24 to 36 months out.You can sell calls between 5 and 10 points higher than current marketvalue and earn significant returns. If the stock’s price rises to strikeprice or above, you can roll out of the position to avoid exercise. Youcan accept exercise and earn current income from call premium, or youcan close the short options at a profit due to reduced time value premium. Include LEAPS options in your study. These are also listed at theCBOE site: go to “Delayed option quotes” from the home page andenter the stock symbol; all options and LEAPS options are shown.LEAPS vastly increase the profit potential because time value is significantly higher for long-term LEAPS contracts.Table 2–1 shows a comparison all 10 stocks in our model portfolio. Thepremium levels available for options expiring in 3-month, 15-month,and 27-month increments are summarized. In each instance, the callselected is the closest out-of-the-money call based on current strikeprice. The option premium is divided by current stock price to arrive atthe initial yield.This comparison between three different calls makes the point that thelonger the call has to go until expiration, the higher the apparent rate of
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OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
Table 2–1 Comparative Call Yields*PremiumStock
Price
Strike Price
3-Month
15-Month
27-Month
Clorox%annualized %
$55.91
60
0.500.9%3.6%
2.855.1%4.1%
5.109.1%4.0%
Coca-Cola%annualized %
$38.90
40
0.852.2%8.8%
2.556.6%5.3%
4.0010.3%4.6%
Exxon Mobil%annualized %
$48.70
50
1.002.1%8.4%
3.106.4%5.1%
4.509.2%4.1%
Fannie Mae%annualized %
$67.65
70
2.603.8%15.2%
6.209.2%7.4%
8.3012.3%5.5%
Federal Express%annualized %
$87.78
90
2.502.8%11.2%
8.209.3%7.4%
12.3014.0%6.2%
General Dynamics%annualized %
$100.01
100
3.803.8%15.2%
9.909.9%7.9%
13.9013.9%6.2%
J.C. Penney%annualized %
$38.20
40
1.203.1%12.4%
3.9010.2%8.2%
5.7014.9%6.6%
Pepsi-Cola%annualized %
$48.48
50
0.851.8%7.2%
2.906.0%4.8%
4.308.9%4.0%
Washington Mutual%annualized %
$38.43
40
0.701.8%7.2%
2.556.6%5.3%
3.108.1%3.6%
Xerox%annualized %
$14.32
15
0.453.1%12.4%
1.7011.9%9.5%
2.5517.8%7.9%
* Values as of October 22, 2004, closing compared to calls expiring in January,2005, 2006, and 2007.Source: CBOE at http://www.cboe.com/home.
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return. To make the analysis accurate, however, we must annualizethese returns—reflect them as a 1-year period in each case. Because weare dealing with 3-month, 15-month, and 27-month options, the outcome changes dramatically upon annualizing. For example, referring tothe J.C. Penney calls,3-month option:
(3.1% ÷ 3) × 12 = 12.4%
15-month option:
(10.2% ÷ 15) × 12 = 8.2%
27-month option:
(14.9% ÷ 27) × 12 = 6.6%
This exercise demonstrates that the shorter term sale is far more profitable than the longer term. Annualizing in this case assumes that theoptions are held to the day of expiration, which makes the comparisonvalid among the three choices. In practice, exercise could occur at anytime the option is in the money, and the longer term options expandthe exposure for a longer period of time. The shorter term call in thisexample is desirable not only because annualized return is higher, butalso because there is a shorter term of exercise risk.In writing options, you also face a reinvestment risk. You may earn 12.4percent on an annualized basis with a 3-month call, but it is not alwayspossible to repeat that experience every 3 months. So, while a study ofcurrent annualized returns is instructive when comparing two or moreoption choices, it does not mean that you will be able to continue thattrend throughout an entire year.However, as long as one annualized return is more favorable thananother, the analysis on an annualized basis is important—as long asyou accept the possibility that shares of stock may be called away. Inthis example, a seemingly modest 3.1 percent return (J.C. Penney) actually would yield 12.4 percent on an annualized basis. The validity of thestrategy assumes that (a) you are willing to accept exercise as one possible outcome, (b) your basis in stock is far lower than current price levels, and (c) you like the rate of return that one or more of these optionsprovides. The obvious offset between time and rate of return has to beconsidered; if you sell a shorter term option, its time value declinesmore rapidly, and it can be closed or allowed to expire, to be replacedwith another call, perhaps even with a higher strike price. Longer term
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OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
options take longer for time value to decline, and the longer period alsorepresents more exposure to the risk of exercise. If the stock rises substantially within the option period, you must accept exercise or roll outof open short positions.You also need to be careful to not fall into the trap of overlookinglower priced stocks. Referring again to Table 2–1, five of the stocksyield double-digit returns for the 3-month calls. As exercise approaches, time value falls away with accelerating speed, and these are the mostattractive annualized returns on the chart. One of those is Xerox,which shows only 0.45 ($45.00) for the 3-month option. However,when annualized, this option represents a 12.4 percent return. So, eventhough Xerox is selling currently at only $14.32 per share, its annualized return is impressive. It yields the same as J.C. Penney, in fact,which sells for close to three times more per share. Employing thisstrategy with 100 shares of J.C. Penney and one option, or with 300shares of Xerox and three options, would produce approximately thesame outcome.This study reveals that it makes more sense to seek shorter term coveredcalls because (a) time value dissipates more rapidly as expiration nears,(b) the exposure to exercise is less than for longer term calls, and (c)annualized yield is greater, so you can sell subsequent calls more oftenusing faster expiration cycles.While we do not consider capital gains as part of this analysis, you mustbe aware of the spread between your original cost and the call’s strikeprice. This is essential in judging whether or not the covered call strategy makes sense. Since exercise is one of the possible outcomes, youcannot ignore that possibility. The potential for exercise if you had purchased J.C. Penney at $10 per share would be viewed differently than ifyou had purchased it at $35 per share.
Limiting Your Strategies to Conservative PlaysRemember the basic premise for conservative options trading: the covered call strategy should be used only on stocks with sound fundamentals that you bought for their value, not used simply to write options
Chapter 2 Option Basics
41
with high implied volatility. You may view exercise as part of a plan toreinvest proceeds in stock with equal growth potential and strong fundamentals. However, if you can hold calls until expiration withoutthreat of exercise, a new covered call can then be written. The processcan be repeated indefinitely, while you continue receiving dividendsand avoiding exercise—hopefully while the stock’s market value risesover time. That scenario—the existence of strong fundamental value inthe stock, long-term growth, dividend income, and repetitive coveredcall writes—maximizes the covered call strategy.Option volatility—for all the detailed and technical study that goesinto it—is not necessarily the sole determining point for selection ofoptions for conservative strategies. It is important, but more weightshould be given to overall rates of return in various scenarios: exercise, expiration, and close of the short position. It is that overallreturn—based on your original basis in the stock—that provides thegreatest flexibility. Remember, too, that out of respect for limitationsyou impose on yourself as a conservative investor, it may be preferableto select options and stocks with average price levels and to avoid highvolatility altogether. If we accept the theory that high price volatilitytranslates to higher market risk, it is ill advised to consider writingcovered calls at all. If risk levels of the stock have increased, it couldsignal the need for reevaluation of the stock itself. Should you sell thatstock and find an alternative issue with safer volatility levels? You maybe better off respecting the conservative stock standards based onfundamental analysis, writing options with “typical” pricing, andstaying away from stocks and options with higher than averagevolatility.The idea of avoiding stocks and options with higher-than-averageimplied volatility makes sense in your conservative portfolio. If yourestrict your activity to long stock positions, you monitor your portfolio constantly. If and when the fundamentals change, you replace yourhold position with a sell. Not only should that standard be retained, butthe implied volatility in option premium can be a red flag, enabling youto check other indicators to decide whether you want to keep your longstock position.
42
OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
Identifying Quality of EarningsThe last word in picking options should always go back to the conceptthat quality of earnings mandates the quantifications of a stock.1 Thefundamentals apply only to the stock because options have no tangiblevalue. So, when option implied volatility changes from the norm, ithappens for a reason. It is a symptom and perhaps a signal that fundamental strength (the quality of earnings) of the stock itself havechanged as well. Anticipation is the spark of the stock market, and moredecisions are made in anticipation of future risk, profit, and otherchange than on any known fundamentals. In adhering to your conservative standards, then, highly volatile option premium may be a morecautionary sign than is a covered call opportunity.
Trading Costs in the Option AnalysisRisk analysis often involves small margins, and it is easy to overlook allof the elements that go into that margin of profit. Trading costs areespecially troublesome when you deal in single-option trades. The percontract cost is relatively high. We prefer using single-option examplesthroughout this book to keep those examples clear, but in practice, thetrading costs affect your likely profits on both sides of the transaction.Trading fees vary widely, so you must shop around. You may discoverthat the brokerage you have been using to execute stock trades is notnecessarily the best-priced for option trades.The problem with multiple-contract trades is the increased risk exposure. It does not make sense to involve 10 options just so that the percontract trading price is lower. Is it practical to increase risk 10 timesby using that many options? It might be in some situations, but reducing trading costs should not be the primary criterion for employingmultiple option contracts. The determining factor is potential return1 Quality of earnings refers to the fundamental strength of the corporation and to its long-term
growth potential. A high quality of earnings translates to greater prospects for long-termgrowth and fewer unpleasant earnings surprises. One definition of this term is “Theamount of earnings attributable to higher sales or lower costs rather than artificial profitscreated by accounting anomalies such as inflation of inventory.” (www.investopedia.com)
Chapter 2 Option Basics
43
and risk level compared to the ultimate conservative goals in yourportfolio. For example, let’s say you own 1,000 shares of stock. Youmight decide to write covered calls on as much as 300 shares, but youdon’t want to write calls on all 1,000 shares; in the event of exercise,you’d profit from option premium income, but you may also like tokeep the remaining 700 shares. In this case, it would not make sense towrite 10 calls just because you own 1,000 shares. Yes, trading costswould be lower, but it may also violate your risk standards. In this case,you would not be willing to have all of your shares called away, so youdecide to write calls on 30 percent of your holdings. The trading costsare only one factor to consider; your desire to retain the other 70 percent of your portfolio is more important. If all 10 calls were exercisedand 1,000 shares were called away, you would regret the decision eventhough it worked out profitably.
Calculating the Net Profit or LossBased on the trading costs of the service you end up using, you mustcalculate that cost into your profit outcome. For example, based on thenumber of options you trade, let’s say that your trading costs are aquarter point on either side of the transaction. You have to deduct ahalf point from estimated profit levels (or add a half point to targetclosing price levels) to cover the cost of trading—a quarter point toopen a position and a quarter point to close.In considering capital gains upon exercise, you have to also include thetrading cost of having stock called away. So, if your selected coveredcall’s strike price is too close to your original basis in the stock, youcould make no profit (or even suffer a loss) if and when the call is exercised. There is no value in programming a net loss into a covered callposition; it only makes sense in the conservative portfolio when the netoutcome is going to be profitable overall, based on your original cost ofthe stock, dividend income, and call premium. Again, while we do notconsider capital gains as part of the return on an options strategy, thelevel of gain (or loss) will certainly affect your decision to open a shortoption against stock you own. If your basis in stock is 30 points belowthe call’s strike price, then exercise will result in 30 points of profit; but
44
OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
if your basis in stock is equal to the strike price, there will be no capitalgain upon exercise. This reality should affect the decision to enter acovered call position.
Tax Rules for Options: An OverviewTax rules for options are, for the most part, the same for options as forother investment activity. Dividend income is taxed at the top rate of 15percent from years 2003 and forward. Capital gains are either longterm or short-term, and the tax rates for long-term gains are lower, alsoat 15 percent.Some very important exceptions apply to taxes on option trades. Themost complex relate to writing in-the-money calls. These rules areexplained in detail in Chapter 5. Otherwise, the following tax rules apply:1. Short-term capital gains. If you hold an investment for less than12 months, you are taxed on profits as short-term. The federaltax rate can be as high as 35 percent.2. Long-term capital gains. If you own stock for 12 months ormore, your maximum rate is 15 percent.3. Wash sales. The “wash sale rule” prevents you from taking a lossat the end of the tax year by selling stock and then repurchasingthe same stock immediately. So, if you sell stock and repurchaseit within 30 days, it is treated as a wash sale. You are notallowed to claim a loss.4. Capital gains for unexercised long options. If you buy an option,it is taxed like other investments. The gain is taxed as shortterm if the option is held less than 12 months and taxed aslong-term if it is held 1 year or more.5. Exercised long options. If you exercise your option, the amountyou paid in premium is not separate: it is taken into basis instock. For a call, your cost is added to the basis in the stock; fora put you exercise, your option cost lowers the gain on stockwhen you sell.
Chapter 2 Option Basics
45
6. Short calls. You pay tax not when you sell the call, but when it isclosed (through expiration or a closing purchase). All profits onshort calls are short-term even when your holding period waslonger than 12 months. If your short call is exercised, your premium adjusts your basis in the stock.7. Taxes on short puts. You pay tax when the short put is closed. Ifthat occurs by way of a closing purchase order or expiration, itis a short-term gain or loss. If the short put is closed throughexercise, your premium adjusts your basis in the stock.Federal tax rules for option trades are exceptionally complex, and youwill probably need an experienced tax advisor to help complete yourtax return. Make certain that your advisor understands the federalrules. As explained in Chapter 5, the calculation of taxes for in-themoney short sales can be quite complex. In some cases, long-term capital gains on stocks can be reverted to short-term status as aconsequence of selling an in-the-money call.
The Importance of Professional Adviceand Tax PlanningWith the potential tax consequences in mind, you need to consult withan experienced tax professional before writing calls, to ensure that youdon’t create higher tax liabilities. Be sure that you know the tax rules ofa particular strategy before you proceed.One possible planning strategy is the intentional creation of short-termprofits. This is a way to close out positions with option premium andcapital gains combined, without regard to tax consequences. This workswhen you have a carryover loss to absorb. The annual limitation ondeduction of net losses is $3,000. Many investors have far greater losses,with little hope of ever using the entire loss. But when you have such aloss carryover, you can apply it against current-year gains. That changesthe entire planning question. You may welcome profitable short-termprofits as long as they are offset by the carryover. It enables you to takeprofits this year and free up capital without having to pay as much as 35percent in taxes.
46
OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
In any case, consult with your tax professional to ensure that you knowthe benefits and consequences of each type of trade in advance. Thebasics of options can be quite straightforward—until you begin studying the tax rules.For a detailed explanation of option tax rules, order or download a freecopy of the CBOE booklet, “Taxes and Investing” from http://www.cboe.com/LearnCenter/Workbench/pdfs/TaxesandInvesting.pdfThe next chapter provides an overview of risk assessment in terms ofreturn calculations and explains rolling strategies when you writecovered calls.
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3OPTIONS IN CONTEXTOption risks affect how we proceed; perceptions, sometimesfalse, inhibit us from taking full advantage of the conservativepotential of options. This chapter provides valuable detailsabout designing conservative short positions, special marginrequirements for option strategies, and calculating optionreturns on a comparative basis.
49
A
Any investment strategy—from plain to exotic—contains specific attributes and can be defined in terms of risk, rates ofreturn, and specific strategies for various market conditions.Options are probably the most flexible investment products available.They can be used alone, in combination with other options, or as hedgedevices to protect other positions. Options can help you to exploit market price swings, and they can be utilized in very speculative or in veryconservative ways.Identifying the conservative applications you can use makes options atool within your long-term portfolio and requires that you viewoptions trading in at least two classifications. First, the primary optionstrader is someone who uses options as the main vehicle for producingprofits. The trader is willing to take higher risks and uses long positionsmainly as coverage to reduce option risks or, at the very least, maychoose stocks due to their volatility and technical attributes more thanfor any fundamental strength. Second, the stock investor is likely to beconservative. This individual picks stocks as the primary means forputting together a portfolio and uses options to protect paper profits,provide downside protection, and augment current income. As long asoptions conform to the conservative standards in your portfolio, this isan appropriate series of strategies. You may want to view options not asa separate form of investing but as a method for enhancing and protecting your portfolio.
The Nature of Risk and RewardAny assessment of an investment decision has to involve a study of riskand reward. Your conservative approach to investing is based on yoursensitivity to risk as a primary means for all of your decisions. You areless likely than the typical investor to react to sudden market changesout of panic or greed; your view is long-term. Rather than watching
50
index-based and volume trends every day, you track a company’s fundamentals. You base your decisions on earnings reports, capitalstrength, and operating trends. The stocks you currently hold will besold if and when you determine that the fundamental strength of thecompany has changed or if you locate another company whose stock isa better candidate for long-term growth and safety.When options are involved, the risk equation changes. You are likelynot only to alter your investing profile to take options-based risks insome circumstances, but to use options to protect paper profits withoutselling or to reduce your basis in stock to create downside protection.The proper use of options can increase the conservative nature of yourportfolio because some strategies protect existing positions against loss.
Using Volatility as the Primary Risk MeasurementThe usual method for defining market risk of stocks involves pricevolatility. This is a starting point. The more erratic the price trend, thegreater the risk and the more difficulty you will have in trying to forecast future price movement. When a stock’s trading range is broad, itfurther complicates the picture; price volatility is a problem for stockinvestors because owning shares in a volatile company means valuationis on an unending roller coaster ride. It is easy to say that long-terminvestors should not be concerned with price volatility; but when livingthe experience, it can be unsettling to see a stock’s value cut in half in asingle trading session, double the following day, and then fall onceagain. It makes any form of portfolio planning difficult.Price volatility in the stock naturally affects option premium value aswell. The greater a stock’s price volatility, the greater the volatility inoption premium. This reality can be a trap for the inexperiencedinvestor who may pick stocks solely to write covered calls. While initialpremium income is high, those current yields may accompanydepressed prices in the stock by the time the short calls expire. Coveredcall writing is not always a conservative strategy. The definition appliesonly when stock has been selected on a conservative basis as a startingpoint. You may need to accept lower premium levels and lower impliedvolatility in exchange for safer overall portfolio positions.
Chapter 3 Options in Context
51
The interaction between risk and opportunity is a fact of life. Thehigher the risk, the higher potential returns, and the lower the risk,the lower those returns. However, with covered call writing, you cancreate an exception to the rule. Premised on the idea that you havefirst picked stocks that meet your conservative criteria, covered callwriting is a potentially profitable method for augmenting shortterm returns and overall profits, with no corresponding change inmarket risk. This is especially true when the stock’s market value hasgrown since acquisition date. It is difficult to create enough of ayield when the stock’s current market value is at approximately thesame level today as it was at purchase, so the more price growth yousee in the stock, the more profitable—and conservative—the covered call strategy. As long as the strike price of the calls would resultin current income if and when exercised, you can create the certainty of profits in any of the three outcomes—exercise, expiration, andclose of the position—while also gaining current income. The premium income you receive may be viewed as a means for takingpaper profits without selling stock. Those profits reduce your basis,providing downside protection.Example: You are reviewing available options on Clorox(CLX). The market value of stock is currently at $55.91, soyou are reviewing 55 and 60 options. Clearly, your selectionof options will be based on your purchase price for thestock. If you pay $56 for shares, the 55 call is not as attractive as the 60. Upon exercise, you would experience a $1capital loss on the 55 call, or a $4 gain on the 60 call. Theselection of an appropriate covered call has to include acritical analysis of your basis in stock, which makes thepoint that if your original basis in stock is far below eitheroption, then you must make comparisons based on exercisewith the certainty of profits. A study of the current 27month options reveals that the 55 option is available at$7.30 and the 60 goes for $5.10. Your selection of either onemust consider the capital gain, even though that gain is nowpart of the option return.
52
OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
Options Used to Mitigate Stock Investment RiskWith well-selected stocks, option premium is likely to be “in the zone”of expectation; in other words, the low risk of the conservatively pickedstock reflects the same low risk in the risk (volatility) of the option. Yougain the advantage, even when dealing with safe stocks and options, inthree ways:1. You select longer term option writes. The LEAPS call brings significant profit potential to the covered call strategy. You want touse out-of-the-money calls so that exercise can be avoided,because the purpose to covered call writing is to generate repetitive current profits; this is somewhat difficult with listed callsbecause time value is limited. But when you use LEAPS calls,premium levels often are high enough that the simple yield ismore attractive than with traditional listed options. The reasonis time. The greater the time left until expiration, the higher thetime value. This does not mean you have to keep the shortposition open for the entire duration; it can be closed andreplaced or rolled forward at any time, based on changing stockprices. It does mean you can acquire higher premium paymentsbecause time value premium on LEAPS calls is far higher thanthe premium on shorter term calls.2. The selection of covered writes is limited to stock that has appreciated.It would be contrary to your goals to write covered calls withstrike prices close to your original basis in the stock. Some ofthe best premium returns are found in calls whose currentmarket value is close to the call’s strike price. This maximizesshort-call income; but the strategy makes sense only if andwhen your basis in the stock is well below that level.Remember, the covered call write is a means for taking profitsand providing downside protection, but without necessarilyselling the stock. The strategy solves the dilemma every stockholder faces: stock has appreciated and the temptation is to takeprofits, but you don’t want the capital gain and you don’t wantto give up the long-term investment. Covered calls solve thisproblem, but they fit your risk profile only when exercise would
Chapter 3 Options in Context
53
yield returns you consider worthy of the exposure. For example, if you acquire stock at $28 per share and sell a 30 call for 3,exercise produces a $500 profit before trading costs. That is anoverall 17.9 percent return (3 points in the option and 2 pointsin the stock—a total of 5 points on stock acquired at $28 pershare). Net return is less when you calculate trading costs. Nowconsider the return if stock has appreciated to $44 per shareand you sell a 45 call for 3 ($300). Upon exercise, your pretrading cost return is 19 points (16 points on the stock and 3 pointson the call), which is a 67.9 percent return. When the stock hasappreciated, writing covered calls programs in those impressiveprofits. Few investors would complain about a 67.9 percentreturn without any increased market risk. This analysis, including both option and stock returns, is not necessarily the soleoutcome for a covered write strategy. If exercise does not occur,you do not count stock profits. You consider option profitsbased on current stock prices only. For example, a $300 gain onstock currently valued at $28 per share is a 10.7 percent return;and when the stock is valued at $44 per share, the $300 profitrepresents a 6.8 percent return.3. Exercise is avoided with rolling techniques. You want to repeatthe cash profits from writing covered calls on appreciated stock.The best of all worlds is to keep a strong long-term growthstock while generating repetitive option profits. If the short callis exercised, you would gladly accept the high yields, but at thesame time, you prefer to avoid exercise. The threat of exerciseoccurs when the market price of the stock is rising, so exerciseavoidance is profitable on two levels. First, you can continuewriting covered calls and gaining premium income. Second,your stock gains value as the price moves upward.Using rolling techniques achieves this. These techniques involve closinga current option and replacing it with another. For example, if youwrite a covered call and the stock price moves close to (or above) thestrike price, you avoid exercise by (a) closing the short call and (b)opening another call that expires later. The later expiring call can be at
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OPTIONS TRADING FOR THE CONSERVATIVE INVESTOR
the same strike price or higher. The objective in rolling forward (to alater expiration date) and up (to a higher strike price) is to avoid exercise and to do so without having to pay for the roll. You often can rollforward and up while also gaining additional net premium. In Chapter5, “Options as Cash Generators,” we explore the various rolling techniques to show how you can avoid exercise in the covered call strategy.
Another Kind of VolatilityAs long as you employ appreciated stock, you can create consistent andlow-risk profits with covered calls. Price volatility is not necessary forthe strategy to work. In fact, if you accept the technical risk of highvolatility stocks, it violates your conservative standards, and coveredcall writing makes no sense either. Your first priority should be to buyand hold growth stocks and to replace those stocks only when the fundamentals have changed.Price volatility is the starting point for identifying market risk, at least inthe short term. However, a related test of safety in the stock is the levelof fundamental volatility. This is the trend in reported revenue and earnings. If a company’s operating results are somewhat predictable, showing similar growth patterns from one year to the next, it is a sign of lowfundamental volatility. But if revenues and earnings change erraticallyfrom one year to the next, the high fundamental volatility translates tohigh risk on a fundamental level. Following are some observations concerning fundamental volatility as a measurement of risk:1. You are likely to see a corresponding level of price volatilitywhen fundamental volatility is present. In other words, stockprice is related directly to revenue and earnings trends.2. Fundamental volatility is as serious a measurement of safety asprice volatility; in fact, because price volatility often is shortterm in nature, it may be less serious than fundamental volatility (especially if the operating trends are chronicallyunpredictable).3. Comparisons between price and fundamental volatility can berevealing. When they do not correspond, it may be due to non-
Chapter 3 Options in Context
55
recurring price spikes. To make the comparison valid, study along-term pricing chart; remove spikes if (a) they are atypical,(