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1、CHAPTER23:FUTURESMARKETS:ACLOSERLOOK1.a.S0´(1+rM)-D=(1,425´1.06)–15=1,495.50b.S0´(1+rf)-D=(1,425´1.03)–15=1,452.75c.Thefuturespriceistoolow.Buyfutures,shorttheindex,andinvesttheproceedsoftheshortsaleinT-bills:CFNowCFin6monthsBuyfutures0ST-1,422Shortindex1,425-ST-15BuyT-bills-1,4251,467.75T
2、otal030.752.a.Thevalueoftheunderlyingstockis:$250´1,350=$337,500$25/$337,500=0.000074=0.0074%ofthevalueofthestockb.$40´0.000074=$0.0030(lessthanhalfofonecent)c.$0.20/$0.0030=67Thetransactioncostinthestockmarketis67timesthetransactioncostinthefuturesmarket.3.a.Fromparity:F0=1,200´(1+0.03)–1
3、5=1,221ActualF0is1,218;sothefuturespriceis3belowthe“proper”level.b.Buytherelativelycheapfutures,selltherelativelyexpensivestockandlendtheproceedsoftheshortsale:CFNowCFin6monthsBuyfutures0ST-1,218Sellshares1,200-ST-15Lend$1,200-1,2001,236Total0323-11c.Ifyoudonotreceiveinterestontheproceedso
4、ftheshortsales,thenthe$1200youreceivewillnotbeinvestedbutwillsimplybereturnedtoyou.Theproceedsfromthestrategyinpart(b)arenownegative:anarbitrageopportunitynolongerexists.CFNowCFin6monthsBuyfutures0ST-1,218Sellshares1,200-ST-15Place$1,200inmarginaccount-1,2001,200Total0−33d.Ifwecalltheorigi
5、nalfuturespriceF0,thentheproceedsfromthelong-futures,short-stockstrategyare:CFNowCFin6monthsBuyfutures0ST-F0Sellshares1,200-ST-15Place$1,200inmarginaccount-1,2001,200Total01,185−F0Therefore,F0canbeaslowas1,185withoutgivingrisetoanarbitrageopportunity.Ontheotherhand,ifF0ishigherthantheparit
6、yvalue(1,221),thenanarbitrageopportunity(buystocks,sellfutures)willexist.Thereisnoshort-sellingcostinthiscase.Therefore,theno-arbitragerangeis:1,185≤F0≤1,2214.a.Callpthefractionofproceedsfromtheshortsaletowhichwehaveaccess.Ignoringtransactioncosts,thelowerboundonthefuturespricethatpreclude
7、sarbitrageisthefollowingusualparityvalue(exceptforthefactorp):S0(l+rfp)–DThedividend(D)equals:0.012´1,350=$16.20Thefactorparisesbecauseonlythisfractionoftheproceedsfromtheshortsalecanbeinvestedintherisk-freeasset.Wecansolveforpasfollows:1,350´(1+0.022p)–16.20=
