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The key to understanding stock splits is that the stock split cannot change the total value of the company and therefore cannot change the total value of your position. If it did, companies could create unlimited value by continually splitting their stock which doesn’t make any more sense than you being able to create infinite wealth by continually splitting ten dollar bills into two fives.

The key to understanding how stock splits affect your options is to understand that if a stock split cannot change the total value of the stock then it cannot change the total exercise value of your options.

Let’s now see how various stock splits will affect your option contracts. Assume you own one $180 call option that is trading for $6. If the stock does a 2:1 split, the split ratio is 2/1 = 2. You will then control twice as many contracts, or two for this example. The strike price will be reduced to $180/2 = $90. In addition, the price of the option will be $6/2 = $3. Your options are packaged a little differently but the total exercise value is the same. You are controlling $18,000 worth of stock before and after the split. In addition, the value of your options is $600 before and after the split.

If the stock does a 3:1 split, the split ratio is 3/1 = 3. You then own three times as many calls. The strike is $180/3 = $60 and you still control $18,000 worth of stock. The price of the option will drop to $6/3 = $2 and the value of your options is still $600.

Now let’s look at how fractional splits affect your option contracts. Recall that fractional splits are anywhere the split ratios have a last digit greater than one, such as 3:2 and 5:4, and 8:7 for example. Fractional splits affect options in a similar way as the whole number splits we just reviewed. However, they create a small problem because the number of shares is not increased in units of 100. To alleviate the problem, the exchanges decided to adjust the number of shares each contract controls.

For instance, if you own one $180 call trading for $6 and the stock does a 3:2 split then the split ratio is 3/2 = 1/5. After the split, you will still own one contract; however, it will now control 150 shares of stock and the strike price will be $180/1.5 = $120. After the split, you still control 150 shares * $120 = $18,000. In this case, the “multiplier” is increased to 150 since that is how many shares the option controls. The option’s price will fall to $6/1.5 = $4. So if you see this option quoted at $4, you must remember to multiply it by 150 to find its total value.

If the stock does a 5:4 split then the split ratio is 5/4 = 1.2. After the split, you will own one contract that controls 100 * 1.2 = 120 shares with a strike price of $180/1.2 = $150 and you will still control 120 * $150 = $18,000 worth of stock. The option’s price would fall to $6/1.2 = $5. All options, calls and puts, are adjusted in the same way. In addition, all short positions are adjusted in the same way as the long positions. After all, the short position is simply on the other side of the trade from the long position.

For any “whole number” split (2:1, 3:1, 4:1 etc.) the number of contracts you own increases by the split ratio. The multiplier stays the same.

For any “fractional” split, (3:2, 5:4, 8:7, etc.) the number of contracts stays the same but the number of shares it controls is multiplied by the split ratio.

The market price of the stock, the strike price of your option, and the market value of the option are always reduced (divided) by the split ratio regardless of the type of split.

The following chart may help you to see the differences. Notice that the procedures for the strike price and market price are the same regardless of the type of split.

Reverse Splits
There is another type of split called a reverse split, which is done for the opposite reasons of a stock split. Companies whose share price is very low may vote for a reverse split to lift the price in hopes of getting it “recognized” as a viable investment. Many times this is done so that the company meets certain listing requirements in order to trade on a nationally recognized exchange.

Reverse splits are most often seen in the penny stocks or other troubled stocks looking for a boost in price (and hopefully awareness). Because of this, you will rarely see reverse splits on optionable stocks since they must be above $10 to meet listing requirements to trade options. However, they can occur. If they do, the math previously described works exactly the same way but in the reverse direction.

For example, assume that XYZ is trading for $4. The company may vote for a 1:3 reverse split. The split ratio is then 1/3 = 0.33. This just means that shareholders will receive one share for every three they currently own and the price will rise by a factor of three. If you own 300 shares today, you have $1,200 worth of stock. After the split, you’ll have 300 * 0.33 = 100 shares after the split. The stock price will rise to $4/0.33 = $12. Once again, this doesn’t affect any the value of your position because the value of your position will still be $1,200 after the split.

Let’s see how the reverse split would affect your option contracts. Assume you own 20 XYZ $10 calls trading for $1 and the company announces a 1:5 reverse split. The split ratio is 1/5 = 0.20. The number of contracts you own is now 20 * 0.2 = 4 and the strike price is increased to $10/0.20 = $50. The price of the option rises to $1/0.2 = $5. Let’s check the math to make sure we got the right answer. The original position was worth $1 * 20 contracts * 100 shares per contract = $2,000 and had an exercise value of $10 * 20 contracts * 100 shares per contracts = $20,000. After the split, it is worth $5 * 4 contracts * 100 shares per contract = $2,000 and the exercise value is 4 contracts * $50 * 100 shares per contract = $20,000. Nothing has changed; only the packaging.

Whenever an option undergoes an adjustment, you’ll probably see a notation stating “adjusted option” or “adj opt” while placing the trade. You may see this in the final “readback” screen where you verify the order before sending it, or you may see it next to the symbol when looking up symbols. Whenever you see this notation, be sure to check the number of shares it controls.

For example, when we get to strategies, we will talk about the “covered call” where we will buy 100 shares of stock and then sell one call controlling 100 shares. If you inadvertently sell a call that controls 150 shares rather than 100 there could be potential problems if the stock price rises substantially. That’s because you own 100 shares but may have to deliver 150 shares if the stock’s price rises above the strike. In essence, you would be short 50 shares of stock.

Just as you should develop habits of checking option symbols when entering orders, you should also check to see if the total cost of the trade is roughly what you think it should be before sending the order. For example, assume you are placing an order to buy one ABC $50 call trading for $4. If you place an order to buy one contract and the computer tells you the estimated cost of the trade is more than $600 including commissions, you should realize that something isn’t right. One contract at $4 should cost $400 plus commissions, so the $600 price is obviously too high. Assuming you entered the right quantity (one contract) you can be sure this discrepancy is a sign that you’re dealing with an option that controls 150 shares.

To be continued…….

By the way, you can always find out which contracts will be available for any stock going to www.cboe.com and then clicking on “Trading Tools” and then “Cycles and Strike Month Codes.”

You can also find similar tools at the homepage for the Options Industry Council (OIC) at www.888options.com. Click on “Tools and Literature,” “Pricing Calculators,” and then “Cycles.”

Double, Triple, and Quadruple Witching
Now that you understand option cycles and how the contract months are determined, let’s talk about the terms double witching or, more commonly, triple witching. These are days when multiple derivative products expire on the same day. For example, if stock futures, stock index options, and stock options all expire on the same day then that is a triple-witching day. Typically, stock futures expire on the quarterly expiration (the last month of each quarter) months of March, June, September, and December so triple witching occurs only in these months. Double witching occurs when any two of the three assets expire at the same time. Less commonly knows is quadruple witching, which occurs when single-stock future contracts expire on the same day as well. It is widely believed that volatility in the market is much greater on these days as traders scramble to close positions. The truth is that few professional traders wait until the very last day to close positions, so these witching days are probably not as disruptive as many believe. Still, it is worth knowing what these terms mean as you will definitely hear them once you start trading or investing in options.

Contract Size (The Multiplier)
In the first chapter, we said that options generally cover 100 shares of stock. In this section, we’re going to show you why we said “generally.” When options first start trading, the contract size is always 100 shares. This 100 share-sized lot is also referred to as the multiplier because that is the amount we must multiply the option premium by to find the total cost of the contract. For example, if a call option is asking $3, you will pay $3 * 100 = $300 (plus commissions). It is also the amount we must multiply by to find the total contract value. If you exercise a $30 call, you will pay $30 * 100 = $3,000 and receive 100 shares of stock. So the “contract size” and “multiplier” are two different ways of expressing the unit of trade of the option.

While all options start with a contract size of 100, there are corporate actions that can change that. The most common event is a stock split. Stock splits generally occur when the price of the stock is perceived to be too high, so the company will split the stock to bring down the price.

A stock split is really a cash dividend, which means the company pays you a dividend in shares of stock rather than cash. With a 2:1 stock split, the company pays you one share of stock for each that you own thus doubling the number of shares you own.

However, because the company is paying a dividend (whether in cash or shares) the price of the stock must be reduced to reflect the fact that some value of the company has been paid out to shareholders. A stock split therefore will always increase the number of shares outstanding (and therefore in your account) and the stock price will always fall.

How many shares will you have and by how much will the stock price fall? These
questions are easy to answer once you understand the mechanics of a stock split. Any time a split is announced, it is always reported as the ratio of two numbers such as 2:1. If you take the first number divided by the second, you get the “split ratio,” which is 2 for this example. The number of shares will always be multiplied by this ratio and the stock price will be divided by the same number.

There are many types of splits with 2:1 being the most popular. However, you will also see variations such as 3:1, 4:1 and so on. We will refer to these as “whole number” splits since you always end up with multiple 100-share lots after the split. In addition to whole number splits, you may see “fractional” splits such as 3:2, 5:4, 8:7, and so on. Any split ratio where the second number is greater than one creates a fractional split. These types of splits increase the number of shares you own just as whole number splits; however, that new number will not be evenly divisible by 100. For instance, a 3:2 split means that you will receive 3 shares for every 2 that you have thus increasing the number of shares by 50%. If you had 100 shares prior to the split, you will have 150 shares after the split. A 5:4 split leaves you with 125 shares for every 100 shares you previously held.

For instance, assume ABC stock is trading for $180 per share. At this price, the company may think its share price is too expensive as it is difficult for many investors to buy shares, at least in round lots of 100, since that will cost $18,000. In order to bring the price per share down, the company may announce a 2:1 split. If you own 100 shares of ABC prior to the split, you will own 200 shares at a price of $90 after the split. Notice that we multiplied the number of shares by two (split ratio) and divided the price by two as well.

Because we doubled the number of shares but cut the price in half, the total number of dollars invested does not change. If you have 100 shares of ABC at $180, then the position is worth $18,000. After the split, you’d have 200 shares at $90, which is still $18,000 worth of stock.

A 3:1 stock split would give you 300 shares at a price of $60 per share after the split ($18,000 worth of stock). A 4:1 split yields 400 shares at a stock price of $45 ($18,000 worth of stock).

Now let’s take a look at some fractional split examples. If the same stock had a 3:2 split, then the split ratio is 3/2 = 1.5. If you had 100 shares prior to the split, you’d have 100 * 1.5 = 150 shares after the split and the price would fall to $180/1.5 = $120. Again, notice that after the split you still have 150 shares * $120 = $18,000 worth of stock. A 5:4 split provides a split ratio of 5/4 = 1.2 so you’d end up with 100 * 1.2 = 120 shares at a price of $180/1.2 = $150 per share. In both of these cases, you still own $18,000 worth of stock.

So a stock split doesn’t change the total value of your investment but only the way in which it’s packaged. It’s no different than when you exchange one $10 bill for two $5 bills. You have twice as many pieces of paper (shares) at half the value so the total value of your wallet hasn’t changed. When viewed in this light, stock splits aren’t really a big deal even though they are often met with much fanfare by the investing public. After a stock split, it is true that the company may create more demand by the public to own it and that certainly can put upward pressure on the price. However, the stock price is now twice as hard to move because there are twice as many shares outstanding, so there are drawbacks to splitting a stock. But regardless of whether stock splits are good or bad, they do occur and they can change the contract size.

To be continued,,,

LEAPS
As options gained in popularity, investors showed an interest in choosing from contracts that included longer times to expiration. In 1990, the CBOE answered by creating LEAPS. While the name makes them sound complicated, they are simply options but with longer lives. LEAPS is a registered trademark of the Chicago Board Options Exchange and stands for Long-term Equity AnticiPation Securities (as if that wasn’t obvious) and have expiration dates nearly three years in length.

When options first started trading, they were available for up to nine months in the future. But with the addition of LEAPS, you can find options nearly three years forward. If a stock has LEAPS options traded, there will be more than four contracts listed at any given time. So while your local newspaper or other sources may only print three expiration months to conserve space, understand that there are always at least four different contract months traded at any given time.

How do option cycles work with the addition of LEAPS? Once you understand the basic option cycle, adding LEAPS into the rotation is not too difficult.

As mentioned earlier, LEAPS usually trade in January for a maximum of three years forward although there are exceptions. If a stock trades LEAPS, then new LEAPS will be issued sometime between May and July. This is difficult to explain without the use of examples so let’s go back to our Intel options.

It is currently July ’05 and Intel has the following months trading: July, August, October, January ’06, January ’07, and January ’08 as shown by the “Xs” in the table below:

At this point, January ’07 and January ’08 are LEAPS contracts. The January ’06 is considered a quarterly contract since it is less than nine months until expiration.

When July expires, September will be added. We will then have August, September, October, and January ’06, thus providing four months of regular contracts (nine months or less):


At the same time, the January ’07 contracts will lose their LEAPS designation because they have less than nine months to expiration. The root symbol will change to show that it is no longer a LEAPS option. If you are holding this option, the symbol will automatically change in your account and there is nothing that you need to do. Just be aware that this can happen as some investors are puzzled when there is a symbol change on some of their LEAPS. This will happen in May, June, or July when the current year LEAPS option becomes a regular option. This process is called melding. Melding is when LEAPS options become regular options. Technically speaking, LEAPS options do not expire; instead, they meld to a regular option and then it is the regular option that expires.

So, depending on which cycle your stock is on, look for new LEAPS to be added sometime in late May, June or July.

Which Cycle Is My Stock On?
As mentioned earlier, there will be times when you will need to know when a particular month will be added to the list. Before you can find out, you will need to know on which cycle your stock is traded. This is easy to find out once you understand the expiration cycles. For example, let’s see if we can figure out which cycle Intel is on. It is now July and Intel has the following months being traded:

• July
• August
• October
• January ‘06
• January ‘07
• January ‘08

From what we learned earlier, we know there must be a July and August contract and we see that there is. You can never tell which cycle a particular stock is on just by looking at the first two months, since all options will have these months being traded. But we can find out which cycle the stock is on by looking at the third month and fourth months. The reason we cannot just look at the third month is that it may be January and we would not be sure if it is a LEAPS contract or not. In this case, the third month is October:

• July
• August
• October
• January ‘06
• January ‘07
• January ‘08

Now we just need to ask which cycle October falls under? It is part of the January cycle (it is the first month or the “January “position of the fourth quarter). So we just figured out that Intel trades on a January cycle.

Let’s try another. Which cycle is Dell Computer on? It is still July and Dell has the following contracts traded:

• July
• August
• November
• January ‘06
• February ‘06
• January ‘07
• January ‘08

Once again, we know that the current and following month must be traded for all stocks so the first two months tell us nothing about which cycle the stock is on. However, the third month is November and that does reveal the cycle. Because that month is November, we know that Dell Computer trades on a February cycle (because November is the middle month or “February” position of the fourth quarter).

• July
• August
• November
• January ‘06
• February ‘06
• January ‘07
• January ‘08

Let’s try one more example but this time we’ll show why you cannot consider January if it falls in the third month. We’ll still use Dell Computer but now assume that the July options have expired. If so, we’d see the following contracts traded:

• August
• November
• January ‘06
• February ‘06
• January ‘07
• January ‘08

We know to not look at the first two month of August and November since all stocks will have those months listed. However, in this instance, if we look at the third month, we’d find January and we’d be led to believe that Dell is on a January cycle. Remember, all stocks that have LEAPS options will have them listed in January so we cannot be sure if this is a January cycle stock or not. To be sure, we’d need to move down to the fourth month, which is February and now we know that Dell is on a February cycle. In order to find which cycle your stock is on, you can never do so by looking at the first two expiration months. All stocks have those months traded. You must find the next quarterly contract (with the exception of January) that is listed and that will guide you to the cycle on which your stock is traded. Once you know which cycle your stock is on, it never changes. You will always be able to determine which months will be traded and which will be added at expiration.

To be continued,,,

Every time you enter an option order, go through the motions of checking those last two letters and the patterns will eventually become second nature. With one quick glance, you will know the month, strike, and type of option (call or put). It is a relatively simple thing to learn over time and it will increase your confidence and speed at which you can enter an order.

Option Expiration Cycles
As you start trading options, you will notice that not all stocks have the same expiration months available. For example, it is now July and Dell Computer has November options listed but Intel does not. Why is that? When will November options become available for Intel? In order to answer these questions, you need to understand option expiration cycles. Understanding the expiration cycles is important for option traders and investors; you might wish to trade an option in a particular month and find that it is not available. Obviously, it would be nice to figure out when it will start trading.

When options started trading in 1973, the Chicago Board Options Exchange (CBOE) decided that there would only be four months of equity options traded at any given time. (This is one of the limitations of having standardized contracts that we talked about in Chapter One.)

Originally, all optionable stocks were assigned to one of three cycles: a January, February or March cycle. (These cycles are also called Cycle 1, Cycle 2, and Cycle 3, respectively.) The assignment was purely random and had nothing to do with earnings cycles of a company or any other reason you might hear; it was purely a random assignment.

Under the original rules, A January cycle (Cycle 1) meant that options would have expirations matching the first month of each quarter. So if a stock were assigned a January cycle, options on that stock could only have the first months of each quarter available:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

A February cycle stock could only have option expirations for the middle months of each quarter available:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

And, of course, the March cycle would have expirations for the end months of each quarter available:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Because these expirations are arranged at equal intervals in each quarter, they were called quarterly expirations. Because of these positions, sometimes you will hear the cycles referred to as front-month (January), mid-month (February) or end-month (March) cycles. Once a stock is assigned a particular cycle, it does not change. For example, a January-cycle stock always trades as January-cycle stock.

As we just showed, when options started trading in 1973, if you were deciding on an option to buy on a January-cycle stock, you would only have four months to choose from: January, April, July, and October. For a February-cycle stock, you would only have February, May, August, and November expirations to choose from. A March-cycle stock would only have March, June, September, and December expirations.

As options gained in popularity, traders were looking for ways to trade or hedge with shorter-term options, which weren’t always available due to the way the cycles were structured. For example, assume it is now January and you were trading options on a January-cycle stock. If you did not want to trade the January expiration then the next month available would be the April contract – more than three months into the future. To insure that there would always be shorter-term options, the CBOE decided to change the rules around 1984.

New Rules Create Shorter-Term Contracts
Under the new rules, there would still be four option expiration months listed at any given time but two must be reserved to represent the current month and the following month (these two contracts are also called the “front month” and “near-term” contracts, respectively). The remaining two months would remain from the original quarterly cycle. The current and following months are referred to as serial months.

Let’s take a closer look at how these rules work. Assume it is now January and we are looking at a stock that trades options on a January cycle. Which months will be traded under the new rules? Remember, under the new rules, the CBOE decided that there would always be the current month plus the following month available. Because it is January in our example, then January and February must be available. Because four months must trade, the remaining two months will be from the original quarterly cycle, which would be April and July:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

So if it was now January and we were looking at a stock that was assigned a January expiration cycle, we would find January, February, April, and July options to choose from. January and February are the serial months (or the serial contracts) while April and July are the quarterly contracts.

What happens when January expires? Looking at the expiration months above, you can see that when January contracts expire we will be left with only three expiration months: February, April, and July. However, we know that we must have four expiration months listed and we also know that we must have February and March listed. This means the March expiration must be added to the list:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

After the March contracts are added, we have four contracts with the current month (February) and following month (March) on the list – exactly what the new rules say we should have.

When February expires, we are left with only three contracts: March, April, and July. However, this time we do have the current month and following months available by default (March and April). Even though April was originally issued as a quarterly contract, it now serves as a serial month. So once February expires, we will add the next quarterly contract, October, to the list:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Once the October contracts are rolled out, we are left with the current month plus following month (March and April) along with two quarterly contracts (July and October).

This pattern continues regardless of which cycle we’re on. The current month and the following month must always be made available. No matter which cycle a stock may be trading, it will always have the current month and following month contracts available. The remaining two contracts will be from the corresponding quarterly cycle.

One problem many investors face is trying to figure out when a particular contract will be traded. For instance, let’s continue with our above example using the January cycle and see if we can figure out when the November contract will be traded. This is easy once you understand option cycles. The first thing you want to ask is this: Is November one of the January cycle months? No, it is part of the February cycle. This means that November can never be added to the list unless it is a serial month. It can never be added months in advance as a quarterly contract. The only time it will become available is when October starts trading (September contract expires). When September expires, October will be the current contract and November will be added to the list as a serial contract.

If you work through the steps outlined above, you will see that the January contract will start trading when May expires. Once May is expired, June will become the current month, so there will be a June, July and October for a total of three months. The fourth month will be the addition of January. The steps are outlined in the following box:

We started with April, May, July and October contracts traded and wonder when the January contract will begin trading:

To be continued….

The first three chapters introduced you to options, critical pricing principles, and profit and loss diagrams. With these tools, you now understand what an option is, how its price behaves and why, and how to read what the profits or losses will be at various stock prices. Our next step is to dive into the market mechanics of options. In this chapter, you will discover practical skills on placing orders, reading symbols, understanding option cycles, trading between the bid and ask, leaning against the book, stock splits, and many other topics you need to master options trading. Let’s start by taking a look at option symbols.

Option Symbols
In Table 1-1, we saw that each option has a unique identifying symbol. For example, the symbol for the July $32.50 call was XBAGZ. Although the letters may appear random, there is actually an organized structure to their makeup. Understanding the symbol structure is important for one critical reason. It serves as a backup that you have, in fact, entered the correct symbol for your option order. Believe it or not, entering the wrong symbol is one of the top mistakes year after year for retail traders (and brokers as well). Most of the time this is due to a simple typing mistake; however, many of these could have been prevented had the traders understood option symbols. Entering wrong symbols creates numerous problems. First, you must pay extra commissions to get out of the wrong trade and into the correct one. Second, the erroneous trade may move against you and thus provide a loss in addition to the extra commissions. Third, you may miss out on any favorable price movement in the option intended to buy. All of these provide reasons for understanding option symbols. In this section, we’ll take a closer look at how these symbols are created and what they mean.

All option symbols follow the format of XXX – MS where “XXX” represents the root symbol. The root symbol is a code that identifies the underlying stock and can be any length from one to three letters. The “M” designates the “month” and “S” tells us the strike price. When you are learning option symbols, train your eye to look at the last two letters of any option symbol; they represent the month and strike, respectively. All other letters make up the root symbol.

If a stock is listed on an exchange such as the New York Stock Exchange or American Stock Exchange for example, the root symbol will usually be the same as the ticker symbol. It is easy to spot a listed security as it will always have a symbol of three or fewer letters. So IBM, GE, and T are all listed securities, and their option root symbol will usually be the same as the stock ticker (although it may be different from splits, mergers, or acquisitions).

For any Nasdaq-traded stock (any stock with four or more letters in the ticker symbol), the option root symbol will usually be reduced to three letters. In many cases it will be similar to the original symbol but with the addition of the letter “Q” to designate Nasdaq. For example, the root symbol for DELL is DLQ, INTC is INQ, and MSFT is MSQ.

Once you have the root symbol, it is fairly easy to find the letters that represent the month and strike. For call options, the letters A through L (the first 12 letters of the alphabet) represent each month of the year. For puts, the letters M through X (letters 13 through 24) are used:

Obviously, this pattern can continue for stocks priced higher than $200. In addition to the above letters strikes, the letters U through Z are usually reserved for $2.50 strike intervals:

It may look confusing but it is actually very easy. Say you want to buy a Microsoft October $45 call. The root symbol is MSQ. The October call symbol is J and the $45 strike symbol is I. So the call option symbol for the option will be MSQJI. Of course, you are not expected to drum up this symbol on your own to enter the trade. When you are looking at a list of option quotes, they will have the symbols listed as in Table 1-1. Most brokerage firms allow you to click on the option to enter an order on that specific option, which means the symbol is automatically entered for you. However, it is still possible to click on the wrong one. Further, some brokers require that you type the symbol into its own field when entering the order. And there is obviously lots of room for error there. Understanding how option symbols are created can keep you out of trouble. If you were comfortable with the symbol construction, you would realize that the letters “JI” in this example represent an October $45 call and this serves as a double check for your order. Just understanding the last two letters will tell you three important pieces of information. They tell you the month, strike, and option type (call or put). Even as a basic check, if you are buying a call option, you know that the “month” designator (second to the last letter of the option symbol) should fall between A and L. If you’re buying a put, that letter should fall between M and X.

Remember, this is only a guideline. You should always check with your broker or with some of the resource sites at the CBOE (www.cboe.com) if you are unsure about an option symbol. The reason is that option root symbols change for different reasons.

Standard root symbols and strikes can change for a number of reasons but splits, mergers, acquisitions, and special dividends are probably the most common. For example, on July 30, 2004, Microsoft declared a special $3 dividend and the option strike prices and root symbols were adjusted to reflect this payment. If any option you are holding goes through a symbol change, it will automatically change in your account. The main point is that you should always check your symbols before entering the trade. Just because MSQ may have been the root symbol for Microsoft while you were last trading those options does not mean that it is still the same the next time you trade. This is especially true if the stock has made recent highs or lows and new strikes are being rolled out. For example, JDS Uniphase (JDSU) currently uses UQD for strike prices up to $65, XXZ for strikes $70 to $90, UCQ for $95 to $140, and YSU for strikes $145 and higher. Don’t try to memorize all the root symbols or to construct them on your own based on past experience. Use your understanding of option symbols covered in this section as a backup measure to ensure you have entered the correct symbol.

As mentioned before, entering the incorrect symbol is always one of the top three errors – even among professional brokers (the others are wrong quantity and wrong action (buy versus sell). With today’s low commissions and traders entering their own orders online, brokers are very unforgiving if you enter a wrong symbol.

Try the following few examples to make sure you have the hang of it. Which options do the following symbols represent? Remember, the last two letters always represent the month and strike. The remaining letters represent the underlying stock, which you will probably recognize. If not, at least try to figure out the month, strike, and whether it is a call or put:

1) FAH
2) DLQOE
3) IBMCE
4) GEXD
5) XBAHH (Hint: “XBA” is the root symbol for eBay)

Okay, let’s see how you did:

1) FAH. We know that all option symbols use the last two letters to designate the month and strike. In this example, we only have one letter remaining, which is F and that must be used to designate the underlying stock. The symbol F is for “Ford” so this symbol represents the Ford January $40 call.
2) DLQOE. We said earlier that DLQ is the root symbol for Dell Computer. This option represents the Dell March $25 put.
3) IBMCE. The last two letters represent the month and strike, so the remaining IBM letters are used for the underlying stock, which is obviously IBM. This represents the IBM March $125 call. (IBM was trading near $125 at the time so the letter “E” would represent $125 rather than $25.)
4) GEXD. Again, the last two letters are used for the month and strike, which means that only GE remains to identify the underlying stock, which is obviously General Electric. This option represents the GE December $20 put.
5) XBAHH. We are told that XBA represents eBay and the last two letters tell us this is an August $40 call. Table 1-1 is reprinted below and you can see that this is the symbol for the August $40 call. (Recall that the “dash E” represents the exchange, which is the CBOE and is not part of the symbol.)

To be continued….

Chapter Three Answers

1) What is a profit and loss diagram?
b) A picture of your profits or losses at various stock prices
Profit and loss diagrams provide a picture of where profits and losses will occur at various stock prices. Further, they show the size of those profits and losses.

2) One of the most insightful observations we can get from profit and loss diagrams is that:
a) No strategy is superior to another for all stock prices
For any two strategies, you will always find that neither is superior to the other across all stock prices. Profit and loss diagrams clearly show that no strategy is superior to another in all respects. It is up to the investor to figure out which attributes are desirable based on the outlook.

3) For any profit and loss diagram, the area that lies above zero represents:
b) The potential rewards
Profit and loss diagrams show us the range of potential rewards and potential losses. All areas that lie above the horizontal “zero” line (the breakeven point) represent gains.

4) Which two pieces of information do you need to construct any profit and loss diagram?
d) How much the asset is worth at various stock prices and the price paid for the asset
Profit and loss diagrams are constructed by plotting the various profits or losses against various stock prices. Because of this, we must know how much the asset (option) is worth at the various stock prices as well as the price paid for the asset (option).

5) The profit and loss diagram for a long stock position shows that:
a) Long stock positions carry a large amount of downside risk
Profit and loss diagrams show that long stock positions carry unlimited downside risk – all the way down to a stock price of zero. Options, on the other hand, have a limited amount of downside risk.

6) When drawing profit and loss diagrams without theoretical values, you always calculate the option values:
c) At expiration
Because we don’t know the values of a particular option prior to expiration, we usually draw profit and loss diagrams based on the option values at expiration. At expiration, we know that an option must be worth either zero or the intrinsic value. If you wish to plot a profit and loss diagram prior to expiration, you must use a theoretical pricing model to generate option values. Profit and loss diagrams drawn prior to expiration are almost always generated by a computer.

7) The breakeven point for any profit and loss diagram is always where:
d) The curve crosses the horizontal axis at zero
If the profit and loss diagram crosses the “zero” axis, then that tells you that the position produces no profit or loss. In other words, it breaks even at that point.

The profit and loss diagram for a long call option shows that:
d) Long calls have limited downside risk and unlimited upside potential

9) The area below the zero horizontal axis for any profit and loss diagram represents:
b) The risk
Any space below the “zero” horizontal mark represents losing territory so it therefore represents the risk of that position at various stock prices.

10) For any profit and loss diagram, a “bend” will occur at:
b) Every strike price
Because options create rights or obligations, there are changes that occur at each strike price of any profit and loss diagram.

11) If you compare any two strategies, you will always find there are points where the two intersect. These intersections are called:
b) Crossover points
Crossover points simply show where the two strategies are equal. You will always find that one strategy does better than the other to the right of the crossover and vice versa.

12) The profit and loss diagram for a long put shows that:
a) Long puts have limited upside risk
The risk of short-selling a stock is the unlimited upside risk. Option traders can effectively short stock without this risk by simply buying a put.

13) Which of the following best summarizes the reason for using profit and loss diagrams?
a) They allow you to clearly see the risks and rewards for any strategy

14) The axes for any profit and loss diagram are always:
d) Vertical = profit and loss; Horizontal = stock price

15) Profit and loss diagrams show that the profit to the long position is exactly the loss to the short position and vice versa. This is another way of saying that options are:
c) A zero-sum game
A zero-sum game is any game where one person wins at the loser’s expense. If you make a $5 profit on an option then somebody had to lose $5 on that same option. In the options market, money simply shifts hands from the losers to the winners. No new capital is created in the market by using options (but none is destroyed either).

16) The profit and loss diagram for a long call position shows that:
a) Long calls have limited downside risk
Profit and loss diagrams easily show that call options have limited downside risk, which is one of the biggest advantages of owning call options.

17) If you plot the profit and loss diagram for a $50 call purchased at $4, it will cross the zero line at:
a) $54
The breakeven point for a $50 call purchased at $4 is $54. As learned in the first chapter, the reason is that if the stock is $54 at expiration, the $50 call would be worth exactly the $4 intrinsic value. Because the zero line represents the breakeven point, the profit and loss diagram would cross zero at $54.

18) If you plot the profit and loss diagram for a $100 put purchased at $3, it will cross the zero line at:
b) $97
The breakeven point for a $100 put purchased at $3 is $97. Put options become more profitable as the stock falls. In this case, the stock must fall $3 by expiration just to break even. If the stock is $97 at expiration, the $100 put will be worth exactly $3. Because you paid $3 for it then you would just break even at this stock price.

19) If you plot the profit and loss diagram for a $50 call sold at $4, it will cross the zero line at:
a) $54
Remember that options are a zero sum game. Therefore, the breakeven points for the long and short position must be the same. If you sell a $50 call at $4, you’d receive $4 up front but would have the obligation to sell stock for $50. If the stock is $54 at expiration, you’d have a $4 loss since you’d have to buy stock for $54 and deliver it for only $50. Because you received $4 up front, you’d just break even at a stock price of $54.

20) If you plot the profit and loss diagram for a $100 put sold at $3, it will cross the zero line at:
b) $97
As with Question 19, options are a zero sum game, which means the breakeven points for the long and short position must be the same. If you sell a $100 put at $3 you’d receive $3 up front but would have the obligation to buy stock for $100. If the stock is $97 at expiration, you’d have a $3 loss since you’d have to buy stock for $100 that is only worth $97. Because you received $3 up front, you’d just break even at a stock price of $97.

To be continued…

1) What is a profit and loss diagram?
a) A picture of the maximum losses
b) A picture of your profits or losses at various stock prices
c) A picture of the breakeven points
d) A picture showing the risks and rewards of long stock

2) One of the most insightful observations we can get from profit and loss diagrams is that:
a) No strategy is superior to another for all stock prices
b) Long call options are definitely better than long stock positions
c) Call options have no risk
d) Some option strategies perform better than others for all stock prices

3) For any profit and loss diagram, the area that lies above zero represents:
a) The potential losses
b) The potential rewards
c) The breakeven point
d) The value of the contract if exercised

4) Which two pieces of information do you need to construct any profit and loss diagram?
a) The breakeven point and the price at which the asset was sold
b) The price paid for the asset and the price at which it was sold
c) The price paid for the asset and the breakeven point
d) How much the asset is worth at various stock prices and the price paid for the asset

5) The profit and loss diagram for a long stock position shows that:
a) Long stock positions carry a large amount of downside risk
b) Long stock has an asymmetrical payoff
c) Long stock has multiple breakeven points
d) Long stock has little reward

6) When drawing profit and loss diagrams without theoretical values, you always calculate the option values:
a) Based on the bid-ask spread
b) Prior to expiration
c) At expiration
d) By subtracting the delta from intrinsic value

7) The breakeven point for any profit and loss diagram is always where:
a) The curve bends at the strike price
b) The curve lies above zero
c) The curve lies below zero
d) The curve crosses the horizontal axis at zero

The profit and loss diagram for a long call option shows that:
a) Long calls have two breakeven points
b) Long calls have a symmetrical payoff
c) Long calls are better than long stock
d) Long calls have limited downside risk and unlimited upside potential

9) The area below the zero horizontal axis for any profit and loss diagram represents:
a) The strike price
b) The risk
c) The reward
d) The breakeven point

10) For any profit and loss diagram, a “bend” will always occur at:
a) Every breakeven point
b) Every strike price
c) The maximum gain
d) The maximum loss

11) If you compare any two strategies, you will always find there are points where the two intersect. These intersections are called:
a) Breakeven points
b) Crossover points
c) Maximum gain points
d) Maximum loss points

12) The profit and loss diagram for a long put shows that:
a) Long puts have limited upside risk
b) Maximum upside risk
c) Long puts have two breakeven points
d) Make money if the underlying stock rises

13) Which of the following best summarizes the reason for using profit and loss diagrams?
a) They allow you to clearly see the risks and rewards for any strategy
b) They can locate superior strategies
c) They allow you to reduce your losses
d) They help you find undervalued stocks

14) The axes for any profit and loss diagram are always:
a) Vertical = option theoretical value; Horizontal = option price
b) Vertical = option price; Horizontal = option theoretical value
c) Vertical = stock price; Horizontal = profit and loss
d) Vertical = profit and loss; Horizontal = stock price

15) Profit and loss diagrams show that the profit to the long position is exactly the loss to the short position and vice versa. This is another way of saying that options are:
a) A way to create wealth in the markets
b) More lucrative by selling
c) A zero-sum game
d) A losing proposition

16) The profit and loss diagram for a long call position shows that:
a) Long calls have limited downside risk
b) Long calls have unlimited downside risk
c) Long calls are superior to long stock for all stock prices
d) Long calls have no downside risk

17) If you plot the profit and loss diagram for a $50 call purchased at $4, it will cross the zero line at:
a) $54
b) $50
c) $4
d) $46

18) If you plot the profit and loss diagram for a $100 put purchased at $3, it will cross the zero line at:
a) $100
b) $97
c) $103
d) $3

19) If you plot the profit and loss diagram for a $50 call sold at $4, it will cross the zero line at:
a) $54
b) $50
c) $4
d) $46

20) If you plot the profit and loss diagram for a $100 put sold at $3, it will cross the zero line at:
a) $100
b) $97
c) $103
d) $3

If the stock price is: At expiration,
$50 put is worth: $50 put cost Profit/Loss
$35 $15 $3 $12
$40 $10 $3 $7
$45 $5 $3 $2
$50 $0 $3 -$3
$55 $0 $3 -$3
$60 $0 $3 -$3
$65 $0 $3 -$3
Let’s now draw a profit and loss diagram for a long $50 put position purchased for $3. Hopefully, you’re starting to understand the steps and realize that we need to know what the $50 put would be worth for various levels of the stock at expiration. Second, we need to know the cost of the put. With those two pieces of information, we can draw the profit and loss diagram. We’ll start by making a profit and loss table to show us the various values for our chart:

Table 3-11: Profit and Loss Table (Long $50 Put)
The explanations of the numbers in this table should be fairly obvious to you now. Reading across the first row, if the stock price is $35 at expiration, the $50 put is worth exactly $15. Because we paid $3 for it, we have a $12 profit. For all stock prices above $50, the put expires worthless and we lose our $3 investment. If we plot the profit/loss values against the stock prices, we get Figure 3-12:

We can see in this chart that long put options gain value as the stock price falls, which tells us this is a bearish position. The chart “bends” at the $50 strike price and all area to the right of $50 results in a maximum loss while all area below the $47 break-even brings a profit. Remember, the breakeven for a put option (long or short) is found by taking the strike minus the premium. In this case, a $50 strike – $3 premium = $47 breakeven. The trader who buys a $50 put for $3 needs the stock to be below $47 at expiration in order to profit. Now, this does not mean that a profit cannot be made prior to expiration even if the stock never falls below $47. The reason is that quick movements in the stock can cause the option to increase in price even if the stock is not below the strike price. It is certainly possible that we pay $3 for this put and the stock quickly falls to $49, which makes the put worth more money. However, remember that these charts are drawn “at expiration” and that’s why Figure 3-12 shows that we need to have the stock below $47 in order to make a profit.

As we stated before, profit and loss diagrams are invaluable for understanding strategies or comparing different strategies. We have just looked at two simple strategies, a long $50 call purchased for $5 and a long $50 put purchased for $3.

Let’s make a small change and see if you can answer a tricky question. Which do you think is better, a long $50 call for $5 or a short $50 put for $3? Many traders might be led to believe that the long call is a superior strategy since it makes more money if the stock rises and loses less if the stock falls. What do you think is the correct answer? Hopefully you now understand that by checking the profit and loss diagrams for each, the answer will be readily apparent. Figure 3-13 shows the two strategies plotted on the same chart:

Now it is easy to see that the long call is not superior over all ranges. Yes, it’s true that the long call makes more money if the stock rises substantially and loses less if the stock falls substantially. However, we can see there are two crossover points at $42 and $58. (Recall that the crossover points are where the two graphs intersect.) This means that the short put will be the superior strategy if the stock closes between $42 and $58 at expiration. And because the stock is currently $50, that is an eight-point swing, or 16%, on either side of the current price, which is a pretty big move. So even though the long call may have some nice qualities in that it makes more than the short put if the stock rises and loses less if it falls, those qualities come at a price. In this example, that price is that the stock must rise or fall more than 16% in order to beat the short put strategy. Once again, note how easy this is to see when you look at a picture rather than trying to figure it out in your head or by hand.

Profit and loss diagrams can also show one of the most fateful characteristics about options. If you look at Figure 3-14, you’ll see the profit and loss diagram for a long $50 call at $5 (solid line) and a short $50 call at $5 (shaded line).

Notice that the two profit and loss lines are mirror images of each other; that is, the gains to one trader are exactly the losses to the other. We say that options are a zero-sum game, which simply means that no new money is created in the markets by their use as there is for stock. For instance, if Intel rises one dollar, then all holders of stock make money. The increase in the value of the stock creates wealth for all investors. There will be some speculators who will lose from the increase in share price; however, the number of short sellers is far less than the number of stock owners. Remember that corporations issue physical shares of stock and there are far more people who own those shares than are short. Therefore, an increase in the stock’s price creates overall wealth to stockholders. Option contracts, however, are not issued by the company. For the options market, it takes a long and short position to create a contract, and that’s why options are a zero-sum game. If Intel rises one dollar, then all long call owners benefit at the expense of the short call writers.

At the same time, Figure 3-14 shows that options do not create a “black hole” where money is funneled out of the financial system inevitably leading to its collapse, which is a theory that many steadfastly believe. Instead, money just shifts from the pockets of the losers to those of the winners. The options market only redistributes the wealth but it does not destroy it.

Let’s revisit a question we posed at the beginning of this chapter: Why do we have an options market? The reason is that the “risk” one investor is trying to avoid by purchasing options might be willingly accepted by the investor who sells the option. For example, if you wish to speculate on a fall in the stock’s price, you might buy a $50 put for $3 to avoid the upside risk of a short stock position. The person who sells you that $50 put might be very willing to buy stock for $50. Now let’s assume the stock falls to $45 at expiration. You could exercise the put and receive $50 for your stock rather than the current $45 market price. This means you have a $5 gain for a $3 cost for a 66% gain. The short put seller must buy your stock for $50 but was willing to do that anyway. The fact that he received $3 for selling the put just offset his losses. Rather than being down $5, he is now only down $2. So you gained $2 on the put while the short put seller lost $2 from the sale. However, both of you see yourselves as better off. This shows that just because one investor “loses” on the option, it doesn’t mean that he is truly worse off than if he hadn’t entered the trade. Options were designed as a way to accept or reject risks in the market. If another party is willing to accept risks another doesn’t want, then all investors can be better off.

Okay, let’s finish this section with one final example to really show the power of profit and loss diagrams. We’re going to name an advanced strategy that you’ve probably never heard of and one that we’re not even going to discuss in this book. That strategy is the Short Iron Condor. This particular example will be constructed by selling the $55 put and $60 call. Next, we will buy the $50 put and $65 call. We will assume that these transactions bring in a $3 credit to the account. Now for the hard part. Can you tell if this a bullish or bearish strategy? What are the maximum gains and losses? Where will the strategy break even? You can see that these questions are nearly impossible to answer without the visual aid of a profit and loss diagram. Figure 3-15 shows the profit and loss diagram for a short iron condor established for a $3 credit:

Now that you have a picture, you should readily see the answers. You can see that the strategy outlined in this example can make a maximum of $3, which occurs if the stock price is between $55 and $60 at expiration. The maximum loss is $2, and that occurs if the stock’s price is below $50 or above $65 at expiration. This strategy is not looking for big price moves in either direction. Instead, it needs the stock to stay relatively quiet between $55 and $60. It is not bullish or bearish – it is a neutral strategy. This strategy has two breakeven points: The first is at $52 and the second is at $63. Even though the ideal situation is to have the stock close between $55 and $60, it can actually close between $52 and $63 at expiration and still be profitable. Below $52 and above $63 is losing territory.

Notice how much we can tell about a strategy that we knew nothing about just by looking at its profit and loss chart. They are invaluable tools for learning strategies and assessing the risks and rewards of any position. As you start trading options, computer software will draw these charts for you. The important thing is that you know how to read them. In fact, most programs will even draw profit and loss diagrams prior to expiration. This requires the aid of an option pricing model to help with theoretical calculations (that’s why we draw them at expiration by hand). The pictures will change but the way you read them is the same. If you take the time to work with profit and loss diagrams, you will have a much better understanding if a particular strategy really is right for you.

To be continued….

In Chapter One, we stated that you can effectively escape any option contract by entering a “reversing” trade. This just means that in order to get out of the contract, you do the opposite set of actions that got you into it. So if you own an option, you can simply sell it. If you sold an option, you can buy it back. These actions effectively get you out of the contract. Now that you understand profit and loss diagrams, you will have a better appreciation for why this works.
Assume you buy a $50 call “to open” for $4 and later sell it “to close” for $6. What has effectively happened? Take a close look at the two trades forgetting about the opening or closing notations:

Buy a $50 call = -$4
Sell a $50 call = +$6

These transactions are really no different from buying and selling stock. If you buy 100 shares of Intel for $30 and sell 100 shares of Intel at $35, you no longer have any Intel shares. All you’re left with is the difference in cash (whether a gain or a loss). The same idea is true for the options. If you buy a $50 call for $4 and then sell a $50 call for $6, you no longer have the call but only the cash difference; in this case, a $2 profit.

We can use profit and loss diagrams to better understand why this works mathematically. Assume for a moment that the above two transactions were “opening” transactions; that is, you bought the $50 call for $4 “to open” and the sold $50 call for $6 “to open.” In the real world, you’re not allowed to be long and short the same contract in the same account; the reason for that will be apparent shortly. But for now, just assume that we could do these transactions in the same account. Figure 3-8 shows a profit and loss diagram for each of these two transactions:

The solid line shows the starting position of purchasing a $50 call for $4. The shaded line shows our profit and loss from selling the $50 call for $6. If we actually held these two positions separately in our account, then our profit and losses from this point forward will be the vertical sum of these two lines. In other words, for any stock price you’d just find the profit or loss of each position and combine them. For example, at a stock price of $45, the green line shows +$6 while the red line shows -$4. The result must be a profit of $2. At a stock price of $55, the red line shows a +$1 gain, as does the green line, so the total profit is $2. At a stock price of $60, the red line shows a profit of $6 while the green shows a loss of $4, which is another gain of $2. We can actually combine these two profit and loss diagrams into one, which gives us Figure 3-9:

Notice that buying and selling the same option creates a flat line from a profit and loss perspective. That is, your profits or losses are not in any way affected by stock price movement. So theoretically, you could buy the $50 call “to open” and then sell the $50 call “to open” and you’d be out of the contract. However, if you have two “opening” contracts then this creates additional “open interest” that really isn’t there. It is for this reason that the OCC (Options Clearing Corporation) does not allow you to be long and short the same option in the same account. Effectively there’s nothing there. That’s why you must either buy the contract “to open” and then sell it “to close” or do the reverse and sell the contract “to open” and then buy it “to close.” One action just undoes the other and you’re effectively out of the contract and hopefully holding onto a profit as a result.

What’s the Best Strategy?
One of the biggest benefits of using profit and loss diagrams is that they allow us to compare strategies or positions. For instance, Figure 3-10 compares the previous two profit and loss diagrams we’ve examined. It compares long stock purchased at $50 with the long $50 call purchased for $5:

We’ve extended the range of stock prices from $20 to $65 so that you can really see that the $50 call provides downside protection. The long stock holder can lose the entire $50 investment while the long call holder can only lose $5. If the stock is trading above $50 at expiration, both the call and stock owner participate dollar-for-dollar. The long call holder participates fully to the upside but does not lose as much to the downside. So why would anybody trade anything other than options? The reason is that this “favorable” risk-reward of the call option does not come for free. Notice in Figure 3-10 that the long stock position intersects the long call position at a stock price of $45. This is called the crossover point. This shows that both strategies are equal at expiration at a stock price of $45. If the stock closes at $45 at expiration, the long stock holder loses five dollars and so does the long call holder.

However, below the crossover point, the long call performs better since its line lies above that of the long stock position. Even though both positions lose in this region, the long call has a fixed loss of five dollars while the long stock position continues to lose all the way down to a stock price of zero.

On the other hand, above the crossover point, the long stock position performs better for all stock prices since its line lies above the $50 call line. In other words, the profit is higher for the long stock holder for all stock prices above $45 at expiration. How much better off is the long stock position? For all stock prices above $50, the long stock holder will have five dollars more profit than the long call holder. The reason is that the long call owner paid a five-dollar time premium thus making his breakeven point $55 while the long stock holder breaks even at $50. So the distance between those two lines above $50 is exactly $5, which is the cost of the call.

This shows that options are all about tradeoffs. Whenever you compare two (or more) strategies on the same graph, you will always find that one strategy is better than the other for certain areas while it is worse off in others. No strategy can be superior to another for all areas on the profit and loss diagram (otherwise arbitrage is possible). In Figure 3-10, you can see that the long stock position performs better for all stock prices above the $45 crossover point and worse for all stock prices below. It is up to the option trader or investor to decide if the cost of the option is worth the benefit it provides. Profit and loss diagrams are the easiest way to visualize exactly what the tradeoffs are.
To be continued…

Let’s take the next step and try a more difficult problem by creating a profit and loss diagram for a long $50 call option that we purchased for $5.

If the stock price is: At expiration,
$50 call is worth: $50 call cost Profit/Loss
$35 $0 $5 -$5
$40 $0 $5 -$5
$45 $0 $5 -$5
$50 $0 $5 -$5
$55 $5 $5 $0
$60 $10 $5 $5
$65 $15 $5 $10
Remember, we always start with a column of stock prices. However, when dealing in options, we pick the stock prices based on the strike price of the option (or options) rather than the purchase price as we did for the long stock example. Because we’re trying to figure out the profit and loss diagram for a $50 call, we would create a column of stock prices starting $50 and then select a few stock prices above and below $50 such as shown in the first column of Table 3-4:

Table 3-4: Profit and Loss Table (Long $50 Call)

Notice that our stock prices are in five-dollar increments rather than one-dollar increments we used for the previous long stock example. In actuality, it doesn’t matter which increments you use since all methods produce the same picture. But in order to keep the tables small, we generally count by five-dollar increments when dealing with options.

The second column in Table 3-4 shows what the $50 call will be worth at expiration. It’s important to understand that when drawing profit and loss diagrams for options, we are drawing them at expiration of the option. For example, we know that if the stock is $50 or less at expiration that the $50 call expires worthless. However, if the stock is $55, the $50 call would be worth exactly $5 at expiration. If the stock is $60 at expiration, the $50 call is worth $10 and so on.

The third column in Table 3-4 shows us the cost of the call, which we assumed was $5 for this example. In this were a real-life example, we may just use the $5 premium for the option or we may be more realistic and include commissions. Either decision will not change the shape of the profit and loss diagram but it would change the profit or loss values. Whether you decide to include commissions or not, the cost you come up with does not change as the stock’s price changes. That’s why the third column in Table 3-4 is the same answer ($5) for the entire column.

Now we have our two necessary pieces of information to draw the profit and loss diagram: (1) We know the value of the $50 call at various stock prices by looking at column 2 and (2) We know the cost of the $50 call by looking at column 3. Now we just need to figure out what our profit or loss will be for the various stock prices in the table. We figure out the profit or loss just as any business would by taking “revenues minus costs.” In this example, if the stock closed at $35 at option expiration, your revenues would be zero from the sale of the option since it is worthless. Because you paid $5 for the option, you’d have a $5 loss with the stock at $35. The formula for the profit/loss column is simply Column 2 – Column 3.

Once we have the necessary pieces of information, all we have to do is plot the profit/loss column against the stock prices (bold columns in Table 3-4) and we get the following profit and loss diagram shown in Figure 3-5:

We read this profit and loss diagram in the same way as we did for the long stock profit and loss diagram. How much would we make or lose if the stock closed at $60 at expiration? We just need to find $60 on the horizontal axis and draw a line to the profit and loss curve. From that point, we just look directly to the left axis to find the answer, which is $5, as shown by the dashed arrows in Figure 3-6:

We can check the answer by hand. If the stock were $60 at expiration, the $50 call would be worth exactly $10. Because we paid $5 for it, our profit must be $5. Hopefully you are convinced that it is much easier it is to look at the picture to arrive at this answer rather than going through all of the steps by hand.

The picture immediately tells us that a long call is a bullish asset since it makes money as the stock price rises. Further, there is no limit to the amount of money that could be made since the chart continues to rise with increasing stock prices. Even if you do not understand a particular strategy, a quick glance at its profit and loss diagram immediately shows what the trader would like to have happen to the stock price.

Notice that the profit and loss diagram for a long call looks more like a “hockey stick” rather than the straight line we saw for a long stock position. This is because the holder of a long call can only lose the purchase price no matter how low the stock’s price may fall below the strike price. If the stock is $50 or lower at expiration, the long call holder loses a maximum of five dollars, which is why the curve flattens out for all stock prices below $50. Any time you see a “flat” segment (running parallel to the horizontal axis) of a profit and loss diagram, it tells you that particular range of stock prices has no effect on your profit or loss at expiration.

But if the stock is above $50 at expiration, the long call holder makes dollar-for-dollar just as the long stock owner does. This demonstrates one of the most important characteristics about long call options. That is, long calls allow traders and investors a way to participate dollar-for-dollar as the stock price rises but not lose dollar-for-dollar if the stock price falls. In other words, long calls provide traders and investors with some downside protection. The diagram visually demonstrates the asymmetric payoff structure of options.

Characteristics of Profit and Loss Diagrams
There are three important characteristics that are common to all profit and loss diagrams:
• A “bend” will occur at every strike price
• There will be a portion above and below zero
• The curve will cross zero at one or more points (the breakeven point)

Let’s think through each of these in a little more detail. First, all profit and loss diagrams will “bend” at each strike price of the option(s). In Figure 3-5, the $50 call bends upward at the $50 strike, but that will not always be the case. Depending on the option, whether it is long or short, and how it is paired with other assets, the profit and loss diagram may bend up, down, or even sideways. But you can always be sure that it will bend at every strike price involved in the strategy.

Key Concepts

1) The area below zero on a profit and loss diagram represents the risk.
2) The area above zero represents the reward.
3) The point(s) where the profit and loss curve crosses zero is the breakeven point.
4) A “bend” in the curve will always occur at a strike price.

To be continued…

In the last chapter, we learned that options have an asymmetrical payoff structure and it is this property that makes them difficult to understand for new traders. As a refresher, if you buy stock, you have a symmetrical payoff structure. If you buy shares of stock, you make one dollar for every dollar it rises and lose one dollar for every dollar it falls. The gains and losses are symmetrical around the purchase price. However, these symmetrical profits and losses are not present for options. If you buy the $50 call, you will make one dollar at expiration for every dollar the stock rises above $50, but you will not lose one dollar for every stock price below $50. Option payoffs are not symmetrical around their purchase price.

Because of this unique asymmetrical payoff property, it can be difficult to understand how an option position will behave over a range of stock prices. Imagine how difficult it would be if you were dealing with two or more options!

Fortunately, there is a handy tool – the profit and loss diagram – that allows us to look at a picture to see how our profits and losses will be affected as the underlying stock price moves. Unfortunately, few investors or traders take the time to understand them and they end up missing out on a wonderful tool that will make their lives easier and also add insightful dimensions to their understanding of options. Profit and loss diagrams can also keep you out of a lot of trouble since they can alert you to potential risks of a particular strategy that you may have never considered. There is probably no better way to sum up the advantage of using profit and loss diagrams than with the saying, “A picture is worth a thousand words.” The risks and rewards of any position, no matter how complex, are brought to life by looking at a simple picture. Even if you’re not familiar with the particular names of strategies, if you can read a profit and loss diagram, you will have a good understanding of what the function of the strategy is.

Let’s take a look at how to construct a profit and loss diagram, and then we’ll show you how easily it reveals the risks and rewards of various option strategies. Please understand that the work we are putting into these exercises is not necessary when trading options in the real world. Computer programs will draw the pictures for you and you will not need to actually create the tables and charts. However, if you work through the calculations by hand while learning, you will understand the pictures much better.

Profit and loss diagrams can be constructed for any asset, not just options. So let’s start with a simple example and create a profit and loss diagram for one of the most basic of all positions, a long stock position.

In order to create any profit and loss diagram, we need two pieces of information. First, we need to know how much our asset in question will be worth at various stock prices. Second, we need to know how much was paid for the asset. With those two pieces of information, we can chart any profit and loss diagram.

Because we need to know what our asset in question is worth at various stock prices, we always start with a table consisting of various stock prices. That’s always the first step. Next, we calculate what the profit and loss would be for our position in question if the stock were at each of those prices.

If the stock price is: Cost of stock Your profit/loss will be:
45 $50 -$5
$46 $50 -$4
$47 $50 -$3
$48 $50 -$2
$49 $50 -$1
$50 $50 $0 (breakeven point)
$51 $50 +$1
$52 $50 +$2
$53 $50 +$3
$54 $50 +$4
$55 $50 +$5
For instance, assume you purchased stock for $50 per share. To construct the profit and loss table, we’d start with a column of stock prices starting with the $50 purchase price and then extend the range somewhat above and below this center price. For example, we may consider a range of stock prices between $45 and $55 as in the first column of Table 3-1:

Table 3-1: Profit and Loss Table (Long Stock)
Next, we calculate what the profit or loss would be for our asset in question (long stock) for each of the listed stock prices. For instance, the first cell in Table 3-1 shows a stock price of $45. If the stock price is $45, you have a $5 loss since you paid $50 per share. If you look further down the list, you can see that if the stock price is $53, you’ll have a $3 profit. If you like working with formulas, we can find the values for the profit/loss column by taking “Column 1 – Column 2.”

Naturally, whether the profit/loss column represents a real loss or a “paper loss” depends on whether you actually sell the stock at that moment. For example, if you sell the stock at $45, you have a $5 “realized” loss. If you do not sell it, you have a $5 “unrealized” loss. Either way, if the stock is $45, there is some type of a five-dollar loss facing us and that’s what Table 3-1 is showing us.

Once our table is constructed, we just need to plot this information on a graph. We will always use the “stock price” column as the horizontal axis (x-axis) and the profit/loss column as the vertical axis (y-axis). Once we do, we get a chart that looks like Figure 3-2:

Figure is the profit and loss diagram for a long stock position and is simply a picture of the information in Table 3-1. Notice that it is simply a straight line sloping upward to the right. To read the chart, you just select any stock price along the horizontal axis and then trace a line up to the profit and loss line. From there you follow it directly to the left axis and that tells you what your profit or loss would be for that particular stock price. For instance, what would our profit (or loss) be if the stock is $54? All we have to do is draw a straight line from the $54 stock price on the horizontal axis up to our profit and loss line and then over to the vertical axis on the left as shown by the dashed lines in Figure 3-3:

You can see that we land on a profit of $4. This tells us that if the stock is $54, then we have a $4 profit. Likewise, if the stock is trading at $46, we’d have a $4 loss, which is shown by the solid arrows.

Notice that the profit and loss line crosses the horizontal axis at $50. This tells us that at a stock price of $50 we have no profit or loss; we are just breaking even. Any time a profit and loss line intersects the horizontal axis that shows a breakeven point. (For some strategies, there will be more than one breakeven point.)

Figure 3-3 shows that we break even at $50 and make one dollar if the stock is $51, two dollars if it is $52, etc. Likewise, it shows that we lose one dollar if it falls to $49, two dollars if it falls to $48, etc. In other words, if we own stock, we gain dollar-for-dollar as the stock price rises and lose dollar-for-dollar as the stock price falls.

Even though Table 3-1 and Figure 3-2 are two different ways of expressing the same information, the picture is easier to follow. It is much harder to visualize the profit and loss behavior by looking at the table. Now, if you are familiar with graphing, you probably figured out that the information in Table 3-1 would plot as a straight line. However, as we move to the asymmetrical payoffs of options and add more complex strategies, the table will be nearly impossible to follow. A picture becomes a much easier way of understanding how your profit or losses will be affected with changes in the underlying stock, which is why we want to understand how to read profit and loss diagrams.

To be continued…

The following are the answers to the questions presented in Part 29

Chapter Two Answers

1) ABC stock is trading for $76 near expiration and your $70 call is bidding $5.20. How do you capture the missing intrinsic value?
b) Short the stock and exercise the call
With the stock trading at $76, the $70 call must be worth at the $6 intrinsic value at expiration. However, sometimes the bid-ask spreads can make the bid price slightly less than this intrinsic value. In this question, there are 80 cents missing from the intrinsic value. Rather than just sell your $70 call in the open market and receive $5.20, you can short the stock at $76 and immediately exercise the $75 call, which will leave you with a $6 gain.

2) ABC stock is trading for $37 near expiration and your $40 put is bidding $2.80. How do you capture the missing intrinsic value?
b) Buy the stock and exercise the put
With the stock trading at $37, the $40 put should be worth the $3 intrinsic value at expiration. But just as for call options, sometimes there is some missing intrinsic value near expiration. In this question, you could place an order to buy shares of the stock for $37 and immediately exercise the put and sell the shares for $40 thus capturing a $3 rather than the $2.80 gain you’d get by selling the put in the open market. It does not matter if you don’t have the cash to buy the shares of stock since the exercise of the put guarantees the funds.

3) What is the key factor that gives an option, whether a call or put, its value?
c) Volatility
The volatility of the underlying stock is the key factor in determining an option’s value. Volatility simply measures the fluctuations in a stock’s price. The greater the fluctuations, the greater the uncertainty of prices and options become more valuable.

4) The higher the risk:
c) The lower the price, the higher the reward
If an investment is risky, the market will bid down its price to a level where it becomes desirable. If the price is low, then the potential return, or reward, will be higher.

5) Out-of-the-money option prices move:
c) Only a small fraction with the underlying stock
Out-of-the-money options have a low delta, which means the option’s price will only move a
small percentage when compared to the move in the stock’s price.

6) The maximum value that a call option could ever be is:
a) The price of the underlying stock
The maximum price a call option could ever reach is the price of the stock (Pricing Principle #5). If the price of any call option were to exceed the stock price then arbitrage would be possible.

7) Interest rates are 6% and you will definitely receive $5,000 six months from now. How much should you be willing to accept if the other party wants to settle the debt today?
b) $4,854
If interest rates are 6% per year then they are effectively 3% per six months. The present value of $5,000 would then be $5,000/1.03 = $4,854. This just means you should be indifferent between receiving $4,854 today and $5,000 in six months from now if interest rates are 6%. If you accepted $4,854 today, you could invest that money at the risk-free rate of 6% and it would grow to $5,000 in six months.

You are looking at quotes on IBM March calls. Which is more expensive, the $80 call or the $85 call?
d) $80 call is more expensive
With all else being equal (that is, same underlying stock and expiration), lower strike calls must be more valuable than higher strikes (Pricing Principle #1). Although we don’t know what the price of either call will be, we do know that the $80 call would be more valuable since it gives the holder the right to buy shares at a lower price.

9) You are looking at Dell Computer April $30 calls and July $30 calls. Which is more expensive?
d) July will be more expensive
With all else being equal, longer-term options will be more valuable than shorter-term expirations (Pricing Principle #2). The reason is simply that more time allows the underlying stock to make bigger moves, whether higher or lower.

10) You are looking at Intel December puts. Which is more expensive, the $30 put or the $40 put?
c) $40 put is more expensive
With all else being equal, higher-strike puts will be more valuable than lower-strike puts (Pricing Principle #1). The reason is that the higher-strike put allows the holder to sell stock at a higher price, which is more beneficial (valuable) than selling at a lower price.

11) Delta measures:
b) The sensitivity of an option’s price compared to the stock’s price
If a call option has a delta of 0.50, then we know that the option’s price will rise 50 cents for the next dollar move in the stock’s price. If a put has a 0.50 delta, then its price will rise 50 cents for the next dollar fall in the stock’s price. Delta therefore shows how sensitive an option’s price is to movements in the stock’s price.

12) One interpretation of delta is:
b) The probability that the option will expire in-the-money
One mathematical interpretation is that it roughly shows the probability that an option will expire in-the-money at expiration. If an option has a delta of 0.70 then there is roughly a 70% chance that it will expire in-the-money at expiration.

13) XYZ stock is trading for $44.50 near expiration. Your $40 call must be worth at least:
b) $4.50
All options must be worth their intrinsic value at expiration. In this example, the $40 call must be worth $4.50. (If it were worth less than that, you’d simply short the stock and immediately exercise the call as in Question 1.)

14) If the $50 call delta is 0.70, the $50 put delta is:
d) -0.30
Same-strike call and put deltas must sum to one (ignoring the minus sign of the put delta). If the call delta is 0.70, the corresponding put delta must be -0.30.

15) The ABC $50 call is trading for $7. What is the maximum amount the $45 call could be trading for?
a) $12
For any two calls (or puts) the difference in their prices cannot exceed the difference in the strikes (Pricing Principle #6). In this question, there could not be more than a five-dollar difference in their prices since there is a five-dollar difference in strike prices. We also know that lower-strike calls must be more valuable than higher strikes so if the $50 call is $7, the $45 call could not be worth more than $12; otherwise arbitrage is possible.

16) What are the only two prices that are possible for an option to have at expiration?
b) Zero or intrinsic value
An option will be worthless if it is out-of-the-money at expiration. If it is in-the-money, it will be worth exactly the intrinsic value. Remember, prior to expiration, out-of-the-money options will certainly have some value since time remains. But at expiration, they are worthless.

17) You purchased a $40 call for $3. What is the breakeven point on the option?
d) $43
The breakeven point for a call option is found by taking the premium and adding it to the strike price. In this question, the breakeven point is $40 strike + $3 premium = $43 stock price. If the stock is $43 at expiration, the $40 call is worth exactly $3, which is the same as the amount you paid – you have just broken even.

18) You purchased a $70 put for $2. What is the breakeven point on the option?
a) $68
The breakeven point for a put option is found by subtracting the premium from the strike price. In this question, the breakeven point is $70 – $2 = $68 stock price. If the stock is $68 at expiration, the $70 put is worth exactly $2, which is the amount you paid so you have just broken even.

19) Because high-volatility stocks have a better chance for price appreciation, you should:
c) Not choose trades based on this fact because the volatility will be priced into the option.
You will hear many traders tell you to only trade options on high-volatility stocks since there is more room for price appreciation. But this is really a big myth. The reason is that the markets are well aware of that advantage so traders bid the prices of the high-volatility options higher. The net result is that there is no net advantage in trading high-volatility stocks.

20) If a 30-day option has a delta of 80 today:
b) It will change over time
The delta of an option does not stay constant over the life of the option. The delta changes as other factors change. The key factors are time, volatility, and price of the underlying stock. But just because you buy an 80-delta option today does not mean that it will be the same next week. In fact, all in-the-money options approach a delta of 1.0 as expiration gets closer, while all out-of-the-money options approach zero. The delta does not stay constant.

To be continued,,,

1) ABC stock is trading for $76 near expiration and your $70 call is bidding $5.20. How do you capture the missing intrinsic value?
a) Buy the stock and short the call
b) Short the stock and exercise the call
c) Buy the stock and exercise the call
d) Short the stock and short the call

2) ABC stock is trading for $37 near expiration and your $40 put is bidding $2.80. How do you capture the missing intrinsic value?
a) Short the stock and exercise the put
b) Buy the stock and exercise the put
c) Buy the stock and short the put
d) Short the stock and short the put

3) What is the key factor that gives an option, whether a call or put, its value?
a) The strike price
b) Price of the stock
c) Volatility
d) Open interest

4) The higher the risk:
a) The higher the price, the higher the reward
b) The lower the price, the lower the reward
c) The lower the price, the higher the reward
d) The higher the price, the lower the reward

5) Out-of-the-money option prices move:
a) Dollar-for-dollar with the underlying stock
b) About 50 cents on the dollar with the underlying stock
c) Only a small fraction with the underlying stock
d) About 75 cents on the dollar with the underlying stock

6) The maximum value that a call option could ever be is:
a) The price of the underlying stock
b) There is no limit
c) Only half of the underlying stock’s price
d) The price of the put

7) Interest rates are 6% and you will definitely receive $5,000 six months from now. How much should you be willing to accept if the other party wants to settle the debt today?
a) $4,716
b) $4,854
c) $4,981
d) $4,622

You are looking at quotes on IBM March calls. Which is more expensive, the $80 call or the $85 call?
a) Cannot be determined with this information
b) They will be about the same price
c) $85 call is more expensive
d) $80 call is more expensive

9) You are looking at Dell Computer April $30 calls and July $30 calls. Which is more expensive?
a) Cannot be determined with this information
b) They will be about the same price
c) April will be more expensive
d) July will be more expensive

10) You are looking at Intel December puts. Which is more expensive, the $30 put or the $40 put?
a) Cannot be determined with this information
b) They will be about the same price
c) $40 put is more expensive
d) $30 put is more expensive

11) Delta measures:
a) The intrinsic value of the option
b) The sensitivity of an option’s price compared to the stock’s price
c) The time value of the option
d) The sensitivity of an option’s price compared to the overall market

12) One interpretation of delta is:
a) The probability that the option will expire out-of-the-money
b) The probability that the option will expire in-the-money
c) The probability that the option will expire without being exercised
d) The probability that the option will expire

13) XYZ stock is trading for $44.50 near expiration. Your $40 call must be worth at least:
a) $4.00
b) $4.50
c) $44.50
d) There is no way to determine based on this information

14) If the $50 call delta is 0.70, the $50 put delta is:
a) There is no way to determine based on this information
b) -0.50
c) -0.70
d) -0.30

15) The ABC $50 call is trading for $7. What is the maximum amount the $45 call could be trading for?
a) $12
b) $7
c) $8
d) There is no way to determine based on this information

16) What are the only two prices that are possible for an option to have at expiration?
a) Premium or intrinsic value
b) Zero or intrinsic value
c) Zero or time value
d) Time value or intrinsic value

17) You purchased a $40 call for $3. What is the breakeven point on the option?
a) $3
b) $37
c) $40
d) $43

18) You purchased a $70 put for $2. What is the breakeven point on the option?
a) $68
b) $2
c) $72
d) $70

19) Because high volatility stocks have a better chance for price appreciation, you should:
a) Only place trades during highly volatile markets to increase your edge
b) Only trade options on low-volatility stocks for more consistent profits
c) Not choose trades based on this fact because the volatility will be priced into the option
d) Only trade options on high-volatility stocks

20) If a 30-day option has a delta of 80 today:
a) It will remain at 80 over the life of the option
b) It will change over time
c) It cannot fall below 80 but could rise above it
d) It can fall below 80 but not rise above it

Answers coming in next part…

If we define delta as the probability of the option expiring with intrinsic value, we can see that if there is a 90% chance of the $32.50 call expiring with intrinsic value then that call will increase by 90 cents for the next dollar move. The $35 call will only appreciate by 39 cents since it only has a 39% chance of expiring with intrinsic value. Since the $32.50 has a 90% chance of expiring with intrinsic value while the $35 call only has a 39% chance, this is yet another way to show that the $35 call is riskier than the $32.50 call. The reason that deltas change is because the probability of an option expiring with intrinsic value changes. Obviously, that probability hinges on the stock price and time to expiration. As time goes by or as the stock price moves, you will get different probabilities and therefore different deltas. The main point you want to understand about delta is that it does not remain the same throughout an option’s life.

Put deltas are always shown as a negative number. This is not because there is a negative probability of them expiring in-the-money but rather it is a notation to remind us that a put loses value as the underlying stock rises and gains value as it falls. For example, in Table 2-10, the $32.50 put has a delta of -0.10. If eBay were to rise by $1 right now, the put would lose 10 cents. But if the stock were to fall by one dollar, the put would gain 10 cents because -$1 * -0.10 delta = +0.10. The negative sign on a put delta is really a reminder that put option profitability moves in the opposite direction of the underlying stock.

Relationship between Call and Put Deltas
If we know the delta of a call, is there anything we can say about the corresponding same-strike put? In other words, if we know the $32.50 call has a delta of 0.90, what can we conclude about the $32.50 put delta? The answer is easy with a little thought about probability. We know from basic probability theory that the sum of all mutually-exclusive events must add up to one. This just means that if you break any event into two or more parts that cannot overlap (mutually exclusive), then the sum of all those probabilities must be one.

For example, if you have a 90% chance of passing an exam then that means there is a 10% chance you will fail since passing and failing are mutually exclusive – you can’t pass and fail at the same time. All probabilities must add up to one and, in this case, 0.90 + 0.10 = 1. If your favorite football team has a 60% chance of winning their next game then they must have a 40% chance of losing since they cannot win and lose. As before, all probabilities must sum to one and we see that 0.60 + 0.40 = 1.

Now think about stock prices. No matter where eBay is currently trading, it will either be above $32.50 at expiration or it won’t. If the stock is above $32.50 then the $32.50 call will be in-the-money. If the stock is below $32.50 at expiration then the $32.50 put will be in-the-money. Therefore, if there is a 90% chance (delta) that the $32.50 call will expire in-the-money then there must be a 10% chance the $32.50 put must be in-the-money. And that means that the delta of the $32.50 put must be 0.10. The delta for the call and put will nearly always add up to one (ignoring the minus sign of the put) since all probabilities must sum to one.

Exercise
Using Table 2-10, check the sums of the deltas for the same-strike calls and put. Ignoring the minus sign of the put deltas, do they add up to one?

If the concept of delta has you confused, don’t worry. Believe it or not, many professional traders confuse the definition and interpretation. The key point to remember is that an option’s price will generally not move dollar-for-dollar with the underlying stock. If you want to get a ballpark figure on how much the option will gain or lose with the next, immediate one-dollar move in the stock you’ll want to look up the delta of that option. The only time that an option will move nearly dollar-for-dollar is when the option is viewed by the market as being guaranteed to expire with intrinsic value. This means the option must either be very deep in-the-money or in-the-money with a very short time until expiration. If it seems as though the options are guaranteed to expire with intrinsic value, then the long call option will behave like long stock (delta = 1) and the put option will behave like short stock (delta = -1). The delta of a stock is always one, since it rises and falls dollar-for-dollar with itself. (Consequently, the delta for short stock is always negative one, since it loses dollar-for-dollar as the price rises and gains dollar-for-dollar as the price falls.) So once a call option’s delta reaches one, it is considered to be long. Once a put option’s delta reaches negative one, it is considered to be short stock.

The relationship between call and put deltas should tell you that it’s pretty difficult to have more than 50% of the options expire worthless. For instance, if all of the call options expire in-the-money, then all of the put options must expire out-of-the-money. Because there are an equal number of call and put strike prices, this means that 50% of the options expire worthless. If the stock’s price closes in the middle of all strike listed strike prices then, again, half of the calls and half of the puts expire worthless. Despite this relationship, there is a persistent myth that 90% of all options expire worthless. You will undoubtedly hear this figure quoted many times but you will never find a single study to substantiate it. In fact, the OCC (Options Clearing Corporation) publishes statistics on its website at www.OptionsClearning.com and you will find that historically the numbers are roughly as follows: 10% of all options are exercised, 30% expire worthless, and 60% are closed in the open market. There are obviously variations in these numbers from year to year, but they rarely fluctuate by more than five percentage points in any direction.

Roughly 60% of all options are closed in the open market. About 30% expire worthless and 10% are exercised. It is NOT true that 90% of all options expire worthless. It is a mathematical impossibility.

Key Concepts

1) An option’s price does generally not move dollar-for-dollar with the underlying stock.
2) An option’s price will rise or fall by its delta on the next, immediate one-dollar move in the underlying stock.
3) Assuming the same expiration, calls and puts with the same strike will generally have deltas that add up to one (ignoring the minus sign of the put delta).

To be continued…

Out-Of-The-Money
If stock price is: At expiration, $100 call will be worth:
91 0
92 0
93 0
94 0
95 0
96 0
97 0
98 0
99 0
100 0
101 1
In our previous examples, we saw that the at-the-money option will move about 54 cents for the next dollar move. Deep-in-the-money options, on the other hand, will move dollar-for-dollar with the underlying stock. What can we expect to happen with out-of-the-money options?
Let’s assume the stock price is now $94 so that the final stock prices will be between $89 and $99. In other words, the option has no chance for a payoff:

If stock price is: At expiration, $100 call will be worth:
89 0
90 0
91 0
92 0
93 0
94 0
95 0
96 0
97 0
98 0
99 0
If stock price is: At expiration, $100 call will be worth:
90 0
91 0
92 0
93 0
94 0
95 0
96 0
97 0
98 0
99 0
100 0
The option’s price is now $0/11 = $0. If the stock rises one dollar to $95, we have removed a zero from the bottom and added a zero to the top so the option’s price is still zero.

This shows that if your option is far enough out-of-the-money, its price may not even move even if the stock rises by a full dollar. Now let’s take it a step further and assume that stock rises another point to $96:

Now the options price is (0+0+0+0+0+0+0+0+0+0+1)/11 = 9 cents. For a full point move in the stock, this option gained only nine cents in value. Further, if we make the comparison from a stock price of $94 then the stock moved two full points from $94 to $96 and yet the option only gained nine cents. This shows that far out-of-the-money options are relatively insensitive to stock price movements.
Deep-in-the-money options respond nearly dollar-for-dollar with changes in the stock’s price.

At-the-money options respond about 50 cents on the dollar.

Out-of-the-money option prices barely move with changes in the stock’s price.

This is a very simple model of stock price movements. In reality, we’d assign higher probabilities for stock prices near today’s price and lower probabilities for the extreme values. But to make the math easy, we just assumed that all stock prices were equally likely and still came up with similar option price movements as those observed in the real world. These fractional movements are in agreement with what we previously said will happen to the price of pizza coupons if we were less than 100% certain of a price increase. Notice that this simplified stock price model is also based on probabilities but in a more subtle way. When the stock was $100, the $100 call was worth $1.36. If the stock rises one dollar to $101, we cannot be sure of retaining the full value of the highest option price possibility. With the stock at $101, the highest price possibility is $6. Since each price is equally likely, we should bid 1/11 * $6 = 54 cents higher for that option. And we did find that the new option price would be $1.36 + $0.54 = $1.90. The price of an option is ultimately determined by the probabilities for a particular range of stock prices.

What makes option pricing so unique is that it is based on an asymmetrical payoff schedule. If a stock trader buys stock, he gains dollar-for-dollar as the stock price rises and loses dollar-for-dollar as the stock price falls. Now look at the option prices in the previous tables. The options only have payoffs (values) for all stock prices above the $100 strike; all other values are zero. It is this asymmetrical payoff schedule that makes the options prices move less than dollar-for-dollar with the underlying (unless the option gets so far in-the-money, in which case it moves dollar-for-dollar).

Now let’s consider the July $32.50 call in Table 2-8. If the stock were to rise by one dollar right now, we are more certain that the $32.50 will retain intrinsic value at expiration when compared to the $35 call. This is because the stock has to fall much further to wipe out all of the intrinsic value on the $32.50 call. This means that the price of the $32.50 call will rise by a larger amount than the $35 call on the next dollar move in the underlying stock. If the stock were to move up one dollar from its current price of $37.11, we might see the $32.50 call rise by, say 85 cents, while the $35 call rise by only 70 cents. The $40 call, on the other hand, may not even budge in price. Once again, we see that the market is pricing the options according to risk. The $32.50 call gets bid up by a higher amount (in terms of dollars not percentages) than the $35 call because the $32.50 call is more certain to retain intrinsic value. In other words, the $32.50 call is less risky than the $35 call, which is what we stated earlier.
Delta of an Option
In the previous paragraph, we said that the $32.50 call may only rise by 85 cents for the next, immediate one-dollar increase in the stock. An alternative wording is that the option is capturing 85% of the stock movement at this time. When traders talk about how an option’s price moves in relation to the underlying stock, they are really talking about an advanced concept called delta. Delta is a measure of how much an option’s price will move for the next, immediate one-dollar move in the underlying stock. We have to include the word “immediate” to remind us that the move must occur immediately and not later today or next week. Delta simply shows us how sensitive an option’s price is to changes in the stock’s price at that moment in time.

Most option trading software will show you the delta of an option. However, if your broker’s platform does not, you can find them at a number of online resources, free of charge, such as at the Options Industry Council’s (OIC) site at www.888Options.com, PC Quote at www.pcquote.com, or from the Philadelphia Stock Exchange at www.phlx.com.

Table 2-10 shows our eBay options at this point in time with their corresponding deltas. Notice that the $32.50 strike has a delta of 0.90 (circled) . This means that if eBay were to immediately move one dollar, then that option will increase in price by 90 cents. Notice that the $35 call listed below shows a delta of only 0.39 so it will only increase in price by 39 cents on the next dollar move in the underlying stock.

We recently stated that the $32.50 call might move 85 cents while the $35 strike might move 70 cents, which is only a 15-cent difference. However, Table 2-8 informs us that the $32.50 strike will move 90 cents while the $35 strike will move only 39 cents, which is a 59-cent difference. Why is there such a big discrepancy between what we previously said versus what Table 2-10 is telling us? Why did we say there would be roughly a 15-cent difference when Table 2-8 shows there is a 59-cent difference? The reason is that eBay has fallen from $37.11 to $34.43 when the quotes in Table 2-10 were taken, which means the $35 strike is now out-of-the-money. It is no longer in-the-money as it was when the stock was $37.11. If eBay were still at $37.11, you’d see a much higher delta for the $35 call in Table 2-10.

This shows that delta changes over time. Just because the $32.50 call delta is 0.90 right now does not mean that it will always be 0.90. Why does delta change? There is another interpretation of delta we can look to for a better understanding. Delta is mathematically an approximate measure of the probability that the option will expire with intrinsic value (in-the-money) at expiration. We must multiply that probability by the stock price move in order to see how the option will respond. In the pizza coupon example, we had a 50% chance of an increase in price and it’s no coincidence that we figured out that the market would bid up the coupon by 50 cents because 50% of $1 = 50 cents.
To be continued…

Let’s run through a couple of scenarios and see what happens. Let’s assume that coupon prices do not change and they are still trading for $3. If we buy the coupon for $3, and the coin lands heads tomorrow, it will be trading for $4 and we will make one dollar. If the coin lands tails, the coupon still trades for $3 and we don’t lose anything. So if we can buy the coupon for $3, we can’t lose but we might make money. Everybody figures this out and buys coupons and their price rises. This shows that $3 is too low of a price given the fact that prices have a 50% chance of rising one dollar.

Is there a price that’s too high for the coupon? Yes. We know that when the storeowner announced that prices would definitely rise, the coupon immediately rose to $4. Now that we’re not so certain of a price increase, $4 should be too much to pay. But just for argument’s sake, let’s assume that prices do rise to $4 and we buy it. If the coin lands heads, the coupon is trading for $4 and we don’t make any money. We paid $4 and could sell for $4 so we make nothing. However, if the coin lands tails, we could certainly lose since we paid $4 and it is now worth $3. By paying $4, we can’t make money but we could certainly lose.

So now we know that $3 is a certainly a favorable price to pay since we can’t lose but might win. We also know that $4 is too high since we can’t win but might lose. This means there must be a price in between that is a fair price to pay. It turns out that price is $3.50. If we pay $3.50 and the coin lands heads, we make 50 cents. If the coin lands tails, we lose 50 cents. If we were able to make such bets over long periods of time, we know that we’d win 50 cents half the time and lose 50 cents half the time and the price is considered fair at $3.50.

In other words, even though there is an announcement of a possible $1 price increase, the coupons only increase in value by 50 cents. The market increased the value by the probability of realizing that increase. In this case, there is a 50% chance that the price will rise one dollar so the market increased the coupon’s price by 50% * $1 = 50 cents. They will not increase the price dollar-for-dollar under uncertainty. Only when the storeowner announced that he would definitely raise prices by one dollar does the coupon rise by that same amount.

This is really the simplest way to help you to understand why option prices will generally not move dollar-for-dollar with the underlying stock. If the stock rises one dollar, it is not guaranteed to stay there by expiration, so the market will not price in the full dollar move. However, if we are in the final seconds of trading and the stock rises one dollar, then the market will price in the full dollar if the call option is in-the-money. It all hinges on the probability of the option retaining that intrinsic value at expiration.

Simplistic Stock Price Model
We can expand our understanding of why option prices generally do not move dollar-for-dollar with the underlying stock by considering an overly simplified model of stock price movements. Let’s assume that a stock is currently trading for $100 and can only move in one-dollar increments. Further, assume the most it can only rise or fall is a maximum of five dollars and that all prices are equally likely. In the real world, all stock prices are not equally likely; a $100 stock has a much better chance of rising to $101 than it does to $105. But just to make the example easier, let’s assume that all prices can occur with equal probability. With the current stock price at $100, this means the lowest it can move is $95 and the highest is $105. Now imagine that you have a $100 call option (at-the-money). In this scenario, your call option can only be worth one of the following values at expiration:
If stock price is: At expiration, $100 call will be worth:
95 0
96 0
97 0
98 0
99 0
100 0
101 1
102 2
103 3
104 4
105 5
What is this $100 call option worth? Assuming that all final stock prices are equally likely, we know that the $100 call is worth the average of all possible prices. We simply add up all possible call values and divide by the total so the $100 call is worth 0+0+0+0+0+0+1+2+3+4+5 = 15 and the average is therefore $15/11 = $1.36. If you pay $1.36 for this call option hundreds and hundreds of times, you would just break even in the long run. If you try to buy this option for less money you can be sure that other traders will outbid you. Likewise, if the price rises above $1.36, traders will start selling, which brings the price down. The end result is that the option’s price should be $1.36 since that is the price at which neither the buyer nor the seller has a long-run advantage. So in theory, if the market feels that the highest stock price is $105 and the lowest is $95 with all prices equally likely, then the option should be trading for $1.36.

Now let’s assume that the stock rises by one dollar to $101. Under our assumptions, the stock can only rise or fall by five dollars so the new range of stock prices will be $96 to $106 and the range of possible option prices will be from $1 to $6:
If stock price is: At expiration, $100 call will be worth:
96 0
97 0
98 0
99 0
100 0
101 1
102 2
103 3
104 4
105 5
106 6
The average price of the option is now found by summing up all the potential option values and dividing by 11. Our new $100 call price is 0+0+0+0+0+1+2+3+4+5+6 = 21 and 21/11 = $1.90

So if the stock rises from $100 to $101, the at-the-money call rises from $1.36 to $1.90. Notice that this is a $1 rise in the stock’s price but only a 54-cent rise in the options price. Even with this simplistic price model, we are coming up with a very realistic price behavior for an at-the-money call option. Most at-the-money calls will have rise a little more than 50 cents on the dollar for the next one-dollar move in the stock’s price.

What would happen for the next dollar move in the stock’s price? If the stock were to rise from $101 to $102, the call would rise by more than 54 cents. The reason is that each time we are dropping off one of the zeros and adding a bigger number. In the first situation, the highest call value was $5. In the second scenario, the highest call value was $6. So each time the stock rises, we add higher and higher values while dropping off zeros. The end result is that the option’s price must rise by bigger and bigger amounts, at least up to a point. After some point, the option will move dollar-for-dollar with the underlying stock since you will eventually be adding one dollar and dropping off one dollar on a net basis. Where is that point? When the option gets sufficiently in-the-money to a point where the market believes it will definitely have intrinsic value at expiration. Let’s take a look at that scenario next.

Deep-In-The-Money-Options
Assume that the stock price is now $106 so that the $100 call is deep-in-the-money. Under our assumptions, the stock price can only move up or down a total of five points from its current price, which means the expiration stock price will be between $101 and $111. The total option price possibilities are as follows:
If stock price is: At expiration, $100 call will be worth:
101 1
102 2
103 3
104 4
105 5
106 6
107 7
108 8
109 9
110 10
111 11
The option’s price is now (1+2+3+4+5+6+7+8+9+10+11)/15 = $4.40. What do you suppose will happen if the stock rises another point to $107? Again, assuming the stock price can only rise or fall five points by expiration, the option values at expiration can range between $2 and $12 as follows:

If stock price is: At expiration, $100 call will be worth:
102 2
103 3
104 4
105 5
106 6
107 7
108 8
109 9
110 10
111 11
112 12
To find the new option’s price, we get to add the new, highest number 12 to the average but drop off the lowest number 1, which is a net gain of 11 to the average. Because we’re dividing by 11, the option’s price will rise by 11/11, which equals exactly one dollar. Using the same reasoning, if the stock rises again to $108, we’ll add 13 to the average but drop off 2, which is again a net gain of 11 and the option’s price will rise by one dollar again. This shows that once an option is sufficiently in-the-money, it will rise dollar-for-dollar with the underlying stock. Prior to that, the option’s price will rise by something less than one dollar. The consequence of these actions is that an option’s price will follow a curved path rather than the straight line, dollar-for-dollar action of the stock’s price.

To be continued…

Comparing Returns Amoung Funds and Managers
You will be persuaded by different types of investments or individual stock pickers to put your money with them because they “beat” the Dow or some other index. While their returns may be higher, it does not mean that they necessarily beat it on a risk-adjusted scale. As an example, assume the Dow increases 10% over the year but a money manager tells you to put your money with him since he earned 20%. On the surface, it seems like he did much better. However, we haven’t considered the risk. What if this manager invested all his clients’ money into lottery tickets to get the 20% gain? Now it doesn’t appear too impressive. If he is taking that much risk, you’d certainly want better than a 20% increase on your money. We’d say that, on a risk-adjusted scale, this manager didn’t perform as well as the Dow even though his return is higher.

Traders and money managers who place their money in high-risk investments will do better than the Dow or S&P 500 or other broad-based index from time to time. But the chances that they will sustain that record are very low. People who place their money with a fund or manager just because they posted the highest numbers are mistakenly assuming that all of them took the same amount of risk. Before you place your money with them, find out what they are investing in before you get too impressed with the numbers. At any given time, there are thousands of speculators and hedge fund managers who speculate with high-risk investments. It shouldn’t be a surprise that a great number of them will beat the Dow or S&P 500 during the course of a year. This doesn’t mean that they are more skilled than the manager who consistently returns a smaller number.

Make sure you understand the risk-reward relationship before you start investing. Risk and reward never separate. They are joined together by a rational force – the same force that caused you to price the earlier games in the order you did. If you always seek the investments that have the highest potential for return, you are by default, seeking the ones with the highest risk. We have tried to give you many examples of how to use the risk-reward relationship so that you do not forget it, which is easy to do. For example, we just received an email promotion from an options trader with the following advice:

Quote in Promotional Email:
“Cheaper options are usually the best plays. They give you the most leverage, the percentage returns are better, and if the market or stock goes against you, you are risking less.”

You can see that even this professional got it wrong. You are not “risking less” by purchasing cheap options – you are taking on more risk. It is true that if you buy a cheap option there is less money to lose, but that is because you have a higher chance of losing it. And why are the percentage returns better? Because there is more risk. Why do cheap options give you the most leverage? Because there is more risk. But if you look at the quote, he is making it sound as if you’re getting all the positive attributes (high leverage and higher percent returns) without any negative consequence since you are “risking less” for all of these benefits. That is simply not true. All of those positive attributes are a direct result of the higher risk in cheap options.

Understandably, it is easy to make this mistake with financial investments since we do not have little pictures (such as the coin and cards) off to the side like we did with the pricing game reminding us of the risk in each game. When you start trading options remember this one thing: Cheap options are priced that way for a reason. That reason is risk.

Key Concepts

1) The time value of an option is determined by the volatility of the underlying stock.
2) The time value is purely determined by what traders are willing to pay for additional time.
3) The higher the risk, the cheaper the price (and the higher the reward).
4) Higher strike calls (and lower strike puts) are riskier.
5) There is no inherent advantage in trading options on high-volatility stocks because they will be priced correspondingly higher. Price is the equalizer.

Option Price Behavior
One of the biggest mysteries to new (and experienced) traders is the way in which option prices move with changes in the underlying stock. For example, let’s assume you buy a $50 call for $3 with the underlying stock trading for $50. Within a few minutes, the stock climbs up $1 to $51. What would you expect to happen to the price of your option? Would it climb $1 too? The answer is, unfortunately, no. Although it seems like it should be trading for $4 at that point, the option will rise by something less than $1. Why is that?

This is a very difficult concept to explain to new traders, and the explanation belongs in a more advanced book, but it’s important that you at least understand that options will generally not move dollar-for-dollar with the underlying stock. Please understand that the following details are not really necessary to understand in order to trade options. We’re just showing you this to explain why options will usually not move dollar-for-dollar with the stock and so you are not alarmed when you see it occur. Let’s see if we can make some sense of why this might happen by going back to our pizza coupons.

Assume that pizzas are selling for $10 and you have a coupon that allows you to buy it for $7. If these coupons were actually traded in a market, we know that it must be worth at least $3. Why? Just as with our call options – arbitrage. Let’s say the coupons were missing $1 of intrinsic value and trading for $2. Arbitrageurs could buy a coupon for $2 and then pay $7 for the pizza thus spending only $9 for the pizza. They could then sell it in the street for $10 thus making a free dollar. The buying pressure on the coupons will raise the price, and the arbitrage opportunity will stop once the coupon is trading for at least $3.

Now let’s assume that the storeowner announces that tomorrow the price of pizzas will go up for certain by one dollar to $11. Upon hearing the news, the market will immediately raise the price of the coupon from $3 to $4. If not, arbitrage is possible again for the same reasons as in the previous paragraph. In other words, if pizzas are now worth $11 then the $7 coupon must fully reflect the $4 intrinsic value. In this case, the pizza price rose one dollar and so did the coupon.

But now let’s go back to the beginning when pizzas were $10 and change the situation a bit. Let’s say that, instead, the storeowner announces that he will flip a coin tomorrow to decide whether or not to increase his prices by $1. If the coin lands heads, he will raise prices to $11. If it lands tails, they stay the same at $10.

We know that when the storeowner announced that pizzas would definitely rise by one dollar that the coupons also rose by the same amount. In other words, because prices were guaranteed to rise, the market immediately priced that $1 increase into the coupons. With the coin flip though, the owner introduces some risk and we’re now only 50% sure that pizza prices will rise. What should we pay for the coupon now?

To be continued….

Price is the Equalizer
The market places a lower price on riskier assets as a way to equalize the demand. In the pricing game, you placed a higher price on the coin game than the card game. This doesn’t mean that the coin game is necessarily the better game. If the coin game and card game were priced the same, then we could say for sure that the coin game is better. After all, it wouldn’t make sense to pay the same price to play the card game. But because there is more risk with the card game, you will bid a lower amount. Once the prices are established for all three games, then all games are theoretically equally attractive. Your decision on which one to play just depends on how much risk you wish to take (or on how much reward you’re looking for). If you don’t like the $51 payoff of the coin game, you can certainly jump to the riskier card game and go for the $99 reward. Just understand that this decision means you are taking more risk and therefore have a higher chance of losing your investment. The important point to understand is that you cannot jump to a better payoff and take less risk. If you want more reward, you must be willing to take more risk.
Now let’s go back and look at some of the eBay option quotes from Table 1-1, which have been reprinted below in Table 2-8:
Table 2-8
Call Options
Strike July August
$32.50 $4.90 $5.50
$35 $2.70 $3.60
$37.50 $1.05 $2.10
$40 $0.35 $1.10

As we pointed out before, the price of the call options gets cheaper as we move to higher strikes. Notice that this is the same progression as with our pricing game when we move from the guaranteed game to the card game. The price gets cheaper as you move in that direction. This can only mean one thing for the options. They must be getting riskier as we move to higher strikes. However, most traders look at the quotes in Table 2-8 and think that all options could theoretically make an unlimited amount of money since they are all tied to the same underlying stock. It only makes sense to buy the cheapest one, which is the $40 strike. And this is usually a fatal mistake for options traders. Traders who use this line of reasoning assume that the risks are all the same. We now know that cannot be true since the prices are not the same. The market is bidding down the prices of the higher strikes due to the higher risk.

Our first pricing principle stated that lower strike calls must be more expensive. We said that a statistical reason for this is that lower strike calls are able to “catch” more intrinsic value and therefore must be more desirable. Lower strikes are more desirable because they are less risky. If it is less risky, it must cost more money.

We can show this effect by considering the breakeven points for a call option. If you buy the $32.50 strike for $4.90, the stock would have to close at $32.50 + $4.90 = $37.40 in order to break even at expiration. Because CYBX is currently $37.11, you’re only 29 cents away from your breakeven point. However, if you elect to buy the cheapest option, the $40 strike, then the stock must climb to $40 + $0.35 = $40.35 just to break even at expiration. With the stock at $37.11, that means the first $40.35 – 37.11 = $3.24 worth of movement doesn’t even count for you at expiration! The stock must climb higher than $3.24 by expiration before you make money. There is a very big difference between the $32.50 strike and the $40 strike – and that difference is the risk.

Using Table 2-8, many new traders still believe that the $32.50 call must be riskier than the $40 call since there is more money to potentially lose. If eBay falls from its current price of $37.11 to $32.50 at expiration, the $32.50 call buyer loses $4.90 while the $40 call buyer loses only 35 cents. However, if eBay falls to $32.50 at expiration then the stock has lost $4.61 worth of value. This means that the first $4.61 worth of loss on the $32.50 call is a risk that is common to both the stock and the option. It is not a risk that is unique to the option, so it should not be counted as a risk in the option. It is only the value above $4.61 – the 29 cents worth of time value – that is a risk of the $32.50 call. The $40 call loses only 35 cents but it does so if the stock falls, stays still, or even rises to $40 at expiration. It is far riskier than the $32.50 call.

Many traders feel uneasy about putting much money into the trade when there are other strikes available for much less money. The key to trading options is to strike a balance between the two. We don’t suggest buying options so far in the money that it costs a fortune but, at the same time, we stay away from buying at-the-money and out-of-the-money options unless we are buying them with a lot of time remaining – perhaps more than a year to expiration. For the most part, you’ll be better off buying options with intrinsic value.

Now let’s look at the July and August calls in Table 2-8 above. Why do you suppose the July $32.50 is cheaper than the August $32.50? You should now understand that it is cheaper because it is riskier. As we stated before, the August call gives you more time for the stock to move higher – to build intrinsic value – and that means there is a better chance to make money. In other words, there is less risk with that option, and that’s why its price is higher. Many option traders make the mistake of buying the shortest-term, cheapest option available thinking they are reducing their risk; this is usually why most people lose with options. The short-term, high strikes should be treated like lottery tickets, not investments. Our basic risk-reward relationship can be found in many other areas outside of the financial markets too. As long as there is a price paid in exchange for a possible financial reward, the risk-reward relationship holds. Let’s look at an example outside of the financial markets.

Lotteries
Why do you suppose that you can pay one dollar for a state lottery ticket for the chance to make $7 million or more? The reason is that the chance of making that huge reward is very small and so the price will also be low. It does not mean that it must be a great investment because of the “great risk-reward ratio” that so many traders talk about. If there is a great reward, there is a low price – and also a lot of risk.

As another example, Figure 2-9 shows two versions of the Florida lottery scratch-off Monopoly game: Instant Monopoly and Super Monopoly.

Figure 2-9: Florida Lottery’s Instant Monopoly and Sly

Instant Monopoly costs $1 and offers a $5,000 grand prize while Super Monopoly costs $5 and offers a whopping $100,000 grand prize. Instant Monopoly offers $5,000 of reward per dollar at risk while the Super version has $20,000 of reward per dollar of risk. As so many players ask, “Why should I risk $1 to make $5,000 when I can risk $5 to make $100,000?”

Is Super Monopoly the better game since it has a “better” risk reward ratio? Not necessarily. In order to answer that, we need to know the probabilities of winning each game. Depending on the probabilities, it may turn out that one is better than the other. However, the point is that you cannot just look at the “risk-reward ratios” and make that determination. What we do know for sure is that the Super Monopoly game must be more difficult to win. The higher payout is a reflection of the higher risk involved in that game. In fact, you can verify this by going to the website www.FloridaLottery.com and looking at the odds. For Super Monopoly, the odds are 1:2,520,000 and are 1:890,000 for Instant Monopoly. Although you are not likely to win either game, there is no doubt that, on a relative scale, you are more likely to win Instant Monopoly; that’s why the payout is lower. However, now that we know the odds, we can make comparisons. In this case, Super Monopoly offers four times the reward but is not four times as difficult to win. On a risk-adjusted basis then, Super Monopoly turns out to be the better game to play. However, in the financial markets, this favorable risk-reward ratio would never exist as arbitrageurs would buy Super Monopoly and simultaneously sell Instant Monopoly until the prices were exactly in line with the risk. Because these games are not subjected to buyers and sellers, it is possible (as we see in this example) to find games that are more favorable than others. Despite the unbalanced risk-reward ratios offered by these two games, one thing is for certain: The creators of these games will not increase your reward without making you assume more risk.

To be continued…

Now that you understand the concept of volatility, we can figure out why options have value while pizza coupons do not. Many are inclined to think that it’s due to the prices; stocks are far more expensive than pizzas. That’s partly true, but the bigger reason is due to the uncertainty of prices. You can be pretty sure that pizza prices will be the same price next week or even next year. And as competitive as the pizza market is, there’s even a good chance that prices may fall. Because we’re pretty certain about the price we’ll pay for pizza in the foreseeable and they don’t make up a large portion of our incomes or net worth, there’s no reason we’d want to “lock in” the price of a pizza. Consequently, pizza coupons have no value. With stocks, it’s a different story. One day the stock is up 2%, the next it could be down 10%; we’re never really sure what’s going to happen. And because stock portfolios typically do make up significant portions of our wealth, investors and traders are willing to pay to hedge those risks. They are willing to give options value. Options have value because stock prices fluctuate. Options were designed to control these fluctuations and therefore reduce risk.

Risk and Reward
While we’re learning about options pricing, this is a perfect point to introduce one of the most misunderstood concepts in option pricing – risk and reward. It is, in fact, so misunderstood that you will find it misinterpreted even among professional traders. Because of this, it is also one of the biggest reasons for option losses by new and seasoned traders. If you are to trade options successfully, you need to understand the indisputable relationship between risk and reward.

Will Rogers once said, “Why not go out on a limb? That’s where the fruit is.” This is one of the simplest ways of expressing the relationship between risk and reward. He was, of course, referring to the fact that in order to get the fruit (reward) you must venture out onto the tiny, unstable limbs. You must take some risk. The same concept applies to every financial decision you will ever make. In financial terms, if an investment is considered risky, that means there is a chance you might lose some or all of your initial investment. The greater the chance for loss, the greater the risk of the investment.

Risk and reward are the inseparable dynamic duo of finance, and they always increase and decrease together. If the potential reward from an investment is great, you can be sure that it comes with a lot of risk. And if the risk is low, you can forget about making a lot of money.

While the concept of risk and reward may make intuitive sense, it is one of the most overlooked concepts among investors and causes many problems for those who only consider the reward side. If you want to succeed in investing, it is crucial that you understand the risk-reward relationship and why this pair cannot be separated. We can easily convince you why risk and reward go hand-in-hand by playing a simple game.

Pricing Game
Imagine that you are offered the chance to play the following three games. An auction is held to play each game for which there is a $100 cash prize. The highest bidder is allowed to play the game one time and does not get his bid amount back. Think about each of the games and then jot down your answers on a piece of paper:

1. For the first game, the highest bidder is guaranteed to win $100 cash. No risk. No hidden strings attached. If you are the high bidder, you walk up and collect $100. How much would you bid to play this game?

2. For the second game, you must correctly call heads or tails at the flip of a coin in order to win the $100 prize. How much do you bid to play the game now?

3. For the third game, you must draw the ace of spades from a well-shuffled deck of cards in order to win $100. How much would you pay to play this game?

Even though we don’t know the particular answers you chose for each game, we are 100% certain that you elected to pay the highest price for the guaranteed game, the next highest amount for the coin game, and the least amount for the card game. How do we know this? It’s because of the relative risks involved in each game. The first game has no risk; we know that the winner always wins $100. And because of this, most people will bid this game up fairly close to the $100 reward. For the coin toss, we know that you would win $100 half the time and lose your bid amount half the time, which is certainly not as good as winning all of the time. In other words, we are less confident in the outcome – there is risk. There is no chance of losing with the first game but a significant chance of losing with the coin game. Because of this, you should be willing to spend less for this game. For the card game, we know you would win $100 only once out of every 52 tries, on average. This means you are almost certain to lose your money. On a comparative basis among the three games, this is the riskiest so you should be willing to spend the least to play it.

We just reviewed each game in terms of risk and found that the higher the risk, the lower the price you are willing to pay. We can also look at the three games in a positive light as we did when considering which strikes should cost more. We do that by simply asking which game is more desirable; that is the one that will carry the highest price. The guaranteed game is more desirable than the coin game and that’s why its price is higher. Or conversely, the coin game is riskier (it is less desirable) than the guaranteed game so it is cheaper. It doesn’t matter which dollar amounts you picked for each game but, just for the example, let’s assume you bid the following amounts:

Guaranteed game: $99
Coin game: $49
Card game: $1

These are results that we typically get when this game is presented at Option University seminars. Once we have some prices to work with, we can look at the three games in a different light. If you were willing to pay $99 for the first game, that’s the same as saying you were willing to invest $99 in order to make a $1 profit. The coin game, on the other hand, represents a game where you could invest $49 for the chance to make a $51 profit while the card game represents an opportunity to invest $1 in hopes of making a $99 profit. These costs and potential profit opportunities are summarized in Table 2-7:

Table 2-7
Game Cost Potential Profit
Guaranteed $99 $1
Coin $49 $51
Card $1 $99

Notice the relationship between the prices and the rewards: The higher the price (cost), the lower the reward (potential profit). The guaranteed game carries the highest price of $99 and comes with the smallest reward of $1. The coin game has a lower price and a correspondingly bigger reward. The card game has the lowest price of all and also has the biggest reward. You can see why it would be easy for someone to just look at the prices and potential profits in Table 2-7 and wonder why they should play anything but the card game. After all, it doesn’t seem to make sense to pay a high price to get a small reward when you can pay a tiny bit and possibly make a fortune. People who interpret the numbers in Table 2-7 this way are unintentionally assuming that the risks are equal across the board. That is easy to do if you’re just looking at the numbers. But once you understand the nature of each game, you start to see why people are willing to pay higher prices for some of the games.

To be continued…

As stated earlier, it is the “scoring potential” of the teams that drives the values of the bets. And that means that time plays a critical role since teams can produce higher scores the longer they are allowed to play. For example, if the basketball bet was only good for the first five minutes of the game then you should be willing to pay less than if it applied to the entire game.

It’s exactly this same reasoning that drives the true time premium component (the component above the cost of carry) of an option. If you have a $20 call, it will have intrinsic value for every price above $20 at expiration. If the stock closes at $23 at expiration, the call will be worth exactly $3. If it closes at $32, the call will be worth $12. How much will you pay for this $20 call? As with the sports bet, the answer depends on the “scoring potential” of the stock. If you are dealing with a stock whose price fluctuates wildly, you will pay much more for the call than if the stock price hardly moves. If there is more ability to make money on the bet, then the bet should be worth more money. In option trading, the “scoring potential” is known as volatility. A high-volatility stock has large price fluctuations. It can be up or down several percentage points in a day. A low-volatility stock, on the other hand, has almost no fluctuations in its price. The time value portion of an option is solely determined by the market’s perception as to the volatility of the stock between now and expiration. There is no way to say for sure if the time premium is too high or too low. It is strictly a value that exists in the minds of the traders.

To further understand volatility using an everyday example, we would say that gas prices are more volatile than milk prices. We’re pretty sure that a gallon of milk will cost about the same next week or next month but we’re not nearly so sure about a gallon of gas. While there are many ways to measure the volatility of a stock, that’s getting a little ahead of our goal. Just understand that the more volatile the stock’s price – the more uncertain its price is from day to day – the more money you’re going to pay for an option. High-volatility stocks have greater potential to move higher, and traders are therefore willing to pay higher time premiums for the option. It is the high-volatility stocks that carry the largest time premiums on their options.

For example, imagine that you are looking at two options:

ABC Jan. $50 call = $2
XYZ Jan. $50 call = $6

Both underlying stocks are $50 and both options expire at the same time. What can we conclude about the relative volatilities of these two stocks? We can conclude that XYZ must be more volatile than ABC, which is why traders are willing to pay more for that call option. XYZ is like a high-flying tech stock while ABC is more like a blue-chip company.

At the beginning of this chapter, Principle #2 conveyed that longer-term options are worth more than shorter-term options, so we know the ABC or XYZ March $50 calls will be worth more than the January $50 calls. Now you probably understand better why that is. For any given stock, the longer the timeframe, the better the chance for “high scores” or high stock prices, and that makes the value of calls and puts rise. Remember that put options will rise too since stock prices behave a little differently from basketball and football games in that they can rise or fall with equal ease.

There is no way to limit what time value traders will place on an option – it is a value that exists in their heads. It depends on how bullish or bearish traders are at that time. Obviously, if traders are extremely bullish, then they are willing to pay more for the time value. If they think the stock will just sit flat, they may not be willing to pay anything. The time value portion of an option is an indication of the volatility that traders believe the underlying stock will exhibit through the life of the option.

Does this mean that you should only buy options on high-volatility stocks? Although there are many traders who will tell you that you should only trade options on high-volatility stocks, that is actually a misconception. Those options, for reasons just stated, also have the highest time premiums, and that makes it that much harder to earn a profit.

For example, assume you are looking at the ABC and XYZ $50 calls we saw previously. The XYZ $50 call was trading for $6 while the ABC $50 call was trading for $2. The XYZ $50 call certainly has more potential for greater profit but it also costs more.

We can show that the high-volatility stock needs more movement to make a profit by calculating the breakeven points for each option at expiration. To find the breakeven point for a call, we simply add the cost of the option to the strike (we subtract it from the strike for a put option). For the ABC $50 call, this means the stock must close at $52 at expiration in order for the trader to break even. If the stock is $52 at expiration, the $50 call is worth exactly the intrinsic amount of $2. This means you paid $2 for the option and sold it for $2 so you just broke even. The XYZ $50 call, on the other hand, must have the stock close at $56 at expiration in order to break even. If the stock is $56 at expiration, that $50 call is worth exactly the intrinsic amount of $6, which is the amount that was paid for it, so you break even. Notice that the benefits of a high-volatility stock are balanced by the higher breakeven price. The market realizes the benefit in buying high volatility and prices those options higher.

When you hear traders tell you to only buy options on high-volatility stocks, they are unknowingly making the assumption that both options will cost the same. If that were true, you can be sure that the high-volatility options would be the right choice. However, the financial markets will always bid the prices higher for options on high-volatility stocks.

Let’s return to our main idea about what gives an option value. We said the first factor was intrinsic value, which is determined by favorable price movement. The second is due to time, which is affected by traders’ beliefs in the future volatility of the stock. This leads to a very important point about the characteristics of option prices: Option prices can rise or fall with no movement (or with adverse movement) in the underlying stock.

This can happen simply because of a change in traders’ outlooks on the volatility of the underlying stock. For example, assume you buy a three-month $50 call option for $3. A month later the stock is still $50 and the option is trading for $2. However, at that time, a buyout rumor starts circulating on the stock. We might see the $50 call trading for more than $3 even though less time remains on the option and the stock price hasn’t moved. The reason is that traders now believe the “scoring potential” or volatility will be greater in the near future so they are willing to bid the option higher than its price a month earlier.

Exercise
Go to www.cboe.com and check out option quotes on Google (GOOG) and McDonald’s (MCD). Look at the prices for the at-the-money calls and puts. Which stock has the more expensive options? Why?

To be continued….

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