a chance to remove the spread early.This strategy could be employed in any case where stock optionsare trading with an extremely inflated volatility. The only two ingredients would be that the stock is trading fairly close to the striking pricewhen you establish the spread and that there is a reasonable chancethat no news will occur before expiration. This latter criterion wouldrule out situations where an earnings report, court verdict, or FDAdecision, for example, was scheduled to be handed down right beforeexpiration.
USING PROBABILITY AND STATISTICSIN VOLATILITY TRADINGSo far, a number of strategies have been discussed—from the simpleapproach to the more complex. You might well be asking, “How canI tell which ones are best in which situations?” It is true that we havegiven guidelines for when to buy volatility or when to sell it, and soforth. But what about times when there are several volatility buyingsituations that you are considering. How can you decide which is thebest? The answer to questions such as these lies in probability andstatistics. With what is called an “expected return,” we can rank
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strategies and compare them with each other— or just comparethem with acceptable market returns at the time.We will show how to compute expected return shortly, but firstlet’s describe what expected return is and what it is not. It is a usefultool in deciding which positions have the best chance for success; itis not a guarantee of success. If we say that the expected return frombuying a certain straddle is, say, 42 percent, you might be quiteexcited—42 percent is a very good return on your money, no matterwhat the position is; but it’s especially good for a strategy with limitedrisk, like a straddle buy. However, there is no guarantee that in thisone case, this position is going to make 42 percent. It could lose 100percent, as all straddles can. It could fail to reach the breakeven andlose a smaller amount. What expected return measures is this: if youwere to invest in this same strategy many times, with the samevolatility and the same option prices, then over time you should average 42 percent for the trade. Now, in reality, you won’t have theopportunity to invest in this same straddle many times in your lifetime, but you will have the opportunity to keep investing in positionswith high expected return. And that’s all you can ask. If you constantly establish positions with high expected returns, you shouldeventually have above-average returns—if your analysis has beendone correctly.What does this have to do with probability and statistics? Theexpected return incorporates the expected stock price movement(i.e., the probability of the stock being at each of the prices over anexpected range). This calculation is, of course, dependent on volatility. And it becomes very important to have a good volatility estimateor perhaps to look at several volatility estimates before deciding onwhat the expected return actually is.You can also use probability calculators to get certain probabilityconclusions, in addition to the expected return. These can be especially important for volatility sellers—where they might be forced tomake an adjustment to the position during its life. Any adjustmentwould alter the expected return, of course, and so we’d like to knowwhat chance there is of that occurring.In 1989, as October expiration was about a month away, the marketseemed range-bound and was trading quietly. OEX options seemed slightly
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overpriced, with an implied volatility nearly 20 percent and OEX tradingnear 166. A naked strangle—the Oct 175 calls and the Oct 160 puts—could be sold for 2.60. The expected return was good, and the probabilitythat the stock would finish within the breakevens—above 157.4 and below177.6—was quite high. The strangle was sold, and OEX closed at 162.20on October expiration. So the maximum return was realized, right?Not so fast! A week before expiration, UAL backed out of a takeoverdeal and caused a minicrash in the market. On a quiet Friday morning, oneweek before expiration, OEX was trading at 165. But then when the market crashed, it fell to 154.30 that afternoon and fell further to 152.10 thenext Monday morning, before prices rallied the rest of the week.A naked strangle seller would surely have made some adjustment on theFriday afternoon or Monday morning when the market was collapsing. Infact, he might have covered his short puts at a high price, since impliedvolatility skyrocketed while this was happening. So later, when OEX ralliedback to 162 (back inside the original profit range), he might not have beena participant any longer.What this trader really needed to know—before establishing the position—was the probability that the index would exceed the break-even pointsat any time during the life of the position, not just the probability at the endof the options’ life.
So these are the kinds of things that probabilities and statisticscan provide us. Let’s delve further into this so that you can see howthese can be used. Let’s discuss probability calculators first, and thenwe can see how they apply to expected returns.The simplest probability calculator gives the probability of thestock being at a certain point at the end of some time period—typically at the end of the options’ life in some position you are considering. The more sophisticated type of probability calculator can giveyou the probabilities of the stock exceeding a certain target price (orprices) at any time before expiration. Both calculators are providedon our web site, www.optionstrategist.com. The simpler version isfree and can be accessed by anyone. The “ever” probability calculator is available only to members of The Strategy Zone on our website, although we do also sell it as a stand-alone piece of software onCD-ROM. The formulae for these calculators are not being suppliedin this book.
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Let’s look at how you might use them. To do so, we will return tothe OEX example just presented—the one in which the market collapsed when UAL pulled out of a takeover bid.The following prices existed:OEX: 166
Oct 175 call: 1.00Oct 155 put: 1.60
Note that the implied volatility of the put is higher than that of the call,reflecting the typical reverse skew that has existed in OEX option since thecrash of 1987.Using a simple probability calculator, assuming a lognormal distribution,these are the inputs required:Stock price: 166Upside target: 177.6Downside target: 152.4Volatility estimate: 20%Length of study: one monthThe simple probability calculator says that the probability of ending abovethe upper break-even point of 177.6 at expiration is 9.7 percent, and theprobability of ending below the downside break-even point of 152.4 is 15.4percent. If you add them together, there is a 25.1 percent chance that thestock will close beyond one limit or the other. If this were an option buyingstrategy, that might be sufficient information to act on. However, since thisis a naked option position, we really need to know the probability of theOEX ever trading beyond the break-even points at any time between theinitial date and expiration. Those probabilities are as follows:Probability that OEX ever exceeds the upside (177.6) = 26.1%Probability that OEX ever exceeds the downside (152.4) = 15.9%Together, then, there is a 42 percent chance that OEX will exceed oneor the other of the break-even points. This is too high a probability; there istoo much risk of having to make an adjustment. I generally want to see the“ever” probability be 25 percent or less for selling strategies. So the tradershould sell farther out-of-the-money options to lower the probabilities ofhaving to adjust the position while it is in place. If those farther out-of-the-
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money options are so low in price that the overall return is minimal, thenthis position should be passed over, and the trader should look for otheropportunities.
Note that we had to enter a probability estimate as input to theprobability calculator. This is always a very crucial input. I generallyuse historical volatility for this input and tend to take a conservativeapproach. By that I mean that if you are looking at an option buyingstrategy, then use a low volatility estimate in your probability calculator. However, if you are considering the sale of an option or a strategy with negative vega, then use a high volatility estimate. By usingthis approach, you will be “penalizing” your probabilities, which issort of a worst-case scenario. You then won’t be overstating yourpotential profits. In fact, you may be understating them, but that’sokay because your actual results may then exceed the projections.In straddle buying situations, you would want to see a high probability of success—80 percent or more. In fact, you might even wantto calculate the probability that the underlying moves past the breakeven price by a reasonable amount—an amount large enough toallow you to make a good profit. For example, if the stock is 50 anda straddle costs 5 points, you might want to calculate the probabilityof the stock rising to 56 or falling to 44—one point more than thebreak-even points. If that probability is 80 percent or higher, thenyou have found a good straddle to buy.Many strategies have break-even points; even calendar spreadsdo. For example, look at the graph in Figure 6.7 or Figure 6.31. Youcan clearly see that there is an upside and a downside break-evenpoint in a calendar spread. Most traders are not too concerned withmaking adjustments at the break-even points of a calendar spread,for the strategy has limited risk inherently. However, you can use aprobability calculator and the break-even points to determine theprobability of making money. Certain assumptions have to be madein order to do this, but again you can adopt a sort of worst-case estimate and arrive at a reasonable projection.These prices existed in early 2004. With IBM at 92, you are considering thefollowing calendar spread, for a debit of 1.90:
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Buy July 95 call: 3.30Sell Apr 95 call: 1.40On this particular day, the various volatility measures were:PercentToday’s composite implied20-day historical50-day historical100-day historical
28262522
If you assume that the underlying will conform to the lowest of these volatilities, you are being conservative (high volatilities are an aid to calendarspread profits). In this case, using a 22 percent volatility, the break-evenpoints in the spread would be about 90.5 and 100.7 at April expiration—the time value remaining in the July option would be 1.90 at those prices.Now, we can use the probability calculator to determine the probabilities of IBM being above 90.5 and below 100.7 at expiration. The “endpoint” calculation is sufficient here; the “ever” probability calculation is notrequired. Again using a volatility of 22 percent in the calculation, we findthe following:Probability of IBM closing above 100.9 = 8%Probability of IBM closing below 90.5 = 41%By inference, then, the probability of IBM closing between the two—inprofitable territory for this calendar spread—would be 100 percent minus49 percent (the sum of those two probabilities), or 51 percent.This isn’t a great probability of profit. There are likely others that arebetter on this day, but at least one has a good handle on his chances of making a profit.
The use of probabilities in calendar spreads can even extend further. We could approximate the odds of making the maximum profitby computing the probability of being within, say, a half point of thestrike at any time during the last couple of days of life of the position.If the stock was that close to the strike with that little time remaining,the calendar spread would be nearly at its maximum value.
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Probability calculations can be made in similar manners fornearly every strategy. They are a useful guide, but not the ultimateone. For example they are useful in a simple strategy like coveredwriting, because we could compute the probability of making themaximum return (i.e., being called away), the probability of losing (ormaking) money, and even the probability that the covered write willoutperform or underperform simple stock ownership. For backspreads, we could compute the probabilities of making money, oflosing the maximum amount, and so forth.All strategies can be assessed in this manner—ratio spreads,backspreads, diagonal spreads, even simple call or put purchases.But what does the probability really tell us? It can tell us when we’reconsidering an unfavorable position; but when the probabilities aregood, that still doesn’t necessarily mean we’ll be making a goodreturn. Some traders, though, would rather have an extremely highprobability of making money—even if it’s a small amount of money—than have the optimal return strategy. For a simple strategy likecovered writing, this would mean writing deeply in-the-money callsthat might have probability of success of 90 percent or higher; butperhaps the return is low—in the single digits. Even calendarspreaders could opt for high-probability spreads, which might notyield large profits, however. So, probability analysis is interestingbut not as complete as the expected return, which we are nowready to discuss.
EXPECTED RETURNIn theory, an expected return analysis is the ultimate form of analysis.It encompasses all of the things we’ve discussed: volatility, probability, and profitability. By inference, it can also show you what delta,gamma, theta, and vega perhaps cannot—how profits look when thestock makes a big move.To compute an expected return, we first must estimate the pricesat which the underlying is going to trade at the end of the studylength. Usually the study length is the time to expiration, but it might
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565
be a different time length in certain, specific circumstances. Ratherthan trying to guess at the prices at which the underlying will trade,one normally makes the assumption that it moves in accordance withstandard price distributions—lognormal distribution, most likely.However, it is certainly acceptable to insert other distributions. Forexample, if a stock has received a takeover bid, but there are chancesthat (1) the deal could fall apart or (2) a higher bid could be receivedfrom another bidder, then that particular stock is certainly not goingto move in accordance with a lognormal distribution, at least not untilthe takeover matter has been concluded.
Let’s use a simple strategy so that the concept of expected return canbe exemplified—a covered call write. It is often the case that expensiveoptions are found in pharmaceutical stocks that are about to announce trialresults of drugs in development or are about to meet with the FDA to gainapproval to manufacture or sell a new drug. Such was the case withNeoPharm Inc. (NEOL):NEOL price: 20.75, in MarchJuly 17.5 call: 5.5100-day historical volatility: 60%Covered write net investment = 20.75 – 5.50 = 15.25This call provides a lot of downside protection, yet it still has a healthyamount of time value premium (2.25 points). So it appears that it offersboth a decent return and decent downside protection. However, the stock isvolatile, so it is unclear just how much protection 5.50 points really is.To compute expected profit, we estimate where the stock would be, theprobability of it being there, and multiply that probability times the profit atthat price. Then we divide the expected profit by the investment to getexpected return. Commissions will not be included in this example.The following table shows the pertinent items, assuming a lognormaldistribution of NEOL stock price. Using a 60 percent volatility, a drop oftwo standard deviations in one-third of a year (from March to July) wouldput the stock down to 10.30; a rise of two standard deviations would putthe stock all the way up to 41.80. So let’s divide up that spectrum—10.30to 41.80—into seven parts and calculate the results:
566
TRADING VOLATILITYStock Price10.3014.8019.3023.7928.2932.7837.2841.78
Probability0.0230.1440.2510.2350.1600.0920.0490.023Sum: 0.977
Profit
Probability × Profit
– 4.95–0.45+2.25+2.25+2.25+2.25+2.25+2.25
–0.11–0.06+0.56+0.53+0.36+0.21+0.11+0.05+1.65
Hence, the expected profit is 1.65 points, the investment is 15.25 points(assuming the covered write was executed in a cash account), and, thus, theexpected return is the division of the two, or 10.8 percent, not annualized.In reality, we would evaluate many more than seven data points. I generally scan the spectrum from –3 standard deviations to +3 standard deviations,dividing it up into 40 parts or more. But even this simplistic approach (sevendata points) provides a reasonable approximation of the expected return.
As mentioned earlier, we cannot say that this position “should”make 10.3 percent or “will” make 10.3 percent. It could lose everything if the company went bankrupt (if accounting fraud were discovered, for example). It could make as much as 2.25 points (14.8percent). But, on average, a position of this type will make 10.3 percent. In this one instance, an investor can’t know for sure what thereturn will be; but if he constantly invests in positions with highexpected returns, he should realize superior returns.In the previous example, the investment was fixed, since it was acovered write. But when you have a position that involves nakedoptions, the investment fluctuates, since the margin required by yourbrokerage firm is dependent on the stock and the option prices at thetime. This is not a real problem for expected returns because one cancompute an expected investment. The calculations are the same asin the previous example, except that the “profit” column is replacedby an “investment” column. Then the expected return itself would bethe expected profit divided by the expected investment.Expected profit calculations can also be used in a “what-if” form.What if the volatility collapses? What if the volatility explodes? What
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if the stock doesn’t adhere to a lognormal distribution? Any and all ofthese questions can be accommodated, merely by changing the factor in the analysis. Traders should be careful about changing the distribution from lognormal to something else; but if a straddle buyerfears the stock will continue to be trapped in a trading range, withperhaps equal probabilities of the stock being at all points within thatrange, he could lower the volatility and make the distribution flat andsee how it affects the return.You might use expected return analysis in this manner: requiringany position to have an expected return at least 20 percent, or somesuch fixed number, or requiring it to be a certain multiple of fixedinterest rates.With expected return analysis, you can also easily compare covered writes with calendar spreads, ratio spreads with backspreads,and so forth. All are reduced to their basic profitability, properlyincorporating volatility all along the way. This is the real worth ofexpected return analysis—the comparison of possibilities—not theprediction of actual returns, for there really is no prediction involved.It’s a statistical projection, not a prediction of how this one particularinvestment will turn out.
SUMMARYThere are two basic approaches to dealing with trading volatility,although they are related in that they both rely on using the currentpercentile level of the implied volatility. In the first approach, welook for the implied to be near the end of its trading range, either ina very high percentile or in a low one, and for the historical volatility to be more in the middle of the range. If that is the case, we willsell volatility when it is high and buy it when it is low. Strategies usedfor selling this type of volatility are the naked sell combo and theratio spread. If implied volatility is low, we will buy it, using longstraddles, backspreads, or calendar spreads as the favorite strategies. These strategies can all be enhanced to remove price risk—especially the sell combo, ratio spread, and calendar spread that arehurt by volatile price movement—by using gamma and delta neutralstrategies.
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TRADING VOLATILITY
The second approach for trading volatility concentrates more onlocating situations in which the individual options on the same underlying security have differing implied volatilities. When this conditionexists, it is called a volatility skew. If the skew is positive—that is,implied volatilities increase at successively higher striking prices—thenthe applicable strategies are put backspreads or call ratio spreads.However, if the opposite situation exists, which is called a reversevolatility skew, then call backspreads and put ratio spreads are the twostrategies that are the ones to use. Finally, a method for mathematically computing the extent of a volatility skew was presented.Experienced option traders tend to view volatility as the mostimportant variable when discussing option pricing and option tradingstrategies. Moreover, it is somewhat more predictable than prices; soif the volatility can be isolated and identified, then you might be ableto construct positions with less risk and more profitability by predicting volatility movements rather than by predicting price movements.
7
Other ImportantConsiderations
In this chapter, we discuss some other important aspects of optiontrading. One is support activities, which include order entry, brokers,data vendors, and software. Also included are some discussions ontrading in general, including procedures and money management.Finally, we look at the psychological aspect of trading options—perhaps the most important facet of trading, no matter what market youare trading.
SUPPORT ACTIVITIESMany of today’s traders are doing their own research and developingtheir own trading systems. I assume that is why you are reading thisbook. Even if you are relying on someone else for advice, such as adaily or monthly newsletter of the type that we publish, you are gathering your own information, apart from your broker. Thus, it isappropriate to discuss brokers and order entry, brokerage, data vendors, and software.
Order EntryWhen you place an order, it can be done in one of two ways: (1) youcan call your broker, or (2) you can use one of the computer orderentry systems where you enter the order directly from your computer(or possibly from the touch pad of your telephone). Regardless ofwhich method you choose, the order has to be sent to the floor ofthe appropriate exchange for execution. This is true for exchange569
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OTHER IMPORTANT CONSIDERATIONS
traded securities. In the over-the-counter (Nasdaq) market, there aresome differences.For most individual customers, the order-entry process begins witha phone call to your broker. Then, depending on the size and complexity of your order, your broker will either put the order over theelectronic entry system (this is often called the wire system) or phoneit to a special-handling desk or order desk at the home office of thebrokerage firm. If you enter the order electronically yourself, it still goesto a brokerage firm, where it is rerouted into their own wire system. Aflow chart of the order-entry process is pictured in Figure 7.1.There are benefits to either method of placing an order. If theorder is small and speed of execution is desired, then the electronicmethod is best, although many customers at home don’t have accessto high-speed Internet connections. However, even if you call yourbroker directly with a small order or if it is a simple market or limitorder, it is most likely then entered electronically by a clerk at thebrokerage office. Thus, it eventually becomes an electronic order aswell. One of two things can happen to your order at this point: (1)either it will go to your firm’s booth on the appropriate tradingfloor, or (2) it will go onto the automatic execution system.
Figure 7.1ORDER FLOWOrder Desk
BrokerCustomerElectronicEntry
Floor
Booth
AutomaticTrading Post
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If an electronic order goes into the automatic execution system, itgoes into a computer that directs it to the appropriate trading post(the place where the trading in a particular stock or option actuallytakes place) and gives an immediate, automatic execution. This system is not available for all orders; however, if the order is a small oneof 10 contracts or less and it is a market order or it is a limit order tobuy at the current offer or to sell at the current bid, then the orderwill go onto the automatic system. Each option exchange has its ownparticular maxima regarding the number of contracts that are available for automatic execution (for example, they may be larger forindex options), and each exchange calls their automatic system by adifferent name. You should check with your broker for specificdetails on automatic order entry. When this system is used, anotherstage in the process—your brokerage firm’s floor trading booth—isbypassed.The other thing that can happen to an electronic order is that itgoes to the firm’s booth on the trading floor. At this point, the orderis given to a floor broker, and he physically goes into the trading pitand executes the order. Your order can also get to a floor brokerthrough what is called an “electronic deck.” That means the order issent electronically from upstairs directly to a broker standing in thecrowd, and he executes the order. This bypasses going through thebrokerage firm’s desk and then having to be sent out to the crowd.Remember, though, that there was another way to get yourorder to the floor. If you are a larger trader, for example, you mightdemand and require the personal attention that a large order sometimes needs. Your order might be called into a special-handlingdesk—or order desk—which will in turn call the order down to thetrading floor. This type of order is then monitored by the order deskin order to stay on top of partial fills or for any other type of personalattention that the order might require. Some clients even give theorder desk or the broker some discretion (i.e., leeway in what priceto pay), figuring that the professionals on the trading desk and on thetrading floor are more in tune with the market.The order desk is staffed by professional traders who are familiarwith the sometimes arcane terminology of options and who generallyhandle larger orders and/or orders involving spreads and more complex situations. In any case, though, there is usually a minimum num-
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OTHER IMPORTANT CONSIDERATIONS
ber of contracts that you must trade in order to receive the benefits ofhaving the order desk take care of your order. Larger customers,money managers, and institutional option traders talk directly to theorder desk to get this special handling. If you are trading in fairlylarge size, then you should request that your brokerage firm allowyou to talk directly to the order desk. Your broker will still receivehis commissions, but you will be getting faster executions becauseyou have bypassed one phone call in the order-entry chain: thephone call from your broker to the order desk now becomes unnecessary. For some large customers, their broker actually sits next tothe order desk so that they effectively gain direct access to the deskby calling their broker; these brokers are generally called institutional brokers and are only available to large trading accounts.Thus, orders that arrive at your brokerage firm’s floor booth—whether sent there by the firm’s wire system or called in by the firm’sorder desk— end up in the hands of a floor broker. Floor brokers areof two general types: (1) those who work for the same firm as yourbroker and (2) independents who work for themselves (sometimescalled two-dollar brokers). The independent broker charges an additional fee for his services, but he may be better at obtaining favorableprice executions and in handling special orders. Unless you are calling the independent broker yourself (which is possible if your brokerage firm will allow it), then you have no control over which type ofbroker winds up with your order.These steps are all summarized in Figure 7.1. Note that thequickest path for large traders is for the customer to call the orderdesk, from where the floor booth is called, which is where the orderis executed. As mentioned in the previous paragraph, it is evenquicker to call a floor booth yourself. In order to take advantage ofthis, however, your brokerage firm would have to agree to processtrades executed by the independent broker. As there is a certainamount of “handshaking” that needs to go on, it may not be easy toestablish such a relationship.
Brokers and BrokerageToday, if a trader uses a full-service broker, he uses him more for theservices provided than for recommendations; that is, he is interested
SUPPORT ACTIVITIES
573
in technical or fundamental reports, summaries of his account,charts, and other products that the full-service firm can provide. Mostimportant, the full-service broker offers the ability to watch a client’saccount and to alert him when a previously agreed-upon eventoccurs. For example, if you are trying to use mental stops—whereyou want to make a decision in real time when the underlying hits acertain price—you can have your full-service broker call you whenthe stock, future, or index hits that price. Thus, you, the client, donot necessarily need real-time quotation capabilities if your brokercan watch your positions for you.A discount broker will not be able to give that level of service, buthis commission rates will often be lower than those of a full-servicefirm. If you are using a discount broker, you will need to have someway of knowing prices so that you can make trading decisions. Ifyour investment horizon is intermediate to long term, you probablyare not so interested in knowing real-time prices. However, if you area short-term trader/investor, then you will most likely need access toprices on a timely basis. A discount broker will not be able to offerthose, but we discuss price quotation services shortly.Perhaps the most important aspect of any brokerage firm—notof your broker himself—is what kind of orders they will take and howthey handle those orders. I have had attendees at seminars tell methat their brokerage firm will only take market or limit orders—nospreads, stops, or contingent orders. My advice is always for them tofind a firm that will take those orders. Similarly, if your orders arerepeatedly slow in getting to the floor and are then sloppily executed,or if you have to argue about executions and partial fills, perhaps youshould look for another brokerage firm with which to do business. Itdoes little good to save on commissions by using a deep-discountbroker if you have to then give those savings back in the form ofrestricted order entry or poor order execution.One thing you should be aware of in selecting a broker and a brokerage firm is commissions, including those for treatment for exercise and assignment. Commissions are important, but they shouldnot be your only concern. I am always hesitant to recommend a specific commission rate that you should seek, because there are otherconsiderations. However, the following are reasonable rates that areattainable from many reputable brokerage firms: stock or index
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OTHER IMPORTANT CONSIDERATIONS
options: $3 per option; stock: 6 cents per share; futures options:$10 per side; futures: $15 per round turn. If your broker charges alittle more than that but you feel you are getting service to justify it,then I would heartily recommend that you stay with him. Exerciseand assignment commissions are an important aspect of option trading, particularly for stock and index options. If you are assigned or ifyou exercise, you should ask your broker for rates comparable to theoption trade that would have occurred.
This situation often arises near expiration: the call option that you own andwant to sell is trading at a discount. It is more efficient for you