Bodie2-IM-Ch11

CHAPTER11-Hedging,Insuring,andDiversifyingEnd-of-ChapterProblems1.Supposeyouownagroveoforangetrees.Theharvestisstilltwomonthsawaybutyouareconcernedaboutpricerisk.Youwanttoguaranteethatyouwillreceive$1.00perpoundintwomonthsregardlessofwhatthespotpriceisatthattime.Youareselling250,000pounds.a.Showtheeconomicsofashorttransactionintheforwardmarketifthespotpriceondeliverydateis$0.75perpound,$1.00perpound,or$1.25perpound.b.Whatwouldhavehappenedtoyouifyouhadnotenteredthehedgeandeachscenarioisequallylikely?c.Whatisthevariabilityofyourreceiptsafterthehedgeisinplace?Solution:a.Theproceedsformthesaleoforangejuicearegivenby:Juiceprice()price250000⋅:=Thecashflowfromthefuturescontractisgivenby:Futuresprice()1price−()250000⋅:=Thetotalvalueoftheposition:Totalprice()Juiceprice()Futuresprice()+:=0.80.911.11.22105×4105×250000Juiceprice()Futuresprice()Totalprice()priceprice0.751.001.25=Juiceprice()187500.00250000.00312500.00=Futuresprice()62500.000.00-62500.00=Totalprice()250000.00250000.00250000.00=b.Youwouldhavehadaone-thirdchanceeachofgettingonly$187,500(lessthanexpected),getting$250,000(thesameasexpected)or$312,500(morethanexpected).c.Novariability.Receiptsarealwaysequalto$250,000.2.Supposeinsixmonths’timethecostofagallonofheatingoilwilleitherbe$0.90or$1.10.Thecurrentpriceis$1.00pergallon.a.Whataretherisksfacedbyaresellerofheatingoilthathasalargeinventoryonhand?Whataretherisksfacedbyalargeuserofheatingoilwithaverysmallinventory?b.Howcanthesetwopartiesusetheheatingoilfuturesmarkettoreducetheirrisksandlockinapriceof$1.00pergallon?Assumeeachcontractisfor50,000gallonsandtheyeachneedtohedge100,000gallons.c.Canyousaythateachpartyhasbeenmadebetteroff?Whyorwhynot?Chapter11-1Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManuala.Theresellerwouldlosemoneyisthepriceofoilfellto$0.90pergallonbecausehepurchasedtheoilat$1.00.Theuserofheatingoilwouldfacetheriskofrisingheatingprices.b.Theusershouldgolongontwofuturescontracts,andthepaymentorcostwouldbe:Costuprice()price−100000⋅:=Futuresuprice()1price−()−100000⋅:=Totaluprice()Costuprice()Futuresuprice()+:=price0.901.10=Costuprice()-90000.00-110000.00=Futuresuprice()-10000.0010000.00=Totaluprice()-100000.00-100000.00=Theheatingoilresellershouldgoshorttwofuturescontracts,andtheexpectedproceedswouldbe:Revenuerprice()price100000⋅:=Futuresrprice()1price−()100000⋅:=Totalrprice()Revenuerprice()Futuresrprice()+:=price0.901.10=Revenuerprice()90000.00110000.00=Futuresrprice()10000.00-10000.00=Totalrprice()100000.00100000.00=c.Eventhoughitappearsthatineachscenarioonepartyhasbenefitedattheexpenseoftheother,bothhavereallybenefitedbecausebothpartieswereabletolockinapriceof$1.00pergallonandeliminateallrisk.3.SupposeyouaretreasurerofalargemunicipalityinMichiganandyouareinvestingincattlefutures.Youpurchasefuturescontractsworth400,000poundsofcattlewithanexercisepriceof$0.60perpoundandanexpirationdateinonemonth.a.Showtheeconomicsofafuturestransactionifthepriceofcattleatdeliverydateis$0.40perpound,$0.60perpound,or$0.80perpound.b.Isthisarisk-reducingtransaction?c.Wouldyouranswerto“b”bedifferentifthetreasurerwereinvestinginoilfutures?Whataboutinterestratefutures?Solution:a.Thevalueofthepositionwouldbe:Valueprice()400000price.6−()⋅:=price0.400.600.80=Valueprice()-80000.000.0080000.00=b.Thisisnotarisk-reducingtransactionbecauseyouarenothedgingasimilarbutoppositeexposure.c.Oilfutures=sameansweras“b”above.Interestratefuturesdependsuponthecontext.Areyouoffsettingsomeinterestriskyoucurrentlyhaveinyourportfolioorareyoutakingwhatissaidtobea“naked”orunhedgedposition?Chapter11-2Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManual4.Yourcousinisahogfarmerandheinvestsinporkbellyfuturesandoptionscontracts.Hehastoldyouthathebelievesporkbellypricesareontherise.Youdecidetopurchaseacalloptiononporkbellieswithastrikepriceof$0.50perpound.Thatway,ifporkbellypricesgoup,youcanexercisethecall,buytheporkbelliesandsellthemforthehigherspotprice.Assumethepriceofanoptionon40,000poundsis$1,000andyoupurchasefiveoptionsfor$5,000on200,000pounds.a.Wouldthisbearisk-reducingorspeculativetransactionforyou?b.Whatisyourdownsideriskindollarsandpercentageterms?c.Ifthepriceperpoundincreasesto$0.55perpound,howmuchwouldyounetafterpayingfortheoptions?Solution:a.Becausethiswouldbeanunhedgedpositionforyou,thiswouldbespeculative.b.-$5,000(theoptionsexpireworthless)or-100%c..55.5−0.050=perpound0.05200000⋅10000.000=$10,000Net:100005000−5000.000=$5,0005.Supposeyouareexpectingyourfourthchildinsixmonthsandyouneedabiggercar.Youhaveyoureyeonausedthree-yearoldminivanwhichcurrentlycostsapproximately$10,000.Youareconcernedaboutthepricingandavailabilityofthisspecificcarinsixmonths’time,butyouwon’thaveenoughmoneytopurchasethecaruntilsixmonthsfromtoday.a.Howcouldyouadvertiseinthenewspaperforaforwardcontractwithacounterpartythatwouldeliminateyourrisk?b.Whowouldbewillingtotaketheshortpositiononyourforwardcontract?(Whoisthelikelycounterparty)?Solution:a.Youcouldadvertisethatyouarewillingtopay$10,