Section 1 - Dow Jones Index Options: Essential terms and definitions

Transcription

1 1 of 17 Section 1 - Dow Jones Index Options: Essential terms and definitions Download this in PDF format. In many ways index options are similar to options on individual stocks, so it is relatively easy to master the subject of this lesson. There are, however, some commonly used option terms which have slightly different meanings when applied to index options. So a quick review of these terms is appropriate. First, it is necessary to define the term index, and, secondly, to discuss the unique aspects of index options. An index is a formula, or a consistent method, which measures the change in value of a group of stocks. The Dow Jones Industrial Average, the S&P 500 Stock Index and the NASDAQ 100 Stock Index are well-know indexes, but there are many others. The calculation of index levels can be very sophisticated, but, fortunately, it is not necessary for an average investor to know the mathematics. It is only necessary to be familiar with the price behavior of the index you follow. A ten-point change in one index may be small, for example, but it may be large for another index. A big difference between index options and stock options is that the underlying for an index option does not exist in the same way that individual stocks exist for stock options. While futures contracts exist on some indexes, these contracts can not be delivered when index options are exercised or assigned. Instead, the exchange of cash, in a process known as cash settlement, was created to handle the exercise and assignment of index options. An index option gives the owner the right to receive a cash payment. Sellers of index options are obligated to make the payment if an assignment notice is received. The amount of a cash payment is equal to the in-the-money amount, if any, times the index multiplier. An index multiplier is the amount by which the quoted price of an option is multiplied to calculate the option s actual market price. With few exceptions, index options in the U.S. have a multiplier of $100. An index option quoted at 8, for example, typically costs $800 (8 x $100) not including commissions. Strike prices of index options are conceptually similar to strike prices of stock options. They are reference points which determine whether an option is in-the-money, at-the-money or out-of-the-money. The terms in-the-money, at-the-money and out-ofthe-money have the same meaning for index options as they do for stock options, and expiration dates for index options are typically the Saturday following the third Friday of the expiration month just like expiration dates of stock options. Another unique aspect of index options is that there are two different types: American-style exercise and European-style exercise. All options on individual stocks are subject to American-style exercise, so many traders of these options are unfamiliar with the differences involved with European-style exercise options. Index options that are subject to American-style exercise may be exercised at any time prior to expiration. Index options that are subject to European-style exercise, however, may be exercised only on the last business day prior to expiration. On expiration day, both European-style and American-style index options are subject to automatic exercise, a process by which The Options Clearing Corporation automatically exercises and assigns all in-the-money index options and debits and credits the appropriate funds to brokerage firms accounts which, in turn, debit or credit customer accounts. Early exercise of American-style options occurs for rational reasons. American-style options on individual stocks are generally exercised early because of dividend payments.

2 of 17 American-style index options are typically exercised early by professional traders who are attempting to profit from perceived arbitrage opportunities between stock index futures and stock index options. A discussion of arbitrage is beyond the scope of this book, but early assignment of index options typically occurs only when an option is deep in-the-money and when it is close to expiration. Options which are exercised early or are assigned early are subject to standard commissions as if the option were sold or repurchased in the market. Therefore, early exercise is not a method of avoiding commissions and other transaction charges. Index settlement value at expiration is the final settlement value of an index at expiration. This value is important, because it is this index level and its relationship to the strike price which determine whether an index option is in-the-money or out-of-the-money and, consequently, whether an exercise or assignment is made and how much money, if any, changes hands. Before the two types of expiration settlements are explained, daily settlement value must be explained. An index s daily settlement value is similar to a stock's closing price. When closing prices for all stocks in an index have been established, an index s daily closing price, or daily settlement value, is calculated using those closing stock prices. An index s settlement value at expiration, however, may be determined by one of two methods. One method is based on closing stock prices, PM settlement, and the other method is based on opening prices, AM settlement. PM settlement, or afternoon settlement, is the most straight forward method of determining an index s expiration settlement value; it is the same index level as the daily settlement value. Closing prices of stocks in an index are used to calculate the index settlement level. Cash payments and receipts from exercise and assignment are determined based on that index level. AM settlement, or morning settlement, is based on opening prices the morning after the last day of option trading. The last day of trading for options subject to AM settlement is typically a Thursday, so Friday opening prices are used to calculate settlement values of those indexes. When opening prices of all stocks in such an index have been established, then the index settlement value is calculated using those opening prices. Settlement values of index options subject to AM settlement have their own ticker symbols. For example, the ticker symbol for the cash settlement level of the DJX Index options, options on the Dow Jones Industrial Average, is DJS. You should be aware that, on some expiration days, the settlement values of some indexes can be delayed for several hours due to delayed openings in individual stocks. A settlement value cannot be determined until opening prices for all stocks in an index have been established. Section 2 - Options on the Dow Jones Averages On October 6, 1997, options based on the three best known Dow Jones Averages began trading. Since these options are used in examples in the lesson, let us review some important facts about these options. Options based on the Dow Jones Industrial Average have the root symbol DJX. The symbol for options based on the Dow Jones Transportation Average is DTX, and DUX is the symbol for options based on the Dow Jones Utility Average. The DJX Index is defined as 1/100th of the Dow Jones Industrial Average. The DTX Index is 1/10th of the Dow Jones Transportation Index, and the DUX Index is the full value of the Dow Jones Index. This means that, if the Dow Jones Industrial Average is trading at 10,750, then the DJX will be If

3 3 of 17 the Dow Jones Transportation Index is 3,225.00, then the DTX is ; and, if the Dow Jones Utilities Index is , then the DUX is Dow Jones options have March, June, September and December expirations, and, in addition, there will be two near-term expirations. There will also be LEAPS (Long Term Equity Anticipation Securities) options with expirations up to two years. If today is January 4, 2008, for example, there will be options expiring in January, February, March, June and December of 2008, December of 2009, and December of Strike prices on the DJX are every This is similar to 100 points on the Dow Jones Industrials. Strike price intervals are 5.00 for the DTX and DUX, and there will be a minimum of five strikes above and below the current index level. With the DJX at and the Dow Industrials at 10,750, for example, option strikes on the DJX are available beginning from , , , etc. up to , and The Dow options are subject to European-style exercise, so they cannot be exercised early. Positions in these options, however, can be closed at any time during trading hours by making a closing and offsetting transaction in the marketplace. Also, DJX, DTX and DUX options are subject to AM settlement. This means that, generally, the last day of trading is the Thursday preceding the third Friday of the expiration month. settlement values are then determined using opening prices for each of the component securities on expiration Friday. Traders accustomed to index options which are subject to PM settlement at expiration should review the section above which describes expiration procedures for these options. The table below summarizes the contract specifications for the DJX, DTX and DUX options. Stock Index Options Based on Dow Jones Averages Options Based on the Dow Jones Industrials: DJX Index (1/100th of the DJIA) e.g., If the DJIA is 10,750, the DJX is Strike Prices Every 1.00 Exercise Style: Last Day of Trading: Settlement Ticker Symbol for Settlement e.g., , , , , etc. European (early exercise is not permitted) Thursday before third Friday of expiration month AM settlement (opening prices on expiration Friday determine index value for cash-settlement transfers) DJS Options Based on the Dow Jones Transports: DTX Index (1/10th of the DJTA) e.g., If the DJT is 3,222.00, the DTX is Strike Prices Every 5.00 Exercise Style: e.g., , , , , etc.. European (early exercise is not permitted)

4 of 17 Last Day of Trading: Settlement Ticker Symbol for Settlement Thursday before third Friday of expiration month AM settlement (opening prices on expiration Friday determine index value for cash-settlement transfers) DNS Options Based on the Dow Jones Utilities: DUX Index (Full of the DJUA) e.g., If the DJUA is , the DUX is Strike Prices Every 5.00 Exercise Style: Last Day of Trading: Settlement Ticker Symbol for Settlement e.g., , , , , etc. European (early exercise is not permitted) Thursday before third Friday of expiration month AM settlement (opening prices on expiration Friday determine index value for cash-settlement transfers) DUS Section 3 - Investor Strategy #1: A conservative way of investing in an index fund In Lesson 3, I stated that "buying stock is, perhaps, the most basic investmentoriented strategy there is." Well, another basic strategy is investing in mutual funds, and index funds are one type of mutual fund. Index funds attempt to replicate a particular index by purchasing all of the stocks in the proper proportions to match the performance of the index. Just as call options on individual stocks can be used to limit the risk of purchasing stocks, so too can index calls be used to limit the risk of purchasing index mutual funds. Heres how it works. Assume Linda is a conservative investor who has money to invest in a Dow Jones Industrial Average (DJIA) Index mutual fund. However, add this twist: On the one hand Linda wants to invest, but on the other hand she is worried about the short term market outlook. Everything she reads suggests that the market might be headed for a 10-15% decline. While such concerns have not been justified in the past, maybe this is the time! If she waits, she could find herself investing at a higher index level in the future. If she invests now and the market declines, then her capital will suffer along with the market. Can Linda get exposure to the market now and protect herself at the same time? The answer is a resounding, "Yes!" The concept of what Linda can do is simple, and it involves two steps. First, Linda can deposit most of her money in a money market fund for the short term and buy DJX Index call options on a dollar-for-dollar basis. Second, at option expiration, she can

5 5 of 17 make her investment in the DJIA Index fund. If the DJIA rises as she hopes, then Linda can exercise her calls, add the cash received to her money market funds and purchase approximately the same number of units of the DJIA Index fund that she could have purchased initially. If, however, the DJIA declines, then Lindas calls will expire worthless, but her money market funds will not have declined with the market. At that point it may be possible for her to purchase more units of the DJIA Index fund than she could initially. Lets look at an example. Assume Linda has $11,500 to invest in a DJIA Index fund and that the DJX Index is , equal to 11,000 on the Dow Jones Industrial Average. Assume also that a 90-day DJX 110 is trading at 5, or $500 not including commissions. Lindas first step is to deposit $11,000 in a money market fund. Second, she can purchase one DJX 90-day 110 for 5 or $500 not including commissions. Why one DJX call? Remember the index multiplier of $100? The index multiplier tells us two things. First, it tells us that the quoted option price of "5" translates into an actual market price of $500 (5 x $100). Second, it tells us that the stated underlying value of "110" is actually $11,000 of real market value (110 x $100 = $11,000). This means that, if the DJX Index is above 110 at expiration, then a 110 will perform like $11,000 invested in the index less the cost of the call. First, lets see what would happen to Linda if the DJX and the DJIA rise. Then lets see what would happen if they decline. If the DJX rises to 130 at option expiration, which is equal to 13,000 on the Dow Jones Industrial Average, for example, then $11,000 invested in an index fund would be worth $13,000, an increase of $2,000. Now look at the DJX 110. With the DJX Index at at expiration, Lindas 110 DJX will be worth 20 ( ), or $2,000. This amount equals the increase that $11,000 invested in the DJIA Index fund would experience. Lindas profit, however, would be $1,500, because the call cost $500. If Linda exercises her call and adds the $2,000 received to her money market funds of $11,000, then she will have $13,000 to invest in a DJIA fund. This is the same position she would have had she invested $11,000 in the DJIA fund initially. It is, of course, less than she would have if she invested $11,500 initially. Now consider what would happen if the DJX falls to 90 at expiration, which is equal to 9,000 on the DJIA. $11,000 invested in the index at 110 would decline to $9,000, a decrease of $2,000. With the DJX at at expiration, Lindas 110 will expire worthless for a loss of $500. But Lindas money market fund balance of $11,000 would remain intact. She could, therefore, invest her $11,000 in the DJIA fund at the current level of 9,000 and have a larger position than if she had invested $11,000 initially. The profit and loss table and profit and loss diagram below illustrate how buying a and investing in a money market fund compares to investing in a DJIA Index fund. Profit and Loss Table Buy DJX 110 and Money Market Fund compared to buy DJIA Index Fund DJX Index a t DJIA Index Fund Purchased at 110 Profit/Loss Profit/loss from Money Market Fund (Ignore Interest for simplicity) DJX 110 Purchased at 5 Profit/Loss DJX Money Market Fund Total Profit/Loss

6 of , ,500 +3, , ,500 +2, , ,500 +1, , , , , , The table and diagram show what happens at expiration if the DJX Index is above or below 110, equal to 11,000 on the DJIA. If the index is above 110, then Lindas call has value. At that point she can exercise the call and invest the cash received along with the balance in the money market fund in a DJIA Index fund. If the index level is below 110, then Lindas call will expire worthless, but her money market funds will not have declined. At that point she can invest in the DJIA Index fund at the then lower level and, perhaps, purchase more units than she could have purchased initially. How should Linda think when considering the strategy of buying an index call combined with a money market fund investment? She must think about risk. Is she so confident that she wants to invest in an index fund right now and live with the risk that that decision entails? Or is she willing to pay the cost of the call which will make less if the market rises, but also limit risk if the market declines. This is a subjective decision that only Linda can make.

7 of 17 A variation on the "Buy Index and Money Market" strategy I also mentioned in Lesson 3 that one technique of long-term investing is making steady, consistent investments. Regardless of the amount, regular savings accumulate over time. If you are a regular saver or investor in index funds, then index call options can help in a way similar to how they can help investors in individual stocks. A weekly contribution of $100 amounts to approximately $10,000 in 2 years. The purchase of an index call option today makes it possible to start controlling an investment of approximately that size right now. In two years, if the index is higher, you can actually invest in the index fund at the effective price of the call which is close to todays index level. If the index is lower, your call will expire worthless, but your hard-earned savings will not have decreased in value. The strategy that targets this goal for individual stocks is "Buy Long-Term now and Start Saving." The same strategy using long-term index calls can also be used for investing in index mutual funds. Consider the situation of an investor named Sue who has $800 now and saves $100 per week. Sue does not have $10,000 to invest in a DJIA index fund right now, but if the DJX Index is 100 right now, equal to 10,000 on the DJIA, and a 2-year DJX 100 is trading for 8, then the index options market has given Sue an alternative that she would not otherwise have. If Sue purchases the 2-year DJX 100 now, then she will have the right to receive the in-the-money amount on the expiration date in two years. If she also saves $100 per week for 2 years, then she will have approximately $10,000 at the option expiration date. If the DJX Index level is above 100 and Sue still wants to invest in the index fund, then she can exercise her 100 and invest the cash received along with the money market funds in a DJIA Index mutual fund. If she does this, she will have nearly the same position she would have if she invested $10,000 today. Alternatively, if the index level is above 100, and if Sue decides that she no longer wants to invest in the DJIA Index fund, then she can sell her call in the market at the prevailing price and use the funds received as she chooses. She will also have the accumulated funds in the money market account. If the DJX Index level is at or below 100 at option expiration, then Sues 100 will expire worthless for a loss of $800 plus commissions. But, regardless of the index level, she will still have the accumulated funds in her money market account. And she will still have two choices. She can invest in the index fund at the lower index level, or she can invest her accumulated funds elsewhere. Investor strategy #2: Protecting a portfolio In the previous section we discussed how a conservative investor who currently has cash or cash-like investments might use index call options to enter the market with limited risk. Now consider how an investor in a different situation might use index put options to limit risk. This investor is fully invested in either index funds or a diversified portfolio that follows an index on which options are traded. Consider the case of Michelle who has $36,000 invested in a DJIA Index fund. If the DJX Index is 120, equal to 12,000 on the DJIA, and if 6-month DJX 120 Puts are trading for 7, or $700, then Michelle can protect her DJIA Index fund investment by purchasing three of these puts. This strategy will limit the risk of owning the index fund until the option expiration date in 6 months. Lets see how this

8 8 of 17 strategy works. As in the previous examples, we will first describe the strategy. Second, we will draw a profit and loss diagram. Third, we will examine what happens if the DJX Index is higher, lower or unchanged at option expiration. And, fourth, we will discuss how Michelle might think about using this strategy. First, the strategy that Michelle is considering is: Own DJIA Index $12,000 = $36,000 Buy 3 6-month each = 2,100 Second, the profit and loss table and profit and loss diagram look like this: Profit and Loss Table: $36,000 Invested in DJIA Index fund at 12,000 and Long 3 DJX 120 Puts at 7 each DJX Index Level a t $36,000 DJIA Index 12,000 Profit/Loss Long 3 DJX each Profit/Loss Long DJIA Index Fund + Long DJX Puts Total Profit/Loss ,000-2,100 +9, ,000-2,100 +6, ,000-2,100 +3, ,000-2, ,100-2, , , , ,900-2, , ,900-2, , ,900-2,100

9 of 17 The diagram shows what happens if the index level is above or below 120 at option expiration. If the DJX index level is above 120 at expiration, then the 120 Put expires worthless. Michelle, of course, will still have her investment in the DJIA index fund which, with the index at or above 12,000, is worth at least $36,000. Above an index level of 12,700, Michelle will have a net profit, because the rise in portfolio value will offset the cost of her puts. Between index levels of 120 and 127, Michelle will have a loss, and hind sight may tell her that she should not have purchased the puts. But Michelle should remember that, because of her fear of a market decline when the puts were purchased, it was the insurance the puts provided that kept her in the market. Otherwise, she may have liquidated her index fund position and "gone to cash." If the DJX Index is below 120 at expiration, then Michelles puts will have value, and she will receive cash when she exercises them. That cash will at least partially offset the decline in her index fund investment. If, for example, the DJX Index declines to 100 at expiration, equivalent to a decline to 10,000 in the DJIA, Michelles $36,00 investment will decline to $30,000 for a $6,000 loss. Sues DJX 120 Puts, however, will have increased to 20 each, or $2,000 each, for a total value of $6,000 on 3 puts. Michelles profit will be 13 index points or $1,300 per option. The is calculated by subtracting the purchase price of 7, or $700, from the value of 20, or $2,000, at expiration. For Michelles 3 puts, this totals a profit of $3,900 (3 x $1,300) which partially offsets the loss of $6,000 on her DJIA Index fund investment in this example. What should Michelle focus on when considering the purchase of index puts for portfolio protection? Once again, the crucial element is her perception of risk. She should not purchase the puts for protection if she is confident that the DJX Index will rise. Should purchase these puts only if her perception of risk justifies the cost. Purchasing puts involves a trade-off. In return for paying a premium, Michelle will limit her loss potential during the life of the put. The decision to buy a put for protection is a subjective one that only Michelle can make. Section 4 - Unique aspects of index option price behavior The following section and the next one are fairly technical, so prepare yourself.

10 10 of 17 In theory, trading index options is the same as trading options on individual stocks. In practice, however, there some differences. One big difference is that the implied volatility level of index options changes noticeably and frequently. Implied volatility, remember, is the volatility percentage which, if used in an option pricing formula, returns the current market price of the option as the theoretical value. Consider the following example. Debra was bullish on the DJIA Index, so she purchased a DJX 110 at 2.10 in an attempt to profit from her forecast. The index rose as much as she predicted and within the time period she expected, but the price of the call declined to 1.90! Debra was understandably frustrated, so lets see how this could happen. When Debra made her forecast, the DJX index was , equal to 10,150 on the DJIA. It was 50 days before option expiration, interest rates were 4% and the dividend yield was 1.4%. Given these factors and a price of 2.10, the Options Calculator was used to determine that the implied volatility of the DJX 110 was 33%. This is how that determination was made: Calculating the implied volatility of Debras DJX 110 Option Price as an Input: Volatility as an Output: Index Level Strike Price Inputs Dividends 1.4% 110 Interest Rates Days to % 50 Outputs Volatility 33.3% Debras forecast was for the DJX to rise to 105 in 5 days, and she used the Options Calculator, as illustrated below, to estimate that the 110 call would rise to 3. Debras forecast for the DJX 110 Index Level Strike Price Original Inputs New Inputs Dividends 1.4% 1.4% Volatility 33.4% 33.4%

11 11 of 17 in Days: Estimate of New Price: Interest Rates Days to % 4.0% Original Outputs New Outputs The index rose to 105 in 5 days as Debra forecast, but, as stated above, the price of the 110 decreased to 1.90!! The question is: what else changed, in addition to the index level and the days to expiration, that caused the change in the price of the DJX 110? Since interest rates, dividends and the strike price are all observable, changes in these factors would be known. The unaccounted for change, therefore, must have been in the implied volatility. And, since the change in option price was a decrease, implied volatility must also have decreased. To determine exactly how much implied volatility decreased, we can use the Options Calculator as follows: Calculating the new implied volatility of the DJX 110 Inputs Index Level Option Price as an Input: Volatility as an Output: Strike Price 110 Dividends 1.4% 110 Interest Rates Days to % 45 Outputs Volatility 25.2% The conclusion is that, as the DJX index level rose over five days from to , the implied volatility of the DJX 110 decreased from 33.3% to 25.2%. The combination of three factors, increase in index level, decrease in days to expiration and decrease in implied volatility, caused the price of the DJX 110 to decrease from 2.10 to Debra accurately forecasted two of the factors, but, when trading index options, you need all three. A three-part forecast is required Index options are frequently difficult for beginners to trade, because the task of forecasting has changed from forecasting two components, price and time, to forecasting three components, price, time and implied volatility. The task of adding time to a price forecast is difficult enough, but for people who enjoy trading options, the adjustment seems possible. After all, if you have traded stocks, then

12 12 of 17 you are accustomed to forecasting price. Adding a second factor, time, is probably not an insurmountable task. But adding a forecast for implied volatility? That is something different. First, the concept of implied volatility is new to most people including experienced stock traders. Second, it takes quite a while to become comfortable with the concept of implied volatility. Third, it takes an equally long time to develop a feel for how much implied volatility can change. If you feel a little intimidated by this discussion of implied volatility, I can give you some good news. Dont worry! You can become comfortable with the concept of implied volatility, and you can learn to incorporate it into your forecasts. Only two things are required. You must be aware of implied volatility, and you must practice including it in your forecasts. Given enough time and experience, I believe that you can master this seemingly difficult aspect of option trading. Section 5 - Reducing the risk of changes in implied volatility Since change in implied volatility is a risk for option traders, it is logical to ask, "How can I reduce this risk?" The answer is: trade spreads. Option spreads are multiple-part positions involving at least one long, or purchased, option and at least one short, or sold, option. In this section, I will introduce you to a two-option spread known as a bull call spread. A bull call spread is created by purchasing one call and selling a second call which has the same expiration date and a higher strike than the purchased call. There are also bearish call spreads and bullish and bearish put spreads. Space does not permit a complete discussion of all these strategies, but the concepts I will discuss involving bull call spreads also apply to the other three spreads Lets see how Debra might have used a call spread to profit from her forecast that the DJX index and the DJIA would rise. When Debra was initially looking at the DJX 110, other calls with different strike prices were also available. Lets see what some of Debras other choices were initially: Strike Price DJX Index Days to Dividend Yield Interest Rates % % 115 Price Implied Volatility % % % % Given hindsight, even though Debra was bullish on the DJX index, she may have been reluctant to purchase any of these calls because of the high level of implied volatility. A beginner at trading index options might not have known that 33% is a "high" level of implied volatility. Also, it is possible that it could have stayed at that level or increased. Nevertheless, an implied volatility level in the 18% to 25% range is "more normal," although it has been lower. Note that relative high and low levels of implied volatility vary depending on the underlying entity. For some stocks the typical implied volatility might be 50% to 60% and for other stocks it may be lower at 40% to 50%. As a rule, the implied volatility for broad-based index options is lower than individual stocks; however, the important point is that traders should develop a familiarity with implied volatility levels so that they can develop good

13 13 of 17 judgment as to whether the volatility is high or low relative to past levels. Lets see how a bull call spread might have been helpful in Debras situation. With the prices listed above, Debra could have established a Bull Spread by simultaneously buying one 100 at 5.75 and selling one 105 at The net cost, therefore, would have been 2.25, or $225 per spread not including commissions. The profit and loss table and profit and loss diagram below show how this position behaves at expiration. Although Debras time forecast is 5 days and not 50 days which is option expiration, the table and diagram are useful starting points. They show the maximum profit potential, maximum risk and break-even point at expiration. After we understand the bull call spread from the perspective of the profit and loss table and profit and loss diagram, then we will compare the two strategies over Debras 5-day time horizon. 110 Compared to Spread DJX Index Level at of 100 of 105 of Spread Spread of Profit/Loss 110 Long 110 Profit/Loss

14 14 of 17 The profit and loss table and profit and loss diagram show how the Bull Spread compares to the long 110 at expiration. The long 110 has unlimited profit potential, maximum risk of 2.10 and a break-even point at expiration of In comparison, the Bull Spread has a maximum profit potential of 2.75, a maximum risk of 2.25 and a break-even point at expiration of You should note that the maximum profit potential of a bull call spread is equal to the difference between the strike prices less the net cost. In this example, the difference between the strikes is 5 ( ), the cost of the spread is 2.25 ( ), and the maximum profit potential is 2.75 (5 2.25). Also, note that the maximum profit potential is realized at expiration if the underlying index is at or above the higher strike, 105 in this example. Recognizing the trade-offs Which is "better," a long call or a bull call spread? Unfortunately, there is no "better" in an absolute sense. Each strategy has a different set of advantages and disadvantages. The bull call spread has a similar cost to the 110, a lower break-even point at expiration and a limited profit potential. The "limited profit potential" aspect may bother some traders who worry that, if a very large move in their direction does occur, then they will not be able to fully participate. And this is a valid observation. But, as the table and diagram indicate, the Bull Spread performs better in some scenarios, and the long 110 performs better in some others. The question is, given Debras 5-day forecast, why should she consider purchasing the call spread as an alternative to purchasing the 110 call? To answer this question, lets recall the concept of a three-part forecast introduced in the last section. Debra, remember, predicted that the DJX Index would rise from at 50 days prior to expiration to 110 at 45 days. Debras forecast did not include a forecast for the level of implied volatility. A beginner, of course might feel unsure about a forecast for implied volatility, so lets consider all three possibilities, a higher level, say 40%; an unchanged level at approximately 33%; and a lower level, say 25%. Now review the three exhibits below. Each shows the calculations from the Options Calculator using Debras 2-part forecast and the indicated level of implied volatility. Forecast #1: Implied Volatility rises to 40% in Index Level: Index Level Strike Price Original Inputs New Inputs / 105 / / 105 / 110 Dividends 1.4% 1.4% in Implied Volatility Volatility 33.4% 40.0%

15 15 of 17 in Days: Estimate of New Price: Interest Rates Days to Spd % 4.0% Original Outputs New Outputs / Forecast #2: Implied Volatility unchanged at 33.4% in Index Level: Index Level Strike Price Original Inputs New Inputs / 105 / / 105 / 110 Dividends 1.4% 1.4% in Implied Volatility Volatility 33.4% 33.4% in Days: Estimate of New Price: Interest Rates Days to Spd % 4.0% Original Outputs New Outputs Forecast #3: Implied Volatility decreases to 25% Original New Inputs

16 16 of 17 in Index Level: Index Level Strike Price Inputs / 105 / / 105 / 110 Dividends 1.4% 1.4% in Implied Volatility Volatility 33.4% 25.0% in Days: Estimate of New Price: Interest Rates Days to Spd % 4.0% Original Outputs New Outputs Comparing the results The three exhibits show that the prices of the 110 and the Spread behave differently as implied volatility changes -- even when the DJX Index level and the time to expiration are the same. The price of the 110 varies from 4 to 1.90 as the implied volatility level changes from 40% to 25%. The price of the spread, however, varies only from 2.75 to The table below compares the price behavior and the profit/loss results of these two strategies. Assumptions DJX Index 105 Days to 45 Interest % Dividend Yield 1.4% Volatility 25% - 40% Forecast of Profit/Loss of Spd. Spread Profit/Loss Imp. Vol. 40%

17 7 of 17 Imp. Vol. 33.4% Imp. Vol. 25% This table shows both the advantages and disadvantages of a bull call spread relative to a long call. The advantage of a bull call spread is that it is less sensitive to changes in implied volatility. The disadvantage is that the highest potential profit of the bull call spread is less than the potential profit of the long call. In this specific example, the highest estimated profit for the bull call spread is.90 per spread, while the highest estimated profit for the 110 is 1.90 per option. There is also the real-world disadvantage of higher commissions for the purchase of a bull call spread relative to the purchase of only a call. Summary of call spreads Prices of spreads behave differently than prices of single options. Generally speaking, spreads tend to change less than single option positions when implied volatility changes. Consequently, spreads may be the preferred choice when a forecast calls for a decrease in implied volatility. Spreads, however, are not "better" in an absolute sense than single options. Each strategy has advantages and disadvantages relative to the other.