. However, don’t let the word premium confuse you. It’s just the market price of the option.

One of the key features of puts and calls is the attractive  leverage  opportunities they offer. Option buyers can invest a relatively small amount of capital, yet the potential return on that capital can be very large. To illustrate, consider a call on a common stock that gives an investor the right to buy a share of stock at a strike price of $45 a share. If that stock currently sells for $45, the call option would cost just a few dollars— for the sake of illustration, let’s say $3 per option or $300 total since the option contract covers 100 shares. Next, suppose that a month or two later the underlying stock’s price has increased by $10 to $55. At that point, the investor might exercise his right to buy 100 shares for $45 each. He pays $4,500 to acquire the shares and then immediately resells them at the market price for $5,500, pocketing a gain of $1,000. Thus, in a short period of time his $300 up-front investment grew to $1,000, a gain of 233%. The percentage increase in the stock over this period was just 22.2% ($10 ÷ $45), so the percentage gain on the option is much greater than the percentage gain on the stock. That’s the benefit of the leverage the options provide.

Seller versus Buyer

 Puts and calls are a unique type of security because they are not issued by the organizations that issue the underlying stock. Instead, they are created by investors. It works like this. Suppose Abby wants to sell Carli the right to buy 100 shares of Fitbit common stock (i.e., Abby wants to sell a Fitbit call option to Carli). Abby does this by “writing a call.” More generally, the individual (or institution) writing the option is known as the  option seller  or option writer. As the option writer, Abby sells the option in the market, so she is entitled to receive the price paid by Carli for the call option. However, Abby does have an obligation. If Carli later decides that she wants to exercise her right to buy Fitbit stock, Abby must sell those shares to her. If Abby does not already own Fitbit shares, she must go into the open market to buy them. Her obligation is legally binding, so she cannot walk away from the deal if it turns out to be a money loser for her. In contrast, Carli has no obligation. She has an option. She can buy Fitbit shares if she wants to, but she is under no obligation to do so. Puts work in much the same way. If Abby sold Carli a put option, then Carli would have the right to sell Fitbit shares to Abby, but she would not be obligated to do so. Abby, on the other hand, must stand behind her promise to buy Fitbit shares from Carli if Carli chooses to sell them. It is important to note that no matter what happens in these transactions between Abby and Carli, Fitbit Inc. is not affected. They do not receive any money, nor do they issue or retire any common shares.

Investors trade calls and puts with the help of securities brokers and dealers. In fact, options are as easy to buy and sell as common stocks. A simple phone call, or a few mouse clicks, is all it takes. Investors trade options for a variety of reasons, many of which we will explore in this chapter. At this point, suffice it to say that trading options can be a viable investment strategy.

Investor Facts

American or European?  Put and call options can be issued in either American or European form. Actually, this has absolutely nothing to do with where the options are traded but rather with when they can be exercised. An American option can be exercised on any business day that the option is traded. A European option can be exercised only on the day of expiration. Because the right to exercise is more flexible with American options than with European options, the American variety is often more desirable, and hence more valuable in the market. But that’s not always true. Having the right to exercise an option prior to its expiration date does not mean that it is optimal to do so. In many cases, an investor is better off selling the option in the open market than exercising it, and in those instances, the prices of American and European options are similar.

How Calls and Puts Work

 Taking the buyer’s point of view, we will briefly examine how calls and puts work and how they derive their value. To start, it is best to look at their profit-making potential. For example, consider the call described earlier that has a $45 strike price and sells for $3. A buyer of the call option hopes for a rise in the price of the underlying common stock. What is the profit potential from this transaction if the price of the stock does indeed move up to, say, $75 by the expiration date on the call?

The answer is that the buyer will earn $30 ($75−$45)$30 ($75−$45) on each of the 100 shares of stock in the call, minus the original $300 cost of the option. In other words, the buyer earns a gross profit of $3,000 from the $300 investment. This is so because the buyer has the right to buy 100 shares of the stock, from the option seller, at a price of $45 each, and then immediately turn around and sell them in the market for $75 a share.

Could an investor have made the same gross profit ($3,000) by investing directly in the common stock? Yes, if the investor had purchased 100 shares of stock. Buying 100 shares of a $45 stock requires an initial investment of $4,500 compared to the $300 investment needed to buy the options. As a consequence, the rate of return from buying the shares is much less than the rate of return from buying the options. The return potential of common stocks and calls differs considerably. This difference attracts investors and speculators to calls whenever the price outlook for the underlying financial asset is positive. Such differential returns are, of course, the direct result of leverage, which is similar to buying a stock on margin. We learned earlier that buying stock on margin raises the potential return that an investor might earn, but it also increases the risk of the investment.

To see the downside of buying a call option, suppose that the stock price in the previous example did not increase to $75, but instead fell to $40.50. That represents just a 10% decline from the initial $45 stock price, but when the stock is worth $40.50, the call option will not be exercised. No investor would choose to pay the $45 strike price to buy the stock when they can simply purchase shares in the open market at a cheaper price. Therefore, if the option contract expires when the stock price is at $40.50, the option will be worthless, and the option buyer’s $300 initial investment will be worth nothing. Another way to say this is that the option buyer earns a return of −100% even though the stock price fell just 10%. Clearly call options have a lot of upside potential, but the risk of a total loss is also very real.

A similar situation can be worked out for puts. Assume that for the same stock (which has a current price of $45) an investor could pay $250 to buy a put option, which gives the investor the right to sell 100 shares of the stock at a strike price of $45 each. As the buyer of a put, the investor wants the price of the stock to drop. Assume that the investor’s expectations are correct and the price of the stock does indeed drop to $25 a share. The investor goes into the market and purchases 100 shares for $25 each, and then she immediately exercises her put option by selling those shares for $45 each (note: the person who sold the put option is obligated to buy these shares at $45 each). The investor makes a gross profit of $20 per share, or $2,000 total on her initial investment of $250. That represents a rate of return of 700%! Of course, put options are risky just as call options are. If the stock price had risen to $50 rather than falling to $25, the put option buyer’s $250 investment would be totally lost.

In some cases, investors who buy calls and puts do not actually have to trade the underlying asset to realize their profits. Instead, investors can “cash settle” their options, meaning that they receive the profits from their option in cash. This arrangement is most common when the underlying asset is difficult to trade, as would be the case when the underlying asset is a stock index rather than stock of a single company. Though most options that have a single common stock as the underlying asset are settled by exchanging the stock, to keep things simple we will illustrate the cash settlement process for a basic stock option. For example, consider once more the call option that had a strike price of $45. Suppose the underlying stock price rises to $75, so on paper at least, the call option buyer has made a gross profit of $30 per share. Rather than pay the $45 exercise price, take delivery of the shares from the call writer, and then resell the shares in the open market for $75, the call buyer may simply receive a $30 per share or $3,000 total cash payment from the call seller in exchange for the option. Settling options in cash eliminates the need for the option buyer and seller to exchange the underlying shares and the need for the option buyer to sell shares in the open market to monetize his or her profit.

Investors can trade options in the secondary market, just as they can trade other securities such as stocks and bonds. The value of both calls and puts is directly linked to the market price of the underlying common stock. For example, the secondary market price of a call increases as the market price of the underlying stock rises. Likewise, the price of a put increases as the underlying common stock price declines. Thus, another way that investors can realize their profits on options is simply to sell them in the secondary market after they have increased in value.

Advantages and Disadvantages

 The major advantage of investing in puts and calls is the leverage they offer. This feature allows investors to earn large profits from relatively small movements in the underlying asset without investing a large amount of money up front. Another advantage is that options allow investors to profit whether the underlying stock price goes up or down. Investors who believe that the underlying stock price will go up can buy calls, and those who believe that the stock price will fall can buy puts.

A major disadvantage of calls and puts is that the holder enjoys neither interest or dividend income nor any other ownership benefits. Moreover, because options have limited lives, there is a limited time during which the underlying asset can move in the direction that makes the option profitable. Finally, while it is possible to buy calls and puts without investing a lot of money up front, the likelihood that an investor will lose 100% of the money that he or she does invest is much higher with options than with stocks. That’s because if the underlying stock moves just a little in the wrong direction, a call or put option on that stock may be totally worthless when it expires.

Options Markets

Although the concept of options can be traced back to the writings of Aristotle, options trading in the United States did not begin until the late 1700s. Even then, up to the early 1970s, this market remained fairly small, largely unorganized, and the almost-private domain of a handful of specialists and traders. All of this changed, however, on April 26, 1973, when the Chicago Board Options Exchange (CBOE) opened.

Conventional Options

 Prior to the creation of the CBOE, options trading occurred in the over-the-counter market through a handful of specialized dealers. Investors who wished to purchase options contacted their own brokers, who contacted the options dealers. The dealers would find investors willing to write the options. If the buyer wished to exercise an option, he or she did so with the writer and no one else—a system that largely prohibited any secondary trading. Options were written on New York and American exchange stocks, as well as on regional and over-the-counter securities, for as short a time as 30 days and for as long as a year. Over-the-counter options, known today as  conventional options , are not as widespread as they once were. Accordingly, our attention in this chapter will focus on listed markets, like the CBOE, where individual investors do most of their options trading.

Listed Options

 The creation of the CBOE signaled the birth of  listed options , a term that describes options traded on organized exchanges. The CBOE launched trading in calls on just 16 firms. From these rather humble beginnings, there evolved in a relatively short time a large and active market for listed options. Today trading in listed options in the United States is done in both calls and puts and takes place on several exchanges, the most active of which are the CBOE, the International Securities Exchange (ISE), the BATS Exchange, and the Nasdaq PHLX. Collectively those four exchanges accounted for more than half of all options trading in 2015. In total, put and call options are now traded on thousands of different stocks, with many of those options listed on multiple exchanges. In addition to stocks, the options exchanges also offer listed options on stock indexes, exchange-traded funds, debt securities, foreign currencies, and even commodities and financial futures.

Investor Facts

Know Your Options  Options trading continues to be increasingly popular with investors. In 2014 trading volume reached 4.3 billion contracts, or about 17.6 million contracts per day.

(Source: The Options Clearing Corporation, 2014 annual report.)

Listed options provide not only a convenient market for calls and puts but also standardized expiration dates and exercise prices. The listed options exchanges created a clearinghouse that eliminated direct ties between buyers and sellers of options and reduced the cost of executing put and call transactions. They also developed an active secondary market, with wide distribution of price information. As a result, it is now as easy to trade a listed option as a listed stock.

Stock Options

The advent of the CBOE and the other listed option exchanges had a dramatic impact on the trading volume of puts and calls. Today 4.3 billion listed options contracts are traded each year, most of which are stock options. In 2015 about 89% of listed options contracts were stock options.

Listed options exchanges have unquestionably added a new dimension to investing. In order to avoid serious (and possibly expensive) mistakes with these securities, however, investors must fully understand their basic features. In the sections that follow, we will look closely at the investment attributes of stock options and the trading strategies for using them. Later, we’ll explore stock-index (and ETF) options and then briefly look at other types of calls and puts, including interest rate and currency options, and long-term options.

Stock Option Provisions

 Because of their low unit cost, stock options (or equity options, as they’re also called) are very popular with individual investors. Except for the underlying financial asset, they are like any other type of call or put, subject to the same kinds of contract provisions and market forces. Two provisions are especially important for stock options: (1) the price—known as the strike price—at which the stock can be bought or sold, and (2) the amount of time remaining until expiration. As we’ll see, both the strike price and the time remaining to expiration have a significant bearing on the market value of an option.

Strike Price

 The  strike price  is the fixed, contract price at which an option holder has the right to buy (in the case of a call option) or sell (in the case of a put option) the underlying stock. With conventional (OTC) options, there are no constraints on the strike price, meaning that two parties can agree to whatever strike price they desire. With listed options, strike prices are standardized by the exchanges on which options trade. Generally speaking, options strike prices are set as follows:

· Stocks selling for less than $25 per share carry strike prices that are set in $2.50 increments ($7.50, $10.00, $12.50, $15, and so on).

· In general, the increments jump to $5 for stocks selling between $25 and $200 per share, although a number of securities in the $25 to $50 range are now allowed to use $2.50 increments.

· For stocks that trade at more than $200 a share, the strike price is set in $10 increments.

· Unlike most equity options, options on exchange-traded funds (discussed more fully later in this chapter) usually have strike prices set in $1 increments.

In all cases, the strike price is adjusted for stock splits. Strike prices are not adjusted for cash dividends (except for large “special” dividends), but they are adjusted when firms pay significant stock dividends (e.g., dividends paid in additional shares).

Expiration Date

 The  expiration date  is also an important provision. It specifies the life of the option, just as the maturity date indicates the life of a bond. The expiration date, in effect, specifies the length of the contract between the holder and the writer of the option. Thus, if you hold a six-month call on Sears with a strike price of, say, $70, that option gives you the right to buy 100 shares of Sears common stock at $70 per share at any time over the next six months. No matter what happens to the market price of the stock, you can use your call option to buy 100 shares of Sears at $70 a share. If the price of the stock moves up, you stand to make money. If it goes down, you’ll be out the cost of the option.

Technically, some options can be exercised at any time up until the expiration date, while others can be exercised only on the expiration date. American options allow investors to exercise their right to buy or sell the underlying asset at any time up to the expiration date, while European options only permit investors to exercise on the expiration date. All exchange-listed options in the United States are American options, so unless otherwise noted, we will focus on those.

Expiration dates are standardized in the listed options market. The exchanges initially created three expiration cycles for all listed options:

· January, April, July, and October

· February, May, August, and November

· March, June, September, and December

Each issue is assigned to one of these cycles. The exchanges still use the same three expiration cycles, but they’ve been altered so that investors are always able to trade in the two nearest (current and following) months, plus the next two closest months in the option’s regular expiration cycle. For reasons that are pretty obvious, this is sometimes referred to as a two-plus-two schedule.

For example, if the current month (also called the front month) is January, then available options in the January cycle would be January, February, April, and July. These represent the two current months (January and February) and the next two months in the cycle (April and July). Likewise, maintaining the assumption that the current month is January, available contracts for the February cycle would be January, February, May, and August; available contracts for the March cycle would be January, February, March, and June. The expiration dates, based on the front months, continue rolling over in this way during the course of the year. The following table demonstrates the available contracts under the two-plus-two system for the months of February and June:

Front Month	Cycle	Available Contracts
February	January	February, March, April, July
February	February	February, March, May, August
February	March	February, March, June, September
June	January	June, July, October, January
June	February	June, July, August, November
June	March	June, July, September, December

Given the month of expiration, the actual day of expiration is always the same: the third Friday of each expiration month. Thus, for all practical purposes, listed options always expire on the third Friday of the month of expiration.

Look Up an Option Chain

Put and Call Transactions

 Option traders are subject to commission and transaction costs when they buy or sell an option. These costs effectively represent compensation to the broker or dealer for selling the option.

Listed options have their own marketplace and quotation system. Finding the price (or premium) of a listed stock option is fairly easy since there are lots of online sources for option quotations.  Figure 14.1  illustrates a quotation from  Nasdaq.com  for an option chain in which Facebook stock serves as the underlying asset. An  option chain  is a listing of all options (calls and puts) on an underlying asset for a given expiration period. The quotation in  Figure 14.1  shows only a small subset of the entire option chain for Facebook, seven call option contracts on the left and seven put option contracts on the right along with their strike prices and premiums for contracts that expire on August 21, 2015. Generating a quotation for all current option contracts on Facebook produces an option chain with several hundred call and put option quotes.

Each row of  Figure 14.1  provides important details about a particular option contract. Notice that in the upper left portion of the figure is a column heading that says “Calls,” indicating that the first several columns in the figure contain information about various call options on Facebook stock. Moving to the right, notice the column header, “Puts,” which indicates that the right side of the figure provides information about put options on Facebook shares. All of the options shown in  Figure 14.1  expire on August 21, 2015. The columns headed “Last” provide the most recent market price (or premium) for each option, and the columns headed “Chg” show the change in the price of each option from the previous day’s closing price. Other columns show the bid and ask prices for the options, the day’s trading volume, and the open interest, which is a measure of the number of outstanding option contracts. Notice that the column headed “Root” shows the ticker symbol for Facebook, which is the underlying asset for all of these options.

Perhaps the most salient information in  Figure 14.1  is the market price of each option. For example, on July 6, 2015, an August Facebook call with a strike price of $85 was quoted at $4.90 (which translates into a price of $490 because stock options trade in 100 share lots), and an August put option with the same strike price sold for $2.68.

Figure 14.1  Quotations for Facebook Stock Options

The quotes for calls and puts of a specified expiration period are listed down either side of the strike price. In addition to the last price the option traded at for the day and its end-of-day bid and ask price, the change from the previous day’s last transaction price is shown.

(Source: Data from  http://www.nasdaq.com , accessed July 6, 2015.)

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 14.1 Describe call and put options. Are they issued like other corporate securities?

2. 14.2 What are listed options, and how do they differ from conventional options?

3. 14.3 What are the main investment attractions of call and put options? What are the risks?

4. 14.4 What is a stock option? What is the difference between a stock option and a derivative security? Describe a derivative security and give several examples.

5. 14.5 What is a strike price? How does it differ from the market price of the stock?

6. 14.6 Why do call and put options have expiration dates? Is there a market for options that have passed their expiration dates?

Options Pricing and Trading

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2. LG 4

3. LG 5

The value of an option depends to a large extent on the price of the underlying asset, but several other factors also influence option prices. Being a good options trader requires an understanding of these factors and how they influence option values. Let’s look now at the basic principles of options pricing. We’ll start with a brief review of how profits are derived from puts and calls. Then we’ll take a look at several ways in which investors can use these options.

The Profit Potential from Puts and Calls

Although the quoted market price of a call or put is affected by such factors as time to expiration, stock volatility, and market interest rates, by far the most important variable is the price of the underlying common stock. This is the variable that drives the most significant moves in an option’s price. When the price of the underlying stock moves up, calls do well. After all, a call option gives an investor the right to buy a stock at a fixed price, and that right is most valuable when the stock price is very high. When the price of the underlying stock drops, puts do well. Again, having the right to sell a stock at a fixed price is most valuable when the market price of the stock is far below the strike price. Clearly investors who are purchasing or selling options need to have some awareness of the potential behavior of the underlying stock.

Call Option Payoff Diagrams

Figure 14.2  illustrates how the ultimate profits that options provide depend upon the underlying stock price. By “profit” we mean the gain that an investor would receive from exercising the option just before it expires—the difference between the stock price and the strike price (as long as that difference is positive) minus the initial cost of the option. The diagram on the left depicts a call, and the one on the right depicts a put. The call diagram assumes that an investor pays $500 for a call option contract

Figure 14.2   The Valuation Properties of Put and Call Options

The payoff of a call or put depends on the price of the underlying common stock (or other financial asset). The cost of the option has been recovered when the option passes its breakeven point. After that, the profit potential of a call is unlimited, but the profit potential of a put is limited because the underlying stock price cannot go lower than $0.

(i.e., 100 calls at $5 per call) and that the call has a strike price of $50. The graph shows how the option profit increases as the stock price rises. Observe that a call provides no cash inflow unless the price of the stock advances past the stated exercise price ($50). In other words, when the underlying stock price is below $50, the call generates a net loss of $500, which is just what the investor spent on the call. If the market price of the stock is below $50, no rational investor would exercise the option and pay $50 to buy the stock—it would be cheaper to simply buy the stock in the open market, and therefore the call expires worthless in that case.

The call option does not begin to move toward profitability until the stock price starts to move above $50. Because it costs $500 to buy the call, the stock has to move up to $55 ($5 above the strike price) for the investor to recover the $500 premium and thereby reach a breakeven point. Note, however, that even if the stock price is between $50 and $55, it’s still best to exercise the option because doing so reduces the option holder’s net loss. For example, if the stock price is $52, exercising the option generates a cash inflow of $200, which partially offsets the $500 option premium. For each dollar by which the stock price exceeds the breakeven point ($55), the call option’s profit goes up by $100. The potential profit from the call position is unlimited because there is no upper limit on the underlying stock’s price.

The value of a put is also derived from the price of the underlying stock, except that the put value goes up when the stock price goes down and vice versa. The put diagram in  Figure 14.2  assumes you buy a put for $500 and obtain the right to sell the underlying stock at $50 a share. It shows that the profit of the put is −$500 unless the market price of the corresponding stock drops below the exercise price ($50) on the put. The further the stock price is below $50, the more the profit of the put option increases. Again, note that because the put cost $500, the put doesn’t reach a breakeven point until the stock price reaches $45. At stock prices lower than that, the put is profitable, and it becomes more profitable the further the stock price drops. However, notice an important difference between puts and calls. The put option has a maximum profit of $4,500 because the stock price cannot fall below zero. As noted, a call’s profit potential is unlimited because there is no upper limit on the stock price.

Intrinsic Value

As we have seen, the payoff of a put or call depends ultimately on the exercise price stated on the option, as well as on the prevailing market price of the underlying common stock. The relationship between an option’s strike price and the underlying stock’s market price determines the options intrinsic value.  Intrinsic value  represents the gross amount of money that an investor would receive if he chose to exercise a call option. For example, suppose a call option has a strike price of $50 and the underlying stock price is $60. By exercising this option an investor could receive $10 (or $1,000 for a call contract on 100 shares of stock), and that is the option’s intrinsic value. If the stock price were just $45, the investor would not choose to exercise the option (because the stock is cheaper in the open market) and the call’s intrinsic value would be zero. More specifically, the intrinsic value of a call is determined according to the following simple formula.

Intrinsic value of a call=(Stock price−Strike price)×100or 0, whichever is greaterIntrinsic value of a call=(Stock price−Strike price)×100or 0, whichever is greaterEquation14.1

In other words, the intrinsic value of a call is merely the difference between the stock’s market price and the option’s strike price times 100. When the stock price is below the strike price, the intrinsic value is zero. As implied in  Equation 14.1 , a call has an intrinsic value whenever the market price of the underlying financial asset exceeds the strike price stipulated on the call. If a call option has a strike price of $50 and the underlying stock sells for $60, then the option’s intrinsic value is $1,000.

A put, on the other hand, cannot be valued in the same way because puts and calls allow the holder to do different things. To find the intrinsic value of a put, we must change the order of the equation a bit:

Intrinsic value of a put=(Strike price−Stock price)×100or 0, whichever is greaterIntrinsic value of a put=(Strike price−Stock price)×100or 0, whichever is greaterEquation14.2

In this case, a put has intrinsic value as long as the market price of the underlying stock (or financial asset) is less than the strike price stipulated on the put.

In-the-Money/Out-of-the-Money

 When a call has a strike price that is less than the market price of the underlying common stock, it has a positive intrinsic value and is known as an in-the-money option. Look back at  Figure 14.1  and notice that the first three call options listed in the figure are highlighted in yellow. Those call options have strike prices of $80, $82.50, and $85, and they are highlighted in yellow because on the day that these option quotes were retrieved, Facebook stock was selling just above $87. This means that the highlighted call options in  Figure 14.1  are in the money (i.e., their strike prices are below Facebook’s stock price).

When the strike price of the call exceeds the market price of the stock, the call has no intrinsic value, in which case it is known as an out-of-the-money option. In  Figure 14.1 , the calls with strike prices of $87.50, $90, $92.50, and $95 are not highlighted because they were out of the money at the time (i.e., Facebook’s stock price was below the strike prices). However, an out-of-the-money call option is not worthless as long as there is still time before it expires because there is a chance that the stock price will rise above the strike price. In other words, when a call is out-of-the-money, its intrinsic value is zero but its market value is greater than zero. In such a case, we say that the option has no intrinsic value but it still has time value. An option’s  time value  is the difference between its market price and its intrinsic value. In  Figure 14.1 , notice that the Facebook call option with a strike price of $87.50 has a quoted price of $3.53. Because the option had more than a month left before it expired, it still had plenty of time value even though its intrinsic value was zero. In the special case when the strike price of the option and the market price of the stock are the same, we say that the call option is  at-the-money .

As you might expect, the situation is reversed for put options. A put is in-the-money when its strike price is greater than the market price of the stock. Remember, a put option grants the holder the right to sell a stock at the strike price, so that right is most valuable when the strike price is higher than the stock’s current market price. In  Figure 14.1 , the in-the-money put options (highlighted in yellow) have strike prices of $87.50, $90, $92.50, and $95. For all four of those put options, the strike price is above the stock’s then-current market price, so the options have a positive intrinsic value. A put option is out-of-the-money when the market price of the stock exceeds the strike price, which is the case in  Figure 14.1  for the put options with strike prices of $80, $82.50, and $85. As with calls, an out-of-the-money put still has a positive market value as long as there is some time before the expiration date. For example, the put option with a strike price of $85 in  Figure 14.1  has a market price of $2.68. This put’s

Famous Failures in Finance Ethical Lapse or Extraordinarily Good Timing?

A finance professor conducting research on executive stock option grants discovered that firms awarding these grants seemed to display extraordinarily good timing, setting the exercise prices just before a large run-up in the stock price. Perhaps firms were withholding good news until after they awarded stock option grants, knowing that when they released the news, their stock prices would rise. A few years later, Erik Lie and Randall Heron solved the puzzle of executives’ remarkable timing abilities. Some firms apparently backdated their option grants, using hindsight to set the exercise price on the one date in the prior several weeks when their stock price was at its lowest point. Backdating works like this. A firm announces on June 1 that it had granted its executives stock options on April 15, using the market price of the stock that day as the option’s exercise price. In fact, the firm did not actually award the options on April 15 but rather chose that date several weeks later. That gave the firm the benefit of hindsight, meaning that the firm knew that the stock’s lowest point in the preceding month or two had in fact been April 15. By the time the firm announced the option grant on June 1, the options were already in-the-money because the stock price was much higher than it had been on the retroactively set grant date. In backdating options, firms failed to disclose the true value of the option grants they awarded, which in turn affected their reported earnings and taxes.

That research and the press coverage it generated prompted investigations of at least 257 firms’ options grants. Some firms launched their own internal investigations, but many other companies became the target of SEC investigations. Firms involved in options backdating scandals endured serious consequences. Some executives paid fines or went to prison. Other firms settled lawsuits without admitting wrongdoing, such as Broadcom, which paid $118 million to settle a shareholder lawsuit. Most of the firms investigated saw their stock prices decline by as much as 10%.

The opportunity for senior management to engage in meaningful options backdating was largely eliminated by the Sarbanes-Oxley Act, which requires companies to publicly disclose option grants within two days. Indeed, researchers verified that the unusual market timing associated with stock option grants seemed to vanish soon after the passage of Sarbanes-Oxley.

(Source: Kenneth Carow, Randall Heron, Erik Lie, and Robert Neal, “Option Grant Backdating Investigations and Capital Market Discipline,” Journal of Corporate Finance, Volume 15, Issue 5, December 2009, pages 562–572.)

intrinsic value is zero, but its time value is $2.68. Finally, a put is at-the-money when the strike price equals the stock price.

When firms grant stock options to their employees, they typically grant at-the-money options, meaning that the strike prices of the options are set equal to the price of the underlying stock on the date of the option grant. However, as the accompanying Famous Failures in Finance box explains, many companies got into trouble for using a bit of hindsight (and failing to disclose that) when selecting their option grant dates. This practice came to be known as options backdating.

Put-Call Parity

 Newcomers to options are often surprised to learn that as different as put and call options are from each other, their prices are linked under certain conditions. As long as a put and call option have the same underlying asset, the same strike price, and the same expiration date, their prices do not, and in fact cannot move independently of each other without creating an arbitrage opportunity. To explain why, consider the following example.

Suppose Nick forms a portfolio containing one share of Dow Chemical common stock and one put option with an exercise price of $50 (which we will denote X=$50X=$50). The Dow put option expires in one year. Nick’s wife Nora forms a different portfolio. She purchases a Dow call option, also having an exercise price of $50 and a one-year expiration, but Nora also buys a risk-free, zero-coupon bond with a face value of $50 (which matches the option’s strike price) and a maturity of one year. Unlike Nora’s call

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Table 14.1 Illustration of Put-Call Parity

	Price of Dow Chemical Stock in One Year
	$35	$40	$45	$50	$55	$60	$65
Nick’s portfolio
Put with X = 50X = 50	$15	$ 10	$     5	$     0	$     0	$      0	$     0
Share of stock	$35	$40	$45	$50	$55	$60	$65
Total value	$50	$50	$50	$50	$55	$60	$65
Nora’s portfolio
Call with X = $50X = $50	$  0	$  0	$  0	$  0	$  5	$  10	$ 15
Bond with FV = $50FV = $50	$50	$50	$50	$50	$50	$50	$50
Total value	$50	$50	$50	$50	$55	$60	$65

option, the bond is an absolutely safe investment that will pay her $50 in one year with certainty. Let’s assume that the put and call options that Nick and Nora have purchased are European options, meaning that they can only be exercised when they expire in one year.

Because Nick and Nora have invested in options on Dow common stock, the value of their portfolios will clearly depend on how Dow’s stock performs.  Table 14.1  shows what each portfolio will be worth next year, just as the options are about to expire, for a range of possible Dow stock values. Let’s look at Nick’s portfolio first. Suppose Dow stock does not perform well at all, trading at $35 next year. In that case, Nick will be fortunate to have purchased a put option. If Dow stock is trading at $35, the put option will be in the money by $15, and its market value will be $15 too since it is about to expire. Combined with the share of stock that Nick owns (which is worth $35), the total portfolio value is $50. Notice that Nick’s portfolio value is fixed at $50 as long as Dow’s stock price is $50 or lower. That should make sense because the put option guarantees that Nick can sell his Dow share for $50. If Dow stock finishes the year above $50 per share, the put option expires out of the money and will be worthless, but the share of Dow that Nick owns gives his portfolio upside potential. To summarize, one year from now, Nick’s portfolio will be worth at least $50, and it could be worth more if Dow’s stock price ends the year above $50.

Now let’s turn to Nora’s portfolio, and again let’s start by asking what happens to her portfolio when Dow’s performance is poor and the stock ends the year at $35. In that case, Nora’s call option expires out of the money and has no value. However, Nora at least receives the $50 payment from her risk-free bond, so her total portfolio value is $50. The same will be true at any Dow price of $50 or lower, because when Dow’s price is in that range, the call option will be worthless, and Nora will only receive the $50 bond payment. What happens if Dow stock ends the year higher, say at $55? In that scenario, Nora’s call option will be worth $5, and her total portfolio will be worth $55. If Dow stock ends the year even higher, then Nora’s portfolio will be worth more too because the call value will increase in step with the underlying stock. To summarize Nora’s position, her portfolio will be worth at least $50, and it could be worth more if Dow’s stock price ends the year above $50.

By now it should be clear that the portfolios that Nick and Nora created have identical future values, no matter what happens to the price of Dow stock. Both investors have guaranteed that their portfolio will be worth at least $50, and both will benefit from an even higher payoff if Dow stock ends the year above $50. In technical terms, we would say that Nick and Nora have replicating portfolios, meaning that their portfolios provide identical payoffs (i.e., Nora’s portfolio replicates Nick’s and vice versa) even though the portfolios contain different securities. This leads to an important concept in option pricing called put-call parity. Put-call parity says that the future payoffs of a portfolio containing a put option and a share of the underlying stock are the same as the payoffs of a portfolio containing a call option and a risk-free bond. Again, remember that the put and call options have to have the same underlying asset, the same exercise price, and the same expiration date. But if those conditions hold, as they do for Nick and Nora’s portfolios, then put-call parity holds.

Put-call parity is important because it tells us something about the market prices of puts and calls. To be specific, if the future payoff of a put option and a stock equals the future payoff of a call option and a risk-free bond, then the prices of those two portfolios must be the same at any moment in time. If that were not true there would be an arbitrage opportunity. Remember that arbitrage means buying and selling identical assets at different prices to earn an instant, risk-free profit. Hypothetically, if the value of the portfolio containing a put and a share of stock exceeded the value of the portfolio containing a call and a risk-free bond, the traders could sell short the first portfolio and buy the second one to earn a profit. Such transactions would put upward pressure on the prices of the call and the bond, and they would put downward pressure on the prices of the stock and the put, until the values of the two portfolios were equal again. Put-call parity says that because the portfolio containing the put and the stock is essentially the same as the portfolio containing the call and the risk-free bond, the prices of those portfolios must also be the same. We can express this mathematically as follows:

Price of a put option + Price of a stock = Price of a call option + Price of arisk-free bondPrice of a put option + Price of a stock = Price of a call option + Price of a risk-free bondEquation14.3

Example

Suppose a certain stock sells for $71.75. You want to know the value of a put option on this stock if the strike price is $70 and the expiration date is three months from now. A call option on the same underlying stock has a strike price of $70, and it expires in three months. That call option currently sells for $6.74. There is also a risk-free, zero-coupon bond available in the market with a maturity in three months and a face value of $70 (notice the bond’s face value is the same as the option’s strike price). The current risk-free rate is 2% per year, or about 0.5% for a quarter (three months). This means that the bond’s market price is just the present value of $70 discounted for three months, or $69.65 ($70/0.005). You can use put-call parity ( Equation 14.3 ) to find the put option’s market price:

Price of a put + Price of a stock = Price of a call + Price of a risk-free bondPrice of a put + $71.75 = $6.74 + 69.65Price of a put = $6.74 + $69.65−$71.75 = $4.64Price of a put + Price of a stock = Price of a call + Price of a risk-free bondPrice of a put + $71.75 = $6.74 + 69.65Price of a put = $6.74 + $69.65−$71.75 = $4.64

Now we know one way to find the value of an option. If we know the price of the underlying stock, the risk-free interest rate, and the price of a call option, we can use put-call parity to find the value of a put. Or, if we know the value of the put, we can use it to find the value of a call. But what if we don’t know the value of either option? To explore that question, let’s turn our attention to the underlying forces that influence option prices.

Table 14.2 Option Price Components for Call Options

Stock Price	Strike Price	Options Expiring in One Month	Options Expiring in Three Months
		Market Price	Intrinsic Value	Time Value	Market Price	Intrinsic Value	Time Value
$71.75	$65.00	$7.69	$6.75	$0.94	$9.68	$6.75	$2.93
$71.75	$70.00	$4.28	$1.75	$2.53	$6.74	$1.75	$4.99
$71.75	$75.00	$2.04	$0.00	$2.04	$4.50	$0.00	$4.50

What Drives Option Prices

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Option prices can be reduced to two separate components. The first is the intrinsic value of the option, which is driven by the gap between the current market price of the underlying financial asset and the option’s strike price. As we saw in  Equations 14.1  and  14.2 , the greater the difference between the market price of the underlying asset and the strike price on the option, the greater the intrinsic value of the call or put. We can summarize these relationships by saying that a call value is greater when (1) the strike price is lower or (2) the stock price is higher. Conversely, a put value is greater when (2) the strike price is higher or (3) the stock price is lower.

Time Value and Time to Expiration

 The second component of an option price is the time value. It represents the amount by which an option’s price exceeds its intrinsic value.  Table 14.2  illustrates this concept by listing market prices, intrinsic values, and time values for six different call options. Three of the options expire in one month, and the other three options expire in three months. In addition, there are two call options with a strike price of $65, two with a strike of $70, and two with a $75 strike price. The current market price of the underlying stock is $71.75, so the call options with $65 and $70 strike prices are in the money, but the options with a $75 strike price are out of the money.

Look first at the call option with a strike price of $65 expiring in one month.  Table 14.2  lists its market price as $7.69. This option is in-the-money and has an intrinsic value of $6.75 because it allows the option holder to buy a stock for $65 when that stock is actually worth $71.75. The option’s market price is $0.94 higher than its intrinsic value, so $0.94 is the option’s time value. Why would investors be willing to pay $7.69 for this option when they will only earn $6.75 if they exercise it today? Because the option does not expire for another month, there is some chance that the underlying stock price will rise, and that possibility gives the option its time value. Moving to the right in  Table 14.2 , observe that the call with a $65 strike price expiring in three months has an even higher market value, $9.68. The intrinsic value of this option is also $6.75, but its time value is higher because there is more time for the stock price to move in a favorable direction.

Watch Your Behavior

Exercising Too Early  Researchers have discovered that customers of discount brokers frequently make the mistake of exercising their options early rather than selling them, and they are particularly prone to this mistake when a stock hits a 52-week high. In contrast, professional options traders almost never make that mistake.

(Source: Allen M. Poteshman and Vitaly Serbin, “Clearly Irrational Financial Market Behavior: Evidence from the Early Exercise of Exchange Traded Stock Options,” Journal of Finance, February 2003, Volume 58, Issue 37, pp. 37–70.)

Now look at the options with a $75 strike price. These options are out of the money, so their intrinsic values are zero. Yet both have time value. The option expiring in one month is worth $2.04, and the option expiring in three months sells for $4.50. Investors are willing to pay for out-of-the-money options because with time left before they expire, there is still a chance that the underlying stock price will rise, and it will become profitable to exercise the options. Clearly the option expiring in three months is more valuable than the one expiring next month.

There are two important general lessons from  Table 14.2 . The first is that the market price of an option will almost always be higher than its intrinsic value. The main exception to that general rule is that an option’s price will equal its intrinsic value just before it expires. As long as an option has some time left before it expires, it will generally be worth more than its intrinsic value. The second important lesson is that an option’s price will usually be higher if the option has more time remaining before it expires.

Volatility and Option Prices

 For most financial assets, higher volatility means higher risk, and higher risk means that investors demand a higher rate of return. Because an asset’s value is linked to the present value of its cash flows, if investors discount those cash flows at a higher rate of interest, the asset’s value will be lower. Think of a bond, for example. A bond’s cash flows are contractually fixed, so if investors perceive that the bond’s risk has increased, they will discount those cash flows at a higher rate, which in turn leads to a lower bond price. So in most cases, we can say that if an asset’s volatility is higher, its value will be lower, holding everything else constant.

That’s not really true with options. The reason is that options have asymmetric payoffs. Consider a call option that is near its expiration date. As the underlying stock price rises above the call’s strike price, the option’s payoff rises too. So on the upside, the call’s payoff moves in step with the stock. But when the stock falls below the call’s strike price, the option is out-of-the-money and will not be worth exercising. That is true whether the stock price is $1 below the call’s strike price or $10 below it or even $100 below the strike price. On the downside, the call’s payoff is fixed at zero no matter how the stock price goes, so there is an asymmetry between a call’s upside and its downside.

This asymmetry makes options more valuable if the underlying stock price is more volatile. To see this clearly, consider two stocks, A and B, which are both currently selling for $50 per share. Suppose we want to evaluate the investment potential of call options on these two stocks. Suppose these call options are at-the-money, so their strike prices are $50, and they expire in one year. Suppose A is not a particularly volatile stock, and you think that a year from now, the value of stock A will be in a range between $40 and $60. The following table shows how the payoff on a call option will vary depending on the price of stock A next year.

Price of Stock A	$40	$44	$48	$52	$56	$60
Payoff of Call	$ 0	$ 0	$ 0	$ 2	$ 6	$10

Now stock B is more volatile than stock A, so you believe that in one year its price will be in a range from $32 to $68. The following table below how payoffs on a call option will vary depending on the price of stock B.

Price of Stock B	$32	$36	$40	$44	$48	$52	$56	$60	$64	$68
Payoff of a Call	$ 0	$ 0	$ 0	$ 0	$ 0	$ 2	$ 6	$10	$14	$18

Notice that the payoffs of this option are the same as the call option on stock A when the stock price ends the year below $50, but call options on stock B offer more upside. This means that the market price of a call option on stock B must be higher than the price of a call option on stock A. To say this more generally, the value of an option (call or put) is greater if the volatility of the underlying stock is greater.

Interest Rates and Option Prices

 Previously we said that one way to value options is by using put-call parity, and part of that valuation process involves pricing a risk-free

Famous Failures in Finance The Volatility Index

Because the volatility of the underlying asset plays a major role in option valuation, options traders track the volatility of individual stocks and of the market as a whole very closely. In fact, there is an index, called the VIX (which stands for volatility index), which provides an estimate of the volatility of the overall market. From about 1990 to 2007, the average volatility of the U.S. stock market as measured by VIX was close to 20% per year. But in the fall of 2008, after the failure of Lehman Brothers, the VIX index peaked at nearly 90%, more than four times its long-run average! Throughout the Great Recession (December 2007 through June 2009) the VIX index spiked several times to levels above its historical average, but it has been mainly below average in recent years.

bond. In general, options prices do depend on interest rates, just as the prices of other financial assets do. The general relationship is that the value of a call rises when the risk-free rate rises, and the value of a put falls with rising interest rates. Intuitively, a call option grants the holder the right to buy something at some future date. In a sense then, part of what a call option provides is the right to defer payment for a stock. When is the right to defer paying for something most valuable? It’s when interest rates are high. With high rates, investors prefer to keep their money invested as long as possible, so having the right to defer payment for something is particularly valuable.

Puts work in just the opposite way. A put option gives the holder the right to sell something, that is, to receive cash in exchange for stock at some future date. Therefore, part of what a put option provides is a deferred receipt. Having to wait to receive money is never a good thing, but it is worse when interest rates are high. Thus, put values fall when the risk-free interest rate rises.

To summarize what we’ve learned so far, there are five major forces that influence the price of an option. They are (1) the price of the underlying financial asset, (2) the option’s strike price, (3) the amount of time remaining to expiration, (4) the underlying asset’s volatility, and (5) the risk-free interest rate. For stocks that pay dividends, the dividend yield can also influence the price of an option, with higher dividends leading to lower call values and higher put values.

Option-Pricing Models

 Some fairly sophisticated option-pricing models have been developed, notably by Myron Scholes and the late Fisher Black, to value options. Options traders use these models to try to identify and trade over- and undervalued options. Not surprisingly, these models are based on the same five variables we identified above. The Black and Scholes option-pricing model prices a European call option using this equation:

Call price=SN(d1)−PV(X)N(d2)Call price=SN(d1)−PV(X)N(d2)Equation14.4

In  Equation 14.4 , S represents the market price of the underling stock, PV(X) represents the present value of the option’s strike price, and N(d1) and N(d2) are probabilities ranging from 0 to 1. Loosely speaking, these probabilities are related to the odds that the call option will expire in-the-money. In other words, as these probabilities get closer and closer to 1.0, the option is more and more likely to be exercised, and hence it is more and more valuable. The probabilities N(d1) and N(d2) depend on the numerical values of d1 and d2, which come from these equations:

d1=ln(SX)+(r+σ22)Tσ√Td1=ln(SX)+(r+σ22)TσTEquation14.4a

d2=d1−σ√Td2=d1−σTEquation14.4b

In these two equations, S and X again represent the stock price and the strike price, respectively, T represents the time remaining before the option expires (expressed in years), σ represents the annual standard deviation of the stock’s return (so σ2 represents the variance of the stock’s return), and r represents the annual risk-free interest rate. Once values for d1 and d2 are calculated, they must then be converted into probabilities using the standard normal distribution function. The normal distribution is simply the familiar bell curve, and the standard normal distribution is a bell curve with a mean of zero and a standard deviation of 1. The probabilities we need in  Equation 14.4  represent the likelihood of drawing a number less than or equal to d1 (and d2) from this distribution.  Figure 14.3  provides a graphical illustration of the probability that we seek. Suppose we use  Equation 14.4a  and find that d1 equals 0.9. To obtain N(d1) for  Equation 14.4 , we need to know the area under the curve in  Figure 14.3  to the left of the value 0.9.

Fortunately, Excel provides a useful function that makes it easy to calculate these standard normal probabilities. That function is denoted with = normsdist(0.9), and Excel reveals that the appropriate probability is 0.8159.

Figure 14.3The Standard Normal Distribution

The standard normal distribution has a 0 mean and a standard deviation of 1. The shaded area to the left of d1 represents the probability of drawing a value at random from this distribution that is less than or equal to d1.

Now we are ready to price a call option using Black and Scholes.

Example

Suppose we want to price a call option that expires in three months (one-quarter of a year). The option has a strike price of $45, and the market price of the underlying stock is currently $44. The standard deviation of this stock’s returns is about 50% per year, and the risk-free rate is 2%.

To price this option, start by solving for the quantities d1 and d2:

d1=ln(4445)+(0.02+0.5022)0.250.50√0.25=−0.0225+(0.145)0.250.25=0.0551d2=0.0551−0.50√0.25=−0.1949d1=ln(4445)+(0.02+0.5022)0.250.500.25=−0.0225+(0.145)0.250.25=0.0551d2=0.0551−0.500.25=−0.1949

Next, use Excel to find the standard normal probabilities attached to these values:

N(d1)=normsdist (0.0551)=0.5220N(d2)=normsdist (−0.1949)=0.4227N(d1)=normsdist (0.0551)=0.5220N(d2)=normsdist (−0.1949)=0.4227

Finally, plug the values for N(d1) and N(d2) into  Equation 14.4  to obtain the call price:

Call price=$44 (0.5220)−[$45÷(1.02)0.25](0.4227)=$22.97−$18.93=$4.04Call price=$44 (0.5220)−[$45÷(1.02)0.25](0.4227)=$22.97−$18.93=$4.04

In this last equation, we calculate the present value of the strike price by discounting $45 at 2% for one quarter of a year. So, according to the Black-Scholes option-pricing model, the call should be priced at $4.04.

Trading Strategies

For the most part, investors can use stock options in three kinds of trading strategies: (1) buying puts and calls for speculation, (2) hedging with puts and calls, and (3) option writing and spreading.

Buying for Speculation

 Buying for speculation is the simplest and most straightforward use of puts and calls. Basically, it is like buying stock (“buy low, sell high”) and, in fact, represents an alternative to investing in stock. For example, if investors feel the market price of a particular stock is going to move up, they can capture that price appreciation by buying a call on the stock. In contrast, if investors feel the stock is about to drop in price, a put could convert that price decline into a profitable situation. Investors may buy options rather than shares due to the leverage that options provide. On a percentage basis, the gains (and losses) that investors can realize on options are typically much higher than on stocks.

Sometimes investors will argue that options offer valuable downside protection. The most an investor can lose is the cost of the option, which is always less than the cost of the underlying stock. Thus, by using options as a tool for speculation, investors can put a cap on losses and still get almost as much profit potential as with the underlying stock. It’s true that the potential dollar losses on one option are less than the potential losses on one share of stock, but don’t be fooled into thinking that options are less risky than stock. The likelihood of buying an option and earning a return of −100% (i.e., losing the entire investment) is quite high, whereas buying a share of stock and seeing its value drop to nothing is very unusual.

Watch Your Behavior

Option Buyers Chase Returns A recent study found that investors bought more call options on stocks that had recently earned high returns. This “return chasing” behavior resembles the surge in inflows to mutual funds with high past returns. There is no evidence that chasing returns, either in options or in mutual funds, benefits investors.

Speculating with Calls

 To illustrate the essentials of speculating with options, imagine that you own a stock that you feel will move up in price over the next six months. What would happen if you were to buy a call on this stock rather than investing directly in the stock? To find out, let’s see what the numbers show. The price of the stock is now $49, and you anticipate that within six months it will rise to about $65. You need to determine the expected return associated with each of your investment alternatives. Because (most) options have relatively short lives, and because we’re dealing with an investment horizon of only six months, we can use holding period return to measure the investment’s performance. Thus, if your expectations about the stock are correct, it should go up by $16 a share and will provide you with a 33% holding period return: ($65−$49)÷$49 = $16÷$49 = 0.33($65−$49)÷$49 = $16÷$49 = 0.33.

But there are also some listed options available on this stock. Let’s see how they would do. For illustrative purposes, we will use two six-month calls that carry a $40 and a $50 strike price, respectively.  Table 14.3  compares the behavior of these two calls with the behavior of the underlying common stock. Clearly, from a holding period return perspective, either call option represents a superior investment to buying the stock itself. The dollar amount of profit may be a bit more with the stock, but note that the size of the required investment, $4,900, is a lot more too, so that alternative has the lowest HPR.

Observe that one of the calls is an in-the-money option (the one with the $40 strike price). The other is out-of-the-money. The difference in returns generated by these calls is rather typical. That is, investors are usually able to generate much better rates of return with lower-priced (out-of-the-money) options, but of course there is a greater

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Table 14.3 Speculating with Call Options

	100 Shares of Underlying Common Stock	Six-Month Call Options on the Stock
		$40 Strike Price	$50 Strike Price
* The price of the calls was computed using the Black and Scholes option-pricing model, assuming a six-month expiration, 2% risk-free rate, and 40% standard deviation.
** Holding period return (HPR) = (Ending price of the stock or option − Beginning price of the stock or option) ÷ Beginning price of the stock or option.
Today
Market value of stock (at $49/share)	$4,900
Market price of calls *		$1,100	$ 530
Six Months Later
Expected value of stock (at $65/share)	$6,500
Expected price of calls		$2,500	$1,500
Profit	$1,600	$1,400	$ 970
Holding Period Return **	33%	127%	183%

risk that these options will expire worthless. A major drawback of out-of-the-money options is that their price is made up solely of investment premium—a sunk cost that will be lost if the stock does not move in price.

Speculating with Puts

 To see how you can speculate in puts, consider the following situation. You’re looking at a stock that’s now priced at $51, but you anticipate a drop in price to about $35 per share within the next six months. If that occurs, you could sell the stock short and make a profit of $16 per share.

Alternatively, you can purchase an out-of-the-money put (with a strike price of $50) for, say, $500. Again, if the price of the underlying stock drops, you will make money with the put. The profit and rate of return on the put are summarized below, along with the comparative returns from short selling the stock. Once again, in terms of holding period return, the stock option is the superior investment vehicle by a wide margin.

Comparative Performance Given Price of Stock Moves from $51 to $35/Share over a 6-Month Period	Buy 1 Put ($50 strike price)	Short Sell 100 Shares of Stock
* The purchase price of the put was computed using the Black and Scholes option-pricing model to value an identical call, then using put-call parity to value the put. Assumed 2% risk-free rate and 40% standard deviation.
** Assumes the short sale was made with a required margin deposit of 50% ($2,550).
Purchase price (today) *	2$  500
Selling price (six months later)	$1,500
Short sell (today)		$5,100
Cover (six months later)		2$3,500
Profit	$1,000	$1,600
Holding period return	200%	63% **

Of course, not all option investments perform as well as the ones in our examples. Success with this strategy rests on picking the right underlying common stock. Thus, security analysis and proper stock selection are critical dimensions of this technique. It is a highly risky investment strategy, but it may be well suited for the more speculatively inclined investor.

Hedging: Modifying Risks

 A  hedge  is simply a combination of two or more securities into a single investment position for the purpose of reducing risk. Let’s say you hold a stock and want to reduce the amount of downside risk in this investment. You can do that by setting up a hedge. In essence, you are using the hedge as a way to modify your exposure to risk. To be more specific, you are trying to change not only the chance of loss but also the amount lost if the worst does occur. A simple hedge might involve nothing more than buying stock and simultaneously buying a put on that stock with a strike price equal to the current stock price. This strategy guarantees that you can sell the stock for at least the strike price of the option, but you might be able to sell the stock for more than the strike price if the stock performs well. Another hedge strategy might consist of selling some stock short and then buying a call. There are many types of hedges, some of which are very simple and others very sophisticated. Investors use them for one basic reason: to earn or protect a profit without exposing the investor to excessive loss.

An options hedge may be appropriate if you have generated a profit from an earlier common stock investment and wish to protect that profit. Or it may be appropriate if you are about to make a common stock investment and wish to protect your money by limiting potential capital loss. If you hold a stock that has gone up in price, the purchase of a put would provide the type of downside protection you need; the purchase of a call, in contrast, would provide protection to a short seller of common stock. Thus, option hedging always involves two transactions: (1) the initial common stock position (long or short) and (2) the simultaneous or subsequent purchase of the option.

Protective Puts: Limiting Capital Loss

 Let’s examine a simple option hedge in which you use a put to limit your exposure to capital loss. Assume that you want to buy 100 shares of stock. Being a bit apprehensive about the stock’s outlook, you decide to use an option hedge to protect your capital against loss. Therefore, you simultaneously (1) buy the stock and (2) buy a put on the stock (which fully covers the 100 shares owned) with strike price equal to the stock’s current market price. This type of hedge is known as a protective put. Suppose you purchase 100 shares of the common stock at $25 a share and pay $150 for a put with a $25 strike price. Now, no matter what happens to the price of the stock over the life of the put, you can always sell the stock for at least $25. Your maximum loss is $150, which occurs if the stock price stays at $25. In that case, there is no gain on the stock and the put expires worthless too, so your loss equals your investment in the put. At the same time, there’s no limit on the gains. If the price of the stock goes up (as hoped), the put becomes worthless, and you will earn the capital gains on the stock (less the cost of the put, of course).

Table 14.4  shows the essentials of this option hedge. The $150 paid for the put is sunk cost. That’s lost no matter what happens to the price of the stock. In effect, it is the price paid for the insurance this hedge offers. Moreover, this hedge is good only for the life of the put. When this put expires, you will have to replace it with another put or forget about hedging your capital.

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Table 14.4 Limiting Capital Loss with a Put Hedge

			Stock	Put *
*  The put is purchased simultaneously and carries a strike price of $25.
Today
Purchase price of the stock			$25
Purchase price of the put				$1.50
Sometime Later
A. Price of stock goes up to:	$50
Value of put				$ 0
Profit:
100 shares of stock ($50 – $25)	$2,500
Less: Cost of Put		−$ 150
	Profit:	$2,350
B. Price of stock goes down to:	$10
Value of put				$ 15
Profit:
100 shares of stock (loss $10 – $25)	−$1,500
Value of put (profit)		$1,500
Less: Cost of put		−$  150
	Loss:	$  150

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Table 14.5 Protecting Profits with a Put Hedge

				Stock	3-month Put with $75 Strike Price
Purchase price of the stock				$ 35
Today
Marketprice of the stock				$  75
Market price of the put					$2.50
Three Months Later
A. Price of stock goes down to:				$  50
Value of put					$ 25
Profit:
100 shares of stock ($50 – $35)		$1,500
Value of put (profit)		$2,500
Less: Cost of put		−$ 250
	Profit	$3,750
B. Price of stock goes up to:				$100
Value of put					$ 0
Profit:
100 shares of stock ($100 – $35)		$6,500
Less: Cost of Put		−$ 250
	Profit:	$6,250

Protective Puts: Protecting Profits

 The other basic use of an option hedge involves entering into the options position after a profit has been made on the underlying stock. This could be done because of investment uncertainty or for tax purposes (to carry over a profit to the next taxable year). For example, if you bought 100 shares of a stock at $35 and it moved to $75, there would be a profit of $40 per share to protect. You could protect the profit with an option hedge by buying a put. Assume you buy a three-month put with a $75 strike price at a cost of $250. Now, regardless of what happens to the price of the stock over the life of the put, you are guaranteed a minimum profit of $3,750 (the $4,000 profit in the stock made so far, less the $250 cost of the put).

You can see this in  Table 14.5 . Note that if the price of the stock should fall to $50, you still earn a profit of $3,750. Plus, there is still no limit on how much profit can be made. For example, if the stock goes up to $100, you earn a profit of $6,250.

Unfortunately, the cost of this kind of insurance can become very expensive just when it’s needed the most—that is, when market prices are falling. Under such circumstances, it’s not uncommon to find put options trading at price premiums of 20% to 30%, or more, above their prevailing intrinsic values. Essentially, that means the price of the stock position you’re trying to protect has to fall 20% to 30% before the protection even starts to kick in. Clearly, as long as high option price premiums prevail, the hedging strategies described above are a lot less attractive. They still may prove to be helpful, but only for very wide swings in value—and for those that occur over fairly short periods of time, as defined by the life of the put option.

Although the preceding discussion pertained to put hedges, call hedges can also be set up to limit the loss or protect a profit on a short sale. For example, when selling a stock short, you can purchase a call to protect yourself against a rise in the price of the stock—with the same basic results as outlined above.

Enhancing Returns: Options Writing and Spreading

 The advent of listed options has led to many intriguing options-trading strategies. Yet, despite the appeal of these techniques, the experts agree on one important point: Such specialized trading strategies should be left to experienced investors who fully understand their subtleties. Our goal at this point is not to master these specialized strategies but to explain in general terms what they are and how they operate. We will look at two types of specialized options strategies here: (1) writing options and (2) spreading options.

Writing Options

 Generally, investors write options because they believe the price of the underlying stock is going to move in their favor. That is, it is not going to rise as much as the buyer of a call expects, nor will it fall as much as the buyer of a put hopes. Option writing represents an investment transaction to the writers. They receive the full option premium (less normal transaction costs) in exchange for agreeing to live up to the terms of the option.

Naked Options

 Investors can write options in two ways. One is to write  naked options , which involves writing options on stock not owned by the writer. An investor simply writes the put or call, collects the option premium, and hopes the price of the underlying stock does not move against him or her. If successful, naked writing can be highly profitable because it requires essentially no capital up front. Remember, though, the amount of return to the writer is always limited to the amount of option premium received. The catch is that there is really no limit to loss exposure. The price of the underlying stock can rise or fall by just about any amount over the life of the option and, thus, can deal a real blow to the writer of a naked put or call.

Covered Options

 The amount of risk exposure is a lot less for those who write  covered options . That’s because these options are written against stocks the investor (writer) already owns or has a position in. For example, an investor could write a call against stock he owns or write a put against stock he has short sold. The investor can use the long or short position to meet the terms of the option. Such a strategy is a fairly conservative way to generate attractive rates of return. The object is to write a slightly out-of-the-money option, pocket the option premium, and hope the price of the underlying stock will move up or down to (but not exceed) the option’s strike price. In effect, you are adding an option premium to the other usual sources of return (dividends and/or capital gains). But there’s more. While the option premium adds to the return, it also reduces risk. It can cushion a loss if the price of the stock moves against the investor.

There is a hitch to all this, of course. The amount of return the covered option investor can realize is limited. Once the price of the underlying common stock exceeds the strike price on the option, the option becomes valuable. When that happens, the investor starts to lose money on the options. From this point on, for every dollar the investor makes on the stock position, he loses an equal amount on the option position. That’s a major risk of writing covered call options—if the price of the underlying stock takes off, the call writer misses out on the added profits.

To illustrate the ins and outs of covered call writing, let’s assume you own 100 shares of PFP, Inc., an actively traded, high-yielding common stock. The stock is currently trading at $73.50 and pays quarterly dividends of $1 a share. You decide to write a three-month call on PFP, giving the buyer the right to take the stock off your hands at $80 a share. Such options are trading in the market at $2.50, so you receive $250 for writing the call. You fully intend to hold on to the stock, so you’d like to see the price of

Table 14.6  Covered Call Writing

			Stock	3-Month Call with $80 Strike Price
Current market price of the stock			$ 73.50
Current market price of the call				$2.50
Three Months Later
A. Price of the stock is unchanged:			$73.50
Value of the call				$0
Profit:
Quarterly dividends received	$ 100
Proceeds from sale of call	$ 250
Total Profit:	$ 350
B. Price of the stock goes up to:			$80	Price Where Maximum Profit Occurs
Value of the call					$0
Profit:
Quarterly dividends received	$   100
Proceeds from sale of call	$  250
Capital gains on stock ($80 – $73.5)	$  650
Total Profit:	$1,000
C. Price of the stock goes up to:			$90
Value of the call					$10.00
Profit:
Quarterly dividends received	$ 100
Proceeds from sale of call	$ 250
Capital gains on stock ($90 – $73.5)	$ 1,650
Less: Loss on call		−$1,000
Net Profit:	$1,000
D. Price of the stock drops to:			$ 71	reakeven Price
Value of the call					$0
Profit:
Quarterly dividends received	$ 100
Proceeds from sale of call	$ 250
Capital loss on stock ($71 – $73.50)	−$ 250
Net Profit:	$ 100

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PFP stock rise to no more than $80 by the expiration date on the call. If that happens, the call option will expire worthless. As a result, not only will you earn the dividends and capital gains on the stock, but you also get to pocket the $250 you received when you wrote the call. Basically, you’ve just added $250 to the quarterly return on your stock.

Table 14.6  summarizes the profit and loss characteristics of this covered call position. Note that the maximum profit on this transaction occurs when the market price of the stock equals the strike price on the call. If the price of the stock keeps going up, you miss out on the added profits. Even so, the $1,000 profit you earn at a stock price of $80 or above translates into a (three-month) holding period return of 13.6% ($1,000 ÷ $7,350). That represents an annualized return of nearly 55%! With this kind of return potential, it’s not difficult to see why covered call writing is so popular. Moreover, as situation D in the table illustrates, covered call writing adds a little cushion to losses. The price of the stock has to drop more than $2.50 (which is what you received when you wrote/sold the call) before you start losing money.

Besides covered calls and protective puts, there are many ways to combine options with other types of securities to achieve a given investment objective. Probably none is more unusual than the creation of so-called synthetic securities. Here’s an example. Say you want to buy a convertible bond on a certain company but that company doesn’t have any convertibles outstanding. You can create your own customized convertible by combining a straight (nonconvertible) bond with a listed call option on your targeted company.

Spreading Options

  Option spreading  is nothing more than the combination of two or more options into a single transaction. You could create an option spread, for example, by simultaneously buying and writing options on the same underlying stock. These would not be identical options; they would differ with respect to strike price and/or expiration date. Spreads are a very popular use of listed options, and they account for a substantial amount of the trading activity on the listed options exchanges. These spreads go by a variety of exotic names, such as bull spreads, bear spreads, money spreads, vertical spreads, and butterfly spreads. Each spread is different and each is constructed to meet a certain type of investment goal.

Consider, for example, a vertical spread. It would be set up by buying a call at one strike price and then writing a call (on the same stock and for the same expiration date) at a higher strike price. For instance, you could buy an August call on Facebook at a strike price of, say, $80 and simultaneously sell (write) an August call on Facebook at a strike price of $85. If you refer back to  Figure 14.1 , you will see that the first option would cost you $8.40, while the option that you sell would bring in $4.90. Therefore, the net cost of this position is $3.50. Strange as it may sound, such a position would generate a hefty return if the price of the underlying stock went up by just a few points. Suppose, for example, that when these options expire, the price of Facebook stock is $88. The call option that you purchased would pay you $8, but you’d have to pay $3 to the buyer of the option you wrote, so your net cash payoff at expiration would be $5. A $5 return on an investment of $3.50 represents a rate of return of almost 43%! Other spreads are used to profit from a falling market. Still others try to make money when the price of the underlying stock moves either up or down.

Whatever the objective, most spreads are created to take advantage of differences in prevailing option prices. The payoff from spreading is usually substantial, but so is the risk. In fact, some spreads that seem to involve almost no risk may end up with devastating results if the market and the difference between option premiums move against the investor.

How Do Straddles Work?

Option Straddles

 A variation on this theme involves an  option straddle . This is the simultaneous purchase (or sale) of both a put and a call on the same underlying common stock. Unlike spreads, straddles normally involve the same strike price and expiration date. Here the object is to earn a profit from either a big or a small swing in the price of the underlying common stock.

For example, in a long straddle you buy an equal number of puts and calls. You make money in a long straddle when the underlying stock undergoes a big change in price—either up or down. If the price of the stock shoots way up, you make money on the call side of the straddle but are out the cost of the puts. If the price of the stock plummets, you make money on the puts, but the calls are useless. In either case, so long as you make more money on one side than the cost of the options for the other side, you’re ahead of the game.

As an example, refer again to  Figure 14.1 . Imagine that you buy a Facebook call and a put, both having a strike of $87.50 and an August expiration date. The call costs $3.53, and the put costs $3.85, so the total cost of this position is $7.38. To make money on this transaction, Facebook stock would have to fall more than $7.38 below the $87.50 strike price or rise more than $7.38 above it. If Facebook stock stays within that range, your position loses money.

In a similar fashion, in a short straddle, you sell/write an equal number of puts and calls with the same underlying stock, the same strike price, and the same expiration date. You make money in this position when the price of the underlying stock goes nowhere. In effect, you get to keep all or most of the option premiums you collected when you wrote the options.

Except for obvious structural differences, the principles that underlie the creation of straddles are much like those for spreads. The object is to combine options that will enable you to capture the benefits of certain types of stock price behavior. But keep in mind that if the prices of the underlying stock and/or the option premiums do not behave in the anticipated manner, you lose. Spreads and straddles are extremely tricky and should be used only by knowledgeable investors.

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 14.7 Briefly explain how you would make money on (a) a call option and (b) a put option. Do you have to exercise the option to capture the profit?

2. 14.8 How do you find the intrinsic value of a call? Of a put? Does an out-of-the-money option have intrinsic value?

3. 14.9 Name five variables that can affect the price of options, and briefly explain how each affects prices. How important are intrinsic value and time value to in-the-money options? To out-of-the-money options?

4. 14.10 Describe three ways in which investors can use stock options.

5. 14.11 What’s the most that can be made from writing calls? Why would an investor want to write covered calls? Explain how you can reduce the risk on an underlying common stock by writing covered calls.

Stock-Index and Other Types of Options

1. LG 6

Imagine being able to buy or sell a major stock market index like the S&P 500—and at a reasonable cost. Think of what you could do. If you felt the market was heading up, you could invest in a security that tracks the price of the S&P 500 Index and make money when the market goes up. No longer would you have to go through the process of selecting specific stocks that you hope will capture the market’s performance. Rather, you could play the market as a whole. Of course, you can do this by purchasing a mutual fund or an ETF that is indexed to the S&P 500, but you can also accomplish that goal with stock-index options—puts and calls that are written on major stock market indexes. Index options have been around since 1983 and have become immensely popular with both individual and institutional investors. Here we will take a closer look at these popular and often highly profitable investments.

Contract Provisions of Stock-Index Options

Basically, a  stock-index option  is a put or call written on a specific stock market index. The underlying security in this case is the specific market index. Thus, when the market index moves in one direction or another, the value of the index option moves accordingly. Because there are no stocks or other financial assets backing these options, settlement is defined in terms of cash. Specifically, the cash value of an index option is equal to 100 times the published market index that underlies the option. For example, if the S&P 500 is at 2,100, then the value of an S&P 500 Index option will be $100×2,100=$210,000$100×2,100=$210,000. If the underlying index moves up or down in the market, so will the cash value of the option. In addition, whereas most options on individual stocks are American options and can be exercised at any time, stock index options may be American or European options, so they may be exercisable only on the expiration date.

Today put and call options are available on more than 100 stock indexes. These include options on just about every major U.S. stock market index or average (such as the Dow Jones Industrial Average, the S&P 500, the Russell 2000, and the Nasdaq 100), options on a handful of foreign markets (e.g., China, Mexico, Japan, Hong Kong, and the Europe sector), and options on different segments of the market (pharmaceuticals, oil services, semiconductors, bank, and utility indexes). In 2015 about 10% of traded option contracts were index options, and a large percentage of these contracts were on five of the leading stock indexes:

· S&P 500 Index (SPX)

· Russell 2000 Index (RUT)

· Nasdaq 100 Index (NDX)

· S&P 100 Index (OEX)

· Dow Jones Industrial Average (DJX)

The S&P 500 Index captures the market behavior of large-cap stocks. The Russell 2000 Index measures the performance of the small-cap stocks in the United States. The Nasdaq 100 Index tracks the behavior of the 100 largest nonfinancial stocks listed on Nasdaq and is composed of mostly large, high-tech companies (such as Intel and Cisco). The S&P 100 Index is another large-cap index composed of 100 stocks, drawn from the S&P 500, that have actively traded stock options. Another popular index is the DJIA Index, which measures the blue-chip segment of the market and is one of the most actively traded index options. Options on the S&P 500 are, by far, the most popular instruments. Indeed, there’s more trading in SPX options contracts than in all the other index options combined. Among the options exchanges that currently deal in index options, the CBOE dominates the market, accounting for more than 98% of the trades in 2015.

Both puts and calls are available on index options. They are valued and have issue characteristics like any other put or call. That is, a put lets a holder profit from a drop in the market. (When the underlying market index goes down, the value of a put goes up.) A call enables the holder to profit from a market that’s going up. Also, as  Figure 14.4  shows, index options have a quotation system that is the same as for stock options, except for the fact that the strike price is an index level.

Putting a Value on Stock-lndex Options

 As is true of equity options, the market price of index options is a function of the difference between the strike price on the option (stated in terms of the underlying index) and the latest published stock market index. To illustrate, consider the highly popular S&P 500 Index traded on the CBOE.

Example

Let’s say the S&P 500 Index recently closed at 2058 and the August call has a strike price of 2055. A stock-index call will have a positive value so long as the underlying index exceeds the index strike price (just the opposite for puts). The intrinsic value of this call is 2058−2053=32058−2053=3.

Suppose that the call actually trades at 49.92, which is 46.92 points above the call’s intrinsic value. This difference is the option’s time value.

If the S&P 500 Index in our example were to go up to, say, 2200 by late August (the expiration date of the call), this option would be quoted at 2200−2055=1452200−2055=145. Because index options (like stock options) are valued in multiples of $100, this contract would be worth $14,500. Thus, if you had purchased this option when it was trading at $49.92, it would have cost you $49.92×$100 = $4,992$49.92×$100 = $4,992 and, in less than a month, would have generated a profit of $14,500−$4,992 = $9,508$14,500−$4,992 = $9,508. That translates into a holding period return of a whopping 90%.

Figure 14.4  Quotations on Index Options

The quotation system used with index options is just like that used with stock options: strikes and expiration dates are shown along with option prices and volumes. The biggest differences are that the option strikes and closing values for the underlying asset are shown as index levels. The closing S&P 500 Index level on the day of this quotation was 2051.

(Source: Data from  http://www.nasdaq.com , accessed July 9, 2015.)

Full Value versus Fractional Value

 Most broad-based index options use the full market value of the underlying index for purposes of options trading and valuation. That’s not the case, however, with two of the Dow Jones measures: The option on the Dow Jones Industrial Average is based on 1% of the actual Industrial Average, and the Dow Transportation Average option is based on 10% of the actual average. For example, if the DJIA is at 11,260, the index option would be valued at 1% of that amount, or 112.60. Thus, the cash value of this option is not $100 times the underlying DJIA but $100 times 1% of the DJIA, which equals the Dow Jones Industrial Average itself: $100×112.60 = $11,260$100×112.60 = $11,260.

Fortunately, the option strike prices are also based on the same 1% of the Dow, so there is no effect on option valuation. What matters is the difference between the strike price on the option and 1% of the DJIA. For instance, suppose that the DJIA closes at 11,260, which means that the DJIA option index would close at 112.60. A call option on this index might have a strike price of 110, which would mean that the call is slightly in-the-money with an intrinsic value of 2.60. If the option were not set to expire immediately, its market price would be higher, with the difference between the market price and 2.60 being the option’s time value.

Another type of option that is traded at 10% (1 ÷ 10) of the value of the underlying index is the “mini” index option. For example, the Mini-NDX Index (MNX) is set at 10% of the value of the Nasdaq 100. “Minis” also exist for the Nasdaq composite, the S&P 500, the Russell 2000, and the FTSE 250 (an index of mid-cap stocks in the United Kingdom), among others.

Investment Uses

Although index options, like equity options, can be used in spreads, straddles, or even covered calls, they are perhaps used most often for speculating or for hedging. When used as a speculative investment, index options give investors an opportunity to play the market as a whole, with a relatively small amount of capital. Like any other put or call, index options provide attractive leverage opportunities and at the same time limit exposure to loss to the price paid for the option.

Index Options as Hedging Vehicles

 Index options are equally effective as hedging vehicles. In fact, hedging is a major use of index options and accounts for a good deal of the trading in these securities. To see how these options can be used for hedging, assume that you hold a diversified portfolio of, say, a dozen different stocks and you think the market is heading down. One way to protect your capital would be to sell all of your stocks. However, that could be expensive, especially if you plan to get back into the market after it drops, and it could lead to a good deal of unnecessary taxes. Fortunately, there is a way to “have your cake and eat it, too” and that is to hedge your stock portfolio with a stock index put. In this way, if the market does go down, you’ll make money on your puts, which you then can use to buy more stocks at the lower prices. On the other hand, if the market continues to go up, you’ll be out only the cost of the puts. That amount could well be recovered from the increased value of your stock holdings. The principles of hedging with stock-index options are exactly the same as those for hedging with equity options. The only difference is that with stock-index options, you’re trying to protect a whole portfolio of stocks rather than individual stocks.

Like hedging with individual equity options, the cost of protecting your portfolio with index options can become very expensive (with price premiums of 20% to 30% or more) when markets are falling and the need for this type of portfolio insurance is the greatest. That, of course, will have an impact on the effectiveness of this strategy.

Also, the amount of profit you make or the protection you obtain depends in large part on how closely the behavior of your stock portfolio is matched by the behavior of the stock-index option you employ. There is no guarantee that the two will behave in the same way. You should therefore select an index option that closely reflects the nature of the stocks in your portfolio. If, for example, you hold a number of small-cap stocks, you might select something like the Russell 2000 index option as the hedging vehicle. If you hold mostly blue chips, you might choose the DJIA index option. You probably can’t get dollar-for-dollar portfolio protection, but you should try to get as close a match as possible.

A Word of Caution

 Given their effectiveness for either speculating or hedging, it’s little wonder that index options have become popular with investors. But a word of caution is in order. Although trading index options appears simple and seems to provide high rates of return, these investments involve high risk and are subject to considerable price volatility. Amateurs should not use them. True, there’s only so much you can lose with these options. The trouble is that it’s very easy to lose all of that investment, however small it may be. These securities are not investments you can buy and then forget about until just before they expire. With the wide market swings that are so common today, you must monitor these securities daily.

Other Types of Options

Options on stocks and stock indexes account for most of the market activity in listed options. But you also can obtain put and call options on various other securities. Let’s now take a brief look at these other kinds of options, starting with options on ETFs.

Options on Exchange-Traded Funds

 In addition to various market indexes, put and call options are also available on several hundred exchange-traded funds (ETFs). As you’ve already learned, ETFs are like mutual funds that have been structured to track the performance of a wide range of market indexes—in other words, ETFs are a type of index fund. They trade like shares of common stock on listed exchanges and cover everything from broad market measures, such as the DJIA, the S&P 500, and the Nasdaq 100, to market sectors like energy, financials, health care, and semiconductors.

There’s a good deal of overlap in the markets and market segments covered by index options and ETF options. In addition to their similar market coverage, they perform very much the same in the market, are valued the same, and are used for many of the same reasons (particularly for speculation and hedging). After all, an ETF option is written on an underlying index fund (for example, one that tracks the S&P 500) just like an index option is written on the same underlying market index (the S&P 500). Both do pretty much the same thing—either directly or indirectly track the performance of a market measure—so of course they should behave in the same way. The only real difference is a structural detail. Options on ETFs are operationally like stock options in that each option covers 100 shares of the underlying exchange-traded fund rather than $100 of the underlying market index, as is the case with index options. In the end, though, both trade at 100 times the underlying index (or ETF). Thus, while operationally ETF options may be closer to stock options, they function more like index options. As such, the market views them as viable alternatives to index options. These contracts have definitely caught the fancy of investors, especially those who track the major market indexes.

Interest Rate Options

 Puts and calls on fixed-income (debt) securities are known as  interest rate options . At the present time, interest rate options are written only on U.S. Treasury securities with 30-year, 10-year, 5-year, or 13-week maturities. These options are yield-based rather than price-based. This means they track the yield (rather than the price) of the underlying Treasury security. Other types of options (equity and index options) are set up so that they react to movements in the price (or value) of the underlying asset. Interest rate options, in contrast, are set up to react to the yield of the underlying Treasury security (i.e., the exercise price is an interest rate). Thus, when yields rise, the value of a call goes up, and the value of a put goes down. In effect, because bond prices and yields move in opposite directions, the value of an interest rate call option goes up at the very time that the price (or value) of the underlying debt security is going down. The opposite is true for puts.

Currency Options

 Foreign exchange options, or  currency options  as they’re more commonly called, provide a way for investors to speculate on foreign exchange rates or to hedge foreign currency or foreign security holdings. Currency options are available on the currencies of most of the countries with which the United States has strong trading ties. These options are traded on several exchanges and over the counter and include the following currencies:

· British pound

· Swiss franc

· Australian dollar

· Canadian dollar

· Japanese yen

· Euro

Puts and calls on foreign currencies give the holders the right to sell or buy large amounts of the specified currency. However, in contrast to the standardized contracts used with stock and stock-index options, the specific unit of trading in this market varies with the particular underlying currency.  Table 14.7  spells out the details. Currency options are traded in full or fractional cents per unit of the underlying currency, relative to the amount of foreign currency involved. Thus, if a put or call on the British pound were quoted at, say, 6.40 (which is read as “6.4 cents”), it would be valued at $640 because 10,000 British pounds underlie this option (that is, 10,000×0.064 = $64010,000×0.064 = $640).

The value of a currency option is linked to the exchange rate between the U.S. dollar and the underlying foreign currency. For example, if the Canadian dollar

Table 14.7 Foreign Currency Option Contracts on the Philadelphia Exchange

Underlying Currency *	Size of Contracts	Underlying Currency*	Size of Contracts
* The British pound, Swiss franc, euro, Canadian dollar, and Australian dollar are all quoted in full cents. The Japanese yen is quoted in hundredths of a cent.
British pound	10,000 pounds	Canadian dollar	10,000 dollars
Swiss franc	10,000 francs	Japanese yen	1,000,000 yen
Euro	10,000 euros	Australian dollar	10,000 dollars

becomes stronger relative to the U.S. dollar, causing the exchange rate to go up, the price of a call option on the Canadian dollar will increase, and the price of a put will decline. (Note: Some cross-currency options are available in the market, but such options/trading techniques are beyond the scope of this text. Here, we will focus solely on foreign currency options (or futures) linked to U.S. dollars.)

The strike price on a currency option is stated in terms of exchange rates. Thus, a strike price of 150 implies that each unit of the foreign currency (such as one British pound) is worth 150 cents, or $1.50, in U.S. money. If you held a 150 call on this foreign currency, you would make money if the foreign currency strengthened relative to the U.S. dollar so that the exchange rate rose—say, to 155. In contrast, if you held a 150 put, you would profit from a decline in the exchange rate—say, to 145. Success in forecasting movements in foreign exchange rates is obviously essential to a profitable foreign currency options program.

LEAPS

 They look like regular puts and calls, and they behave pretty much like regular puts and calls, but they’re not regular puts and calls. We’re talking about  LEAPS , which are puts and calls with lengthy expiration dates. Basically, LEAPS are long-term options. Whereas standard options have maturities of eight months or less, LEAPS have expiration dates as long as three years. Known formally as Long-term Equity AnticiPation Securities, they are listed on all of the major options exchanges. LEAPS are available on hundreds of stocks, stock indexes, and ETFs.

Aside from their time frame, LEAPS work like any other equity or index option. For example, a single (equity) LEAPS contract gives the holder the right to buy or sell 100 shares of stock at a predetermined price on or before the specified expiration date. LEAPS give you more time to be right about your bets on the direction of a stock or stock index, and they give hedgers more time to protect their positions. But there’s a price for this extra time. You can expect to pay a lot more for a LEAPS than you would for a regular (short-term) option. That should come as no surprise. LEAPS, being nothing more than long-term options, are loaded with time value. And as we saw earlier in this chapter, other things being equal, the more time an option has to expiration, the higher the quoted price.

Concepts in Review

Answers available at  http://www.pearsonhighered.com/smart

1. 14.12 Briefly describe the differences and similarities between stock-index options and stock options. Do the same for foreign currency options and stock options.

2. 14.13 Identify and briefly discuss two ways to use stock-index options. Do the same for foreign currency options.

3. 14.14 Why would an investor want to use index options to hedge a portfolio of common stock? Could the same objective be obtained using options on ETFs? If the investor thinks the market is in for a fall, why not just sell the stock?

4. 14.15 What are LEAPS? Why would an investor want to use a LEAPS option rather than a regular listed option?