THE COMPLETE BOOK OF OPTION SPREADS...

THECOMPLETE

BOOK

OFOPTION

SPREADSAND

COMBINATIONS

StrategiesforIncomeGeneration,Directional

Moves,andRiskReduction

ScottNations

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www.wiley.com.Library of Congress Cataloging-in-PublicationData:Nations,Scott.The complete book of option spreadsand combinations : strategies forincome generation, directional moves,andriskreduction/ScottNations.pagescm.–(Wileytrading)Includesindex.ISBN 978-1-118-80545-9 (paperback);ISBN 978-1-118-80639-5 (ebk); ISBN978-1-118-80620-3(ebk)1. Options (Finance) 2. Options(Finance)–Mathematics. 3. Investmentanalysis.I.Title.HG6024.A3N3472014332.64′53–dc23

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2014016781

Formymother,whoalwaysmadethetimetoanswera

questionfromacuriouskid.

CONTENTS

1. Foreword2. Preface

1. TheSpreadsandCombinations

3. Chapter1:NotJustMoreorLessbutDifferent

1. The“Flavors”:CallsandPuts

2. TheExpirationDate

3. TheStrikePrice4. AnOption

Correspondsto100SharesofStock

5. DefininganOption6. Moneyness7. WhatWeMeanby

Spreadand

Combination8. AFinalThought

4. Chapter2:JustaLittleMath1. TheOptionPrice2. Volatilityandthe

VolatilityImpliedbytheOptionPrice

3. OptionErosion4. OptionPrice

Sensitivities5. Sensitivitytothe

PassageofTime6. Sensitivitytothe

PriceoftheUnderlyingStock

7. ChangesinVolatility

8. OtherSensitivities5. Chapter3:Vertical

Spreads1. BuyingandSelling

VerticalSpreads2. VerticalSpread

MaximumandMinimumValues

3. Naming4. Moneynessand

VerticalSpreads5. BullishandBearish

VerticalSpreads6. SellingaCall

VerticalSpread7. BreakevenPoints8. TheNecessary

PriceAction

9. VerticalSpreadsandYourMarketOutlook

10. AsymmetryofRiskandRewardforVerticalSpreads

11. OptionDeltaandLikelihood

12. VerticalSpreadValuePriortoExpiration

13. TheOtherGreeks

14. TheBestMeasureofVerticalSpreadCost

15. In-the-MoneyVerticalSpreads

6. Chapter4:CoveredCalls1. Profitability2. CoveredCallsand

DownsideProtection—NotAsMuchAsWe’dLike

3. UsingCoveredCallsto“Create”Dividends

4. HavingYourSharesCalledAway

5. Don’tFearAssignment

6. StockCoveredVerticalCallSpread

7. Chapter5:CoveredPuts

1. TheRegretPoint2. MarketOutlook3. Out-of-the-Money

CoveredPuts4. In-the-Money

CoveredPuts5. At-the-Moneyor

NearlyAt-the-Money

6. CoveredPutversusCoveredCall

8. Chapter6:Calendar

Spreads1. CallCalendar

Spreads2. SellingCalendar

Spreads3. Directionality4. Catalysts5. TheSuperCalendar

9. Chapter7:Straddles1. TheShortStraddle2. Likelihoods

3. SellingCoveredStraddles

10. Chapter8:Strangles1. SellingStrangles2. SellingCovered

Strangles11. Chapter9:Collars

1. WiderCollars2. In-the-Money

Collars3. PotentialOutcomes4. AZero-CostCollar

5. Skew6. HowaCollarIs

SimilartoOtherSpreadsandCombinations

7. PutSpreadCollar8. CallSpreadCollar

12. Chapter10:RiskReversal1. Likelihoods2. HowSkewHelpsa

RiskReversal

3. CallSpreadRiskReversal

13. Chapter11:Butterflies1. BuyingandSelling

Butterflies—TheTerminology

2. PutButterflies3. ButterfliesPriorto

Expiration4. Butterfliesand

YourMarketExpectations

5. BrokenButterflies14. Chapter12:Condorsand

IronCondors1. SellingaCondor2. TheBid/Ask

SpreadandCondorSpreads

3. IronCondor4. Directional

Condors15. Chapter13:

Conversion/Reversal

1. Reversal2. Dividends3. PinRisk

16. Chapter14:RatioSpreadsandBackSpreads1. VerticalSpreads,

Butterflies,andRatioSpreads

2. CallRatioSpreads3. CallRatioSpreads

forStockRepair

4. BackSpreads5. SuperBackSpreads

17. Chapter15:OtherSpreadsandCombinations1. MarriedPut2. DiagonalSpread3. IronButterfly4. ChristmasTree5. BoxSpread6. JellyRoll

7. Stupid8. Guts9. OtherPotential

SpreadsandCombinations

18. AbouttheWebsite19. AbouttheAuthor20. Index21. EndUserLicense

Agreement

ListofTables1. Table1.12. Table1.23. Table1.34. Table1.45. Table2.16. Table3.17. Table3.28. Table3.3

9. Table3.410. Table3.511. Table3.612. Table3.713. Table3.814. Table3.915. Table3.1016. Table3.1117. Table3.1218. Table3.13

59. Table12.460. Table12.561. Table12.662. Table12.7

ListofIllustrations1. Figure1.1SomeOptions

inGM2. Figure1.2ProfitorLoss

forOurLong37StrikeCallInGM

3. Figure1.3ProfitorLossforOurShort37StrikeCallinGM

4. Figure1.4ProfitorLossforOurLong33Strike

PutinGM5. Figure1.5ProfitorLoss

forOurShort33StrikePutinGM

6. Figure1.6MoneynessExamples

7. Figure2.1OptionValuebyTimetoExpiration

8. Figure2.2OptionErosionbyTimetoExpiration

9. Figure2.3Option

ErosionbyUnderlyingStockPrice

10. Figure2.4SensitivitytothePriceoftheUnderlyingStock

11. Figure2.5DeltabyStockPrice

12. Figure2.6HowOptionValueChangeswithChangesinVolatilityAssumption

13. Figure2.7Gamma

14. Figure3.1SomeCallOptions

15. Figure3.2CallOptionsandVerticalSpread

16. Figure3.3PutOptionsandVerticalSpreads

17. Figure3.4PayoffforBuyingaLongVerticalCallSpread

18. Figure3.5StockMustRallyforLongCallVerticalSpreadtoBe

Profitable19. Figure3.6Payofffor

SellingaCallVertical20. Figure3.7Payofffor

BuyingaVerticalPutSpread

21. Figure3.8PayoffforSellingaVerticalPutSpread

22. Figure3.9ShortPutVerticalandtheMarginofError

23. Figure3.10PayoffsandLikelihoodsforBuyingaVerticalCallSpread

24. Figure3.11PayoffforaLongVerticalCallSpreadandValueBeforeExpiration

25. Figure3.12PayoffforaLongVerticalCallSpreadandValuebeforeExpiration

26. Figure3.13PutSpreadTheta

27. Figure4.1WouldYouMakeThisTrade?

28. Figure4.2The60StrikeJPMCoveredCall

29. Figure4.3JPM60StrikeCoveredCallPricebyTimetoExpiration

30. Figure4.4OurCoveredCalloveraLongerTimePeriod

31. Figure4.5CoveredCallPricebyTimeto

ExpirationforSeveralStrikePrices

32. Figure4.6OneLong-DatedCoveredCalloraSeriesof30-DayCoveredCalls?

33. Figure4.7DownsideProtectionfromaCoveredCall—NotasMuchasWe’dLike

34. Figure4.8CoveredCallYieldandLikelihoodofGettingStockCalled

Away35. Figure4.9CoveredCall

TimeValueforSeveralStrikePrices

36. Figure4.10ThreePotentialGLDCoveredCalls

37. Figure4.11AStockCoveredVerticalCallSpreadinGLD

38. Figure4.12AStockCoveredverticalCall

SpreadversusaTraditionalCoveredCall

39. Figure5.1ACoveredPutinMSFT

40. Figure5.2MSFTCoveredPutPayoffChart

41. Figure5.3MSFT36StrikeCoveredPutversusMSFTStock

42. Figure5.4MSFT36StrikeCoveredPutby

TimetoExpiration43. Figure5.536Strike

versus34Strike44. Figure5.6AnAt-the-

MoneyPutversusaDeepOut-of-the-MoneyPut

45. Figure5.7WFCDeepIn-the-MoneyCoveredPutversusAt-the-MoneyCoveredPut

46. Figure5.8AWFCDeep

In-the-MoneyCoveredPutversusOwningtheStock

47. Figure5.9DeepIn-the-MoneyCoveredPutsinGMandtheBid/AskSpread

48. Figure5.10MSFTAt-the-MoneyCoveredPutandtheImportantLikelihoods

49. Figure5.11ThreeCoveredPutsinGLD

50. Figure5.12In-the-Money,Out-of-the-Money,andAt-the-MoneyOptionsinGLD

51. Figure6.1TwoPutCalendarSpreadsinORCL

52. Figure6.2TwoCallCalendarSpreadsinOracle(ORCL)

53. Figure6.3TheMay/June34StrikeCall

CalendarPayoff54. Figure6.4The

May/June33StrikeCallCalendarPayoff

55. Figure6.5DailyNetErosionCollectedfor33StrikeCallCalendar

56. Figure6.6TheShortJune/July30StrikePutCalendarPayoff

57. Figure6.7CallCalendarSpreadsand

Directionality58. Figure7.1AStraddle59. Figure7.2ThePayoff

forOurLong21StrikeStraddle

60. Figure7.3WhereOurStraddleBreaksEven

61. Figure7.4BuyingaSPYStraddlebeforeaFedMeeting

62. Figure7.5BuyingaStraddleInSPY

63. Figure7.6OurLongStraddleinSPYversustheConstituentOptions

64. Figure7.7SellingaStraddleinDeutscheBank(DB)

65. Figure7.8AShortStraddleinDeutscheBank(DB)

66. Figure7.9OurShortStraddleinDeutscheBank(DB)

67. Figure7.10DoublingOurMoneywithaStraddleinSPY

68. Figure7.11StockChartofFordforOurCoveredStraddle

69. Figure7.12SellingaCoveredStraddleinFord

70. Figure7.13PayoffforaCoveredStraddleinFord

71. Figure8.1BuyingaStrangleinBlackberry(BBRY)

72. Figure8.2BuyingaBullishStrangleinBlackberry(BBRY)

73. Figure8.3BuyingaBearishStrangleinBlackberry(BBRY)

74. Figure8.4ThePayoffforOurLong9.50/11.50StrangleinBlackberry(BBRY)

75. Figure8.5TheCostofOurGoogleStrangleversustheLikelihoodofBreakingEven

76. Figure8.6OptionsforaStrangleinEEM,theEmerging-MarketsETF

77. Figure8.7SellingaStrangleinFacebook(FB)

78. Figure8.8ThePayoffforOurShortStranglein

Facebook(FB)79. Figure8.9SellingA

CoveredStrangleinford80. Figure8.10ThePayoff

forOurCoveredStrangleinFord

81. Figure8.11TheStockChartofFordandOurEffectivePrices

82. Figure9.1AnOptionCollaronMGM

83. Figure9.2Payoffforthe

23/24CollarinMGM84. Figure9.3Payofforthe

22/24CollarinMGM85. Figure9.4AWider

CollarinMGMThat’sAlsoaZero-CostCollar

86. Figure9.5AnIn-the-MoneyCollaronMGM

87. Figure9.6AnIn-the-MoneyCollaronMGM

88. Figure9.7AZero-CostCollarinIWM

89. Figure9.8PayoffforaZero-CostCollaronIWM

90. Figure9.9WhyaZero-CostCollarIsn’tReallyZeroCost—OptionSkew

91. Figure9.10VIXSkew92. Figure9.11Similarities

betweenaCollarandBullishVerticalSpreads

93. Figure9.12APut

SpreadCollarinIWM94. Figure9.13Payofffora

PutSpreadCollaronIWM

95. Figure10.1ARiskReversalinWal-Mart(WMT)

96. Figure10.2TheWMT75/82.50RiskReversal

97. Figure10.3PayoffforOur75/82.50RiskReversalinWal-Mart

(WMT)98. Figure10.4HowOur

75/82.50RiskReversalErodeswithoutAnyMovement

99. Figure10.5ASecondRiskReversalinWal-Mart(WMT)

100. Figure10.6Payoffforthe72.50/80RiskReversalinWal-Mart(WMT)

101. Figure10.7HowOurMoreBullishRiskReversalErodes

102. Figure10.8HowOur72.50/80RiskReversalWillErodeafteraRally

103. Figure10.9ImpliedVolatilitySkewinWMTOptions

104. Figure10.10ACallSpreadRiskReversalinWMT

105. Figure10.11Payofffor70/82.50/80CallSpreadRiskReversalinWMT

106. Figure11.1CreatingaLongCallButterfly

107. Figure11.2CallOptionsandBuyingaButterflySpread

108. Figure11.3AButterflyIsReallyJustaSpreadofTwoVerticalSpreads

109. Figure11.4The

UnderlyingCanMoveTooFarforOurLongCallButterfly

110. Figure11.5GenericBreakevenPointsforaLongButterfly

111. Figure11.6SellingaCallButterfly

112. Figure11.7PayoffforOurShortCallButterfly

113. Figure11.8PutOptionsandBuyingaPut

Butterfly114. Figure11.9ALongPut

ButterflyIsaSpreadMadeUpofTwoPutVerticalSpreads

115. Figure11.10PutOptionsandSellingaPutButterfly

116. Figure11.11PayofffortheShort62.5/67.5/72.5PutButterfly

117. Figure11.12Profitand

LossforaButterflyPriortoExpiration

118. Figure11.13ButterflyBreakevensandThoseLikelihoods

119. Figure11.14DistancefromAt-the-Money,Cost,andLikelihoodofBreakingEven

120. Figure11.15CallOptionsandBuyingaBrokenCallButterflyinXOP

121. Figure11.16BrokenCallButterflyinXOP

122. Figure12.1BuyingaCallCondorinApple

123. Figure12.2LongtheApple410/440/470/500CallCondorandtheConstituentVerticalSpreads

124. Figure12.3TheAAPLCallCondor

125. Figure12.4BuyingaPut

CondorinAAPL126. Figure12.5ALongPut

CondorinAAPL127. Figure12.6SellanIWM

CallCondortoTakeAdvantageofExpectedVolatility

128. Figure12.7AShortCallCondorinIWM

129. Figure12.8AnIronCondorinAAPL

130. Figure12.9A

410/440/470/500IronCondorinAAPL

131. Figure12.10BuyingaDirectionalCallCondorinNFLX

132. Figure12.11ADirectionalCallCondorinNFLX

133. Figure14.1AnAprilPutRatioSpreadandaMayPutBackSpreadinQQQ

134. Figure14.2TheApril87/89PutRatioSpreadinQQQ

135. Figure14.3TheApril86/89PutRatioSpreadinQQQDoneataNetDebit

136. Figure14.4ARatioSpreadIsAlmostaButterfly

137. Figure14.5PutRatioSpread,PutButterfly,andPutVerticalSpread

138. Figure14.6AMayCallRatioSpreadandaJuneCallBackSpreadinDIA

139. Figure14.7The167/169CallRatioSpreadinDIA

140. Figure14.8HowtheDIA167/169CallRatioSpreadChangesasTimePasses

141. Figure14.9StockChartofAmazon(AMZN)for

aCallRatioSpread142. Figure14.10AMZN

CallOptionsforStockRehab

143. Figure14.11EffectiveSellingPricewithandwithoutRatioSpreadStockRehab

144. Figure14.12AJulyCallBackSpreadinAMD

145. Figure14.13TheAMD5/6CallBackSpread

146. Figure14.14TheAMD5/6CallBackSpreadbeforeExpiration

147. Figure14.15OptionPricesforAbercrombie&Fitch(ANF)BackSpreads

148. Figure14.16Abercrombie&FitchBackSpreadandSuperBackSpread

149. Figure15.1AMarriedPutonNetflix(NFLX)

150. Figure15.2AMarriedPutonNetflix(NFLX)

151. Figure15.3ACallDiagonalinXLF

152. Figure15.4AnIronButterflyonExxonMobil(XOM)

153. Figure15.5AnIronButterflyinExxonMobil(XOM)

154. Figure15.6ALongPutChristmasTreein

Costco(COST)155. Figure15.7ALongPut

ChristmasTreeinCostco(COST)

156. Figure15.8AShortCallChristmasTreeinPfizer(PFE)

157. Figure15.9AShortCallChristmasTreeinPfizer(PFE)

158. Figure15.10ASyntheticLongPosition

onJohnson&Johnson(JNJ)

159. Figure15.11ABoxSpreadinJohnson&Johnson(JNJ)

160. Figure15.12APutStupidonVisa(V)

161. Figure15.13ALongPutStupidinVisa(V)

162. Figure15.14AGutsinStarbucks(SBUX)

163. Figure15.15AGutsin

Starbucks(SBUX)

FOREWORD

In this book, OptionsSpreads and Combinations,Scott takes the subject ofoptions and option spreadsandshowsinvestorshowthey

can be easy to understandthrough interesting, realworld examples. Just as hedoeseveryweekonCNBC’sOptionsActionandinhisfirstbook, Options Math forTraders, Scott takes whatmany have viewed asintimidating concepts andbreaks down the barrier ofentry for the self-directedinvestor. Scott has awonderful ability to use hisyears of experience and vast

knowledge of markets andrather than use industryjargon or high-levelmathematics,hebreaksthingsdown to a level that isinteresting and easy to graspfor all levels of investor—from the novice to theseasoned. This ability torelate toandwrite forpeopleof all knowledge levels,without arrogance orcondescension is impressivewhen you review his track

record which includes beingthe brains behind the“Nations VolDex®” impliedvolatilityindex.This book encouragesyou todig deeper, through poignantexamples and real-lifesituations that can help yourdecision-making processwhen you face similarsituations. Most importantly,as Scott has done this for aliving and has the “battle

scars”toshowforit,hehelpsyouset realisticexpectations.He is not here to give a fly-by-night or get-rich-quickscheme. He is helping youbecome educated in thetheory and reality of optionstrading so you can puttogetherarealisticgameplanand give yourself theopportunity for optionstradingsuccess.A prominent and important

partofthisbookistoaddresssome of the most commonmistakes that retail tradersmake. All too often, whenfolks are starting out in theworldofoptionstrading,theyonlybuyorsellsingleoptionsindirectionaltrades.Thiscanbe a successful strategy forsomepeople but over time itis probably not a strategywith which the averageperson can have long-termsuccess. This book

encourages you to considerspreading your trades, whichspreadsoutyour riskand thecost of your trades. As youread along, you will quicklygraspthatthistypeoftradingallowsyoutouselesscapitaland define your risk right upfrontonyourtrades.Youwillhave the opportunity in thisbook to learn about everytype of spread trade that isrealisticandimaginable.

Chapter 1 addresses thedifferences in risk and returnand the fundamentaldifference inoptionspayoffs,which sets the pace for therest of this book and thedifference in thinking aboutoptions as compared to justbuying or selling stock. AsScott emphasizes, the abilityfor one to manage risk andexposure to the market ismucheasierifyouunderstandthesespreads.Thisconceptof

risk differentiates this bookfrom others and is one tokeep in mind as you read.Scott gives insight in to howa professional looks attrading.Thatis,thefirstthinghe looksat ishowmuch riskor how much exposure do Ihave, then he looks atpotential return.Thisconceptis so important and helps tomitigate one of the primarymistakes that many neweroptions traders have. By

defining risk right up front,which most spreads do, itkeepstheinvestorawayfroma situationwhere they are inovertheirheadorhaveriskedtoomuchcapital,whileatthesametimesettingoutaworst-case scenario right up front.You can see this clearlyillustrated in Chapter 3 onvertical spreads, nomatter ifyouarebuyingor selling thespread, you should view themoney you can lose and the

potential return on the trade.This is not to be minimizedand should be heeded inevery example. Read this tobetter understand risk and,more importantly,understandhowtodefinetheappropriaterisk for you, and it can helpyouonyourroadtosuccess.Scottalsodoesagreat jobofaddressing the size of yourtrades and keeping riskappropriate. This helps to

address another mistake thattradersofalllevelsmake;thatis, they trade more contractsonatradethantheyarereadyto. Spreads help to mitigatethis situation, but equally asimportant is the reminder todowhat is right for you andwhatyouarereadyforinanymarket situation. This is animportant step in achievingsuccessinawaythatdoesnothave you up all nightworrying.

As someone that talks toretail traders on a regularbasis,Ifinditsorefreshingtosee someone teaching in asensible, risk-definedmannerto help the average personhave a greater chance ofsuccess in the market. Icommend Scott’s thoughtfulwork delivered in fun andlogicallessonsinthisbook.Iconsider him one of the bestoptions teachers. One of thegreat benefits of this book is

thatit isnotgoingtobereadand put away; this book canserveasareferenceguideforthe rest of your tradingcareer. As you step up inknowledge or want to takedifferent types of risk, youcan reread the chapters ondifferent spreads as youchange your strategies basedon market conditions. Theselessons are timeless. I hopeyouenjoy thisbookasmuchasIdidasyougetthechance

to learn from a great teacherandagreatfriend.

—JJKinahan

PREFACE

Thegoalofoptiontradingisto make money. The vitalelement of making moneyover thelongrunis todefineriskwhenyoucanandreduce

the cost of your trade whenyoushould.Anoptionspread(essentiallybuyingoneoptionand selling a similar option)or an option combination(usuallyusing twooptions intandemsuchasbuyingbothaput and a call or using anoption in tandem withsomething else such asownership of the underlyingstock)isusuallythebestwayto define risk and/or reducethe cost of your trade. Not

every option spread orcombination limits your riskbut most do and they do itsensibly, without paying ahugepenaltythatdestroysthemathematical advantage youroption strategy mightgenerate. In fact, certainoption spreads generate evenmoremathematicaladvantagethanoutrightoptionpositionscan.Thepurposeofthisbookis to help you understandthese strategies and apply

them intelligently because,again, the goal is to makemoney. We can and shouldenjoy both learning aboutoptions and trading themeffectively,butbotharea lotmorefunwhenwe’remakingmoney.Notrader isrighteverytime,but you should make moneymore often than you losemoney and your profitabletradesshouldmakemorethan

your losing trades lose. Theeasiest way to do all thesethingsistouseoptionspreadsand combinations and to doso in a disciplined manner.That discipline includestaking your loss when youroption spread trade isn’tworking. You will probablyhave lost a lot less moneythan if you had traded thestock or an outright option(rather than an option spreador combination) but using a

lower-cost, lower-risk spreador combination doesn’tmeanwecan ignorefirstprinciplesand not take our loss whenwe should. A spread orcombination is also a greattool when doing the hardestthing to accomplish whentrading—adding to a winnerwell.As we’ve mentioned, somespreads and combinationshaveabuilt-inadvantage.For

example, we’ll discuss onebuilt-in advantage when wediscuss risk reversals.Covered calls are anothercombination with a differentbuilt-in advantage—overtime, the call option you sellwill generate more inpremium received than theoption is ultimately worth.Some spreads andcombinations have a built-indisadvantage. Collars are agreatwaytodefineriskifyou

own appreciated stock butyou’re swimming against thetideabit.That’sokayaslongas you don’t use collarsconstantly and understandwhythatis.TheCompleteBookofOptionSpreads and Combinationsisn’t intended for someonewho’s a complete newcomerto options. We discussoutright options, that is,options that aren’t part of a

spread or combination, butoutrightoptionsarerarelytheright strategy, particularly ifyou’re a speculative seller ofoptions, so we’ll focus onspreadsandcombinationsandwhile they’re not necessarilycomplicated, if you’re stillstuck on the differencebetween a put option and acall option then read thisbook but reread the firstcouple of chapters beforediving into the strategies

whichbeginwithChapter3.

■ The Spreads andCombinationsWe’ll take a detailed look atnearly every common optionspread or combination andwe’ll look at some rare,quirky spreads that even aprofessional option tradermay never actually execute.I’ve been a professionaloption trader for a long timeincluding decades in the

option pits of Chicago andI’ve traded some oddcombinations, sometimesincluding as many as eightlegs but I don’t believe I’veever actually traded a “guts”spread.Buteach strategyhassomething to recommend itandmanyshowsymmetryorsimilarity toanotherstrategy.Once you start to recognizethese similarities you canstart to construct the best,cheapest-to-execute strategy

given your market point ofview.Onceyoucanrecognizethesesymmetries,you’realsoon your way to reallyunderstandingoptions,whichmeans you’re able to createreturnprofilesthataren’t justaboutmoreor less returnbutrather are fundamentallysuperior to the risk/returnprofiles that are possible ifyou’re just trading stock.These fundamentallydifferent return profiles are

the real power of optionspreadsandcombinations.

CHAPTER1

NotJustMoreorLessbutDifferent

Options are about choiceand the freedom to dosomething, exercise youroption, or not do thatsomethingandletyouroptionexpire.Anoption is the rightbut not the obligation to dosomething;inourcontext,it’sthe right to buy or sell stockat a predetermined pricebeforetheoption’sexpirationdate. For this reason, optionsare obviously very different

than ownership of theunderlying stock. While it’struethatifyouownstockyoualwayshave thefreedom, the“option,” of selling yourstock, that’s a pretty drasticchoice; there’s no middleground. It’s the choiceinherent in ownership of anoption, or the premiumcollectedinsellinganoption,and the ability to enjoy theshades of gray betweenowning the underlying stock

and not owning theunderlying stock that makeoptions such a useful tool.Theownerof theoptiongetstomake this choice but paysmoney for the privilege. Theseller of the option doesn’tget to make the choice, he’sat the mercy of the optionownerbutheispaidforbeingat the mercy of the optionbuyer and he’s often paidveryhandsomely.

This choice also means thatoptions,whencombinedwithother options in spreads andcombinations and whencombinedwithstock,resultinrisk/reward payoffs that arevery different than stockalone or options alone cangenerate. If standard assetallocation between stocks,bonds,commodities,preciousmetals, and so on isdiversification, then it’sdiversification in two

dimensions. Allocation usingdifferent asset classes andoption spreads orcombinations isdiversification in threedimensions.

“As we see it, theprincipal function ofoptions is to provide asignificant expansion ofthe patterns of portfolioreturns available toinvestors. Such

expansions makeinvestorsbetteroff...”

MyronScholesandRobertMerton

If you buy a share of stockand the price goes up by $1,then you’ve made $1. If theprice goes down by $1, thenyou’ve lost $1. Prettystraightforward but not verynuanced either. By usingoptions, particularly in aspread or combination, it’s

possible to create a tradestructure that will makemoney if the stock goes up;it’s possible to create a tradestructure that will makemoney if the stock goesdown;it’spossibletocreateatradestructurethatwillmakemoney if the stock doesn’tmove. It’s possible to createtrade structures that losemoney if the stock moves alittle but make money if thestockmovesalot.It’snotjust

about more or less, withoptions the pattern of returnsarefundamentallydifferent.Butmerelyaddingalternativestructures isn’t what reallymatters.Whatmatters is thatoneofthosepayoffscenariosislikelytocoincidewithyouroutlook for the price action,or lackofpriceaction, in theunderlying stock. It’s thisability tomakemoney if thestock does what you believe

it’sgoingtodo,regardlessofwhatthatbeliefis,evenifit’sthe belief that the stock isn’tgoing to go anywhere, thatmake spreads andcombinationssouseful.While every investor orstudent of finance has heardof options, we’ll focus onlisted options on stocks,indexes and exchange-tradedfunds (ETFs). We won’tdiscussoptionstobuythereal

estate next door, norwillwediscuss employee stockoptions, the sort of optionsgiventoemployeesaspartoftheir compensation or as anincentive and that allow theemployee to buy stock at adiscount. Rather, we’ll focuson the options nearly everyinvestor can and probablyshould be using—listedoptions.

■The“Flavors”:CallsandPutsListed stock options come intwo “flavors”—the right tobuystock(acalloption,oftenreferred to simply as a call)and the right to sell stock (aput option, often referred tosimplyasaput).It’susefultoremember the terms bythinkingof theoption tobuystock as the right to call it

away from the existingowner.Therighttosellstockis the right to put the stockbackintothemarket.The owner of a call optiongetstochoose,thatis,hehasthe option, whether toexercisehisrightandbuytheunderlying stock at theexercise price before theoption expires. The seller ofthecalloptionhas to sell thestock at the exercise price if

theowneroftheoptionelectstoexerciseit.Inthatcase,theseller of the call option isrequired to sell the stock atthe exercise price regardlessofhowfarabovetheexerciseprice the stock is currentlytrading.Inexchangeforbeingwilling to do so, he willcollect an option premium inthe form of cash when hesells the option. This cash ishistokeepnomatterwhat.

The owner of a put optiongets to choose whether toexercisehisrightandsell theunderlying stock at theexercise price before theoption expires. The seller oftheputoptionhas tobuy thestock at the exercise price ifthe owner of the put optionelects to exercise it. In thatcase, the seller of the putoption is required to buy thestock at the exercise priceregardless of how far below

theexercisepricethestockiscurrentlytrading.Inexchangeforbeingwillingtodoso,hewill collect an optionpremium in the formof cashwhen he sells the options.This cash is his to keep nomatterwhat.Onenote:noonekeepstrackofwhomyouactuallyboughtyour option from or whomyou sold it to. Rather, alloptions that share the

underlying stock, expirationdate, strike price, and type(call or put) are identical,regardlessofwhichexchangethey were executed on orwhich brokerage executedthem, so when it’s time foryou to exercise your calloption, the Options ClearingCorporation, theclearinghouse for optiontrades, will more or lessrandomly pick someone whois short one of those options

tosatisfythedutytoyou.

■TheExpirationDateFor exchange-listed options,there are a number ofexpiration dates, usually bycalendarmonth,tosatisfythehedging and speculationneeds of all sorts of marketparticipants, but for standardoptions, the expiration isfixed within the expirationmonth. The last trading dayfor these standard options isthethirdFridayofthemonth,

and while the optionstechnically expire the nextday, the Saturday followingthat third Friday, for allintents and purposes the lastday that matters is that lasttrading day. You can tradethese options right up untiltheclosingbellonthatFridayand make the all-importantdecision about whether toexerciseyouroptionandbuy(in the case of owning a calloption)orsell (in thecaseof

owning a put option) theunderlying stock. We’lldiscuss this decision toexercise your option ingreaterdetailwhenwedefinemoneyness.There are a few nonstandardexpiration date regimes, andthey can be useful. Manyunderlying stocks now haveoptions with weeklyexpirationstrading.Insteadofexpiring on the third Friday

of the month, these willexpire on the next Friday, orthere might be two or moreweekly expirations listed,each expiring on subsequentFridays.The goal is to allowtraders to take advantage ofmarket events and catalystssuch as earningsannouncements; market-moving governmentannouncements, such asunemploymentand jobsdata;or major corporate events,

like a new productannouncementoraFoodandDrugAdministrationdecisionfor a pharmaceuticalcompany and to isolate thateventorcatalyst.Some stocks, ETFs, andindexes also have quarterlyexpirations. These optionsexpire on the last day of thecalendar quarter and areintended for institutions thatare judged by quarterly

results.As an example, Table 1.1shows expiration dates foroptions that were recentlytrading on MicrosoftCorporation(MSFT).

Table1.1MSFTOptionExpirations

ExpirationMonth/Year

LastTradingDate

OptionExpiration

DateMay

May 17,2013

May18,2013

MayWeekly

May23,2013

May24,2013

JuneJune21,2013

May22,2013

July July19,2013

July20,2013

AugustAugust16, August17,

2013

2013

OctoberOctober18,2013

October19,2013

January’14January17,2014

January18,2014

January’15January16,2015

January17,2015

This sort of range ofexpiration dates is about

normalforamajorstocklikeMicrosoft. While some otherstocks will have slightlydifferent expiration cycles,most will have optionsexpiringinthecurrentmonth,if the third Friday hasn’tpassed,orthenextmonthandthe following month. Afterthose first couple ofexpirations, the expirationmonthswillusuallyfallintoamoreorlessquarterlypattern.For example, options on

McDonald’s Corporation(MCD) follow aSeptember/December cyclerather than theAugust/October cycle thatMSFT did. For longer-termoptions,moststockswillhavelisted options expiring nextJanuary and one or twoJanuarys after that.Note thatthe last trading day is thethird Friday of each month,whiletheoptionexpirationisthenextday,aSaturday.You

cantradeeachoptionuntiltheclose of trading on thatFriday, but in reality you’llhave to make your decisionabout exercising any optionsyou’re long within a fewhours of that market close.Your broker will havespecific guidelines on whenyou must enter anyinstructions to exercise theoptions you own, but notethat nearly every option youown that is in-the-money at

the close of trading on thatFriday will be automaticallyexercised. We’ll define in-the-money in the moneynesssectionofthischapter.There’snota lotofrhymeorreason to the expirationcycles, so don’t get tooinvolved in trying to figureout what expirations exist orwhy they’re set up the waytheyare.Therewillbeplentyof expiration alternatives for

youtouse.

■TheStrikePriceIfanoptionallowstheoptionowner to buy a stock at apredetermined price (in thecaseofacalloption)orsellastockatapredeterminedprice(in the case of a put option),what is that predeterminedprice? That is the price theoption owner would pay orreceive if they chose toexercise their option. Hence,it’s called theexercisestrike.

Some call it the strike price.The two terms areinterchangeable,butwe’llusethetermstrikeprice.While the incrementsbetween strike prices used tobeconsistent and logical, it’salittlemoreadhocnow.Forstocks below $50 withactively traded options, theincrement between strikeprices is usually $1. If thestock and options are less

actively traded, meaningthere’s less demand fornarrower strike priceincrements, then theincrement is usually $2.50.The increment will increaseas the stock price increases.With stock prices above$100, the strike priceincrement isusually$5, afterall, with IBM trading above$200, a $5 strike priceincrement isonly2.5percentofthestockprice,whilewith

MSFT just over $30, a $1strike price increment is justover 3 percent of the stockprice.For these IBMoptions,we’dsay they are “struck” every$5, and that’s about as wideas the increment will get.Even with Google close to$1,200 a share, the optionsare still struck at $5increments.Remember that strike price

increments are subject tomarket demand. If optionexchanges hear from theircustomers that they’d like tosee narrower strike priceincrements in XYZ stock,then the options exchangesare likely to offer narrowerstrike price increments forXYZ. Expanding bandwidthfor exchange data feeds hasmade it easier for optionexchanges to offer morestrikeprices,sotheydo,even

if it ends up being a littleconfusing to the new optiontrader. Don’t look for hard-and-fast rules forwhat strikeprices will be listed; they’resubjecttothismarketdemandfor strike prices. In addition,as a stock moves around, itwillnearthetoporbottomofthe band of listed strikeprices. It may seem thattraders are “running out of”strike prices. Soon, theexchangeswilllistnewstrike

prices for trading, but untilthat happens the strikes andtheir increments will seemodd. Don’t be confused. Thelistedstrikepriceswillalmostcertainly satisfy any tradingor hedging need you mighthave.

■ An OptionCorresponds to 100SharesofStockEachregularoptiongivestheright to buy, in the case of acalloption,100sharesof theunderlyingstockortosell,inthe case of a put option, 100shares of stock—each optioncorresponds to 100 shares ofstock. If you’ve sold one putoption and the owner of the

putoptionchoosestoexerciseit, then you’re going to havetobuy100sharesof stockattheexerciseprice.Just as stock is priced pershare, regardless of howmany shares you intend tobuy, options are priced pershare even though eachoption corresponds to 100shares. If the option you buyis trading at 1.25, then yourtotal outlay, assuming you

buyasingleoptionis$125.00(1.25×100shares).

■DefininganOptionSo we know what theunderlying stock or ETF forour option is. We see theexpiration and know that forregular options the thirdFridayofthemonthisthelasttrading day. For otheroptions, like weekly orquarterly options, theexpiration date is givenexplicitly. The strike price isunderstood. The type of

option is easy—call or put.We know that each optioncorresponds to 100 shares ofstock. With those pieces ofinformation,wecanpreciselydefine any option so thatevery market participant,even a new option trader,understands exactly what theterms of the option are andhowmuchanyoutlaywillbefor buying it and how muchwillbecollectedforsellingit.

IfweweretodiscusstheSPYJune 150 put, then everyonewouldbe inagreementaboutwhich option we’rereferencing. The underlyingETF is ticker symbol SPY,the S&P 500 ETF. Theexpiration date is the thirdFriday in June. If the thirdFridayinJuneforthecurrentyearhasalreadypassed, thenwe’re discussing an optionthat will expire on the thirdFriday of June of the next

year.IfthethirdFridayhasn’talready passed, then we’retalking about an option thatwillexpirethethirdFridayofJune of this year. Theexercise price or strike price(the two terms aresynonymous) is 150. Thebuyerofthisputgetstherightbut not the obligation; theyget the freedom to sell 100sharesofSPYat$150ashareatorbeforeexpiration. If thequotedpriceof thisoption is

1.35,thenthetotaloutlaywillbe $135.00, ignoringcommissions.Let’s jump in and look atsome options listed on GM.WeseetheseinFigure1.1.

Figure1.1SomeOptionsinGM

ThatJune37strikecallthatishighlighted?Weknowthat ifwe buy that call option, weassume the right but not theobligation to buy 100 sharesat GM at 37.00. We haveuntiltheendofthedayonthethird Friday in June toexercise our option. Thecurrent market price of theoption is close to 1.36, so

we’llpayclosetothatforthisoption. The option marketmay demand a little morefromusifwewanttobuythisoption than they’ll give us ifwe want to sell this option.The market may “ask” 1.37of us if we want to buy thisoption,whilethemarketmay“bid” 1.35 ifwewant to sellthisoption.We’lldiscussthis“bid/ask” spread and how itcan impact your optiontradingandthedecisionsyou

make throughout this book.For simplicity’s sake we’llgenerallyassumeeachoptionhas a single price that isbetweenthebidpriceandaskprice. If we indeed pay 1.36for one of these GM calloptions then our total outlayis$136.00.And ifwe sold that37 strikecalloptionat1.36?Wewouldcollect$136.00,whichwouldbe ours to keep no matter

what.Iftheownerofthecalloption chose to exercise it atany time before it expired,we’d have to deliver 100shares of GM stock. Wewouldbepaid37.00persharefor thestockwedeliverednomatterwhereGMistradingatthe time. Ifwe don’t alreadyown100sharesofGMstock,then we would have to gointo the market, buy 100shares atwhatever price it iscurrently offered at, and

deliverthose100shares.Theimportantconcepthereisthat all the specifics of theoption and the potentialoutcome are explained if weknow the underlying stock,the strike price, whether theoption is a put or a call, andtheexpirationdate.Buying that call option onGM, in fact, buying any callis a defined risk, unlimitedpotential profit position that

profitsiftheunderlyingstockrallies enough. Let’s look athowbuyingthis37strikecalloption inGMwould fare fora variety of prices of GMstock at the call option’sexpiration. We see this inTable1.2.

Table1.2ProfitorLossfortheGMCallOptionWeBought

GMStockPriceatExpiration

ProfitorLoss

33.00 –1.3634.00 –1.3635.00 –1.3636.00 –1.3637.00 –1.3638.00 –0.3639.00 0.6440.00 1.6441.00 2.64

Notice that no matter how

lowGMstockdropsinprice,themostourtradecanloseisthe 1.36we paid for our calloption, while the potentialprofit is theoreticallyunlimited since GM stockcould theoretically rallyinfinitely. Let’s look at achartoftheseoutcomesinthesortofpayoffchartthatwe’lllook at for other trades.Youcan see this payoff in Figure1.2.

What if we were to sell that37 strike call option at 1.36?Selling a call option is adefined potential profit butunlimited potential lossstrategy that collects andkeepsthepremiumbutwouldrequire the call option sellerto deliver 100 shares of theunderlying stockat the strikeprice, 37.00 in this case,regardless of where theunderlying stock was tradingatthetime.Let’slookathow

selling this 37 strike calloption inGMwould fare fora variety of prices of GMstock at the call option’sexpiration. We see this inTable1.3.

Table1.3ProfitorLossfortheGMCallOptionWeSold

GMStockPriceatExpiration

ProfitorLoss

33.00 1.3634.00 1.36

35.00 1.3636.00 1.3637.00 1.36

38.00 0.3639.00 –0.6440.00 –1.6441.00 –2.64

Selling this call results in aprofit of 1.36 if GM is at orbelow37.00atexpirationbut

losses money if GM ralliesfar enough. In this case thatbreakevenpoint is38.36 (thestrike price of 37 plus thepremium received of 1.36).Let’s see how this payoffchart would look. You canseethatinFigure1.3.

Figure1.2ProfitorLossforOurLong37StrikeCallInGM

Figure1.3ProfitorLossforOurShort37StrikeCallinGM

Notice that the maximumpotential profit is the 1.36 inpremium received, and we’llkeepthataslongasGMisator below 37.00 at Juneexpiration. Above 37.00, ourprofitstarts toerodeuntilwereach breakeven at 38.36.Above there, we losemoneyhaving sold this call, and theamount of our loss keeps

increasing as long as GMstockkeepsrallying.WhataboutthoseputoptionswesawinFigure1.1?Whatifwe were to purchase thatSeptember 33 put that ishighlighted? We would payabout2.25forthatputoption.Buying a put option is adefined risk way to profitfromadropinthepriceoftheunderlying stock. Ourpotentialprofitislimitedonly

because the price of GMstock can’t drop below zero.Let’s look at a payoff chartforbuying thisSeptember33strike put at 2.25.You’ll seethatinFigure1.4.

Figure1.4ProfitorLossforOurLong33StrikePutinGM

Andifweweretosellthat33strike put in GM at 2.25?We’d collect and keep the2.25 butwe’d be required tobuyGMstockat33.00if theput owner chose to exercisehis option, which he woulddoifGMwerebelow33.00atthat September expiration.We’d have to buy thoseshares regardlessofhow low

GM stockwas trading at thetime.Thismeans that sellinga put, like selling a call, is adefined potential profit tradewith huge potential losses.The only difference betweensellingaputandsellingacallis that the stock is limited inhow far it can fall onlybecause it can’t fall belowzero.Let’s lookat thepayoffchartforsellingaput.WeseethatinFigure1.5.

Figure1.5ProfitorLossforOurShort33StrikePutinGM

You’ll notice that selling acalloptionisnot thesameasbuying a put option.Similarly,sellingaputoptionis not the same as buying acall option. The long calloption needs the underlyingstock price to increase. Theshort call option needs theunderlyingstockpricetostaywhere it is, increase slightly

whilestayingbelowthestrikeprice, or fall. The long putoption needs the underlyingprice to fall. The short putoption needs the underlyingprice to stay where it is,decrease slightly whilestayingabovethestrikeprice,orrise.

■MoneynessIfyou’rebuyingaputoptiontoprotectalongpositioninastock that’s currently tradingat $100 a share, then youmight very well buy a putoption with a strike price of$100. You’d be protectingyour position against anyloss, although you’d bepaying for the option thatwoulddoso.Youmightverywell buy a put optionwith a

strikepriceof$95.You’dbewillingtoacceptasmallloss,$5pershare in thiscase,andthe put option that providesthat protection would costquite a bit less than the 100strikeput,soyoumightthinkthis is a reasonable risk andaccept a small loss inexchangeforasmalleroutlayto buy the cheaper put. Youprobablywouldn’t bewillingto buy a put with a strikeprice of $105, that is, a put

option that would give youthe right to sellyour stockat$105 per share. That’s notreally insurance and that 105strikeputoptionwouldlikelybeprettyexpensive.Each of these hypotheticalput options are identicalexcept for the strike pricesandwhatreallymattersisnotthe absolute strike price butrather the relationship of thestrike price to the current

priceoftheunderlyingstock.The first put, the 100 strikeput, had a strike price thatwasequaltothecurrentstockprice.Thisputwouldbepureprotection—if the underlyingstock drops at all, then thisputbuyerwouldbeprotectedbutwouldalsoenjoyanyandall appreciation in the stockprice.Suchanoption,eitheraput or call option, that has astrikepricethatisequaltothecurrent stock price is said to

beat-the-money.The95strikeputwouldhaveto have the market movebefore it would have anyvalue at expiration. If theunderlying stock weren’tbelow $95.00 at expiration,then this option would beworthlessandthebuyeroftheoption would let it expireworthless.Sincethis isaput,the underlying stock has todrop.Thisoptionissaidtobe

out-of-the-money because amove in the price of theunderlying stock is requiredfor the option to have anyvalue at expiration. In thiscase, the option is a putoption so the underlyingstockmustdrop.Iftheoptionwere a call option and thestrike price were 105, thenthat call option wouldsimilarlybeout-of-the-moneybecausetheunderlyingwouldhave tomove; in thiscase, it

would have to rally in orderforthe105strikecalltohaveany value at expiration. Andthat 105 strike put? Thatoption is in-the-money, aswould a 90 strike call optionbe. Table 1.4 explainsmoneyness;thatisout-of-the-money,at-the-money,andin-the-money for all puts andcalls.

Table1.4OptionMoneyness:TheRelationshipbetweenthe

StrikePriceandthePriceoftheUnderlyingAsset

CallOptions

PutOptions

In-the-Money

Thestrikepriceisbelowthepriceoftheunderlying.

Thestrikepriceisabovethepriceoftheunderlying.

At-

Thestrikepriceis

equalto,or

Thestrikepriceis

equalto,or

the-Money

verynearto,theprice

oftheunderlying.

verynearto,theprice

oftheunderlying.

Out-of-the-Money

Thestrikepriceisabovethepriceoftheunderlying.

Thestrikepriceisbelowthepriceoftheunderlying.

Let’s look at Figure 1.6 forspecific examples ofmoneyness.

Figure1.6MoneynessExamples

■ What We Mean bySpread andCombinationWe’llfocusonoptionspreadsand combinations rather thanthe outright option positionswe examined earlier in thischapter. We’ll focus onoption spreads andcombinations because theyallow us to use options intandem with an existing

position in the underlyingstock, resulting in a superiorposition that might provideprotectionorgenerateincomein the form of optionpremium collected, or intandemwith other options togenerate premium whilelimiting risk or using themath of option trading suchas differential erosion ofoption values to ouradvantage or tomakemoneyif there’s a big move in the

underlyingstockregardlessofthe direction of that move.Outright options have theirplace,butoption spreadsandcombinations are so muchmore versatile, which raisesthe question: what do wemean by an option spread,andwhat dowemean by anoption combination, andwhat’sthedifferencebetweenthetwo?Generally,anoptionspreadis

constructedwhenwebuyoneoption and sell a similaroption. The similar optionmay differ only in theexercise price (a verticalspread) or in the expirationdate(acalendarspread)or inboth(adiagonalspread).An option combination isgenerally constructed whenwe combine options with aposition in the underlyingstock such as owning the

underlyingstockandsellingacall option against it (acovered call) or when wecombineoptionsinawaythatdoesn’t really qualify as aspread. For example, if wethoughttherewasgoingtobeabigmove in theunderlyingstock but didn’t know thedirection,wemightbuyanat-the-moneycallandanat-the-money put (since bothoptionsare likely tohave thesame strike price, thiswould

beastraddle).

■AFinalThoughtThe objective of optiontrading is to makemoney ortomake the same amount ofmoney with less risk. It’susually the case that usingoptions in concert with eachother or in concert with theunderlying stock—that is, asa spread or combination—istheeasiestwaytodoso.Andit’salsoagreatwaytoreducerisk in your trading. For

example, selling a naked calloption generates an infiniteamount of risk since,theoretically, the price of thestock could increaseinfinitely. That’s a prettyremote likelihood, but thepoint is that selling a callvertical spread defines therisk—it’snowknowable.Butreducing your risk in anoption trade is good only if,overtime,yourtradingmakesmoney. Trading can be fun,

but it’s awhole lotmore funwhen it’sprofitable, so focuson the making money partand not necessarily on thetrading part. That meansdon’t trade just to trade.Trade when you have someinsight. And use the bestpossible trade structure. Thatwill often be a spread orcombination.

CHAPTER2

JustaLittleMath

Understandingjustalittleof

the math inherent in optiontrading will make you avastly better trader. You’llunderstand that certainstrategies are fundamentallysuperior to other strategies,but most importantly, you’llunderstand why that is thecase. Once you understandthe “why,” you can start toweave this knowledge intoyour decision making, bothwhen selecting an initialoption strategy and when

closingorspreadingoutofanexistingtrade.Inthischapterwe’llfocusonthe price of an option versusthevalueof that option, howoptionpriceserodeovertimeandwhat thismeansforbothoption buyers and optionsellers, and, finally, howchanges in the inputs to anoption price—inputs such astime to expiration, volatility,movement in the underlying

stock, and a couple of others—will impact thepriceofanoption.We’llalsodiscussthewebsitethataccompaniesthisbook,www.OptionMath.com.We’llexplainhow touse thesite and how the tools therecan help you make bettertradingdecisions.

http://www.optionmath.com

■TheOptionPriceThe price of an option isdetermined solely by marketdemand and supply. Willingbuyers and sellers cometogether, usuallyelectronically, and trade atmutually agreeable prices.Butdon’tthinkforamomentthat this price is equal to thevalue of the option.While anumber of sophisticatedformulas exist to determine

the value of an option,ultimately the value isunknowable until expiration.Optionmarketparticipantsallhave their thoughts on whatthe value will ultimately be,and those estimates of futurevaluearewhatdrivethepricethat’sseen today,but today’soption price isn’t necessarilytoday’s option value. Thecurrent price for an optionmayturnouttobeafantasticbargain or insanely high, but

it is thebestestimatenowofthe ultimate value. It’s alsoimportant to remember thatthe ultimate value isn’t howmuch the option is worth atexpiration; rather, it’s ameasure of how volatile theunderlying stock was duringthetermoftheoption.Whyisthisso?Becauseeveryoptiontrader could, if they wantedto, hedge the directionalityoutoftheiroptiontradeusingthe underlying stock. The

result of this hedging is thatthe trade becomes purely avolatility trade. The value ofthis volatility trade isdifferentthanthevalueoftheoption at expiration. What’simportanttotakeawayisthatoptions have value even ifthey ultimately expireworthless. Option pricingmodels or formulas use thisvolatilityoverthetermoftheoptionratherthanthepriceofthe option at expiration to

determinevalue.These sophisticated formulasareintendedtobeusedtoday,with the knowable inputssuch as strike price,expiration date, currentunderlying stock price,interestrate,andsoon,alongwith the single unknowableinput, how volatile theunderlyingstockwillbefromtodayuntil theoptionexpiresatsomepointinthefuture,to

estimate the value of theoption.Notethatwe’retryingtodetermine thevalueof theoption, which may be verydifferent than the currentpriceof theoption.Thebest-known formula is the Black-Scholes option pricingformula.Itopenedthedoortological option pricing basedon a fixed number ofparametersratherthansimpleguessing or even learnedintuition.It’snotimportantto

memorize the Black-Scholesequation, it’s not evennecessaryto lookat it,sowewon’t, particularly becauseBlack-Scholes is reallyintended for a very smalluniverse of options (optionsthat can be exercised only atexpiration rather than themuch more common optionthat can be exercised at anytime and options on stocksthat pay zero dividends) andmakes a number of

assumptions that simplyaren’t valid in the realworld(for a discussion of theseassumptions and the optionmarket’s response to the factthat the assumptions aren’tvalid, refer to Part Two ofOptions Math For Traders).ButBlack-Scholesisthegoldstandard,sothat’swhatwe’lluse and it’s the model that’savailable atwww.OptionMath.com. Andwhile most options can be


exercised at any time, theprice difference betweenoptions that can be exercisedonlyatexpirationandoptionsthat can be exercised at anytimeisusuallyverysmall.Alloption pricing formulas,including some otherformulas that get moresophisticated to account forsome of these issues, useessentially the same inputs.Whataretheseinputs?

Inputs to an option’s valueinclude:

Thepriceoftheunderlyingstockorexchange-tradedfund(ETF).Thetypeofoption;isitacalloptiongivingustherighttobuytheunderlyingstock,oraputoptiongivingustherighttosellthe

underlyingstock.Thestrikepriceoftheoption.Theexpirationdate,althoughwe’rereallyinterestedintheamountoftimefromtodayuntilthatexpirationdate.Thecurrentrisk-freeinterestrate.Anydividendstobepaidduringthetermofthe

option.Thevolatilityoftheunderlyingstockduringthetermoftheoption.

You’llnoticethatalloftheseinputs, except for one, aregiven or are observable. Forexample, the strike price is agiven as is the time toexpirationandtheoptiontype(callorput).Thepriceoftheunderlying stock and the

current risk-free interest rateare observable. Dividends tobepaidduringthetermoftheoption are also knowable,given the existing dividendsdeclared or the currentdividend policy, to a veryhigh degree of certitude,particularlyforoptionswitharelatively short time toexpiration. The only inputthat isn’t knowable orobservable is thevolatilityofthe underlying stock during

thetermoftheoption.That’sbecause the input is thevolatility of the underlyingstock from now until theoption expires.Knowing thattoday would require theabilitytopeerintothefuture.We could look backward atthehistoricalvolatilityof thestockbutthatmayormaynotbe meaningful. If a bigcatalyst such as earningsrelease is imminent, then thestock is likely to be very

volatile over the next coupleof days, which would beimportant if our option wereexpiring next week. In thissituation, the averagevolatilityofthestockoverthepast20yearsisn’tgoingtobevery helpful. Since all theinputs with the exception ofvolatility are knowable, youmight think that volatility isthe most confounding andimportant of the inputs.You’d be correct in both

cases. If you could beabsolutely certain of howvolatile the underlying stockwas going to be for the termof the option, you would beable to calculate the value—not just the price but thevalue—of the option today.Youcould thencompare thatvalue to the price that’savailable in the market andbuy the option if it werepricedbelow itsvalueor sellitifitwereaboveitsvalue.

■ Volatility and theVolatility Implied bytheOptionPriceSince we know or canobserve thevalues forall theinputs with the exception ofvolatility, and since we canobserve the price of theoption as it trades, it’spossible to use an optionpricing formula to workbackward and calculate the

volatility for the underlyingstock that is assumed by themarketandisthusimpliedbythe observed option price.This implied volatility is theapples-to-apples measure ofhow expensive the option is,since it accounts for time toexpiration, stock price, strikeprice,andeveryotherinputtoanoptionpricingformula.Assuch, option traders considerimplied volatility to be thereal cost of the option rather

thanthedollaramount.We’llcontinue to use impliedvolatilityasthemeasureofanoption’s price because youmight think that an optionpriced at $3.00 is moreexpensive than an optionpricedat$1.00untilyoufindout that the $3.00 option isdue to expire in 12 monthswhilethe$1.00optionisduetoexpirenextweek.Volatility is expressed in

terms of the annualizedstandard deviation of returnsof the underlying stock,meaning that an impliedvolatilityof20percentmeansthat thestandarddeviationofannualizedreturnsisexpectedtobe20percentforthelifeofthe option. The marketexpects the annualized returnfor the relevant stock to bewithin a range of ± onestandard deviation about 68percent of the time,meaning

thatwe’dexpectthisstocktohave an annualized returnthat’s greater than −20percent and less than +20percent 68 percent of thetime. Notice that we’rediscussing annualized return,not annual return. We cantake the return for any timeperiodless thanoneyearandannualizeittotelluswhattheannual return would be ifevery timeperiod in theyearexperiencedthatreturn.Thus,

if we’re discussing a timeperiod of one day or oneweek or one month, we’recomparing apples to applesbecausewe’veannualizedthereturn.

■OptionErosionThe price and the value ofoptionserodeovertime.Thisobviously makes sense; youwouldn’t expect an option tomaintain all of its value formonths and months, thenfinallybecomeworthlessonlyonexpiration.Thiserosion isa large part of the thirddimension of diversificationwe mentioned in Chapter 1.This erosion is what makes

options so fundamentallydifferent from a simpleposition in the underlyingstock or ETF. This optionerosion can also be used toour advantage, such aswhenselling an option, selling avertical spread, or buying acalendar spread.This erosionis theprice thatwepay eachdayweownanoption,soit’sthe headwind that our longoption position mustovercome. The result of

erosionisthatwecanberighton the direction theunderlying stock is going inand still lose money if itdoesn’t accomplish themoveto a big enough degree orquickly enough. Somereaderswill realize thatabigmoveoraquickmove in theunderlying stock means thatthestockhasbeenvolatile.But how does erosionactuallytakeplace?Whatcan

we expect in terms of optionerosion over time? Ifwe usethe option calculator atwww.OptionMath.com, wecan create a hypothetical calloption, leaving all the inputsunchanged but changing thetime toexpirationandseeinghow the value of thehypothetical call option willerode:

Priceofthe $100.00


underlyingstock:Strikepriceofthe

calloption: 100

Therisk-freeinterestrate:

1percent

Dividendstobepaidduringthetermoftheoption:

0.00

Estimatedvolatilityoftheunderlyingstockduringthetermof

20percent

theoption:

Whatwe’dexpectthisoptiontobeworthbasedon time toexpiration:

100daystoexpiration: 4.31




Obviously,theerosionofthisoption isn’t linear. Let’sconnectthedotsbyplottingachart of the value of theoptionforeachdayfrom100days to expiration to the dayof expiration. You can seethatgraphinFigure2.1.

Figure2.1OptionValuebyTimetoExpiration

Obviously,erosionspeedsupas time to expiration nears.This means that the day-to-dayownershipofalong-termoption is relativelyinexpensive, particularlywhencomparedtotheday-to-day cost of ownership of avery short-term option. Theerosion we’d expect thisoption to experience on the

day 100 days prior toexpiration is about 0.03,while we’d expect it toexperienceerosionof0.42onthedayofexpiration.

■ Option PriceSensitivitiesWe’ve seen the factors thatinfluence the value of anoption, including how thepassage of time changes thepriceofanoption.Ifanyoneofthoseinputvalueschanges,the value of the option willchange. It’s easy to getbogged down in thesesensitivities, so we won’t

delve too deeply, but it’simportant to have afamiliarity with some ofthem. Let’s look at the mostimportant.

■ Sensitivity to thePassageofTimeWe’ve already seen how thepassage of time, from 100days until expiration to theday of expiration, changedthe price of our hypothetical100strikecalloptionwiththeunderlying stock at 100.00.This parabolic erosion asexpirationnears is somethingwecantakeadvantageof,and

we talk about that, mostspecifically in Chapter 6,“CalendarSpreads.”Sensitivity to the passage oftime is usually measured intermsoftheexpectederosionin price for a single day,again assuming that all theother inputs are unchanged.Since we’re talking abouthow the option price isexpectedtochange,andsincetheoptionpricewilldecrease

as time passes, again giventhat all the other inputs areunchanged, this measure isusually in the form of anegativenumber.Option traders call this dailyerosion theta. It’s a handymeasure to understand. Theoption price calculator atwww.OptionMath.com willcalculate the theoretical thetaforyouroptionortheoptionsmaking up your spread or


combination. Since we’veseen how erosion increaseswiththepassageoftime,thistheta value is valid only fortoday, but it’s easy tocalculate for any number ofdaystoexpiration.Wesawhowthevalueoftheoption decreased as timepassed, but let’s look at averysimilarchart,theamountof daily erosion expected foreach of those days (Figure

Figure2.2OptionErosionbyTimetoExpiration

This erosion is for the 100strikecallwiththeunderlyingstockat100.00.Buthowdoesthiserosionworkforthat100strikepricecallwiththestockat other prices? Figure 2.3showstheerosionofthat100strikepricecalloptionontheday that is 100 days beforeexpiration for a range ofunderlying prices for the

stock. You’ll notice thaterosionisgreatestforthe100strike call when the stock isvery close to 100.00. That’sbecause that is when theoption has the most timevalue.It’sthistimevaluethatis eroding away. Thetadecreases as an option getsfarther from at-the-moneybecause the amount of timevalue decreases. You mightthink that an option that isvery expensive in absolute

terms because it is in-the-money will experience a lotoferosion,butinherentvaluedoesn’terodeaway,onlytimevalue erodes, and since adeepin-the-moneyoptionhasso little time value, it willexperiencelittleerosion.

Figure2.3OptionErosionbyUnderlyingStockPrice

■ Sensitivity to thePrice of theUnderlyingStockThe price of the underlyingstock was the first input wementioned,andobviouslythepriceof thestockwillhaveasubstantial impact on theprice of our option. As theprice of the underlying stockincreases, the value of a calloption should increase

(everything else remainingunchanged, a usefulassumptionforthisdiscussionbutunlikelyintherealworld,wheretimewillelapseevenifnothingelsechanges),andasthe price of the underlyingstock decreases, the value ofa call option should decrease(making the sameassumption).Similarly,astheprice of the underlying stockdecreases, the value of a putoptionshouldincrease,andas

the price of the underlyingstockincreases,thevalueofaputoptionshoulddecrease.Let’s use the spreadsheet atwww.OptionMath.com todetermine the value of ourhypothetical 100 strike calloption with 30 days toexpiration and assuming arange of prices for theunderlyingstock.What we’d expect this calloption to be worth based on


the price of the underlyingstock:Underlyingstockat

80.00: 0.00

Underlyingstockat90.00: 0.07



Underlyingstockat

120.00: 20.08

Let’s connect the dots againand see what this option isworth for a large range ofunderling stock prices. YoucanseethisinFigure2.4.

Figure2.4SensitivitytothePriceoftheUnderlyingStock

As you can see, when thestockiswellbelowthestrikeprice of the call option, theoption isn’t worth much andthe value of the call optionchangesverylittleforeach$1change in the price of theunderlying. This change inthe value of the call optionfor each $1 change in theprice of the underlying stock

increases as the price of theunderlying stock increasesuntil the underlying stockprice iswell above the strikepricewheneach$1changeinthe price of the underlyingresultsina$1increaseinthevalueofthecalloption.Whyis this?When the underlyingmoved from 80.00 to 81.00,theoddsofour100strikecalloption being in-the-money atexpiration increased, but byjustatinybit,sowe’dexpect

thevalueofourcalloptiontochange by just a tiny bit.However, when theunderlyingstockmovedfrom99.00 to 100.00, the odds ofour 100 strike call optionbeing in-the-money atexpirationbecame essentially50/50; if the stock is at100.00, then it’spreciselyat-the-money. If the underlyingdropsbyasinglepennyfrom100.00 to 99.99, the calloption is out-of-the-money

and will expire worthless. Ifthe underlying climbs by asingle penny from 100.00 to100.01,thecalloptionisnowin-the-money and will beexercisedatexpiration.If thepriceof theunderlyingiswellaboveourstrikeprice,say it moves from 119.00 to120.00, then the odds arenearly 100 percent that ourcall option will be in-the-money at expiration. But the

oddswerenearly100percentwith the stock at 119.00. At120.00 the odds are greaterbut only by a small amountbecause they were alreadycloseto100percent.We’ve already mentionedhowsomeonemighttradetheunderlyingstockagainsttheiroption position in order towringthedirectionalityoutofthe combined position. Howmany shares should they

trade? They should trade thenumberofsharesthatisequalto the odds of their optionexpiring in-the-money.Why?Becausethatishowmuchtheprice of the option shouldmoveforeach$1moveinthepriceoftheunderlyingstock.Our 100 strike call shouldchange in price by a verysmall amount if theunderlying stock rallies from80.00 to 81.00 because thereis a small chance of the

option being in-the-money atexpiration.Our100strikecallshould change in price byabout 0.50 if it is at 100.00and moves by 1.00 becausethe odds of the option beingin-the-money at expirationare about 50 percent. Andwith the underlying stock at119.00? The odds of theoption being in-the-money atexpiration are very close to100 percent, so we’d expectthe price of the option to

movebyabout$1.00foreach$1.00moveinthepriceoftheunderlying.For those trying towring thedirectionalityoutof the tradeand turn it into a volatilitytrade, this measure of theexpected change in the priceof the option given a $1.00change in the price of theunderlying is the hedge ratiothey should use. For thoseusing options for

directionality, thismeasure isthe likelihood that the optionwill be in-the-money atexpiration.Since this measure is theexpected change in the priceoftheoption,it’scalleddelta.Youcanuse it inbothways,as ameasureof the expectedchange in the price of theoptiongivena$1moveintheprice of the underlying, aswellasthelikelihoodthatthe

option will be in-the-moneyatexpiration.Bothusesmeanit’s also the hedge ratio forsomeone who is trying towringthedirectionalityoutoftheir position. Table 2.1shows how to use theunderlying stock to wringdirectionalityoutofanoptiontrade. The resultingcombination is purely avolatilitytrade.

Table2.1UsingtheUnderlying

toCreatea“Directionless”TradeOptionPosition

UnderlyingPosition

Longacall

option

Shortshares—thenumberofsharesisequaltotheoption’sdeltaor“hedgeratio”

Shortacall

option

Longshares—thenumberofsharesisequaltotheoption’sdelta

Longaput

option

Longshares—thenumberofsharesisequaltotheoption’sdelta

Shortaput

option

Shortshares—thenumberofsharesisequaltotheoption’sdelta

Delta is calculated as afractionsoitcanhavealowerlimit of 0.00 (the odds ofanything happening can’t be

below zero) and an upperlimit of 1.00 (the odds ofanything happening can’t begreaterthan100percent).Theconvention is to truncate thepercent sign, meaning that acalculateddeltaof0.50,a50percent chance of the optionexpiring in-the-money, isusuallyreferredtoas50.Thisis done because this is thenumber of shares that shouldbe executed to turn oneoption into a directionless

volatility trade, since oneoption corresponds to 100shares of stock. Theworksheet atwww.OptionMath.com willcalculate the option delta foryou.Ifwedothat,wefindthefollowingdeltas:Deltaof30-day100strikecallwiththeunderlyingstockat

80.00:

0


Deltaof30-day100strikecallwiththeunderlyingstockat

100.00:

52

Deltaof30-day100strikecallwiththeunderlyingstockat

120.00:

100

The odds of the 30-day 100strikecallbeingin-the-moneyatexpirationiftheunderlyingis at 80.00 now aren’t

actuallyzero.They’reslightlyhigher than zero, as you’dexpect.It’snotimpossibleforthe stock to rally from 80.00to above 100.00 in those 30days.It’sjustveryunlikely—so unlikely that when weround the decimal, we getzero. If we expand ourcalculation to more decimalplaces, we find, using thecalculator atwww.OptionMath.com, thatthe odds are actually 0.006


percent,meaning the delta is0.006, which rounds to zero.Similarly,theoddsofthe100strikecallbeingin-the-moneyat expiration even if it’s at120.00 now, meaning thestock doesn’t drop from120.00 to below 100.00, areslightlylessthan100percent.It’s actually 99.937 percent.Weroundourdeltato100.Observant readers will bewondering why an option

with a strike price preciselyequal to the current price ofthe underlying stock won’thave a delta of exactly 50.Remember that deltameasures the likelihood thatthe option will be in-the-money at expiration and thatexpiration is still 30 daysaway. The Black-Scholesoptionpricingmodelassumesthe underlying stock willappreciate by the risk-freerate of return (1 percent in

ourexample)duringthose30days, meaning the modelexpects the underlying stockto be at about 100.08 atexpiration—the 100 strikecall would be in-the-moneyby 0.08; hence, the delta isgreater than 50. There areother phenomena at work aswell that result in a delta ofmore than 50, includingissues like lognormal returns,but those are topics formoreextensivestudy.

Figure2.5showsthedeltaforour hypothetical option forthesamerangeofunderlyingprices.

Figure2.5DeltabyStockPrice

■ Changes inVolatilityWesaidearlier thatvolatilityisthemostconfoundinginputin our effort to know thevalue of an option. Again, ifwecouldpeer into the futureand know how volatile theunderlyingstockwasgoingtobeforthetermofouroption,thenwewouldknowjusthowvaluable the option is. We

alsosawearlierthatwecoulduse an option pricing modeland all the knowable orobservable inputs, as well asthe price the option iscurrently trading at, andreverseengineerthevolatilitythe market expects for theunderlyingstockfor the termof the option. This is thevolatility implied by theobserved option price. Youcan use the tools atwww.OptionMath.com to


calculate the impliedvolatility for the optionsyou’relookingat.What happens to an optionprice if the volatilityassumption changes? Howmuch does the option pricechangegivenachange in thevolatility input?Let’s lookata slightly differenthypothetical 110 strike calloption with the underlyingstockat100.00and365days

to expiration for a range ofvolatilityinputsandseewhatthe option pricing model atwww.OptionMath.com saystheoptionisworth.

Annualizedvolatilityof5percent:

0.94

Annualizedvolatilityof10

percent:1.14

Annualized


volatilityof20percent:

4.61


percent:16.46


percent:35.68

Let’s connect the dots again,this time in Figure 2.6, andsee what the option pricewouldbeforthefullrangeof

volatilityinputs.

Figure2.6HowOptionValueChangeswithChangesinVolatilityAssumption

As you can see, when thevolatility input rises abovesomeverysmallandunlikelylevel, the relationship isessentially linear. Theimportant takeaway here isthatvolatilityistheinputthatmatters the most in anoption’s price and thatvolatility is the best measureof the true cost of an option

since it winnows out thevariables such as strike priceandtimetoexpirationandthepriceoftheunderlyingstock.The change in option pricethatwe’dexpect toseegivena1percentchange(from,say,20 percent to 21 percent) involatilityiscalledvega.Vegaisusuallyquotedasapositivenumber, and that’s the waywe do it atwww.OptionMath.com, so it


is the increase in an option’sprice if the volatility inputincreases by 1 percent withall the other inputsunchanged. An increase involatility will increase thepriceofbothaputoptionandacalloption;theoptionpricewill increase by vega. Adecrease in volatility willdecrease the price of both aput option and a call option;theoptionpricewilldecreasebyvega.

■OtherSensitivitiesAs we saw, there are otherinputs to option pricingmodelsincludingtherisk-freeinterest rate. Changes in theinterest rate will generatechanges in option prices.Owningacalloptionis,afterall, something of a proxy forownershipoftheshares,butitrequiresmuchlesscapital,sowe’d expect interest rates tohave some impact.However,

theimpactofinterestratesonoption prices is very small.It’s toosmall for theaveragetrader tobeconcernedabout.For the professional, thissensitivity is called rho, andyoucancalculaterhoforyouroption, option spread, oroption combination atwww.OptionMath.com, butwhenyoudo,you’llfindthatthe impact is indeed verysmall.


One other sensitivity thatsome option traders considerhastodowiththefactthatthesensitivity of an option tochanges in the price of theunderlyingstock,thedeltawediscussed earlier, changes asthe price of the underlyingchanges.Aswesaw,thedeltaforour100strikecallwith30days to expiration wasinfinitesimal when theunderlying stock was tradingat 80.00,while the deltawas

52with the underlying stockat100.00,andwas99.9whenthe underlying stock was at120.00. Clearly, the deltachanges as the underlyingpricechanges,andthatmakessense as the likelihood thatthe option will be in-the-moneyatexpirationisclearlyrelated to itsmoneyness; thatis, where the stock iscurrentlytradinginrelationtothestrikeprice.

The fact that the delta is thehedge ratio necessary towringthedirectionalityoutofavolatility-basedtrademeansthat as the price of theunderlying stock moves, thehedge ratio changes,necessitating adjustments tothe amount of underlyingstock that is hedging theoption position. How muchwill the delta change if theunderlying stockmoves from100.00 to 101.00 (or from

80.00to81.00orfrom119.00to 120.00)? That is theamount of stock that willhave to be executed in theadjustment trade to keep thecorrecthedgeratio;thisistheamount by which the deltawill change. The measure iscalled gamma. Traders usingoptions for directional tradesdon’t have much use forgamma since they’re notworried about adjusting theirposition to remove

directionality. Instead, theywant the directionality. Fordirectional traders, gammacantellthemhowquicklythedirectionality of their tradewill change. If gamma ishigh, then the directionalityof the trade will increase ordecreasequickly.Ifgammaislow,thenthedirectionalityofthe tradewill change slowly.You can calculate gamma atwww.OptionMath.com.


Figure2.7 shows the gammaforour100strikecallwith30days to expiration over arange of prices for theunderlyingstock.Thegammais greatest with the stock at-the-money for the reasonswe’ve already discussed. Amove from80.00 to81.00ora move from 119.00 to120.00 won’t change thelikelihood of the optionexpiring in-the-money byverymuch.With the stockat

81.00, the likelihood is stillpretty remote.With thestockat120.00,it’sverycertainbutonly a tiny bit more certainthan it waswith the stock at119.00.

Figure2.7Gamma

Nowyouknowwhat optionsare, the inputs to their value,and how changes in thoseinputs will impact the valueof the option. The websitewww.OptionMath.com wasconstructed to help you dosome of these calculationsyourself. The calculationworksheet will calculatetheoretical option values and


sensitivitiesgivenyourinputsas well as the volatilityimpliedbytheobservedpricefor an option. Use the site,but keep checking back, aswe’ll post new educationalcontentregularly.Nowlet’slookatthoseoptionspreadsandcombinations.

CHAPTER3

VerticalSpreads

Vertical spreads are just

about the simplest optionspread imaginable.Averticalspread is constructed bybuyingoneoptionandsellingan option that is identical tothefirstoptionexceptfor thestrikeprice.Itmightbeeasiertothinkofaverticalspreadasa “strike spread” since thestrike is the only differencebetween the two options; theunderlyingasset, type(putorcall), and expiration date arethesame.Tomakecertainthe

trade is a true spread, asopposed to a combination,we’re long one option andshorttheother.We begin with verticalspreads because they are,simply said, a necessary toolfor option traders. Whetherlong or short a verticalspread, both risk and rewardaredefined,sosellingverticalspreads(we’lldefinewhatwemean by selling a vertical

spreadlaterinthischapter)isa great way to get a payoffthat is much like selling anoutrightoptionwhiledefiningrisk.Ifyou’reinclinedtoselloptions,andit’snotacoveredcall or a cash-secured put,then selling a vertical spreadis preferable because youhave reduced your risk to atinyfractionofwhatitwouldbeifyouwerenakedshortanoutrightoption.

Vertical spreads will alsobecomeimportantelementsinother combinations when wereplace an outright optionwithaverticalspreadinorderto improve a strategy. Forexample,ifyouwantedtosellacoveredcallbutalsowantedtoparticipate to theupside ifthere’s a really big movefrom, say, a takeover, thenyou’dreplacetheshortcallinyourcoveredcallwithashortcall vertical spread.We’ll do

the same sort of replacementof outright options in collarsand risk reversals, but moreaboutthosestructureslater.Vertical spreads likely gottheir name because strikeprices run vertically in mostoption listings. Usually, theexpirations run horizontallyso calendar spreads are oftencalled “horizontal spreads,”but we’ll stick with callingthese two spreads vertical

spreads (or verticals) andcalendar spreads (orcalendars).Let’slookatsomecalloptionsandacallverticalspread you might execute.You’llseetheseinFigure3.1.

Figure3.1SomeCallOptions

For example, given the calloptionpricesinFigure3.1, ifweboughttheJune41callat1.00andsoldtheJune44callat 0.23, we would haveexecuted the June 41/44vertical call spread. Wewould have bought that callspread(wewouldbelong)ata net price of 0.77 (1.00 –0.23).

■ Buying and SellingVerticalSpreadsYou buy a call spread whenyoubuy the lower strike callandsellthehigherstrikecall.You sell a call spread whenyou sell the lower strike callandbuythehigherstrikecall.You buy a put spread whenyoubuy thehigher strikeputand sell the lower strike put.You sell a put spread when

you sell the higher strike putand buy the lower strike put.Itmaybeeasiertorememberit likethis: ifyoupaymoneyfor the spread,whether it’s acall spread or put spread,you’re buying the spread.And as you can see inTable3.1, ifyoureceivemoneyforthespread,whetherit’sacallspreadoraputspread,you’resellingthespread.

Table3.1BuyingandSelling

VerticalSpreadsBuyaCall

Spread

SellaCall

Spread

BuyaPut

Spread

Sella

SpreadBuythelowerstrikeprice

Sellthelowerstrikeprice

Buythe

higherstrikeprice

Sellthehigherstrikeprice

Sellthehigherstrike

Buythe

higher

Sellthelowerstrike

Buy

lower

price strikeprice

price strikeprice

Payforthe

spread

Bepaidforthespread

Payforthe

spread

Bepaidforthespread

■ Vertical SpreadMaximum andMinimumValuesVertical spreads are a greattool because they limit risk,even when sold. As with anoutrightoption,theminimumvalue for a vertical spread iszero.Nomatter how high orlow the underlying stockgoes,there’safloorunderthevalueofaverticalspread,and

that floor is zero. But unlikeanoutright option, there’s anupwardlimittothevalueofavertical spread; there’s aceilingabovewhichthevalueof a vertical spread cannotrise.Thatceilingisthewidthof the spread or simply theupper strike price minus thelower strike price. Forexample, let’s return to theJune41/44callspreadthatwelooked at previously. Thisspread is 3.00wide, but let’s

see what that vertical callspread would be worth withthe stock at some extremeprices at the June optionexpiration.YoucanseetheseinTable3.2.

Table3.2VerticalSpreadMaximumandMinimumValues

StockPriceatOption

Expiration

Valueof41CallatExpiration


0 0.00 0.0041 0.00 0.0044 3.00 0.00100 59.00 56.00

Even if the stock dropped to0.00 at expiration, the callspread could never be worthlessthanzero.Nomatterhowhighthestockgoes,evenifitmore than doubles, even if itrallies infinitely, themaximum value of the call

spread will be the width ofthe spread, which is thedistancebetweenthestrikes.This is a vitally importantelementofverticalspreads.Itmeans we can use them insituations when sellingoutright options isn’tappropriate, such as sellingnakedcallsornakedputs.

■NamingSomewhere in the optionnomenclature, someonedecidedtocomplicateverticalspreads by giving themconfusingnameslikebullputspread and bear call spread,andsoon.Professionalsdon’tuse that terminology, withgood reason, and we won’teither. In the precedingexample,weboughtthelower(41) strike call and sold the

higher (44) strike call, and itcost us a net of 0.77 (1.00 –.023). We bought the callspread, as you saw in Table3.1, and that’s how we’lldescribe that trade: buyingthe call spread. We are nowlong that call spread.However, if we had sold thelower (41) strike call andbought the higher (44) strikecall, then we would say wehad sold the call spread, wewould have gotten paid for

selling it, and we would beshort it. You can see this inFigure3.2.

Figure3.2CallOptionsandVerticalSpread

Thesamegeneralideaappliestoverticalputspreads:ifyoupayfortheputspread,you’rebuying it; if you are paidmoney,thenyou’resellingit.For example, using the putoptionpricesinFigure3.3, ifwe’d bought the June 41 putat 1.44 and sold the June 38put at 0.35, we would havebought the put spread and

wouldhavepaid1.09(1.44–0.35) for it. We bought thehigherstrikeputandsoldthelower strike put, so weboughttheputspread.

Figure3.3PutOptionsandVerticalSpreads

IfwehadsoldtheJuly42putat2.65andboughttheJuly38put at 0.81, we would havesold the put spread andreceived 1.84 (2.65 – 0.81)forit.

■ Moneyness andVerticalSpreadsWe discussed moneyness ofoptions in Chapter 1. Torecap, if the strike price of acall is below the currentmarket price of the stock,then thecalloption is in-the-money.Ifthestrikepriceofaput is above the currentmarket price of the stock,then the put option is in-the-

money.If the strikepriceof a call isabove the current marketprice of the stock, then thecall option is out-of-the-money.Ifthestrikepriceofaput is below the currentmarket price of the stock,then theputoption is out-of-the-money.If thestrikeprice isequal to,orverynearly so, thecurrentmarket price of the

underlying stock, then theoptionisat-the-money.Moneyness is really, reallyeasyforasingleoption.Whatabout for a vertical spreadwithtwooptions?Oneoptioncould be in-the-money, andanother could be out-of-the-money. There are severalcombinations andpermutations of moneynessforaverticalspread,butwe’llprimarily look at out-of-the-

money vertical spreads (bothlegs are out-of-the-moneywhen the trade is executed)and vertical spreads whereone leg is at-the-money andthe other leg is out-of-the-money, which behave justlike fully out-of-the-moneyvertical spreads, since that’susuallywhatwe’llbeusing.Vertical spreads where oneleg is at-the-money and theother is in-the-money behave

very much like fully in-the-moneyverticalspreads.Laterin this chapter, we’ll look atin-the-money verticals sincetheybehavealittledifferentlythan out-of-the-moneyverticalspreads.

■ Bullish and BearishVerticalSpreadsAs with buying an outrightcall, buying an out-of-the-money (both legs of thespread are out-of-the-moneyor one leg is at-the-moneyand the other is out-of-the-money)callspreadisbullish,we need the market to rallyfor the spread to beprofitable.However,sellinga

callspread,atleastonethat’sout-of-the-money, needs theunderlying stock or asset todo anything as long as itdoesn’t rally sharply. Thismeans a short call verticalisn’t really bearish. It can dowell if the stock goes down,sideways, and even if thestockgoesup a little as longas it isbelow thestrikepriceweare shortwhenexpirationarrives.

Buying an out-of-the-moneyputspreadcertainlyneedstheunderlying stock to fall inordertomakemoney.Sellingan out-of-the-money putspread,needs the stock todoanything but fall sharply inorder to be profitable. It canrally,itcanmovesideways,itcanevenfallalittlebit.Thefactthatsellingaverticalspreadmeans any number ofthingscanhappenandwecan

still make money is theprimary reasonwewon’tusethe bullish/bearishterminology for verticalspreads.Let’s revisit the simple out-of-the-money call spread wefirst looked at in Figure 3.1.IfweboughttheJune41callat 1.00 and sold the June 44callat0.23,wewouldbelongthe June 41/44 call spread at0.77. The underlying stock

was at 40.56 at the time weobserved theseoptionvalues,so both legs are out-of-the-money. As we’ve discussed,thisisabullishtrade,andwewould execute it only if weexpectedthisstocktogoup.How would this tradeperform across a range ofprices for the underlyingstock? Let’s construct aprofit-and-loss (P&L) tablebecause this is often the

easiest way to understandhowthetradeworks,whenitdoesn’t work, and what weneedtheunderlyingmarkettodo. We won’t construct aP&Ltableforeverytradewediscuss,but it’shelpful todoitafewtimestomakecertainwe understand the conceptsfully. The P&L informationfor buying this vertical callspread can be seen in Table3.3.

Table3.3PayoffTableforBuyingaCallVertical

StockPriceatOption

Expiration


ProfitorLosson41Callat

Expiration

37 0.00 –1.00

38 0.00 –1.00

39 0.00 –1.00

40 0.00 –1.00

41 0.00 –1.00

42 1.00 0.0043 2.00 1.0044 3.00 2.0045 4.00 3.0046 5.00 4.0047 6.00 5.0048 7.00 6.00

As with any vertical spread(or outright option) that webuy,themaximumlossisthenet price thatwe pay for thespread. In this case that’s0.77. Themaximum profit isa little different. It’s themaximum potential value ofthe spread, or 3.00 (44–41)in this case, minus the pricewepaidforthespreador0.77in this case. That means themaximumprofit for this longcall spread is 2.23 (3.00 –

0.77). Notice also that thetotal profit or loss starts tochange when the underlyingstock is right at the strikeprices of the constituentoptions.The strikeprices areinflection points for ourpayoff.Whatwould that spread looklike graphically?We can seethatinFigure3.4.

Figure3.4PayoffforBuyingaLongVerticalCallSpread

Thiscallverticaldoesbest ifthe underlying stock rallies.In fact, it needs theunderlyingstocktorallyfromthe current price of 40.56 toat least 41.77 if it’s going toavoid losing any of the 0.77paid for it. That meansbuying this out-of-the-moneycall vertical is bullish so,again, you’d buy it only if

you expected the underlyingstock togoup. InFigure 3.5you can see how theunderlying stock must rallyfor the spread to beprofitable.

Figure3.5StockMustRallyforLongCallVerticalSpreadtoBeProfitable

■ Selling a CallVerticalSpreadButwhatifwe’dsoldthiscallvertical? What if we’d soldthat 41 call at 1.00 andbought the 44 call for 0.23,collecting a net of 0.77 (I’dneversellanakedcall,sonotonlydoesbuying that44callturn this into a verticalspread,italsodefinestheriskof selling the 41 call). That

payofftablelooksdifferentasyoucanseeinTable3.4.

Table3.4PayoffTableforSellingaCallVerticalSpread

StockPriceatOption

Expiration



Expiration37 0.00 1.0038 0.00 1.0039 0.00 1.00

40 0.00 1.0041 0.00 1.00

42 1.00 0.00

43 2.00 –1.00

44 3.00 –2.00

45 4.00 –3.00

46 5.00 –4.00

47 6.00 –5.00

48 7.00 –6.00

Thegraphicalpayoffchartforsellingthis41/44callverticalcanbeseeninFigure3.6.

Figure3.6PayoffforSellingaCallVertical

The risk/reward for selling avertical spread is certainlydifferent than the risk/rewardfor buying a vertical spread.In selling this call spread themaximumwecanmakeisthe0.77 received.Themaximumwe can lose is themaximumvalue of the spread (3.00)minus the net premiumreceived (0.77) or 2.23 (3.00

– 0.77). We’ll discuss thisasymmetry later in thischapter, but it’s an importantelement of trading verticalspreads.

■BreakevenPointsIf we buy a vertical spread,then themarket has tomoveinorderforittobeprofitable.How far does it have tomove? If we sell a verticalspread, then the market canmoveandthespreadcanstillbe profitable.How far can itmove? The point wherelossesturntoprofitforalongvertical is the breakevenpoint.Thepointwhereprofits

turn to losses for a shortvertical is also thebreakevenpoint.How can we quicklydetermine these breakevenpoints without creating aP&L chart or drawing thegraph?For a long vertical, theunderlyingstockhastomoveso that it’s in-the-money byenoughtopayforthespread.Thatmeansforacallvertical,

ithastorallyabovethelowerstrike price, the strike pricewe’relong,bytheamountwepaidforthespread.Foraputvertical, it has to drop belowthe upper strike price, thestrikepricewe’relong,bytheamount we paid for thespread.For a short vertical, theunderlyingstockcanmovesothat it’s in-the-money by theamount we received for

selling the spread. You canseethisinTable3.5.

Table3.5Breakevens

Trade BreakevenPoint

Longacall

verticalspread

Lowerstrikeprice+Costofthespread

Shortacall Lowerstrike

price+Costof

verticalspread

thespread

Longaputverticalspread

Upperstrikeprice–Costofthespread

Shortaputverticalspread

Upperstrikeprice–Costofthespread

■TheNecessaryPriceActionIn selling that call verticalspread,themarketactionthatweneedisverydifferentthanitwould be ifwe bought thespread.Ashortcallverticaliscertainly profitable if themarket moves lower, so wemightthinkwewanttocallitbearish, but it is alsoprofitable if the market

moves sideways, and it’seven profitable if the marketmoves up a little, so it’sobviouslynotjustbearish.Aslong as the market price forthis stock stays below thatlower strike price, 41 in thiscase, the call vertical willmake the maximum profit,0.77inthiscase.Inthiscase,the stock could rally from40.56,whereitwaswhenweexecuted this spread, all thewayupto41.00atexpiration

and still achieve maximumprofit. That maximum profittrails off as the stock ralliesabove 41.00 until it reachesthebreakevenpriceof41.77.You can see that the payofflineinFigure3.6 intersects0with the underlying stock at41.77. That’s the breakevenpoint, so the stock can evenrally just short of 41.77 forthis vertical spread to beprofitable, although we’llenjoy a profit that’s lower

thanthe0.77maximum.The same sort of marketaction is needed for putvertical spreads. Previously,we lookedatbuying the July40putat1.53andsellingtheJuly 38 put at 0.81. Buyingthat vertical spread wouldcost us a net of 0.72 (1.53 –0.81), and as you can seefrom the payoff chart inFigure 3.7, buying this putverticalmeans that this stock

hastofallfortheputverticalto be profitable. In fact, asyoucansee, ithas todropto39.28 just to break even anddoesn’t become profitableuntil it has dropped belowthatlevel.You’donlyexecutethis trade ifyouexpected thestock to fall well below the39.28level.

Figure3.7PayoffforBuyingaVerticalPutSpread

If we had instead sold thisJuly 38/40 put vertical (soldthe July 40 put at 1.53 andbought the July 38 put at0.81), we would havecollected that 0.72 instead ofpayingit.Ouroutlookforthemarket would have beendifferentifwehaddecidedtoestablish this short putvertical trade, as this trade

makes money if theunderlying stock rallies,goessideways,andevenifitdropsa littlebit, as longas it staysabove the 39.28 breakevenlevel,asyoucanseeinFigure3.8.

Figure3.8PayoffforSellingaVerticalPutSpread

■VerticalSpreadsandYourMarketOutlookBuying an out-of-the-moneyvertical spread, either a callspread or put spread, meansyou have an affirmativeoutlook on the underlyingstock, not necessarily apositive one in the case of aput vertical, but rather youthink it’s going tomove andyou’ve picked a direction. If

you think it’s going to rally,youmight buy a call spread;ifyouthinkit’sgoingtofall,youmightbuyaputspread.Selling a vertical spreadmeans you have a differentsortofoutlook.Youthinkthestock is not going to do X,meaning it might do theopposite ofX or itmight donothing. Just as the non-negativenumbers include thepositive numbers and zero,

selling a vertical put spreadmakes money if theunderlyingstockgoesuporifit does nothing. In fact, aswe’veseenfromthepreviouspayoff charts, there’s even amargin of error where theunderlyingstockcandowhatwethinkit’snotgoingtodo,as long as it only does it alittle bit. You can see thatmargin of error clearly ifwetake another look at thepayoffchartforthisshortput

spreadinFigure3.9.

Figure3.9ShortPutVerticalandtheMarginofError

Comparethismarginoferrorto themovement in thepriceof the stock that is requiredforalongverticalcallspreadtobeprofitable.We saw thisrequired move clearly inFigure 3.6. This margin oferror is the reason thatvertical spread sellers arewillingtoriskmorethantheymight make. On the other

hand, the stock has to movein the right direction and gettoatleastthebreakevenpointforavertical spreadbuyer torealize a profit. Since theodds of that are less thaneven, the vertical spreadbuyer demands a potentialprofitthatisgreaterthantheirpotentialloss.You can see these marketoutlooks and the verticalspreads you might use in

Table3.6.

Table3.6Out-of-the-MoneyVerticalSpreadsandMarketExpectations

LongVerticalCall

Spread

ShortVerticalCall

Spread

Vertical

Spread

Marketneedsto:

Rally

Fall,move

sideways,rallyonly

slightlyYou’ddoifyouwere:

BullishNotreallybullish

Bearish

■ Asymmetry of Riskand Reward forVerticalSpreadsAswe’ve seen,when buyingan out-of-the-money verticalspread, the sort of verticalspread we’ve beendiscussing, there’s anasymmetry of the maximumrisk and the maximumreward. This asymmetryexists in almost every option

strategy; it’s what makesoptionssoverydifferentfromtheir underlying assets. Buyhow is this asymmetrystructured, and how can weuseittoouradvantage?You might be tempted tothink, “I alwayswant to buyvertical spreads because Iwant to be in a situationwhereIcanmakemanytimeswhat I might lose,” eventhough we’ve seen that the

stockhas tomoveandhas tomove in the right directionand by at least the rightamount.Butwhatifsomeoneofferedyouthesortofbetweseeinthis41/44callspread—you can buy the spread andrisk0.77tomake2.23oryoucan sell the spread and risk2.23 to make 0.77—and youknew that the entire spreadwould expire with thelikelihood of a certain valuethatweseeinTable3.7?

Table3.7HypotheticalAsymmetricOutcomes

ValueofSpreadatExpiration

Likelihood

0.00 90%1.50 5%3.00 5%

Remember that while ourmaximum profit would be2.23ifwebought thespread,

thevalueofthespreadwouldbe 3.00 if the stock wereabove 44.00 at optionexpiration. Obviously, in thereal world, the spread couldexpirewithavalueas lowas0.00 and as high as 3.00 andany number in between, butto make the math easier inthis example, we’re limitingthe outcomes to just three.Thesethreeoutcomesandtherelevant likelihoodsmean thespreadisworth:

0.00×90%=0.000+ 1.50×5%=0.075+ 3.00×5%=0.150 0.225

Given just these threepotential outcomes andlikelihoods, the spread isworth0.225. Ifweknewthatthose were the potentialoutcomes and the likelihoodofeach,thenwe’dgladlysell

this vertical spread at 0.77,even though itmeans risking2.23becausethemathtellsusthe spread is only worth0.225andtheoddsoflosingamoderate amount of money(2.23 in this case) by sellingthespreadareverysmall.Since the amount of moneywe can lose in selling averticalisdefined,andinthiscase is reasonable given thepotential profit and the

likelihoods, it’s sometimessmart to risk more than youstand to make by sellingvertical spreads. Readers ofOptionsMathalsoknowthat,over time, options cost morethanthey’reultimatelyworth,meaning that there’s anadvantage to selling options.Just as your homeowner’sinsurerchargesmorethanthecoverage is worth (thedifferencecoverstheircostofdoingbusinessandprovidesa

little profit), options, overtime, cost more than they’reworth; the price is greaterthanthevalue.Thedifferencemakes up for the asymmetryof payoffs for the optionseller,butit’salsosomethingthat the vertical spread sellercan takeadvantageof.Whilethe benefit is reduced in avertical spread, it’s generallypositive. There are otherphenomena discussed inOptions Math that impact

vertical spreads.Skew is oneof those phenomena, and itgenerally helps vertical callspreadsellersandverticalputspreadbuyers.

■ Option Delta andLikelihoodWe’ve seen that we may bebetter off riskingmuchmorethan we stand to make byselling a vertical spread. Inour previous example, wemade up some potentialoutcomes and likelihoods.Butanoption’sdeltagivesusthemarket’s expectations forthelikelihoodthatoptionwill

expire in-the-money. Let’ssee if we can use thoselikelihoods to betterunderstand how our verticalspreadwillperform.Deltaisthemostbasicgreek,and it tells us two thingssimultaneously. First, it tellsus howmuch theprice of anoption (or of a spread orcombination if we do somesimple math) should changeasthepriceoftheunderlying

stock moves by $1. This istrue because delta is also ameasureofthelikelihoodthatan option will be in-the-money at expiration. Thismeans we can use the deltasof theoptionsmakingupourvertical spread to determinethelikelihoodofeachlegandof theentire spreadbeing in-the-money (or out-of-the-money) at expiration (wecouldn’t use actual deltas inthehypotheticalexamplewith

just three potential outcomesthatwejustlookedatbecausedelta assumes the spread canbeatanypricebetween0and3.00 inclusive at expiration,notjustoneofthreepricesweexamined). Let’s check thedeltasoftheJunecallswe’vebeen looking at.Your optionbroker will provide deltas aspart of the option chain yousee on theirweb site, or youcan calculate them atwww.OptionMath.com. You


can see these deltas in Table3.8.

Table3.8CallandVerticalCallSpreadDeltas

StrikePrice

JuneCallOptionPrice

OptionDelta

38 2.90 8439 2.15 7340 1.52 6041 1.00 46

42 0.65 3243 0.40 2144 0.23 12

We’re long the June 41/44vertical call spread, and wepaid 0.77 for it. How muchmightweexpect thevalueofour spread to change witheach$1changeinthepriceoftheunderlyingstock?Thedeltaofthiscallspreadis

34 (46 – 12). We wouldexpectthevalueofthespreadto increase by 0.34 if theprice of the underlying stockrallied by $1. We wouldexpectthepriceofthespreadto decrease by 0.34 if theprice of the underlying stockfell by $1. We see how thisplays out in Tables 3.9 and3.10.

Table3.9OurVerticalCallSpreadaftertheUnderlying

StockHasRalliedUnderlyingStockPriceRallied$1to:

41.56

StrikePrice

NewOptionValue

Profit/Loss

41 1.46 0.4644 0.35 –0.12Profit/lossfortheentirespread

0.34

Table3.10OurVerticalCallSpreadaftertheUnderlyingStockHasFallen

UnderlyingStockPriceFellby$1to:

39.56

StrikePrice

NewOptionValue

Profit/Loss

41 0.54 –0.4644 0.11 0.12

Profit/lossfortheentirespread

–0.34

The value of this 41/44 callspreadshouldchangeby0.34if the underlying stockchanges in value by $1,although there are otherfactorsthatmightresultinthechange’s being slightly moreorlessthan0.34.Thedeltaofeach option will be different

atthenewstockprice(duetothe impact of gamma wediscussed earlier), so the netdelta won’t be 34 anymore,and for this reason,we can’tprecisely know what thevalueof the spreadwouldbeiftheunderlyingstockmovedbymorethan$1.Moreimportantly,canweusethese deltas to help us figureoutwhat themarket says thelikelihood of these options

and this spread being in-the-money and out-of-the-moneyare at expiration? Certainly,that’s the other thing thatdeltatellsus.BasedonthedeltaswesawinTable 3.8, we know that themarket says there’s a 46percentlikelihoodthat the41call will be in-the-money atexpiration. That likelihoodmakes sense because theunderlying stock was at

40.56,which isvery close to41. The odds of its rallyingfrom 40.56 to over 41 atexpiration are close to 50percent.The delta of the 44 call islower, and that makes senseaswellbecausethelikelihoodof the underlying stock’srallying past 41 and gettingabove 44 is obviously lessthanthe46percentlikelihoodof the underlying stock’s

simply being above 41 atoption expiration,remembering that it could beabove41andbelow44.The market tells us that thelikelihood of the underlyingstock’s being above 44 atoption expiration is 12percent. In order for thisverticalspread tobefully in-the-money at expiration, the44 call has to be in-the-money. We know the

likelihood of that is 12percent.Whatisthelikelihoodthatthespreadwillatleastbreakevenifwebuyit?Thatissimilartodetermining the chance thatthestockwillbeabove44atexpiration, but instead of itsbeing above 44, we wonderwhat theoddsare that itwillbe at or above the 41.77breakeven price that wecalculatedbefore.Wecanuse

the tools atwww.OptionMath.com tocalculate the delta of ahypothetical option with astrikepriceequal to41.77. Ifwedo that,we find thedeltaof that option is 35,meaningthelikelihoodof itsbeingin-the-moneyatexpirationis35percent.That’s the likelihoodthat the spread will at lastbreakevenforthecallspreadbuyer.


And what does this tell usabout thepriceof thisspreadversus the value of thisspread?Thespreadcosts0.77andhasamaximumpotentialprofitof2.23.Theoddsofatleast breaking even are 35percent.Youcanseealltheselikelihoods in Figure 3.10.Now that we’ve shown youhow to determine them forbuying a call vertical spread,you should be able todetermine them for any

verticalspread, longorshort,callorput.

Figure3.10PayoffsandLikelihoodsforBuyingaVerticalCallSpread

Let’sdothesameanalysisforthe July38/40put spreadwewere thinking about buying.InTable3.11,wesee theputoptionpricesanddeltas.

Table3.11PutandVerticalPutSpreadDeltas

StrikePrice

JulyPutOption Option

Delta

Price38 0.81 1439 1.13 2040 1.53 2941 2.04 4142 2.65 5343 3.33 6644 4.08 77

Ifwebought thatverticalputspread,wewouldbuy the40putat1.53andsellthe38put

at 0.81. We’d pay a net of0.72, and that would be ourmaximum loss. Ourmaximum potential profitwouldbethemaximumvalueofthespread,2.00(40–38),minuswhatwe’dpaidforthespread(0.72),foramaximumprofitof1.19(2.00–0.72).The delta of the put spreadwouldbe15(29–14).Someoptionuserswillrefertoaputdelta as a negative number

since the price of the optionwill decrease by the delta ifthe price of the underlyingstock rises. I don’t like that.The delta is really twomeasures. First, it’s theamount by which the optionwill change in price if theunderlying stock moves by$1.00, regardless of whetherthe stockmovesupordown.The option price can’t moveby a negative number. It canmovedown,butsayingitcan

movebyanegativenumberisalittleliketellingyoutowalknorthbynegativethreemiles.What I’m probably saying istowalk southby threemiles,but you can’t walk negativemilesandastockcan’tmoveby a negative amount.Second, the delta is thepercentagelikelihoodthattheoption will be in-the-moneyat expiration. Everylikelihood is greater than orequaltozero.

Sothedeltaoftheputspreadis 15.We’d expect the priceof the spread to change by0.15 if the underlying stockmovedby $1.00. Since it’s aput spread, itwouldmove inthe opposite direction of theunderlying stock. If theunderlying stock fell by$1.00, then we’d expect theprice of the put spread toincrease by 0.15. If theunderlying stock rallied by$1.00, then we’d expect the

priceof theputspreadtofallby 0.15. As we said before,afterthatmove,thedeltasforthese options will havechanged(theywillactuallybechangingslightlyasthestockis making that $1.00 move),so after the move the deltawillnolongerbe15.It’salsopossible that other factorsmean the price of the spreadwon’t have changed byexactly 0.15, but with otherinputs unchanged we’d

expectthepriceofthespreadtochangeby0.15.What’sthelikelihoodthattheentire spread will be in-the-money at expiration? Thatwould require the underlyingstocktobebelow38atoptionexpiration,and the likelihoodof that happening is exactlywhat the delta of the 38 puttells us: the odds of thathappeningare14percent.The breakeven for this

vertical put spread is 39.28.What are the odds that thestock is below 39.28 at Julyexpiration? While there’s nooption struck precisely at39.28, we can again use thetools atwww.OptionMath.com tofind that the delta of thishypotheticalputoption is23.That’s the percentagelikelihood that the stock willbe below 39.28 at Julyexpiration.


■ Vertical SpreadValue Prior toExpirationSo far,we’ve lookedatwhata vertical spread will beworth at expiration. We dothisinpartbecauseithelpstoexplain the concepts andbecauseit’spossibletoknowprecisely what any verticalspread will be worth atexpirationgivenanypricefor

the underlying; we canconstruct the sort of P&Lchart that we saw previouslyand do some simplearithmetic. We also look atwhat the spread is worth atexpiration because it’simpossible to know withcertaintywhatthespreadwillbe worth prior to expiration.We can put some variablesinto the tools available atwww.OptionMath.com andget a really good estimate of


what the spread will beworth, but it’s an estimatebecause we don’t knowexactly what each individualoption will be worth. Theamount of volatility that themarket will estimate for theremaininglifeoftheoptionistheunknowablevariable.What is our spread likely tobeworth prior to expiration?At expiration our 41/44 callspread was worthless if the

underlying stock was at40.75.Whatiftheunderlyingstock was at 40.75 but therewere 20 days to expiration?Wouldyoubewilling topaysomething for the spreadthen? Probably, because allthe underlying stock wouldhave todo is rallya little forthe spread to have some sortof inherent value. If theunderlying rallies by 0.50,then the spread is inherentlyworth 0.25. And given 20

days to expiration, that justmighthappen.At expiration our 41/44 callspreadwasworth 3.00 if theunderlying stock is at 44.25.With 20 days to expirationand the underlying stock at44.25, would you be willingto pay $3.00 for this spread?Probablynot,because there’szeropotentialforprofit.Evenif it were a metaphysicalcertainty that the underlying

stock was going to be at44.25 at expiration 20 dayshence, you wouldn’t pay$3.00 for the call spreadbecause you’d lose moneyaftercommissions.Andintherealworld,there’salwaysthepossibilitythattheunderlyingstock won’t be at 44.25 atexpiration. If it falls backbelow 44.00, then the spreadisgoingtobeworthlessthan$3.00,sothere’snoreasontopaythemaximumvaluefora

spread, particularly if there’stimelefttoexpiration.Whatisthevalueofaverticalspread prior to expiration?Figure 3.11 shows the linearpayoff at expiration thatwe’re familiar with and alsoshows the curved payoff linefor this spread with 45 daystoexpiration.

Figure3.11PayoffforaLongVerticalCallSpreadandValueBeforeExpiration

If immediately after buyingthiscallspreadtheunderlyingjumpedto45.00,we’dhaveaprofit, but the spreadwouldn’t be worth themaximum value of 3.00 likeitwouldbeifitwereat45.00at expiration. At 45.00,assuming nothing elsechanged (pretty unlikely, but

anecessaryassumptionforustogeneratesomehypotheticaloption prices), the spreadwould be worth 2.27, so ourunrealized profit would be1.50 (2.27 – 0.77). Thischanges things for us. Wenowwantexpirationtoarriveas quickly as possiblebecause along withexpiration,we’regoingtogetthe maximum value of thespread. The value of thespreadwillchangeovertime,

and the curved line that wesee in Figure 3.12 willbecomemoreliketheangularpayoff at expiration that wesee. That’s the importantconsideration—as timepasses, the curved line willbecomemore angular until itexactlymatchesthepayoffatexpiration.InFigure3.12yousee how the curved payoffline for our spread with 45days to expiration becomesangular with 22 days to

expirationasthepayoff isonits way to being completelyangularatexpiration.

Figure3.12PayoffforaLongVerticalCallSpreadandValuebeforeExpiration

While long the 41/44 callspread after the underlyingstockhasjumpedto45,we’rewaitingfor thecurvedlinetomovehigherastimepasses.Thisverticalcallspreadisnolonger an out-of-the-moneyverticalandisnowanin-the-moneyvertical.In-the-moneyspreads behave differently,

andwe’ll discuss themmorelaterinthischapter.If immediately after buyingthiscallspreadtheunderlyingfell to 39, then the spreadwouldfall invalue,butsincethere’s still time left in theoptions, the value of thespread wouldn’t fall to zero.Instead, the spread would beworth 0.38 (again assumingnothing else changed)meaning we would have an

unrealized loss of 0.39 (0.77–0.38).Thisspreadisstillanout-of-the-money spread; it’sjust more out-of-the-moneynow,anditstillneedsarallyin the underlying stock inordertobeprofitable.

■TheOtherGreeksWe saw that the delta for avertical spread was verysimilar to the delta for anoutright option, just a littlesmaller.ThedeltaoftheJuly40 putwe looked atwas 29,while the delta of the July38/40verticalputspreadwas15. The put spread willincrease in value as theunderlying stock drops, justliketheoutrightput.

Thesameistruefortheothergreekwe focuson: theta, theexpected daily erosion ofoptionvalue; thenet thetaoftheverticalspreadwillbelessthan the theta of the July 40put alone. Each option in avertical spread will erodeover time, and as we saw inChapter2,theerosiondoesn’thappen in a straight line.Thus, theerosionofour longvertical put spread won’thappen in a straight line

either, although the exactshape of the erosion chart isdependentonhowfarout-of-the-money each option is.Table 3.12 shows the thetafor each of the July puts welookedatearlier.

Table3.12PutandVerticalPutSpreadTheta

StrikePrice

JulyPutOptionPrice

OptionTheta

38 0.81 0.01739 1.13 0.01940 1.53 0.02041 2.04 0.02142 2.65 0.02043 3.33 0.01944 4.08 0.017

The July 40 put would beexpected toerodebyabout2centstoday.Thaterosionwillaccelerateasexpirationnears,

but for the July options,expiration is still 45 daysaway.TheJuly38putwouldbeexpectedtoerodebyabout1.7 cents today; again, thaterosion would speed up asexpirationneared.Butlookatthe net expected erosion forour vertical put spread—it’sonly0.3centstoday.If nothing else changed, howwould we expect that dailythetatochangeastimepassed

and we got closer toexpiration? Figure 3.13shows the theoretical erosionfor both options and for theoption spread if nothingchanged but time toexpiration.Noticethatastimepasses, the erosion for theout-of-the-money leg, the 38put in our case, falls off.That’s because it’s too farout-of-the-money.Theat-the-money leg, however, doesn’tsee this happen because it’s

alwaysclosetoat-the-money.

Figure3.13PutSpreadTheta

Thismeans that the theta, ordaily erosion, for the putspread really accelerates asexpirationapproaches.Itevenaccelerates faster than theerosion for the at-the-moneyoption alone because theerosion of the out-of-the-money option is actuallytrailingoff.Whenthechangein theta starts to go in

opposite directions, then thistrade ceases to be a realspread.It’scertainlytruethatthe risk isdefined ifyou sellit,buteachoptionstartstoactdifferently than the other.This can happen to any“spread” if the strike pricesare too far apart or if theoptions are close toexpiration,asinthiscase.What does this mean abouthowwe should trade vertical

spreads?Itmeansthattheneterosion for a vertical spreadthathasamoderateamountoftime to expiration is reallysmall. This is great if you’relongaverticalspreadbutnotgoodifyou’reshortaverticalspread.Italsomeansthat theerosion for a vertical spreadcan really accelerate asexpiration nears. With lessthan 15 days to expiration,the net daily erosion of ourvertical put spread is picking

up speed. It will never bequite as high as the dailyerosion for the at-the-moneyoption by itself, but theerosion for the spread willeventuallybecomeveryclosetothatfortheoutrightat-the-money option. This increaseinerosionforverticalspreadsis great if you’re short avertical spread, but not goodif you’re long. This is thecase because the out-of-the-money leg, the leg that

definestheriskoftheverticalspread if you are short thespread, has eroded almost tozero and the erosion slowswhile the erosion for the at-the-moneyoptionaccelerates.

■TheBestMeasureofVerticalSpreadCostThe very first vertical callspreadwelookedat,theJune41/44 vertical call spread,could be traded for about0.77.Isthatagoodprice?Forthe buyer or the seller? The42/43 vertical call spreadcould have been traded forabout 0.25. That’s certainlycheaper,butisitabetterdeal

forthebuyer?This leads to the question:how dowemeasure the costof a vertical spread? That41/44 call spread cost 0.77,butthe42/43spreadcostlessthana thirdof that.Which isthebetterdeal?Wehavetolookatthespreadin another way to determinethebetterdeal.This iswhereyour outlook for the marketbecomes important. We saw

previously that for the buyerof the 41/44 call spread, themaximum profit is achievedwith the underlying stock ator above 44 at Juneexpiration.Thatmeansyou’dcertainly look at a differentstrategy or a different spreadifyouthoughttheunderlyingwas going to get all thewayto$50byJuneexpiration.Onegreatmeasureofthecostof a spread, with one

important caveat, is tocompare the cost of thespread to the width of thespread. The 41/44 verticalcall spread could be tradedfor 0.77. That spread is $3wide(44–41),sothecostis25.67percentof thewidthofthe spread. That’s prettycheapforaspreadwithalongleg that was just barely out-of-the-money.And that’s theimportant caveat. Verticalspreadswillbecomecheaper,

as a percentage of the widthof the spread, as they getfurther from at-the-money.Thismakessensebecausetheodds of the spread beingprofitablearefalling.First, let’s look at anotherunderlying, one with morestrike prices, sowe can lookat a bigger range of verticalspreadsandseehowthecost,as a percentage of the widthof the spread, changes as the

spread gets wider. We seethisinTable3.13.

Table3.13SPYPutPricesandVerticalPutSpreads

StrikePrice

JulyPut

OptionPrice

Costofthe

VerticalPut

SpreadwithThisOption

Costof

Vertical

Spreadas

Percentageofthe

and160Put

Widthof

Spread130 0.02 1.87 6.23%135 0.03 1.86 7.44%140 0.06 1.83 9.15%145 0.12 1.77 11.80%150 0.29 1.60 16.00%155 0.76 1.13 22.60%

As you can see, the cost ofthese vertical spreads, as a

function of the width of thespread,decreasesasthewidthincreases. That makes sense.The likelihood of collectingthefullwidthofthespreadispretty remotefor thosewiderspreads.

■ In-the-MoneyVerticalSpreadsSo far, we’ve looked at out-of-the-moneyverticalspreadsalmost exclusively. Butwhatabout in-the-money verticalspreads? While you mightneverinitiateanin-the-moneyverticalspread—andtherearegood reasons you’d neverinitiate an in-the-moneyvertical, as we’ll see later,

how should you look at thetradeifthemarketmovesandthe vertical spread you haveisnowin-the-money?The wonderful symmetry ofputs versus calls comes intoplay here, making it reallyeasy to understand your in-the-money vertical spread.Being long an in-the-moneycall vertical spread is exactlythe same as being short anout-of-the-moneyput vertical

spread with the same strikeprices. Being long an in-the-money put vertical spread isexactly the same as beingshort an out-of-the-moneycallverticalspread.How is this? Let’s look atsome prices to make certainthis is correct.Thepriceswesee in Table 3.14 aretheoretical, but let’s assumethe price of the underlyingwas100.00.

Table3.14In-the-MoneyCallSpreadandOut-of-the-MoneyPutSpread

StrikePrice

CallOptionPrice

PutOptionPrice

ValueofCallSpread

70 30.25 0.25 9.7580 20.50 0.50

Howcanbeing long thatcallspread (long the 70 call andshortthe80call),theonethatcosts9.75,belikebeingshort

that put spread (being longthe70putandbeingshortthe80 put), the one that costs0.25?Let’s look at the maximumprofitandlossandwheretheyoccur.What is themaximumpotentialprofitifyoubuythatcall spread and pay 9.75 forit?Themaximumthatthecallspread can beworth is 10.00(80 – 70) so the maximumprofit is 0.25 (10.00 – 9.75).

That maximum profit isrealizedwiththisstockabove80 at option expiration.What’s the maximum loss ifyoubuythatcallspread?Themaximumlossiswhatwepayforit,9.75,andthat’srealizedwith this stock below 70 atoptionexpiration.What’s the maximum profitfrom selling the put spread?The maximum profit fromsellingaverticalspreadisthe

netpremiumreceived,0.25inthis case. That maximumprofit is realized with thestock above 80 at optionexpiration. What’s themaximum loss from sellingthat put spread? Themaximumlossisthewidthofthe spread, 10.00, minus thepremium received. Thatmaximum loss is9.75 (10.00–0.25),andit’srealizedwiththe stock below 70 at optionexpiration.Wecanseethisin

Table3.15.

Table3.15VerticalSpreadSymmetry

Spread MaximumProfit

Realizedat

ExpirationwithStock

Long70/80call

spread

0.25 Above80

Short70/80put

spread

0.25 Above80

These two trades, long the70/80 call spread and shortthe 70/80 put spread, areidentical.Thisisn’tjustaneattrick; it can help us when itcomes time to trade. How?By reducing the cost ofclosing the trade.Thosedeep

in-the-money options aregoingtohavebid/askmarketsthatarereallywide.Whiletheproblem of bid/ask spread issomewhat alleviated byexecuting your closing tradeasaspread, it’sstill likely tobewiderforthein-the-moneyspreadthanfortheout-of-the-money spread. Let’s look atsome actual option prices tosee how this works. Theunderlying was at 121.65when the option prices in

Table3.16wereobserved.

Table3.16In-the-MoneyBid/AskSpreadsversusOut-of-the-MoneyBid/AskSpreads

Option OptionBidOptionAsk

95put 0.06 0.1895call 26.35 27.05105put 0.40 0.42

105

call 16.85 17.30

Wecanseefromthesepricesthat ifwewanted to sell our95/105 call spread and wesimplysold the95callat thebid and bought the 105 callon the ask, we’d get 9.05(26.35–17.30).Okay,maybethat’s what the spread isworth. But let’s see if thosemarketsmakesenseforusbylookingatwhat itwouldcost

tobuythatspreadinthesameway—buying the 95 call atthe ask and selling the 105callonthebid.Ifwedidthat,wewouldpay10.20(27.05–16.85) for a spread that canonlybeworthamaximumof10.00. Maybe those widebid/ask markets don’t makesense for us after all.Maybetheyonlymake sense for themarketmaker.Since selling the 95/105 call

spread (selling the 95 call,buying the 105 call) isidenticaltobuyingthe95/105putspread(sellingthe95put,buying the 105 put) can webuy the 95/105 put spread toclose the long position wehave in the call spread?Wouldwesavemoneydoingso?Let’s see. Ifwe did that,we would end up with apositionthatlookedlike:

Long95callShort95putShort105callLong105put

Being long the 95 call andshort the 95 put is just likebeing long the stock. Beingshort the 105 call and longthe105put is just likebeingshort the stock. The twostrikeswill cancel eachotherout,meaning that buying the

95/105 put spread willeffectively close the longposition in the 95/105 callspread. Will it save usmoney?If we were to buy that putspread, we would pay 0.36(0.42 – 0.06), and all of that0.36 would be time valuebecausetheoptionswereout-of-the-money. Ifwesold thatcallspreadtoclose,wewouldhave collected 9.05, but how

much of that would be timevalue?By selling the 95 callat 26.35, how much timevalue would we becollecting? The underlyingwas at 121.65, so that optionhas an inherent value of26.65. Oops, we sold that at26.35, so we sold the optionfor less than its inherentvalue.Wepaid 17.30 for the105callwhen theoptionhadaninherentvalueof16.65,sowe paid 0.65 in time value.

Factor in the 95 call thatwesold for less than its inherentvalue, and it looks like wesurrendered 0.95 in timevalue by selling the callspread rather thansurrendering 0.36 in timevalue for buying the putspread.Anotherway to examine thisis to imagine that we’d paid$1.00 for that call spread along time ago because we

thought the underlying stockwasgoingtorally.Wedidn’tthinkitwasgoingtorallyallthe way to 121.65 or wewouldn’t have sold the 105calltomakeaspread,butwegot the direction correct.What would be our totalprofit on the trade if weclosed it by selling the callspread versus buying the putspread?We paid $1.00 for the call

spread and sold it for 9.05.Ourprofitis8.05.We paid $1.00 for the callspreadandboughttheclosingput spread at 0.36. Thisleavesuslongthe95callandshortthe95put,whichislikebeinglongthestockat95.00.Italsoleavesusshortthe105call and long the 105 put,which is like being short thestockat105.00.Wecollectanet of 10.00 from the option

positions at expiration, theoriginal trade cost $1.00 andwe paid 0.36 in buying theput spread to close. Thatprofit is8.64(10.00–1.00–0.36).Wemadeanextra0.59by closing the tradewith theputspreadratherthanthecallspread. Given the limitedreward potential of a verticalspread,traderscan’taffordtosquander0.59ona trade thathad limited upside to beginwith.

The caveat? By selling thatputspread,we’releftwiththepositionwesawpreviously:

Long95callShort95putShort105callLong105put

This is only a problem if theunderlying stock drops abunch and is near one of

those strike prices atexpiration.Then you may not know ifyou’ll be assigned on yourshortleg,soyouwon’tknowwhethertoexerciseyourlongleg. This is called getting“pinned” as the underlyingstock price is pinned at thestrike price.What do you doif the underlying stock hasdropped and is now at yourstrike price? We’ll discuss

that when we talk aboutconversions and reversals inChapter13.

VerticalSpreadCheatSheet

LongCallVerticalSpread

Description

Longcall,shortfurtherOTMcall

Example

ATM=100Long105call

Short110call

PayorCollect

Premium

Pay

NeededDirectionality

PassageofTimewithout

MarketMovement

--

IncreaseinImpliedVolatilitywithoutMarket

Movement

+

Payoff

ThumbnailChart

MaximumRisk

Costofthespread

MaximumProfit

Widthofthespreadminuspremiumpaid

BreakevenPoints

Longstrike

pluspremiumpaid

CHAPTER4

CoveredCalls

Youprobablyownstocks.Ifyou do, and someone was

willing to pay you moneynowbuttheygotaportionofthe potential appreciation ofthat stock, the appreciationabove a certain level if yourstock rallied within a certaintime period, would you takethat deal? Would you taketheir money now and sell aportion of your futurepotential appreciation? Youmight if you liked the stockfor the long termbut thoughtthat itwas going to be stuck

in neutral for some time,either because of the stockitself or because of thebroadermarket.Oryoumightjustthinkthatthevalueofthecash now is greater than thevalue of the appreciationyou’re potentially giving uponce you’ve discountedwhatyou might give up by theprobability that you actuallyhavetogiveitup.Thisdeal,youreceivingcash

now and giving up a portionof the potential appreciationof a stock you already own,would look something likeFigure4.1.

Figure4.1WouldYouMakeThisTrade?

Would you be willing tomake that trade, giving uppotential appreciation above60.00 for 0.57 in cash nowgiven that the stock is at58.50?WhatifItoldyoutheodds of giving up anyappreciation above 60.00wereonly33percentandthatthe odds of giving up moreappreciation than you’ve

receivedincashwereonly27percent?Wouldyoumakethetradenow?Youmightchoosenot to if you thought themarket was wrong and thatthe stock was going toappreciate above those levelsor you might opt not tobecause you’re getting afinite sum now in exchangefor what might be a muchlarger sum if the stockappreciates substantially. Butyoumightbewillingtomake

that trade if you liked thoseodds or if you thought thestock was going to gosideways or up only slightlyduringthenextfewweeksorifyourecognizedthatastockcanrallysubstantiallybutthatsuchamovementisrelativelyrare.Thistrade,sellingawaysomepotential appreciation onstock you own in exchangefor receiving cash now is a

covered call. And thehypothetical chart we lookedat above? It’s the real chartfor a 60 strike covered callwe might execute if weownedJPMstock,whichwasthenat58.50.Howwouldthischart look if we added thenakedstockpayofflinetothepayoff line for thecombination trade, whichincludes the 0.57 in cashwewould collect for our newcombination trade of long

JPM stock and short the 60strike covered call. We seethisinFigure4.2.

Figure4.2The60StrikeJPMCoveredCall

A covered call is acombination of long stock,preferably stock you alreadyown, and a short call optiononthatstock.Asthesellerofthe covered call, you collectandkeeptheoptionpremium.We’ll refer to the combinedposition as a covered call,although it is sometimescalled an overwrite. Another

term that you might see,buywrite, is slightly differentbecause a buywrite is thesimultaneous purchase of theunderlying stock and sale ofthe covered call. You mightthinkthisisthetradetomakeif you don’t already own thestock,butthere’snoreasontopay twocommissions,one tobuy the stockand the secondtosellthecoveredcall,whenthe exact same exposure canbecreatedbysimplysellinga

covered put.We discuss thismore in Chapter 5 when wediscuss covered puts. Sincethere’s no reason to pay twocommissions, in this chapterwe’llfocusonsellingcallsonstock that we already own,which means we’ll focus oncovered calls, also known asoverwrites.The advantage of a coveredcall is that the covered callseller collects and keeps the

option premium. Over time,thepremiumreceivedwillbegreater than the value of theoptiongiven;theoptionpricereceivedbyusasthecoveredcall seller is, over time,greater than the option valuewe give in the form ofvolatility or potentialappreciation. When we say“over time,” we mean thatgiven a large number ofobservations, enough toeliminate pure luck as a

factor,thepriceoftheoptionwillbegreater thanthevalueof the option. This won’t bethecaseeachandeverytime,and it’s entirely possible thatyou’ll end up selling acoveredcall for less than it’sultimately worth, either involatilitytermsorintermsofthe option’s value atexpiration, but, in general,options cost more thanthey’re worth. For a morecomplete discussion of this

phenomena see Chapter 5 ofOptionsMathforTraders.The premium receivedgenerates outperformanceover a substantial range ofpotential stock prices atoption expiration meaningthat the combined position(long stock and short thecoveredcall)will outperformthe naked stock by theamount of call premiumreceived as long as the stock

isatorbelowthestrikepriceof the call at expiration.YoucanseethisinFigure4.2.Thecombined positionoutperforms the naked stockpositionby the0.57 receivedwith JPM anywhere at orbelow 60.00, the strike priceof the covered call, at optionexpiration. Above 60.00, theownerofthecallwillexercisethe call and buy theunderlying stock from us at60.00, meaning that the

outperformance diminishesand eventually turns intounderperformance as thecombined position ceases toappreciateabovethere.But even if the underlyingstock isabove thatcallstrikeprice at expiration, thecovered call seller gets tokeep the premium hecollected, 0.57 in thisexample. At some point asthe outperformance

diminishes the premiumcollected is equal to theappreciation that we soldaway.Thisisthepointwheretheunderlyingstockisabovethe strike price by preciselytheoptionpremiumreceived.In the case of our JPMcovered call, that point isreached at 60.57 (the 60.00strike price plus the 0.57 inoptionpremiumreceived).Atthispoint,wherethepremiumcollected equals the

appreciation that wassurrendered, the covered callsellerisindifferenttothetwopositions, long the stock orlong the stock and short thecoveredcall.Atthispoint,thetwo outcomes generate thesame profit, but above thislevel the covered call sellerregrets selling the coveredcall, the appreciationsurrendered is now greaterthan the call premiumreceived.Wecallthispointof

indifference, the point wherethe stock is above the strikepricebypreciselytheamountof option premium received,theregretpoint.Abovehere,thecoveredcallsellerregretsselling the covered call. Theregretpointisalwaysequaltothe strike price plus theoption premium received.You can see the regret pointof60.57forourJPMcoveredcallinFigure4.2.

With the underlying stock atthe regret point, the onlydifference between thecombined covered callposition and the naked stockposition is that the nakedstock position will remainlong the stock afterexpiration, while thecombined covered callposition will have the stockcalled away and will insteadhave$60.57incashpershare.SinceJPMistradingat60.57,

we could very easilyexchange our cash for sharesofstockbybuyingthesharesback meaning the twopositions are equivalent toeachotherrightnow.Covered call sellers get paidwhen they sell the call; thepremiumistheirstokeep,butthe goal is to have the calloption expire worthless.When that happens, thepotential of giving away any

appreciation has expired andthe shareholder can sellanother covered call, sell hisstock, not sell a covered callif he thinks the stock is nowgoingtorallyabovethestrikeprice of the covered call hemight sell, or use anotherstrategy. Since he wants theoption to expire worthless,the covered call seller getspaid when he sells thecovered call but “earns” thatmoney through daily erosion

forthetermoftheoption.The60strikecoveredcallwesold in JPM had 30 days toexpiration. Since shorter-dated options erode morequickly than longer-datedoptions,wegenerallywanttosellshorter-datedoptions,andthisistrueforcoveredcalls.Let’s look at how this 60strike call with 30 days toexpiration will erode overtime.Youcanusethetoolsat

www.OptionMath.com tocalculate the erosion for anyoption you’re thinking ofbuyingorselling.WeseetheexpectedpriceforthisoptionasiterodesinFigure4.3.


Figure4.3JPM60StrikeCoveredCallPricebyTimetoExpiration

Thefirstthingyou’llnoticeisthat thisoptiondoesn’terodein the same parabolic waythat we saw some optionserode previously. That’sbecause this optionwas 1.50out-of-the-money, and giventhat the underlying was at58.50, that’sover2.5percentout-of-the-money, quite a bitfor a low volatility (17.02

percent) name like JPM thatdoesn’thaveacatalystbeforetheoptionexpires.Theresultis this more straight-lineerosionforthelast30daysofits life. But this straight-lineerosion for the final 30 daysis an illusion because the 60strike option is out-of-the-money. If we look at thisoptionoveralongerterm,wesee the characteristic erosionwe expect. We see this inFigure4.4.

Figure4.4OurCoveredCalloveraLongerTimePeriod

If we’re in the final 30 daysoftheoption’s term,thenthe“big picture” of erosion getsblurry.Sinceerosion is so importantto somany option strategies,let’s look at how otheroptions thatare in-the-moneyor at-the-money or fartherout-of-the-money should

erode over the 30-day periodwe’re interested in. We canseethisinFigure4.5.

Figure4.5CoveredCallPricebyTimetoExpirationforSeveralStrikePrices

The 57.50 call will nevererode all the way to zero,assumingJPMstaysat58.50,because it’s in-the-money, ithas $1.00 of inherent value,and that inherent value willnot erode away, but its timevalue does erode, alongwiththe out-of-the-money 60strike callwe already lookedat, in more or less a straight

line. They’re both too farfrom at-the-money toevidence the parabolicerosion that we sawpreviously, including inFigure 4.4, but that doesn’tmean we shouldn’t focus onshorter-dated options whenselling options, includingcovered calls. If we were togo to the tools atwww.OptionMath.com, wewould find this covered callhas an implied volatility of


17.02percent (given30daysto expiration, an underlyingpriceof58.50,andarisk-freerate of 1 percent. Since nodividendswereduetobepaidduringthetermofthisoptionthe dividend yield is zero).Leavingallthoseinputsfixedbut changing the time toexpiration we find thetheoretical option values inTable4.1.

Table4.1TheoreticalCall

ValuesasTimetoExpirationChanges

DaystoExpiration Price

PriceifItWere

aMultipleofthe30-DayOptionPrice

30 0.57 60 1.02 1.14

90 1.39 1.71120 1.71 2.28360 3.53 6.84

Let’s connect the dots againandseejusthowthediscountincreases with time, eventhough our 30-day, 60 strikeJPM covered call is out-of-the-moneysuchthatiterodesinastraight line.WecanseethisinFigure4.6.

Figure4.6OneLong-DatedCoveredCalloraSeriesof30-DayCoveredCalls?

It’s obvious from this thatyou’rebetteroffsellinga30-day covered call, having itexpireandsellinganother30-day covered call, rather thanselling a single 60-daycoveredcall.Inthisexample,you’d be 0.12 ahead byselling the series of 30-daycovered calls and sincewe’d

collect a total of only 1.14(0.57 × 2), assuming theunderlying didn’t move andnothing changes (admittedly,a pretty outlandishassumption but necessary forourpurposes),givingup0.12of that 1.14 would meangivingupjustover10percentof the total premium wemightcollect.Ifwe took this to the logicalextremeandwereabletosell

a series of 30-day options at0.57,wewouldcollectatotalof 6.84 (0.57 × 12) over a360-day “year.” And thevalue of that hypothetical360-day call? It’s 3.53, or a3.31 discount to what we’dcollectfromsellingaseriesofcoveredcalls.Again,youcansee this in Figure 4.6. Thesimple takeaway? You’rebetter off selling shorter-datedoptions.

■ProfitabilityHow profitable is our JPMcoveredcall trade? If JPM isbelow 60.00 at optionexpiration, we’ll pocket that0.57 so we’ll be 0.57 betteroff no matter how far below60.00 JPM is. With JPM at58.50 right now, that 0.57wouldbeayieldofverycloseto 1 percent (0.57/58.50) forthose 30 days. Annualized,that’s 12.68 percent with

compounding,asyoucanseein Table 4.2. That’s prettygoodforsellinganoptionthathas only a 33 percentlikelihood of being in-the-money at expiration (this 33percentlikelihoodisthedeltaof the 60 strike covered callas calculated atwww.OptionMath.com).

Table4.2YieldfromOurCoveredCall


OptionPremiumYieldCurrentstock

price 58.50

Coveredcallpremiumreceived 0.57

Optionpremiumyield 0.97%

Annualizedoptionpremiumyield 12.34%

But what would ourpercentage return be if the

option is in-the-money atexpiration and our stock getscalled away? Our effectiveselling price would be thestrike price, 60 in this case,plus the option premiumreceived,0.57inthiscase,soour effective selling pricewould be 60.57. You’ll notethatoureffectivesellingpriceis equal to our regret point.Thiswillalwaysbethecase.With JPM at 58.50 now that

wouldbea$2.07profitwhichis3.5percent(2.07/58.50)forthe 30-day term of our tradeor over 51 percentannualized, as is shown inTable4.3.

Table4.3YieldifCalledAwayReturnifCalledAway(BecauseStockIsAbove

StrikePriceatExpiration)

Currentstock

price 58.50

Effectsellingprice(strikeplusoptionpremiumcollected)

60.57

Returnifcalledaway 3.54%

Annualizedreturnifcalledaway 51.78%

■ Covered Calls andDownside Protection—Not As Much AsWe’dLikeWe discussed our results ifJPM rallies, but the 0.57 inoption premium that wecollect also provides a littleprotectionagainstJPMfallingin price. Too often,stockholders sell coveredcalls to generate premium

exclusively for thisdownsideprotection. That reallyshouldn’tbe the rationale forselling covered calls becausethe amount of downsideprotection generated isusually pretty small and,second, if you thought youneeded downside protection,thenthereisprobablyabetterstrategy than selling acovered call. Simply sellingyourstockwouldbeonesuchstrategy. A little downside

protection is just a happysecondarybenefit tosellingacovered call. And just howmuch downside protection isgenerated from our JPMcovered call? The stock iscurrently at 58.50. Wecollected 0.57 for selling thecall, which means that ourdownside breakeven for thecombination trade is 57.93(the current price of 58.50minus the premium receivedof 0.57), which is 0.97

percent worth of downsideprotection. But if JPM falls,thenitdoesn’tmatterhowfarit falls, we’re 0.57 better offfor having sold the coveredcall. You can see thisprotectioninFigure4.7.

Figure4.7DownsideProtectionfromaCoveredCall—NotasMuchasWe’dLike

■UsingCoveredCallsto“Create”DividendsCovered calls can be used to“create” dividends for non-dividend-paying stocks andthe strategy usually workswell because non-dividend-paying stocks tend to havehigher implied volatilitiesmeaning the covered callyou’ll sell is going to befairly expensive. Why are

options on non-dividend-paying stocks moreexpensive? Because adividend tends to bufferchanges in the price of astock and those changes inthepriceisvolatility.One non-dividend-payingstock that many investorswouldliketoown—ifitpaidadividend—isGLD,thegoldexchange-traded fund (ETF).If an investor needs their

portfolio to generate someincome in the form ofdividends,thennon-dividend-payingGLDisn’tacandidatefortheirholdings.Selling a covered call onGLD is similar to havingGLD pay a dividend. Ittruncates a little of thepotential appreciation, sincethe company, or ETF in thiscase, doesn’t have that cashtoputtoworkortoholdgold

with.Let’s look at some coveredcallswemightsellwithGLDtrading at 131.75 and we’llinclude the option price, thetime to expiration, theimplied volatility, and theamount of erosion expectedtoday(theta) tohelpusmakeour decision. We can seethese in Table 4.4. Theimplied volatility and thetawere calculated at

www.OptionMath.com.

Table4.4PotentialCoveredCallsinGLD

StrikePrice

DaystoExpiration

OptionPrice

131 30 3.35132 30 2.81133 30 2.34


134 30 1.93135 30 1.58140 30 0.56145 30 0.21150 30 0.09175 30 0.01131 58 4.40132 58 3.88133 58 3.40134 58 2.98135 58 2.59

140 58 1.24145 58 0.59150 58 0.31175 58 0.03131 121 6.15132 121 5.65133 121 5.15134 121 4.70135 121 4.28140 121 2.62145 121 1.59

150 121 0.98175 121 0.16

Wow, that’s a bunch ofoptions.Let’strytofocusouralternatives a little bit. Eventhough the 121-day optionsoffer the highest call price,the annualized yield is lowerthan for the 30-day optionswith the same strike price.The same is true for the 58-daycalls.Thisisafunctionof

thewayoptionsexpireaswesaw previously and inChapter 2, so let’s limit ourcandidates to the 30-dayoptions.Among the 30-day options,there’sa rangeof likelihoodsthatwe’llseeourGLDsharescalled away. Let’s connectthe dots and see thelikelihoodofhavingourGLDsharescalledawayforeachofthosestrikepricesalongwith

the annualized yield for eachof those strike prices. YoucanseethatinFigure4.8.

Figure4.8CoveredCallYieldandLikelihoodofGettingStockCalledAway

You’ll notice that therelationship is pretty stable,the higher the likelihood ofgettingourstockcalledaway,thehighertheyieldgeneratedbut in the very upper left ofthecharttheannualizedyieldstarts to fall. That’s becausethe time value of the optionhas started to fall as those

calls start to get further in-the-money. Only the timevalue will erode away andgenerateyield.Inherentvalueisn’treallyyieldbecauseitisjust the reduction in pricewe’llseeforourGLDshareswhen we sell them at thestrikeprice.Let’stakealookatallthe30-dayoptionsandexaminetheirtimevalue.WecanseethisinFigure4.9.

Figure4.9CoveredCallTimeValueforSeveralStrikePrices

The time value peaks whentheoption is at-the-moneyorclosest to at-the-money aswith the 132 strike (theunderlyingETF,GLD,wasat131.75,sothe132strikewasclosest to at-the-money) forour GLD options. It’s noaccident that this option hasthe highest annualized yieldof all thoseGLDoptionswe

lookedatinitially.Butitalsohas a relatively highlikelihood of getting ourstockcalledawaywithadeltaof50,andthat’snotourgoal.So how do we balance yieldwith the goal of having theoptionerodeawayandexpireworthless? That’s the art ofoptiontrading.You’ve seen that therelationship between yieldand the odds of getting our

stockorexchangetradedfundcalled away is pretty stable.Using the delta which youcan calculate atwww.OptionMath.com pickthe strike that you feelcomfortable selling, and thatis the best balance of yieldandgettingcalledaway.Oneway to do this analysis is tolook at the chart for eachcombined position. Figure4.10 shows the payoff chartfor a covered call that is


slightly in-the-money, the131 strike in this case,slightly out-of-the-moneywith a likelihood of gettingcalled away of about 33percent, the135strikeinthiscase, and deeply out-of-the-money with a likelihood ofgettingcalledawayofonly3percent, the145 strike inourcase.

Figure4.10ThreePotentialGLDCoveredCalls

The145strikecoveredcallisbarely distinguishable fromthe naked ETF. The 0.21 inpremium collected is only atinyfractionoftheunderlyingETF value, so the combinedposition will act very muchlikethenakedstock.The131strikecoveredcallhasadeltaof 56, so the odds are verygood that you’ll end upwith

134.35insteadofyoursharesof GLD when these optionsexpire, so this position can’tbe expected to actmuch likeGLD.The135strikecoveredcallhasadeltaof32, so thisis truly a hybrid position; itcollects 1.58 in time valueanddoesn’t stopappreciatinguntilGLDralliesfrom131.75to135.00.Let’stakealookatthe breakeven points, regretpoints,andyieldsforallthreecovered calls. You can see

theseinTable4.5.

Table4.5BreakevenPoint,RegretPoint,andYieldsforOurCoveredCalls

OptionPremiumYield

131Strike

135Strike

Currentstockprice 131.75 131.75

Coveredcalltimevalue 2.60 1.58

receivedBreakevenPoint 129.15 130.17

RegretPoint 133.60 136.58

Optionpremiumyield

1.97% 1.20%

Annualizedoptionpremiumyield

26.43% 15.38%

Now let’s look at the returnsandyieldsifcalledaway.WeseetheseinTable4.6.

Table4.6ReturnsandYieldsifCalledAway

ReturnifCalledAway

131Strike

135Strike

Currentstockprice 131.75 131.75

Effective

sellingprice(strikeplusoptionpremiumcollected)

133.60 136.58

Returnifcalledaway

1.40% 3.67%

Annualizedreturnifcalledaway

18.21% 54.04%

It’seasytolookatTable4.5,the one that describes theoption’s yield, and think the131 strike, the in-the-moneystrike that generates anannualized yield of over 26percent,isthecoveredcalltosell. But that would mean abetter than even chance ofgetting your shares of GLDcalledaway.It’seasytolookat Table 4.6, the one thatdescribes the return if calledaway, and think the 145

strike, the deeply out-of-the-money strike that generatesan annualized return of over221 percent, is the coveredcall to sell. But the odds ofrealizing that return byhaving your shares calledawayat145areveryremote.The delta tells us thelikelihood is only about 3percent. And if our sharesaren’t called away the 145strikegeneratesanannualizedyieldoflessthan2percent.

Ultimately, the selection ofthe strike price will dependonyouroutlook forGLDforthe term of the options andyourstomachforhavingyoursharescalledawaybutin-the-moneyanddeeplyout-of-the-money calls are rarely thebest choice for your coveredcall.

■HavingYourSharesCalledAwayGetting an assignment noticedemanding thatyousellyourshares to the owner of thecovered call you’ve soldmightseemdaunting,but it’snot to be feared.We’ve seenthat for many covered callsit’s to be expected thatwe’lleventually have our stockcalledaway.

Theonly time to fear havingstock called away is if youenjoyasubstantialunrealizedprofit in the shares. In thatcase,havingyourstockcalledaway will result inrecognizing that substantialprofit and having to pay taxon it. If the prospect ofpayingtaxonthatprofitissoterrifying, thenyoushouldn’tbe selling covered calls onthatstock.Pickanotherstockin your portfolio for selling

coveredcalls.These threepotentialcoveredcalls inGLD, the 131 strike,135 strike, and 145 strike,have very different returnprofiles depending on whatGLD does during their term.The145strikeneedsGLDtorally in order to achieve itsmaximum return if calledaway. This would be a tradefor someone who was verybullish GLD. The 131 strike

doesbestifGLDfallsslightlyif your goal is to keep yourGLD shares, so this coveredcall is actually best forsomeone who’s slightlybearishGLD. The 135 strikeis the strike for nearly anyoutlook for GLD, a littlebullish, a little bearish, orsideways.In fact, having your sharescalled away may mean thatyou realize an effectiveprice

(strike price plus optionpremium received) that ishigherthanthestockhasevertraded. In that case havingyour stock called away maybe exactly what you weretrying to accomplish. If youthink your stock has moreroom to the upside, then youcan always buy your calloption back before you areassigned to sell your shares.Howwill youknow thatyouarelikelytobeassigned?

The academic literature iscertain about one thing:theoretically,there’sonlyonereason the owner of the calloption you are short mightexercise his option prior toexpiration. And that onereason?A looming dividend.Onlyownersof the stockgetpaid the dividend.Nomatterhow far a call is in-the-money, the owner of the callwon’t receive the dividend,andinfact,sincethepriceof

the stock will drop by theamountofthedividendontheday the stock goes ex-dividend, the call ownerwillactuallylosemoneywhenhiscalldropsinvaluealongwiththe stock on the ex-dividenddate. So someone holding along call with no time valuehas nothing to lose and thedividend to gain byexercising his call early,takingownershipofthestockbefore the ex-dividend date,

and receiving the dividend.Thismeans that if a coveredcall is in-the-money, adividend is looming, and thecall has less time value thanthe value of the dividend,then it’s likely that the callwill be exercised and as acovered call seller we’ll berequired to deliver our stockand we’ll miss out on thedividend.Other than a looming

dividend,there’snoreasontoexercise a call option early,so for the covered call sellerit’s pretty easy to figure outwhen your call will beexercised and you’ll berequiredtodeliveryourstock.If there’s no dividend on thecalendar, then your in-the-money covered call will beexercisedonlyonthelastdayortwoofitsterm.Ifthereisadividend and the time valueremaining in your covered

call is less than the dividendto be paid, then expect tohavethecallexercisedbytheowner early enough that hewill take ownership of thestockbeforethedaythestockgoesex-dividend.There is also a smallpopulation of option tradersthat will early exercise a putoption if in doing the maththey realize that the interestearned on the cash they will

receiveforsellingorshortingthe stock via put optionexercise is greater than thetime value of the put option.Thisisrare—muchrarerthanearly exercise of a call tocaptureadividend.

■ Don’t FearAssignmentHaving your covered callassigned and having to sellthe underlying stock at thestrike price doesn’t meanyou’ve done somethingwrong, and if you werehoping to have your stockcalled away as a means ofexiting a longposition in thestock, then congratulations—

your trade worked well. Ifyour effective selling price(the strike price plus theoption premium received) ishigher than the stock hasactuallytradedat,thenyou’redue a double dose ofcongratulations—yourcovered call workedperfectly.Assignment of short optionpositions is at least partlyrandomforalloptionscleared

through theOptionsClearingCorporation (OCC),which iseveryequity, index,andETFoption traded in the UnitedStates. Options on futures,including index futures likeS&P 500 futures, aregenerally cleared through therelevant futuresexchangebutsimilarrulesapply.TheOCCrandomly allots assignmentsto brokerage firms that haveshort positions in theparticular option that has

been exercised. Thebrokeragefirmthenallotstheassignment notices to theshort option positions itscustomers have using a fairassignmentmethod.This fairassignmentmethodmightnotbe random. It might insteadbe “first-in, first-out.” Yourbroker can tell you whichtheyuse,but itdoesn’treallymatter.Your trading strategyshouldn’t hinge on avoidinganassignment thatyouknow

iscoming.Yourbrokerwillhandlealloftheassignmenttransaction.Inthecaseofyourcoveredcall,yourbrokerwilldeliveryourshares to the call exerciser,removing the shares fromyouraccount,andwilldepositthe cash received for theshares in your account. Foryour purposes, assignment isexactly like selling yourstock. Think of it as being

similartoalimitordertosellyourstockthatyouhadinthemarket for some time.Assignment is like havingyoursellorderfilled—younolonger own the stock; itmaybe trading much higher thanwhere you sold it, but youhave received cash. It’s nowtime to execute your nextoptionstrategy.

■ Stock CoveredVerticalCallSpreadA covered call sacrifices allthe potential appreciationabove the strike price of thecall in exchange for thepremium collected today.That’s usually a good tradesince, as we’ve discussed,over time, thevalue receivedintheformofcallpremiumisgreater than the value given

up in the form of potentialappreciation.Butwhat ifyoudidn’twant togiveupall thepotentialappreciation?You shouldn’t be sellingcovered calls on stocks youbelieve will appreciatestrongly,butwhatifthere’sapotential catalyst that mightpropel the stock substantiallyhigheror ifyou think there’sasmallbutreasonablechancethat the stock is a takeover

candidatebutyoubelievethelikelihood is overwhelmingthat the stock will movesideways despite a generallypositive long-term outlook?Then you might want anoptionstructurethatgeneratespremium but which resumesparticipating in a rally if thestock rallies enough. Thatwould be a stock coveredverticalcallspread.In a stock covered vertical

call spread you’re long theunderlying stock and sell averticalcallspreadagainst it.The ownership of theunderlying stock “covers”thatportionof theriskof thecall spread that exceeds thepremium received for sellingit.A stock covered verticalspread is the first structurewe’lldiscuss that replacesanoption, in this case the

covered call option, with avertical spread, in this case acall vertical spread. We canalsodothiswithacallspreadintheriskreversalwediscussin Chapter 10 and we canreplace the put option in acollar with a vertical putspread. We discuss collarsincluding put spread collarsinChapter9.Let’s return to our GLDexample and see how selling

a stock covered vertical callspreadratherthananoutrightcovered call changes thetrade. Figure 4.11 showssomeof thecallsavailable inGLD and how we mightconstruct a stock coveredverticalcallspread.

Figure4.11AStockCoveredVerticalCallSpreadinGLD

Weinitiallysawtheseoptionsin Table 4.4. Instead ofselling the 135 covered callfor 1.58 and having a regretpoint of 136.58, we can sellthe 134/140 vertical callspread and create a hybridposition that will resumeparticipating in the rally ifGLD is above the 140.00level before expiration. The

payoff profile for this stockcovered vertical call spreadcanbeseeninFigure4.12.

Figure4.12AStockCoveredverticalCallSpreadversusaTraditionalCoveredCall

Once GLD gets above thestrike price of the long callportionoftheverticalspread,the140strikeinthiscase,thetotal position starts toparticipate again. Above thislevel the hybrid positionwillalways lag an outright longposition inGLD but by howmuch? Itwill lagby the loss

ontheverticalspreador4.63(the6.00widthof the spreadminus the 1.37 collected forselling the spread) in thiscase. But above a certainlevel the stock coveredvertical spread willoutperform the traditionalcoveredcall.Thatlevelistheupper strike of the spread,140 in this case, plus theadditional amount ofpremiumcollectedforsellingthe traditional covered call,

0.21 in this case (1.58 –1.37),or140.21.Abovehere,thestockcoveredverticalcallspread will outperform thetraditional covered call.Below theupper strikeprice,the traditional covered callwill outperform the coveredspread by the additionalpremiumcollected.How does using a stockcovered vertical call spreadchange the likelihood of

havingourGLDcalledaway?Our traditional covered callhada32percentlikelihoodofseeingourGLDcalledaway.The134strikecallthatwe’reshort in our stock coveredverticalcallspreadhasadeltaof 38 meaning it has a 38percent likelihood of seeingour GLD called away butwe’realsolongthe140strikecall and if GLD is above140.00 at option expirationwe’llbeabletocallourGLD

shares back.The delta of the140strikecall is11meaningthe likelihood of GLD beingabove 140.00 is 11 percent.The net likelihood of havingour GLD called away is 27percent (38 – 11). The netlikelihood of our call spreadhavingoursharescalledawayis slightly lower than thelikelihood of our traditionalcovered call having ourshares called away and ifGLDralliesenoughourstock

covered vertical call spreadstartsparticipatingagain.Theprice we pay for this lowerlikelihood of getting calledaway and ability toparticipate in a rally above140.00isthatwecollect0.21lessforsellingthecallspreadthanwecollectforsellingthetraditionalcall.Also, thecallspread will see our GLDcalled away ifGLD is above134.00 but below 140.00 atexpiration, while the

traditional covered calldoesn’t see our GLD calledaway until it’s above 135.00atexpiration.Between 134.00 and 135.00,we’re not only susceptible tohavingourGLDcalledawaywhenwewouldn’totherwise,but we also receive less intotaloptionpremium.

CoveredCallCheatSheet

CoveredCall

Description

Long

underlyingstock,short

call

Example

ATM=100Long100sharesofstock

Shortone105strike

callPayorCollect

Premium

Collect



MarketMovement

+++

IncreaseInImpliedVolatilitywithoutMarket

Movement

−−−

PayoffThumbnailChart

MaximumRisk

Priceofthestockwhenthecoveredcallissoldminus

premiumreceived(if

stockdropstozero)

MaximumProfit

Regretpoint(callstrikepricepluspremiumreceived)minuspriceofthestockwhenthe

coveredcallissold

BreakevenPoints

Stockpricewhenthe

coveredcallissoldminuspremiumreceived

CHAPTER5

CoveredPuts

The seller of a put optionagrees, in exchange for the

premiumreceived, tobuytheunderlying stock at theexercisepriceiftheownerofthe put chooses to exercisehisoption.Sellinganakedput, that is,aput that isn’t covered byeither another put option, ashort position in theunderlying stock or enoughsegregated cash to buy thestock at the strike price, is alittlelikegettingpaidtoserve

as a target. Usually, themarket will miss the target,sometimes the minimaldamage done is more thanmadeup for by the premiumreceived. Sometimes theimpact will really hurt. Themaximumpotential loss fromanakedputissubstantialandismanytimestheinvestment,in the formofmarginpostedtocoverthepotentialloss.However, if the put option

seller were to segregate thecash necessary to satisfy hisduty to buy the underlyingstock at the exercise price,thenhe’dbecertaintobeabletosatisfythatdutyasopposedto the naked put seller, whomay or may not be able tofully satisfy the duty to theowneroftheoption.A covered put is acombination of a short putandcash.Theamountofcash

is the sum necessary to buythe underlying stock at thestrike price. Because the putis covered by cash it issometimes called a cash-securedput.Coveringtheputby segregating the cashnecessarytobuythestock, ifrequired, doesn’t reduce theriskofthetrade,thestockcanstill drop to zero, it justmakes certain the put sellercansatisfyhisduty.

Acovered put is a trade thatgeneratesadefinedmaximumprofit, the put premiumreceived, while carrying riskequaltothestrikepriceoftheoption minus the premiumreceived. The risk willcertainly be many timesgreater than the potentialprofit, but the risk is nogreater than, and almostcertainly less than, the riskfrom buying the stockoutrightandthelikelihoodof

realizing a profit is generallymuch greater than thelikelihoodofrealizingaloss.Acash-securedput isagreattool for investors as well astraders and has a payoffprofile that’s very differentthan that of short putscovered by ownership ofanotherput(thisisoneoftheformsofaverticalputspreaddiscussedinChapter3)orbya short position in the

underlyingstock.Traderscansell a covered put confidentthat they can satisfy theirobligation while speculatingthatimpliedvolatilitywillfallor that the underlying stockwill be sideways, higher, oronly slightly lower atexpiration. Investors can sella covered put as a way topotentiallybuytheunderlyingstockatadiscount, that is,atan effective price that islower than the price that is

available today for the stockwhile getting paid, in theform of the option premiumreceived, for the risk taken.This option premium meansthat the seller of a coveredput may end up buying thestockataneffectivepurchaseprice lower than is ever seenin themarket.Youcan seeacovered put in Microsoft(MSFT)inFigure5.1.

Figure5.1ACoveredPutinMSFT

The segregated cash of$3,600.00 can include the$165.00 received for sellingtheput,butwith thatamountofcashwecanbecertainthatwe’ll be able to satisfy ourduty to the put buyer to takepossession of the stock andpay her $3,600.00 if shechoosestoexercise.What’s the maximum profit

from selling a covered put?Aswithmost short optionoroption spread positions, it’sthepremiumreceived.Inthiscase, it’s 1.65 (a total of$165.00). And themaximumloss? Segregating the cashdoesn’t reduce the risk fromthe trade; it simply makescertain that we can pay forthe stock if necessary. Thatmeansthestockcanstilldroptozeroand the loss from thetradewouldbe34.35(36.00–

1.65)pershare.If covering the put doesn’treduce the riskbut tiesupsomuchmoney,thenwhycoverit?Consideracoveredput tobe like a limit order to buythe stock, but a limit orderthat pays us in the form ofoption premium receivedwhile we wait to see if ourorder gets filled. If youplaced a limit order to buy,you’d have the cash in the

account to pay for it,wouldn’t you? Most brokerswill require you to leavesubstantialmargininordertoshort puts, but that marginusually won’t come close toactuallypaying for the stock.Tomake certain we can payfor the stock if necessary,we’llcovertheputwithcash.Thepayoffchartforourcash-secured MSFT put can beseeninFigure5.2.

Figure5.2MSFTCoveredPutPayoffChart

The strike price of the put isthe inflectionpoint, thepointat which the profit starts tofall. Below this inflectionpoint, the profit is less thanthe premium received, andeventuallytheprofitbecomesa loss once the underlyingstock drops below thebreakevenpoint.

Below the inflection point—thestrikepriceofthecoveredput we’ve sold—the payoffchart is shaped just likeownership of the stockbecause below the strikeprice, the put seller willeventually own the stock; itwill be put to him by theowner of the put. For ourMSFTcoveredput,thisstrikepriceandinflectionpointwas36.00. Let’s look at ourcoveredputversusownership

of the underlying MSFTstock(Figure5.3).

Figure5.3MSFT36StrikeCoveredPutversusMSFTStock

You’ll notice that as long asMSFT is below the strike ofthe option, the covered putwill outperform the stock bythe option premium receivedplustheamountbywhichtheput option was out-of-the-moneywhenitwasexecuted.The breakeven point is thepoint at which the loss from

being put the stock at thestrikeprice ispreciselyequalto the premium received.Thus, the breakeven point isthe strike price minus thepremium received, and forour MSFT covered put, thiswas34.35(36.00–1.65).Since we’re selling timevalue, and sincewe’ll collectit slowly, this covered putwill generate its profit overtime.Sinceweknowoptions

erodemoreslowlywithmoretime to expiration, wewouldn’t expect to make asmuch money in the first 15days aswe’d expect tomakeinthe last15days.But ifwehadtoclosethetradepriortoexpirationbybuyingbackourcovered put, this payoff overtime isgoing tobe importanttous.Let’slookatFigure5.4,whichshowshowthepriceofthis covered put will changeover time for a range of

underlyingstockprices.

Figure5.4MSFT36StrikeCoveredPutbyTimetoExpiration

The amount of cash requiredtocoverashortputissimplythe amount required to buythe underlying stock at theexercise price. This meansthatwehavetosegregatelesscash if we sell a put with alower strike price. In ourMSFT example, wesegregated a total of $3,600($165 of the $3,600 came

from the premium generatedby the sale of the put)because we sold 1 of the 36strikeputs.We’donlyhavetosegregate$3,400ifwe’dsold1 of the 34 strike puts.Unfortunately, looking atFigure5.1,we’d only collect0.96 if we sold the 34 strikeput rather than the 1.65received for selling the 36strike put. However, ourmaximum potential losswouldbeonly33.04(34.00–

0.96)ifwesoldthat34strikeput. Figure 5.5 shows thepayoffchartforsellingthe34strike put, along with theoriginal payoff chart forsellingthe36strikeput.

Figure5.536Strikeversus34Strike

The shape of any of thesecash-secured put payoffchartsisidenticaltotheshapeof the payoff chart for anyshort put. Segregating thecashdoesn’tchangetheshapeof the payoff chart but thatdoesn’t mean it won’t affectthe trade. How so? Imaginethat you’d sold a naked put,the underlying stock had

dropped substantially, andyou didn’t have the cash ormargin to buy the stock tosatisfy the duty to the putoption owner. You have solittle roomforerrornow thatyou’dlikelybeforcedtobuyback your short put at theworstpossibletime,whenthestockisonitslowandtheputoptionistradingatitshighestimplied volatility (i.e.,highesttimevalue).Comparethis to the flexibility that

comes from selling a cash-secured put. Successfultrading isn’t just aboutavoiding mistakes; it’s aboutavoiding situationswhere themistakesyoumightmakeareboth expensive and morelikelytooccur.

■TheRegretPointSince the goal of a coveredput is to either pocket thepremium received or to buythe stock at a discount to itscurrent price by getting paidwhilewaitingtoseeifwegetourbuyorderfilled,isthereasituationwhenthatwaitingisa mistake? Is there anoutcome where simplybuying the stockwould havebeen better than trying to

pocket the premium? Sincethe profit from a short put iscapped at the premiumreceived,theanswerisyes.Ifthe stock rallies, then it’spossible that the profitforegonefromnotbuyingthestock is greater than thepremium received and kept.Thepoint atwhich theprofitfromsimplybuyingthestockis equal to the premium thatwould be received is theregretpoint.Abovethislevel,

the put seller will regret notsimply buying the stockbecause the profit missedfrom not buying the stock isgreater than the premiumreceived.Carefulreaderswillrecognizethetermregretpointfromourdiscussion of selling acovered call in Chapter 4.That’s because selling acovered call, particularly ifbuying the stock and selling

the call at the same time, isvery similar to selling a cashcovered put. We’ll discussthis similarity later in thischapter.

■MarketOutlookThe appropriate marketoutlook for a covered put isgenerally slightly bullish,slightlybearish,orneutral.Inany of those outcomes, thecovered put seller will keepthe entirety of the premiumreceived,and,ingeneral,fewstrategies would have beensuperior. Usually, if a traderwereverybullish,theywouldexecute a different strategy,

since a covered put can onlymake the original premiumcollectednomatterhowhighthe underlying stock goes. Ifa trader is very bearish, thenhemightbuyaputratherthanselling a covered put, butselling a covered put will beprofitable if the stock dropsonly slightly yet remainsabovethebreakevenpoint.Acovered put will realize itsmaximumpotentialprofit,thefull amount of the premium

received, if the underlyingstock does anything,including dropping, but isabove the strike price at thetimeofoptionexpiration.Ifatraderbelievestheunderlyingstock will move sideways,that is will neither rallysignificantly nor dropsignificantly, then a coveredput would be a very logicalchoice.Notice that all three market

outlooks that are appropriateforacoveredput(upslightly,down slightly, or sideways)need the underlying stock tobe rather docile or notvolatile. That’s becauseselling a covered put is ashort volatility strategy, itdoes best with low realizedvolatility from the time theoptionissolduntilexpiration.But it’s possible to constructa covered put that can make

moneyevenifthestockdropssubstantially (by selling adeep out-of-the-money put),and it’s possible to constructa covered put that makesmoney without reaching theregretpoint even if the stockrallies substantially (byselling an in-the-money put).In fact, by selling an in-the-money put themarkethas torally inorder for thepositionto achieve its maximumprofit. Let’s look at all three

strategies because they’redifferentandassumedifferentmarketoutlooks.

■ Out-of-the-MoneyCoveredPutsThecoveredputswe’vebeendiscussing so far havegenerally been struck fairlyclose to at-the-money. Thatis, the strike price of theoptionhasbeenfairlyclosetothecurrentpriceofthestock.The first covered put welookedat, theMSFTcoveredput,wasstruckat36withthe

underlying stock at 37.15.Thiswasnot the first out-of-the-money put—that wouldhavebeenthe37strikeput—but the 36 strike was fairlyclose to at-the-money.Normally, the strike price ofthe covered put will beslightly below the currentstockprice,asourMSFTputwas, but even if it’s slightlyabove the current stock pricethis trade does best, inabsolutetermsandrelativeto

other strategies, when theunderlying stock doesn’tmoveverymuch.Again, thistradeisshortvolatility,sowewant realized volatility, theamount by which the stockmoves,tobelow.What ifwe thought thestockwould likely move sidewaysbut that there was a smallchance that it would dropsubstantially? What if thestock had earnings coming

outsoonorifitwasabiotechcompanythathadgoodlong-termprospectsbutthatwouldhave results of an importantclinical trial released in thenearfuture?Ineithercase,wemight be willing to buy thestockat a reallybigdiscountif we could get paid optionpremiumwhilewaitingtoseeif we buy the stock. In thiscasewemight sell a put thatis substantially out-of-the-money. Since the option is

struck substantially out-of-the-money, the amount ofpremium received will likelybeverysmall.Buttheoddsofbeing put the stock are low,and the effective purchaseprice if we are put the stockwould be much lower thanthecurrentstockprice.Table5.1showstheputswithapproximately 35 days toexpiration for a volatilebiotechstockthatwastrading

at17.45.

Table5.1BiotechCoveredPutsandLikelihoods

StrikePrice

OptionPrice

BreakevenPoint

11 0.15 10.8512 0.20 11.8013 0.35 12.6514 0.55 13.4515 0.85 14.15

16 1.30 14.7017 1.70 15.30

The third column is thebreakevenpointforasellerofthatput;notethateachoptionhas a different breakevenpoint. The fourth column isthe percentage move thatwould be required to reachthat breakeven point, but thefifth column is mostinteresting—it’s the

likelihood, measured byoption delta, that theunderlying stockwill at leastreach that breakeven point atoptionexpiration.It’seasytothink that you’d be happy tosell that11 strikeput at0.15becausethestockcouldneverdrop 38 percent in such ashort time, and you’d get topocket the 0.15 as “freemoney.” But the delta of thehypothetical 10.85 strike putis5percentmeaning that the

optionmarkettellsusthatonetime out of every 20, thestock will drop to or belowthat breakeven point atexpiration.Remember, that 5deltarepresentsthelikelihoodthat theunderlyingstockwilldrop to at least that level atexpiration. It could go wellbelow that level and if thisstock drops at least 38percent, then there’s notelling how far below thatbreakeven point momentum

andsellingpressurewill takeit, meaning that lossessustainedcouldbehuge,eventhough the maximumpotentialprofitwasonly0.15.Again, professional optiontradersknow that this sort ofextreme move happens morefrequentlythanpredictedbyanormaldistributionofreturns.Professional option tradersalso consider selling naked,that is, uncovered, deep out-of-the-money puts to be a

great way to get rich slowlyand go bankrupt suddenly.The covered put seller,however, knows that he’ll beable to pay for the stockthat’s put to him, regardlessofhowfaritdropsbelowthestrike price.Covering a deepout-of-the-money put doesn’tchange the math; it justmeans that the put sellerknowshowhe’sgoingtopayforthestockthat’sputtohim.

Let’s look at a morereasonable candidate forselling a covered put. Whatdoes the first out-of-the-moneyput, the17 strikeput,look like compared to thatdeep out-of-the-money put,the 11 strike? Figure 5.6showsbothpayoffcharts.

Figure5.6AnAt-the-MoneyPutversusaDeepOut-of-the-MoneyPut

Selling a deep out-of-the-money put obviouslyprovides a tremendousamountofroomforerror;thatis,thestockcandropsharplyand still not reach the pointwhere the put is in-the-money, but it doesn’tgenerate much premiumeither. In this case, thebreakeven for the 11 strike

put is 10.85, as selling theoptiongeneratesonly0.15ofpremium. And mark-to-marketlossesontheshortputwilllikelybesubstantial.Thisisn’t a huge concern for thecovered put seller, but thecoveredputsellerwillseetheimpact on their tradingaccount.A final word about sellingdeep out-of-the-money puts.Since options started trading,

even before there wereoptions exchanges, sometradershavesolddeepout-of-the-money puts, sometimescalled “teeny” puts, havedone souncovered, andhavebeen happy to collect a“teeny” amount of premiumbecause they think there’snochance that the market candrop far enough and fastenough to cause thema loss.They are wrong—oftenenormously wrong. When

they’re ultimately wrong,havingsoldtheseputsnaked,then they’ve gone broke.Every professional optiontrader knows some optiontraders(thatshouldbeformeroption traders) who haveregularly sold teeny puts andwent broke doing it. Pleasedon’t. While the academicliterature is full of studiesshowing that puts,particularly deep out-of-the-money puts, are, over time,

more expensive than theyshould be, the academicliterature is also full ofstudies pointing out thatstocks can anddodropmoreand more frequently thanwould be explained by thenormaldistributionofreturns.This is one reason deep out-of-the-money puts are soexpensive. While you’lltheoretically have the mathonyoursidesellingdeepout-of-the-money puts, because

overtimetheycostmorethanthey’reworth,youmightwellgo broke before you canmakeasubstantialamountofmoney. States make lots ofmoney selling lottery tickets,buttheytakeinlotsofmoneyfirst and then pay only aportion of it out. When yousell deep out-of-the-moneyputs, you’re selling lotterytickets without taking inanythingbut that teenybitofpremium.And these extreme

“tail risk” events willbankruptthenakedputseller.

■ In-the-MoneyCoveredPutsAnin-the-moneycoveredputneedstheunderlyingstocktorally in order to achieve itsmaximumpotentialprofit.Aswith any short put, themaximumprofitforanin-the-money covered put will berealized with the underlyingstock at or above the strikeprice at expiration so an in-

the-money put seller isassuming the stockwill rallyto at least the strike price.Becauseofthis,sellinganin-the-money covered put,particularly one that is deepin-the-money, is very muchlike buying the underlyingstock with a cap on howmuch money can be made,since the total maximumprofit from selling any put,including one that’s in-the-money,isthetotalamountof

premiumreceived.Table5.2showsanumberofin-the-money puts for WellsFargo & Company (WFC)when WFC was trading at43.60.

Table5.2WFCPutsandBreakevens

StrikePrice

OptionPrice

BreakevenPoint

43 1.75 41.25

44 2.25 41.7545 2.80 42.2046 3.50 42.5047 4.25 42.7548 5.10 42.9049 5.90 43.1050 6.85 43.15

The 43 strike put, the firstout-of-the-money put, has abreakeven price of 41.25.What is the likelihood of

WFC’s dropping to 41.25?We know that likelihood isthedeltaofahypotheticalputstruck at 41.25. Using thetools atwww.OptionMath.com, wedetermine that likelihood is32percent.The likelihoodofWFCbeingatorbelow41.25atexpirationis32percent.Ofcourse, that’s not a measureofhowfarbelow41.25WFCcoulddrop.


The50strikeput,aputthat’sdeep in-the-money, has abreakeven price of 43.15. IfWFC is below 43.15 atexpiration, then selling thiscovered put is going to losemoney. Notice how muchcloserthebreakevenofthe50strike put (43.15) is to thecurrent stock price (43.60)than is the breakeven of the43 strike put (41.25). This islargely a function of thelower strike price, but it’s

alsoafunctionofthatamountof time value in the option.The 50 strike put has only0.45 of time value while the43strikeputhas1.75oftimevalue.Infact,allof thepriceof the 43 strike put is timevalue.Figure 5.7 shows the payoffchart of a 43 strike coveredputcomparedtothe50strikecoveredput.The43strikeputis just out-of-the-money, a

common strike selection,while the 50 strike coveredput is substantially in-the-money, a much less likelychoice.

Figure5.7WFCDeepIn-the-MoneyCoveredPutversusAt-the-MoneyCoveredPut

Since an in-the-moneycovered put is so much likebuying the underlying stock,it’s susceptible to significantlosses if theunderlyingstockdrops just a little. Thebreakevenpointforanin-the-money covered put is likelyto be just a tiny bit belowwere the stock is currently

trading as you saw in Table5.2 and in Figure 5.7, whereWFCstockwas at 43.60andthebreakevenpointofthe50strike put was 43.15. Theowner of the put is going toexercise the put if the stockpriceremainsbelowthestrikeprice and the seller of thecoveredputisgoingtobeputthestockatthatstrikeprice.It’s important to rememberthat Table 5.2 shows the

likelihood of WFC’sdropping to or below thebreakeven at expiration.That’s not the same as thelikelihood that WFC will beatorbelowthestrikepriceofthe option at expiration. Thedelta of the hypothetical43.15 strike put is 47meaning theoddsofbeingator below 43.15 at expirationis 47 percent. That 50 strikeputhasadeltaof89meaningthe odds of the put seller

having to buy the stock at50.00 are 89 percent. Ofcourse,theeffectivepurchaseprice is reduced from 50.00by the option premiumreceived. That 89 percentlikelihood of eventuallyowning the stock is whyselling a deep in-the-moneyputissosimilartoanoutrightpurchaseofthestock.The odds of being put thestockat50.00are89percent.

While the effective purchasepriceislowerthan50.00(it’sthe strike price minus thepremium received or 43.15),this doesn’t change the oddsof being put the stock. Thismeans the odds of buyingWFCat an effective price of43.15 are 89 percent. Theother11percentare theoddsthat WFC is above 50.00 atoption expiration, meaningtheputownerwon’t exerciseandwewon’t buy the stock,

butwe’llgettokeepthe6.85inpremiumreceived.Figure 5.8 compares thepayoffchartforthis50strikeputtoanoutrightpurchaseofthestock.

Figure5.8AWFCDeepIn-the-MoneyCoveredPutversusOwningtheStock

Sellingthedeepin-the-moneyputresultsinapositionthatisverymuch like ownership ofthe stock, but it’s notidentical. The put seller getstocollectandkeepthe0.45oftime value in the put, whilethe stock buyer doesn’t haveany limit on his profit. Themaximum profit for the putseller is the 6.85 collected

regardless of howhighWFCstockgoes.There’sanotherhurdleforthesellerofanin-the-moneyput,the bid/ask spread. Thebid/ask spread for in-the-money options is generallywiderthanthebid/askspreadfor at- and out-of-the-moneyoptions. For example, Figure5.9 shows the bid/ask spreadfor a number of deep in-the-moneyputoptionsonGM.If

a trader wanted to getexposure to GM stock, hemightthinkaboutsellingoneoftheseputs.

Figure5.9DeepIn-the-MoneyCoveredPutsinGMandtheBid/AskSpread

Even if a trader thoughtGMwas due to rally sharply anddidn’tmindhavingalimitonhis potential profit, wouldselling a deep in-the-moneyput be the best strategy? Ifthis trader sold theMarch55strike put, he could sell it atthe bid price of 14.85. Hemightofferhisputforsaleatanother price including at a

price somewhere in themiddle of thebid/ask spread,but then there’snoassurancethat he’d get his order filled.Hemightendupneversellingtheput.Let’s assume our put sellersold that March 55 put at14.85andthatGMdidindeedrallysharply.Howwouldthiscovered put sale fare if GMrallied to 50.00 (a nearly 25percent rally)? How would

this covered put sale fare ifGM rallied to the 55 strikeprice (a 37 percent rally)?How would this covered putsale fare ifGMralliedabovethe55strikeandwasat60.00when the option expired?Table 5.3 shows the resultsfor those three outcomesalong with the results forsimply buying the stock at40.12.

Table5.3SellingIn-the-Money

PutsinGM

StockPriceatOption

Expiration

ProfitfromSellingthe55StrikePutat14.85

ProfitfromBuyingGMStockat

40.1250.00 9.85 9.8855.00 14.85 14.8860.00 14.85 19.88

Thereisnopriceforthestockatoptionexpirationforwhichselling the covered putgeneratesasuperioroutcome.Theoutcomedoesn’timproveifthestockdropseither.Ifthestock were at $30.00 atexpiration, thenthelossfromselling the 55 strike put at14.85 would be 10.15 (theloss on the stockwill be the25.00 difference betweenwhere the put sellerwill buythe stock, 55.00, and the

valueofthestock,30.00,lessthe 14.85 option premiumreceived).Comparethistothelossof10.12(30.00–40.12)realized from simply buyingthestockat40.12.Selling this deep in-the-money put at 14.85 wassuboptimal compared tosimply buying the stock inevery circumstance becausetheputsellersoldthisputforless than its inherent value.

With the stock at 40.12, the55 strike put is inherentlyworth 14.88 (55.00 – 40.12).Any time a trader sells anoption for less than itsinherent value, he will findthe outcome trails simplytradingthestock.Thebidpricefordeepin-the-moneyputs (andfordeep in-the-money calls, althoughdeep in-the-moneycallshavea strike price significantly

below the current marketprice of the stock) is veryoften below the inherentvalue of the option. Blamethe market maker’s need tomakeaprofitandtoexecuteabunch of stock to hedge theoptionstheybuyfromyou.

■ At-the-Money orNearlyAt-the-MoneyAt-the-money options havethe greatest time value. Forthat reason alone, it mightmake themost sense to stickto selling at-the-money ornearat-the-moneyputs.Let’stake another look at MSFT,theveryfirststockwelookedatinFigure5.1butextendthedatatoincludetheamountof

time value in each of thoseoptions.Youcanseethistimevalue in Table 5.4. The 37strike put is trading at 2.10,and all of that 2.10 is timevalue.Thatmeansthatthe37strike put has the greatesttime value of any of theoptions trading in theMarchexpiration. It’s no accidentthat the option that is struckclosest toat-the-moneyis theoption with the greatest timevalue.

Table5.4MSFTPutPricesandTimeValue

StrikePrice

OptionPrice

OptionTimeValue

34 0.96 0.9635 1.28 1.2836 1.65 1.6537 2.10 2.1038 2.65 1.8139 3.25 1.41

40 3.90 1.06

The breakeven for that 37strike put is 34.90, meaningthat ifMSFT is below 37 atMarch expiration, then ourcoveredputseller isgoing tobuy the stock at an effectiveprice of 34.90.What are theodds of buying at thateffective price? It’s thelikelihood thatMSFTwillbebelow 37.00 at expiration.

Remember that as long asMSFT is below that strikeprice,nomatterhow far it isbelow 37.00, the put ownerwill exercise that put. Thedeltaofthat37strikeputwas47, meaning the odds ofbuying MSFT at thateffectivepriceof34.90are47percent.That’s pretty good, the oddsare nearly 50/50 that we’llbuyMSFT at a big discount

totoday’sprice.Butwhatarethe odds that we’ll losemoney at March expiration?That’s the likelihood thatMSFTisbelowthebreakevenprice of 34.90 at expiration.And the delta of ahypotheticalputoptionstruckat precisely 34.90?The toolsatwww.OptionMath.com tellus that delta is 27. Thelikelihoodoflosingmoneyonthiscoveredputis27percent.And interestingly, the

http://www.OptionMath.com

likelihood of MSFT’s beingbelow the 37 strike price butabove that 34.90 breakevenare 20 percent (47 percent –27 percent). One time out ofevery five, this covered putsellerwillendupinthesweetspotwherewe buy the stockat an effective price lowerthanit’sthentradingat.Let’slook at all the importantlikelihoods for this coveredput sale in Figure 5.10 andTable5.5.

Table5.5LikelihoodsforOur37StrikeCoveredPut

OutcomeRelevantPriceat

ExpirationLikelihood

Putsaleisprofitable

MSFTatorabove34.90

73%

Putsaleisnot

profitable

MSFTbelow34.90

27%

Put MSFT

exercisedbyowner

below37.00

47%

Putexpires

worthless

MSFTatorabove37.00

53%

Putexercised

buteffectivepurchasepriceofstockisbelow

MSFTbelow

37.00butabove34.90

20%

currentmarketprice

Outrightstock

purchaseis

profitable

MSFTabove37.16

50%

MSFTdropsbutstaysabovestrike

MSFTbelow

37.16butabove37.00

3%

Figure5.10MSFTAt-the-MoneyCoveredPutandtheImportantLikelihoods

Calculating these likelihoodsincluding the likelihoods ofthe hypothetical levels canhelp you understand thedynamics of the positionyou’reconsidering.Let’s compare in-the-money,out-of-the-money,andat-the-moneycoveredputsforanewstocksothatwecanseehow

theydiffer.Figure5.11showspotential covered puts inGLD, the gold exchange-tradedfund(ETF).

Figure5.11ThreeCoveredPutsinGLD

The106putwasdeepout-of-the-money, the 126 put wasdeep in-the-money, and the116 putwas precisely at-the-money.Figure5.11showsthepayoff charts for all of thosecovered puts. In Figure 5.12you can clearly see that thein-the-money covered put isverymuch like ownership ofthe stock with a tiny

difference generated by the0.60oftimevaluecollected.

Figure5.12In-the-Money,Out-of-the-Money,andAt-the-MoneyOptionsinGLD

The out-of-the-money put isverydifferentfromownershipof GLD; it generates a verysmall net profit, the 0.95 ofoption premium collected,overaverylargepricerange.The at-the-money put’spayoffisdifferent.Belowtheinflectionpointat116.00,itisalways superior to the

performance of GLD by the3.60 in premium collected.Abovetheinflectionpoint,itsprofit is the 3.60 collected,but above 119.60, it trailssimple ownership of GLDbecause GLD is now abovetheregretpoint.

■ Covered Put versusCoveredCallWe noted earlier that both acash-secured put and acovered call have a regretpoint, abovewhichwe regretsellingtheoption.Inthecaseof the coveredput,we regretselling the put rather thansimply buying the stock. Inthe case of the covered call,we regret selling the call

because the profit we foregoon the stockwe already ownis greater than the callpremium received. Thepayoff charts for the twocombinations are also verysimilar. Why all thesimilarity?Becauseassumingtheputandcallhavethesameexpiration and strike price,the trades are identical.Earlier,wesawthattheGLD116 put was trading at 3.60.The 116 call was trading at

3.60 as well because GLDwasat116.00—ifthecallhadbeen trading at any otherprice, therewould have beenan arbitrage opportunity.Let’s see how the twopositionswouldworkout fora variety of prices atexpiration:

Selling the February116 Strike CoveredPutat3.60

Totalpremiumcollected=$360Totalcapitalrequired=$11,240($11,600tobuy100sharesofGLDat116.00ifassignedminus$360ofputoptionpremiumreceived)Breakevenpoint=112.40Regretpoint=119.60

Profit/losswithGLDat110.00atexpiration=–2.40Profit/losswithGLDat116.00atexpiration=+3.60Profit/losswithGLDat122.00atexpiration=+3.60

BuyingGLDat116.00and Selling the

February 116 StrikeCallat3.60

Totalpremiumcollected=$360Totalcapitalrequired=$11,240($11,600tobuy100sharesofGLDat116.00minus$360ofcalloptionpremiumreceived)Breakevenpoint=

112.40Regretpoint=119.60Profit/losswithGLDat110.00atexpiration=–2.40(lossof6.00onlongGLD,gainof3.60onshortcallposition)Profit/losswithGLDat116.00atexpiration=+3.60(nogainorlossonGLDposition,gainof3.60onshortcallposition)

Profit/losswithGLDat122.00atexpiration=+3.60(gainof6.00onlongGLDposition,lossof2.40onshortcallposition)

While the covered call mayresultincontinuedownershipofthestock,itdoesn’timpactthe profit or loss, and theowner of the stock is free toclose that position at the

example prices at optionexpiration. Other than that,the two positions areidentical. That’s because theputandthecallwillhavethesameamountoftimevalue.Buying stock soyoucan sella covered call doesn’t makemuch sense when thealternative is selling acovered put. Why pay acommission tobuy thestock,thenpayacommissiontosell

the covered call, when youcould instead pay a singlecommission to sell thecovered put? No logicaltraderwoulddoso.

CoveredPutCheatSheet

CoveredPut

Description

Shortput,longcashtobuystockatthestrikeprice

Example

ATM=100Shortone95strikeputLong$9,500

PayorCollect

Premium

Collect


Passageof

TimewithoutMarket

Movement

+++


Movement

−−−

PayoffThumbnail

Chart

MaximumRisk

Strikepriceminus

premiumreceived(ifstockdropstozero)

MaximumProfit

Premiumreceived

BreakevenPoints

Strikepriceminus

premiumreceived

CHAPTER6

CalendarSpreads

Ifwethoughtacompanywas

going to report disappointingearnings we might want tobuy a put option on thatstock. We have a particularcatalyst in mind, theupcoming earnings report,and we know when thatreport will be issued. We’retryingtogetexposureforthatcatalyst, but we probablythink that the stock will bemostly sideways until theevent so we don’t wantexposurefortheentireperiod

fromnowtotheevent.Wecouldbuythatputoptionand we’d make money aslong as the stock fell belowthe strike price of the put bymore than the cost of theoption.Butlotsoftradersandinvestors are going to wantexposure to, or protectionfrom, that event, so they’relikely to bid up the price oftheputoptionwe’re thinkingof buying. Is there a way to

reduce thecostofbuying theput that we want to own forthat catalyst by selling ashorter-dated put that expiresbefore the catalyst but thatwill erode away during theperiod between now andexpiration, aperiodwhenweexpect the stock will movesideways?We might not have aparticulareventorcatalyst inmind butmight want to take

advantageofthedifferenceinoption erosion by time toexpiration that we discussedin Chapter 2. Shorter-datedoptions erode more quickly;their theta is higher, thanlonger-dated options. If wewere to buy a longer-datedoptionandsellanoptionthatwas identical except for thetime to expiration, that is, itwas identical except for anearlier expiration date, thenwe could collect the daily

erosionfromtheoptionthatiserodingquicklywhilepayingthe smaller amount of dailyerosionfromtheoptionthatiseroding slowly. Eventually,thefrontoptionwouldexpireand we’d be left long thatlonger-datedoption.What if we thought that astock was going to rallysubstantially? If we thoughtthis was the case we mightsell an at-the-money put

option expecting to collectandkeepallof thatpremiumwhen the stock rallies. Butthis means that we havesubstantial risk if the stockdrops. We would end upbeing put the stock at thestrike price. While oureffective purchase pricewould be reduced by the putpremium received, this isn’tour thesis. We’re notinterested in owning thestock,wejustwant tocollect

and keep the put optionpremium when the stockrallies. One way toaccomplish this after sellingour at-the-money put wouldbe tobuya shorter-datedputwith the same strike price.Thenifthestockdroppedtheshorter-term put option weown would protect us fromthe risk of the longer-datedput we’re short. While thisprotection would ultimatelydisappear when that shorter-

dated put expired we couldthen buy another short-datedputorbuybacktheputoptionwe’reshort.If theunderlyingstock has rallied as weexpected then that putwouldhavedeclinedinvalueandwewouldbuyitback,realizingaprofit.All of these trades arecalendar spreads. A calendarspread is executedwhen youbuy (or sell) a longer-dated

option and simultaneouslysell (or buy) a shorter-datedoptionthatisidenticalexceptfortheexpirationdate.Calendar spreads aresometimes called horizontalspreads because optionlistingsinthenewspaperusedto have the strike prices foreach expiration runningvertically up and down thepage (hence, the strikespreads we looked at earlier

are called vertical spreads)and the different expirationsare running horizontallyacross the page. Calendarspreads are also called timespreads, but we’ll generallystick with the term calendarspread.Calendar spreads can beexecuted using either puts orcalls and by buying thelonger-dated option whileselling the shorter-dated

option or by selling thelonger-dated option whilebuying the shorter-datedoption. When buying thelonger-dated option, we’rebuying the calendar spreadand we’ll have to pay somenet premium. When sellingthe longer-dated option,we’re selling the calendarspread and we’ll collectpremium. The easy way toremember this is if we’repaying net premium then

we’re buying. If we’recollecting net premium thenwe’reselling.Calendar spreads can bebullish, bearish, or neutral,dependingon the strikepricewe select and its relationshipto the at-the-money level.This means that somecalendar spreads, such asneutral calendar spreads, dobestwithvery littlevolatilityand that some calendar

spreads do best with atremendous amount ofvolatility. Generally, thefurtherthestrikepriceisfromat-the-money, the morevolatilityneededforthetradeto be profitable, so themorevolatility you would beexpecting if you chose toinitiatethattrade.Figure 6.1 shows some putson Oracle (ORCL) that wemight use to construct some

putcalendarspreads.

Figure6.1TwoPutCalendarSpreadsinORCL

ORCL stock was trading at32.78 when these optionprices were observed andORCL was due to reportearnings on the Thursdaybefore those June optionsweretoexpire.IfwethoughtORCLearningswere going to disappoint,then we might buy the

May/June 32 put calendarspread.Wewould do this bybuying theJune32strikeputat0.72andwereducethecostof the trade by selling theMay 32 strike put at 0.26.The calendar spread wouldcostus0.46(0.72–0.26).Thegoalof thisput calendarspread, in fact for all longcalendar spreads, is for thefront option, the put optionexpiring inMay in this case,

to expire worthless, leavingus long the back monthoption, the June put in thiscase.Forthistradewehaveacatalystinmind:theearningsannouncement. Other longcalendar spreadsmay simplytry to reduce the cost of theultimate position or takeadvantage of the differentialoption erosion for optionswith different expirations. IftheMayputexpiresworthlesswehavemanaged to be long

the June put outright for thecatalyst and we’ve reducedthecostofownershipby0.26,a36percentdiscount.What does the payoff chartfor this calendar spread looklike at expiration? That’stough to say. All the otherpayoffchartswe’velookedathad objective inputs; weknewwhattheoptionswouldbe worth at expiration giventhe price of the underlying

stock. In a calendar spread,we might know what theshorter-dated option is worthat the front expiration, butwe’d have to guess what thelonger-dated option is worthatthatpoint,andthatdependson lots of things includingvolatility, the unknowableinput.Similarly,wecanknowwhat the longer-dated optionis worth at the secondexpirationbutthenwe’dhaveto assume a price for the

stock,andthusavalueforthefront option, on the frontexpiration date. Because ofthis,wewon’tuseasmanyofthe type of payoff chartswe’ve used elsewhere. Thatdoesn’t mean calendarspreads are that much morecomplicatedorthatyoucan’tfigure out the payoff; it justmeans that in order to chartthe payoff,we have tomakeseveralassumptions.

It may not be possible tograph the payoff withcomplete certainty, but it ispossible to know themaximumpossible riskwhenbuyingacalendarspread.Themaximum possible risk iswhatwepaidforthecalendarspread. Let’s look at thisMay/June 32 strike putcalendar and see how themaximumpotentialriskisthe0.46 paid. We’ll look at theprofit or loss at June

expiration first assuming theMayoptionexpiredworthlessand then again assuming theMayoptionwasin-the-moneyat expiration and we wereassigned,meaningwehadthestock put to us at 32.00 ashare. Table 6.1 shows theoutcome assuming the Mayoptionexpiredworthless.

Table6.1OutcomesforOurLongPutCalendarSpreadinORCL

StockPriceatJune

Expiration

PositionatJune

ExpirationAssumingMayOptionExpiredOut-of-the-

Money

ValueofPositionat

JuneExpiration

28.00 LongJune 4.00

32put

30.00 LongJune32put 2.00




Thislongputcalendarlosesamaximum of 0.46 assuming

the May option expiredworthless. The breakeven is31.54 (32.00 – 0.46)assumingtheMayoptionwasout-of-the-money atexpiration and expiredworthless. The profitincreases as ORCL fallsbelow 31.54 and stopsincreasing only when ORCLfallstozero.Let’s look at these sameoutcomes assuming that the

May option had been in-the-money at expiration and thatwehad thestockput tousat32.00. We see this in Table6.2.

Table6.2OutcomesforOurLongPutCalendarSpreadinORCL

StockPriceat

PositionatJune

ExpirationAssuming Valueof

Positionat

JuneExpiration

MayOptionExpiredIn-the-Money

JuneExpiration

28.00

LongsharesandlongJune32put

32.00(stockworth28.00,optionworth4.00)32.00

30.00


(stockworth30.00,optionworth2.00)

32.00


32.00(stockworth32.00,optionworth0.00)

34.00


34.00(stockworth34.00,optionworth0.00)

36.00


36.00(stockworth36.00,optionworth

0.00)

No matter what happens atthe first expiration and nomatter where the underlyingstock is at the secondexpiration,themaximumlossfrombuyingaputcalendaristhe initial cost of the putcalendar. In fact, themaximum loss from buyingany calendar spread, put orcall, is the price paid for the

calendarspread.But the nature of the tradechanges completely,depending onwhether or notthe front month option, theMayexpirationinthiscase,isin-the-money or out-of-the-money at expiration (and ifthe option was precisely at-the-moneyatMayexpiration?Then the option wouldprobablynotbeexercisedandwe would likely be left long

the June put but if the Mayoption was exercised ourmaximum riskwould still be0.46but, again, thenatureofthe resulting position wouldbe very different than wewant).It’s great to know that ourrisk is limitedbutweboughtthe put calendar spreadbecause we thought ORCLwas going to drop after thefront option expired. Having

thefrontmonthexpirein-the-money(orat-the-moneyifwegetputthestock)leavesusina situation where we nowneedORCLtogoupinorderto make money. No optiontrader wants to be in asituation where he thinks astock is going down but heneeds it to go up in order tomakemoney.Thismeansweneed to close the trade orspread into another trade ifour frontmonth option is in-

the-moneyatexpiration.Observant readers willrecognize that the positionthat results from the frontmonthoptionexpiringin-the-money,longstockandlongaput, is synthetically identicalto a long call option. SeeChapter 13 on conversionsand reversals to learn moreaboutsyntheticpositions.

■ Call CalendarSpreadsWhat if we were bullishORCL and thought theearnings release just prior tothe June expiration wouldbring good news?We mightbuy a call calendar to getexposure to the event we’refocused on while loweringthe cost of the trade. Figure6.2 shows some ORCL call

options we might use toconstruct call calendarspreads.

Figure6.2TwoCallCalendarSpreadsinOracle(ORCL)

We could buy the May/June34strikecallcalendarspreadat0.41bybuyingtheJune34strike call at 0.52 andsimultaneously selling theMay34strikecallat0.11.Even though this is a callcalendarthemaximumriskisstillwhatwepaidfor it,0.41inthiscase.Let’sdothesame

sort of math we didpreviously to confirm this.Table6.3shows thepotentialprofit and loss for a rangeofunderlying prices at Juneexpiration assuming theMaycall option had expiredworthless.

Table6.3OutcomesforOurLongCallCalendarSpreadinORCL

Position

StockPriceatJune

Expiration

atJuneExpirationAssumingMayOptionExpiredOut-of-the-

Money

ValueofPositionat

JuneExpiration

30.00 LongJune34call 0.00


34.00 LongJune34call

0.00



Thislongcallcalendarlosesamaximum of 0.41 assumingthe May option expiredworthless. The breakeven is34.41 assuming the May

option was out-of-the-moneyat expiration and expiredworthless. The spread isprofitable above thatbreakeven point and theamount of profit increases aslong at ORCL stock keepsrallying. Let’s look at thesesameoutcomesassumingthattheMay option had been in-the-money at expiration andthatwehadtosellthestockat34.00 by borrowing it(borrowing stock to sell it is

shortingthestock).Table6.4showsthepotentialprofitandlossforarangeofunderlyingprices at June expirationassumingthemaycalloptionwas in-the-money atexpiration.

Table6.4OutcomesforOurLongCallCalendarSpreadinORCL

PositionatJune

StockPriceatJune

Expiration

ExpirationAssumingMayOptionExpiredIn-the-Money

CosttoClose

PositionatJune

Expiration

30.00

ShortsharesandlongJune32call

30.00(buystockat30.00,selloptionat0.00)

32.00



34.00

ShortsharesandlongJune

34.00(buystockat34.00,selloptionat

32call 0.00)

36.00



Shortsharesand

34.00(buystockat

38.00 longJune32call

38.00,selloptionat4.00)

No matter what happens atthe first expiration and nomatter where the underlyingstock is at the secondexpiration,themaximumlossfrombuyingacallcalendaristhe initial cost of the callcalendar. Again, with the

front month in-the-money atexpiration the directionalityof profit after that expirationiscontrary toouroutlookforthe market. Some sort offollowuptradeisrequired.We’ve now seen that buyinga calendar spread, regardlessof put or call, regardless ofin-the-money or out-of-the-moneyatthefrontexpiration,hasamaximumpotentiallossequaltowhatwepaidforthe

spread.Now that we recognize thesortsofassumptionswehavetomake togeneratepotentialpayoffchartsandthatmakingthose assumptions isdangerousandthatacalendarspread that sees the shorter-datedoptionassignedcanendupmakingmoneyonlyifourmarketoutlookiswrong,let’slook at a hypothetical payofffor that May/June 34 strike

call calendar that wecontemplated buying. We’llassumearangeofunderlyingprices at the May expirationand we’ll calculate thehypotheticalvalueoftheJune34 call using the tools atwww.OptionMath.comassuming the volatility inputdoesn’t change. You can seethispayoffinFigure6.3.


Figure6.3TheMay/June34StrikeCallCalendarPayoff

Notice that the theoreticalprofit or loss for this callcalendarisslightlynegativeifORCL doesn’t move at alland remains at 32.78 at Juneexpiration. That’s becausethis call calendar is struckrelatively far out-of-the-money (34.00 strike priceversustheunderlyingpriceof32.78) and because the June

option catches the earningsrelease while May doesn’t.This call calendar requiresORCL to rally inorder tobeprofitable. All calendarspreads have directional risk.Somecalendarspreads, thosestruck close to at-the-money,need the underlying stock tostayclosetothepresentlevel.Some calendar spreads needtheunderlyingtomovealittlebut in the right direction.These, like our 34 strike call

calendar, have been struck alittleout-of-the-money.Someneed the underlying stock toreallymove; thesehavebeenstruck substantially out-of-the-money.Thismeansthatlongcalendarspreads can be very versatilefrom a market outlook pointof view. It’s possible toconstructalongcallcalendarthat is very inexpensive toinitiate but that requires a

significant rally in theunderlying stock in order forthe call calendar to beprofitable. It’s possible toconstruct a long put calendarthat is very inexpensive toinitiate but that requires theunderlying stock to drop invalue substantially in orderfor the put calendar to beprofitable. It’s also possibleto construct a calendar thatneedstheunderlyingstocktonot move very much during

the term of the front monthoption in order to beprofitable but these calendarspreadscostmoretoexecute.Let’s look at the at-the-money call calendar, theMay/June 33 call calendarandseehowthiscallcalendarneedsORCL to stay close toitscurrentpriceof32.78tobeprofitable at June expiration.WecanseethisinFigure6.4.

Figure6.4TheMay/June33StrikeCallCalendarPayoff

This33strikecallcalendarisprofitable as long as ORCLdoes not move too muchbefore that May expiration;theassumed lowerbreakevenpoint is 32.35 and theassumed upper breakevenpoint is 33.70. But this callcalendar cost 0.51 versus the0.41the34callcalendarcost.

How is it that this long callcalendarmakesmoneyat theMay option expiration ifORCL doesn’t move? Thedifferential erosion of optionprices based on time toexpiration generates thisperformance. Let’s use thetools atwww.OptionMath.com andcalculate the erosion of thecomponents of this callcalendar spread at severalpointspriortoexpiration.We


seetheseinTable6.5.

Table6.5DifferentialErosionforOurCallCalendar

DaystoExpirationofMayCall

Option

ExpectedChangeinMayCall

OptionPriceDue

toErosion(Theta)

ExpectedChangeinJuneCall

OptionPriceDue

toErosion(Theta)

20 –0.013 –0.01115 –0.015 –0.01110 –0.018 –0.0125 –0.025 –0.0121 –0.043 –0.013

And what would this looklikeifweconnectedthedots?You can see that in Figure6.5.

Figure6.5DailyNetErosionCollectedfor33StrikeCallCalendar

You can see that the neterosioncollected increasesasexpiration of theMay optionnears.Thisisexactlywhatwewould expect given what weknow about the difference inoption price erosion betweenoptions with differentexpirationdates.

■ Selling CalendarSpreadsIn Figure 6.1, we saw someputoptionsthatwemightuseto construct calendar spreadsandwe specifically saw howwe could sell the July 30strikeputat0.46andbuytheJune 30 strike put at 0.28 tosell the June/July 30 strikeput calendar at 0.18. Wemight do this ifwe expected

ORCL to rally substantiallybecauseifORCLrallies,thenthe price of both put optionswillmovetowardzero.Whileneither option price will getall the way to zero beforeexpiration, if ORCL ralliessubstantially we should beable to buy the calendarspread back very cheaply,close our risk and realize aprofit.Aswithnearly anyoptionor

spreadwesell, themaximumprofit for selling a calendarspread is the premiumcollected, 0.18 for ourJune/July 30 strike putcalendar. But if the frontoption expires worthless, theJune expiration in this case,we’re left short the backmonth option and thatgenerates significant risk inthe case of a put calendaronly because the underlyingstock can’t drop below zero

and that generates infiniterisk in the case of a callcalendar since we’re nakedshort the back month callwhich can rally in priceinfinitely.Let’stakealookatFigure6.6whichshowsthesamesortofpayoff chart we’ve used forcalendar spreads,understanding all theassumptions and estimationsthatareinherent,andseehow

thisshortputcalendarspreaddoesatthefrontexpiration.

Figure6.6TheShortJune/July30StrikePutCalendarPayoff

We know that this payoffmakes several assumptionsincludingthatthebackmonthoption, the July put in thiscase, maintains the sameimplied volatility from thetimeweinitiatethetradeuntilthe June option expires. In asituation where theunderlying dropssubstantially,that’snotlikely

tobethecase.It’s likelythatimplied volatility willincreasemeaningthatthelossat June expiration will beevengreatersinceitwillcostmore than expected torepurchase that July put toextinguish the trade and therisk.How is it that this short putcalendar is profitable ifORCL drops substantially orrallies substantially? Let’s

look at our assumed optionprices with ORCL at 24.00and at 37.00 at the Juneexpiration. We see this inTables6.6and6.7.

Table6.6OurShortPutCalendarSpreadifORCLDrops

InitialPrice

AssumedPricewith

ORCLat24.00

LongJune30put

0.28 6.01

ShortJuly30put

0.46 6.02

June/Julyput

calendar0.18 0.01

Table6.7OurShortPutCalendarSpreadifORCLRallies

InitialPrice

AssumedPricewith

ORCLat37.00

LongJune30put

0.28 0.01

ShortJuly30 0.46 0.02

putJune/July

putcalendar

0.18 0.01

Thegoalofsellingacalendarspread is tohaveall the timevalue come out of bothoptions so that the longer-dated option can berepurchased very cheaply,thereby extinguishing thatrisk. When this occurs, the

maximum potential profit, orvery nearly the maximumpotentialprofit,isrealized.Thegoalofbuyingacalendarspread is tohaveall the timevalue out of the front optionwhile having as much timevalue as possible in the backoption. Since an option hasthemaximumamountoftimevaluewhenitisat-the-moneythis means that a longcalendar maximizes its value

at the front expiration whenthestockisatthestrikepriceof the long calendar. If thestrikepricewasat-the-moneywhen we executed thecalendar then this means wewant it to stay there. If thestrike price was out-of-the-moneywhenweexecutedourlongcalendarspread thenwewant the underlying stock tomove to that strike price.Calendar spreads can bedirectionaltrades.Ifthestrike

price was substantially out-of-the-money then we needtheunderlyingstock tomovesubstantially. In thiscaseourlong calendar is not only adirectional trade but it needssubstantialvolatilityaswell.

■DirectionalitySince a long calendar spreaddoesbestwiththeunderlyingstockatthestrikepriceoftheoptions at the expiration ofthe front month, a longcalendar has significantdirectionality. We couldestablish a long calendarspread to satisfy nearly anymarket outlook. The furtherthestrikepriceisfromat-the-money themoreweneed the

market to move in order toachieve maximum profit. Ifthe strike is close to at-the-money, as with the 33 strikecall calendar we looked at,we don’t need the market tomove in order to generate aprofit at the first expiration.Infact,wewantORCLtonotmove. But the 34 strike wasfurther from at themoney, itwas 3.7 percent out-of-the-money, so it needs ORCLstock tomove upward to get

to breakeven since Juneexpiration catches earningsand May does not. Thatbreakeven is about 33.08.What would happen if weselected strike prices for ourcallcalendarspreadthatwereeven further out-of-the-money? Then we’d createcalendar spreads that wouldcost less to initiate, thatwould potentially generategreater profit, that wouldrequire more movement to

breakeven, and that wouldrequire more movement toachieve that maximumpotential profit. Let’s look atthe34callcalendaraswellasthe 36 and 38 strike callcalendarstoseethedifferencegenerated by moving furtherout-of-the-money. You cansee all three hypotheticalpayoffsinFigure6.7.

Figure6.7CallCalendarSpreadsandDirectionality

As the strike price of thecalendar spread increases thedirectionality of the spreadincreases; the lowerbreakeven point rises, theupper breakeven point rises,and the point of maximumprofit rises—this point ofmaximum profit is also thestrike price of the calendarspread. The same is true of

put calendars. As the strikeprice of the call calendarspread decreases the upperbreakeven point decreases,the lower breakeven pointdecreases and the point ofmaximum profit (the strikeprice)decreases.YoucanseethesepointsforourthreecallcalendarsinTable6.8.

Table6.8ThreeOut-of-the-MoneyCallCalendarSpreads

Lower

BreakevenPoint

NecessaryMovetoReachLower

BreakevenPoint

34strikecall

calendar

33.08 0.9%

36strike 33.63 2.6%

callcalendar

38strikecall

calendar

33.65 2.7%

We can use the tools atwww.OptionMath.com tofigureoutthelikelihoodsthateach of these call calendarswill be profitable. We findthat the likelihood of the 34


call calendar being profitableis38percent.For the36callcalendar, it’s 29 percent. Forthe 38 call calendar it’s 38percent. Don’t be misled bythe 38 call calendar; the factthat those options were veryinexpensive in absoluteterms, 0.01 and 0.02, meanswe should be careful aboutwhat any option model tellsus as all models tend togenerate strange results forvery inexpensive options.

Andthere’snoguaranteethatwe could buy this 38 strikecall calendar for the 0.01difference between the twonominal option prices. If theMay 38 call market isactually no bid/0.01 ask andthe June 38 call market isactually 0.02 bid/0.03 askthen the best we could do isto just buy the June 38 calloutright at 0.03. That resultwouldverydifferentfromthecall calendar we’ve been

examining.

■CatalystsThe ORCL earnings releasewe’re focused on occurs justa few days prior to the Juneoptions expiration. Thatmeans the June and JulyoptionswillparticipateintheresultingmovewhiletheMayoptions will have alreadyexpired when that earningsreport is released. Users ofcalendar spreads have to beaware of catalysts and how

they might impact the laterexpiration but not the firstexpiration of their calendarspread. Catalysts can includeearnings releases, dividends,newproduct releases, releaseofclinicaltrialdataandmanyothertypesofmarketmovingevents.The fact that the catalystdoesn’t impact the frontexpirationmeansthatthesortof differential erosion we’re

hoping to capture may notexist. In Chapter 2, wediscussed differential erosionand how we’re generallybetter off selling a series ofshorter-dated options ratherthan a single longer-datedoption. Let’s look at our calloptions on ORCL and see ifthis holds when oneexpirationcatchesthecatalystandtheotherdoesn’tcatchit.Remember that the Mayoptionshad about20days to

expiration, the June optionshad about 50 days toexpiration and the Julyoptionshad about80days toexpiration.We can see theserelationshipsinTable6.9.

Table6.9ORCLOptionPricesandCatalysts

May34Callwith

WhatJune34CallPrice Actual

20DaystoExpiration(MarketPrice)

WouldBeifItWereaFunctionofMayCallPrice

June34CallPrice

0.110.275(0.11×(50/20))

0.52

Obviously, an importantcatalyst like an earnings

release impacts therelationship between optionswith an expiration thatcatches the catalyst andoptions that don’t catch thecatalyst. That doesn’t meanyoushouldn’tusethesetypesofcalendarspreads;itsimplymeansthattheywon’tactlikeothercalendarspreads.

■TheSuperCalendarSoyour longcalendarspreadhas worked; the front optionis going to expire worthlessand you’ll be left long thebackmonthoption.Theprofiton the expiring option isgreater than the loss on thebackmonth option thatwe’llbe left long.But ifyourgoalwastocapturethedifferentialerosion rather than setyourself up for a catalyst,

then you can’t simply staylong that naked back monthoption. It will continue toerode away, and since it’snowcloser toexpiration thanit was when you initiallyboughtit,itwillstarttoerodemore quickly. Erosion madeour calendar spreadprofitable.Erosionoftheloneremaining option can makeour calendar spreadultimately unprofitable if wedon’t do something. We

could sell the remainingoptionand takeourprofit,orwe could add to our winnerbyturningourcalendarintoasuper calendar by sellinganother option, identical totheremainingoptionbutwitha shorter time to expiration.For example, if our initialcalendar had us long anoption with 120 days toexpirationandshortanoptionwith 30 days to expiration,then when that front option

expireswe’llbe leftwithourlong option, which now has90 days to expiration. If wesell anewoption identical tothe 90-day option but withonly 30 days to expiration,we’ll have a new calendarspread and we’ll haveexecuted a super calendar.Table 6.10 shows how wemight execute a super callcalendarspread.

Table6.10ASuperCall

CalendarSpreadTheMarch/June50StrikeCallCalendarWhen

Initiated

StockPrice 49.00March50StrikeCallOption 1.25

June50StrikeCallOption 3.00

CostoftheCallCalendarSpread 1.75

AttheMarchExpiration

StockPrice 49.00March50StrikeCallOption 0.00


ValueoftheCallCalendarSpread 2.55

UnrealizedProfit 0.80AfterSellingthe

April50StrikeCall

OptiontoCreateaSuperCalendar

StockPrice 49.00April50StrikeCall

Option 1.25


CostoftheNewCalendarSpread 1.30

AttheAprilExpiration

StockPrice 49.00April50StrikeCall

Option 0.00


ValueoftheCallCalendarSpread 1.95

UnrealizedProfit 0.65TotalProfit(FromBothCalendarSpreads)

1.45

We’ve turned our initial callcalendar spread, theMarch/June call calendar,into a super calendar byselling anApril call after theMarch call has expiredworthless.OncetheAprilcallexpires,wecando thisagainby selling a May 50 strikecall.Note that the profit from thesecond calendar, theApril/June calendar, is less

than the profit from the firstcalendar. That’s because thedifference in daily erosion isdecreasingastheJuneoptiongets closer to expiration andstarts to erodemore quickly.If we did this again andcreated the May/June callcalendar, we’d find that theprofitwoulddecreaseagain.A super calendar is a greatway to sensibly add to awinner, since the risk for a

long calendar is limited. It’salso a good way to rehab acalendar spread that didn’twork out because the frontmonth option was in-the-money at expiration. Byclosing that expiring optionand executed a new optionthatexpiresbeforethelonger-dated option we’ve reset thefavorableerosion.

CalendarSpreadCheatSheet

LongCallCalendarSpread

Description

Longlonger-datedcall,short

shorter-dated

callwithsamestrike

Example

ATM=100Long105

callexpiringJune

Short105callexpiring

MarchPayorCollect

Premium

Pay


Then


MarketMovement

++

IncreaseinImpliedVolatilitywithout

++

MarketMovement


Toomanyassumptionsrequired

MaximumRisk

Costofthespread

MaximumProfit

Theoreticallyunlimited

BreakevenPoints

Toomanyassumptionsrequired

CHAPTER7

Straddles

A straddle isn’t an optionspread; rather it’s an option

combination. It’s acombination of optionsbecause a straddle buys bothacallandaputwiththesamestrike price and expiration orsells both a call and a putwiththesamestrikepriceandexpiration.Thestrikepriceisusually the strike pricenearesttoat-the-money.If you thought that a stockwasgoingtoexperienceabigmove you’d buy options to

take advantage of thatmove.If you thought themovewasgoingtobeupwardyou’dbuycall options. If you thoughtthe move was going to bedownward you’d buy putoptions. What if you knewthere was a big catalystimminentsuchasanearningsrelease,courtverdict,orFoodand Drug Administrationdecision andyou thought thecatalystwould result inabigmove,butyoudidn’tknowin

which direction? You couldbuy both a call and a put.Thatisalongstraddle.If you thought a stock wasnotgoingtomoveverymuch,then you might sell options.You could sell a put andcollect, and ultimately keep,most or all of the premiumreceivedwhen theputoptionexpired as long as the stockdidn’t drop too much. Youcould sell a call and collect,

and ultimately keep, most orall of the premium receivedwhen the call option expiredas long as the stock didn’trallytoomuch.Oryoucouldsellbothacallandaputandkeep most of the premiumreceived as long as the stockdidn’t move too much ineither direction. It would betough to keep absolutely allofthepremiumreceivedfromselling a straddle, as thatwould require the underlying

stocktoclosepreciselyatthestrikepriceof theoptionsonexpiration,butwe’dkeep thevastmajorityof thepremiumreceived if the stock closednear the strike price onexpiration.A long straddle is a definedrisk strategy with unlimitedprofit potential. Theunderlyingstockcanmoveineither direction butsubstantial volatility is

requiredforalongstraddletobeprofitable.A short straddle is a definedmaximumprofitstrategywithunlimitedlosspotential if theunderlying stock movesenough in either direction.Ashort straddle would beexecutedonlyifyouassumedtherewouldbelittlevolatilityforthetermofthestraddle.Just like a politician who“straddles the fence” in an

effort to be on both sides ofan issue simultaneously, along option straddle is bothbullish and bearish at thesame time. A long straddleneeds the stock to move. Inmostcases,itneedsthestockto move a bunch, in somecases it needs the stock tomove a whole bunch. Thisneed for the stock to reallymoveisthepricepaidfornothaving to get the directioncorrect.

This need for the stock toreally move, that is, to bereally volatile, is why we’dsay a long straddle is longvolatility, the buyer hasbought volatility in the formof both options; if impliedvolatility increasesimmediately after buying thestraddle, then the trade willshow an unrealized profit.However,ashortstraddleisashort volatility trade. Wewant as little volatility as

possible, since a straddle isusually struck very close toat-the-money. We’ll discussthegreeksofstraddleslaterinthis chapter, and you canalways calculate the greeksfor your straddle atwww.OptionMath.comorseethe most important onesexplainedinsimplerlanguagein the Cheat Sheet thatfollows this and everychapter, but the importanttakeaway is that volatility is


critically important for astraddle. A long straddledemands it; a short straddleabhorsit.Soanoptionstraddleincludesthepurchase(orsale)ofbothacalloptionandaputoptionwiththesamestrikepriceandexpiration date. Since youdon’t know the direction ofthe ultimate move or can’tdecide which you think ismost likely and instead buy

bothaputandacall,buyingastraddle is the bluntinstrument of the optioncombinationworld.For example, if abiotechnology or drugcompany was about to learnthe fate of their problematicbut potentially lucrative newdrug, then the stock wouldlikely experience a bigmoveonce the news was released.If the drug is approved, then

themovewouldbeupward.Ifthe drug is denied approval,then the move would bedownward.Figure 7.1 shows how youmight buy a straddle on abiotechnology stock whichwastradingat20.95.

Figure7.1AStraddle

The underlying stock was at20.95, so the 21 strike wasthe at-the-money strike andstraddles usually use thestrike price that is closest toat-the-money. You couldstrike a straddle far from at-the-money but that straddlehas substantial directionalityand since one of theconstituent options will be

deeply in-the-money, thebid/ask spread will createproblemsfortheexecutionofany deeply in-the-moneystraddle. We’ll focus on at-the-money straddles. In thiscase, we would execute along straddle by buying oneof the 21 strike calls at 2.40and buying one of the 21strike puts at 2.45. Thestraddlewouldcosta totalof4.85. As we’ve said, thisunderlying stock is a

biotechnology stock, whichtendtobeveryvolatile,sotheoptions are very expensive;thestraddlecost23percentofthepriceofthestock.We’re long the straddle andlong straddles have limitedrisk. As with nearly everylong spread or combination,that risk is the cost of thespreadorcombination.Inthiscase, that’s 4.85. Longstraddles also have unlimited

profitpotential,at least if thestock rallies. The profitpotential to the downside issubstantial but is limited bythe fact that the stock pricecan’t drop below zero. If thestock does go to zero, thenthe profit is 16.15 (21.00 –4.85), but the stock couldrallyindefinitelysothere’snoway to calculate themaximum profit if the stockrallies.Butgoingtozeroandrallying to infinity are both

pretty unlikely outcomes.What is theprofit or loss forour straddle if the stockmoves in a way that’s morereasonable? Let’s calculatethose numbers using the sortof profit and loss table thatwe’ve used before. We’llrevisitthissortoftable,sincethis is the first combinationwe’ve discussed with bothputs and calls.And note thatwe’re figuring the profit orloss for our straddle as we

should,asthecombinationofa long call and a long put.YoucanseethisinTable7.1.

Table7.1ProfitandLossforOurLongStraddle

StockPriceatOption

Expiration



Expiration

15 0.00 –2.4016 0.00 –2.40

17 0.00 –2.4018 0.00 –2.4019 0.00 –2.4020 0.00 –2.4021 0.00 –2.4022 1.00 –1.4023 2.00 –0.40

24 3.00 0.6025 4.00 1.6026 5.00 2.60

27 6.00 3.60

As we’ve seen previously,nearly every option spreadrealizes its maximum profitwhen theunderlying isat theshort strike at expiration andrealizes its maximum losswhen theunderlying isat thelong strike at expiration. Astraddle isn’t a spread, it’s acombination but the sameguideline holds, a long

straddle experiences itsgreatest loss, the price paidfor the straddle, when theunderlying is at the strikeprice of the options atexpiration. In a long straddlethere’s no short option, thereisnothingbutlongoptionssothe damage done if theunderlying is at the longstrike at expiration can besevere. You can see this inFigure7.2.

Figure7.2ThePayoffforOurLong21StrikeStraddle

Our 21 strike straddle losesthe entire 4.85 if theunderlying stock is atprecisely 21.00 at optionexpiration.Beingatprecisely21.00 at expiration is prettyunlikely so let’s see how farfrom21.00theunderlyinghastobeinorderforthisstraddleto at least break even atexpiration.

Just how far does a straddlehave to move in order tobreakevenandhowarethosebreakeven points calculated?The downside breakeven isthestrikepriceminusthecostof the straddle. The upsidebreakeven is the strike priceplus the cost of the straddle.At both of those points thevalue of the straddle atexpiration is exactly equal totheamountoriginallypaidforit. You can see these

breakeven points in Figure7.3.

Figure7.3WhereOurStraddleBreaksEven

The breakeven points makesense.At25.85, the21strikeputwillexpireworthless,butthe 21 strike call will beworth4.85.Sincethat’swhatwe paid for our straddle,we’ll break even. At 16.15,the 21 call will expireworthless, but the 21 strikeputwillbeworth4.85.Sincethat’s what we paid for our

straddle,we’llbreakeven.InbothFigure7.2andFigure7.3 you can see the longstraddle as the sum of theparts, as the sum of the longcall and the long put. InFigure 7.3, you can also seethat the downside breakevenis 16.15 (21.00 – 4.85) andtheupsidebreakevenis25.85(21.00+4.85).Betweenthesetwo breakeven points, 16.15and 25.85, the straddle loses

money. That’s a huge range,9.70 for a $21 stock, whereour straddle will beunprofitable. This straddle iscertainlymoreexpensivethanmost because the underlyingbiotechnology stock ispotentially volatile and theoptions are displaying a highimplied volatility but thisstockwouldhavetomoveupor down about 23 percent inordertosimplybreakeven.Along straddle is the blunt

instrument of optionweapons,butit’salsoaprettyexpensiveweapontowield.Let’s look at a morereasonablypricedstraddlebutagain, let’smake certain thatit’s a market situation whenwemight think themarket isreally going to move but wedon’t have an opinion aboutdirection.The SPY option prices inFigure 7.4 were observed

during the morning of a daywhen an important FederalReserve announcement wasexpected. The announcementcould have been bullish orbearish.

Figure7.4BuyingaSPYStraddlebeforeaFedMeeting

These options were due toexpire in just three days andtheimpliedvolatilityofSPY,even though there was amajor event due, was muchlower than the impliedvolatility of thebiotechnology stock welookedatearlier.Youcanusethe tools atwww.OptionMath.com to


calculate these impliedvolatilities.If we bought this straddlewe’dbuyboththe170callat1.31and the170putat1.25.The straddle would cost atotal of 2.56. As with allstraddles, the lowerbreakeven point is the strikeprice minus the cost of thestraddle or 167.44 (170.00 –2.56).Theupperbreakevenisthe strike price plus the cost

of the straddle or 172.56(170.00+2.56).Thisstraddlewouldrequireamoveofonlyabout 1.5 percent to breakeven. You can see this inFigure7.5.

Figure7.5BuyingaStraddleInSPY

This long straddle profit andloss chart shows the straddleas a combination of a longcall and long put for aspecific reason. The straddlepayoff moves up in bothdirections at a 45-degreeanglefromthemaximumlossof2.56.Similarly, thepayofffor each individual optionmoves up at a 45-degree

anglefromitsmaximumloss.But the payoff for eachindividual option, once theindividual option value startsto move higher, will alwaysbe greater than that of thestraddle because the straddlehas to pay for the otheroption, the option that’s notvaluable at expiration. If thelong call alone has value atexpiration the straddle stillhas to pay for the worthlessput, if the longputalonehas

value at expiration thestraddle still has to pay fortheworthlesscall.Thestraddlewillneverbeasprofitable as the individualoption that has value atexpiration. Of course, with astraddleyoudon’thavetogetthedirectioncorrectbutwithan individual option, whileyouhave to get the directionright, you’re not paying foranoption thatwillultimately

be worthless and onecertaintywitha longstraddletakentoexpirationisthatoneof the options will beworthless.The lower breakeven pointforthestraddlewillalwaysbelower than the breakeven forthe put alone by the cost ofthecall.Theupperbreakevenpoint for the straddle willalways be higher than thebreakeven for the call alone

by the cost of the put. Theprofit or loss of the straddlewill always be below that oftheindividualputbythecostofthecalliftheunderlyingisbelow the strike price of thestraddle at expiration. In thiscasewe’relongastraddle,sothe breakeven points beingfurther away is a bad thing.Laterwe’lldiscussshortingastraddle and in that case thebreakeven points beingfurther away is to our

advantage.Similarly, the upperbreakeven point for thestraddlewillalwaysbehigherthan the breakeven for thecallbythecostoftheput;theunderlying has to movehigher for the straddle to beprofitable. The profit or lossofthestraddlewillalwaysbebelow that of the individualcall by the cost of the put.You can see this in Figure

Figure7.6OurLongStraddleinSPYversustheConstituentOptions

■TheShortStraddleIf the long straddle has thepotential forunlimitedprofit,then the short straddle musthave the potential forunlimited loss, and it does.But that doesn’t mean youshouldneversellastraddle.Ifthe straddle has to move alongwaytogettobreakeven,the biotechnology stock hadtomove 23 percent to get tobreakeven, then maybe

sellingastraddle isn’tsuchacrazy idea. We’ll discussspecific situations when wemight sell a straddle a littlelater in this chapter but first,let’s look at Figure 7.7 andthe numbers generated inselling a straddle. Theseoption prices on DeutscheBank (DB) were recentlyobserved.We could sell this DeutscheBank straddle at 3.00.

DeutscheBankwasobviouslyverycloseto49.00.Weknowthis because the call and putprices are nearly identical. Ifthe underlying stock wasbelow 49.00 then the putwouldbeworthmorethanthecall. If the underlying stockwasabove49.00thenthecallwouldbeworthmorethantheput.What does the payoff chartfor this short straddle look

like? We see that in Figure7.8.

Figure7.7SellingaStraddleinDeutscheBank(DB)

Figure7.8AShortStraddleinDeutscheBank(DB)

The lower breakeven for thisshortstraddle is46.00(49.00– 3.00) and the upperbreakeven for this shortstraddle is 52.00 (49.00 +3.00). If theunderlyingstockisbetweenthosetwolevelsatexpiration then this shortstraddlewill be profitable. Ifit’s outside that range, thenthe short straddle will lose

money because the in-the-money option we’re shortwill be worth more than thetotalpremiumcollected.Just as a long straddle ishindered by the fact that theprofitable option has to payfor the unprofitable option,theshortstraddleishelpedbythe fact that the moreprofitable option, whichexpires worthless, can offsetsome or all of the loss, if

there is a loss, on the optionthat expires in-the-money.And remember, unless theunderlying stock closespreciselyat-the-money,49.00inthiscase,atexpiration,oneofthelegsofourstraddle,nomatter whether long thestraddleor short the straddle,willbein-the-money.Forourshort straddle this in-the-money option might still beprofitable for us; it might bein-the-moneyatexpirationby

anamountthatislessthanthepremium originally receivedfor selling it. For example,given the short straddle onDeutsche Bank (DB), if thestockisat48.50atexpirationthen the call is going toexpire worthless and will beprofitable by the full 1.50collected.But theputwillbeprofitable for us too, wereceived1.50forsellingitbutitwillonlycost0.50tocloseout at expiration.One option

expires worthless, the otherwasprofitableeven though itexpiredin-the-money,andtheshort straddle was profitableby2.50intotal.The fact that at least oneoption comprising thestraddlewillexpireworthlessmeans that the lowerbreakevenforashortstraddleis always below thebreakeven for a short put.That is, thestockhas todrop

farthertogettothestraddle’slowerbreakeventhanithastodrop to get to the short put’sbreakeven; the stock has todrop farther before thestraddle starts losing moneythan the stock has to dropbefore the short put alonestarts losing money. Theupper breakeven for a shortstraddle is always above thebreakevenforashortcall;thestock has to rally further toget to the straddle’s upper

breakeven than ithas to rallyto get to the short call’sbreakeven. You can see thisinFigure7.9.

Figure7.9OurShortStraddleinDeutscheBank(DB)

■LikelihoodsWe’ve seen where thebreakevensareforastraddle,whetherit’slongorshort,andwe know that the lowerbreakeven point is the strikeprice minus the price of thestraddle while the upperbreakeven point is the strikeprice plus the price of thestraddle.What is the likelihood of at

least reaching one of thosebreakevens? That’s thelikelihoodthattheunderlyingstock is below the lowerbreakevenpointorabove theupper breakeven point. Weknow that the delta of anoptionisthelikelihoodthatitwill be in-the-money atexpiration so let’s use thetools atwww.OptionMath.com tocalculate the delta of ahypotheticalputwithastrike


price equal to that lowerbreakeven and the delta of ahypotheticalcallwithastrikeprice equal to that upperbreakeven.Adding those twolikelihoods together is thelikelihood that the shortstraddlewilllosemoney.Thedeltaof the46strikeputwas20. And the delta of that 52call? That was 23. Thatmeans the odds of theunderlyingstockbeingbelowthelowerbreakevenorabove

the upper breakeven is 43percent. Since above thatupperbreakevenorbelowthelower breakeven means thestraddle loses money for theseller, that 43 percent is thelikelihood this straddle willlose money. As an aside,some are probably askingwhythedeltaoftheputisoflower magnitude than thedelta of the call if they’reboth equidistant from at-the-money. It’s because option

models don’t think they’reequidistant. They may bothbe 3.00 from at-the-moneybut,tooversimplify,3.00isabiggerportionof46thanitisof 52 making a move to 46lesslikelythanamoveto52.This relationship isn’talwaysthe case. Puts may havehigherdeltas thanequidistantcallsifoptionskewresultsinthe puts displaying a higherimplied volatility than thecalls.

So the likelihood of thisstraddle being beyond thosebreakevensis43percent.Thesame would be true if wewere long this straddle, theodds of the underlying beingbeyond the breakevens areagnostic as to whether we’relongorshortthestraddle,theonlythingthatmattersisthatthe long straddle wants andneedstheunderlyingtomovebeyond those breakevenswhiletheshortstraddlewants

and needs the underlying tonotmoveandtostaybetweenthosebreakevens.Let’sfigurethe same likelihood for theother straddleswe’vealreadylookedatandsomeadditionalstraddles on otherunderlyings. We see theselikelihoodsinTable7.2.

Table7.2BreakevenPointsfortheStraddlesWe’veExaminedandSomeOthers

StraddleLower

BreakevenPoint

DeltaoftheLowerBreakevenPoint

Biotechstock21strike(60daysto

expiration)

16.15

SPY170strike(3days 167.44

toexpiration)Internationalbank49strike(30daysto

expiration)

46.00

Troubledtechnologycompany8strike(38daysto

expiration)

6.71

Globalrestaurantchain94strike(23daysto

expiration)

90.58

Wow, the odds of theunderlyingstocksgettingpasta breakeven is always veryclose to 43 percent. One ofthose straddles only had 3daystoexpiration,onehad60

days to expiration and onewas inbetweenwith30daysto expiration. The biotechstockhadaveryhighimpliedvolatility,asthosestockstendto display. SPY had amoderate implied volatility.Is there something about astraddle that makes that 43percent value consistent?Yes.As impliedvolatilitygoesupthe option price goes up as

wellbut anout-of-the-moneyoption (like our theoreticaloptions with strike pricesequaltothebreakevenprices)sees its delta increase asimplied volatility increase,everythingelseremainingthesame.Weseethattheoddsofalongstraddlegetting tooneof thebreakeven points are prettyslim; they’re less than 50percent.Andjustgettingback

to breakeven doesn’t do usmuch good; we’re tradingoptions tomakemoneyor toreducerisk,nottobreakeven,and a long straddle doesn’treduce our risk very much.Let’s do the same sort ofanalysisusingoptiondelta tofind the likelihood of a longstraddlemaking a reasonableamount of money, sayearningwhatwewererisking.WeseethisinFigure7.10.

Figure7.10DoublingOurMoneywithaStraddleinSPY

WeseeinFigure7.10thattheunderlying has to drop to164.88 or rally to 175.12 atexpiration in order togenerate aprofit equal to thecost—and the risk—of thestraddle of 2.56.What is thelikelihoodofgettingtoeitherof those “doubling points”?The delta of the hypotheticalput with a strike price of

164.88was5(theoddsoftheunderlying being below164.88 at expiration were 5percent). The delta of thehypotheticalcallwithastrikeprice of 175.12 was 6 (theodds of the underlying beingabove 175.12 were 6percent).Thatmeanstheoddsof at least earning what wewere risking was only 11percent (5 percent + 6percent).Notverygoododds.

Butthemaximumprofitfroma long straddle is huge if thestockdropsandinfiniteifthestock rallies.Sowhat are theodds of hitting a home runandgeneratingareturnthatisat least 5 times what werisked?What are theoddsofour trade generating a profitofatleast12.80?Thatwouldrequire SPY to be below157.20 or above 182.80 atoption expiration. If we dothe same delta calculations,

wefindthat theoddsofSPYbeing below 157.20 are0.00130percent.TheoddsofSPY’s being above 182.80are 0.00587 percent. Theodds of this straddlegeneratingareturnof5timesourinitialinvestmentof2.56,a return of at least 12.80, is0.00717 percent, meaningwe’dexpecttoreturn5timesour investment about onceevery14,000timesweputthetradeon.Thatsaid,don’trush

outandstartsellingstraddles.Asoption traders like to say,that’s agreatway toget richslowly and go broke quicklybecauseamovelikethatwilloccur and the option mathsays they occur morefrequently than standardoption models predict. So,what is a logical way to sellstraddles?

■ Selling CoveredStraddlesBuying a straddle is a toughwaytomakemoney,theoddsof theunderlying justgettingtooneofthebreakevenpointsis low. The odds of makingmoney are even lower. Theodds of making a lot ofmoney are lower still. Butblindly selling straddles isoneofthoseoptionstrategies

that works until it doesn’t,andthenitreallygetsugly.Isthere a good way to sellstraddles? There is: sellingcoveredstraddles.In selling a covered call weown stock and sell callsagainst that stock. The riskinherent in the short call iscovered by the ownership ofthe stock. Even if the stockappreciates infinitely the riskfor our short call is covered

because we own the stock.Wemayregretsellingthecallorwemaysellthestockataneffective price that is higherthanthestockevertradedbuteven if that effective price islowerthanthecurrentmarketprice, we know that we’llhave effectively sold ourstock at a price higher thanwas available when we soldthecall.Andifthestockgoesdown or sideways, then wepocket the call premium

receivedandwestillownourstock.In selling a covered put, thatis a put that is covered byenoughcash tobuy thestockatthestrikepriceifit’sputtous, we collect the premiumthatanyoptionsellercollects.If the stock moves sidewaysor up, and even if it movesdown a little if our put wasslightly out-of-the-money atinitiation,wewon’t have the

stockputtous,yetwe’llkeepthe premium received andstill have all our cash. If thestock moves down enough,thenwe’llhave the stockputto us but wemight buy it atan effective price lower thanthestockeveractuallytraded.And if we regret buying thestock because the effectivepurchase price is higher thanthe current market price?Well,we bought the stock atan effective price that is

lower than was availablewhenwesoldtheput.Whatifweweretocombineacovered call and a coveredputsuch that thecallandputhadthesamestrikepriceandexpiration? That would be acoveredstraddle.You might own stock thatyou think is fairlyvaluedbutif thepricewentupyou’dbewillingtosellsomeandiftheprice went down you’d be

willing to buy more becauseyoumaynotownasmuchasyou’dlike.Onewaytomakecertainyoudooneofthoseisto sell a covered straddle.Howcanwebe certainwe’lldo one of those? Becauseunless the underlying stockcloses precisely at the strikeprice, to the penny, onexpiration,oneoftheoptionsis going to be in-the-moneyand that option will beexercised. If the call is

exercised,we’regoingtosellourstockataneffectivepricehigher than the strike priceandhigher thanwhere itwaswhenwesold the straddle. Ifthe put is exercised, we’regoing to buy more of thestock at an effective pricelower than the strike priceand lower than were it waswhen we sold the straddle.And if the underlying stockdoes the very unlikely andcloses precisely at the strike

price at expiration? Thenwekeep all of that optionpremium and our stockposition is unchanged. Let’slook at an example of acovered straddle in Ford (F),whichwasat15.00.YoucanseeachartofFordstockoverthe previous 12 months inFigure7.11.Noticethatit’sinthe middle of the range forthatperiod.

Figure7.11StockChartofFordforOurCoveredStraddle

If we owned Ford stock, wemight think that we’d bewilling to sell it if we couldsell at an effective price of15.80orsosincethat’sabouta5percentpremiumtowherethesharesaretradingnowbutwe might be willing to buymore if we could pay aneffectivepriceof14.20or sosincethat’sabouta5percent

discount to where shares aretrading now. Figure 7.12shows the options that wemight use to construct acoveredstraddle.

Figure7.12SellingaCoveredStraddleinFord

If we sell this 15 strikecoveredstraddle,we’llcollecta totalof0.86,which isoursto keep. Since we’re short a15strikecoveredcall,ifFordis above 15.00 at optionexpiration, we’re going tohave our 100 shares calledawayandwe’llbepaid15.00foreachof them,sincethat’sthe strike price of the call

we’reshort.Sincewe’reshorta 15 strike covered put, ifFord stock is below 15.00 atoption expiration, we’regoing to have another 100shares put to us, and we’llpay 15.00 for them, sincethat’s the strike price of theputwe’reshort.Sowe’llreceive15.00forourshares ifwe’re forced to sellthem or we’ll pay 15.00 formoresharesifwe’reforcedto

buy them, but our effectiveprice is aided by the 0.86 instraddle premiumwe collect.Thatmeansoureffectivesaleprice would be 15.86 or oureffective purchase pricewould be 14.14. Figure 7.13shows the payoff atexpirationforthisposition.

Figure7.13PayoffforaCoveredStraddleinFord

A covered straddle is similartoacoveredcall. In fact, it’sacoveredcallplusacoveredput, so that makes sense.Since a covered put isidentical toacoveredcall,aswe discussed inChapter 5, acoveredstraddleisreallyliketwocoveredcalls.

StraddleCheatSheet

LongStraddle

Description

LongATMcall,longATMput

ATM=100Long100

Example CallLong100

Put

PayorCollect

Premium

Pay


Passageof

TimewithoutMarket

Movement

−−−−−


Movement

+++++

PayoffThumbnail

Chart

MaximumRisk

Costofthestraddle

MaximumProfit


BreakevenPoints

Strikeprice±Costofthestraddle

CHAPTER8

Strangles

When we discussedstraddles in Chapter 7, we

described an optioncombination created bybuying(orselling)aputandacall with the same strikeprice, usually the at-the-money strike price, and withthesameexpiration.Straddlesare pretty expensive becausetoexecutealongstraddleyoubuythetwooptionsthathavethe greatest amount of timevalue. If you’re selling astraddle, that’s good news;you’re selling the two most

expensiveoptions,intermsoftime value, in that expirationmonth, but you’re prettymuch assured of having oneof your short options expirein-the-money,meaningyou’llhaveapositioninthestock,aposition that you might notwant.Ifyouwantedtomakemoneyif the underlying stockexperienced a big move butdidn’twanttospendasmuch

asalongstraddlemightcost,or if you wanted even moreleverage than a straddle willgenerate, thenyou couldbuyout-of-the-money options;you could buy an out-of-the-money call,meaning that thestrike price of the call isabovethecurrentpriceoftheunderlying stock, and youcould buy an out-of-the-money put, meaning that thestrike price of the put isbelowthecurrentpriceofthe

underlying stock. Thiscombinationofanout-of-the-money call and out-of-the-money put with the sameexpiration date is a strangle.When buying both optionswe’re buying the strangle,when selling both optionswe’resellingthestrangle.A long strangle is a definedrisk strategy that you mightuse when you expect asubstantialmove in the price

oftheunderlyingstockbythedate of the options’expiration; the risk is limitedto the total amount ofpremiumpaid.Unlikebuyingan outright option or avertical spread, buying astrangledoesn’t requireus toget the direction correct. Abig move either up or downwill generate a profit for along strangle.But bigmoveslike the kind needed for astrangle to be profitable are

rare.Strangles can be much lessexpensive than straddles, andif options are substantiallyout-of-the-money, then ourstrangle will cost a tinyfraction of what a straddlemight cost. Like a straddle,we don’t have to get thedirectioncorrect forour longstrangle to be profitable, butaswithastraddle,thatcomesatacost.Inalongstrangle,at

least one of our options willexpire worthless, and if wedon’tseeabigenoughmove,then both may expireworthless, meaning we lostall the premium we paid forour strangle. A long strangleisablunt instrumentbecausewe don’t have to get thedirectioncorrectbutitcanbea low cost, on an absolutebasis,bluntinstrument.Conversely, a short strangle

has a high likelihood ofgenerating a profit, but themaximum potential profit isthe total amount of optionpremium received and themaximum potential loss istheoretically unlimited if theunderlying stock were torally.Themaximumpotentialloss if thestockweretodropislimitedonlybythefactthatthe price of the stock can’tdropbelowzero.

A long strangle is a highlyleveraged trade in that arelatively small amount ofmoney spent to buy thestrangle can result in profitsthat are many times the costofthetrade.Butthatleveragecomes at a cost—thelikelihoodofastranglebeingprofitable is small. Thelikelihoodofastranglebeingveryprofitableisverysmall.Let’slookatsomeoptionson

astockthatmightexperiencea big move, Blackberry(BBRY). At the time, it wasthoughtthatBlackberrymightrally substantially if theycould agree to a strategicpartnership with anothersmartphonemaker,anditwasthought that BBRY coulddrop substantially if theirbusiness continued todeteriorate or if the nextearnings release wasdisappointing. BBRY was at

10.49 when these optionprices were observed. Sinceearnings are a potentialcatalyst,we’lllookatoptionsthatcapturethenextearningsannouncement. You can seethisinFigure8.1.

Figure8.1BuyingaStrangleinBlackberry(BBRY)

There are seven strike pricesinFigure8.1,sowecouldusemany different combinationsto create our strangle. If weused the 10.50 call and the10.50 put, we would havebought a straddle rather thana strangle, since the twooptions would share a strikeprice. Strangles use out-of-the-money options, so we’ll

look at the 9.50/11.50strangle,whichwecouldbuyfor1.21.Thereareotherout-of-the-money options wecould combine to create astrangle. The two optionsmaking up our 9.50/11.50strangle are about equidistantfrom at-the-money, that is,from the current stock priceof10.49.There’snorulethatyour strike prices have to beequidistant from at-the-money. Figure 8.2 shows a

bullishstrangleinBBRYthatyou might execute if youthought the company wasgoingtorecoverandthestockwas going to rally. Noticethat this bullish strangle costprecisely the same 1.21 thatthe original strangle did butnow the upper breakevenpointisonly12.21ratherthantheoriginal12.71.

Figure8.2BuyingaBullishStrangleinBlackberry(BBRY)

Figure 8.3 shows a bearishstrangle in BBRY that youmight execute if you thoughtthe company’s stock pricewasgoing to continue lower.The bearish strangle cost1.28,butonly0.07morethanbothouroriginalstrangleandthe bullish strangle, and thelower breakeven is now8.72versus the original lower

breakevenof8.29.

Figure8.3BuyingaBearishStrangleinBlackberry(BBRY)

If both of the options fromour strangle were in-the-money, buying the 9 strikecall and buying the 12 strikeput, for example, that wouldbe a structure called a guts.Guts are very rarely used,even by professional traders.Onereasonthey’rerareistheimpact of the bid/ask spreadonyourtradeexecutionofin-

the-moneyoptions.WemightthinkBBRYcouldmake a big move, but themarketthinksthataswell,sothese options are veryexpensive in the term thatmatters: implied volatility.Since we’re buying the9.50/11.50strangleinBBRY,we’re limitingour risk to the1.21thatwepay.but that’salot for a $10.50 stock.We’llrealize that maximum loss if

BBRY doesn’t drop below9.50 or rally above 11.50 byexpiration. The strike pricesof the options that make upour long strangle are theinflection points; above andbelowthesestrikeprices,ourlong strangle loses less thanthe maximum possible. Ourpotential profit is essentiallyunlimited if BBRY were torally, although there’s apractical limit to the amountby which BBRY could rally

during the term of ourstrangle. Our potential profitif BBRY were to drop islimited only by the fact thatthe stock can’t drop belowzero. That means ourmaximum potential profit tothedownsideis8.29,whichistheputstrikeprice,9.50,lessthecostof thestrangle.Let’sconnect thedots again to seethe payoff chart for our longBBRY 9.50/11.50 strangle.You can see this in Figure

Figure8.4ThePayoffforOurLong9.50/11.50StrangleinBlackberry(BBRY)

Obviously our long stranglein BBRY needs Blackberrystock tomovea lot,weneedittobeveryvolatile.Weneeda move of nearly 10 percentin either direction to get tooneof those inflectionpointswhere we don’t lose themaximum possible.We needa move of over 20 percent

just to get to breakeven.Weknowwecanuse the toolsatwww.OptionMath.com tocalculate the likelihoods ofthese levels being reached.Let’slookatTable8.1 toseewhatthoselikelihoodsare.

Table8.1ImportantLikelihoodsforOurBBRYStrangle

OutcomeProfitor

Loss

MoveRequired


Reachlower

inflectionpoint(9.50)

–1.21 9.4%

Reachupper


–1.21 9.6%

Reachlower

breakeven 0 21.0%

point(8.29)Reachupper

breakevenpoint(12.71)

0 21.1%

Profittodownsidebyamountrisked(7.08)

1.21 32.5%

Profitto

upsidebyamountrisked(13.92)

1.21 32.7%

Those deltas tell us thatreachingthoseprofitlevelsispretty unlikely and there’s a29percent (100percent–30percent – 41 percent)likelihood that we’ll lose theentire 1.21. That might bebecause we picked strike

prices that were so far fromat-the-money. What if wepicked the strikes that are asclose to at-the-money aspossible? That would be the10/11 strangle and it wouldcost1.58 (0.79 tobuy the11strikecallandanother0.79tobuy the 10 strike put). Let’slookatTable8.2 toseewhatthe outcomes would be forthatstrangle.

Table8.2ImportantOutcomes

foraNarrowerStrangleinBBRY

OutcomeProfitor

Loss

MoveRequired

Reachlower


–1.58 4.7%

Reachupper


–1.58 4.9%

Reachlower


0 19.7%

Reachupper


0 19.9%

Profittodownsidebyamountrisked(6.84)

1.58 34.8%

Profittoupsidebyamountrisked(14.16)

1.58 35.0%

The likelihood of reachingone of the inflection points

such that we don’t lose themaximum amount is greater;the likelihood of losing themaximum amount for thisstrangle is only 15 percent.But the likelihood of gettingall the way to breakeven isonly 44 percent and thelikelihood of generating aprofit at least equal to theamount risked is actuallylower than it was with our9.50/11.50strangle.

The fact that BBRY optionsare soexpensiveand that thestockpriceandhencetheputstrike prices for any stranglewe might consider arerelatively close to zerodistorts some of therelationships forourstrangle.Let’s look at some stranglesonGoogle(GOOG)sincethatstock price, and hence thoseput strikes, are going to be along way from zero, butrather than listing all of the

optionsavailable andpickinga strangle, let’s look at howthe likelihoods change as thestrangle gets wider and thelegs get further from at-the-money. You can see this inFigure8.5.

Figure8.5TheCostofOurGoogleStrangleversustheLikelihoodofBreakingEven

The cost of the strangleincreases as the strangle getsnarrower. This makes sensebecause the width of thestrangleisdecreasingasbothoptions are getting closer toat-the-money, and thus bothoptions are getting moreexpensive. The interestingaspectofthischartisthatthe

odds of having the stranglebreakeven are at theirmaximumwiththestrangleasnarrow as possible and theodds of breaking evendecrease as the width of thestrangle increases, that is, asthestrikesgetfartherfromat-the-money. Unfortunately,thenarroweststranglemaybethe one that’s most likely tobreak even, but it’s also theone that’s most expensive.With GOOG very close to

1,200.00, the 1,195/1,205stranglecostover73.00.Thatmeansasinglestranglewouldrequire an outlay of over$7,300.00. Much of that isdue to the fact that stockswith high absolute prices,such as GOOG at 1,200.00,have high absolute optionprices. But, regardless, thestranglethatisgoingtoenjoythe highest likelihood of atleast breaking even is goingto be the most expensive

strangleinabsoluteterms.The strangle that cost theleast may not require us topay much but the odds of itbreaking even are prettysmall. Sometimes they getreally small, as we saw inTable8.1.So why would anyone buyreally cheap stranglesmeaning strangles that arequiteabitfromat-the-moneyin relative terms? Because

out-of-the-money stranglesmay rarely break even, butthey generate enormousleverage. We’ve looked atstrangles on a really cheapstock in BBRY. We’velookedatstranglesonareallyexpensive stock in GOOG.Let’slookattheleveragethatstrangles can generate, butlet’s look at a reasonablypriced stock or exchange-traded fund (ETF). EEM isthe emerging-market ETF,

and on the day the optionprices in Figure 8.6 wereobserved,EEMwasat39.43.

Figure8.6OptionsforaStrangleinEEM,theEmerging-MarketsETF

Let’s assume that we createsome strangles from theseavailable options and thateach leg is about equidistantfrom the 39.43 at-the-moneyprice. What would eachstrangle cost and what profitor loss would each stranglegenerateifEEMmovedby10percent during the term oftheseoptions?Wesee this in

Table 8.3. Since these arestrangles, the only reason itmatters whether the move isupordownisthatthelegsofour strangles aren’t exactlyequidistantfrom39.43.

Table8.3StranglesandLeverage

Strangle Cost

NetProfitwith10% Leverage

MoveDown

36/43 0.22 0.2936.50/42.50 0.28 0.73

37/42 0.38 1.1337.50/41.50 0.52 1.49

38/41 0.72 1.79

38.50/40.50 1.00 2.0139/40 1.37 2.14

These strangles all exhibit

tremendous leverage. Someofthemcouldreturnasmuchas 3 times the initial cost ofthe trade given a 10 percentmove,andtheydidn’trequiregetting the direction correct.Butaswe’veseenbefore,theoddsof thatsortofmovearereallysmall.

■SellingStranglesSellingstranglesisadefined-profit, unlimited-risk tradethat collects the premiumfrom simultaneously sellingan out-of-the-money call andanout-of-the-moneyput.Since the likelihood of thesort of move required togenerateaprofitforastrangleis so rare, you might thinkthat selling strangles would

be a great way to collectsomeoptionpremiumwithoutmuch risk. Strangles are likestraddles in that professionaloption traders considerconsistently selling stranglesto be a greatway to get richslowlyandgobrokequickly.That’sbecausetheseexpectedlikelihoods of certainoutcomes tend tounderestimate the likelihoodof extreme events over time.That’s due to both the way

markets actually operate andsome of the assumptionsmade by option pricingmodels. This means that thesort of move that wouldbankrupt a strangle seller ismore likely than you think itis and it’s actually morelikely than the delta wecalculate would have usthink. It’s notpossible to seeit coming since these areoften external events that aregeopolitical or financially

systemicinnatureratherthansimplyeconomic.But if you’re committed tosellingastrangle,let’slookatsome options on Facebook(FB) that we might use toconstruct our short strangle.You can see these options inFigure8.7.

Figure8.7SellingaStrangleinFacebook(FB)

Bysellingthis67/70stranglein FB, we collect a total of4.75. That 4.75 is ours tokeep no matter what. Thisshort strangle will profit bythat4.75ifFBisbetweenthetwo strike prices, 67 and 70,at expiration; the lowerbreakeven is 62.25 (67.00 –4.75) and the upperbreakeven is 74.75 (70.00 +

4.75). You can use the toolsat www.OptionMath.com todetermine the deltas for allfourpoints,thetwoinflectionpointsandthetwobreakevenpoints, to know what themarket currently says aboutthe likelihood of getting tothosepoints.Figure 8.8 connects all thedots and shows the payoffchartwe’refamiliarwith.


Figure8.8ThePayoffforOurShortStrangleinFacebook(FB)

You’ll notice that the chartkeeps moving down,representing losses, as theunderlying stock price falls.You’ll also notice that thechart keeps moving down,again representing losses, asthe underlying stock pricerallies. A short strangle hastheoretically unlimited lossesif theunderlyingstockrallies

andthelossifthestockdropsislimitedonlybythefactthatthe underlying stock can’tdrop below zero. Regardless,a short strangle is aspeculation that theunderlying stock willexperience low volatilityduring the term of thestrangle.

■ Selling CoveredStranglesIs thereanyway todefineorlimit the risk of a shortstrangle if we wanted tocollect that premium? Well,you could sell this strangleand simultaneously buy awider strangle and this longstranglewouldlimityourriskbut those options that aresubstantially out-of-the-

money, the options that wemight buy to define our risk,areusuallyveryexpensive inrelative terms. This spread,created by buying onestrangle and selling anothernarrowstrangle,isverymuchlike selling an iron condor,which we’ll discuss more inthe Chapter 12. Is thereanother way to define ourrisk,oratleastbecertainthatwecanbear the risk,withoutbuying those expensive, far

out-of-the-money,options?We could sell a strangle onstock that we already ownand that we’d be willing tosell above the current stockprice while being willing tobuymoreatapricebelowthecurrentstockprice.Wewouldsell an out-of-the-money callthat is covered by ownershipof the underlying stock, andwe would sell an out-of-the-moneyput that iscoveredby

cash equal to the price we’dhavetopayforthestockifitwas put to us at expiration.Thiscombinesacoveredcallandacoveredputandwouldbe a covered strangle. InChapter 7, we looked at acoveredstraddleonFord(F).Let’s look at those sameoption prices and see if wewouldn’t want to sell acoveredstrangleinFord.YoucanseethosepricesinFigure8.9.

Figure8.9SellingACoveredStrangleinford

This strangle only collects0.25 but that’s largely afunctionof the fact thatFordstock at 15.00 is cheap indollar terms.That0.25 is1.7percent of the cost of Fordstock, so it’s not nothing. Ifwe could sell a coveredstrangle each month andprofit by 1.7 percent eachtime,we’dhaveatotalprofit

of22percentattheendoftheyear.As long as Ford is above14.00 and below 16.00 atoptionexpiration, theoptionswe’re short will expireworthless, our potential dutyto deliver our shares or buymore stock will beextinguished, and we canreexamine the fundamentalsto determine our next step.Let’s lookat thepayoffchart

for this covered strangle(Figure8.10).

Figure8.10ThePayoffforOurCoveredStrangleinFord

One of the benefits ofcovered strangles is that wecan collect that optionpremium in exchange forselling our stock at aneffective pay that we’d behappy to receive or forbuying more stock at aneffectivepricewe’dbehappyto pay. With our originalcovered straddle in Ford we

would sell our stock at aneffective price of 15.86 andwe would buy more at aneffectivepriceof14.14.Withour covered strangle oureffective selling price, if ourstock were called away,would be 16.25, and oureffective purchase pricewould be 13.75 if we hadadditional stock put to us.The trade-off for those moreattractive effective prices?We only collect 0.25 in total

option premium versus the0.86 the covered straddlecollected.Butlet’slookattheFord stock chart again andsee how our new effectiveprices look in comparison tothe old effective pricesgenerated by our coveredstraddle. You’ll see this inFigure8.11.

Figure8.11TheStockChartofFordandOurEffectivePrices

If you’d truly be happysellingyourstockat16.25orbuying more at 13.75, thensellingacoveredstrangleandcollecting0.25thatyougettokeep regardless may seemlike a “must do” trade, butanyone who has more stockputtothemorhastheirstockcalled away and regretshavingeitherofthosehappen

because the stock is wellthrough their effective pricehas to be disciplined enoughto remember why theyexecutedthetradeoriginally.

StrangleCheatSheet

]

LongStrangle

Description

LongOTMcall,longOTMput

ATM=

Example 100.00Long105call

Long95putPayorCollect

Premium

Pay


Passageof

TimewithoutMarket

Movement

----


Movement

++++

PayoffThumbnail

Chart

MaximumRisk

Costofthestrangle

MaximumProfit


Callstrike

BreakevenPoints

pricepluscostofthestranglePutstrikepriceminuscostofthestrangle

CHAPTER9

Collars

WesawinChapter4thatacovered call generates

premium thatwe get to keepand that call premiumprovides a little downsideprotection. The downsideprotection isn’t infinite; itstops when the optionpremium received has beenexhausted by the drop in thestock price. What if wewanted or needed moredownside protection? Wemight think instead aboutbuyingaputoptionbutwe’dhave to pay for that put

option. If we sold a coveredcall and then used thepremiumreceivedtobuythatprotective put, we could getthesortofprotectionwewantbut without paying much, ifany, net premium. Thiscombination of long stock, acoveredcall,andalongputisacollar.Thetwooptionswillhavethesameexpirationdatebut will have different strikeprices,withthestrikepriceofthe covered call generally

above at-the-money andcertainly higher than thestrike price of the protectiveput, which will generally bebelow at-the-money (if theoptions had the same strikeprice we would haveconstructeda conversion; seeChapter 13 for more onconversions).Since a collar is short acoveredcall,there’sanupperlimit to how high the

underlying stock can rallybefore getting called away,meaning there’s an upperlimittotheeffectivepricewecould receive for the stockand an upper limit to thevalue of the completecollared position. A collar isalso longaprotectiveput, sothere’s a lower limit on howmuch we would receive forourstockandalowerlimittothe value of the completecollared position. This band,

or collar, of possibleoutcomes with a cap definedby the covered call and afloordefinedbytheputgivestheoptioncollaritsname.A collar is a defined riskstrategyinthatthereisafloorto the effective price we’dcollectforsellingourstockifitwasbelowtheputstrikeatexpiration but it’s also alimited profit strategy in thatthereisacapontheeffective

pricewe’d collect for sellingour stock if itwas above thecallstrikepriceatexpiration.Often,astockiscollaredafterit has shown substantialgains. Collaring newlypurchased shares doesn’tmakemuchsenseforreasonsthat we’ll discuss whendiscussing“zerocost”collars.Figure 9.1 shows someoptions on MGM and onecollarwemightconstruct.

Figure9.1AnOptionCollaronMGM

Since we show seven strikeprices and each strike pricehasbothputsandcalls, thereare dozens of potentialcombinations that wouldresult in a collar. But we’llfocus on those collars thathave the call struck higherthan the put with both beingout-of-the-money when thetrade is initiated. MGM was

at23.20so the tightestcollarwould be the 23/24 collar,meaningwe’dbe longMGMstock, we’d be short a 24strikecoveredcallat0.33andwe’d be long a 23 strikeprotective put at 0.55.Generally,acollarisinitiatedagainst an existing stockposition,sowecouldbelongMGMfromnearlyanyprice,but we’ll use the currentprice, 23.20, for profit andloss purposes, which is

appropriate because that’swhereit’satnow(andyou’reonly long stock from thecurrent price since you’vemade a decision, eitherovertlyornot,tostaylongthestock at the current price),and ifMGMwere trading atanyotherprice, theseoptionswould be trading at otherprices.Theputportionofthiscollar,the 23 strike put, was more

expensive than the 24 strikecall so this collarwould costus money to execute. Wewould only collect 0.33 forselling that covered call, butthe put would cost us 0.55,meaningthecollarwouldcostanetof0.22.Whatwouldtheprofit and loss for this stockandcollarposition look like?You can see that in Figure9.2.

Figure9.2Payoffforthe23/24CollarinMGM

The maximum loss on thecollared stock is 0.42, andthat is realizedwithMGMatorbelowthe23strike.Whileweexperiencealoss,thelongputlimitsthelosstothat0.42no matter how far MGMstock falls. We wouldexperience this loss of 0.42because with MGM at orbelow23.00atexpiration,we

would lose0.20onourstock(23.20 – 23.00) plus 0.22(0.55 – 0.33), the collar costtoexecute.The maximum profit on thecollaredstockpositionis0.58and that is realized withMGM at or above the strikeprice of the covered call, 24in this case. Above that callstrike price, the stock keepsappreciating, but the coveredcall offsets all of that

appreciation.Wewouldmake0.58 becausewewould havemade 0.80 on our stock(24.00–23.20),butthecollarcost0.22.Whatwould the payoff chartlook like if we had selectedoptions that would havegenerated either no netpremium or a slight credit?Wecouldhavesoldthesamecoveredcall,the24strike,for0.33 but gone further out-of-

the-money when selectingwhich put to buy, goingfurther down the availablestrikesuntilwehadreachedaput that could be purchasedforthecallpremiumreceived.Thatfirstputwouldbethe22strike put, which could bepurchased for 0.20, leaving0.13 as a net credit that weget to keep no matter wherethe stock is at expiration.What would that chart looklike?Would the payoff chart

look substantially different?You can see that in Figure9.3.

Figure9.3Payofforthe22/24CollarinMGM

The 22/24 collar isn’tsubstantially different fromthe23/24collarwelookedatinitially. In fact, this generalshape for the payoff of thecollared stock will existregardless of the precisestrike prices selected. Thetwo important things to noteare, first, that the maximumpotential profit (0.93 in this

case) plus the maximumpotentialloss(1.07)equalthedistance between the twostrike prices (2.00) andsecond, between theinflection points; that is,between the strike prices (22and 24 in this case), thecollared position will beabove (more profitable than)the stock position by theamount of the net creditreceived if the collargeneratesanetcredit(0.13in

this case) and will be below(less profitable than) thestockpositionby the amountof the net debit if the collarwasexecutedatanetdebitasit was with our 23/24 collar.In the lower left of Figure9.3,youcanseethatifMGMisbetweenthestrikepricesatexpiration, the collared stockpayoff is above that of thenakedstockbythe0.13ofnetpremiumcollected.

■WiderCollarsThe very first MGM collarwe looked at was as narrowas possible; the differencebetweenthestrikepriceswasonly $1 and MGM optionswere struck $1 wide. If wewere willing to take moredownsideriskinexchangeformore upside potential, wemightexecuteawidercollar.The widest collar we couldexecute in MGM given the

options that were tradingwould have been the 20/26collar.Wewouldcollect0.05for selling the 26 strike call,andwewouldusethat0.05tobuy the 20 strike protectiveput. The net would be zero,so this would be called a“zero-cost” collar. We’lldiscuss zero-cost collars inmore depth later in thischapter.This 20/26 is the widest we

could construct, andprotection wouldn’t kick inuntilMGMhaddroppedfrom23.20 to 20.00. In exchangefortakingthatadditionalrisk,our stock isn’t called awayuntil MGM has rallied to26.00.Whatwouldthepayoffchartforthiscollarlooklike?Again, the general payoffshapeisidenticaltotheothercollars we’ve looked at. Theonly differences are thepotentialprofit,potentialloss,

and where those payoffs arerealized. You can see this inFigure9.4.

Figure9.4AWiderCollarinMGMThat’sAlsoaZero-CostCollar

Since these strike prices areso far out-of-the-money, thelikelihoodsofactuallygettingprotection from the put orhavingourstockcalledawayarepretty remote.This is thereal difference between thiswide collar and thosenarrowercollarswelookedatpreviously.Let’scalculatethelikelihoods of needing that

protection or getting calledawayforboththe23/24collarandfor the20/26collar.Youcan use the tools atwww.OptionMath.com tocalculate thedeltaswesee inTable9.1.

Table9.1OutcomesforOurCollarsinMGM

Measure 23/24Collar Likelihood

Maximum


profit(stockatorabovecallstrikeat

expiration)

0.58 33%

Maximumloss(stockatorbelowputstrike)

0.42 44%

As you can see, the odds ofthe 20/26 collar actuallycomingintoplayatexpiration

are only 12 percent. Thiscollared position will reallyact as if the stock wasn’tcollared unless there is asubstantialmoveupordown.Whether you use a narrowercollar that’s likely to comeintoplaylikethe23/24collar,whichhada likelihoodof77percent of your putting yourstock via exercise or havingyour stock called away, or awider collar like this 20/26collar depends on your

appetite for risk and yourexpectations for theunderlyingstock.

■ In-the-MoneyCollarsWhat if we wanted to makecertain that we lost lessmoney on our collar? Wemight choose a put optionthatwasstruckin-the-money.The general shape of thepayoff chart shouldn’tchange, but let’s see if thecollared stock position isgoing to be above or below

thepayoffofthenakedstock,and let’s see where theinflection points are. Figure9.5 shows the same MGMoptions that we looked atearlier but constructs adifferentcollar.

Figure9.5AnIn-the-MoneyCollaronMGM

The protective put in thiscollar, the 24/25 collar, isstruck in-the-money sinceMGM was at 23.20. Thecollar can still lose money,butthemaximumlossis0.19,and that occurs with MGMbelow 24.00 at expiration.SinceMGMisat23.20now,this collar actually requiresour stock to rally or it will

lose money because we hadto pay 0.99 to put the collaron. IfMGM doesn’t rally to24.00, this collared positionwilllosemoney.AsyoucanseeinFigure9.6,thisin-the-moneycollartrailsthe naked stock over a bigrange and underperforms thenaked stock by the 0.99 netdebitpaidaslongasMGMisabove 24.00 at expiration.Below 24.00, the collar still

losesmoney although it onlyloses 0.19 meaning that ifMGMwere to drop bymorethan 0.19 the collar wouldoutperform the naked stockbecause both would losemoney, but the losses on thecollar would be limited to0.19, while the stock coulddropallthewaytozero.

Figure9.6AnIn-the-MoneyCollaronMGM

An in-the-money collar is agreat way to generate a highlikelihood of a small loss,0.19 in thiscase,andasmalllikelihoodofaprofit,0.81 inthiscase.A collar with the put struckin-the-money doesn’t makemuchsense;thelikelihoodofasmalllossisveryhigh,and

the position is bullish in thatthestockhastorallytoavoidthat loss. We could alsoexecute a collar with an in-the-moneycall, that is, acallwith a strike price below thecurrentpriceofthestockandanout-of-the-moneyput.Thiscollar will certainly generatenet premium. But theunderlying will almostcertainlybecalledaway.

■PotentialOutcomesAt expiration, there are threepossible outcomes for anycollar. The stock can beabove the strike price of thecovered call sold and thestock will be called away atthat exercise price. The netproceeds will be the callstrike price plus any netpremiumgenerated,orminusanynetpremiumpaid,forthecollar.Thispoint,atorabove

the call strikeprice, iswherethe maximum profit will beachieved.Thesecondpotentialoutcomeis that the stock is below thestrike price of the protectiveput purchased. We wouldchoose to exercise our putand sell our stock at thatstrikeprice.Thenetproceedswill be the put strike priceplus any net premiumgenerated, or minus any net

premium paid, for the collar.Thispoint,atorbelowtheputstrike price, is where themaximum loss will berealized.It’s possible that the stockcould be precisely at a strikeprice.Thelikelihoodofthisisvery small, but the profitfrom the stock beingprecisely at the call strike isidenticaltotheprofitfromthestock being above the call

strike price. Similarly, theloss from the stock beingprecisely at the put strikeprice is identical to the lossfrom the stock being belowtheputstrikeprice.Thethirdpotentialoutcomeisthat the stock is between thestrike prices; that is, it’sbelowthecallstrikepricebutabovetheputstrikeprice.Atthis point, both options willexpireworthless,andwe’llbe

leftwithouroriginalpositionin that we’ll be long thestock. If theunderlyingstockisbetweenthestrikepricesatexpiration,theoutcomecouldbe either a profit or a loss.Unless the stock hasn’tmovedsinceweexecutedourcollar, we’ll have a profit orloss on the stock even if it’sabove the put strike andbelowthecallstrike.Anynetpremium paid for our collarwill reduce this profit and

furtherincreaseanyloss.Anynetpremiumreceivedforourcollarwillincreasethisprofitorreducethisloss.Of course, any time prior tothe call option beingexercised by the owner or atany time prior to expiration,we could close the collarposition by buying back thecall option we’re short andselling the put option we’relong. If the underlying stock

has dropped since weexecutedthecollarbuthasn’tgotten below the put strikeprice andouropinion is nowthatitwon’tgetbelowtheputstrike price, then we mightvery well choose to sell theput, collect the premium forselling the put, and be leftwith a position that is longstock and short a coveredcall. In thisway, by taking aprofit in theputoptionwe’relong, we might offset a

portionofthelossofvalueofthe stock. This would leavethe stockholder with nodownsideprotection,butoncethe existing covered call hasexpired, or once it’s closedoutthroughrepurchase,anewcollar that’smore relevant tothe current price levels andoption expiration dates couldbeexecuted.Andit’sneverpossibletobuyan in-the-money put and pay

foritbysellinganout-of-the-money call, so a collar withanin-the-moneyputisalwaysgoing to cost money toexecuteandwillalwayshavea range over which it willexperienceasmallloss.

■AZero-CostCollarStock hedgers will often trytocreateacollarthathaszerocost; that is, the covered calland the protective put havethe same price. This meansthat the call premiumgenerated pays for the put,there’s “zero cost,” butthere’s no credit generatedeither. The wide collar welooked at in MGM was azero-cost collar.We received

0.05 for selling the 26 strikecovered call and paid that0.05 to buy the 20 strikeprotectiveput.The appeal of a zero costcollar is that there’s no needto pay for the collar, thehedger probably feels thathe’s getting the protectionfromtheputforexactlywhathe’s receiving for selling thepotential upside via the call.He’s right ifhe looksonlyat

the premiums paid andreceived, but is the potentialupside given equal to theprotection received? Wecould reexamine our 20/26collar in MGM but, as wesaw,thosestrikepricesaresofarout-of-the-moneythatthatcollar doesn’t act like anormalcollar,solet’slookatanother stock to see if theprotectionfromtheputequalsthe potential upsidesurrendered.

Figure 9.7 shows someoptions in IWM, the Russell2000 exchange-traded fund(ETF), that we might use toconstructazero-costcollar.

Figure9.7AZero-CostCollarinIWM

In this collar, IWM wastradingat114.95,andwesoldthe118strikecoveredcall at1.25tobuythe110strikeputat 1.25. Since the netpremium is zero, this is azero-costcollar.Figure 9.8 shows the payoffforthiscollar.

Figure9.8PayoffforaZero-CostCollaronIWM

We call this a zero-costcollar, andwedidn’thave tolay out any premium toexecute it, but can we reallydo this for zero cost? IWMwasat114.95so the110putis 4.95 away from at-the-money.Thismeansthiscollarcan lose 4.95 (114.95 –110.00)andIWMhastodrop4.3 percent (from 114.95 to

110.00) before protectionkicks in. Since the 118 callwas only 3.05 (118.00 –114.95) away from at-the-money,ourcollaredstockcanonlyprofitby3.05(118.00–114.95) and will then stopappreciating and our stockwill be called away with arallyofonly2.7percent.Thisdiscrepancy between whenprotection kicks in andwhenappreciation stops is the realcost of a zero-cost collar.

While it’s true that thelikelihood of making that3.05 profit is greater (thedelta of that 118 strike callwas 31 meaning the odds ofmaking3.05were31percent)than the likelihood ofsustaining that 4.95 loss (thedelta of that 110 strike putwas 25 meaning the odds oflosing4.95were25percent),if we do a little math(multiplying the potentialprofit or loss by the

likelihood of that profit orloss to calculate an expectedvalue), we find that thedifference in likelihoodsdoesn’t make up for thedifference inoutcomes.Evenwith the difference inlikelihoods, there is adiscrepancy in the potentialprofitandpotential loss fromourcollaredposition.What causes thisdiscrepancy? It is other

tradersbuyingprotectiveputsandsellingcoveredcalls.Theresult is that strike pricesbelow at-the-money getrelativelymoreexpensivedueto put buying demand andstrike prices above at-the-money get relatively cheaperdue to the selling pressurefrom covered calls. Thephenomenon is called skew,and you can see it clearly inFigure 9.9, which shows theimplied volatilities for each

of the strike prices availablein IWM at the time. Impliedvolatility is just the “apples-to-apples” measure of thecostofanoption.

Figure9.9WhyaZero-CostCollarIsn’tReallyZeroCost—OptionSkew

The implied volatility paidwhenpurchasing the110putis 17.48 percent while theimplied volatility receivedwhen selling the 118 call isonly13.53percent.Theresultis thatazero-costcollarmaynot requireus topayanynetpremium,but it has a cost inthat the protection receiveddoesn’t begin as quickly as

the upside appreciate sold isforfeited.Youmightaskifwecouldn’tturnthistradearoundandsellthe expensive put whilebuyingthecheapercall.Ifwedid this without anyunderlying position in IWM,we’d get bullish exposure(bullish exposure from beinglongacallplus thebullishtosideways exposure frombeingshortaput)whilebeing

helped by this skew. Thatstructure,shortaputandlonga call, is a risk reversal,which we’ll discuss inChapter10.

■SkewSkew has been a fixture inequity index markets sincethe 1987 crash, wheneveryonelearnedthatmarketscangodownmore,andmorequickly, than anyoneimagined. But skew worksdifferently in other marketsandwhileit’sveryprominentin equity index markets it’slesspronounced in individualequities.

Skew is abig issue in equityindex products because theycan drop further and fasterthen they rise. What aboutskew in assets that can risefarther and faster than theydrop? Things like U.S.government bonds, crude oil,gold, and VIX, the CBOEvolatility index, tend to risefaster than they fall becausethey spike on geopoliticalturmoil or supply shocks.Figure 9.10 shows skew in

optionsonVIX,ameasureofimpliedvolatilityontheS&P.

Figure9.10VIXSkew

WithVIXat12.46,wecouldhave executed the 10/15collar, that is, sold the 15strike covered call, assumingwe were long a VIX proxy,and bought the 10 strike putand done so for a credit of1.15bysellingthat15callat1.20 and paying 0.05 for the10 put. The fact that VIX isnot directly investable is

partlyresponsibleforthis,butadditionally,notmanypeopleare interested in collaringtheir long VIX position;they’re usually looking tocapture all of any spike inVIXsothere’srelativelylittlesellingpressureaboveat-the-money from sellers ofcovered calls. Below at-the-money, VIX by its naturecan’t go to zero so there’slittle demand for puts withlowstrikeprices.

■ How a Collar IsSimilar to OtherSpreads andCombinationsObservant readerswill noticethat the payoff shape for acollar is identical to thepayoff shape for selling avertical put spread or buyinga vertical call spread. That’sno accident. A collar is likeselling a vertical put spread

becauseacollarbuysalowerstrike put while thecombination of long stockand short a covered call isidentical to a short put withthe strike price of the call.This result, long a lowerstrike put and short a higherstrike put (although asynthetichigherstrikeput) isa short put spread. Similarly,a collar is like buying avertical call spread becausethecombinationoflongstock

and long the put is identicalto being long a callwith theput’s strike price. Combinethatlowerstrikesyntheticcallwith the short position in thehigher strike call and youhave a position that isidentical to buying a verticalcallspread.You can see how these threetrades are identical in Figure9.11.

Figure9.11SimilaritiesbetweenaCollarandBullishVerticalSpreads

A collar is often useddifferently than either ofthosevertical spreads sinceacollar is executed versus anexisting long position in theunderlying stock and isusually intended to protectunrealized gains in that longstock. The similar verticalspreads are executed withoutanyunderlyingstockpositionandareusuallyselectedbasedonthetrader’soutlookfortheunderlying stock. If they

think it’sheadedhigher, theycan buy the vertical callspread. If they think it’sheaded sideways, they cansellaverticalputspread.Youwouldn’t do either if youwere afraid the underlyingstockwould head lower, andthat’sexactlywhenyou’daddacollartoyourstock.The concept of syntheticpositionsisdiscussedChapter13, “Conversions and

Reversals.”

■PutSpreadCollarIf our stock has appreciated,we might want to get someprotection, and we might bewilling to surrender somepotential upside for thatprotection. This would be atraditional collar, butwhat ifwe want a put strike pricethat’s really close to at-the-moneyanddidn’twanttopayabunchofpremium inordertoput the tradeon?Or ifwe

wanted protection to kick inwithout paying the hiddenprice that skew charges? Ifwe were looking to onlyprotectaportionofourgainsratherthanpayforprotectionagainst the underlying stockdroppingall theway to zero,then we might replace thelong put in our collarwith along vertical put spread. Theput spread would certainlycostlessthantheoutrightputwould. This combination of

long stock, short a coveredcall,andlongaprotectiveputspread is a put spread collarand is another example ofreplacinganoption inoneofour spreads or combinationswith a vertical spread tochange the nature or cost ofthe trade. Figure 9.12 showsthe same IWM option priceswe looked at earlier butshows how we mightcombine them differently toconstructaputspreadcollar.

Figure9.12APutSpreadCollarinIWM

This put spread collar inIWM replaces the long 110strike put with the 110/114put spread (long the 114strike put at 2.35, short the110strikeputat1.25).Inthatput spread, we buy the 114put at 2.35 to get downsideprotection and sell the 110putat1.25toreducethecostofthetrade.

Since a put spread collarreplaces the long put of atraditional collar with a longput spread, there’s a limit tothe downside protection. Asyou can see in Figure 9.13,the loss isonly0.80betweenthe strike prices of the putspread, 114 and 110, but theloss starts to increase againonce IWM has droppedbelow that 110 strike price.At110.00theprotectionfromthe put spread has been

exhaustedandlossesresume.

Figure9.13PayoffforaPutSpreadCollaronIWM

As with any vertical putspreadwebuy,theputspreadwill have achieved itsmaximumvalueat expirationwith the underlying at orbelow that lower strike priceso the put spread will beworth 4.00 at and below110.00,andwe’llget tokeepthat 4.00 nomatter how lowIWM goes. Unfortunately,

losses on the IWM shareswe’re long will continue toincrease, and losses on ourtotal position will resumewith the underlying stockbelow the put spread. Thismeansthataputspreadcollaris intended to provide amoderate amount ofdownside protection for areasonable cost, but notcomplete protection all theway down to zero. Thebenefit of aput spread collar

is that the call can be struckfartheroutofthemoneythanthelongput,meaningthatweget protection more quicklythanweceasetoparticipateinupside appreciation. Forexample, in our IWM putspread collar, the 118 callwas 3.05 (2.7 percent) awayfrom at-the-money so IWMcouldrally2.7percentbeforewestoppedparticipating.The114 put was only 0.95 (0.8percent) from at-the-money

meaning that protectionwouldkick inafteradropofonly 0.8 percent. Again, byreplacing the protective putwith a protective vertical putspread, that protection iseventually exhausted. In thiscase, that happens at 110.00,so IWMwould have to drop4.95(4.3percent)before thathappened.

■CallSpreadCollarOne of the fundamentalelements of a collar is that acollarwilleventuallyceasetoparticipate in anyappreciationintheunderlyingstock. If you thought therewasarealopportunityforthestock to rally significantly,then might you replace thecoveredcallinacollarwithashortcallspread?Thiswouldessentiallybelikeexecutinga

traditionalcollar,thenbuyingan upside call to guaranteethat if the underlying stockrallied enough, we’d resumeparticipating in theappreciation.Callspreadcollarsaren’tverycommon, and with goodreason. If you thought therewas a reasonable likelihoodthat your stock would rallysignificantly, then a collarisn’tthebeststrategy.Buying

anoutrightput forprotectionor replacing your long stockwith a long call wouldgenerate absolute downsideprotection without truncatingupsideappreciation.

CollarCheatSheet

Collar

Description

Long

underlyingstock,short

OTMcoveredcall,longOTM

put

Example

ATM=100

Long100sharesofstock

Shortone105strike

callLongone95strikeput

PayorCollect

Premium

Payorcollectvery

smallamountof

netpremium



MarketMovement

Littleornonetimpact

Increasein

ImpliedVolatilitywithoutMarket

Movement

Littleornonetimpact


Priceofthestockwhen

MaximumRisk

thecollarisexecutedminusputstrikepriceplusanynetpremiumpaidor

minusanynetpremiumreceived

Callstrikepriceminus

MaximumProfit

priceofthestockwhenthecollarisexecutedminusanynetpremiumpaidorplusanynetpremiumreceived

BreakevenPoints

Current

stockprice

CHAPTER10

RiskReversal

If you were bullish on astock,youmightbuyanout-

of-the-money call option. Ifthe stock rallied above thestrike price of the call bymore than the price of theoption, thenyouwouldmakemoney.Buttherallyrequired,to a level that is above thestrikepricebythecostoftheoption, can be pretty big,particularlyifwe’veboughtacall on a stock with a highimplied volatility or ifwe’vebought a call that’ssubstantially out-of-the-

money.And in buying a calloption we can be right, thestock can rally, and we canstill lose money if it doesn’trallyenough.Or youmight sell an out-of-the-money put. This is abullish to sideways position.As long as the stock didn’tdropbelowthestrikepriceofthe put by more than thepremium received this tradewouldbeprofitable.Inselling

a put, you wouldn’t have topay any premium; in fact,you’dbecollectingpremium,and that premium would beyourstokeep,nomatterwhatthe underlying stock did. Ifthe stock is below the strikeprice at expiration, thenyou’re going to end upbuyingthestockatthatstrikeprice,butsellingaputworksbest if the stock has movedup or sideways at expirationand if the stock appreciates

enough then the amount ofputpremiumcollectedwillbetiny in relation to the profitfrom buying a call optioneven though the call optionrequires us to pay for theoption.Ifyouweretocombinethesetwo positions, long a calloptionandshortaputoption,you would have a riskreversal. A risk reversal is acombination made up of a

longcallthatisstruckout-of-the-money and a short putthat is struck out-of-the-money.Thetwooptionssharethesameexpirationdate.Likealongpositioninthestock,ariskreversal isbullish in thatit does best when theunderlying stock ralliessignificantly. For the riskreversal, this is because it’slongacall.Likeapositioninthestock,ariskreversaldoesmost poorly when the

underlying stock dropsbecause it’s short a put andwill end up buying the stockat that put strike priceregardless of how low thestockdrops.A risk reversal will generatenetpremiumwegettocollectand keep if we collect morefor selling the put than wespend to buy the call.A riskreversalwillrequireustopaysomenet premium ifwe pay

moretopurchasethecallthanwecollectforsellingtheput.A risk reversal has nearlyunlimited loss potential sincebeing short the put is muchlike being long the stock.Bothashortputpositionanda long stock position havelimited risk only because theprice of the underlying stockcan’tdropbelowzero.Ariskreversal has unlimited profitpotential, since it is long a

call option and the value ofthat call will increase as theprice of the underlying stockincreases.Figure10.1showsoptionsonWal-Mart (WMT), includingsome call options that wemight buy and some putoptionswemight sell. It alsoshows how we mightcombine those two positionsinto a risk reversal. WMTwas trading at 78.13 when

these option prices wereobserved.

Figure10.1ARiskReversalinWal-Mart(WMT)

We could execute the75/82.50 risk reversal for anet credit by selling that 75strike put at 0.95 and usingthat premium to buy the82.50 strike call at 0.38.Wewould keep the 0.57 netdifference.Howwould this risk reversalmake money? Since we

received that 0.57 net credit,thistradeisprofitableaslongas WMT is above 74.43(75.00 – 0.57) at expiration.Butweexecuteariskreversalbecause we’re bullish, wethink the stock is goinghigher, so our goal isn’t tojust collect and pocket thatnet premium. Our goal is tomake more money byparticipating when WMTrallies while buying it at adiscount to the current stock

price if WMT drops. In thiscase,withWMTabove82.50at expiration, we’ll exerciseour call option and get longWMTataneffectivepriceof81.93 (82.50 – 0.57), butwe’d do so only if WMTwere above the 82.50 callstrikeprice.Sincewe’rebullishandmighthave bought WMT stockinstead of executing this riskreversal,we’rewillingtotake

some downside risk and beforced to buy WMT if itdrops. Our effective pricewould be 74.43, but sincewe’reshortthisput,wedon’tget todecide;we’regoing tobuyWMTifit’sbelow75.00at option expiration becausethe owner of the put willexercise the option and putthe stock to us. Figure 10.2showsthepayoffchartforthecallwe’relong,theputwe’reshort and the combined risk

reversalposition.

Figure10.2TheWMT75/82.50RiskReversal

Figure 10.2 shows theconstituent long 82.50 strikecall and short 75 strike putbecause that’s what a riskreversal is,we’re selling thatput topayfor thatcallandifWMT drops enough and isbelow the put strike price atexpiration or rallies enoughand is above the call strikepriceatexpiration,thenwe’re

going to get long WMTstock. It also shows theresulting 75/82.50 riskreversal.You’ll notice that theinflection points for the riskreversal occur at the strikeprices of the constituentoptions, 75 and 82.50 in thiscase. At 82.50, the strikeprice of the call option, theprofit from the risk reversalstarts to increase from the

0.57collectedasthevalueofthecallatexpirationstarts torise. Below 75, the strikeprice of the put option, therisk reversal starts togiveupitsprofituntil reachingbreakeven at 74.43 (the 75 putstrike price minus the netcredit of 0.57 collected) andfor all WMT prices below74.43atoptionexpirationtherisk reversal loses moneywith the loss increasing asWMT drops just as the loss

would increase if we weresimplylongthestock.Betweenthestrikeprices,this75/82.50 risk reversal isprofitable because wereceivedmore for selling the75strikeputthanwepaidforpurchasing the 82.50 strikecall. IfWMT is between thestrike prices at expiration,then the put we’re short willexpire worthless and wewould let the call option

we’re long expire worthless.We would pocket the netcredit of 0.57 and have noposition. At this point, wecould buy WMT, execute anewriskreversal,or lookforanotheropportunity.Thisrangebetweenthestrikeprices provides some marginof error. Between there weend up with zero position atexpiration. The underlyingstock might have gone up a

little and a risk reversal willmiss that move, but theunderlying stock might havegone down a little and therisk reversal will miss thatloss aswell.Thismeans thata risk reversal is generallyagnostic to changes involatility.Ifimpliedvolatilitygoes up, the price of the calloption will increase, whichhelps,butthisisoffsetbytheincrease in the price of theshort put. A risk reversal

wants realized volatility onlyifit takesplaceinthecorrectdirection—up.Ariskreversalisn’t a volatility play; it’salmost exclusively adirectionalplaywhilegettingsome help from skew. Wediscussed skew in Chapter 9when we looked at collars.Here, we’ll examine howskew can help our riskreversal. We’ll also look atthegreeksforriskreversalsinthe greek cheat sheet at the

end of this chapter, but it’simportant to remember thatsince implied volatility tendsto increase when a stock’sprice declines and tends todecreasewhenastock’spriceincreases, taking a riskreversal off after the stockpricehaschangedcanbehurtby volatility slope, thetendency for volatility toincrease or decrease as thestock price decreases orincreases.

Until the profit from the riskreversal turns upward again,with the underlying stockabove the strike price of thelong call,WMT above 82.50in this case, the risk reversalis less profitable than theshort put option alonewouldbe.Thismakessense,wehadtopayforthecalloptionthatwe’relongandbelowthecallstrike price the differencebetween the result for theshortputandtheresultforthe

riskreversalisthecostofthecall option bought. You cansee these differences andinflection points in Figure10.3.

Figure10.3PayoffforOur75/82.50RiskReversalinWal-Mart(WMT)

We’ll be paid this 0.57 netcredit as soon as we executethis risk reversal, and that0.57isourstokeepnomatterwhat, but we won’t actuallyearn that 0.57 until theoptions erode away andexpire. We’re familiar withoption erosion and how itaccelerates as expirationnears, but in a risk reversal

we’re short a put, whicherosion will help, and we’relong a call, which erosionwill hurt. What will thiserosion actually look likeovertime?Figure10.4showsthe erosion for this 75/82.50riskreversal.

Figure10.4HowOur75/82.50RiskReversalErodeswithoutAnyMovement

You’llnoticethat theerosionoccurs ina relatively straightline. This is because the twoconstituent options wererelativelyequidistantfromat-the-money when the riskreversalwas initiatedandweassume the underlying didn’tmove for the term of theseoptions. When this risk

reversal was executed, thecall option was 4.37 awayfrom at-the-money (82.50 –78.13), while the put optionwas 3.13 away from at-the-money(78.13–75.00).Thisriskreversalgeneratedanet credit and that will oftenbethecasebecause,allthingsbeing equal, puts tend to bemoreexpensivethancallsforthe reasons we discussed inthe section on skew in

Chapter 9. But not all riskreversals will generate a netcredit and, just as whenselectingstrikeprices forourcollar, if spending a littlemoney results in a riskreversalwithstrikepricesthataremoreappealinginrelationto an important level on thestock chart or your desiredentry point, then spending alittle bit of net premium toexecute a better risk reversalisprobablymoneywellspent.

The very nature of a riskreversal means that youshouldn’t spend a lot ofpremium; if you want tospenda lot ofpremium, thenthere are better tradestructuresthanariskreversal.But regardless of the netpremium paid or received,skewwillalmostalwayshelpariskreversalonanequityorequity index and will almostalwayshurt a collaron thoseunderlyings.

Paying net premium toexecute a risk reversal willchange the payoffs for thetradeslightly.Forexample,ifthe underlying stock isbetween the strike prices atexpiration the risk reversaldoneatanetdebitwillrealizea net loss. That loss will bethenetpremiumspent.Figure10.5 shows the same WMToptionspriceswesawearlierbutusesdifferentstrikepricestogenerateariskreversalthat

would require a smallpaymentwhenexecuted.

Figure10.5ASecondRiskReversalinWal-Mart(WMT)

Thissecondriskreversal, the72.50/80 risk reversal,wouldcost0.50(1.00paidforthe80strike call optionminus 0.50receivedforselling the72.50strikeputoption)andthatnetdebit of 0.50 would be theloss if WMT is between thestrikeprices,72.50and80 inthiscase,atexpiration.We’llsustainthatlossbecauseboth

options will expire worthlessand we’ll be left with noposition, but we will havespent that 0.50 to establishtheriskreversal.Inexchangefor that potential loss, thisrisk reversal startsparticipating to the upsidewith WMT above 80.00 (asopposedto82.50for thefirstrisk reversal we looked at)and doesn’t get WMT stockput to us unless it’s below72.50 at expiration (the first

riskreversalwelookedathadWMT stock put to us withWMT below 75 at optionexpiration). Figure 10.6showsthepayoffforthisriskreversalexecutedatadebit.

Figure10.6Payoffforthe72.50/80RiskReversalinWal-Mart(WMT)

Thesetwoconstituentoptionsdiffered quite a bit in theamount theywereout-of-the-money. The 72.50 put was5.63out-of-the-money(78.13– 72.50), while the 80 strikecallwasonly1.87out-of-the-money (80 – 78.13). Doesthis change how this riskreversalwillerodeovertime?Yes, it does. Since the put

optionweare short is fartherout-of-the-money, the riskreversalwill erodemore likean outright option, meaningthaterosionwillaccelerateasexpiration nears. Figure 10.7shows how this risk reversalwillerode.

Figure10.7HowOurMoreBullishRiskReversalErodes

■LikelihoodsAswith selling a put to buystockatadiscount,we’renottryingtododgeabulletwhenusing a risk reversal. Wethink the stock is goinghigher and we want toparticipateifitdoesso,whilebeingwillingtopurchaseitata discount from the currentprice ifwehave to.With thefirst risk reversal, the75/82.50 risk reversal, we

wantedtoparticipateifWMTbroke out to the upside andwe were willing to buy at adiscount if it dropped. Inusing a risk reversal, we canget this exposure whilespending very little premiumor even collecting netpremium.Insellingacoveredputwe’rewilling to buy at adiscount while being paid tofind out if we will. With ariskreversal,we’rewillingtobuy at a discount, but we

don’t want to miss a bigmovetotheupside.Since we’re trying to getbullish exposure, it’simportant to know thelikelihoodofhavingthestockput to us as well as thelikelihoodofhavingthestockabove the strike price of thecall meaning we’d exerciseourcallandgetlongthestockat the effective purchaseprice. These likelihoods are

theoptiondeltaswelookedatearlier.Table 10.1 shows thetwo risk reversals we’velooked at so far and thelikelihoods of getting longWMTforeach.

Table10.1ImportantLikelihoodsforOurRiskReversals

75/82.50RiskReversal

LowerPurchase Likelihood

UpperPurchase

Price Price

75.00 28% 82.50

The likelihood of eventuallyowningWMTstockusingthefirst risk reversal, the75/82.50, is 44 percent (28percent of getting put thestock plus 16 percent ofexercisingourcall)while thelikelihood of eventuallyowningWMTstockusingthe

second risk reversal is 49percent (16 percent plus 33percent). These twocombined likelihoods arevery similar, each riskreversal has a slightly lessthan 50 percent chance ofeventually owning the stock,and that makes sense, wedidn’tchangethewidthoftherisk reversal, we just movedeachstrikedownalittle.Theeffective purchase priceswould be slightly different

than these strike pricesdepending on the netpremiumpaidorreceivedfortheriskreversalbutthestrikeprices are howwe figure thelikelihood of paying thoseeffective prices. Note thatthese odds are the deltas ofthese options because ifWMTisbelow theput strikeby just 0.01 at expiration,theoretically,we’llgetputthestock. Similarly, if WMT isabove thecall strikepriceby

just 0.01, we’ll theoreticallychoosetoexerciseourcall.Since we’re bullish WMT ifwe’reusing a risk reversal, alessthan50percentchanceofbuying the stockmay not beenough for us. We couldtightenupthestrikepricesasmuchaspossibleandtherebyincrease the likelihood thatwe’llenduplongthestockatexpiration. For example, thetighteststrikepricesinWMT

would result in the 77.50/80risk reversal. We wouldexecute that risk reversal bysellingthe77.50strikeputat1.82andusethatpremiumtobuythe80strikecallat1.00.Thedeltaof that77.50put is46and thedeltaof80call is33 meaning that thelikelihood of owning WMTafterexpirationis79percent.This is just about as high alikelihood as a risk reversalwillgenerate.

Butactuallybuyingthestockat expiration isn’t the onlyway to make money with arisk reversal. In fact, if webuythestockbyhavingitputtousthenwe’lllosemoneyifthe stock is below theeffectivepurchaseprice.How else might our riskreversal make money? Howcan we make money even ifour underlying stock doesn’tget above the strike price of

the call? By watching as theunderlying stock rallies,causingour shortput todropin value and our long call toincrease in value. Forexample,whatwouldhappento our 72.50/80 WMT riskreversal, the one that cost us0.50 to execute, if WMTrallied by 1.50 immediatelyafter we executed the trade?That means WMT wouldrally from 78.13, which iswhere it was when we saw

thoseoptionprices, to 79.63,which is still below the callstrikepriceandiswellbelowour breakeven point atexpiration of 80.50. Let’slookatTable10.2 tosee justhow much profit this riskreversal would generate,despite never getting abovethe call strike price, if itralliedlikethat.

Table10.2OurRiskReversalafteraRallybutPriorto

Expiration

OptionPosition

ValueatExecution(75DaystoExpiration)

Valueafter1.50JumpinWMTtheDayafter

Execution(74DaystoExpiration)

Short72.50put

0.50 0.30

Long80call

1.00 1.62

Table 10.2 shows that theunrealized gain on the shortput after this jumpwould be0.20 (0.50–0.30), theput isprofitablebecausewe’reshortit and the price has fallen.The unrealized gain on thelong call after this jumpwould be 0.62 (1.62 – 1.00),the call is also profitable

becausewe’relongitandtheprice has risen. In total, therisk reversal has anunrealized gain of 0.82becausewecouldsellthecallfor1.62andbuytheputbackfor0.30,leavingus1.32.Therisk reversal initially cost0.50 to execute, so ourunrealizedprofitis0.82.But this profit of 0.82 isunrealized,andsinceWMTisstill below the breakeven

price at expiration of 80.50,we’reinabitofarace.Timedecay will start eating at thevalue of our long call to agreater degree than we’llbenefit from time decay ofourshortput,sincethecallisnow worth so much morethan the put. As with someother option strategies, it’spossible to get the directionright(up)andstilllosemoneywithariskreversalevenifwehaveahugehead-start,aswe

doafterWMThasmade thishypotheticaljumpto79.63.IfWMTstayedat79.63untilexpirationwewouldhavehada profit and turned it into aloss, since we would end uplosingthat0.50netdebitpaiddespite having an unrealizedprofitof0.82.How will this risk reversalerode after this hypotheticaljump?Figure10.8showshowthisriskreversalwoulderode

after this jump.Note that theerosion occurs in the sort ofcurve that we expect fromoutright options, erosionwillaccelerateasexpirationnears.That’sbecause thecall strikeis now so close to at-the-money. This risk reversalafter the jump ismuchmorelikethatofa longcall thanariskreversal.

Figure10.8HowOur72.50/80RiskReversalWillErodeafteraRally

■ How Skew Helps aRiskReversalIn Chapter 9, we saw howskew, the tendency fordifferentstrikepricestohavedifferent implied volatilitiesdue to factors like jump risk,buyingdemandforputsfromhedgers and selling pressureon calls from covered callsellers, can increase the costofourcollar.Sincetheoption

portion of a collar is theopposite of a risk reversal,which is selling a put—andthat put should be moreexpensive due to this buyingdemand—andbuyingacall—and that call should be lessexpensive due to that sellingpressure—skew should helpourriskreversal.Let’slookattheimpliedvolatilityforeachof these WMT strike pricesand see if that’s the case forthe risk reversalswe’vebeen

considering. Figure 10.9shows those impliedvolatilities and the skew isevident once you connectthem.

Figure10.9ImpliedVolatilitySkewinWMTOptions

As the strikeprices fall fromthe at-the-money price of78.13, implied volatilityclimbs. As the strike pricesrise from that at-the-moneyprice, the implied volatilityfallsuntiltheoptionsgetverycheap in dollar terms, whenthe implied volatility startsrising again. This is thetypical shape of a volatility

skew chart for an equity orequityindexunderlying.The first risk reversal weexamined, the 75/82.50 riskreversalshowsadifferenceof2.07volatilitypoints(14.90–12.83) in implied volatility.The second risk reversal, the72.50/80 risk reversal, showsadifferenceof2.83volatilitypoints (16.25 – 13.42). Howdoes that differencemanifestitself? As we saw when

discussing collars, one wayskew impacts our riskreversal is the distance thestrike prices are from at-the-money. In the 72.50/80 riskreversal, the 72.50 put, thepointatwhichwewouldhavetobuythestock,is5.63awayfromat-the-money,while the80 call, the point at whichwe’dstarttoparticipatetotheupside, is only 1.87 awayfrom at-the-money. It’s truethat this tradecostus0.50 to

put on but for that 0.50 andthanks to skew,WMTwouldhave to fall over 7 percentbeforewe’dbeforced tobuythestockwhile ithas torallyonly 2.4 percent beforewe’dstart to make some moneyback.Another way skew ismanifested is in the optionprices,and this isusually theeasier way to recognize theimpact,particularlywhen the

strike prices are notequidistant from at-the-money as in these riskreversals. Table 10.3 showstheimpactofskewonbothofthese risk reversals by usingthe tools atwww.OptionMath.com andcalculating the option pricesas if both options had thesameimpliedvolatility.

Table10.3HowSkewHelpsaRiskReversal


RiskReversal

PutOptionImpliedVolatility

CallOptionPriceifItHadPutOption’sImpliedVolatility

75/82.50 14.90 0.7272.50/80 16.25 1.59

Both trades benefit fromskew.The82.50callwebuy

in the 75/82.50 risk reversalwould be 0.34 moreexpensive if it had the same,higher, implied volatility asthe 75 put. The 80 call webuy in the 72.50/80 riskreversal would be 0.59moreexpensive if it had the sameimpliedvolatilityasthe72.50put.

■ Call Spread RiskReversalWhatifwewantedtobelonga callwith a strikeprice thatwas very close to at-the-money without paying anynetpremiummeaningthatwewouldparticipateinarallyinthe underlying stock even ifthe rally was minor but thatwe would do soinexpensively? What if we

wantedtobeshortaputwitha strike price that wassignificantly below at-the-money, meaning that theunderlying stock would haveto drop substantially beforewe would get put the stock,butagainwewantedtodosoinexpensively?We could replace our longcall with a long call verticalspread because this wouldreduce the cost of that long

exposure. This would allowus to buy a call that wascloser to at-the-money,although we’d also be shortan out-of-the-money call,meaningthatourparticipationinanyrallywouldeventuallyend.Or it would allow us tosell a put that was fartherfrom at-the-money, meaningthat the underlying stockwould have to drop furtherbefore we had it put to us.This would be a call spread

riskreversal.A call spread risk reversalreplaces the long call with along call vertical spread,which results in a finiteamount of potential profit ifthe underlying stock were torally. Our downside risk isstill limited only by the factthat the underlying stockcouldn’t fall below zero.Figure 10.10 shows a callspreadriskreversalwemight

construct from the WMToptions we’ve been lookingat.

Figure10.10ACallSpreadRiskReversalinWMT

If we were to sell the 70strike put at 0.25, we coulduse that premium to buy the82.50/85 call vertical spread.We’dbe longa call thatwas5.6 percent from at-the-money requiring that 5.6percent move for our callspread to have any value atexpiration, butwe’d be shortaputthatwasover10percent

fromat-the-money,aputthatwould require that move ofover 10 percent before weexperienced losses and hadthe stock put to use atexpiration.Our potential loss from thatshort put is 70.00, but thatwouldrequirethestocktofallall theway to zero—aprettyunlikely outcome. Sincewe’re long a call spreadrather than an outright call

like our previous riskreversals, our profit is nowcapped, just as it is for anyvertical call spread. In thistrade, our profit is capped atthe width of the call spread,sincewedidn’tpayorcollectany net premium to put thetrade on. Our maximum netprofitfor thiscallspreadriskreversalis2.50.Let’sconnectthe dots and see the payoutfor this call spread riskreversalatexpirationacrossa

range of stock prices. YoucanseethatinFigure10.11.

Figure10.11Payofffor70/82.50/80CallSpreadRiskReversalinWMT

You’ll notice that eventhough we were able toexecute this risk reversalwithout paying any netpremium,theupperinflectionpoint, 85.00, where profitsstarttoaccrue,ismuchcloserto the at-the-money price of78.13 than the lowerinflectionpoint,70.00,wherelosses start to accumulate.

That’s the result of buyingthatcheapercallspreadratherthan the more expensiveoutright call.The trade-off isthatourprofits are cappedat2.50,withWMTat or above85.00.

RiskReversalCheatSheet

RiskReversal

Description

LongOTMcoveredcall,shortOTMput,long

cashtobuystockatthestrikeprice

Example

ATM=100Longone105strike

callShortone95strikeputLong$9,500

Payor

Payor

CollectPremium

collectverysmall

amountofnetpremium



MarketMovement

Littleornonetimpact

IncreaseinImplied

VolatilitywithoutMarket

Movement

Littleornonetimpact


Strikepriceoftheput

MaximumRisk

minusanynetpremiumreceived(ifstockdropstozero)

MaximumProfit


Breakeven

Callstrikeprice±Anynetpremium

Points receivedPutstrikeprice±Anynetpremiumreceived

CHAPTER11

Butterflies

In constructing a verticalspread,weboughtoneoption

and sold a very similaroption. What happens if wetake that thinking a stepfurther and buy one verticalspreadandsellaverysimilarvertical spread? We wouldreduce the cost of the tradedramatically, that means wewould reduce risk, and wewould potentially increaseleverage if our cost falls butourmaximumprofitstaysthesame. Those are all goodthings.

Ifwemadeitapointtoselectthe strike prices of ourvertical spreads carefully sothat the long leg of the firstvertical spread and the longleg of the second verticalspread are the same option,thenwe’vecreatedabutterflyspread.We’ve also created abutterflyiftheshortlegofthefirst vertical spread and theshort leg of the secondvertical spread are the sameoption.Abutterflyisthefirst

spread that we’re going tolook at that’s really a spreador combination of otherspreads. Figure 11.1 showshow we might execute abutterfly.

Figure11.1CreatingaLongCallButterfly

In this generic butterfly,we’re buying the 51/54 callspread and selling the 54/57call spread. The resultingposition is long one 51 call,short two 54 calls, and longone 57 call. This cumulativeposition is longone51/54/57callbutterfly.A long butterfly is a defined

risk strategy that is generallyvery inexpensive to establishand has a defined potentialprofit that is usually severaltimes greater than the risk,which is the cost of thebutterfly. The likelihood ofrealizingthismaximumprofitis very small, as we’lldiscuss.Ashortbutterfly isadefinedrisk strategy with a definedpotential profit that is very

small in relation to the riskbut the likelihood ofsustainingany loss isusuallysmall and the likelihood ofsustain the maximum loss isverysmall.Let’s look at some actualoption prices and pick twovertical spreads to combineinto a butterfly. Figure 11.2shows option prices and thevertical spreads we mightselect.

Figure11.2CallOptionsandBuyingaButterflySpread

InFigure11.2,weconstructacall butterfly by buying the130/132 call spread at 0.80(buying the 130 call at 2.98and selling the 132 call at2.18) while also selling the132/134 call spread at 0.61(selling the 132 call at 2.18and buying the 134 call at1.57). The entire position islong the 130/132/134 call

butterfly, sometimes referredtosimplyasafly,at0.19.The entire trade costs 0.19(0.80 paid for the 130/132call spread minus 0.61received for selling the132/134 call spread), andwhen buying a butterfly(buying the “wings” andselling the “body”) we’llalways pay money. If you’llstop and think about ourbutterfly as a spread of two

vertical spreads, it willbecome clear why we willhavetopaymoneytobuyourbutterfly if we’re buying thewings and selling the body.The vertical spread we buy,the one that is closer to at-the-money, will be moreexpensive than the verticalspreadwesell,theonethatisfarther from at-the-money.Since the likelihood of thatfirst vertical spread reachingits maximum potential value

is greater, because it’s closerto at-the-money, we’d bewilling to pay more for it.That’s why we have to paywhenwebuyabutterfly.As with any spread we buy,and a butterfly is a spreadmadeupoftwootherspreads,ourmaximumlossiswhatwepay, 0.19 in this case.Whileit’s more important to lookdown than up before wejump,we’realsointerestedin

profit and when we realizethat profit. Let’s create thesort of profit and loss tablethatwe’vedonepreviouslytosee how andwhen this trademakes and loses money, butlet’s be certain to treat thisbutterfly as a spread of twoother spreads.We do this inTable 11.1 and we see theresultingbutterfly.

Table11.1CallSpreadsandtheResultingButterfly

StockPriceatOption

Expiration

Valueof130/132Call

SpreadatExpiration

ProfitorLosson130/132

SpreadatExpiration

128 0.00 –0.80129 0.00 –0.80130 0.00 –0.80131 1.00 0.20132 2.00 1.20

133 2.00 1.20134 2.00 1.20135 2.00 1.20136 2.00 1.20

Themaximumlossis0.19,aswe’ve already discussed, andwesustainthatlossbelowthelowest strike, the 130 strike,and above the highest strike,the134strike.Themaximumprofit is 1.81, but that isrealized only with the

underlying stock precisely atthe middle strike, 132.00.Thatmaximumprofitfallsoffsharply as the underlyingstock falls from, or ralliesabove our middle strike,132.00. This means that abutterflymakes itsmaximumprofit only when theunderlying stock is preciselyat that middle strike price,unlikeasingleverticalspreadwhere themaximumprofit isachievedwith the underlying

at any point above or belowthe spread, depending onvertical call spread versusvertical put spread and onlong versus short. It alsomeansthatabutterflyhastwopoints at which the tradebreaks even: the lowerbreakeven and the upperbreakeven.Thepayoffchartatexpirationfor the long call butterflyshowsavery small lossover

a large range of strike pricesboth below the strike pricesof the butterfly as well asabove the strikepricesof thebutterfly. This makes senseandisconsistentwiththeideathatabutterflyisreallyjustaspread made up of twoverticalspreads.Forthislongcallbutterfly,the130/132callverticalwe’re long is a loserbelow the breakeven of130.80, but then makesmoney up to the maximum

profit of 1.20, which isrealized with the underlyingstock at or above 132.00 atexpiration.Theshort132/134callverticalisprofitablewiththe underlying stock belowthe132.61breakeven.Itstartsto lose money above thereandexperiencesitsmaximumpossiblelossof1.39withtheunderlyingatorabove134atexpiration. The long callspreadachieves itsmaximumprofit above 132.00, but the

short call spread realizes itsmaximum loss above134.00.That $2.00 range is prettysmall for a $130 stock, andwe haven’t even factored inthecostofthebutterflyyet.That’s a whole lot ofnumbers. Let’s look at thepayoff chart. This130/132/134 call butterflycost0.19andwecanseethispayoff chart in Figure 11.3.Note that we’ve added the

constituentverticalspreadstothechartsoyoucanseehowtheyinteractwitheachother.

Figure11.3AButterflyIsReallyJustaSpreadofTwoVerticalSpreads

The fact that a longbutterflyshowsalossoveraverylargerange of strike prices, bothabove and below the spread,is probably the biggestdifferencebetweenabutterflyand a simple long verticalspread. In a simple longvertical spread, the marketcannot move too far. If thestock rallies, then at some

point, a long call verticalspreadwill have achieved itsmaximum profit, and thatprofitatexpirationwillneverdecrease as longas the stockprice remains above the callspread. That’s not the casewith a call butterfly; themarket can move too far ifwe’veboughtabutterfly.Yousaw this in Figure 11.3 afterthestockgotabove134.00.Similarly, if the stock drops,

then at some point the longvertical put spread will haveachieved its maximum profitand that profit will neverdecrease as longas the stockprice remains below the putspread. That’s not the casewithaputbutterfly.Thepriceof the underlying stock candrop too far for a long putbutterfly. We’ll look at putbutterflies more closely laterinthischapter.

For a long call butterfly,you’re long a vertical callspread,whichwillincreaseinvalueas theunderlyingstockappreciates, and you’re shorta slightly different callvertical that is a little furtherout-of-the-money and willlosemoney,sincewe’reshortit, as the underlying stockappreciates.Ifthepriceoftheunderlying stock drops, thenthe price of the verticalspreadyou’re longwilldrop,

whichisbad,butthepriceofthe vertical spread you’reshort will drop as well, andthat’sgood.Theresultisthatthe long call vertical and theshortcallverticalareworkingagainst each other. One willhave realized its maximumprofit, and one will haverealized its maximum loss ifthe underlying stock movesenough, regardless ofdirection.

Let’s look at the samebutterfly that we saw inFigure11.3,butlet’sexaminespecifically how theunderlying price can movetoofarforourbutterfly tobeprofitable.WecanseethisinFigure11.4.

Figure11.4TheUnderlyingCanMoveTooFarforOurLongCallButterfly

The lower breakeven pointforourcallbutterflyis130.19and the maximum profit isachievedat132.00.Sincetheunderlying stock was at128.07, this butterfly needsthe underlying stock to rally,and you’d buy it only if youwere bullish (however, aswithotherspreads,youdon’thavetobecompletelybearish

in order to sell it; youmightvery well sell it if you wereeither bearish or neutral butmoreabout sellingbutterflieslater). And how much doestheunderlyinghavetorallyatexpiration? It has to rally atleast to 130.19, which is thelower strike price, 130.00,plus the costof thebutterfly,0.19, but can’t rally above133.81, which is the higherstrike price, 134, minus thecost of the butterfly, to at

leastbreakeven.What are all the importantbreakeven and inflectionpoints, and how can wecalculatethemeasily,withoutbuilding the sort of profit-and-loss table we didpreviously every time we’rethinking about trading abutterfly? Figure 11.5 showsthe generic breakevens andtheinflectionpointsforeverylongbutterfly,whethercallor

Figure11.5GenericBreakevenPointsforaLongButterfly

So a call butterfly is simplyoneverticalcallspreadversusanother vertical call spread.As we’ll see later, a putbutterfly is simply onevertical put spread versusanother vertical put spread.What if we sell that firstvertical call spread and buytheverticalcallspreadthatisfarther from at-the-money?

Let’stakeanotherlookattheoptions we saw earlier andsee how we can turn thingsaroundalittle.InFigure11.6we’re creating different callverticals and arranging themdifferently.

Figure11.6SellingaCallButterfly

This time we constructed aslightly different butterfly byselecting different verticalspreads. We’ll sell the131/134 call vertical (sellingthe 131 call at 2.56 andbuying the 134 call at 1.57),collecting0.99 (2.56–1.57),and buy the 134/137 callvertical (buying the 134 callat 1.57 and selling the 137

call at 0.94), paying 0.63(1.57 – 0.94).By selling thisbutterfly, we will havecollectedanetof0.36(0.99–0.63). What does this profitand loss look like over arange of prices for theunderlying stock atexpiration? We see that inFigure 11.7 and notice thatwe’re not looking at thisbutterfly as if it werecomposed of three options,but ratherwe’re lookingat it

as we should—as if it werecomposed of two verticalspreads.

Figure11.7PayoffforOurShortCallButterfly

We’re selling the butterflyandaswithnearlyanyspreador combination, we see themaximum potential profit isthe premium collected, 0.36in this case. We keep that0.36 no matter where theunderlying is at expirationand that’sourprofitwith theunderlying stock below131.00 or above 137.00 at

expiration. Once the stockgets above131.00, our profitstarts to trail off until thestock gets to the 131.36breakeven. From 131.36 to136.64, this short butterfly isa loser with the maximumpotentiallossof2.64realizedwith the stock at precisely134.00atexpiration.Thelosstrails off as the stock ralliesabove134untilitreachestheupside breakeven of 136.64andabovethatleveltheshort

butterfly is profitable againbefore reaching the level ofmaximum profit again whenit’sabove137.00.

■ Buying and SellingButterflies—TheTerminologyAs you’ve probably figuredout, if we’re buying theoutsidestrikes,the“wings”ofthe butterfly, and sellingtwice as many of the insideoptions, the “body” of thebutterfly, then we’re buyingthe butterfly. This isconsistentwithourdiscussion

of buying and selling anyother spread or combinationbecause if we’re buying thewings, then we’re going topay for the butterfly, andwhat we pay will be ourmaximum risk. However, ifwe sell the wings, the outerstrikes, and buy twice asmanyofthebody,themiddlestrike, then we’re going tocollect premium, and this islogical because the verticalspread thatwe’re selling, the

one that is closer to at-the-money, is going to be moreexpensive than the verticalspreadthatwearebuying,theone that is fartherout-of-the-money.Whatwe collectwillbe our maximum profit as itis with any other spread wesell. This assumes that ourbutterfly is out-of-the-moneyand symmetrical, that thewidth of the two verticalspreads is identical. Youmight occasionally want to

use a slightly asymmetricalbutterfly, and if you have agood reason for selecting thespecific strike prices, thenmore power to you. You’lljust have to do the math tounderstand whether you’llpay or collect and what themaximum profit and loss is.This sort of asymmetricalbutterfly is sometimes calledabrokenbutterflyandisoftenusedtoget“long”abutterflywithoutpayingoutanycash.

■PutButterfliesPut butterflies are nearlyidenticaltothecallbutterflieswe’ve seen; we’ll buy (orsell) one put vertical spreadandsell(orbuy)asimilarputvertical spread. Let’s look atanother underlying stock andsee how we might create aput butterfly. We see theseputpricesinFigure11.8.

Figure11.8PutOptionsandBuyingaPutButterfly

To initiate this put butterflywe sold the60/65put spreadat0.71(byselling the65putat1.30andbuyingthe60putat0.59)andboughtthe65/70putspreadat1.49(bybuyingthe70putat2.79andsellingthe 65 put at 1.30). We’relong the 60/65/70 putbutterfly at 0.78. What doesthis payoff chart look like?

WeseethatinFigure11.9.

Figure11.9ALongPutButterflyIsaSpreadMadeUpofTwoPutVerticalSpreads

The first thing to notice isthat the general shape of thepayoff and risk of the longputbutterflyisidenticaltothelong call butterflywe lookedat earlier. In this case thestockhastodropbecauseweboughtaputbutterflyandtheunderlying stock was at72.47, which was above our

breakeven prices (rememberthere are two breakevenprices foreachbutterfly)andmaximum profit level, butthat justmeans that we havethe same sort of affirmativedirectional outlook, we thinkthestockisgoingtomoveina particular direction, in thiscase that direction is lower.This put butterfly realizes itsmaximum potential profit of4.22 (the 5.00 width of eachspreadminusthe0.78costof

the butterfly) with the stockprecisely at 65.00 atSeptember expiration. Thebreakeven points are 60.78and 69.22. Above 69.22 thebutterfly loses money, andabove 70.00 it loses themaximum possible, the 0.78wepaidforthebutterfly.Below 60.78 this longbutterflylosesmoneybecausethestockhasdroppedtoofar.This is the risk in buying a

butterfly—the stock canmove too much and therebywipe out our gains. It is theprice paid for a butterflycosting so much less than asimpleverticalspread.Below60.00 this put butterfly losesthe maximum possible, the0.78thatwepaidforit.Sellingaputbutterflyisverysimilar to selling the callbutterfly that we sawpreviously.Let’stakeanother

lookatthoseputoptionpricesand a put butterfly that wemight sell. We see such ashort put butterfly in Figure11.10.

Figure11.10PutOptionsandSellingaPutButterfly

If we buy the 62.5/67.5 putspreadbybuyingthe67.5putat 1.93 and selling the 62.5put at 0.88, then we’ll pay1.05. Ifwe sell the67.5/72.5put spread and collect 1.97,then we will have sold the62.5/67.5/72.5 put butterflyand collected a net of 0.92.Although it’s easy to getturned around because these

areputspreads,weknowthatwe’re short the butterflybecause we collected moneyand because we’re short the“wings,” the 62.5 and 72.5puts in this case. What doesthis payoff chart look like?WeseethatinFigure11.11.

Figure11.11PayofffortheShort62.5/67.5/72.5PutButterfly

Our maximum profit is the0.92 that we collect and werealize that with theunderlyingstockabove72.50or below 62.50 at expiration.The maximum loss is 4.08,but that’s realizedonly if theunderlying stock is atprecisely67.50atexpiration.

■ Butterflies Prior toExpirationSo far, we’ve looked at ourbutterfly’s outcomes atexpiration but since theunderlying stock can movetoo far if we’re long abutterfly, and because thezone of maximum profit ornear maximum profit atexpiration is so small for along butterfly, it’s often

necessary to close thebutterfly position prior toexpiration to realize areasonableprofitandtomakecertainourprofitdoesn’tturninto a loss. We’ll neverrealizethemaximumprofitifwe take the trade off beforeexpiration.Abutterflycanmovetoofar,so the maximum profit isrealized only with theunderlying stock precisely at

thatmiddlestrikepreciselyatexpiration, but if we enter along butterfly understandingthat we’ll likely take it offprior to expiration and thatwe’ll not realize thattheoretical maximum profitthenwecansizeour trade ina way that’s appropriate andthentakeitoffwhenit’sdonewhat we wanted it to dowithout feeling that we’reforegoing a bunch ofpotentialprofit.

Similarly, youmightwant toclose your short butterflypositionprior toexpiration ifit shows a profit because theremaining value, theadditionalprofitwe’llmakeifweholdtheshortbutterflytoexpiration, canbevery smallin relation to the maximumpotential loss if theunderlyingstockmovesinthewrongdirection.WesawinChapter3thatthe

payofflinepriortoexpirationis more rounded than thelinear result we get atexpiration. Let’s look at thesamesortofpayofflinespriorto expiration for somebutterflies. We see these inFigure11.12.

Figure11.12ProfitandLossforaButterflyPriortoExpiration

Figure11.12assumesthatwebought a hypothetical105/110/115 call butterflywhen there were 60 days toexpirationand theunderlyingstock was at 100.00. As youcansee,wepaid0.54forourbutterfly so that’s ourmaximum loss. If the stockwas at 110.00 at expirationthenwe’dstandtomake4.46

(5.00–0.54).Ourbutterflyisclearly bullish, our lowerbreakeven is 105.54, so weneedthestocktorally to justbreak even at expiration andany of these time framesrequire the stock to rally inordertorealizeaprofit.Butifthe trade is bullish, thenshouldn’t it show at leastsome profit if the underlyingrallies after we buy thebutterfly,evenifthere’squiteabitof time toexpiration?It

certainlyshould,anditdoes.As with all of the payoffcharts, these preexpirationpayoff charts aremuchmoreroundedandthepreexpirationprofitandlosslinesgraduallybecome more linear, morelike the completely linearprofit and loss line atexpiration, as expirationnears. The flattest curve isthisbutterflywith30days toexpiration,thesteepestcurve,

other than the expirationpayoff,isthisbutterflywith5days to expiration and themiddle curve is this butterflywith15daystoexpiration.Asyoucansee, theshapeof thecurve is morphing into thelinear chart that is the profitorlossatexpiration.At 30 days to expiration ourbutterfly is clearly bullish, ifthe underlying hasn’t movedfrom the 100.00 it was at

when we executed ourbutterfly, we still need it torallyinorderforourbutterflytobeprofitable,butitdoesn’thavetorallymuch.Withjust30 days to expiration thebutterflythatwepaid0.54forwould break even; that is, itwould be worth the 0.54 wepaid,iftheunderlyingwereatabout101.00.Eventhough30days have passed, we needthe underlying to rally byonly 1 percent to get to

breakeven. But as timepasses, that lower breakevenprice continues to increaseand the speed by which itincreases accelerates. From60 days to 30 days itincreases about 1 percent,from 60 days to 15 days itincreases 2.35 percent, from60daysto5daysitincreases4.00 percent, and from 60daystoexpirationitincreasesthecomplete5.54percent.

Thesameistruefortheupperbreakeven. With 30 days toexpiration it’s about 120.00,with15daystoexpirationit’sabout 118.50,with 5 days toexpiration it’s about 116.30,andatexpirationitis114.46.Notice again that this upperbreakeven level is movingtoward the 114.46 upperbreakeven that the butterflyhasatexpirationand that thespeed of that movementincreasesasexpirationnears.

The profitable range isobviously broader with moretimetoexpiration;itcoversawider swath of underlyingpricesaswecanseebythesebreakeven prices and by thefact that the profitable rangenarrowsas time toexpirationnears.Thiswiderprofitrangeis great; it means that ourmarginoferror regarding theprice of the underlying islarger. The price of theunderlying still has tomove,

in the case of our long callbutterfly it has to movehigher,butwithmoretimetoexpiration it doesn’t have tomove as much. We see thatwith everything else beingequal the breakeven at 30days to expiration is 101.00.The price of the underlyingcan stillmove toomuch, butwithmore time toexpiration,it has tomovemore in orderto move too much. Withsubstantial time to expiration

(30 days in this case), theunderlying doesn’t have tomove all the way to that105.54 breakeven in order togenerateaprofitandcanstillshow a profit if it’s movedpast the upper breakeven of114.46.Again,refertoFigure11.12 and notice how thebreakevenlevelsapproachthemiddle strike price—theynarrow—as time passes andexpiration approaches. Butwhat do we give up for that

increased margin of safety,for the fact that theunderlying doesn’t have tomove as far to show a profitbut can move more and stillshowaprofit?Theanswer islower maximum profit. Themaximum profit is lowerwhenthetimetoexpirationisgreater. With the underlyingat 110.00 with 59 days toexpiration, our 105/110/115butterflywouldbeworth1.10versus the 5.00 it would be

worthatexpiration.As you can see from ourhypothetical butterfly, themaximumprofitwith30daysto expiration is pretty smallwhen compared to the othertime frames. With theunderlying at 110.00—regardless of the time toexpiration, the maximumprofit is still going to berealized with the underlyingat the middle strike price—

the butterfly with 30 days toexpiration shows a profit ofabout0.96;wehavenotquitedoubledourinitial0.54.With15 days to expiration thebutterfly shows a profit ofabout1.49;wehavenotquitetripledourinitial0.54.With5days to expiration thebutterfly shows a profit of2.45; we have not quitequintupledourinitial0.54.This shape to the profit or

loss chart is the reason thatusers of butterflies should bethinkingofthisasatradethatneeds to be tended, probablytaken off before expiration,and as the sort of trade thatmight double or triple yourmoney but not as the sort ofthat that will turn your 0.54(the initial cost of thisbutterfly) into 4.46 (themaximum potential profit ifthe underlying stock isprecisely at 110.00 at

expiration) because the oddsoftheunderlyingstockbeingat precisely 110.00 atexpiration are extremelyremote. The math says thatlikelihood is just less than0.05 percent or about 1 in2,000.

■ButterfliesandYourMarketExpectationsAs we’ve just seen, a longbutterfly is made with aspecificmarketoutlook, longan out-of-the-money callbutterfly is a bullish trade,longanout-of-the-moneyputbutterfly is a bearish trade.However, a short butterfly,like almost every other shortoption position, isn’t a

speculation that somethingwill happen—it’s aspeculation that thesomething won’t happen. Along call butterfly assumesthemarketwillrally.Ashortcall butterfly assumes themarketwill not rally, at leastnot very much, so it makesmoney if the market drops,moves sideways, and,depending on the strikes,even if the market rallies alittle aswell as if themarket

rallies “too much” and isabovethehigheststrikepriceat expiration. A short callbutterfly is a speculation thatthemarketwon’tbebetweenthe strike prices of the wingoptionsatexpiration.Similarly,alongputbutterflyassumesthemarketwilldropand a short put butterflyassumesthemarketwillrally,move sideways, drop onlyslightly, again depending on

theparticularstrikeprices,ordrop far enough to be belowtheloweststrike.We’ve seen how much themarket must move for ourlongbutterflytobeprofitable.We’ve seen how much themarketcanmoveforourlongbutterfly to stay profitable,that is, how far is too far.We’ve see how the marketcan move for our shortbutterflies to be profitable.

Now that we know theseprice levels, how can wefigure out the likelihood thatthe underlying stock will beat or beyond those pricelevels?That likelihood is thedeltawediscussedearlier.Let’stakeanotherlookatthathypotheticalcallbutterflyanddetermine the likelihood thatthe underlying stock will atleast get to the lowerbreakeven without going

above the higher breakeven.Figure11.13showstheprofitand loss chart with thebreakevens and thelikelihoods that theunderlying stock will beabovethosebreakevenlevels.

Figure11.13ButterflyBreakevensandThoseLikelihoods

The delta of an option is,among other things, thelikelihood that it will be in-the-money at expiration. Ofcourse,noactualoptionsexistwith strike prices preciselyequaltoourbreakevenprices,but we can use the tools atwww.OptionMath.com topretend there are such strikeprices and to calculate the


deltas for those fictionaloptions. If we do that, thenwefindthatthedeltaofa60-day (the time to expirationwhenthistheoreticalbutterflywaspriced)calloptionwithastrike price of 105.54 (thelowerbreakevenprice) is27.Thus, the likelihood that theunderlying stock,which is at100.00now,willbeabovethelower breakeven price of105.54 at expiration is 27percent. The delta of the 60-

daycallwithastrikepriceof114.46 (thehigherbreakevenprice) is 5, so what is thelikelihoodthattheunderlyingstock will be in the rangebetween those twobreakevenprices?That’s22percent (27percent – 5 percent). Theodds of this butterfly beingprofitableatexpirationare22percentorabout1in5.That’snot very likely, and it’sanother indication that youshould expect to close your

butterfly position beforeexpiration when there’s awider range of profitableprices.But it also recognizesthatalongbutterflygeneratesenormous leverage. Ourhypothetical butterfly cost0.54andcouldbeworth5.00at expiration, which wouldgenerate a profit of 4.46, an825 percent profit. And theodds of at least quintuplingour money? About 11percent. We see these

likelihoodsinTable11.2.

Table11.2OurCallButterflyandHowLikelyIsIttoBeReallyProfitable

Outcome

atExpiration

RelevantPriceat

ExpirationLikelihood

Maximumloss

realized

<105or>115

76%(71%+5%)

Atleast >105.54 22%(27%

breakeven and<114.46

–5%)

Doubleourmoney

>106.08and<113.92

19%(25%–6%)

Quintupleourmoney

>107.70and<112.30

11%(20%–9%)

What if we turned thisbutterflyaroundandsolditat0.54? The odds of the stockbeing between 105.54 and

114.46 at expiration are still22 percent. It doesn’t matterif we’re long or short thebutterfly—the odds are thesame.Sofarwe’veseenthatout-of-the-money butterfly spreadshave some specific marketoutlook; a long butterflyexpectsthemarkettomoveina particular direction by aparticular amount while ashortbutterflyexpectsittodo

the opposite which meansmove the opposite direction,notmove at all, ormove toomuch. But the questionbecomes how out-of-the-money is our butterfly, andhow far do we expect theunderlying stock to move ornotmove?Two specifics affect ourbutterfly: how wide thebutterfly is and how out-of-the-moneyitis.

Asthelongcallbutterflygetsfurtherfromat-the-moneythelower breakeven point getsfurther from at-the-money,the likelihood that theunderlyingwillgetatleasttothat lower breakeven pointbecomes lower. That meansthebutterflyshouldcost less,assuming the maximumpotential value remains thesame. If the potential valueremains unchanged but thelikelihoodofatleastbreaking

even drops then the tradeshould cost less. Let’s see ifthat’showitworksout.Table11.3 shows the theoreticalbutterfly prices using thesame data we used for our105/110/115 call butterfly.There were 60 days toexpiration, the underlyingstock was at 100.00 and theimplied volatility for all theoptionswas20percent.

Table11.3SomeCallButterflies

andtheOddsofaProfit

Butterfly Cost LowerBreakeven

100/105/110 0.94 100.94101/106/111 0.86 101.86102/107/112 0.78 102.78103/108/113 0.70 103.70

104/109/114 0.62 104.62105/110/115 0.54 105.54106/111/116 0.47 106.47107/112/117 0.40 107.40108/113/118 0.34 108.34109/114/119 0.29 109.29110/115/120 0.24 110.24111/116/121 0.20 111.20112/117/122 0.16 112.16113/118/123 0.13 113.13114/119/124 0.10 114.10

115/120/125 0.08 115.08

As you can see, as thebutterflygetsfartherfromat-the-money, the cost goesdownbutthelikelihoodofthebutterfly at least breakingeven drops as well. You canseethisinFigure11.14.

Figure11.14DistancefromAt-the-Money,Cost,andLikelihoodofBreakingEven

A trader long a butterflywants it to achieve itsmaximumvalueatexpiration.A trader short a butterflywantsittohavevalueofzeroat expiration. The importantelement is that the cost stayspretty closely tied to thelikelihood of the butterflyhaving any value at

expiration. There’s not anyone of those trades that’s amuch better deal than anyothers, particularly onceyou’ve factored in theexecution cost including thewidth of the bid/ask spread.Simply said, the farther thebutterfly is from at-the-money,thefartheritneedstomove to break even. A longcall butterfly that is fartherout-of-the-money is morebullish. A long put butterfly

that is farther out-of-the-moneyismorebearish.

■BrokenButterfliesSo far we’ve examinedsymmetrical butterfliesexclusively. These were allmade up of two verticalspreads that had the samedistance between the strikeprices. The fact that thevertical spreads making upour butterfly are the samewidth—that is, they have thesame distance between thestrike prices—means that the

spreadthatisclosertoat-the-money is going to be moreexpensivethantheonethatisfurther from at-the-money.This is what generates thepotentialprofitforabutterflyseller, but it also means thebutterflybuyerhastopaythenet cost and the butterflybuyer ends up with a tradestructure that has a fairlynarrow profit window and aminiscule window to realizethemaximum profit. Since a

butterfly is a spread of twovertical spreads, couldn’t wechange the width of thespread that is further out ofthemoney,therebycollectingmoreforsellingitaspartofalong butterfly, and reducingoreliminating thecostof theentire trade? We’d end upwith a trade that wasn’tsymmetrical, which is whyit’s often called a brokenbutterfly.

While thebuyerofa regular,symmetrical butterfly losesallofthepremiumpaidiftheunderlying stock isn’tbetween the strike prices ofthe wings, the buyer of abrokenbutterflycanoftenputthe trade on without payingany net premium. But weknow there’s no free lunch,so what’s the downside of abroken butterfly if it doesn’tcost us any premium? Thepotential loss isgreater if the

underlyingmakesabigmove,a move that extends beyondthe most distant strike price.In Figure 11.15, we look atsome call option prices inXOP, the crude oil andnatural gas exploration anddevelopmentexchange-tradedfund and examine a brokenbutterflywemightexecute.

Figure11.15CallOptionsandBuyingaBrokenCallButterflyinXOP

This is a butterfly becausewe’re buying a nearbyvertical call spread—the80/82 in this case—andselling a further out-of-the-money vertical call spread—the 82/85 call spread in thiscase—that shares a strikewithourfirstcallspread.Itisabrokenbutterflyratherthanatraditionalbutterflybecause

this butterfly is made up ofspreads that aren’t the samewidth; the spread we’rebuying is $2wide,while thespread we’re selling is $3wide.Observant readers will notethatwe’rebuyingthisbrokenbutterfly because we’rebuying the outer strikes, thewings, but we’re alsocollecting a little netpremium.Ifwe’rebuyingthe

wings we’re buying thebutterflyandwhilewemightcollect some premium indoing so, we’re payingelsewhere, probably in thefact that we’ve changed therisk, the maximum potentialloss,aswe’llsee.Thisisoneof the very few instanceswhen we might say we’rebuying a spread whilecollectingpremium.Whatwillbetheprofitorloss

for this broken butterfly atexpiration?Previously,we’vebuilt a complete profit andloss table and generated theresults for a bunch of strikeprices or we’ve created apayoff chart. Those can bothbehelpful,andwe’llcreateatraditional payoff chart later,butinsteadofcreatingaprofitand loss table with everysingle strike, let’s create asmarter profit and loss tablewith only the inflection

points. We see this in Table11.4.

Table11.4ProfitandLossforOurBrokenCallButterflyattheInflectionPoints

InflectionPoint

80/82VerticalCall

SpreadProfit/Loss

82/85VerticalCall

SpreadProfit/Loss

80.00 –0.68 0.7682.00 1.32 0.76

85.00 1.32 –2.24

As long as XOP is below80.00 at expiration,we’ll getto keep the 0.08 we initiallycollected, all the optionswillexpireworthless, andwe canreevaluate. With XOP at82.00atoptionexpiration,the80/82 call spread will haveachieved its maximum valueof2.00, the82/85callspreadwillbeworthless,andwewill

also have our original 0.08.At the body of the brokenbutterfly, our profit will be2.08, which is the net weoriginally collected plus thewidthofthefirstspread.OnceXOPhaspassedbeyondthemostdistantstrike,the85strike in this case, we willsustain our maximumpotentialloss:we’lllosemorefrom shorting the 82/85 callspread thanwe’llmake from

buying the80/82 call spread,and the 0.08 we originallycollected won’t make up thedifference. Our loss will bethedifferenceinthewidthsofthespreads—1.00inthiscase(3.00 width minus 2.00width)—less/plus the initialnetpremiumcollected/paid.Let’s extend the prices welook at to make certain this0.92 loss is our maximumlossandseewherewesustain

that loss.Youcansee this inFigure11.16.

Figure11.16BrokenCallButterflyinXOP

The maximum loss for ourbroken butterfly is 0.92, andthat occurs with XOP at orabove 85.00 at optionexpiration. This greaterpotential loss is the pricewepay for the fact that weactually collected 0.08 whenwe initiated this trade ratherthanpayingaswewouldwitha traditional, symmetrical

butterfly.Inorder totrulyevaluate thisbroken butterfly, we have tocompare it to the genericbutterfly we might haveexecuted. Ifwe’d bought the80/82/84 call butterfly, wewouldhavebought the80/82callspreadfor0.68(sofarthetwo trades are identical) andwould have sold the 82/84call spread for 0.56 (this iswhere the two trades differ),

meaningwepayanetof0.12for this traditional butterflyversus collecting 0.08 forbuying the broken butterfly.The difference between thetwo trades is 0.20, and thatmakes sense, as this was thedifference in price betweenthe 84 strike call which wastrading at 0.76 and the 85strike callwhichwas tradingat0.56.Since we would have paid

0.12 for the traditionalbutterfly, that would havebeen ourmaximum loss, andwe would have lost that fullamount with XOP above84.00 or below 80.00 atoptionexpiration.Instead, with the brokenbutterflywe collect 0.08, butourmaximumlossis0.92andwe sustain that with XOPabove 85.00 at optionexpiration. This leads to the

question,istheextra0.20wesaveworththeaddedrisk?Let’s use the tools atwww.OptionMath.com todetermine the likelihood thatwe’ll lose that entire 0.92. Ifwedothatmath,wefindthatthedeltaforthis85strikecallis 19, meaning there’s a 19percent chance we lose thefull0.92.It’snoaccidentthat19percentof0.92is0.175,oralmostexactlythe0.20we’re


saving (the differencebetween 0.20 and 0.175 isgenerated by the bid/askspreadsofalltheoptions;forourpurposesthenumbersareessentiallyequal).Soareyoubetter off buying the brokenbutterfly or the traditionalbutterfly? The math saysyou’re equally well off, butyourinsightintowhatXOPisgoing to do, your ability toinitiate the trade effectively(it’smadeupof3 legsand4

optionssoexecution isgoingtobekey),andyourabilitytomanage the trade prior toexpiration will make thedifference.You could apply the sameprinciple and generate abroken put butterfly thatcould be initiated for no netpremium or that wouldgenerate a small net credit.By buying a put spread andthen selling another put

spread that isbothwiderandmore out-of-the-money,you’ll spend less money upfront, and maybe generatethat small credit, but facemore risk if the underlyingdropsbelowtheloweststrikeprice.As such, broken butterflies,whether using calls or puts,are trades that expect amoderate movement in aspecific direction—up for a

broken call butterfly, downfor a broken put butterfly—but think a large move thatwould take the underlyingpast the furthest strike byexpirationisunlikely.

CallButterflyCheatSheet

LongCallButterfly

Description

LongoneOTMcallShorttwo

furtherOTM

callsLongoneevenfurtherOTMcall

Example

ATM=100Longone105callShorttwo110callsLongone115call

Payor

CollectPremium

Pay



MarketMovement

--

IncreaseinImplied


Movement

+


MaximumRisk

Costofthebutterfly

MaximumProfit

Differencebetween

wingstrikeandbody

strikeminusnetpremium

paid

BreakevenPoints

Lowest

strike+NetpremiumpaidHighest

strike-Netpremiumpaid

PutButterflyCheatSheet

LongPutButterfly

Description

Longoneput

Shorttwo

furtherOTM

putsLongoneevenfurtherOTMput

Example

ATM=100Longone95

putShorttwo90

putsLongone85

putPayor

CollectPremium

Pay



MarketMovement

--

IncreaseinImplied


Movement

+


MaximumRisk

Costofthebutterfly

MaximumProfit

Differencebetween

wingstrikeandbody

strikeminusnetpremium

paid

BreakevenPoints

Lowest

strike+NetpremiumpaidHighest

strike-Netpremiumpaid

CHAPTER12

CondorsandIronCondors

Verticalspreadswereoneof

the very first structures weexamined because they’reincredibly versatile,particularlywhenwereplacedan individual option with avertical spread such as in acallspreadriskreversalor inaputspreadcollaraswellaswhen we combined twosimilar vertical spreads tocreate a butterfly. But if webuy the wings and sell thebody of an out-of-the-moneybutterfly, then theunderlying

stockhastomoveinorderforthe butterfly to be profitableand the maximum profit isonly achieved if theunderlying stock is preciselyat the middle strike price atoptionexpiration.Ifthestockisevenalittleaboveoralittlebelow that middle strikeprice, then theprofit realizedis less than the maximumpotential profit. Since abutterflyisreallytwoverticalspreads that share a middle

strike price, what happens ifweusetwoverticalspreadsinthe same sort of generalconfiguration but selectvertical spreads that don’tshare a central strike pricemeaning that the range ofmaximum profit is wider?That would be a condor. Acondor is a spread of twovertical spreads. In a longcondor,we’llbuyoneverticalspread and sell anotherverticalspread;thespreadwe

buy is an in-the-moneyvertical spreadmeaning bothlegs are in-the-money, whilethe spreadwe sell is an out-of-the money vertical spreadin that both legs are out-of-the-money. Let’s look atsome call options on Apple(AAPL) and see how wemightusethemtoconstructalong call condor.Since someof these options are in-the-moneyandhavewidebid/askspreadswe’llusetheaverage

ofthebidpriceandaskprice.We see these options inFigure12.1.

Figure12.1BuyingaCallCondorinApple

This longcall condor is longan in-the-money call verticalspread, the 410/440 callspread (long the 410 call,shortthe440call),whichcost24.52. Since we’re long thiscallverticalandsinceitisin-the-moneywewantAAPLtostay near its current price of456.68, rally, or declineonlyslightly while staying above

440.00, because those threeoutcomes result in this callvertical spread achieving itsmaximum value of 30.00 atexpiration. If any of thosethree outcomes occur, nomovement at all, a rally or asmall decline, then we’llrealize the maximumpotential profit of 5.48becauseAAPLwillbeabove440.00 at option expirationand the call spread we paid24.52forwillbeworth30.00

at expiration. But a callcondorisalsoshortanout-of-the-money call verticalspread, the 470/500 callspreadinthiscase,forwhichwe receive 5.65. Sincewe’reshort this 470/500 callvertical and since it’s out-of-the-moneywewantAAPLtostay near its current price of456.68, decline, or rally onlyslightly while staying below470.00 so that this callvertical expires worthless

which it will do as long asAAPLisbelowthe470strikeat expiration. The in-the-money vertical spread needslittlemovementorarally,theout-of-the-money verticalneeds little movement or thestocktofall.Inthenet,alongcondor needs the stock toexperience little movement,weneedtheunderlyingstock,AAPL in this case to exhibitlittlevolatility.

A long condor, either call orput, is a limited risk,nondirectionaltradethatwe’dexecute when we expectedlittlevolatility.Acondor isaspread of two verticalspreads. It’s similar to abutterfly, which is also aspread of two verticalspreads, but a butterfly usesonly three strike prices withthe middle strike, called thebody,beingsharedbythetwovertical spreads. A condor

splits the body and insteaduses two different strikeprices. In the case of ourApple call condor the bodywassplitintothe440and470strike calls. A long condorwantsthestocktobebetweenthe two vertical spreads,meaning between the twocenter strikeprices, (440 and470 in this example) atexpiration. That’s when itachieves its maximum profitbecausethelongverticalwill

achieve its maximum valuewhile the short verticalexpires worthless. The twovertical spreads are usuallythe samewidth,measured asthe distance between thestrike prices, althoughchanging the width of onespread slightly might alignthecondorwithaparticularlyimportantpointonthestock’schart.Themaximumriskforalong

condor is the net premiumpaid,18.87forourSeptemberAAPLcallcondor.Let’slookat the sort of payoff chartwe’refamiliarwithtoseethisandwe’ll chart the payoff aswe should, as a combinationof two call vertical spreads.We can see this in Figure12.2.

Figure12.2LongtheApple410/440/470/500CallCondorandtheConstituentVerticalSpreads

SinceFigure12.2showsboththe component verticalspreads and the resultingcondoritcanbealittletoughto figureoutwhich iswhich.It’s important to rememberthat a condor is a spreadmade up of two verticalspreads but let’s look at justthe condor for clarity’s sake.

See Figure 12.3, which alsoshows the importantinflection points for thiscondor.

Figure12.3TheAAPLCallCondor

The cost of the condor is18.87 so that’s themaximumrisk, themost thecondorcanlose.We’llrealizethatlossifthe long call vertical, thelower vertical (the 410/440call spread in this case) isworthless, meaning that allthat we spent to buy it hasbeen lost while the premiumreceived for selling the short

vertical, the upper vertical(the 470/500 call spread inthis case), isn’t enough tooffsettheloss.IfthelongcallverticalexpiresworthlessthisAAPLcallcondorwouldlose24.52 by buying the lowervertical spread, the 410/440callspread,butweonlymake5.65 for selling the uppervertical, the 470/500 callvertical.Thenetlossis18.87(24.52–5.65).

We’ll also realize thatmaximumlossof18.87iftheshort vertical is worth itsmaximum value of 30.00meaning that we onlycollected 5.65 to sell a callvertical spread that is nowworth 30.00, but the gainfrom buying the lowervertical spread, the 410/440call vertical spread, is only5.48. In this case, we lose24.35sellingthe470/500callverticalspreadandonlymake

5.48 (30.00 – 24.52) frombuyingthelowercallverticalspread. The net loss again is18.87 (24.35 – 5.48). We’lllose the maximum value iftheunderlyingstockisbelowthe lowest strike price orabovethehigheststrikepriceatexpiration.But what’s the maximumprofit? The maximum profitis the maximum potentialprofit from the call vertical

we’ve purchased plus themaximum potential profitfromthecallverticalwesold.This maximum potentialprofit will be realized whenthelowercallverticalspread,the 410/440 call verticalwe’vepurchased, isworth itsmaximum value of 30.00 atexpiration meaning we’vemade the maximum profitpossible in being long it,while the upper call verticalspread, the one we’ve sold,

the 470/500 call vertical,expires worthless meaningwe’ve made the maximumpotential profit from beingshortit.Thismaximumprofitwill be realized when theunderlying stock is betweenthe vertical spreads atexpiration meaning theunderlying stock is betweenthe two short legs. You canseethisinTable12.1.

Table12.1OurAAPLCall

CondorandtheImportantPotentialOutcomes

Outcome Result

WhereDoesThis

Occur?

Maxprofit

+11.13(5.48+5.65)

Between440.00and

470.00

–18.87 Below410.00

Maxloss (24.54–5.65)

orabove500.00

Breakeven(lower)

0.00(–5.65+5.65)

428.87

Breakeven(upper)

0.00(5.48–5.48)

481.13

What are the likelihoodsthese outcomes will occur?Whatisthelikelihoodthatthe

underlying stock will bebetween the two verticalspreadsatexpirationmeaningthat we’ll realize themaximum profit? You canseetheselikelihoodsinTable12.2.Wecanuse the toolsatwww.OptionMath.com tocalculate these likelihoodssince, as we know, theselikelihoods are the optiondeltas.

Table12.2Important


LikelihoodsforOurAPPLCallCondor

CallOptionStrikePrice

CallOptionDelta

410 88428.84(lowerbreakeven) 74

440 65470 33

481.13(upper

breakeven) 25

500 12

Today’slikelihoodofthe440strikecallbeingin-the-moneyat expiration, given all thevariables including time toexpiration, current stockprice, volatility, and so on is65percent.Wewantthis440call to be in-the-money atexpiration so that we realizethe maximum value of the

410/440 call spread. Today’slikelihood of the 470 strikecallbeingin-the-moneyis33percent;wewantthis470callto be out-of-the-money atexpirationsothatwekeepthepremium received for sellingthe470/500call spread.Thatmeans the likelihood ofAAPLbeingbetweenthetwostrike prices at expiration,AAPL being above 440 butnot above 470, is 32 percent(65 percent – 33 percent).

The likelihood of realizingthemaximumprofit of 11.13for thiscallcondor is that32percent.What is the likelihood ofrealizing the maximum loss?That’s the likelihood thatAAPL is above 500 plus thelikelihood that AAPL isbelow 410 at optionexpiration because eitheroutcome will result in themaximum loss. The delta of

the410call is88, so today’slikelihood of AAPL beingbelow there at optionexpiration is 12 percent. Thedelta of the500 strike call is12, so the odds of AAPLbeing above there at optionexpirationarealso12percent.Thatmeans the likelihood ofthis AAPL call condorrealizingitsmaximumlossof18.87 is 24 percent (12percent + 12 percent). Andwhat are the odds of at least

breakingeven?Thedownsidebreakeven is 428.87; this isthe point at which the lossfrom the long call spread isprecisely offset by the profitfrom the short call spread.Wecancalculatethedeltaforthis hypothetical 428.87strike call using the tools atwww.OptionMath.com,but itmeans that we’ll have to“borrow” the volatility inputfrom a nearby option. If wedothatwedeterminethat the


deltaof thishypothetical calloption is 74. The odds oflosing the maximum amountbecause AAPL droppedbelow410are12percent,theodds of losing anymoney atall because AAPL droppedtoofar,thatis,becauseAAPLdropped below 428.87, is 26percent.The odds of losing themaximum amount becauseAAPL rallied too far are 12

percent, the odds of losingany money at all becauseAAPL rallied too far are 75percent.It’senoughtosaythatalongcondorcanbeagoodstrategyif you’re looking for adefined risk way to profitfrom low realized volatilityover the term of the options,although the maximum losscan be substantially morethanthemaximumprofit.

We’velookedatbuyingacallcondor in AAPL. Condorsworkwell with puts as well.Since long put condors arevery similar to long callcondors, we’ll take a veryquick look at a long putcondor. Figure 12.4 showssome puts onAAPL that wemight use to construct a putcondor.

Figure12.4BuyingaPutCondorinAAPL

Again,we’regoingtobuyanin-the-money vertical spreadand sell an out-of-the-moneyvertical spread. In this case,the in-the-money verticalspread we are buying is the470/500 put spread (buyingthe500strikeput,sellingthe470strikeput)andtheout-of-the-money vertical spreadwe’re selling is the 410/440

put spread (selling the 440strike put, buying the 410strike put). The 470/500 putspread cost 24.35, while wereceive 6.45 for selling the410/440putspread.Thetotalcost of this put condor is17.90.Noticethattheverticalspreadshave thesamewidth,andtheyareaboutequidistantfrom where the stock iscurrentlytrading.Andwhatisthemaximum profit and lossfor this Apple September

410/440/470/500put condor?Wherearethoserealized?WecanseethisinTable12.3.

Table12.3OurAAPLPutCondorandtheImportantPotentialOutcomes

OutcomeProfitor

Loss

WhereDoesItOccur?

Maximum +12.10(5.65+

Between440.00

profit 6.45) and470.00

Maximumloss

–17.90(24.35–6.45)

Below410.00orabove500.00

Breakeven(lower)

0(5.65–5.65) 427.90

Breakeven(upper)

0(6.45–6.45) 482.10

Let’s connect the dots again

andsee the traditionalpayoffchartforthislongputcondorinAAPL.YoucanseethisinFigure12.5.

Figure12.5ALongPutCondorinAAPL

The general payoff for thisput condor and the callcondor that used the samestrikes are very similar.Whyaren’ttheyidentical?Becausethe underlying stock wasn’tprecisely between the twovertical spreads when wepriced them. AAPL was at456.68 so it was slightlyclosertothe470/500vertical.

But the general shape of thetwo payoff charts is verysimilar, as we’d expect. Sowhich condor to use? If thecall condor is easier for youto understand, then use thecall condor. If for somereason the bid/ask spread forin-the-money puts is tighterthan for in-the-money calls,then use the put condorbecause it will be easier andcheapertoexecute.We’lltalkmoreaboutthebid/askspread

shortly.

■SellingaCondorSincethemaximumprofitforalongcondorisrealizedwiththeunderlying stockbetweenthe two vertical spreads atexpiration, we want theunderlyingstocktostandstill,to not move, to not bevolatile. This means that ifwe thought the underlyingstock was going to do theopposite and be very volatileand make a big move we

might want to sell a condor.For example, if we thoughtIWM, theRussell2000ETF,wasgoingtobeveryvolatile,thenwemightwanttosellanIWMcondor.Let’slookatanIWM call condor that wemight sell with IWM at94.71.We see this in Figure12.6.

Figure12.6SellanIWMCallCondortoTakeAdvantageofExpectedVolatility

We sell this IWM condor at1.44 by selling the in-the-money vertical spread, the91/94 call spread (selling the91 strike call and buying the94 strike call), at 2.13 whilesimultaneously buying theout-of-the-money verticalspread,the97/100callspread(buyingthe97strikecalland

sellingthe100strikecall),at0.69. Let’s take a look atFigure12.7which shows thepayoff for selling this IWMcondor.

Figure12.7AShortCallCondorinIWM

This short condor losesmoney, a maximum of 1.56,if IWM doesn’t move. Wecollectedanetof1.44,but ifIWMdoesn’tmove, then the97/100 call spread we paid0.69forwillexpireworthless,meaning we’ll lose that 0.69while the 91/94 call spreadwesoldat2.13willexpireatits maximum value of 3.00,

meaningwe’velost0.87.Ourtotallosswillbe1.56(0.69+0.87).It’snoaccidentthatourmaximumpotentiallossisthewidth of one of the spreadsminus the net premiumcollected.IWMhas tomove below the94 strike or above the 97strike inorder tonot lose themaximum, it has to movebelow 92.44 or above 98.56in order to make anymoney

and it has to move below91.00 or above 100.00 inordertorealizethemaximumpotentialprofitof1.44.Let’sseehowbig thosemoves areinpercentagetermsandwhatthe delta says the likelihoodofeachmoveis.WeseetheseinTable12.4.Again,youcanuse the tools atwww.OptionMath.com tocalculate these deltas foryourself.


Sothelikelihoodoflosingthemaximum amount is only 24percent, but the likelihoodofrealizing themaximumprofitis38percent.Sellingacondorisalittlelikebuyinga straddle.Weexpectsubstantial volatility in thepriceoftheunderlyingbutwedon’t know in whichdirection so we’re going tocover all our bases andestablish a position that

makes money regardless ofthedirectionofthemove.It’scheaper to establish than astraddle, for example, theJuly 95 strike straddlewouldhavecost4.29,although0.29of that is inherentvalue.Ourmax loss from the straddlewould be that 4.29 spent ifIWM was at precisely 95.00atoptionexpiration.Boththeshort condor and longstraddle need IWM to reallymove and both have limited

riskbutonly the straddlehasessentially unlimited profit.The short condor, however,has its maximum potentialprofit fixedat1.44nomatterhow far IWM falls below91.00orralliesabove100.00.Selling a condor is likebuyingastraddleinthatbothare blunt instruments oftrading because we don’thave to be correct as todirection but the condor alsohaslimitedprofitpotential.

■TheBid/AskSpreadandCondorSpreadsIn buying a condor we saidthat we were essentiallyagnostic as to whether weestablish our condor usingputsorcallswithonecaveat.Ifcallsorputsthatarein-the-moneyshowparticularlytightbid/ask spreads then wegenerally want to use thattypeofoptiontoestablishour

condor. It would be unusualforin-the-moneyputstooffergood (i.e., tight) bid/askspreads and in-the-moneycalls to have wide bid/askspreads but it’s possible;usually, both will havebid/ask spreads that are tightor wide with tight being theexception if the option is in-the-money. Butwhat generalimpact might the bid/askspread have on our condor?After all, we’re trying to

executefourdifferentoptionsand we’ll certainly try toexecuteourcondorasasingletrade minimizing the impactof the bid/ask spread butwe’ll still have to pay aliquidity provider somethingin the form of a bid/askspread. Let’s return to ourvery first condor andremember that the singlepricewesawforeachoptionwas,forsimplicity’ssake,theaverageofthebidandaskfor

each option. Table 12.5shows the bid and ask foreach component of that firstcondor that we bought, theAAPL 410/440/470/500 callcondor, to see how thebid/ask spread might impactourcondor.

Table12.4ImportantLikelihoodsforOurShortCallCondorinIWM

Describe Price Likelihood

Move (Delta)Move

downwardenoughtoavoidmax

loss

94.00 44%

Moveupwardenoughtoavoidmax

loss

97.00 32%

Movedownward

enoughtoreach

breakeven

92.44 35%

Moveupwardenoughtoreach

breakeven

98.56 19%

Movedownwardenoughtoachievemax

91.00 27%

profitMoveupwardenoughtoachievemaxprofit

100.00 11%

Table12.5BidandAskPricesforOurAAPLCallCondor

Option Bid AskSeptember

410call 46.70 47.30

September440call 22.25 22.70



Ifwewere to simplypay theask price for the options weneed to buy and collect thebid price for the options we

need to sell, we would pay19.50 for this AAPL callcondor rather than the 18.87weassumedearlier.We’dpay0.63 more, driving ourmaximum profit from 11.13to 10.50 without any changein how or where thatmaximum profit is achieved.Given that we’d hope toexecute our condor at thosemidpointswe originally usedbutthatwe’dhavetogiveupsomething to get our trade

done,afterall,marketmakersaren’tinbusinesstofacilitateourtradewithoutmakinganyprofit for themselves, it’svery likely that our actualexecution price, the priceweactually pay, is going to behigher than 18.87. Is there away to reduce the impact ofthe bid/ask spread on the in-the-money call verticalspread?Ifwelookatthefouroptions making up our callcondor we’ll notice that the

out-of-the-moneyoptions,the470 call and 500 call, havenarrowerbid/askspreadsthanthe in-the-moneyoptions, the410calland440call.Isthereaway to replace that portionof our condor, the in-the-money 410/440 call spread,with something that’s out-of-the-money and has bid/askspreadssimilar to thebid/askspreadsoftheseotherout-of-the-money options? What ifinstead of buying that

410/440 call spread we soldthe 410/440 put spreadmeaningthatwesoldthe440put and bought the 410 call?Figure 12.8 shows what thatwouldlooklike.

Figure12.8AnIronCondorinAAPL

Themaximum profit for thistrade would be the total of12.10 received, 5.65 forselling the out-of-the-moneycall spread and 6.45 forselling the out-of-the-moneyput spread and would berealized if both verticalspreads expired worthlessmeaningAAPLwas between440 and 470 at option

expiration, the same rangeofunderlyingpricesthatyieldedthe maximum profit for ouroriginal call condor. Thatmaximum profit of 12.10 isnot very different from themaximumprofit of 11.13 forthefirstcondorwelookedat.The maximum loss for thistrade would be 17.90, the30.00maximumvalueofbothspreads less the 12.10received. We would

experience that maximumlossifeitherof thoseverticalspreads was fully in-the-money at expiration. Thatmeans AAPL would have tobebelow410orabove500atexpiration for this trade torealizeitsmaximumloss.It’sinteresting that this is thesame range thatwould resultin the maximum potentialloss forourcall condor.Thismaximum potential loss of17.90 is not that much

different than the maximumpotentiallossof18.87forourcallcondorspread.And how would the bid/askspreadimpactthisnewtrade?Let’s take a look at thebid/ask spreads for all of theoptionsinthisnewtrade.While we initially assumedwe executed this trade at12.10, even if we sold everyoptionthatwehadtosell,the440 put and 470 call, at the

bid and simultaneouslyboughteveryoptionwehaveto buy, the 410 put and 500call, at theask,we’dexecuteour trade at 11.83 (6.28 +5.55). That’s only a 0.27penaltychargedby thewidthof themarket rather than the0.63 penalty we might havepaid for our original condor.What is this new, magicalstructure called? It’s an ironcondor.

■IronCondorAn iron condor is executedby simultaneously selling anout-of-the-money put spreadand an out-of-the-money callspread. Both spreadsgenerally have the samewidth and they are roughlyequidistant from the currentstockprice,although,aswithallspreadsandcombinations,if changing a strike priceresultsinamorelogicaltrade

or a trade that makes moresense given an importantlevelon the stock chart, thendon’t feel bound by thetraditional definitions. In thiscase, we execute an ironcondorbysellingthe410/440put spread andsimultaneously selling the470/500 call spread. An ironcondor is a limited risk,nondirectionaltradethatwe’dexecute when we expectedlittlevolatility.Thegoalisto

have both vertical spreadsexpire worthless. What doesthis payoff chart look like?WeseethatinFigure12.9.

Figure12.9A410/440/470/500IronCondorinAAPL

The condor that resulted inthenearly identicalpayoffasthis iron condor was a longcondor so this iron condor isconsidered a “long” ironcondor even though we’resellingbothspreads.Observant readerswill noticethat our resulting optionposition is short one option

strangle and long anotherwider option strangle thatserves to define the risk.Wesold the 440/470 strangle bysimultaneously selling the440 put at 8.65 and the 470call at 7.93 to collect a totalof 16.58. That 16.58 wouldbe ours to keep, but we’dhave unlimited risk so wesimultaneously bought the410/500 strangle by buyingthe 410 put at 2.20 and the500callat2.28.Thatstrangle

cost4.48butagain,itdefinesour risk. This “stranglespread” generates a net of12.10 (16.58 – 4.48) inpremium. That 12.10 is themaximum profit. Themaximum potential loss is17.90. The maximumpotentialprofitandmaximumpotential loss are identical tothepotentialoutcomesforouriron condor because the twotradesareidentical.Onceyoustart to see these symmetries

in your option positions,you’ll understand the bestwaytomakeadjustingtrades,andyou’llbeonyourwaytobeingarealoptiontrader,notjust an investor who usesoptions.

■DirectionalCondorsSo far, all the structureswe’ve looked at have had anoutlookastovolatilitybutnotnecessarily direction. Weboughtacondorifwethoughtthe underlying wasn’t goingto be volatile and would bebetween the middle strikeprices at expiration. Or, wesold a condor if we thoughtthe underlying was going tobeveryvolatileandgetbelow

the lowest strike price orabovethehigheststrikeprice.We didn’t care aboutdirection as long as it wentfar enough in whicheverdirectionitfinallypicked.The samewas truewith ironcondors. We either wantedtheunderlying tositormoveand if it moved, we didn’tcareinwhichdirection.What if we had a point ofviewondirection?Wemight

buy a vertical spread. Indoing so, we’ll have gottenexposure in the desireddirection while reducing thecost of simply buying anoption outright. But we’vealready seen how we mightreplace an option with avertical spread, what if wereplaced both of the optionsin a vertical spread withverticalspreads.We’dhaveadirectional condor and we’dprobably have it pretty

cheaply. Figure 12.10 showssome options in Netflix(NFLX)thatwemightusetocreate a directional condor ifwewerebullishNLFX.

Figure12.10BuyingaDirectionalCallCondorinNFLX

We pay a net of 6.40 forbuying the 450/465 callspread,butwecollectanetof5.00 for selling the 480/495call spread.Ournetoutlay isjust 1.40, but if NFLX isabove 465.00 and below480.00 at the optionexpiration, our directionalcondor will be worth 15.00(450.00 – 465.00). We will

have turned our 1.40 into15.00 for a profit of 13.60.Youcan see thepayoff chartinFigure12.11.

Figure12.11ADirectionalCallCondorinNFLX

NFLX was at 443.00 whenthis condorwas priced so allthe options were out-of-the-money. Unless NFLX ralliesto the lower strikeprice, 450in this case, we’ll lose theentire 1.40. If NFLX ralliestoo much and is above the495strikeatexpiration,we’lllose the entire 1.40 as well.Butthere’saprettybigsweet

spot,465.00to480.00,wherewe’ll make the maximumprofit and an even widersweetspot,451.40to493.60,where this condor willgenerate a profit even if theprofit isn’t the maximumpotential profit.What are thelikelihoods of theseoutcomes? We see that inTable12.7.

Table12.6BidandAskPricesforOurNewOptionStructurein

AAPL

Option Bid AskSeptember410

put 2.13 2.27

September440put 8.55 8.75

September470call

7.85 8.00


Table12.7ImportantLevelsand

LikelihoodsforOurDirectionalCondor

DescribeMove Price Likelihood(Delta)Moveupwardenoughtoavoidmax

loss

450.00 53%

Moveupwardenoughto 451.40 52%

reachlowerbreakevenMoveupwardenoughtorealizemaxprofit

465.00 48%

Moveupwardenoughtobegin

surrenderingmaxprofit

480.00 43%

Moveupwardenoughtoreachupperbreakeven

493.60 39%

Moveupwardenoughtofully

surrendervalueandrealizemax

loss

495.00 38%

The likelihood of NFLXbeing between 465.00 and480.00atoptionexpirationisjust 5 percent (48 percentminus 43 percent) and thelikelihood of generating anyprofit is just 13 percent (52percentminus39percent),sothe odds of turning our 1.40to 15.00 are pretty remote.But that’swhatwe’d expect.It’snevergoingtobeeasytogenerate a 1,000 percentprofit.

A directional condor is justthat, a directional trade. Youwouldn’t execute this callcondor in NFLX unless youexpected NFLX to rallygently until Decemberexpiration. And since all thelegs are out-of-the-money,the bid/ask spread should belessofanissuethanitwouldbe for a traditional condorwith one of the constituentspreads in-the-money, butyou’re still executing four

different legs, so executionwill be important to theultimateprofitability.

CallCondorCheatSheet

LongCallCondor

Description

LongITMcallverticalspread

ShortOTMcallvertical

spread

Example

LongOne90strikecallShortOne95strikecallShortOne105strike

callLongOne110strike

callPayor

CollectPremium

Pay



MarketMovement

++

Increasein

ImpliedVolatilitywithoutMarket

Movement

+


MaximumRisk

Netpremium

paid

Maximum

WidthofITMspread−Costof

Profit ITMspread+PremiumreceivedforOTMspread

BreakevenPoints

Second

loweststrike−Maxprofit

Second

higheststrike

+Maxprofit

PutCondorCheatSheet

LongPutCondor

Description

LongITMputverticalspread

ShortOTMputvertical

spread

Example

Longone110strikeput

Shortone105strikeputShortone95strikeputLongone90strikeput

PayorCollectPremium

Pay

Needed

Directionality

Passageof

TimewithoutMarket

Movement

++

IncreaseinImplied


Movement

+

Payoff

ThumbnailChart

MaximumRisk

Netpremium

paid

MaximumProfit

Widthof

ITMspread−CostofITMspread+

PremiumreceivedforOTMspread

BreakevenPoints

Second

higheststrike−Maxprofit

Secondloweststrike+Maxprofit

IronCondorCheatSheet

LongIronCondor

Description

LongOTMcallverticalspread

LongOTMputvertical

spread

Example

Longone105strikecall

Shortone110strikecallLongone95strikeputShortone90strikeput

PayorCollectPremium

Pay

Needed

Directionality


MarketMovement

−−

IncreaseinImplied


Movement

+

Payoff

ThumbnailChart

MaximumRisk

Netpremiumpaid

MaximumProfit

Widthofonespreadminusnetpremium

paid

Breakeven

Lowercall

strikeplusnetpremium

paid,higher

Points putstrikeplusnetpremiumpaid

CHAPTER13

Conversion/Reversal

Aconversionorareversalisan option combination that

retail traders will executevery rarely as a package(meaning as a single trade)and professional marketmakers will execute onlyoccasionally. But aconversion or reversal is anoption combination that asmart retail trader might enduphavingon;however,itwillonly be because of separatetradesthatleadtotheultimateconversion or reversalposition.

A conversion is a three-legged combinationmade upof a long position in theunderlying stock and asyntheticshortpositioninthestockmade up of a long putand short call, both with thesame strike price andexpirationdate.Aconversion:

Long100sharesofKOat39.70

Short1November39callat0.95Long1November39putat0.25

How does this conversionmake money? We start with0.70 in our pocket becausewesoldthe39callat0.95butpaidonly0.25forthe39put.The combination of the twooptionpositionsisasyntheticshort position in KO stock.

Howso?Shortacallandlongaputwiththesamestrikeandexpiration date will end upselling the stock—either thecall will be assigned andwe’ll sell the stock at theexercise price of 39.00, orwe’llexercisetheputandsellthestockattheexercisepriceoftheput;againthat’s39.00.For example, if KO is at35.00atexpiration,belowthestrike price of our put, thenthe call would expire

worthless and we wouldexercise our put, therebyselling our KO shares at39.00.Butwepaid39.70 forthe stock, so the net of 0.70wecollectedfromouroptionspaysforthelossonourstock.Ignoringcommissions,we’vebroken even on ourconversion, so itdidn’tmakeany money with KO belowthestrikeatexpiration.If KO is at 40.00 at

expiration, above the strikeprice of our options, thenwe’d still startwith that 0.70in our pocket from thesynthetic short position. Thelong put would expireworthless but our short callwould be in-the-money andthe owner would exercise it.That means we would beforced to sell our stock at39.00, the strike price of thecallwe’re short, even thoughKO was at 40.00. We’d be

sellingstockat39.00thatwehad just bought at 39.70, sowe would experience a 0.70lossonthestock.Thiswouldbepreciselyoffsetby thenetof 0.70 we collected fromsellingthecallandbuyingtheput. Again, ignoringcommissions, we’ve brokeneven on our conversion so itdidn’tmake anymoneywithKO above the strike atexpiration.

The conversion didn’t makemoney with the stock belowthe strike price and didn’tmake money with the stockabove the strike price. Whathappens with the stock rightatthestrikeprice?IfKOisatprecisely39.00atexpiration, then both optionswill expire worthless; whowould pay for an option tobuyorsellKOat39.00ifyoucouldjustbuyorsellat39.00

directly?Westartedwith0.70in our pocket and that willprecisely offset the 0.70 losswe experienced as KOdroppedfrom39.70to39.00.In this case,we still own thestock,butwecouldeasilysellit at 39.00 and be donewiththetradefornoprofitorloss.In fact, if we don’t sell itwe’re making a consciousdecision to keep it. Thissituation, when the stock ispreciselyatthestrikepriceat

expiration, causes specialconcerns for the option user.Why?Iftheownerofthecallisalsoshortthestockthenhemay choose to exercise hiscall thereby closing his shortpositioninthestock.Ifthatisthe case, we own KO stockand have it called away thenwecanletourlongputexpireworthless and we’ll deliverour shares to the call ownerand we’ll be left with noprofitorlossandnoposition.

If the owner of the calldoesn’t exercise his option,then it will expire worthlessand we might chose toexercise our put, therebyselling our shares. Again,we’dbeleftwithnoprofitorloss and no position. If wewant out of the positioncompletely, including sellingourstock,thenweeitherwantour short call assignedorwewant to exercise the put weown,butnotboth.

Theproblemforthispositionis thatwewon’t know if thecall owner has exercised hiscall until it’s too late tochoose to exercise our put.We would have to guesswhethertheownerofthecallis going to exercise beforemakingadecisionaboutwhatto do with our put—exerciseitorabandonit.This is the situation when atrader might execute one of

these three-legged trades—inorder to take thewhole tradeoff and eliminate this risk ofthe stock closing precisely atthestrikepriceonexpiration.Because the long stock isprecisely offset by thesyntheticshortpositioninthestockthatiscreatedbysellinga call and buying a put withthe same strike price andexpiration, a conversionshould never make or lose

money ignoring commissionsandthebid/askspread.All this doesn’t mean youmightnotlegintothepositionover time at prices that areultimately profitable. We’lldiscuss how this can happenlaterinthischapter.Itsimplymeans that you shouldn’t beable to execute such a three-legged tradeasapackage,asa single trade, and do so atprices that would generate a

profitatexpiration.

■ReversalAreversalistheoppositeofaconversion. A reversal is athree-legged combinationmadeupofashortpositioninthe underlying stock and asynthetic longposition in thestockmade up of a long calland short put, both with thesame strike price andexpirationdate.Areversal:

Short100sharesofKOat39.70Long1November39callat0.95Short1November39putat0.25

Let’s do the same exercisesandseeifareversalcanmakemoney.WithKO at 36.00 atexpiration, the owner of theput we’re short would

exerciseitandwewouldbuyKOat39.00, thestrikeprice.The call we’re long wouldexpire worthless. We wouldhavemade 0.70 on the stock(shorted at 39.70, bought at39.00), which would offsetthenetof0.70thatwepaidtobuythecallandshorttheput.Ignoring the bid/ask spreadand trading costs we didn’tmake or lose any money. Ifwewere to do the same sortof math for a closing price

above the 39.00 strike pricewe’d find the sameoutcome.If we were to do the samemath for a closing price ofprecisely39.00,we’dfindthesame outcome. Conversionsdon’t make money andreversals don’t make money.In fact, after accounting forthebid/askspreadandtradingcosts, both a conversion andreversal will likely losemoney. So you’d neverinitiate either combination;

howmightyouendupwithaconversion or reversal as aposition?Let’s assume I’m long 100shares of XYZ stock. Thestock has appreciated nicely,andIthinkit’slikelytomovesideways to down slightlyoverthenextseveralmonths.If I could sell it at a slightlyhigher level than the currentprice,thenI’dliketodothat.IfIcouldgetalittledownside

protection,thenI’dliketodothat, too, but I’m not hugelyworried, and I’m happy toholdmystockotherwise.Thisis the perfect time to do acovered call; if the stockrallies, then it will be calledawayandwewillhavesolditataslightlyhigherpricethanI could get right now. Thepremium we collect fromselling the covered call willgenerate a little bit ofdownside protection. Perfect!

Ifwe sell a covered call, weendupwiththisposition:Acoveredcall:

Long100sharesofXYZwhichisnowat56.35Short1April57callat1.25

Let’sassumethatafterwe’vesold the covered call XYZstockralliesslightly,whichiswhat we thought might

happen. If XYZ is at 57.75with a couple of weeks toApril expiration, then ourcovered call has workedperfectly. Assuming XYZdoesn’tdropbackbelow that57 strike price then we’regoing to sell our stock at57.00,butwe’llalsohavethe1.25 in premium. We’ll sellourstockataneffectivepriceof58.25eventhoughitwasat56.35 when we sold thecoveredcall,isat57.75now,

anddespitethefactthatXYZmay never trade as high as58.25. But this all assumesXYZ doesn’t drop backbelow the 57 strike price. Ifthat happens then the ownerof the callwe’re shortwon’texerciseitandwe’llstillownthe stock, something wedidn’t want. In fact, if XYZdropsbelow55.10thenwe’reworseoff forhavingsold thecovered call rather than justselling our stock at 56.35. In

this case, that’s not what wewanted; we wanted to sell ifwe could do so above thecurrent market. So how canwebecertainwe’llgettosellour stockat apriceno lowerthan 57.00 after it’s risen to57.75,ratherthanbeingatthemercyoftheownerofthecallwe’re short and at themercyof the market? By buying a57 strike put! Time haspassed and XYZ stock ishigher, so that put should be

fairly inexpensive. If wecould buy it today at 0.10thenwewouldstillhave1.15(1.25 – 0.10) in our pocketandwe’dbealmostcertainofselling our stock at 57.00.Theonlytimewewouldn’tbecertainisifXYZclosedrightat 57.00 on the day theseoptions expire.Why not justsellthestockandbuythecallback? Because the bid/askspread for the in-the-moneycall option is likely to be

prettywide,whilethebid/askspread for the out-of-the-money put will probably beonly 0.01 and the time valuefor the put, 0.10, will beidentical to the timevalueofthe call so we’re better offpaying the same amount oftime value but paying asmaller bid/ask spread bybuying the put. What wouldthisnewpositionlooklike?Ournewposition:

Long100sharesofXYZShort1April57callat1.25Long1April57putat0.10

Our new position is aconversion.You can see thatit’s identical to thedefinitionofconversionwestartedwith.We’re long stock and have ashortsyntheticpositioninthe

stock thanks to the short calland long put of the sameexpiration date and strike.This is how a trader ends upwith a conversation eventhoughhemightneverinitiatethe trade as a conversion.We’dsayheleggedintoit.IfXYZ drifted back down andwas at 57.00 at Aprilexpiration, then we mightdecide to closeout the entireposition, selling the stockwe’re long, buying the call

we’re short, and selling theput we’re long in order toeliminate the risk of notknowing what the owner ofthe call will do. This risk ispinrisk,thatis,theriskofthestock closing right at that57.00 strike.We’ll talkmoreabout pin risk later in thischapter.

■DividendsSowe’ve seen howwe can’tmakeanymoneybyinitiatingaconversionorareversalbutthatwemight end up havingthe position on. Let’s takeanother look at KO optionsand make certain we can’tmakeanymoneybyinitiatingaconversionor reversal.ThefirstKOoptionsweexaminedexpired in November; theseoptionsexpireinDecember.

Areversal:

Short100sharesofKOat39.70Long1December39callat1.16Short1November39putat0.65

Let’s make certain this tradecan’tbeprofitable.Wespendanetof0.51forthesyntheticlongstockthatweexecuteby

sellingtheputandbuyingthecall. With KO at 35.00 atDecemberexpiration,ourcallwill expireworthless,but theowner of the putwe’re shortwillexerciseitandwe’llbuyKOat39.00, thestrikeprice.We’llmake0.70onthestockwe were short. That meanswe will have made a net of0.19 (0.70 – 0.51)! What ifKOisabovethatstrikeprice?With KO at 41.00 atexpiration, wewill have still

spent0.51fortheoptionsthatcreate the synthetic longstock position. The put willexpire worthless and we’llexerciseourcallandbuyKOat 39.00. We were short at39.70, so we make a net of0.19 again! And if KO is at39.00atexpiration?Well,wefacethesamepinriskthatwediscussedearlierbuttheoddsof that are small and we’llstillmake0.19.Howcanthisbe? Why wouldn’t I do this

trade as many times as mybrokerwillletmeandpocket0.19 for each contract?Because there is a dividendthat will be paid after theNovemberoptionsexpireandbefore the December optionsexpire. If you’ve shortedstock, that means youborrowed it first and you’llhavetopaytheamountofthedividendtowhoeverlentyouthe stock. That’s thediscrepancy.There’sno“free

money”tobemade.

■PinRiskWe’ve mentioned pin risk,it’s the risk that the stockcloses right at, or very closeto, the strike price shared byboth the put and call, on thedayofexpiration.Inthatcasewe don’t know if the ownerof the short leg of ourconversion or reversal willexercise it—it may havesimplybeenaspeculationforthem so they may not have

anyreasontoexerciseit,oritmay be a hedge in order toliquidate their position suchas a long call versus shortstock; inthatcase, theownerof the call may very wellexercise it—and we won’tknowiftheyhaveexercisedituntil it’s too late for usrespond. That’s one of thebenefits of owning optionsand one of the liabilities ofshortingoptions.

Rather than taking the entiretradeoff to avoidpin risk, isthere an easier way to avoidpin risk while potentiallyspendinglessoncommissionsand thebid/askspread?Sure,we can just buy back theoption we’re short. With afew hours of trading left onthe day of option expirationwe have the followingconversionon:

Long100sharesofABCat90.00Short190calltradingat0.10Long190puttradingat0.10

Rather than taking thisentiretradetoexpirationandhopingthat we can figure out whatthe owner of the call we’reshortwilldo,wecanjustbuythat call back, pay 0.10 and

have the destiny of the tradein our own hands. After wedothat,we’releftwiththis:

Long100sharesofABCat90.00Long190puttradingat0.10

With thenewposition,we’regoingtogetnothinglessthan90.00 for our stock becauseevenifit’sbelow90.00atthe

endoftheday,we’llexerciseour put. If ABC is above90.00 at the end of the day,we can sell our stock forwhatever we can get and letthelongputexpireworthless.And if ABC is at precisely90.00 at the end of the day,wecangoaheadandexerciseour put and sell the stockthere. This is one of thosesituations when someonemightexerciseanoption thatispreciselyat-the-money.

We’ve avoided all the perilsofpinrisk,anditonlycostusthe0.10wepaidtobuybackourcall.Ifyou’recertainyouwant to completely exit theposition, including theposition in the underlyingABCstock,thenonceyou’vebought your short call backyou can offer the stock forsale at 90.10 using a limitorder. If your offer is liftedandyou sell the stockat thatprice then you’vemade back

the 0.10 spent to close theshort call position. We’veexitedourpositionjustaswewanted, we don’t have theuncertainty of pin risk, andwe’resimply left long the90strike put. Since there’s solittle time until expiration,probably just a couple ofhours, and since ABC istrading higher, at 90.10, weprobablycan’tsell thisputatany price. But once we’vesold our stock, we can offer

thisput forsaleat, say,0.10,again using a limit order. IfABC drops again beforeexpirationthenwemightendupsellingourputandwewillhaveactuallymade0.10morethanifwe’dsimplytakentheentire position to expirationwiththeattendantpinrisk.

ConversionandReversalCheatSheet

Conversion

Description

LongsharesShortsharessynthetically

Long100

Example

sharesShortone100strike

callLongone100strike

put

PayorCollect

Premium

Payifstrikepriceis

aboveshareprice,collectifstrikeprice

isbelowshareprice


Doesnotmatter,nomovementwillgenerateaprofitorloss


MarketMovement

Noimpact


Movement

Noimpact


MaximumRisk

Pinriskistheonlyriskinherentinaconversion

MaximumProfit

Shouldbezero

BreakevenPoints

Aconversionshouldbreakevenatevery

priceforunderlyingatexpiration

CHAPTER14

RatioSpreadsandBackSpreads

Nearly all the spreads andcombinations we’veexamined so far offer oneelement, an option or avertical spread, versus or incombination with only oneother element, anoptionor avertical spread or shares ofstock or cash to buy theshares if they’re put to us.Finally, in ratio spreads andback spreads,we lookat oneoptionatastrikepriceversus

more than one option at astrike price that is fartherfromat-the-money.Ratiospreadsbuyoneoptionand sell two options of thesametypeandexpirationwitha strike price that is fartherfromat-the-money.Theresultisatradethatmakesmoneyifthere’s a modest move in aparticulardirection,upwardifwe’re using a call ratiospread, and downward if

we’re using a put ratiospread, but since we’re netshortanoption—wesoldtwooptions but bought only one—the trade losses money ifthe move is too extreme.Since we’re net short anoption, the loss can besubstantial.Back spreads, however, sellone option and buy twooptionsof the same type andexpirationwith a strike price

that is farther from at-the-money. A back spread is atrade that requires asubstantialmove, upward fora call back spread anddownward for a put backspread. If the underlyingmoves only a little, eventhough it moves in ourdesireddirection, thenabackspreadcan losemoney,butasubstantial move in theexpected direction willgenerateunlimitedreturnsfor

acallbackspreadandreturnsthat are limited only by thefact that theunderlyingstockcan’t drop below zero for aput back spread. Figure 14.1shows some put options inQQQ, the Nasdaq 100exchange-traded fund (ETF),andaputratiospreadthatwemight construct in the Aprilexpiration as well as a putback spread that we mightconstruct in the Mayexpiration.

Figure14.1AnAprilPutRatioSpreadandaMayPutBackSpreadinQQQ

Ratiospreadandbackspreadstrike prices are generallyselected so that the trade isdoneforzeroorverylittlenetpremium,butthat’swherethesimilaritiesend.We’lllookatthetwostrategiesseparately.The put ratio spread that weconstructusingtheoptionsinFigure 14.1 buys one of the

April 89 strike puts at 1.25and sells twoof theApril87strike puts at 0.73 each,collecting a total of 1.46 forsellingthetwoputs.Theratiospread generates 0.21 in netpremiumthatwegettokeep.Let’s look at Figure 14.2 tosee the payoff for this putratiospread.

Figure14.2TheApril87/89PutRatioSpreadinQQQ

As QQQ falls below thestrikepricewe’relong,the89strike, this put ratio spreadstarts to make money inaddition to the 0.21 net thatwecollectedatinitiation.Themaximum profit is achievedwhen the underlying ispreciselyatthestrikepriceoftheoptionswe’reshort,87.00inthiscase.Atthatpoint,the

89strikeput isworth2.00atexpiration, the 87 strike putswe’re short are worthless atexpiration, and we have thatadditional0.21inourpocket.As we’ve seen before, themaximum profit is realizedwith the underlying stock atthestrikepriceoftheoptionswe’reshortatexpiration.As QQQ falls below the87.00 level, those 87 putsstart to have value at

expiration; they’re no longerworthless at expiration.Theystart to eat into the 0.73 wereceived for selling each ofthem. And since we’re shorttwo of them and long onlyoneof the89strikeputs,ourlosses increase as QQQdrops.And thebreakevenforourputratiospread?Wehaveto account for the long putmaking money and the shortputs losing money. Thebreakeven for a put ratio

spread is the lower strike, 87in our case,minus the widthof the spread, 2.00 in ourcase, less any net premiumreceived or plus any netpremium paid since this is aput ratio spread.We subtractif we received premiumbecause that moves thebreakevenlower,fartherfromat-the-money, and we add ifwe paid premium becausethatmoves thebreakevenup,closertoat-the-money.Inour

putratiospread,wecollected0.21 of premium, so ourbreakeven point is 84.79(87.00–2.00–0.21).Thegeneralshapethatweseein Figure 14.2 will hold forallputratiospreads,althoughif we’d paid a small amountof net premium, the payoffchart would look slightlydifferent and the payoff forprices higher than the upperstrike price would be a net

loss of the net premium wepaid.For example, ifwehadinstead executed the 86/89put ratio spread by buyingone of the 89 strike puts at1.25andsellingtwoofthe86strike puts at 0.56 each wewouldpayanetof0.13.WithQQQ above 89.00 atexpiration our put ratiospread is going to lose that0.13.That’snottheonlywayour payoff chart would lookslightlydifferent.Weseethat

inFigure14.3.

Figure14.3TheApril86/89PutRatioSpreadinQQQDoneataNetDebit

Below that breakeven (thelowerbreakevenforput ratiospreads done at a debit) thetrade thatwasmildly bearishhas gone too far—it’sdropped too much. Ratiosspreadsarelikeabutterflyinthat the underlying stock canmove too much. Observantreaderswillnoticethataratiospread is very similar to a

butterfly except that abutterflyisalsolongoneevenfarther out-of-the-moneyoptioninordertodefinerisk.Ifwestartedwithouroriginalputratiospread,the87/89putratio spread, and bought an85 strike put at 0.44 wewouldhave turnedour 87/89put ratio spread into an85/87/89 put butterfly. WecanseethisinFigure14.4.

Figure14.4ARatioSpreadIsAlmostaButterfly

■ Vertical Spreads,Butterflies, and RatioSpreadsBy now you recognize thatvertical spreads, butterflies,and ratio spreads are similareven though they’re notidentical. A butterfly is aspreadoftwoverticalspreadsand a ratio spread is both abutterfly without the mostout-of-the-moneywing and a

long vertical spread that ispaid for by selling an extraout-of-the-money option(what would be the body ofthebutterfly).Aswegofromvertical spread to butterflyspread to ratio spread, thecost of the trade goes downuntilwe’reattheratiospread,whichwillbedonefornearlyzero net premium or thatmight actually generate alittle net premium for us tocollect aswe saw in the first

putratiospread,the87/89putratio spread that weexamined.Butwhile thecosthasdroppedaswemovefromvertical spread to butterflyspread to ratio spread, thedanger from the underlyingmovingtoofarhasincreased.Foralongverticalspread,theunderlying can’t move toofar.Aslongastheunderlyingstock hasmoved beyond ourlong vertical spread, that isabovebothstrikepricesfora

call vertical or below bothstrikepricesforaputvertical,then we will make themaximum profit possible atexpiration, and it doesn’tmatter how far it movesbeyond our vertical spread.At expiration, $100 past ourlong vertical spread is asgood as $0.10 past ourspread. For a long butterflyspread the underlying canmove too far and the profitwe had when the underlying

was at the strike of theoptions making up the bodyof our butterfly becomes aloss with that additionalmovement, but our loss islimited to what we paid forthe butterfly no matter howfar the underlying stockmovespastourbutterfly.Fora ratio spread, not only canthe underlying move too farbuttheprofitwewouldenjoywith the underlying at theshort strike at expiration

becomes a loss and that lossis essentially unlimited. Asthecostof thetradestructuredrops,theriskincreases.Youcan see this in Figure 14.5.Notethattheriskincreasesasthe cost of the spreaddecreases but note also thatthemaximumprofitisalwaysrealizedorfirstreachedatthestrike of the option we’reshort,87.00forthesespreads.

Figure14.5PutRatioSpread,PutButterfly,andPutVerticalSpread

■CallRatioSpreadsCall ratio spreads need theunderlying stock to rallyslightly, and like put ratiospreads, they sustainsubstantial losses if theunderlying stock moves toomuch, even if themove is inthe desired direction. Let’slookatsomeoptionsonDIA,the Dow Jones IndustrialAverage exchange tradedfund, and see howwemight

construct a call ratio spreadand a call back spread. YoucanseetheseinFigure14.6.

Figure14.6AMayCallRatioSpreadandaJuneCallBackSpreadinDIA

This call ratio spread isconstructedthesamewayweconstructed the put ratiospread. We buy one calloption and sell two calloptions that are farther out-of-the-money to pay for thecalloptionwebuy.TheMay167/169 call ratio spread isdone for nearly zero netpremium as we collect only

0.01 for executing it. Sincewe’reshorttwocallsandlongonlyonecall,thisratiospreadwould have unlimited risk ifDIA rallied enough. Themaximum profit of 2.01 isrealizedwithDIAattheshortstrike price, 169.00 here, atexpiration. You can see thepayoff at expiration across arangeofpricesinFigure14.7.

Figure14.7The167/169CallRatioSpreadinDIA

Sinceanyratiospreadisshortmore options than it is long,there will be a tendency towant to close the positionprior to expiration, therebyextinguishing that risk.We’ve seen previously thatourspreadsandcombinationsdon’t realize their full profituntil expiration. Let’s seehow the value of our DIA

167/169 ratio spread changesastimepasses,assumingDIAdidn’tmove.YoucanseethisinFigure14.8.

Figure14.8HowtheDIA167/169CallRatioSpreadChangesasTimePasses

As we’ve seen before, thepayoff at expiration is linearandthepayoffsbecomemorelinearasexpirationnears.Butwith 30 days to expiration,thereisnopriceaboveat-the-moneythatgeneratesaprofit.Whyisthat?With substantial time toexpiration, the 169 calls

we’reshortwillappreciateinprice too quickly for the 167call we’re long. The loss onthe two 169 calls willoverwhelm any profit on thesingle167call.With51daysto expiration, the day weobserved these prices, thedelta of the 167 callwas 27,whilethedeltaofthe169callwas17.Thatmeansthatwith51days to expiration, a rallyof 1.00 in DIA wouldincrease the price of the 167

call by 0.27, andwe’dmake0.27 sincewe’re long one ofthose.Butthepriceofthe169strike call would increase by0.17, and since we’re shorttwo of those our loss wouldbe0.34resultinginanetlossof 0.07. And this problemonly gets worse as DIArallies. At 166.00 with 51days to expiration, the deltaof the 167 call is 43, whilethedeltaofthe169callis31.And the problem doesn’t

really get better with thepassage of just a little time.Why?Because with 30 days toexpiration, the delta of our167strikecall,assumingDIAhasn’tmovedfrom163.16,is22.And thedelta of our 169strike call is 11. That meansthat with 30 days toexpiration, the167strikecallwe’relongwillgoupinvalueby 0.22 if DIA moves from

163.16 to 164.16, while the169 callswe’re shortwill goup in value by 0.11. Butwe’re short two of the 169calls so the 0.22 we makefrom our long 167 call isalmost exactly offset by thelossinour169calls.AndthisonlygetsworseasDIAralliesbecause those deltas willchange over time—they’llboth increase as DIA rallies.Thosedeltaswere22and11,respectively, with DIA at

163.16 and 30 days toexpiration.At 166.00 and 30days to expiration, thosedeltas are 42 and 26. Thetools atwww.OptionMath.com areavailable so you canexperiment with any ratiospreadyou’reconsidering.Until the options are verycheaparatiospreadisashortvolatility position, we needrelatively little movement,


and we need it in the rightdirection—upward for a callratio spread, and downwardfor a put ratio spread. But aratio spread isn’t really adirectionalpositioninthatwewon’t make money justbecause the underlying hasmoved in the right direction;weneedtheunderlyingstockto be very near the shortstrike at expiration. If ithasn’t moved enough, wewon’t make much money,

and we’ll lose money if weput the ratio spread on for adebit.Ifit’smovedtoomuch,we’ll lose money as well.Like a butterfly, a ratiospread has a “sweet spot,”and we need the underlyingstock to be there atexpiration.

■ Call Ratio SpreadsforStockRepairA call ratio spread is shortmore call options than it islong. We could cover thatextra short call if we ownedthe underlying stock, as wediscussed in Chapter 4. Thepotential exists to have ourstock called away, but itwouldbeataneffectivepricethat’s much higher than the

current stock price andpotentially higher than asimple covered call. It’spossible to use a call ratiospreadtosellstockatapricemuchhigherthanthestockisatnow;infact,it’spossibletosell the stock at an effectiveprice that is higher than thestock ever actually trades at.Andsinceweexecuteourcallratio spread for no netpremium,we’renoworseoffifourstock isn’tcalledaway

than ifwe’ddonenothing. Ifwe’re facing an unrealizedloss on our stock and wouldbehappytoclosethepositionandsellourstockifwecouldsell at an effective pricegreater than thecurrentstockprice, thenwe can use a callratiospread;callratiospreadsare a great tool for stockrepair.Let’s lookat thepriceofAmazon (AMZN)becauseit’swidely held, but it’s alsowell off its recent high.

Figure 14.9 shows the 52-weekchartforAMZN.

Figure14.9StockChartofAmazon(AMZN)foraCallRatioSpread

Let’s assume we’re longAMZN from 390.00 and it’scurrently trading at 344.00.We need some stock rehab.Let’s look at some calloptions in AMZN that wemight use for that stockrehab. You can see thoseoptions and the call ratiospread we might execute inFigure14.10.

Figure14.10AMZNCallOptionsforStockRehab

You’ll notice that for theresulting position in Figure14.10 we treat our AMZNstock as if we were long itfrom the current price of344.00,ratherthanthe390.00we originally paid. That’sbecauseinmanywayswearelongat thecurrentprice.Themarket neither knows norcares where we bought the

stock, and in making thedecision to not sell at thecurrent price, 344.00, we’reeffectively making thedecision to own it, that is, tobuyit,there.While we’re buying one ofthe at-the-money calls, andthat might seem as if we’readdingtoalosingtradewhichisano-no,ourgoalistohaveAMZNabove370.00atMayexpiration. It’s easier to see

howthisworksasstockrehabif we break the trade downdifferently. Instead ofthinking of it as a ratiospread, think of it as buyingthe 350/370 call verticalspread at 6.90 (buying the350 strike call at 14.65 andselling the 370 strike call at7.75) and paying for thatverticalcallspreadbysellinga 370 strike covered call(coveredbyownershipoftheunderlyingstock)at7.75.Our

ratiospreadgenerates0.85innet premium that we get tokeep no matter what, andwhile that 0.85doesn’tmakeupformuchofourunrealizedlossinAMZNstock,itmeansthat if AMZN continueslower, we’re no worse offthanifwe’ddonenothing; infact, we’re 0.85 better offeven if AMZN continueslower.ButthegoalistohaveAMZN rally a little bit, andthe wonder of stock rehab

using a ratio spread is thatAMZN doesn’t have to rallyall thewayback toourentrypoint, 390.00, for us toeffectively sell our AMZNstockataneffectivepricethatisabove390.00. IfAMZNisabove 370.00 at Mayexpiration, then the 350/370call spread thatwe paid 6.90for will be worth 20.00. Wecollected7.75forselling that370 strike covered call aswell. Our effective selling

pricewill be 390.85, andwerealize that effective sellingprice as long as AMZN isabove 370.00,meaningwe’llhaveourstockcalledaway,atMay expiration.You can seethisinFigure14.11.

Figure14.11EffectiveSellingPricewithandwithoutRatioSpreadStockRehab

Below 390.85 this call ratiospread for stock rehab leavesus better off, and between350.00 and 390.00 we’resubstantially better off.Below 350.00 we’re onlybetter off by the net of 0.85collected, butwe’re certainlyno worse off. As long asAMZN is above 370.00 at

May expiration, we’ll haveour stock called away at aneffective price of 390.85,higherthanourentrypointof390.00. As we’ve donebefore,wecanusethetoolsatwww.OptionMath.com tocalculatethedeltaofthat370strike call and therebydetermine the likelihood thatwe’ll sell our stock at thateffective price of 390.85. Ifwe do that, we find thatlikelihoodisabout30percent


because the delta of the 370strikecallis30.Nothugebutcertainly meaningful, andmuch higher than if we donothing and wait for AMZNto actually get all theway to390.85beforeselling.We’ve fully rehabilitated ourstock position. A call ratiospread is no replacement fortrading discipline and takinga loss when a trade isn’tperforming, but in situations

like this, it canhelp save theday.

■BackSpreadsIn a ratio spreadwebuyoneoption and sell two options,what if we turn that aroundand sell one option and buytwo options with the sameexpiration date but that arefurther out-of-the-money?This structure, short oneoption and long two fartherout-of-the-moneyoptionsisabackspread.Abackspreadisatradethatdoesn’tcostmuch

toexecute,likearatiospreadwe’llputabackspreadonfornearlyzeronetpremium,andthat makes a tremendousamount of money if theunderlying stock movesenough but a back spreadlosesmoneyiftheunderlyingstockmoves only a little bit,even if it moves in ourdesired direction. A ratiospreadwantedrelativelylittlevolatility but in the desireddirection;abackspreadneeds

substantial volatility in thedesired direction. Let’s lookatsomeoptionsonAdvancedMicro Devices (AMD), astock that many consider atakeover candidate, and seehow we can use them toestablish a back spread. YoucanseetheseinFigure14.12.

Figure14.12AJulyCallBackSpreadinAMD

We construct this July 5/6call back spread by sellingoneoftheJuly5callsat0.16and using that premium tobuytwooftheJuly6callsat0.07each.Wecollectanetof0.02, but that’s not how wemakemoneywithacallbackspread. We want AMD torallyabunch.Whatdoesthispayofflooklike?Youcansee

thepayoffchart for thisbackspreadinFigure14.13.

Figure14.13TheAMD5/6CallBackSpread

Once the underlying stock isabove the strike price we’reshort, 5.00 in this case, theback spread starts to losemoney and loses themaximum amount, 0.98 (thewidth of the back spreadminus any net premiumreceived or plus an netpremium paid), when theunderlying stock is precisely

atthestrikepricewe’relong,6.00.Thatmakessense,the5strikecallwe’reshortwillbeworth 1.00 there and the 6strikecallswe’relongwillbeworthless.Butoncethestockrallies above the strike pricewe’re long,6.00 in this case,thosecallsstarttohavevalueat expiration. Breakeven is6.98, and above there theprofitforourcallbackspreadcontinues to increase. Sincewe’re long two options and

onlyshortoneoption, there’sno limit to our potentialprofit. A back spread is alimited risk structure withessentially unlimited profitpotential.Let’s use the tools atwww.OptionMath.com tocalculate the likelihood thatthis underlying stock will beabove that 6.98 breakeven atJuly expiration.We find thatlikelihood of the underlying


stock being above the 6.98breakeven at expiration isonly about 4 percent. Thatmeans back spreads areunlikely to generate a profit,but if they do, the profit canbe substantial. Some traderslike to use back spreads instocks theyconsider takeovercandidates. If a company isacquired then the jump inprice is expected to get usinto the profitable range andpotentially into the very

profitable range. And if thecompany isn’t acquired, it’sunlikely that the stock willget much above the strikepriceof thecalloptionwe’reshort, meaning it’s unlikelywe’ll sustain the maximumpotentialloss.Butenjoyingabigmoveisn’ttheonlyway tomakemoneyusing a back spread. Wenoticedthatacallratiospreadloses money with significant

time to expiration if theunderlying stock ralliesbecause the total delta of thecall options we’re short isgreater than the delta of thecall option we’re long. Wesaw the resultof thisback inFigure 14.8. Our call backspread in AMD loses themaximum amount of moneywith AMD at 6.00 atexpiration, butwhat ifAMDis at 6.00 with a significantamountoftimetoexpiration?

We can see this in Figure14.14.

Figure14.14TheAMD5/6CallBackSpreadbeforeExpiration

With 60 days to expirationand AMD at 6.00, our backspread breaks even and with60daystoexpirationitmakesmoney above that level.That’sbecause the totaldeltaofthecallswe’relongisnowgreater than the delta of thecall we’re short. Rememberthat delta is not only thelikelihood that anoptionwill

be in-the-money atexpiration; it’s also theexpected change in price forthe option for each $1.00change in the price of theunderlying.Wemakemoneyas AMD rallies, althougherosionwillstarttokickin.Unfortunately, the ratiospread is generally hurt bythisdifference indeltawhichis doubly painful because aratio spread, which is short

more options than it is long,is the spread we’d most liketo be able to close prior toexpiration in order toextinguishtheriskfrombeingnet short options. And it’salsounfortunatethatthebackspread isgenerallyhelpedbythisdifferenceindeltadespiteourwillingness to leave itonto expiration since we’re netlongoptions.It is difficult to take a ratio

spreadoffforaprofitpriortoexpiration even though wemight want to. It’s mucheasier to take a back spreadoff for a profit prior toexpiration even though wemight be willing to leave iton. And it’s much easier totake a back spreadoff as thetimetoexpirationincreases.

■SuperBackSpreadsA back spread is a volatilityspread and a directionalspread. It needs a lot ofvolatilityanditneedsitintheright direction, up for a callback spread and down for aput back spread.But the riskfor a back spread is definedas we saw in Figure 14.13.Whatifwethoughttherewasgoing to be a tremendousamount of volatility? Instead

of selling a single option tobuytwooptionswemightsellasingleoptiontobuythreeormore options (we couldconstruct a back spread withnearly any ratio we wanted,for example selling twooptions to pay for threeoptionsorselling1topayfor10,althoughthat1×10backspread would behave like asingle short, naked optionover a huge range of pricesfor the underlying stock and

would require a giganticmove in order to beprofitable).Aswebuymoreoftheoptionthat is farther from at-the-money the costof the “superback spread” will increaseandwegenerallywantabackspread tobedone for little ifany net premium if we’redoingitatadebit,orwewantit done at a credit. To offsetthe cost of the additional

options bought and stillexecute our back spread forlittle if anynetpremium, it’snecessary tobuyoptions thatare farther from at-the-money. Figure 14.15 showssomeoptionsinAbercrombie& Fitch (ANF), the teenretailer, thatwemight use tocreatesomeputbackspreadsandsuperbackspreads.

Figure14.15OptionPricesforAbercrombie&Fitch(ANF)BackSpreads

We could create a typicalbackspreadbysellingoneofthe August 38 puts at 3.32and using that premium tobuy two of the August 34puts at 1.72 each. The entiretrade would cost 0.12. Thebreakevenwouldbe29.88soANFwouldhavetobebelow29.88atAugustexpiration in

orderforthisputbackspreadto be profitable but if ANFdropped substantially, say to25.00, then the profit wouldbe4.88.Orwecouldexecuteasuperbackspreadbysellingoneofthesame38strikeputsat3.32andbuyingfourofthe30 strike puts at 0.79. Thistrade would generate netpremium of 0.16 and thebreakevenforourANFsuperback spread would be 27.38,ANF would have to drop

quite a bit for us to breakeven,butifANFwasat25.00at expiration, our total profitwould now be 7.16, and wewouldmakemoremoney foreach $1 drop in the price ofANF.Youcanseethepayofffor both back spreads inFigure14.16.

Figure14.16Abercrombie&FitchBackSpreadandSuperBackSpread

A super back spread istrading more risk (7.84maximum loss versus 4.12maximum loss) for morepotential return (7.16 profitversus 4.88 profit at 25.00).Butwe’recountingonalotofdownward volatility for oursuper back spread to makeanymorethanthe0.16wegetatexecution.

RatioSpreadCheatSheet

CallRatioSpread

Description

LongoneOTMcallShorttwo

furtherOTM

calls

Example

ATM=100Longone105

callShorttwo110calls

PayorCollect

Premium

Eitheris

possible,netpremiumshouldbeverysmall



MarketMovement

+


Movement

-


MaximumRisk

Unlimited

MaximumProfit

Higherstrikepriceminuslowerstrikepriceminus(plus)anynetpremiumpaid(received)

BreakevenPoints

Higherstrikepricepluswidthoftheratiospread

plus(minus)netpremiumreceived(paid)

BackSpreadCheatSheet

CallBackSpread

Description

ShortoneOTMcallLongtwo

furtherOTM

calls

Example

ATM=100Shortone105callLongtwo110calls

PayorCollect

Eitheris

possible,netpremium

Premium shouldbeverysmall

Needed

Directionality

Passageof

TimewithoutMarket

Movement

-


Movement

+

Payoff

ThumbnailChart

MaximumRisk

Lowerstrikepriceminushigherstrikepriceplus(minus)anynetpremium

paid(received)

(received)

MaximumProfit

Theoreticallyunlimited underlying

BreakevenPoints

Higherstrikepricepluswidthofthebackspreadplus(minus)netpremium

paid(received)

(received)

CHAPTER15

OtherSpreadsandCombinations

There are any number ofadditional ways to combineoptions into spreads andcombinations. Some work tomake use of the bestattributesofotherspreads,asa diagonal spread combinesthebestelementsofaverticalspread and the best elementsof a calendar spread. Somestrive to take advantage ofother elements that don’t getmuch attention in option

trading. For example, a boxspread, even in the equityworld, is really an interestrate play or a way for anoption trader to borrow orlend money. Others don’thave much to recommendthem. A guts spread is astrangle inwhichbothof theoptions are in-the-money;thereareotherwaystogetthesame or similar exposurewithoutpayingthepenaltyofthe bid/ask spread for in-the-

moneyoptions.Andtherearesome combinations that mayor may not be particularlyusefulbutthathaveintriguingnamessuchasChristmastree,jelly roll, and stupid. Sinceevery trader, evenprofessionals, will have littlecall to use some of these,we’llcovereachonebriefly.

■MarriedPutYou probably own stock. Ifyou own stock and wereworried that the price of thatstock might drop, then youmight sell a covered callalthough, as we saw inChapter 4, that doesn’tprovide very muchprotection. You might buy aputbutputs are expensive toalwayshave inplace,even ifyou buy longer-dated puts,

which are cheaper thanbuying a series of shorter-dated puts. How expensive?Historically, if you’d boughtanat-the-moneyone-yearputon the S&P, that put wouldtend to cost about 8 percentofthevalueoftheS&P.Sure,you’d be protected againstany loss for the next 12monthsbutyou’dhavetopayfortheput.Andthehistoricalannual return of the S&Pduring that period? About 8

percent.Yourputwouldhaveeatenupallyourstockgains.But what if you had a largeunrealized profit in a stockand didn’t want to sell it,thereby realizing your profitfor tax purposes, this year.Thenyoumightdecidetobuya protective put. Thisprotective put is sometimescalled amarried put becausethe long stock position andthelongprotectiveputbelong

together. Figure 15.1 showshow we might construct amarriedputposition.

Figure15.1AMarriedPutonNetflix(NFLX)

Welookatthistradeasifwewere long NFLX from itscurrent market price of424.50becausebynotsellingwe’re making a decision tostay long at that price, butwhen these option priceswere observed, NFLX hadjustenjoyedahugemultiyearrally. Figure 15.2 shows thepayoff for the married put

position.

Figure15.2AMarriedPutonNetflix(NFLX)

You’ll notice that the payofffor amarried put and a longcall with the same strikeprice, 420 in this case, areidentical. That’s because amarried put is a syntheticlong call position. They bothhave risk limited to theamount of time value in theoption and they both haveunlimited profit potential to

theupside.

■DiagonalSpreadAdiagonalspreadisahybridof a vertical spread and acalendar spread. A diagonalspread buys one option andsells another option of thesame type (put or call) butwith a different expirationandadifferentstrikeprice.Itcan take advantage ofdifferentialerosionbytimetoexpiration,aswediscussedinChapter6whenweexamined

calendar spreads, as well asthe lower cost of a verticalspread. A long put diagonalcanalsotakeadvantageoftherelatively higher impliedvolatilityofout-of-themoneyputs. Figure 15.3 shows howwe might construct a calldiagonalinXLF,thefinancialsector exchange-traded fund(ETF).

Figure15.3ACallDiagonalinXLF

Theresultingdiagonalislongthe June 22 strike call andshort theMay 23 strike call.This long call diagonal cost0.46,andthat’sthemaximumloss. The maximum gain isunlimited if the May callexpiresworthlessbecausetheresulting position is long theJune call outright. Thediagonal is nearly 25 percent

cheaper than theJunecallbyitself.Charting the payoff for thiscall diagonal would requireustomakemanyassumptionsabout where XLF was whenthe May option expired, thesame sort of assumptionswediscussed in Chapter 6 whenwe examined calendarspreads, sowewon’t draw apayoff chart but the goal forthisdiagonalis,asitiswitha

calendar spread, to have thefront option expire worthlessleaving us long the longer-datedoptionoutright.

■IronButterflyAbutterflyisaspreadoftwospreads; all the options arethesame typeand theysharea center strike price. Wediscussed butterflies inChapter 11. A condor is aspreadoftwospreads;alltheoptionsarethesametypebutthey don’t share a centerstrike price. We discussedcondors in Chapter 12. Anironcondorisaspreadoftwo

spreads; one spread is a callspreadandonespreadisaputspreadandtheydon’tshareacenter strike price. Wediscussed iron condors inChapter12.An ironbutterflyis a spread of two verticalspreads; one spread is a callspreadandonespreadisaputspread, but they share acenter strike price. Figure15.4 shows some options inExxonMobil(XOM)thatwemightusetoconstructaniron

butterfly, sometimes calledsimplyanironfly.

Figure15.4AnIronButterflyonExxonMobil(XOM)

Thegoalistocollectmostofthepremiumfromsellingthatcentral straddle, the 95straddle in XOM, whiledefining risk by buying that85/105strangle.Figure15.5shows thepayoffchart for this 80/95/110 ironbutterflyinXOM.

Figure15.5AnIronButterflyinExxonMobil(XOM)

An iron butterfly is usuallyconstructed as you see inFigure 15.4, which sells thebody and buys the wings tocreate a trade that collectspremium and that’s likely togenerate a profit but thatlimitspotentiallosses.Noticethat the maximum potentialloss is nearly double themaximum potential profit.

Youwould only execute thistrade if you expected littlevolatility.

■ChristmasTreeA Christmas tree spread issimilartotheratiospreadswelookedat inChapter14. Inalong Christmas tree, we buyone option, either a put orcall, that is fairlyclose toat-the-money and sell twooptionsof the same type andexpirationthatarefartherout-of-the-money but that havedifferent strike prices fromeachother.Thegoalistoget

exposuretoasmallermoveinthe underlying withoutspending much in premiumand to reduce risk bystaggeringthestrikepricesofthe two short options. Youwould buy a Christmas treeonly if you thought theunderlying was unlikely toget to either of the strikeprices of the two optionswe’ve sold. Figure 15.6shows a long put ChristmastreeinCostco(COST).

Figure15.6ALongPutChristmasTreeinCostco(COST)

And Figure 15.7 shows thepayoffchart for this longputChristmastree.

Figure15.7ALongPutChristmasTreeinCostco(COST)

AChristmastreeisaversatilestructure. Figure 15.8 showshow we might construct ashort call Christmas tree inPfizer.

Figure15.8AShortCallChristmasTreeinPfizer(PFE)

ThisshortcallChristmastreeinPfizercollectsanetof0.29and so as long as Pfizer isbelow the lowest strike atexpiration we’ll pocket thatpremium. This short callChristmas tree losses moneybetween33.29 and38.71butabove there the profits areunlimited.YoucanseethisinFigure15.9.

Figure15.9AShortCallChristmasTreeinPfizer(PFE)

■BoxSpreadIn Chapter 13, we looked atconversionsandreversalsandsaw how we could useoptions to create a syntheticlong or short position in theunderlying stock usingnothing but options. The callandput thatweuse to createthe synthetic position sharean expiration date and strikeprice. For example, Figure15.10 shows how we might

use options to create asyntheticlongpositioninJNJwiththestockat93.88.

Figure15.10ASyntheticLongPositiononJohnson&Johnson(JNJ)

Theseoptionshad40daystoexpiration.Wecouldbuy the100 strike call at 0.31 andsimultaneously sell the 100strike put at 6.42 (we’reignoring the impact of thebid/ask spread).Wecollect anet of 6.11. If JNJ is below100.00 at expiration, we’regoing to buy the stock at100.00 because we’ll be

assigned on our short put. IfJNJ is above 100.00 atexpiration, we’re going tobuy the stock at 100.00because we’ll exercise ourcall. Unless JNJ is preciselyat100.00atexpiration,we’regoing to buy JNJ at 100.00.Butwe get to keep that 6.11for those 40 days, meaningthat money will be sitting inour account earning interest.Butthatinterestdoesn’tcovermuch of our risk from being

synthetically long JNJ. Sowhatifweexecutedasimilarsynthetic short position andcollected more premium byselling an in-the-money calloption and buying an out-of-the-money put option? Thatcompletepositionwouldbeaboxspread.Youcanseehowwe complete the JNJ boxspreadinFigure15.11.

Figure15.11ABoxSpreadinJohnson&Johnson(JNJ)

Wecollectandkeepatotalof14.98, which is good, but atexpirationwe’regoingtobuy100 shares of JNJ at 100.00thanks to the synthetic longposition, and we’re going tosell 100 shares of JNJ at85.00 thanks to the syntheticshortpositionof short the85strike call and long the 85strikeput.Wecollected14.98

in option premium and lost15.00 on our stock. But wehad that 14.98 in our tradingaccount, earning interest forthe40dayswehad the tradeon. It’s no accident that theinterest earned on 14.98 for40daysat1percent,therisk-free rate when these optionpriceswereobserved,isabout0.02.A box spread is an interestrate trade even when we

make it in an equity namelike JNJ. A box spread isappropriate only forprofessionaltraderswithverylow execution costs.Otherwise, the cost ofexecuting the trade will costmany times what the tradegeneratesininterest.

■JellyRollA jelly roll, sometimessimply called a roll, is verysimilartoaboxspreadinthatit has a synthetic longpositionandasyntheticshortpositionbutthetwosyntheticpositions have differentexpirations.Jelly rollscanbeused to get long stock via asynthetic longpositionwhichis hedged via a longer-datedshort synthetic position or

vice versa. The pricedifference between the twosynthetic positions will begreater than in a box spreadinordertooffsetthecarryingcosts of the stock positionbetween the first expirationandthesecondexpiration.Jelly rolls are generally usedby professional traders whohave delta exposure in anexpiringoptionmonth that isoffset by delta exposure in a

later expiration. Since theexpirationof the frontmonthwould result in a large netdelta exposure, exposure tothe raw directionalmoves ofthe underlying stock,professionals will use a jellyroll to move the deltaexposure from one month toanother, offsetting theexposure in both monthsleavingnonetdeltaexposureoncethefrontmonthexpires.

■StupidIf you can’t make up yourmind which strike to buywhat are your alternatives?Well, you might just decideto buymore than one strike.That would be an optionstupid, sometimes called anoption double. Figure 15.12shows how you might useoptions on Visa (V) toexecuteaputstupid.

Figure15.12APutStupidonVisa(V)

And Figure 15.13 shows thepayoff for this 190/200 putstupid as well as the payofffor simplybuying twoof the195put.Abovethe200leveland below the 190 level thetwo payoffs are very similarbut not identical. It’s reallybetween the strike prices ofthestupidthatyoucanseethedifference and this is the

range where the put stupidbuyer is looking for adifferentsortofpayoff.

Figure15.13ALongPutStupidinVisa(V)

■GutsA guts spread is acombinationofalongin-the-moneycallandalongin-the-moneyput.Theoptionshavethe same expiration but willhavedifferentstrikeprices.Aguts is very similar to astrangle, although in astrangle both of the optionsare out-of-the-money. Figure15.14 shows how we mightconstruct a guts in Starbucks

(SBUX) when SBUX wastradingat74.65.

Figure15.14AGutsinStarbucks(SBUX)

This60/85gutscostatotalof27.90andcanresultinoneofseveral different positions atexpiration. If SBUX isbetweenthestrikesthenwe’llend up with no positionbecause we’ll exercise bothoptions, buying SBUX at60.00 and selling it at 85.00.If SBUX is below 60.00 atexpiration,thenwe’llbeshort

the stock because we’llexercise our put but let ourcall expire worthless. IfSBUX is above 85.00, thenwe’ll end up long the stocksince we’ll exercise our calland let our put expireworthless. Figure 15.15shows the payoff for this60/85guts.

Figure15.15AGutsinStarbucks(SBUX)

Themaximumlossisthe2.90intimevaluepaid,0.70inthecall and 2.20 in the put. Thepayofflooksverysimilartoastrangle.Infact,ifweweretograph the60/85strangle,youwould see that the guts andthe strangle lie precisely ontopofeachother.Thereisnodifferenceinthetwotrades.

■ Other PotentialSpreads andCombinationsAs we’ve seen, there’s anearly infinite way tocombine options into spreadsandcombinations.Youcouldsell a straddle in the frontmonth and buy a straddlewiththesamestrikepriceinalater expiration. You mightcall this a straddle calendar.

Youmight do the samewithstrangles and you could varythe width of the strangles sothatyoudidthetradeforverylittle or no premium out ofpocket.You’renowreadytocombineall the underlying, options,spreads, and combinations inmore sophisticated tradestructures that are preciselyalignedwithyouroutlookforthe market you’re trading.

Use the tools atwww.OptionMath.com todetermine the greeks for thestructures you’recontemplating then bedisciplined in your tradingand with the flexibility ofspreads and combinationsyou’re on your way toprofitable option trading.Goodluck.


ABOUTTHEWEBSITE

The website atwww.OptionMath.com wasoriginally created as acompanion to my first book,


Options Math for Traders,and it’s been revised,extended, and updated toserve as a companion to thiswork as well. You’ll findoption price and dataspreadsheets that will allowyoutopriceoptionsgivenallthe required inputs andwe’llguide you on selecting thoseinputs.The spreadsheets alsohelp you determine just howvolatile the options on aparticular stock or ETF say

that stockorETF isgoing tobefor the termof theoption.This is a little like peeringinto the future with theoptions telling us what toexpect.Thewebsitealsoprovidesallthe cheat sheets that followeachstrategychapter,butlikemost things, the realunderstanding comes fromthereadingandunderstandingof the material, not from

perusing the cheat sheets,which are intended to distillthe information from thechapter,nottoreplaceit.Finally, the web site willinclude annotated examplesof all the option spreads andcombinations we discuss,including actual recentnotable option tradesincluding commentary aboutthe trade, the risks andpotential rewards, why it

might have been made, andthemathadvantageorpenaltyinherent in it. It’s anopportunity to look over theshoulder of professionaloptiontraders.You’llalsobeabletodiscussoption tradingwithusande-mail your questions becauseoptions are an incrediblyuseful tool. Let’s get startedusingthem.

ABOUTTHEAUTHOR

ScottNations isbestknownasoneofthecastofCNBC’sOptions Action and from hisregular appearances on

CNBC’sFastMoney,FuturesNow, and Squawk Boxprograms, but he was anoptiontraderinthepitsoftheChicago Board of Trade andChicago MercantileExchange for over twodecades.Today, Scott is the chiefinvestment officer ofNationsShares, the world’sleading independentdeveloper of volatility-based

andoption-enhancedindexes.AstheheadofNationsShares,Scott has created VolDex®(ticker symbol: VOLI), animproved measure of optionimpliedvolatility;SkewDex®(ticker symbol: SDEX), thebestmeasureofoptionskew;TailDex® (ticker symbol:TDEX), the first measure ofthe risk of a “black swan”eventinthestockmarket;andTermDex®, the firstquantitative measure of the

term structure of optionmarkets. Scott is also thecreator of the EnhancedCovered Call, EnhancedCollar, and Better Beta®OptionLeveredstrategies.

INDEX

Ask,defined.SeealsoBid/askspreadAssignment,coveredcallsandAt-the-money

coveredputsdefinedstraddlesandverticalspreadsSeealsoCalendarspreads

Backspreads cheatsheet

definedexamplessuperSeealsoRatiospreadsandbackspreads

BearishverticalspreadsBid/askspread ask,defined

bid,definedcondorsand

in-the-moneycoveredputsand

Black-Scholesoptionpricingformula“Body,”ofbutterflyBoxspreadsBreakevenpoints,definedBrokenbutterfliesBullishverticalspreadsButterflies

brokenbutterfliescallbutterfliescheatsheetdefinedironbutterflieslong,definedmarketoutlookandpriortoexpirationputbutterfliesratiospreads

comparedtoshort,defined“wings”and“body”of

Buywrite

Calendarspreads call

catalystscheatsheet

defineddiagonalspreadsanddirectionalityandsellingsupercalendar

CallbutterfliesCallcalendarspreadsCallcondorsCalloptions

callspread,buyingandselling(SeealsoVerticalspreads)definedsellingSeealsoVerticalspreads

CallspreadcollarCallspreadriskreversalCash-securedputs.See

alsoCoveredputsCatalystsCheatsheets backspreads

butterfliescalendarspreadscondorsconversion/reversalcoveredcallscoveredputs

ratiospreadsriskreversalstraddlesstranglesverticalspreads

ChristmastreespreadsCollars callspread

definedin-the-money

narrowpotentialoutcomesofputspreadriskreversalcomparedtoskewverticalspreadscomparedtowidezero-cost

Combinations,definedCondors bid/askspreadand

condorspreadscallcondorscheatsheetsdefineddirectionalcondorsironcondorslongcondors

longironcondorsputcondorssellingshortcondors

Conversion/reversal cheatsheet

conversion,defineddividendsfrequencyofusepinrisk

reversal,definedCoveredcalls advantageof

assignmentcheatsheetcollarsandcoveredputsversusdefineddividends“created”with

downsideprotectionexpirationanderosionprofitabilitysellingcoveredstraddlesstockcoveredverticalcallspread

Coveredputs at-the-money

cheatsheetcoveredcallsversusdefinedin-the-moneymarketoutlookforout-of-the-moneyregretpointofsellingcoveredstraddles“teeny”puts

Coveredstraddles defined

sellingCoveredstrangles,selling

“Deep”in-the-moneycalls“Deep”out-of-the-moneycoveredputs

Delta defined

straddlesandverticalspreadsand

DiagonalspreadsDirectionalcondorsDirectionality calculating

calendarspreadsand

defined“directionless”volatilitytrade

Dividends conversion/reversal

andcoveredcallsandassignmentcoveredcallsfor“creating”dividends

Downsideprotection,collarsand

Earningsreleases,ascatalystsErosion calendarspreads

andcoveredcallsanddefined

SeealsoExpirationdates;Theta

ETFs expirationdatesand

GLD(goldexchangetradedfund)example

Exercisestrike(strikeprice)Expirationdates calendarspreads

and(SeealsoCalendarspreads)collarsandpotentialoutcomescoveredcallscoveredputsdefinedoptionerosionandsensitivitytopassageoftimestraddlesand

stranglesandverticalspreadvaluepriortoexpiration

“50” defined

strikeputFutures,optionson

GammaGLD(goldexchangetradedfund)GutsGutsspread

HedgeratioHorizontalspreads.SeealsoCalendarspreads

ImpliedvolatilityIncrements,ofstrikepriceInflectionpointIn-the-money collars

coveredputsdefinedstraddlesverticalspreads

SeealsoCalendarspreads

IronbutterfliesIroncondors

Jellyrolls

Longbutterflies,defined.SeealsoButterflies

Longcalls,shortputsand.SeeRiskreversalLongstock,shortcalloptionand.SeeCoveredcallsLongstraddlesLongstrangles

Marketoutlook calendarspreads

andforcoveredputsverticalspreadsand

MarriedputsMaximumvalue,verticalspreadsMinimumvalue,verticalspreadsMoneyness defined

verticalspreadsand

Nakedcalls,sellingNakedputs,sellingNations,Scott OptionMath.com

(website)OptionsMathforTraders

Optiondouble(stupid)

http://OptionMath.com

OptionMath.com(website) calculating

directionalitycalculatingerosioncalculatingvolatilitychangeoptioncalculatoroptionpricingformulaspreadsheettool

http://OptionMath.com

toolsfoundonworksheettool

Optionprice defined

deltagammaimpliedvolatilityoptionerosionoptionpricingformulas

rhosensitivities,generallysensitivitytopassageoftimesensitivitytopriceofunderlyingstockthetavegavolatility,definedvolatilitychanges

Options callsandputs,

defineddefinedexpirationdatesmoneynessobjectivesoftradingsellingputsandcallsspreadsand

combinations,definedstockequivalentandstrikepriceSeealsoOptionprice;Optionvalue

OptionsClearingCorporation(OCC)OptionsMathforTraders(Nations)

Optionvalue estimating

verticalspreadsandasymmetryofriskandrewardverticalspreadvaluepriortoexpiration

Out-of-the-money coveredputs

defined

stranglesandverticalspreadsSeealsoCalendarspreads

Overwrite

Package,definedPassageoftime,sensitivityto.SeeExpirationdates

Payoffcharts,explainedPinriskPremium,definedProfit-and-loss(P&L)tables,forverticalspreadsProtective(married)putsPutbutterfliesPutcondorsPutoptions defined

moneynessandputspreads,buyingandselling(SeealsoVerticalspreads)sellingSeealsoCalendarspreads

Putspreadcollar

Quarterlyexpiration

dates

Ratiospreadsandbackspreads backspreads

callratiospreadscheatsheetsputratiospreadsratiospreads,defined

ratiospreads,forstockrepairratiospreadscomparedtoChristmastreespreadsratiospreadscomparedtoverticalspreadsandbutterfliessuperbackspreads

Regretpoint

ofcoveredputsdefined

Reversal,defined.SeealsoConversion/reversalRhoRiskreversal callspreadrisk

reversalcheatsheetdefined

erosionoflikelihoodsprofitandlosspotentialofskewandstrikepricesof

Rolls(jellyrolls)

SellingcalendarspreadsShortbutterflies,

defined.SeealsoButterfliesShortcalloption,longstockand.SeeCoveredcallsShortputs,longcallsand.SeeRiskreversalShortputs,cashand.SeealsoCoveredputsShortstraddlesShortstrangles

Skew defined

riskreversalandSpreads,definedStocks expirationdates

highabsolutepricesofoptionequivalentand

optionscomparedtoratiospreads,forstockrepairstockcoveredverticalcallspreadunderlyingstockprice

Straddles breakevenpoint

examples

breakevenpointlikelihoodcheatsheetcondorscomparedtodefinedlongsellingcoveredstraddlesshort“straddlecalendar”

stranglescomparedto

Strangles breakevenpoint

cheatsheetdefinedironcondorcomparedtoleverageandlongselling

sellingcoveredstranglesshort

Strikeprice ofcoveredputs

definedstraddlesandasvertical(SeealsoVerticalspreads)

Stupid(optiondouble)Superbackspreads

SupercalendarSyntheticpositions collarsand

conversions/reversalsanddefined

“Tailrisk”events“Teeny”putsTheta

definedverticalspreadsand

Timevalue.SeeExpirationdates

Underlyingstock,sensitivityto

Vega

Verticalspreads at-the-money

breakevenpointsbullishandbearishbutterfliesasbuyingandsellingcheatsheetcollarscomparedtoascondors(SeealsoCondors)

defineddeltafordiagonalspreadsandin-the-moneyironbutterfliesandmarketactionformarketoutlookandmaximumandminimumvaluesmeasuringcostof

moneynessandnomenclatureout-of-the-moneyprofit-and-loss(P&L)tablesforratiospreadscomparedtoriskandrewardasasymmetricsellingacallverticalspread

stockcoveredverticalcallspreadthetaforvaluepriortoexpiration

Volatility calendarspreads

andchangestodefinedimplied

shortvolatilitystrategystraddlesandSeealsoOptionprice

“Wings,”ofbutterfly

Zero-costcollar

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TableofContents

ForewordPreface

The Spreads andCombinations

Chapter 1: Not JustMore orLessbutDifferent

The “Flavors”:CallsandPutsThe Expiration

DateTheStrikePriceAn OptionCorresponds to 100SharesofStockDefininganOptionMoneynessWhatWeMean bySpread andCombinationAFinalThought

Chapter2:JustaLittleMathTheOptionPriceVolatility and the

Volatility ImpliedbytheOptionPriceOptionErosionOption PriceSensitivitiesSensitivity to thePassageofTimeSensitivity to thePrice of theUnderlyingStockChanges inVolatilityOtherSensitivities

Chapter3:VerticalSpreads

Buying and SellingVerticalSpreadsVertical SpreadMaximum andMinimumValuesNamingMoneyness andVerticalSpreadsBullishandBearishVerticalSpreadsSelling a CallVerticalSpreadBreakevenPointsThe Necessary

PriceActionVertical Spreadsand Your MarketOutlookAsymmetryofRiskand Reward forVerticalSpreadsOption Delta andLikelihoodVertical SpreadValue Prior toExpirationTheOtherGreeksThe Best Measure

of Vertical SpreadCostIn-the-MoneyVerticalSpreads

Chapter4:CoveredCallsProfitabilityCovered Calls andDownsideProtection—NotAsMuch As We’dLikeUsing CoveredCalls to “Create”Dividends

Having YourShares CalledAwayDon’t FearAssignmentStock CoveredVertical CallSpread

Chapter5:CoveredPutsTheRegretPointMarketOutlookOut-of-the-MoneyCoveredPutsIn-the-Money

CoveredPutsAt-the-Money orNearly At-the-MoneyCovered Put versusCoveredCall

Chapter6:CalendarSpreadsCall CalendarSpreadsSelling CalendarSpreadsDirectionalityCatalystsTheSuperCalendar

Chapter7:StraddlesTheShortStraddleLikelihoodsSelling CoveredStraddles

Chapter8:StranglesSellingStranglesSelling CoveredStrangles

Chapter9:CollarsWiderCollarsIn-the-MoneyCollarsPotentialOutcomes

AZero-CostCollarSkewHow a Collar IsSimilar to OtherSpreads andCombinationsPutSpreadCollarCallSpreadCollar

Chapter10:RiskReversalLikelihoodsHowSkewHelps aRiskReversalCall Spread RiskReversal

Chapter11:ButterfliesBuying and SellingButterflies—TheTerminologyPutButterfliesButterflies Prior toExpirationButterflies andYour MarketExpectationsBrokenButterflies

Chapter12:CondorsandIronCondors

SellingaCondor

The Bid/AskSpread and CondorSpreadsIronCondorDirectionalCondors

Chapter 13:Conversion/Reversal

ReversalDividendsPinRisk

Chapter 14: Ratio SpreadsandBackSpreads

Vertical Spreads,

Butterflies, andRatioSpreadsCallRatioSpreadsCall Ratio SpreadsforStockRepairBackSpreadsSuperBackSpreads

Chapter 15: Other SpreadsandCombinations

MarriedPutDiagonalSpreadIronButterflyChristmasTreeBoxSpread

JellyRollStupidGutsOther PotentialSpreads andCombinations

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