ChapterPreviewStockIndexInterest-RateHedginginvolvesengaginginafinancialtransactionthatreducesoreliminatesDefinitions針對標(biāo)的資產(chǎn)的longposition:anassetwhichispurchasedorowned現(xiàn)在有或買了、將來會獲shortposition:anassetwhichmustbedeliveredtoathirdpartyasafuturedate,oranassetwhichisborrowedandsold,butmustbereplacedinthefuture針對衍生工具的positionThepartythathasagreedtobuyhaswhatistermedalongpositionThepartythathasagreedtosellhaswhatistermedashortpositionHowtohedgeoffsetsalongpositionbytakinganadditionalshortposition,oroffsetsashortpositionbytakinganadditionallongposition.ForwardForwardcontractsareagreementsbytwopartiestoengageinafinancialtransactionatafuturepointintime.Althoughthecontractcanbewrittenhoweverthepartieswant,thecontactusuallyincludes:–Theexactassetstobedeliveredbyoneparty,includingthelocationofdelivery—underlying–Thepricepaidfortheassetsbytheotherparty—forwardprice–Thedatewhentheassetsandcashwillbeexchanged—maturitydateForwardAnExampleofanInterest-Rate–FirstNationalBankagreestodeliver$5millioninfacevalueof6%Treasurybondsmaturingin2023–RockSolidInsuranceCompanyagreestopay$5millionforthebonds–FNBandRockSolidagreetocompletethetransactiononeyearfromtodayattheFNBheadquartersintownForwardLongAgreetobuysecuritiesatfutureHedgesbylockinginfutureinterestrateoffundscominginfuture,avoidingratedecreasesShortAgreetosellsecuritiesatfutureHedgesbyreducingpriceriskfromincreasesininterestratesifholdingForwardLackofliquidity:hardtofindacounter-partyandthinornon-existentsecondarymarketSubjecttodefaultrisk—requiresinformationtoscreengoodfrombadriskFinancialFuturesFinancialfuturescontractsaresimilartoforwardcontractsinthattheyareanagreementbytwopartiestoengageinafinancialtransactionatafuturepointintime.However,theydifferfromforwardcontractsinseveralsignificantways.ExamplesStockfutures,foreignexchangefutures,stockindexfuturesFinancialFuturesFinancialFuturesArbitrage:atexpirationdate,priceofcontract=priceoftheunderlyingassetF=SHedgingsimilartoforwards:microTradedon GlobalcompetitionregulatedCFTC(CommodityFuturesTradingCommodityFuturesOptionsTrading,Inc.homepagePDF"pdfFactoryPro"試用版本創(chuàng)建FinancialFuturesSuccessofFuturesOverFuturesaremoreliquid:standardizedcontractsthatcanbeDeliveryofrangeofsecuritiesreducesthechancethatatradercancornerthemarketMarktomarketdaily:avoidsdefaultDon'thavetodeliver:cashnettingofpositionscontractbetweentwoDeliveryorcashsettlementatexpiryUsuallyonedeliveryNocashpaiduntil

TradedonanContractisusuallyclosedoutpriortomaturityRangeofdeliveryCashpaymentsinto(outof)marginaccount,dailyNegotiablechoiceofdeliverydates,sizeof

PDF"pdfFactoryPro"?WidelyTradedFinancialFuturesHedgingwithfuturesstockbasisHowtohedgingwithFandSarepositivelyCreateanegativeIfyouarelongspot(ie.own1-share):shortthefuturescontract(ontheshare) Hopethatthelossinthecash/spotmarketis(partly)offsetbygainonthefutures(‘dollarfor FinalValue=CashMarketValue+gainonfutures,“l(fā)ocksin”aknown“price”PDF"pdfFactoryPro"?Hedge=LongUnderlying+Short PDF"pdfFactoryPro"試用版本創(chuàng)建?SimpleOwn(long)1-share SpotpriceS0=$100Fearpricefallovernext3-mths3-monthfuturescontracthascurrentprice,F0=TooffsetsomeofthelossinSbyprofitonFTo“l(fā)ockin”a“finalvalue”ofF0= FandSareperfectly(positively)correlatedStrategy:‘Long’share+‘short’onefuturescontractPDF"pdfFactoryPro"試用版本創(chuàng)建?SimpleHedging =$100, =Lossinspotmarketoffsetbygainonthefutures3MONTHSLATER(SpotPricehasfallen)SpotPriceS1=$90FuturesPriceF1=NotethatwehaveassumedthecontractisclosedoutjustbeforematuritysothatS1=F1GainonFutures=(101-90)=(F0-F1)=$11Lossonthespot=(100-90)=(S0-S1)=$10NetProfit=(F0-F1)-(S0-S1)=11-10=$1Notethatyoucannotguaranteethatthehedgewillgiveanetprofitofzero,onlythatthenetprofitinthehedgewillbelessuncertainthansimplyholdingthestocks(ie.herealossofSimpleHedging =$100, =Canwe“l(fā)ockin”apriceofF0=101?If3MONTHSLATER(SpotPricehasfallen)SpotPriceS1= FuturesPriceF1=ProfitonFutures=(101-90)=F0-F1=FinalValue=FinalValueofstocks+profitfrom=90+11=(S1)+F0-F1=HencewehavelockedinafinalvalueofF0=PDF"pdfFactoryPro"試用版本創(chuàng)建?SimpleHedging-BASISRISKSomeFinal S1+(F0-F1)==(S1-F1)+ +where“Finalbasis”=b1=S1-Note:Atmaturityofthefuturescontractthebasisiszero(sinceS1=F1).Ingeneral,whenthecontractisclosedoutpriortomaturityb1=S1-F1maynotbezero.ThisiscalledBASISRISK.Howeverb1willusuallybe“smallinrelationtoF0.SourceofbasisriskischangesinrF=SPDF"pdfFactoryPro"試用版本創(chuàng)建?ButwhynotjusttakedeliveryatF0=101Answer:deliveryEasiesttoseeifyouareafarmerinNewOrleanswhowantstosellhis”livehogs”in3-monthstimewhentheyhavebeenfattenedup.IfhedeliverstheminthefuturescontracthewillhavetosendthehogstoChicago(thedeliverypoint).Thisisexpensive,soinsteadhesellstheminthelocalcattlemarketinNewOrleansforS1=90Buthealsomakes$11cashprofitonthefutures,givinganeffectivepriceof$101,whichEQUALStheF-pricehadhetakendeliveryPDF"pdfFactoryPro"試用版本創(chuàng)建?HedgingwithfuturesGoldMarktomarket:ExampleofaFuturesAninvestortakesalongpositionin2DecembergoldfuturescontractsonJune5contractsizeis100futurespriceisUS$400/marginrequirementis$2,000/contract(US$4,000inmaintenancemarginUS$1,500/contract(US$3,000inPDF"pdfFactoryPro"試用版本創(chuàng)建?Theexchangewillrequiretheinvestortodepositcashintoamarginaccount.Astheexchangeratefluctuatesduringthetwomonths,thevalueofthemarginaccountwillfluctuate.Ifthevalueinthemarginaccountfallstoolow,additionalfundsmayberequired.Thisishowthemarketismarkedtomarket.Ifadditionalfundsarenotdepositedwhenrequired,thepositionwillbeclosedbytheexchange.APossible 5-Jun

+.

+ HedgingwithfuturesFXHedgingFXExample:Amanufacturerexpectstobepaid10millioneurosintwomonthsforthesaleofequipmentinEurope.Currently,1euro=$1,andthemanufacturerwouldliketolock-inthatexchangerate.HedgingFXThemanufacturercanusetheFXfuturesmarkettoaccomplishthis:Themanufacturersells10millioneurosoffuturescontracts,1euro=$1.Assumingthat1contractisfor$125,000ineuros,themanufacturertakesasshortpositionin80contracts.Theexchangewillrequirethemanufacturertodepositcashintoamarginaccount.Forexample,theexchangemayrequire$2,000percontract,orHedgingFXAssumethatactualexchangerateis1euro=$0.96attheendofthetwomonths.Themanufacturerreceivesthe10millioneurosandexchangestheminthespotmarketfor$9,600,000.Themanufactureralsoclosesthemarginaccount,whichhas$560,000init—$400,000forthechangesinexchangeratesplustheoriginal$160,000requiredbythe(assumesnomarginIntheend,themanufacturerhas$10,000,000desiredfromtheHedgingwithfuturesBONDAhedgertakesashortpositioninfiveT-billfuturescontracts.theprice Eachcontract.for$100,000principal.Whenthepositionisunraveled,thepriceis

.Whatisthegain/lossthis/tract= ) Totalgain=2,781.255=Laura,abondportfoliomanager,administers$10millionportfolio.Theportfoliocurrentlyhasadurationof8.5years.Laurawantstoshortenthedurationto6yearsusingT-billfutures.T-billfutureshaveadurationof0.25yearsandaretradingat$975(facevalue=$1,000).HowmanyT-billfuturescontractsdoesLaurarequire? Theaverageportfoliodurationneedstobe6years.10,000,0006=(10,000,0008.5)+(Y60,000,000=85,000,000+(Y-25,000,000=YY=-Lauramusttakeashortposition$100,000,000worthofT-billfutures.Atthecurrentprice,thisrequires100,000,000/975=102,564SpringerCountryBankhasassetstotaling$180millionwithadurationof5years,andliabilitiestotaling$160millionwithadurationof2years.Bankmanagementexpectsinterestratestofallfrom9%to8.25%shortly.AT-bondfuturescontractisavailableforhedging.Itsdurationis6.5yearsandiscurrentlypricedat99532.manycontractsdoesSpringerneedtohedgeagainsttheexpectedratechange?Assumeeachcontractishasafacevalueof$1,000,000.$180million5=($160million2)+(TB6.5)TB=89,230,769Sincethecurrentpriceis$991,562.50,thisrequires90contracts.TheyshouldtakealongHedgingwithfuturesStockIndexPDF"pdfFactoryPro"試用版本創(chuàng)建?StockIndexFinancialinstitutionmanagers,particularlythosethatmanagemutualfunds,pensionfunds,andinsurancecompanies,alsoneedtoassesstheirstockmarketrisk,theriskthatoccursduetofluctuationsinequitymarketprices.Oneinstrumenttohedgethisriskisstockindexfutures.StockIndexStockindexfuturesareacontracttobuyorsellaparticularstockindex,startingatagivenlevel.Contactsexistformostindexes,includingtheS&P500,DowJonesIndustrials,Russell2000,etc.The“best”stockfuturescontracttouseisgenerallydeterminedbythehighestcorrelationbetweenreturnstoaportfolioandreturnstoaparticular

NiWin n n 初始保證金：$15000

期貨合約份 資產(chǎn)組合的總價 交易單位（$) 股票指數(shù) 資產(chǎn)組合的系X11X221共$15000萬股票進(jìn)行保值，該日的股指 股票資產(chǎn)組合：-6.63%1.2$15000萬=-$11934300（贏利HedgingwithStockIndexExample:RockSolidhasastockportfolioworth$100million,whichtrackscloselywiththeS&P500.Theportfoliomanagerfearsthatadeclineiscomingandwhattocompletelyhedgethevalueoftheportfoliooverthenextyear.IftheS&Piscurrentlyat1,000,howisthisaccomplished?HedgingwithStockIndexValueoftheS&P500FuturesContract=250index–currently250x1,000=Tohedge$100millionofstocksthatmove1for1(perfectcorrelation)withS&Pcurrentlysellingat1000,youwould:sell$100millionofindexfutures=400contractsHedgingwithStockIndexSupposeaftertheyear,theS&P500isat900andtheportfolioisworth$90Andfuturespositionisup$10i.e.250x(1,000-900)x400=10Ifinstead,theS&P500isat1100andtheportfolioisworth$110million.futurespositionisdown$10millionEitherway,netpositionis$100millionHedgingwithStockIndexNotethattheportfolioisprotectedfromdownsiderisk,theriskthatthevalueintheportfoliowillfall.However,toaccomplishthemanagerhasalsoeliminatedHowtoprotectsagaindownsiderisk,butdoesnotsacrificetheupside.Ofcourse,thiscomesataprice!premiumofanRighttobuy(calloption)orsell(putoption)aninstrumentattheexercise(strike)priceupuntilexpirationdate(American)oronexpirationdateOptionsareavailableonanumberoffinancialinstruments,includingindividualstocks,stockindexes,Figure1.1:BuyoneEuropeanCallStrikepriceK=$80$PDF"pdfFactoryPro"?ProfitfromaLongForwardK=

PriceofUnderlyingatMaturity,STPDF"pdfFactoryPro"?Figure1.8:Leveragefromoption(on100Callpremium,C=$3Premiumpaid=$300Strikeprice,K=$80CASHMARKETSpotprice,S=Cashpaid=Profit=$8=($88-$80)Netprofit=$800-Return=$500/$300=CASHMARKETProfit=$10=($88-$78)Totalprofit=$1000Return=$1000/$7800=PDF"pdfFactoryPro"?Figure1.2:Sell(write)aEuropeanCallStrikepriceK=$80$PDF"pdfFactoryPro"?PutAEuropeanputoptiongivestheholder(thelong)theright(butnotanobligation)toselltheunderlyingassetatspecifiedfuturedate(knownastheexpiration,expiryormaturitydate)foracertainprice(theexerciseorstrikeandinanamount(contractsize)whichisfixedinForthisprivilegeyoupaytoday,theputPDF"pdfFactoryPro"?Figure1.3:Buy(long)aEuropeanPutStrikepriceK=0

K=

PutPDF"pdfFactoryPro"?ProfitfromaShortForwardPriceof atMaturity,PDF"pdfFactoryPro"?ConsideraputcontractonaT-bondwithanexercisepriceof1011232.Thecontractrepresents$100,000ofprincipal,andhadapremiumofTheactualT-bondpricefallsto9816 theexpiration.Whatisthegain/lossontheposition? Thegainpercontract includethepremiumpaid,thegain$2,125perFigure25.1ProfitsandLossesonOptionsversusFuturesFactorsAffectingHigherstrikeprice,lowerpremiumoncalloptionsandhigherpremiumonputoptions.Greatertermtoexpiration,higherpremiumsforbothcallandputGreaterpricevolatilityofunderlyinginstrument,higherpremiumsforbothcallandputoptions.HedgingwithExample:RockSolidhasastockportfolioworth$100million,whichtrackscloselywiththeS&P500.Theportfoliomanagerfearsthatadeclineiscomingandwhattocompletelyhedgethevalueoftheportfolioagainstanydownsiderisk.IftheS&Piscurrentlyat1,000,howisthisaccomplished?HedgingwithValueoftheS&P500OptionContract=100index–currently100x1,000=Tohedge$100millionofstocksthatmove1for1(perfectcorrelation)withS&Pcurrentlysellingat1000,youwould:buy$100millionofS&Pputoptions=1,000contractsHedgingwithThepremiumwoulddependonthestrikeprice.Forexample,astrikepriceof950mighthaveapremiumof$200/contract,whileastrikepriceof900mighthaveastrikepriceofonly$100.Let’sassumeRockSolidchoosesastrikepriceof950.ThenRockSolidmustpay$200,000(i.e.$0.2m)fortheposition.Thisisnon-refundableandcomesoutoftheportfoliovalue(nowonly$99.8million).HedgingwithSupposeaftertheyear,theS&P500isat900andtheportfolioisworth$89.8optionspositionisup$5million(since950strikeprice),i.e.100x(950-900)x1000=$5innet,portfolioisworth$94.8Or$90m+5m–0.2m(premium)=$94.8Ifinstead,theS&P500isat1100andtheportfolioisworth$109.8million.optionspositionexpiresworthless,andportfolioisworth$109.8millionHedgingwithNotethattheportfolioisprotectedfromanydownsiderisk(theriskthatthevalueintheportfoliowillfall)inexcessof$5million.However,toaccomplishthis,themanagerhastopayapremiumupfrontof$200,000.Themainadvantageofusingoptionsonfuturescontractsratherthanthefuturescontractsthemselvesisthatinterest-rateriskiscontrolledwhilepreservingthepossibilityofgains.ThemaindisadvantageoffuturescontractsascomparedtooptionsonfuturescontractsisthatfuturesremovethepossibilityofConsideraputcontractonaT-bondwithan$100,000ofbondprincipalandhasaof$750.TheactualT-bondpriceis0 .HowcanyouarbitragethisPurchasetheactualT-bondPurchasetheputoptionforExercisetheoption,andselltheT-bondfor$101,375.Thisrepresentsagainof$593.75.Ifallthreestepscanbedonesimultaneously,thereisnoriskorcapitalInterest-RateInterest-rateswapsinvolvetheexchangeofonesetofinterestpaymentsforanothersetofinterestpayments,alldenominatedinthesamecurrency.Simplesttype,calledaplainratesbeingexchanged,typeofpayments,Interest-RateSwapContractMidwestSavingsBankwishestohedgeratechangesbyenteringintovariable-ratecontracts.FriendlyFinanceCompanywishestohedgesomeofitsvariable-ratedebtwithsomefixed-ratedebt.Notionalprincipleof$1Termof10MidwestSBswaps7%paymentforT-bill+1%fromFriendlyFinanceInterest-RateSwapContractFigure25.2Interest-RateSwapHedgingwithInterest-RateReduceinterest-rateriskforbothMidwesthas$1millionlessofrate-sensitiveassetsthanithasofrate-sensitiveliabilities,heisworriedabouti↑,soconverts$1moffixedrateassetstorate-sensitiveassets,RSA,lowersFriendlyFinancehas$1millionmoreofrate-sensitiveassetsthanofrate-sensitiveliabilities,heisworriedabouti↓,soconverts$1mofrate-sensitiveassetstofixedrateassets,lowersGAPAswapagreementcallsforDurbinIndustriestopayinterestannuallybasedonarateof1.5%overtheone-yearT-billrate,currently6%.Inreturn,Durbinreceivesinterestatarateof6%onafixed-ratebasis.Thenotionalprincipalfortheswapis$50,000.WhatisDurbin’snetinterestfortheyearfromtheSolution:Durbinpays7.5%$50,000andreceives6%ornet,pays1.5%50,000=HedgingwithInterest-RateAdvantagesofReducerisk,nochangeinbalance-LongertermthanfuturesorLackofSubjecttodefaultFinancialintermediarieshelpreducedisadvantagesofswaps(butatacost!)ChapterHedging:thebasicideaofenteringintoanoffsettingcontracttoreduceoreliminatesometypeofriskwaspresented.ForwardMarkets:thebasicideaofcontractsinthishighlyspecializedmarket,aswellasasimpleexampleofeliminatingriskwasChapterSummaryFinancialFuturesMarkets:theseexchangetradedmarketswerepresented,aswellastheiradvantagesoverforwardcontacts.StockIndexFutures:thespecificapplicationofstockindexfutureswaspresented,exploringtheirabilitytoreduceoreliminateriskforequityportfolios.ChapterSummaryOptions:thesecontracts,whichgivethebuyertherightbutnottheobligationtoact,werepresented,aswellasanexampleshowingtheirInterest-RateSwaps:theideaoftradingfixed-rateinterestpaymentsforfloating-ratepaymentswaspresented,aswellastheprosandconsofsuchDurationandInterest-RatenDurationisaweightedaverageofthematuritiesofthecashnDU

CP DF t1 CPt DFtt1

tCP ntt 1 t 1intPDF"pdfFactoryPro"試用版本創(chuàng)建?FormulaforDUR

tCt CPntt t11ntKeyfactsaboutAllelseequal,whenthematurityofabondlengthens,thedurationrisesaswellAllelseequal,wheninterestratesrise,thedurationofacouponbondfallFormulaforThehigheristhecouponrateonthebond,theshorteristhedurationofthebondDurationisadditive:thedurationofaportfolioofsecuritiesistheweighted-averageofthedurationsoftheindividualsecurities,withtheweightsequalingtheproportionoftheportfolioinvestedineachDurationandInterest-Rate%PDUR1i10%toTable3-4,10%coupon%P6.76 1%P0.0615DurationandInterest-RateRisk(cont.)i10%to20%couponbond,DUR=5.72%P5.72 1%P0.0520DurationandInterest-RateRisk(cont.)Thegreateristhedurationofasecurity,thegreateristhepercentagechangeinthemarketvalueofthesecurityforagivenchangeininterestratesTherefore,thegreateristhedurationofasecurity,thegreaterisitsinterest-rateriskDurationGapOwnersandmanagersdocareabouttheimpactofinterestrateexposureoncurrentnetincome.Theyarealsointerestedintheimpactofinterestratechangesonthemarketvalueofbalancesheetitemsandtheimpactonnetworth.Theconceptofduration,whichfirstappearedinchapter3,playsarolehere.DurationGapDurationGapAnalysis:measuresthesensitivityofabank’scurrentyearnetincometochangesininterestrate.Requiresdeterminingthedurationforassetsandliabilities,itemswhosemarketvaluewillchangeasinterestrateschange.Let’sseehowthislooksforFirstDurationofFirstNationalBank'sAssetsandLiabilitiesDurationo