投资学10版习题答案20.docx
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投资学10版习题答案20.docx
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投资学10版习题答案20
CHAPTER20:
OPTIONSMARKETS:
INTRODUCTION
PROBLEMSETS
1.Optionsprovidenumerousopportunitiestomodifytheriskprofileofaportfolio.Thesimplestexampleofanoptionstrategythatincreasesriskisinvestinginan‘alloptions’portfolioofatthemoneyoptions(asillustratedinthetext).Theleverageprovidedbyoptionsmakesthisstrategyveryrisky,andpotentiallyveryprofitable.Anexampleofarisk-reducingoptionsstrategyisaprotectiveputstrategy.Here,theinvestorbuysaputonanexistingstockorportfolio,withexercisepriceoftheputnearorsomewhatlessthanthemarketvalueoftheunderlyingasset.Thisstrategyprotectsthevalueoftheportfoliobecausetheminimumvalueofthestock-plus-putstrategyistheexercisepriceoftheput.
2.Buyingaputoptiononanexistingportfolioprovidesportfolioinsurance,whichisprotectionagainstadeclineinthevalueoftheportfolio.Intheeventofadeclineinvalue,theminimumvalueoftheput-plus-stockstrategyistheexercisepriceoftheput.Aswithanyinsurancepurchasedtoprotectthevalueofanasset,thetrade-offaninvestorfacesisthecostoftheputversustheprotectionagainstadeclineinvalue.Thecostoftheprotectionisthecostofacquiringtheprotectiveput,whichreducestheprofitthatresultsshouldtheportfolioincreaseinvalue.
3.Aninvestorwhowritesacallonanexistingportfoliotakesacoveredcallposition.If,atexpiration,thevalueoftheportfolioexceedstheexercisepriceofthecall,thewriterofthecoveredcallcanexpectthecalltobeexercised,sothatthewriterofthecallmustselltheportfolioattheexerciseprice.Alternatively,ifthevalueoftheportfolioislessthantheexerciseprice,thewriterofthecallkeepsboththeportfolioandthepremiumpaidbythebuyerofthecall.Thetrade-offforthewriterofthecoveredcallisthepremiumincomereceivedversusforfeitofanypossiblecapitalappreciationabovetheexercisepriceofthecall.
4.Anoptionisoutofthemoneywhenexerciseoftheoptionwouldbeunprofitable.Acalloptionisoutofthemoneywhenthemarketpriceoftheunderlyingstockislessthantheexercisepriceoftheoption.Ifthestockpriceissubstantiallylessthantheexerciseprice,thenthelikelihoodthattheoptionwillbeexercisedislow,andfluctuationsinthemarketpriceofthestockhaverelativelylittleimpactonthevalueoftheoption.Thissensitivityoftheoptionpricetochangesinthepriceofthestockiscalledtheoption’sdelta,whichisdiscussedindetailinChapter21.Foroptionsthatarefaroutofthemoney,deltaisclosetozero.Consequently,thereisgenerallylittletobegainedorlostbybuyingorwritingacallthatisfaroutofthemoney.(Asimilarresultappliestoaputoptionthatisfaroutofthemoney,withstockpricesubstantiallygreaterthanexerciseprice.)
Acallisinthemoneywhenthemarketpriceofthestockisgreaterthantheexercisepriceoftheoption.Ifstockpriceissubstantiallygreaterthanexerciseprice,thenthepriceoftheoptionapproachestheorderofmagnitudeofthepriceofthestock.Also,sincesuchanoptionisverylikelytobeexercised,thesensitivityoftheoptionpricetochangesinstockpriceapproachesone,indicatingthata$1increaseinthepriceofthestockresultsina$1increaseinthepriceoftheoption.Underthesecircumstances,thebuyerofanoptionlosesthebenefitoftheleverageprovidedbyoptionsthatarenearthemoney.Consequently,thereislittleinterestinoptionsthatarefarinthemoney.
5.
Cost
Payoff
Profit
a.
Calloption,X=$190.00$100.00¤$$100.00¤¤$$$100.00====$100.00==$100.00¤¤¤$100.000¤$$$1$$$100.00
$6.75
$5.00
-$1.75
b.
Putoption,X=$190.00
3.00
0.00
-3.00
c.
Calloption,X=$195.00
3.65
0.00
-3.65
d.
Putoption,X=$195.00
5.00
0.00
-5.00
e.
Calloption,X=$200.00
1.61
0.00
-1.61
f.
Putoption,X=$200.00
8.09
5.00
-3.09
6.Intermsofdollarreturns,basedona$10,000investment:
PriceofStock6MonthsfromNow
StockPrice
$80
$100
$110
$120
Allstocks(100shares)
8,000
10,000
11,000
12,000
Alloptions(1,000options)
0
0
10,000
20,000
Bills+100options
9,360
9,360
10,360
11,360
Intermsofrateofreturn,basedona$10,000investment:
PriceofStock6MonthsfromNow
StockPrice
$80
$100
$110
$120
Allstocks(100shares)
-20%
0%
10%
20%
Alloptions(1,000options)
-100
-100
0
100
Bills+100options
-6.4
-6.4
3.6
13.6
7.a.Fromput-callparity:
b.Purchaseastraddle,i.e.,bothaputandacallonthestock.Thetotalcostofthestraddleis$10+$7.65=$17.65
8.a.Fromput-callparity:
b.Sellastraddle,i.e.,sellacallandaput,torealizepremiumincomeof
$5.18+$4=$9.18
Ifthestockendsupat$50,bothoftheoptionswillbeworthlessandyourprofitwillbe$9.18.Thisisyourmaximumpossibleprofitsince,atanyotherstockprice,youwillhavetopayoffoneitherthecallortheput.Thestockpricecanmoveby$9.18ineitherdirectionbeforeyourprofitsbecomenegative.
c.Buythecall,sell(write)theput,lend$50/(1.10)1/4
Thepayoffisasfollows:
Position
ImmediateCF
CFin3months
ST≤X
ST>X
Call(long)
C=5.18
0
ST–50
Put(short)
–P=4.00
–(50–ST)
0
Lendingposition
50
50
Total
C–P+
ST
ST
Bytheput-callparitytheorem,theinitialoutlayequalsthestockprice:
S0=$50
Ineitherscenario,youendupwiththesamepayoffasyouwouldifyouboughtthestockitself.
9.a.i.Alongstraddleproducesgainsifpricesmoveupordownandlimitedlossesifpricesdonotmove.Ashortstraddleproducessignificantlossesifpricesmovesignificantlyupordown.Abullishspreadproduceslimitedgainsifpricesmoveup.
b.i.Longputpositionsgainwhenstockpricesfallandproduceverylimitedlossesifpricesinsteadrise.Shortcallsalsogainwhenstockpricesfallbutcreatelossesifpricesinsteadrise.Theothertwopositionswillnotprotecttheportfolioshouldpricesfall.
10.Notethatthepriceoftheputequalstherevenuefromwritingthecall,netinitialcashoutlays=$38.00
Position
<35
35
40X2X2XX2X2X2X2X2
40<
Buystock
Writecall($40)
0
0
40-
Buyput($35)
35-
0
0
Total
$35
$40
11.Answersmayvary.For$5,000initialoutlay,buy5,000puts,write5,000calls:
Position
=$30
=$40X2X2XX2X2X2X2X2
=$50
Stockportfolio
$150,000
$200,000
$250,000
Writecall(X=$45)
0
0
-$25,000
Buyput(X=$35)
$25,000
0
0
Initialoutlay
-$5,000
-$5,000
-$5,000
Portfoliovalue
$170,000
$195,000
$220,000
Comparethistojustholdingtheportfolio:
Position
=$30
=$40X2X2XX2X2X2X2X2
=$50
Stockportfolio
$150,000
$200,000
$250,000
Portfoliovalue
$150,000
$200,000
$250,000
12.a.
Outcome
ST≤X
ST>X
Stock
ST+D
ST+D
Put
X–ST
0
Total
X+D
ST+D
b.
Outcome
ST≤X
ST>X
Call
0
ST–X
Zeros
X+D
X+D
Total
X+D
ST+D
ThetotalpayoffsforthetwostrategiesareequalregardlessofwhetherSTexceedsX.
c.Thecostofestablishingthestock-plus-putportfoliois:
S0+P
Thecostofestablishingthecall-plus-zeroportfoliois:
C+PV(X+D)
Therefore:
S0+P=C+PV(X+D)
Thisresultisidenticaltoequation20.2.
13.a.
Position
ST X1STX2 X2 X3 Longcall(X1) 0 ST–X1 ST–X1 ST–X1 Short2calls(X2) 0 0 –2(ST–X2) –2(ST–X2) Longcall(X3) 0 0 0 ST–X3 Total 0 ST–X1 2X2–X1–ST (X2–X1)–(X3–X2)=0 b. Position ST X1STX2X2X2XX2X2X2X2X2 X2 Buycall(X2) 0 0 ST–X2 Buyput(X1) X1–ST 0 0 Total X1–ST 0 ST–X2 14. Position ST X1STX2XX2 X2 Buycall(X2) 0 0 ST–X2 Sellcall(X1) 0 –(ST–X1) –(ST–X1) Total 0 X1–ST X1–X2 15.a.Bywritingcoveredcalloptions,Jonesreceivespremiumincomeof$30,000.If,inJanuary,thepriceofthestockislessthanorequalto$45,thenJoneswillhavehisstockplusthepremiumincome.Butthemosthecanhaveatthattimeis($450,000+$30,000)becausethestockwillbecalledawayfromhimifthestockpriceexceeds$45.(Weareignoringhereanyinterestearnedoverthisshortperiodoftimeonthepremiumincomereceivedfromwritingtheoption.)Thepayoffstructureis StockpricePortfoliovalue lessthan$4510,000timesstockprice+$30,000 greaterthan$45$450,000+$30,000=$480,000 ThisstrategyofferssomeextrapremiumincomebutleavesJonessubjecttosubstantialdownsiderisk.Atanextreme,ifthestockpricefelltozero,Joneswouldbeleftwithonly$30,000.Thisstrategyalsoputsacaponthefinalvalueat$480,000,butthisismorethansufficienttopurchasethehouse. b.Bybuyingputoptionswitha$35strikeprice,Joneswillbepaying$30,000inpremiumsinordertoensureaminimumlevelforthefinalvalueofhisposition.Thatminimumvalueis($35×10,000)–$30,000=$320,000. Thisstrategyallowsforupsidegain,butexposesJonestothepossibilityofamoderatelossequaltothecostoftheputs.Thepayoffstructureis: StockpricePortfoliovalue lessthan$35$350,000–$30,000=$320,000 greaterthan$3510,000timesstockprice–$30,000 c.Thenetcostofthecollariszero.Thevalueoftheportfoliowillbeasfollows: StockpricePortfoliovalue lessthan$35$350,000 between$35and$4510,000timesstockprice greaterthan$45$450,000 Ifthestockpriceislessthanorequal
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