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PROBLEMS
975
Q25.29 Ifthe$/=Cforwardrateisataforwarddiscount
relativetothespotrate(thatis,theforward
rateislowerthanthespotrate),isthenominal
interestrateinEuropeorintheUnitedStates
higher?
Q25.30 Explainthedifferencebetweencoveredand
uncoveredinterestrateparity.
Q25.31 In2007,accordingtotheCIAWorldFactbook,
Zimbabwehadaninflationrateof976%per
annum—theworld’sundisputedinflation
leader.Botswana,itsneighbortotheeast,had
aninflationrateof11.4%.IfPPPholds,how
wouldyouexpecttheircurrencyexchangerates
tomoveoverthenext12months?
Q25.32 Ifeveryoneexpectsacurrencyexchangeratein
6monthstobehigherthanitistoday(sothatit
willcomebacktoPPP),wouldthisbereflected
inthedifferentialbetweentoday’sspotrateand
theforwardrate?
Q25.33 Whatkindofcharacteristicsofgoodsare
mostlikelytoobeyPPP(anddrivediverging
economiesbacktowardit)?
Q25.34 Wouldyouexpectimportandexportfirmsto
helpmakeinterestrateparitycometrue?
Q25.35 LookupwheretheBigMacindexstandstoday.
WhereistheUnitedStatesrelativetoother
countries?Whicharethemostexpensiveand
whicharethecheapestcountries?Howwould
thisindexsuggestthattheU.S.dollarshould
moverelativetothesecurrenciesinthefuture
ifyoubelievedinlong-runPPP?
Q25.36 TheAustralianfirmCommSechasrecently
createdtheiPodIndex.Whatareitsconceptual
advantagesanddisadvantagesrelativetothe
BigMacIndex?SearchtheWebtofindwhere
thetwoindexesstandrelativetooneanother.
Q25.37 Constructatextbookpriceindex.Thatis,
takesomeofyourschooltextbooksandsee
howtheirpricesdifferinfivecountriesof
yourchoice.DotextbooksobeyPPP?Canyou
arbitragethepricedifferences?
Q25.38 Inyourassessment,doreal-goodsmarketsor
financialcapitalmarketshavemoreinfluence
onexchangerates?Why?
Q25.39 Downloadthemostrecent3yearsofhistorical
dailystockreturnsforvariousinternational
stockmarketindexesfromYahoo!Finance.
Computethebetaofthesestockmarkets
withrespecttotheS&P500marketindex.
Whatdoyourmarketbetassuggestaboutthe
diversificationbenefitsofthesemarkets?
Q25.40 RedrawFigure25.2,butdosoassuminga6-
monthperiodandacurrencyexchangerate
thatisinlinewiththosefromMarch2008:
Theeurostoodat$1.57,andthe6-month
forwardratestoodat$1.55.Workwithan
equalprobabilityofanup-movementto$1.50
oradown-movementto$1.60.
Q25.41 Assumethatthelocalstockmarketbetaofa
Britishprojectis3.Assumethatthebetaofthe
BritishstockmarketwithrespecttotheU.S.
stockmarketis0.75.Assumethatthemarket
betaof$/£exchangeratemovementsis0.What
wouldyouexpecttheU.S.marketbetaofthis
Britishprojecttobe?
Q25.42 Whydofirmsintherealworldnothedgeall
foreignexchangerisk?Isthisnecessarilyabad
thingfortheirinvestors?
Q25.43 SupposeyouareaU.S.oilcompanythinking
aboutinvestinginRussia.(TheKremlinhas
atrackrecordofchangingcontractsafterthe
fact.)HowwouldyoufinanceyourRussian
operations?
Q25.44 SearchtheSEC’sEdgardatabasefora424(b)(5)
filingbyKfWon2007/09/28.Whatkindof
bondisthis?
Q25.45 Assumeyouareacorporatemanagerinthe
UnitedKingdom.Youarethinkingoflisting
ontheNYSE.IfBritishinvestorsareprimarily
investingintheUnitedStates, andBritish
investorsmostlyconsumeinBritain,thenhow
shouldyouthinkaboutinvestinginanewplant
inChina?
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CHAPTER25APPENDIX
ProminentInternationalInstitutions
TheInternationalMonetaryFund(http://www.imf.org)isaUnitedNationsnon-
profitagencyestablishedin1946with38membersandcurrentlymadeupof185
membernations(in2008).Itsprimepurposeistoencouragethesmoothfunction-
ingofmoneyflowsandtoaidinthestabilityofcurrencies(e.g.,bypreventingruns
oncountrycurrenciesorbyfacilitatinginformationdisclosure).TheIMF’soper-
ationsconsistof“surveillance,financialassistance,andtechnicalassistance.”(For
example,inSeptember2002,itlent$30billiontoBraziltodispeldoubtsthatBrazil
mightdefaultonitsforeigndebt.)Membercountries’votingpowerisdeterminedby
theircontributionstotheIMFcapitalpool.TheIMF’sboardofgovernorsconsists
offinanceministersandcentralbankheads.Day-to-dayoperationsareperformed
bya24-personexecutivecommittee.Eightcountrieshavepermanentrepresenta-
tions,whiletheremaining16rotate.TheIMFheadquartersisinWashington,D.C.
Inearly2008,theIMFhadabout$362billionatitsdisposal,fromwhichitcould
maketemporaryloans.
TheWorldBank (http://www.worldbank.org)isalsoa United Nations nonprofit
agency(reallyfivecloselyassociatedinstitutions).Itwasalsoestablishedin1946,
andismadeupofthesame185membercountries.(WorldBankmembersmustbe
membersoftheIMF.)TheWorldBankwassetuptoreducepovertyindeveloping
nations.Itbothextendsloansitselfandattemptstocoordinatethird-partyprivate
andbilateralloans.TheWorldBankraisesfinancingthroughWorldBankbonds
(ithasanAAArating)andpassestheresultinglowinterestratesontodeveloping
countryclientloans.TheWorldBankheadquartersisinWashington,D.C.About
20%ofthe$23billionraisedbytheWorldBankin2006wasusedforoutrightgrants
(notloans)topoorcountries.
TheWorldTradeOrganization(http://www.wto.org)wassetupin1995todealwith
theglobalrulesoftradebetweennations,setoutintheGeneralAgreementonTariffs
andTrade(GATT).In2007,theWTOhad150membercountries,accountingfor
over97%ofworldtrade.Itsmainfunctionistoensurethattradeflowsassmoothly,
predictably,andfreelyaspossible.Ithandlestradedisputes,administersWTOtrade
agreements, offersaforumfor tradenegotiations,monitorsnationaltrade, and
providessometechnicalassistanceandtrainingfordevelopingcountries.TheWTO
headquartersisinGeneva.Its2007budgetwas182millionSwissfrancs.
TheOrganizationforEconomicCooperationandDevelopment(http://www.oecd
.org),foundedin1961,grewoutoftheMarshallPlanforreconstructionafterWorld
WarII.In2007,its30membercountriesproducedabout2/3oftheworldGDP.
(Another70countrieshadinformallinks.)TheOECDisasortofthink-tankagency
OECDcountries,Section
25.1,p.944
and/ormeetingplaceand/orinformationagencythatseekstoaideconomiccoop-
erationamonglike-minded,democratic,well-developed,andmostlyopeneconomy
countries.ItiscommontorefertothedevelopedcountriesasOECDcountries.The
OECDheadquartersisinParis.Its2008budgetwas
=
C
343million.
976
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KEYTERMS
977
ANECDOTE
FreeTrade—WhereConvenient
T
heOECDnations aregenerallyproponents offree
trade.Mosteconomistswouldagreethatfreetrade
generallyhelpsallnationsdevelop.Unfortunately,the
OECDcountriesshowlittleconsistency.Ononehand,
forexample,theirfarmershaveenormousdomesticvot-
ingpower,whichhasmadeOECDcountrieserecthigh
tradebarriersagainstpotentiallycompetitiveagricultural
importsfromThirdWorldcountries.Ontheotherhand,
theysubsidizetheirfarmingindustriesandregularlyget
intomutualdisputesastowhichnation(amongthem)is
“mostunfair.”Unfortunately,theThirdWorldjustdoes
nothaveenoughpowertodemandalevelplayingfield.
Naturally, the e OECD nations will press and penalize
ThirdWorldnationsiftheyerecttradebarriersagainst
theirgoods.Aparticularlyegregiousexampleisthefact
thattheUnitedStates pressesothernations not to tax
Americantobaccoandcigarettecompanies.
Butthinkingofthisasaself-interestedconspiracyistoo
simplistic. Forexample, theUnitedStates and Europe
havepermittedSoutheastAsian(especiallyJapaneseand
Chinese)importsaplenty,evenwhentheplayingfieldhas
notbeenlevelforU.S.industries(someofwhichthereby
sufferedhugejoblossesordestruction).Inreality,trade
policyisaratherincoherentandhighlypoliticizedarea.
ANECDOTE
ProtestingWorldBankPolicies
D
espitetheirseeminglyuncontroversialmissionsand
intents,alltheseinternationalagencieshavebeen
widelycriticized.Thecriticsmakestrangebedfellows—
thereare,forexample,bothanalyticaleconomistsand
politicalactivistswithMolotovcocktails.This is nota
lightmatter:Thedecisionsofthesefinancialorganiza-
tionsdecidenotonlythefortunesofbillionsofpeople
buttheverylivesofmillionsofpeopleinthedeveloping
world.(Personally,Ithinkitisfairto saythatboththe
internationalorganizations and theircritics havegood
intentions,buttheissuesthemselvesaresocomplexthat
thereistremendousdisagreementaboutwhatisrightand
whatiswrong.Therearenoeasyandobviousanswers.)
Onthelighterside, oneofthemoreunusualpolitical
soapoperaswasinstigatedbyWorldBankchiefecono-
mistJosefStiglitz(formerprofessorofeconomicsatStan-
ford)inlate1999.ItbeganwhenStiglitzsharplycriticized
theIMFanditsformermanagingdirector,StanleyFischer
(formerprofessorof economics atMIT).In turn, Larry
Summers (professorof economics and aformerpresi-
dentofHarvard),tried toinfluencetheWorldBankto
quietStiglitz’sview.TheWorldBankpresidentrefused—
onlytofindStiglitzstartingtopubliclycriticizetheWorld
Bank,too.Eventually,Stiglitzresignedwithabigsplash
inanattempttobringmoreattentiontohispolicyviews.
Partialsource:http://www.globalpolicy.org.
keyterms
InternationalMonetaryFund
,976
OrganizationforEconomicCoop-
erationandDevelopment
,976
WorldBank
,976
WorldTradeOrganization
,976
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OptionsandRiskManagement
...ANDSOMEOTHERDERIVATIVES
T
hischapterprovidesabriefintroductiontothemostimportantaspectsofthe
areaofoptions.Itcoversoptionsbasics,arbitragerelationships,put-callpar-
ity,theBlack-Scholesformula(andbinomialoptionpricing),andcorporate
applicationsofoptionpricingideasandmethods—butallinaverycondensedform.
Youmayprefertoresorttoafullbookonoptionsandderivativesifthischapteristoo
telegraphicforyou.
Mostoftheconceptsintheworldoffinancialoptionsrelyonarbitrage,whichis
primarilyaperfect-marketconcept.Fortunately,forlargefinancialinstitutions,the
marketforoptionsseemsfairlyclosetoperfect.Forsmallerinvestors,transaction
costsandtaximplicationscanplayarole.Inthiscase,thearbitragerelationsdiscussed
inthischapterholdonlywithintheboundsdefinedbythesemarketimperfections.
26.1 OPTIONS
Optionsareexamplesofderivatives(alsocalledcontingentclaims).Aderivativeis
Baseassetsandcontingent
claims(derivatives).
aninvestmentwhosevalueisitselfdeterminedbythevalueofsomeotherunderlying
baseasset.Forexample,a$100sidebetthataVanGoghpainting—thebaseasset—
willsellformorethan$5millionatauctionisanexampleofacontingentclaim,
becausethebet’spayoffsarederivedfromthevalueoftheVanGoghpainting(the
underlying baseasset).Similarly, acontractthat statesthatyouwillmakeacash
paymenttomethatisequaltothesquareofthepriceperbarrelofoilin2010isa
contingentclaim,becauseitdependsonthepriceofanunderlyingbaseasset(oil).
Aswithanyothervoluntarycontract,bothpartiespresumablyengageinaderiva-
Voluntarycontracting⇒both
partiesarebetteroffex-ante.
Onlyonepartyisbetteroff
ex-post.
tivescontractbecausedoingsomakesthembetteroffex-ante.Forexample,yourcar
insuranceisacontingentclaimthatdependsonthevalueofyourcar(thebaseas-
set).Ex-ante,boththeinsurancecompanyandyouarebetteroffcontractingtothis
978
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26.1 OPTIONS
979
ANECDOTE
ABriefHistoryofOptions
O
ptionshavebeeninusesinceAristotle’stime.The
earliestknownsuchcontractwas,infact,notafi-
nancialbutarealoption.ItwasrecordedbyAristotle
in the e story of Thales s the e Milesian, , an n ancient Greek
philosopher.Believingthattheupcomingoliveharvest
wouldbeespeciallybountiful,Thalesenteredintoagree-
mentswiththeownersofalltheoliveoilpressesinthe
region.In exchangeforasmalldepositmonths ahead
of theharvest, Thales obtained the right to lease the
pressesatmarketpricesduringtheharvest.Asitturned
out,Thaleswascorrectabouttheharvest,demandforoil
pressesboomed,andhemadeagreatdealofmoney.
Manycenturies later, in 1688, Joseph delaVegade-
scribedinConfusiondeConfusioneshowoptionswere
widelytradedontheAmsterdamStockExchange.Itis
likelythat he actively exploited put-callparity, an ar-
bitrage relationship p between options discussed d in n this
chapter.IntheUnitedStates,optionshavebeentraded
overthecountersincethenineteenthcentury.Adedi-
catedoptionsmarket,however,wasorganizedonlyin
1973.Insomeothercountries,optiontradingisbanned
becauseitisconsideredgambling.
Source:Wisegeek’s“WhatAreFutures?”
contingentclaimthaneitherwouldbewithouttheinsurancecontract.Thisdoesnot
meanthatbothpartiesexpecttocomeouteven.Onaverage,yourinsurancecompany
shouldearnapositiverateofreturnforofferingyousuchacontract,whichmeans
thatyoushouldearnanegativeexpectedrateofreturn.Ofcourse,ex-post,onlyone
ofyouwillcomeoutbetteroff.Ifyouhaveabadaccident,theinsurancewasagood
dealforyouandabaddealfortheinsurancecompany.Ifyoudonothaveanaccident,
thereverseisthecase.
26.1A CALLANDPUTOPTIONSONSTOCK
Optionsareperhapsthemostprominenttypeofcontingentclaim.Andthemost
Callandputoptionsare
contingentclaims.
prominentoptionissimplythechoicetowalkawayfromanunprofitableposition
withoutretaininganyobligation.Acalloptiongivesitsholdertherightto“call”
Limitedliability,Section
6.4,p.155
(i.e.,tobuy)anunderlyingbasesecurityforaprespecifieddollaramount—calledthe
strikepriceorexerciseprice—usuallyforaspecificperiodoftime.Aputoptiongives
itsholdertheequivalentrightto“put”(i.e.,tosell)thesecurity.Naturally,thevalues
oftheserightsdependonthevalueofthebaseasset,whichcanfluctuateovertime.
Let’slookattheseoptionsinmoredetail.
CallOptions
Table26.1showsanumberofoptionsthatweretradingonMay31,2002.Forexample,
Example#1:Calloptionsgive
therighttobuy—upside
participation.
youcouldhavepurchasedaJulyIBMstockcalloptionwithastrikepriceof$85,
therebygivingyoutherighttopurchaseoneshareofIBMstockatthepriceof$85
anywherebetweenMay31andJuly20,2002.Calloptionsincreaseinvalueasthe
underlyingstockappreciatesanddecreaseinvalueastheunderlyingstockdepreciates.
IfonJuly20,2002,thepriceofashareofIBMstockwasbelow$85,yourrightwould
havebeenworthless:Shareswouldhavebeencheapertopurchaseontheopenmarket.
(Indeed,exercisingwouldhavelostmoney:Purchasingsharesthatareworth,say,$70,
for$85wouldnotbeabrilliantidea.)Again,thebeautyofowningacalloptionisthat
youcanjustwalkaway.However,ifonJuly20,2002,thepriceofashareofIBMstock
wasabove$85,thenyourcalloption(purchaseright)wouldhavebeenworththe
differencebetweenwhatIBMstockwastradingforandyourexercisepriceof$85.You
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980
CHAPTER26
OPTIONSANDRISKMANAGEMENT
TABLE26.1 SomeIBMOptionPricesonMay31,2002
Underlying
Strike
Call
Put
BaseAsset
ExpirationT
PriceK
Price
Price
IBM
$80.50
July20,2002
$85
$1.900
$6.200
DifferentStrikePrices
IBM
$80.50
July20,2002
$75
$7.400
$1.725
IBM
$80.50
July20,2002
$80
$4.150
$3.400
IBM
$80.50
July20,2002
$90
$0.725
$10.100
DifferentExpirationDates
IBM
$80.50
Oct.19,2002
$85
$4.550
$8.700
IBM
$80.50
Jan.18,2003
$85
$6.550
$10.200
ThesourceofthesepriceswasOptionMetrics.July20wasabout0.1333yearsaway.(IBM’sclosingpriceat
4:00pmESTwas5centslowerthanwhatthewebsitereported.)Theprevailinginterestrateswere1.77%
over1month,and1.95%over6months.Forup-to-dateoptionpricesonIBMoptions,see,forexample,
http://finance.yahoo.com/q/op?s=IBM,oroptionmetrics.com.
Source:ReproducedwithpermissionofYahoo!Inc.©2008byYahoo!Inc.YAHOO!andtheYAHOO!logoare
trademarksofYahoo!Inc.
shouldhaveexercisedtherighttopurchasetheshareat$85fromthecallwriter.For
example,ifthepriceofIBMstockturnedouttobe$100,youwouldhaveenjoyedan
immediatenetpayoffof$100−$85=$15.Therelationshipbetweenthecallvalue
andthestockvalueaninstantbeforethecalloptionexpiresis
C
T
(K=$85, atTonJuly20,2002⇔ ⇔ remainingtimet=0)=max(0,S
T
−$85)
C
T
(K,t=0)
= max(0,S
T
−K)
whereC
T
isthevalueofthecalloptiononthefinaldateT,giventhe(pre-agreed)
strikepriceK.Ifthestockpriceatexpiration,S
T
,isaboveK,theoptionownerearns
thedifferencebetweenS
T
andK.IfS
T
isbelowK,thentheoptionownerwillnot
exercisetheoptionandearnzero.(Themaxfunctionmeans“takewhicheverofits
argumentsisthebigger.”)Notethat,likeotherderivatives,anoptionislikeasidebet
betweentwooutsideobserversofthestockprice.Neitherpartynecessarilyneedsto
ownanystock.Therefore,becausethepersonowningthecallispaidmax(0,S
T
−K)
atthefinaldate(relativetonotowningthecall),thepersonhavingsoldthecallmust
paymax(0,S
T
−K)(relativetonothavingwrittenthecall).
Whywouldsomeonesell (“write”)anoption?Theansweris“for themoney
Theupfrontpriceoftheoption
compensatestheoptionwriter. upfront.”Table26.1showsthatonMay31,2002(whenIBMstockwastradingfor
$80.50),anIBMcallwithastrikepriceof$85andanexpirationdateofJuly20,2002,
cost$1.90.Aslongastheupfrontpriceisfair—andmanyoptionmarketstendtobe
closetoperfect—neitherthepurchasernorthesellercomesoutfortheworse.Indeed,
asalreadynoted,becausebothpartiesvoluntarilyengageinthecontract,theyshould
bothbebetteroffex-ante.Ofcourse,ex-post,thefinancialcontractwillforceoneside
topaytheother,makingonesidefinanciallyworseoffandtheothersidefinancially
betteroff,relativetonothavingwrittenthecontract.
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26.1 OPTIONS
981
Calloptionsareoftenusedbyshareholderstoselloffsomeoftheupside.For
Whatcouldbetheparticipants’
deepermotives?
example,thefollowingarecommonmotivationsforparticipants:
Thebuyer:Whywouldsomeonewanttopurchaseacalloption?It’sjustanotherway
tospeculatethatIBM’sstockpricewillgoup—anditisveryefficientintermsof
itsuseofcashupfront.InMay2002,theoptiontopurchaseIBMat$90untilJuly
20,2002,costonly$0.725pershare,muchlessthanthe$80.50thatoneIBMshare
costatthetime.
Theseller:AsalargeIBMshareowner,youmayhavedecidedthatyouwantedto
keeptheupsideuntil$90butdidnotcareasmuchabouttheupsidebeyond$90
(oryoubelievedthattheIBMsharepricewouldnotrisebeyond$90byJuly20,
2002).Inthiscase,youmighthavesolda$90calloptiontoday.Thiswouldhave
givenyouanimmediatepaymentof$0.725.Youcouldhaveinvestedthisanywhere
(includingintomoreIBMsharesorTreasuries).Theextracashof$0.725would
haveboostedyourrateofreturniftheIBMstockpricehadremainedbelow$90.
ButifIBMhadendedupat$120,youwouldhaveparticipatedonlyinthefirst
$9.50gain(from$80.50to$90).(Ofcourse,youwouldalsohavekepttheupfront
optionpayment.)Theremaining$30oftheIBMupsidewouldhavegonetoyour
calloptionpurchaserinsteadoftoyou.
Ifyouwriteanoptiononastockthatyouareholding,itiscalled“writinga
Doyouwanttobecaught
naked?
coveredoption.”Effectively,thisislikeahedgedposition,beinglonginthestock
andshortinthecall.Thus,ifproperlyarranged,itsriskismodest.However,there
arealsosomesellersthatwriteoptionswithoutowningtheunderlyingstock.This
iscallednakedoptionwriting.(Ikidyounot.)Lackingthelonglegofthehedge,
thiscanbeaveryriskyproposition.Inourextreme$120example,theoptionbuyer
wouldhavehadarateofreturnontheoptionaloneof($30−$0.725)/$0.725≈
4,038%.Thus,theoptionsellerwouldhavelost4,038%.(Youcanexceed−100%
becauseyourliabilityisnotlimitedtoyourinvestment.)Writingnakedout-of-
the-moneyoptionsissometimescomparedtopickinguppenniesinfrontofa
steamroller—profitablemostofthetime,butwithahugerisk.
PutOptions
Insomesense,aputoptionistheflipsideofacalloption.Itgivestheownertheright
Example#2:Putoptionsgive
therighttosell—downside
protection.
(butnottheobligation)to“put”(i.e.,sell)anunderlyingsecurityforaspecificperiod
oftimeinexchangeforaprespecifiedprice.Forexample,againinMay2002,you
couldhavepurchasedaputoptionfortherighttoselloneshareofIBMstockatthe
priceof$75upuntilJuly20,2002.Thisoptionwouldhavecostyou$1.725,according
toTable26.1.Unlikeacalloption,aputoptionspeculatesthattheunderlyingsecurity
willdeclineinvalue.IfthepriceofashareofIBMstockhadremainedabove$75
beforeJuly20,2002,theputrightwouldhavebeenworthless:Sharescouldbesoldfor
moreontheopenmarket.However,ifthepriceofashareofIBMstockwasbelow$75
ontheexpirationdate,theputrightwouldhavebeenworththedifferencebetween
$75andIBM’sstockprice.Forexample,iftheIBMsharepricehadbeen$50,the
putownercouldhavepurchasedoneshareofIBMat$50ontheopenmarketand
exercisedtherighttoselltheshareat$75totheoptionwriterforanimmediatenet
payoffof$25.Therelationshipbetweentheputvalueandthestockvalueatthefinal
momentwhentheputoptionexpirescanbewrittenas
982
CHAPTER26
OPTIONSANDRISKMANAGEMENT
P
T
(K =$75, , atTonJuly20,2002⇔ remainingtimet t =0)=max(0,$75−S
T
)
P
T
(K,t =0)
= max(0,K K −S
T
)
Putoptionsareoftenpurchasedas“insurance”byinvestors.Forexample,ifyou
Acommonuseofaputis
protection(insurance).
hadownedalotofIBMshareswhentheyweretradingat$80.50/shareonMay31,
2002,youmayhavebeenwillingtolivewithalittlebitofloss,butnotalot.Inthis
case,youmighthavepurchasedputoptionswithastrikepriceof$75.IfIBMwereto
haveendedupat$60pershareonJuly20,2002,thegainonyourputoption($15/put)
wouldhavemadeupforsomeofthelosses($20.50/share)onyourunderlyingIBM
shares.Ofcourse,buyingthisputoptioninsurancewouldhavecostyoumoney—
$1.725persharetobeexact.
solvenow!
Q26.1 Howisowningacalloptionthesameassellingaputoption?Howisit
different?
26.1B MOREINSTITUTIONALSTOCKOPTIONARRANGEMENTS
Thereareavarietyofotheroptioncontractfeatures.Onecommonfeatureisbased
Americanoptionscanbe
exercisedbeforeexpiration.
Europeanoptionscanbe
exercisedonlyatexpiration.
onthetimeatwhichexercisecanoccur.AnAmericanoptionallowstheholderofthe
optiontoexercisetherightanytimeupto,andincluding,theexpirationdate.The
largestfinancialmarketfortradingoptionsonstocksistheChicagoBoardOptions
Exchange(CBOE)anditsoptionsareusuallyoftheAmericantype.Alesscommon
formiscalledaEuropeanoption.Itallowstheholderoftheoptiontoexercisethe
rightonlyattheexpirationdate.ThepopularS&PindexoptionsareoftheEuropean
type.
WhathappenstothevalueofaCBOEstockoptionwhentheunderlyingstock
Splitsanddividends?
paysadividendorexecutesastocksplit?Inastocksplit,acompanydecidestochange
themeaning,butnotthevalue,ofitsshares.Forexample,ina2-for-1split,anowner
whoheld1,000sharesat$80.50/sharewouldnowown2,000sharesat$40.25pershare
(atleastinaperfectmarket).Splittingitselfshouldnotcreateshareholdervalue—it
Stocksplits,Section19.1A,
p.705
shouldnotchangethemarketcapitalizationoftheunderlyingcompany.
ANECDOTE
GeographyandOptions
T
heoriginoftheterms“European”and“American”is
ahistoricalcoincidence,notareflectionofwhatkind
ofoptionsaretradedwhere.Althoughnooneseemstore-
membertheoriginsofthesedesignations,oneconjecture
isthatcontractscalled“primes”weretradedinFrance.
Thesecouldonlybeexercisedatmaturity—buttheywere
notexactlywhatarenowcalledEuropeanoptions.In-
stead,theoptionownereitherexercised(andreceived
S−K)ordidnotexerciseandpaida“penalty”feeof
D calleda“dont”(not “don’t”).Therewas noupfront
cost.(Thebeststrategyfortheprimeownerwastoexer-
ciseifS−X >−D.)Becausethesecontractscouldonly
beexercisedatmaturityandbecauseAmericanoptions
couldbeexercisedatanytime,theterminologymayhave
stuck.
Incidentally,“Bermudaoptions,”or“Atlanticoptions,”
canbeexercisedperiodicallybeforematuritybutnotat
anyothertime.Theyaresonamednotbecausetheyare
usedinBermuda,butbecauseBermuda(andofcourse
theAtlanticOcean)liesbetweenEuropeandAmerica.
26.1 OPTIONS
983
Althoughsuchasplitshouldmakelittledifferencetotheownersoftheshares
Mostoptionsareadjustedfor
splits.
($80,500worthofshares,nomatterwhat),itcouldbebadnewsfortheownerof
acall option.Afterall, acall with astrikepriceof$75wouldhavebeenin-the-
money(i.e.,theunderlyingsharepriceof$80.50wasabovethestrikeprice)before
thesplit.IftheoptionwereAmerican,thecallwouldbeworth$5.50pershareif
exercised immediately.Afterthesplit, however, thecall wouldbefarout-of-the-
money(i.e.,theunderlyingsharepriceof$40.25wouldbefarbelowthestrikeprice
of$75).Fortunately,theoptioncontractsthataretradedonmostexchanges(e.g.,the
CBOE)automaticallyadjustforstocksplits,sothatthevalueoftheoptiondoesnot
changewhenastocksplitoccurs:Inthiscase,theoption’seffectivestrikepricewould
automaticallyhalvefrom$75to$37.50andthenumberofcallswouldautomatically
doublefrom1to2.(Completingtheoptionsterminology,notsurprisingly,at-the-
moneymeansthatthesharepriceandthestrikepriceareaboutequal.)
Butcommonoptionsaretypicallynot adjustedfordividendpayments:Ifthe
Butoptionsareusuallynot
adjustedfordividends.
$80.50IBMshareweretopayout$40individends,andunlessdividendsfalllike
mannafromheaven,thenthepost-dividendsharepricewouldhavetodroptoaround
Dividendex-dayprice
drop,Section19.4B,p.721
$40.50.Therefore,thein-the-moneycalloptionwouldbecomeanout-of-the-money
calloption.Consequently,ifyourcallwasAmerican,youmightdecidetoexercise
yourcallwitha$75strikepricetonet$5.50justbeforethedividenddate.
IMPORTANT: When you purchase/valuea a typical l financial stock option, the
contractiswritteninawaythatrendersstocksplitsbutnotdividendpayments
irrelevant.
Thereareotherimportantinstitutionaldetailsthatyoushouldknowifyouwant
Oneoptioncontractis(a
bundleof)100options.
to tradeoptions.First, becausethevalueofoptionscanbeverysmall(e.g., 72.5
centsforeachIBMcalloption),theyareusuallytradedinbundlesof100.Thisis
calledanoptioncontract.FiveoptioncontractsonIBMaretherefore500options
(optionson500shares),whichintheexamplewouldcost$0.725
.
500=$362.50.
Second,CBOEoptionstypicallyexpireontheSaturdayfollowingthethirdFridayof
eachmonth,whichiswhereour20thofJulycamefrom.Third,publishedoption
pricescanbemismatchedtotheunderlyingstockprice.TheCBOEclosingpriceis
at4:00pmCST(5:00pmEST),whichis1hourlaterthantheclosingpricefromthe
NYSE(4:00pmEST).Thissometimesleadstoseemingarbitragesinprintedquotes,
whicharenotreallythere.Instead,whatusuallyhappensisthattheunderlyingstock
pricehaschangedbetween4:00pmand5:00pmandtheprintedquotesdonotreflect
thechange.(Inaddition,theclosingpricemaybearecentbidorrecentaskquote,
ratherthanthepriceatwhichyoucouldactuallytransact.)
solvenow!
Q26.2 Anoptionisfarin-the-moneyandwillexpiretonight.Howwouldyou
expectitsvaluetochangewhenthestockpricechanges?
984
CHAPTER26
OPTIONSANDRISKMANAGEMENT
Q26.3 Inaperfectmarket,wouldaputoptionholderwelcomeanunexpected
stocksplit?Inaperfectmarket,wouldaputoptionownerwelcomean
unexpecteddividendincrease?
26.1C OPTIONPAYOFFSATEXPIRATION
Itiseasiesttogainmoreintuitionaboutanoptionbystudyingitspayoffdiagram
Payoffdiagramsdescribe
(European)options.
(andpayofftable).Youhavealreadyseentheseinthebuildingandcapitalstructure
contexts.Theyshowthevalueoftheoptionasafunctionoftheunderlyingbaseasset
Payoffdiagramsinthe
buildingandcapitalstructure
context,Section6.4,p.155
atthefinalmomentbeforeexpiration.Figure26.1showsthepayofftablesandpayoff
diagramsforacallandaputoption,eachwithastrikepriceof$90.Thecharacteristic
ofanyoption’spayoffisthekinkatthestrikeprice:Forthecall,thevalueiszerobelow
thestrikeprice,anda+45-degreelineabovethestrikeprice.Fortheput,thevalueis
zeroabovethestrikeprice,anda−45-degreelinebelowthestrikeprice.
Optional:MoreComplexOptionStrategies
Payoffdiagramscanalsohelpyouunderstandmorecomplexoption-basedstrategies,
Somecommoncomplexoption
strategies.
whichareverypopularonWallStreet.Suchstrategiesmaygolongand/orshortin
differentoptionsatthesametime.Theycanallowyoutospeculateonallsortsof
futuredevelopmentsforthestockprice—forexample,thatthestockpricewillbe
above$60andbelow$70.Inmany(butnotall)cases,itisnotclearwhysomeone
wouldwanttoengageinsuchstrategies,exceptforspeculation.
Twoimportantclassesofcomplexoptionstrategiesarespreads,whichconsistof
Payoffdiagramsforspreads
andcombinations.
longandshortoptionsofthesametype(callsorputs),andcombinations,which
consistofoptionsofdifferenttypes.
Asimplespreadisapositionthatislongoneoptionandshortanotheroption,on
thesamestock.Theoptionshereareofthesametype(putsorcalls)andhavethe
sameexpirationdatebutdifferentstrikeprices.Forexample,asimplespreadmay
purchaseoneputwithastrikepriceof$90andselloneputwithastrikepriceof
$70.Figure26.2plotsthepayoffdiagramforthisposition.
Acomplexspreadcontainsmultipleoptions,someshort,otherslong.Youwillgetto
graphthepayoffdiagramofaso-calledbutterflyspreadinQuestion26.6.
Astraddlemaybethemostpopularcombination.Itcombinesoneputandonecall,
botheitherlongorshort,oftenwiththesamestrikepriceandwiththesametime
toexpiration.YouwillgettographthepayoffdiagraminQuestion26.25.
Insum,
OptionStrategy
VersionA
VersionB
SimpleSpread
LongCall,ShortCall
LongPut,ShortPut
Combination
LongCall,ShortPut
ShortCall,LongPut
Straddle
LongCall,LongPut
ShortCall,ShortPut
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