Rente Trading Strategier Eurex

Navigasjon Eurex Fixed Income Options: en mulighet til ikke å bli savnet 13 Markedsførere støtter likviditet permanent i Eurex-renteprogrammene. I HY1 2015 hadde daglig omsetning i opsjoner på Bund, Bobl og Schatz Futures over 350.000 kontrakter (pluss 70 prosent y-o-y). Av dette har 30 prosent blitt handlet via orderbok og 30 prosent via Eurex Strategy Wizard SM. Ordinære anførselstegn er kontinuerlig tilgjengelig for 1000 kontrakter. Strategi sitater varierer mellom 500 og 1000 kontrakter. Eurex-alternativer på Bund, Bobl og Schatz Futures er tilgjengelig som samtaler og setter med en rekke tenorer i en rekke treningspriser og gir dermed en høy grad av skreddersy. I tillegg kombinerer investorer ofte flere alternativer til en handel for å utføre en raffinert handelsstrategi. Handelsinteresse spredes dermed bredt i disse dimensjonene, i motsetning til rentemarkedet futures markedet hvor handel er fokusert på den svært flytende frontmånederserien. Futures drives ofte i ordrevurderte markeder, hvor likviditet er gitt av den varierende toveis ordreflyten fra den sentrale ordreboken. Optiehandel er sitat drevet ettersom likviditet ikke kan konsentreres i en enkelt kontrakt på grunn av den store spredningen av handelsinteressen over streik og utløp og de mange kombinasjonsmulighetene i opsjonsstrategier. Investorer finner prisveiledning for risikostyring og faste omsettelige priser fra spesialiserte markedsførere som leverer elektroniske sitater i bestillingsboken og telefonnotering for off-trade-handel. I skjermhandelen kan investorer handle direkte på noterte priser og benytte ytterligere kilder til likviditet når Market Maker-sitater fylles på ved utførelse. Market Maker-sitater er også viktige for grenseordrer som inngås av investorer som initierer opsjonshandler. Eurex Exchange har etablert elektronisk notering i renterett og tilbyr permanente og avanserte Markedsføringsprogrammer. Streaming sitater tilbys av over et dusin høyt spesialiserte Markedsføringsfirmaer som betjener etterspørsel etter direkte henrettelse fra institusjonelle sluttbrukere. Handler i 1000 kontrakter og mer kan enkelt utføres i punkt-og-klikk-handel av investorer med direkte markedsadgang. I HY1 2015 var daglig elektronisk handelsvolum i Bund, Bobl og Schatz Options over 90.000 kontrakter. I løpet av de siste tre årene har andelen av bokvolum i Bund Options økt fra rundt 20 prosent og i 2015 opprettholdt en andel på 33 prosent. Andelen bokvolum i Bobl Options doblet fra 10 til 20 prosent i 2014. På samme måte i 2015 blir opptil 25 prosent av volumet av Schatz Options utført elektronisk. Alternativer handler ikke bare som samtaler og setter, men også som opsjonsstrategier. I november 2013 lanserte Eurex et skreddersydd Market-Making-program for opsjonsstrategier som i økende grad tiltrekker volum direkte fra henrettelsen av ordrer mot anførselstegnene fra Market Makers. I 2015 ser vi nå et daglig gjennomsnitt på 5000 opsjoner for rentekostnadsopsjoner som handler mot Market Maker-sitater i opsjonsstrategier. Som i handel med direkte anrop og setter, er mid-market trading med grenseordrer også utbredt i opsjonsstrategier. Siden slutten av 2013 økte strategimengden både på grunn av økt bruk av strategibetingelser for blokkbransjer og høyere skjermvolumer etter introduksjonen av strategien Markedsføringsprogram. I 2015 økte daglig ordrevolum i strategier til 32 000 kontrakter i renter. Samlet handler strategiproduksjon om lag 30 prosent av volumet både i ordrebok og off-book trading. I tillegg til å sitere opsjonsstrategier, markedsfører Markedsførere også faste priser. Dermed er likviditet gitt for et vidt spekter av strategier. Strategibestemmelsesbøker er vanligvis sitert for 500 til 1000 kontrakter på det indre markedet, avhengig av risikoprofilen for opsjonsstrategien i spørsmålet. Interessant er strategiske sitater ofte strammere enn den kumulative spredningen fra enkelthåndsutførelse av bena individuelt. Dette reflekterer riktig risikoprofilen for opsjonsstrategier, og oversetter også til lavere implisitte transaksjonskostnader for investorer som bare trenger å krysse en budbudsspredning. SubnavigationInterest Rate Derivatives Fixed Income Trading Strategies. eurex 1 Renteavledninger Vederlagsrettede strategier eurex 2 Vær oppmerksom på Definisjonene av grunnlag og bærekostnad er endret i denne versjonen av brosjyren. I den forrige versjonen ble følgende definisjoner brukt: Basis Futures Prispris på kontantinstrument Kostnad for bæregrunner I denne versjonen brukes følgende definisjoner: Basispris på kontantinstrument Fremtidspris Kostnad for bæregrunn Disse endringene er gjort i rekkefølge for å sikre at definisjonene av begge elementene er konsistente i hele Eurex-materiale, inkludert Trader-eksamen og tilsvarende forberedende materialer. 3 Renterettederivater Renteinntekter Strategier eurex 4 Innhold Brosjyre Struktur og mål Egenskaper for fastinntekter Verdipapir Obligasjoner Definisjon 08 Levetid og gjenværende levetid 09 Nominell og faktisk rentesats (kupong og avkastning) 09 Opptjent rente 10 Avkastningskurven 11 Obligasjonsvurdering 14 Macaulay Varighet 16 Endret varighet 16 Konveksitet sporingsfeil for varighet Eurex Fixed Income Derivatives 18 Egenskaper for Exchange-Traded Financial Derivatives 18 Innledning 18 Fleksibilitet 18 Transparens og Likviditet 18 Utnyttelse Effekt Innføring i Fast Income Futures 19 Hva er Fast Income Futures Definisjon 19 Futures Positions Forpliktelser 20 Avregning eller utelukkelse 21 Kontraktspesifikasjoner 22 Eurex Fixed Income Futures Oversikt 22 Fremtidsspredningsmargin og tilleggsmargin 23 Variasjonsmargin 24 Fremtidsprisen Virkelig verdi 26 Kostnad ved kjøp og grunn 27 Konverteringsfaktor (Prisfaktor) og Billigeste å levere CTD) Obligasjon 28 Identifisering av Billigeste-å-levere Obligasjoner 5 Applikasjoner med Fast Income Futures 32 Handelsstrategier 32 Grunnleggende Futures Strategier 33 Langt Posisjoner (Bullish Strategies) 35 Korte Posisjoner (Bearish Strategier) 36 Spread Strategies 37 Tidsspredning 38 Inter-Product Spread 40 Sikringsstrategier 41 Valg av Futures Contract 41 Perfect Hedge versus Cross Hedge 41 Sikringshensyn 42 Fastsettelse av Hedge Ratio 43 Nominell Verdi Metode 43 Modifisert Varighet Metode 45 Følsomhetsmetode 47 Statisk og Dynamisk Sikring 47 Cash-and-Carry Arbitrage Introduksjon til opsjoner på faste inntekter Futures 49 Alternativer på Fastsetting Futures Definisjon 49 Alternativer på fast inntekt Futures Rettigheter og forpliktelser 50 Closeout 50 Utøvelsesmuligheter på faste inntekter Futures 51 Kontraktspesifikasjoner Alternativer på faste inntekter Futures 52 Premium Betaling og risikobasert marginering 54 Alternativer på faste inntekter Futures Oversikt 6 Alternativpris 55 Komponenter 55 Intrinsic Value 55 Tidsverdi 56 Bestemme faktorer 56 Volatilitet av U nderlying Instrument 56 Resterende levetid for alternativet 57 Berøringsfaktorer Viktige risikoparametre Grekker 58 Delta 60 Gamma 61 Vega (Kappa) 61 Theta Trading Strategies for opsjoner på faste inntekter Futures 62 Langt anrop 63 Korttelefon 65 Langt sett 66 Kortsett 67 Bull Call Spread 68 Bear Put Spread 69 Long Straddle 71 Long Strangle 72 Virkning av Time Value Decay og Volatilitet 72 Time Value Decay 73 Effekt av svingninger i markedsvolatilitet 74 Handelsvolatilitet Opprettholde en Delta-nøytral posisjon med Futures Hedging Strategies 77 Sikringsstrategier for en fast tidshorisont 79 Delta Hedging 80 Gamma Hedging 82 Zero Cost Collar 7 FuturesOptions Relasjoner, Arbitrage Strategies 83 Syntetisk Fixed Income Options og Futures Posisjoner 83 Syntetisk Langt Call 85 Syntetisk Korttall 86 Syntetisk Lang Put 88 Syntetisk Short Put 88 Syntetisk Lang FutureReversal 90 Syntetisk Short FutureConversion 91 Syntetisk Alternativer og fremtidsposisjoner Oversikt Ordliste 92 Tillegg 1: Verdsettelsesskjema ulae og indikatorer 100 Engangsperiode gjenværende levetid 100 Multi-periode gjenværende levetid 100 Macaulay Varighet 101 Konveksitet Tillegg 2: Konverteringsfaktorer 102 Obligasjoner denominert i euro 102 Obligasjoner denominert i sveitsiske franc Tillegg 3: Liste over diagrammer Kontakter 105 Ytterligere informasjon 8 Brosjyrestruktur og Mål Denne brosjyren beskriver de rentebærende derivatene som handles på Eurex, og illustrerer noen av de viktigste applikasjonene. Disse kontraktene består av futures på rentepapirer (renter med fast rente) og opsjoner på renteterminaler. For å gi bedre forståelse av de beskrevne kontraktene, vil de grunnleggende egenskapene til rentepapirer og indikatorene som brukes til å analysere dem, skisseres. Grunnleggende kunnskaper om verdipapirindustrien er en forutsetning. Forklaringer av rentepapirer som er indeholdt i denne brosjyren, refererer hovedsakelig til slike problemer som Eurex-rentebærende derivater er basert på. 6 9 Egenskaper for verdipapirobligasjoner med fast inntekt Definisjon En obligasjon kan beskrives som storskala lån på kapitalmarkedet, hvor kreditorens rettigheter er sertifisert i form av verdipapirer. Tilbudene om verdipapirer er kjent som emisjoner og den respektive debitor som utsteder. Obligasjoner er kategorisert i henhold til deres levetid, utsteder, renteopplysningsdetaljer, kredittvurdering og andre faktorer. Fastrentede obligasjoner har en fast rente, kalt kupongen, som er basert på obligasjonens pålydende verdi. Avhengig av spesifikasjonene, er rentebetaling vanligvis halvårlig eller årlig. Renteinntekter som handles på Eurex, er basert på en kurv av enten tyske eller sveitsiske obligasjonsobligasjoner i offentlig sektor. I Sveits styrer Sveitsiske Nationalbanken (SNB) lånekravene til den sveitsiske føderale finansdepartementet. Kapital økes ved utstedelse av såkalte pengemarkedsregnskapsskader samt statsobligasjoner og statsobligasjoner. Bare Confederation Obligasjoner med ulike livstider er fritt omsettelige. Andre statsobligasjoner utveksles kun mellom SNB og banker, eller i interbankhandel. Det tyske finanskontoret (Bundesrepublik Deutschland Finanzagentur GmbH) har vært ansvarlig for utstedelsen av tyske statsobligasjoner (på vegne av den tyske regjeringen) siden juni. Andre omsettelige saker inkluderer obligasjoner utstedt fram til 1995 av det tidligere privatiseringsbyrået Treuhandanstalt og den tyske forbundsregeringen s spesielle midler, for eksempel det tyske enhetsfondet. Disse obligasjonene tilskrives samme kredittverdighet som følge av Forbundsrepublikken Tysklands forutsetning om ansvar. Tyske regjeringsproblemer som er relevante for Eurex-rentederivatene, har følgende livstids - og kupongbetalingsdetaljer. Regjeringsproblemer Livstid Kupongbetaling Tyske Federal Treasury Notes 2 år Årlig (Bundesschatzanweisungen) Tysklands gjeldsforpliktelser 5 år Årlig (Bundesobligationen) Tyske statsobligasjoner 10 og 30 år Årlig (Bundesanleihen) Vilkårene for disse problemene gir ikke tidlig innløsning ved å ringe inn eller tegning. 1 1 Jf. Deutsche Bundesbank, Der Markt für deutsche Bundeswertpapiere, 2. utgave, FrankfurtMain, 10 I dette kapittelet vil følgende informasjon bli brukt til en rekke forklaringer og beregninger: Eksempel: Gjeldsspørsmål Tysklands Obligasjon. av utstederen Forbundsrepublikken Tyskland. ved utstedelsesdato 5. juli, med en levetid på 10 år. en innløsningsdato 4. juli, en fast rente på 4,5. kupong betaling årlig. en pålydende verdi på 100 levetid og gjenværende levetid En må skille mellom levetid og gjenværende levetid for å forstå rentebinding og tilhørende derivater. Livstiden angir tidsperioden fra utstedelsestidspunktet til sikkerhetsbeløpet er innløst, mens gjenværende levetid er gjenværende tidsperiode fra verdsettelsesdagen til innløsning av verdipapirer som allerede er utstedt. Eksempel: Obligasjonen har en levetid på som på verdsettelsesdagen er gjenværende levetid 10 år 11. mars 2002 (i dag) 9 år og 115 dager 8 11 Nominell og faktisk rentesats (kupong og avkastning) Den nominelle renten på en Renteinntekter er verdien av kupongen i forhold til den pålydende verdien av sikkerheten. Generelt svarer hverken emisjonsprisen eller den omsatte prisen på en obligasjon til sin pålydende verdi. I stedet handles obligasjoner under eller over par, d. v.s. deres verdi er under eller over den nominelle verdien på 100 prosent. Både kupongbetalinger og den faktiske investerte kapitalen tas i betraktning ved beregning av avkastningen. Dette betyr at med mindre obligasjonen handles til nøyaktig 100 prosent, vil den faktiske rentesatsen med andre ord: avkastningen avvike fra den nominelle renten. Den faktiske rentesatsen er lavere (høyere) enn den nominelle rentesatsen for en obligasjonshandel over (under) dens pålydende verdi. Eksempel: Obligasjonen har. en pålydende verdi men handles til en fast rente på 4,5. en kupong på 4,5 100 et utbytte på 4,17 2 I dette tilfellet er obligasjonens avkastning lavere enn den nominelle rente. Opptjent rente Når et obligasjonslån utstedes, kan det senere kjøpes og selges mange ganger i mellom de forutbestemte fremtidige kupongdatoer. Som sådan betaler kjøperen selgeren renter påløpt opp til salgsdatoen for transaksjonen, da han mottar full kupong ved neste kupongbetalingsdato. Renter påløpt fra siste kupongbetalingsdato frem til verdsettelsesdato refereres til som påløpte renter. Eksempel: Obligasjonen er kjøpt 11. mars 2002 (i dag) Renten betales årlig 4. juli. Kupongrenten er 4,5. Tidsperioden siden den siste kupongen 250 dager. 3 betaling er. Dette medfører en påløpt rente på 4,5 250365 3,08 2 På dette tidspunktet har vi ennå ikke dekket nøyaktig hvordan utbyttet beregnes. For dette formål må vi se nærmere på begreper nåverdi og påløpte renter, som vi vil dekke i de følgende avsnittene. 3 Basert på aktuelt. 9 12 Avkastningskurven Obligasjonsrenter er i stor grad avhengig av utstederens kredittverdighet og gjenværende levetid for emisjonen. Siden de underliggende instrumentene for Eurex-rentederivater er regjeringsproblemer med kredittkvaliteter av topp kvalitet, fokuserer forklaringene nedenfor på sammenhengen mellom avkastning og gjenværende levetid. Disse presenteres ofte som en matematisk funksjon, den såkalte yieldkurven. På grunn av deres langsiktige kapitalforpliktelse har obligasjoner med lengre gjenværende levetid generelt en tendens til å gi mer enn de med kortere gjenværende levetid. Dette kalles en normal avkastningskurve. En flat avkastningskurve er der alle resterende levetider har samme interesse. En invertert avkastningskurve er preget av en nedadgående skråningskurve. Avkastningskurver Utbytte Overlevende levetid Invertert yieldkurve Flat yield curve Normal yield curve 10 13 Obligasjonsvurdering I de forrige avsnittene så vi at obligasjoner har et visst utbytte for en viss gjenværende levetid. Disse utbyttene kan beregnes ved bruk av obligasjonsmarkedsverdien (pris), kupongbetalinger og innløsning (kontantstrømmer). Til hvilken markedsverdi (rentesats) samsvarer med gjeldende markedsrenter. I de følgende eksemplene brukes en ensartet pengemarkedsrente (EURIBOR) til å representere markedsrenten for å få klarhet, men dette gjenspeiler ikke forholdene på kapitalmarkedet. En obligasjon med årlige kupongbetalinger som modnes på nøyaktig ett års tid, brukes til denne trinnvise forklaringen. Kupongen og pålydende verdi tilbakebetales ved forfall. Eksempel: Pengemarkedsrente p. a. 3,63 Obligasjon 4,5 Forbundsrepublikken Tysklands gjeldssikring på 10 juli 2003 Nominell verdi 100 Kupong 4,5 100 4,50 Verdivelsesdato 11. juli 2002 (i dag) Dette gir følgende ligning: 4 Nåverdi Nominell verdi (n) Kupong (c) Pengemarkedsrente (r) For å bestemme nåverdien av et obligasjonslån, fordeles fremtidige utbetalinger med avkastningsfaktoren (1 Pengemarkedsrente). Denne beregningen refereres til som diskontering av kontantstrømmen. Den resulterende prisen kalles nåverdien, siden den genereres på det nåværende tidspunktet (i dag). Følgende eksempel viser fremtidige betalinger for et obligasjonslån med gjenværende levetid på tre år. 4 jfr. Vedlegg 1 for generelle formler. 11 14 Eksempel: Pengemarkedsrente p. a. 3,63 Obligasjon 4,5 Forbundsrepublikken Tysklands gjeldssikring på 11 juli 2005 Nominell verdi 100 Kupong 4,5 100 4,50 Verdivelsesdato 12. juli 2002 (i dag) Obligasjonsprisen kan beregnes ved å bruke følgende ligning: Nåverdi Kupong (c1) Kupong c2) Nominell verdi (n) Kupong (c3) Avkastningsfaktor (Avkastningsfaktor) 2 (Avkastningsfaktor) Nåverdi () () 2 () 3 Ved beregning av obligasjon for en dato som ikke sammenfaller med kupongbetalingsdagen, Første kupong må kun diskonteres for gjenværende levetid frem til neste kupongbetalingsdato. Eksponeringen av avkastningsfaktoren til obligasjonen forfaller, endres tilsvarende. Eksempel: Pengemarkedsrente p. a. 3,63 Obligasjon 4,5 Forbundsrepublikken Tysklands gjeldssikring på 4 juli 2011 Nominell verdi 100 Kupong 4,5 100 4,50 Verdivelsesdato 11. mars 2002 (i dag) Gjenværende levetid for første kupong 115 dager eller 115 365 år Periodisert rente 4,5 250365 3,08 Årlig Renten beregnes pro rata for vilkår på mindre enn ett år. Diskonteringsfaktoren er: () Renten må økes til en høyere effekt for gjenværende levetid utover ett år (1.315, 2.315, år). Dette er også referert til som sammensetting av interessen. Følgelig er obligasjonsprisen: Nåverdi () () () 15 Diskonteringsfaktoren på mindre enn ett år økes også til en høyere effekt med det formål å forenkle. 5 Den foregående ligningen kan tolkes på en slik måte at nåverdien av bindingen er summen av dens individuelle nåverdier. Med andre ord er det lik summen av alle kupongbetalinger og tilbakebetaling av pålydende verdi. Denne modellen kan kun brukes over mer enn en tidsperiode dersom en konstant markedsrente antas. Den impliserte flatrentekurven har en tendens til ikke å reflektere virkeligheten. Til tross for denne forenkling danner nåverdien med en flat avkastningskurve grunnlag for en rekke risikoindikatorer. Disse beskrives i de følgende kapitlene. Man må skille mellom nåverdien (skitten pris) og ren pris når man siterer obligasjonspriser. I henhold til gjeldende konvensjon er handlet pris den rene prisen. Den rene prisen kan bestemmes ved å trekke den påløpte renter fra den skitne prisen. Det beregnes som følger: Rent pris Nåverdi Opptjent rente Rentepris Følgende avsnitt skiller mellom nåværende verdi av en obligasjon og en obligasjonspris (ren pris). En endring i markedsrenten har en direkte innvirkning på diskonteringsfaktorene og dermed på nåverdien av obligasjoner. Basert på eksemplet ovenfor, resulterer dette i følgende nåværende verdi dersom renten øker med ett prosentpoeng fra 3,63 prosent til 4,63 prosent: Nåverdi () () () Den rene prisen endres som følger: Rent pris En økning i renten førte til et fall på 7,06 prosent i obligasjonens nåverdi fra til Den rene prisen falt imidlertid med 7,26 prosent, fra til Følgende regel gjelder for å beskrive forholdet mellom nåverdien eller ren pris på en obligasjon og rentesats Utviklingen: Obligasjonspriser og markedsutbytte reagerer omvendt til hverandre. 5 jfr. Vedlegg 1 for generelle formler. 13 16 Macaulay Varighet I forrige avsnitt så vi hvordan en obligasjonspris ble påvirket av en renteendring. Rentefølsomheten til obligasjoner kan også måles ved å bruke begreperne Macaulay-varighet og endret varighet. Macaulay varighetsindikatoren ble utviklet for å analysere rentefølsomheten i obligasjoner eller obligasjonsporteføljer, med sikte på å sikre ugunstige renteendringer. Som tidligere forklart, er forholdet mellom markedsrenter og nåverdien av obligasjoner omvendt: den umiddelbare effekten av stigende avkastning er et pristap. Likevel betyr høyere rente også at mottatte kupongbetalinger kan reinvesteres til mer lønnsomme priser, og dermed øke porteføljens fremtidige verdi. Macaulay-varigheten, som vanligvis uttrykkes i år, reflekterer perioden ved utgangen av hvilke begge faktorene er i balanse. Det kan således brukes til å sikre at sensitiviteten til en portefølje er i tråd med en sett investeringshorisont. Legg merke til at konseptet er basert på forutsetningen om en flat avkastningskurve, og et parallelt skifte i rentekurven der avkastningen på alle løpetider endres på samme måte. Macaulay-varighet brukes til å oppsummere rentefølsomheten i et enkelt nummer: endringer i varigheten av et obligasjonslån, eller varighetsforskjeller mellom forskjellige obligasjoner, bidrar til å måle relative risikoer. Følgende grunnleggende forhold beskriver egenskapene ved Macaulay-varighet: Macaulay-varigheten er lavere, jo kortere gjenværende levetid desto høyere er markedsrenten og jo høyere kupongen. Vær oppmerksom på at en høyere kupong faktisk reduserer risikoen for et obligasjonslån, sammenlignet med et obligasjonslån med lavere kupong: dette indikeres av lavere Macaulay-varighet. Macaulay-varigheten av obligasjonen i det forrige eksemplet beregnes som følger: 14 17 Eksempel verdsettelsesdato 11. mars 2002 Sikkerhet 4.5 Forbundsrepublikken Tysklands gjeldssikring på 4 juli 2011 Pengemarkedsrente p. a. 3,63 Obligasjonspris Beregning: () Macaulay varighet () () Macaulay varighet 7,65 år De 0,315, 1,315, faktorene gjelder for gjenværende levetid på kupongene og tilbakebetaling av den pålydende verdien. De gjenværende levetidene multipliseres med nåverdien av de enkelte tilbakebetalinger. Macaulay varighet er summen av gjenværende løpetid for hver kontantstrøm, vektet med andelen av denne kontantstrømmen s nåverdi i den samlede nåverdien av obligasjonen. Derfor er Macaulay-varigheten av et obligasjonslån dominert av gjenværende levetid for de betalingene med høyest nåverdi. Macaulay Varighet (gjennomsnittlig gjenstående levetid veid av nåverdi) Nåverdi multiplisert med forfall av kontantstrøm År Vekter av individuelle kontantstrømmer Macaulay varighet 7,65 år Macaulay varighet kan også påføres obligasjonsporteføljer ved å akkumulere varighetsverdiene for individuelle obligasjoner, vektet i henhold til deres andel av porteføljens nåverdi. 15 18 Endret varighet Den modifiserte varigheten er bygget på konseptet med Macaulay-varigheten. Den endrede varigheten reflekterer prosentandringen i nåverdien (ren pris pluss påløpt rente) gitt en endring i markedsrenten på en enhet (ett prosentpoeng). Den modifiserte varigheten svarer til den negative verdien av Macaulay-varigheten, diskontert over en tidsperiode: Modifisert varighet Varighet 1 Utbytte Den modifiserte varigheten for eksemplet ovenfor er: Modifisert varighet 7,65 7,38 Ifølge modifisert varighetsmodell er et ett prosentpoengpunkt økning i renten bør føre til en 7,38 prosent fall i nåverdien. Konveksitet Sporingsfeilen for varighet Til tross for gyldigheten av forutsetningene nevnt i forrige avsnitt, er beregningen av verdiendringen ved hjelp av den modifiserte varigheten en tendens til å være upresent på grunn av antagelsen om en lineær korrelasjon mellom nåverdien og renten. Generelt er imidlertid prisen på forholdet mellom obligasjoner tendens til å være konveks, og derfor er en prisøkning beregnet ved hjelp av den modifiserte varigheten under - eller overestimert. Forholdet mellom Obligasjonspriser og Rentemarkedsrente P 0 16 Nåverdi Markedsrente (yield) r 0 Priceyield-forhold ved hjelp av modifisert varighetsmodell Faktisk priceyield-forhold Konveksjonsfeil 19 Generelt er jo større endringene i renten, jo mer upresise Estimatene for nåværende verdiendringer vil bruke endret varighet. I eksemplet som ble brukt, resulterte den nye beregningen i et fall på 7,06 prosent i obligasjonens nåverdi, mens estimatet ved hjelp av den modifiserte varigheten var 7,38 prosent. Unøyaktigheten som følge av ikke-linearitet ved bruk av modifisert varighet kan korrigeres ved hjelp av den såkalte konveksitetsformelen. Sammenlignet med modifisert varighetsformel, multipliseres hvert element i summeringen i telleren med (1 t c1) og den nevnte nevnt av (1 t r c1) 2 ved beregning av konveksitetsfaktoren. Beregningen nedenfor bruker det samme forrige eksempelet: () () () () Konveksitet () () () Denne konveksitetsfaktoren brukes i følgende ligning: Prosentandel verdiendring av obligasjon Modifisert varighet Endring i markedsrater Konveksitet (Endring i markedsrenter) 2 En økning i renten fra 3,63 prosent til 4,63 prosent vil resultere i: Prosentandeler i verdiendring 7,88 (0,01) (0,01) 2 7,03 Resultatene av de tre beregningsmetodene er sammenliknet nedenfor: Beregningsmetode: Resultater Beregne nåverdi 7.06 Projeksjon ved bruk av modifisert varighet 7.38 Projeksjon med modifisert varighet og 7.03 konveksitet Dette illustrerer at å ta hensyn til konveksiteten gir et resultat som ligner prisen som ble oppnådd i omberegningen, mens estimatet ved hjelp av den modifiserte varigheten avviker vesentlig. Det skal imidlertid bemerkes at en ensartet rentesats ble brukt for alle gjenværende levetid (flat yield curve) i alle tre eksemplene. 17 20 Eurex Fixed Income Derivatives Egenskaper for Exchange-Traded Financial Derivatives Innledning Kontrakter hvor prisene er avledet fra underliggende pengemarkedsverdipapirer eller varer (som refereres til som underliggende instrumenter eller underlying) som aksjer, obligasjoner eller olje, er kjent som derivatinstrumenter eller bare derivater. Handelsderivater er preget av at oppgjøret finner sted på bestemte datoer (avregningsdato). Mens betaling mot levering for kontantmarkedet transaksjoner må skje etter to eller tre dager (oppgjørstid), valutahandlet futures og opsjonskontrakter, med unntak av opsjonsopsjoner, kan sørge for oppgjør på bare fire bestemte datoer i løpet av året. Derivater handles både på organiserte derivatutvekslinger som Eurex og i OTC-markedet. For det meste skiller standardiserte kontraktspesifikasjoner og prosessen med markering til markeds eller marginering via et clearinghus utvekslingshandlede produkter fra OTC-derivater. Eurex lister opp futures og opsjoner på finansielle instrumenter. Fleksibilitet Organiserte derivatutvekslinger gir investorer mulighetene til å inngå en posisjon basert på deres markedsoppfattelse og i samsvar med deres appetitt for risiko, men uten å måtte kjøpe eller selge verdipapirer. Ved å inngå en motvirkningstransaksjon kan de nøytralisere (lukke ut) sin stilling før kontraktens forfallstidspunkt. Eventuelle gevinster eller tap på åpne posisjoner i futures eller opsjoner på futures krediteres eller debiteres på daglig basis. Transparency and Liquidity Trading standardiserte kontrakter resulterer i en konsentrasjon av ordrestrømmer og sikrer dermed likviditet i markedet. Likviditet betyr at store mengder av et produkt kan kjøpes og selges til enhver tid uten overdreven innvirkning på prisene. Elektronisk handel på Eurex garanterer omfattende gjennomsiktighet av priser, volumer og gjennomførte transaksjoner. Utnyttelseseffekt Når du inngår en opsjon eller futureshandel, er det ikke nødvendig å betale hele verdien av det underliggende instrumentet foran. På grunn av den investerte eller pantsatte kapitalen er prosentandelsresultatet eller tapspotensialet for disse terminkontraktere mye større enn for de faktiske obligasjonene eller aksjene. 18 21 Introduksjon til faste inntekter Futures Hva er fast inntekt Futures Definisjon Rentekost futures er standardiserte transaksjoner mellom to parter, basert på rentebærende instrumenter som obligasjoner med kuponger. De omfatter forpliktelsen. å kjøpe Kjøper Lang fremtid Lang fremtid. eller for å levere Selger Kort fremtid Kort fremtid. et gitt finansielt underliggende tysk sveitsisk forbundsinstrument instrument statsobligasjonsobligasjoner. med en gitt år 8-13 år gjenværende levetid i et bestemt beløp Kontraktstørrelse EUR 100.000 CHF 100.000 nominelt nominelt. på et fast tidspunkt Løpetid 10. mars 2002 10. mars 2002 i tide. Til en bestemt fremtidig prispris Eurex-rentebærende derivater er basert på levering av en underliggende obligasjon som har en gjenværende løpetid i samsvar med et forhåndsdefinert utvalg. Kontraktens leverbare liste vil inneholde obligasjoner med en rekke forskjellige kupongnivåer, priser og forfallstidspunkt. For å bidra til å standardisere leveringsprosessen brukes konseptet med en ideell binding. Se avsnittet nedenfor på kontraktspesifikasjon og konverteringsfaktorer for mer detaljer. Fremtidsposisjoner Forpliktelser En futuresposisjon kan enten være lang eller kort. Lang posisjon Kjøper en futureskontrakt Kjøperens forpliktelser: Ved forfall oppnår en lang stilling automatisk forpliktelsen til å kjøpe leverbare obligasjoner: Forpliktelsen til å kjøpe rentesystemet relevant for kontrakten på leveringsdagen til forutbestemt pris. Kort stilling Selge en futures kontrakt Selgerens forpliktelser: Ved forfall oppstår en kort stilling automatisk i plikten til å levere slike obligasjoner: Forpliktelsen til å levere rentesystemet relevant for kontrakten på leveringsdagen til forutbestemt pris. 19 22 Avregning eller avslutning Futures er vanligvis avgjort ved kontant oppgjør eller ved fysisk levering av det underliggende instrumentet. Eurex-renteterminkontrakter sørger for fysisk levering av verdipapirer. Kortinnehaveren er forpliktet til å levere enten langsiktige sveitsiske statsobligasjoner eller kort-, mellom - eller langsiktig tyske statsobligasjoner, avhengig av den handlede kontrakten. Innehaveren av den tilsvarende lange stillingen må godta levering mot betaling av leveringsprisen. Verdipapirer fra de respektive utstedere hvis gjenværende levetid på futures leveringsdato er innenfor rammene for hver kontrakt, kan leveres. Disse parametrene er også kjent som modningsområder for levering. Valget av obligasjon som skal leveres skal varsles (notifikasjonsplikten til innehaveren av den korte stillingen). Verdsettelse av obligasjon er beskrevet i avsnittet om obligasjonsvurdering. Det er imidlertid verdt å merke seg at når det inngår en futuresposisjon, er det ikke nødvendigvis basert på hensikten å faktisk levere eller overføre de underliggende instrumenter til forfall. For eksempel er futures utformet for å spore prisutviklingen til det underliggende instrumentet i løpet av kontraktens levetid. I tilfelle en prisøkning i terminkontrakten, er en originalkjøper av en futureskontrakt i stand til å realisere en fortjeneste ved ganske enkelt å selge et like antall kontrakter til de opprinnelig kjøpte. Det motsatte gjelder en kort stilling, som kan lukkes ved å kjøpe tilbake futures. Som et resultat oppstår en merkbar reduksjon i åpen interesse (antall åpne lange og korte posisjoner i hver kontrakt) i dagene før forfall av en futureskontrakt for obligasjoner. Mens kontraktens levetid kan åpne renter muligens overskride volumet av leverbare obligasjoner som er tilgjengelige, er denne figuren en tendens til å falle betydelig så snart åpent interesse begynner å skifte fra den korteste leveringsmåneden til den neste, før forfall (en prosess kjent som rollover ). 20 23 Kontraktspesifikasjoner Informasjon om de detaljerte kontraktsspesifikasjonene for rentekost futures som handles på Eurex, finnes i Eurex Products brosjyre eller på Eurex nettside. De viktigste spesifikasjonene for Eurex-rentetermin futures er beskrevet i følgende eksempel basert på Euro Bund Futures og CONF Futures. En næringsdrivende kjøper: 2 Kontrakter Transaksjonen på futures er basert på en pålydende verdi på 2 x EUR 100 000 av leverbare obligasjoner for Euro Bund Future, eller 2 x CHF 100 000 av leverbare obligasjoner for CONF Future. Juni 2002 Forfallsmåned De neste tre kvartalsmånedene i syklusen MarchJuneSeptemberDecember er tilgjengelig for handel. Dermed har Euro Bund og CONF Futures en maksimal gjenværende levetid på ni måneder. Den siste handelsdagen er to børshandel dager før den 10. kalenderdagen (leveringsdag) i forfallsmåneden. Euro Bund eller Underliggende instrument Det underliggende instrumentet for Euro Bund Futures CONF Futures, er en 6 frivillig langsiktig tysk regjering henholdsvis Bond. For CONF Futures er det en 6 frivillig sveitsisk forbundsobligasjon. til eller futures pris futures prisen er sitert i prosent, til to. desimaltall, på den nominelle verdien av den respektive underliggende obligasjonen. Minste prisendring (tick) er EUR eller CHF (0,01). I dette eksemplet er kjøperen forpliktet til å kjøpe enten tyske statsobligasjoner eller sveitsiske statsobligasjoner, som er inkludert i kurven med leverbare obligasjoner, til en pålydende verdi på EUR eller CHF 200 000, i juni 24 Eurex Fixed Income Futures Oversikt Spesifikasjonene for Renteinntekter er i stor grad preget av kurver av leverbare obligasjoner som dekker ulike forfallstidspunkter. Tilsvarende gjenværende levetid er angitt i følgende tabell: Underliggende instrument: Nominell gjenværende levetid på Produktkode Tysk stats gjeldskontrakt verdier de utstedte obligasjonene Verdipapirer Euro Schatz Fremtid EUR 100, 4 til 2 1 4 år FGBS Euro Bobl Fremtid EUR 100, 2 til 5 1 2 år FGBM Euro Bund Fremtid EUR 100, 2 til 10 1 2 år FGBL Euro Buxl Fremtid EUR 100 til 30 1 2 år FGBX Underliggende instrument: Nominell gjenværende levetid på Produktkode Sveitsiske Forbund Obligasjoner kontraktsverdi de leverbare obligasjonene CONF Future CHF 100 000 8 til 13 år CONF Futures Spread Margin og tilleggsmargin Når en futuresposisjon opprettes, blir kontanter eller annen sikkerhet deponert hos Eurex Clearing AG Eurex Clearing House. Eurex Clearing AG søker å gi en garanti til alle clearingmedlemmer i tilfelle medlemmet misligholder. Denne tilleggsmargin innskudd er utformet for å beskytte clearinghuset mot en vesentlig ugunstig prisbevegelse i futures kontrakten. Rydningsfirmaet er den ultimate motparten i alle Eurex-transaksjoner og må sikre integriteten til markedet i tilfelle et clearingmedlems standard. Avskjedende lange og korte stillinger i ulike forfallsmåneder av samme futureskontrakt refereres til som tidsposisjoner. Den høye korrelasjonen mellom disse stillingene betyr at spredemarginene er lavere enn for tilleggsmargin. Ekstra margin er belastet for alle ikke-spredte posisjoner. Marginsikring må stilles i form av kontanter eller verdipapirer. En detaljert beskrivelse av marginkrav beregnet av Eurex Clearing House (Eurex Clearing AG) finner du i brosjyren om risikobasert marginering. 22 25 Variation Margin A common misconception regarding bond futures is that when delivery of the actual bonds are made, they are settled at the original opening futures price. In fact delivery of the actual bonds is made using a final futures settlement price (see the section below on conversion factor and delivery price). The reason for this is that during the life of a futures position, its value is marked to market each day by the clearing house in the form of Variation Margin. Variation Margin can be viewed as the futures contract s profit or loss, which is paid and received each day during the life of an open position. The following examples illustrate the calculation of the Variation Margin, whereby profits are indicated by a positive sign, losses by a negative sign. Calculating the Variation Margin for a new long futures position: Futures Daily Settlement Price Futures purchase or selling price Variation Margin The Daily Settlement Price of the CONF Future in our example is The contracts were bought at a price of Example CONF Variation Margin: CHF 121,650 (121.65 of CHF 100,000) CHF 121,500 (121.50 of CHF 100,000) CHF 150 On the first day, the buyer of the CONF Future makes a profit of CHF 150 per contract (0.15 percent of the nominal value of CHF 100,000), that is credited via the Variation Margin. Alternatively the calculation can be described as the difference between 15 ticks. The futures contract is based upon CHF 100,000 nominal of bonds, so the value of a small price movement (tick) of CHF 0.01 equates to CHF 10 (i. e. 1, ). This is known as the tick value. Therefore the profit on the one futures trade is 15 CHF 10 1 CHF 26 The same process applies to the Euro Bund Future. The Euro Bund Futures Daily Settlement Price is It was bought at The Variation Margin calculation results in the following: Example Long Euro Bund Variation Margin: EUR 105,700 (105.70 of EUR 100,000) EUR 106,000 (106.00 of EUR 100,000) EUR 300 The buyer of the Euro Bund Futures incurs a loss of EUR 300 per contract (0.3 percent of the nominal value of EUR 100,000), that is consequently debited by way of Variation Margin. Alternatively 30 ticks loss multiplied by the tick value of one bund future (EUR 10) EUR 300. Calculating the Variation Margin during the contract s lifetime: Futures Daily Settlement Price on the current exchange trading day Futures Daily Settlement Price on the previous exchange trading day Variation Margin Calculating the Variation Margin when the contract is closed out: Futures price of the closing transaction Futures Daily Settlement Price on the previous exchange trading day Variation Margin The Futures Price Fair Value While the chapter quotBond Valuation focused on the effect of changes in interest rate levels on the present value of a bond, this section illustrates the relationship between the futures price and the value of the corresponding deliverable bonds. A trader who wishes to acquire bonds on a forward date can either buy a futures contract today on margin, or buy the cash bond and hold the position over time. Buying the cash bond involves an actual financial cost which is offset by the receipt of coupon income (accrued interest). The futures position on the other hand, over time, has neither the financing costs nor the receipts of an actual long spot bond position (cash market). 24 27 Therefore to maintain market equilibrium, the futures price must be determined in such a way that both the cash and futures purchase yield identical results. Theoretically, it should thus be impossible to realize risk-free profits using counter transactions on the cash and forward markets (arbitrage). Both investment strategies are compared in the following table: Time Period Futures purchase Cash bond purchase investmentvaluation investmentvaluation Today Entering into a futures position Bond purchase (market price (no cash outflow) plus accrued interest) Futures Investing the equivalent value of Coupon credit (if any) and lifetime the financing cost saved, on the money market investment of the money market equivalent value Futures Portfolio value Portfolio value delivery Bond (purchased at the futures Value of the bond including price) Income from the money accrued interest Any coupon market investment of the credits Any interest on the financing costs saved coupon income Taking the factors referred to above into account, the futures price is derived in line with the following general relationship: 6 Futures price Cash price Financing costs Proceeds from the cash position Which can be expressed mathematically as: 7 Futures price C t (C t c t t0 ) t r c T t c T t Whereby: C t Current clean price of the underlying security (at time t) c Bond coupon (percent actualactual for euro-denominated bonds) t 0 Coupon date t Value date t r c Short-term funding rate (percent actual360) T Futures delivery date T-t Futures remaining lifetime (days) 6 Readers should note that the formula shown here has been simplified for the sake of transparency specifically, it does not take into account the conversion factor, interest on the coupon income, borrowing costlending income or any diverging value date conventions in the professional cash market. 7 Please note that the number of days in the year (denominator) depends on the convention in the respective markets. Financing costs are usually calculated based on the money market convention (actual360), whereas the accrued interest and proceeds from the cash positions are calculated on an actualactual basis, which is the market convention for all euro-denominated government bonds. 25 28 Cost of Carry and Basis The difference between the proceeds from and the financing costs of the cash position coupon income is referred to as the cost of carry. The futures price can also be expressed as follows: 8 Price of the deliverable bond Futures price Cost of carry The basis is the difference between the bond price in the cash market (expressed by the prices of deliverable bonds) and the futures price, and is thus equivalent to the following: Price of the deliverable bond Futures price Basis The futures price is either lower or higher than the price of the underlying instrument, depending on whether the cost of carry is positive or negative. The basis diminishes with approaching maturity. This effect is called basis convergence and can be explained by the fact that as the remaining lifetime decreases, so do the financing costs and the proceeds from the bonds. The basis equals zero at maturity. The futures price is then equivalent to the price of the underlying instrument this effect is called basis convergence. Basis Convergence (Schematic) Negative Cost of Carry Positive Cost of Carry Price Time Price of the deliverable bond Futures price 0 The following relationships apply: Financing costs gt Proceeds from the cash position: gt Negative cost of carry Financing costs lt Proceeds from the cash position: gt Positive cost of carry 26 8 Cost of carry and basis are frequently shown in literature using a reverse sign. 29 Conversion Factor (Price Factor) and Cheapest-to-Deliver (CTD) Bond The bonds eligible for delivery are non-homogeneous although they have the same issuer, they vary by coupon level, maturity and therefore price. At delivery the conversion factor is used to help calculate a final delivery price. Essentially the conversion factor generates a price at which a bond would trade if its yield were six percent on delivery day. One of the assumptions made in the conversion factor formula is that the yield curve is flat at the time of delivery, and what is more, it is at the same level as that of the futures contract s notional coupon. Based on this assumption the bonds in the basket for delivery should be virtually all equally deliverable. Of course, this does not truly reflect reality: we will discuss the consequences below. The delivery price of the bond is calculated as follows: Delivery price Final Settlement Price of the future Conversion factor of the bond Accrued interest of the bond Calculating the number of interest days for issues denominated in Swiss francs and euros is different (Swiss francs: 30360 euros: actualactual), resulting in two diverging conversion factor formulae. These are included in the appendices. The conversion factor values for all deliverable bonds are displayed on the Eurex website The conversion factor (CF) of the bond delivered is incorporated as follows in the futures price formula (see p. 25 for an explanation of the variables used): Theoretical futures price 1 C t (C t c t t0 ) t r c T t c T t CF The following example describes how the theoretical price of the Euro Bund Future June 2002 is calculated. 27 30 Example: Trade date May 3, 2002 Value date May 8, 2002 Cheapest-to-deliver bond 3.75 Federal Republic of Germany debt security due on January 4, 2011 Price of the cheapest-to-deliver Futures delivery date June 10, 2002 Accrued interest 3.75 (124365) 100 1.27 Conversion factor of the CTD Money market rate p. a. 3.63 1 Theoretical futures price ( ) Theoretical futures price Theoretical futures price In reality the actual yield curve is seldom the same as the notional coupon level also, it is not flat as implied by the conversion factor formula. As a result, the implied discounting at the notional coupon level generally does not reflect the true yield curve structure. The conversion factor thus inadvertently creates a bias which promotes certain bonds for delivery above all others. The futures price will track the price of the deliverable bond that presents the short futures position with the greatest advantage upon maturity. This bond is called the cheapest to deliver (or CTD ). In case the delivery price of a bond is higher than its market valuation, holders of a short position can make a profit on the delivery, by buying the bond at the market price and selling it at the higher delivery price. They will usually choose the bond with the highest price advantage. Should a delivery involve any price disadvantage, they will attempt to minimize this loss. Identifying the Cheapest-to-Deliver Bond On the delivery day of a futures contract, a trader should not really be able to buy bonds in the cash bond market, and then deliver them immediately into the futures contract at a profit if heshe could do this it would result in a cash and carry arbitrage. We can illustrate this principle by using the following formula and examples. Basis Cash bond price (Futures price Conversion factor) 28 31 At delivery, basis will be zero. Therefore, at this point we can manipulate the formula to achieve the following relationship: Cash bond price Futures price Conversion factor This futures price is known as the zero basis futures price. The following table shows an example of some deliverable bonds (note that we have used hypothetical bonds for the purposes of illustrating this effect). At a yield of five percent the table records the cash market price at delivery and the zero basis futures price (i. e. cash bond price divided by the conversion factor) of each bond. Zero Basis Futures Price at 5 Yield Coupon Maturity Conversion factor Price at 5 yield Price divided by conversion factor 5 0715 0304 0513 We can see from the table that each bond has a different zero basis futures price, with the 7 05132011 bond having the lowest zero basis futures price of In reality of course only one real futures price exists at delivery. Suppose that at delivery the real futures price was If that was the case an arbitrageur could buy the cash bond (7 051302) at and sell it immediately via the futures market at and receive This would create an arbitrage profit of two ticks. Neither of the two other bonds would provide an arbitrage profit, however, with the futures at Accrued interest is ignored in this example as the bond is bought and sold into the futures contract on the same day. 29 32 It follows that the bond most likely to be used for delivery is always the bond with the lowest zero basis futures price the cheapest cash bond to purchase in the cash market in order to fulfill a short delivery into the futures contract, i. e. the CTD bond. Extending the example further, we can see how the zero basis futures prices change under different market yields and how the CTD is determined. Zero basis futures price at 5, 6, 7 yield Coupon Maturity Conversion Price Price Price Price Price Price factor at 5 CF at 6 CF at 7 CF 5 0715 0304 0513 The following rules can be deducted from the table above: If the market yield is above the notional coupon level, bonds with a longer duration (lower coupon given similar maturities longer maturity given similar coupons) will be preferred for delivery. If the market yield is below the notional coupon level, bonds with a shorter duration (higher coupon given similar maturitiesshorter maturity given similar coupons) will be preferred for delivery. When yields are at the notional coupon level (six percent) the bonds are almost all equally preferred for delivery. As we pointed out above, this bias is caused by the incorrect discount rate of six percent implied by the way the conversion factor is calculated. For example, when market yields are below the level of the notional coupon, all eligible bonds are undervalued in the calculation of the delivery price. This effect is least pronounced for bonds with a low duration as these are less sensitive to variations of the discount rate (market yield). 9 So, if market yields are below the implied discount rate (i. e. the notional coupon rate), low duration bonds tend to be cheapest-to-deliver. This effect is reversed for market yields above six percent. 9 Cf. chapters Macaulay Duration and Modified Duration. 30 33 The graph below shows a plot of the three deliverable bonds, illustrating how the CTD changes as the yield curve shifts. Identifying the CTD under Different Market Conditions CTD 7 05132011 CTD 5 0715 Zero basis futures price Market yield 6 7 5 07152012 6 03042012 7 0513 34 Applications of Fixed Income Futures There are three motives for using derivatives: trading, hedging and arbitrage. Trading involves entering into positions on the derivatives market for the purpose of making a profit, assuming that market developments are predicted correctly. Hedging means securing the price of an existing or planned portfolio. Arbitrage is exploiting price imbalances to achieve risk-free profits. To maintain the balance in the derivatives markets it is important that both traders and hedgers are active thus providing liquidity. Trades between hedgers can also take place, whereby one counterparty wants to hedge the price of an existing portfolio against price losses and the other the purchase price of a future portfolio against expected price increases. The central role of the derivatives markets is the transfer of risk between these market participants. Arbitrage ensures that the market prices of derivative contracts diverge only marginally and for a short period of time from their theoretically correct values. Trading Strategies Basic Futures Strategies Building exposure by using fixed income futures has the attraction of allowing investors to benefit from expected interest rate moves without having to tie up capital by buying bonds. For a simple futures position, contrary to investing on the cash market, only Additional Margin needs to be pledged (cf. chapter Futures Spread Margin and Additional Margin ). Investors incurring losses on their futures positions possibly as a result of incorrect market forecasts are obliged to settle these losses immediately, and in full ( Variation Margin). During the lifetime of the futures contract this could amount to a multiple of the amount pledged. The change in value relative to the capital invested is consequently much higher than for a similar cash market transaction. This is called the leverage effect. In other words, the substantial profit potential associated with a straight fixed income future position is reflected by the significant risks involved. 32 35 Long Positions ( Bullish Strategies) Investors expecting falling market yields for a certain remaining lifetime will decide to buy futures contracts covering this section of the yield curve. If the prediction turns out to be correct, a profit is made on the futures position. As is characteristic for futures contracts, the profit potential on such a long position is proportional to its risk exposure. In principle, the priceyield relationship of a fixed income futures contract corresponds to that of a portfolio of deliverable bonds. Profit and Loss Profile on the Last Trading Day, Long Fixed Income Futures 0 Profit and loss Bond price PL long fixed income futures Rationale The trader wants to benefit from a forecast development without tying up capital in the cash market. Initial Situation The trader assumes that yields on German Federal Debt Obligations (Bundesobligationen) will fall. Strategy The trader buys ten Euro Bobl Futures June 2002 at a price of. with the intention to close out the position during the contract s lifetime. If the price of the Euro Bobl Futures rises, the trader makes a profit on the difference between the purchase price and the higher selling price. Constant analysis of the market is necessary to correctly time the position exit by selling the contracts. 33 36 The calculation of Additional and Variation Margins for a hypothetical price development is illustrated in the following table. The Additional Margin is derived by multiplying the margin parameter, as set by Eurex Clearing AG (in this case EUR 1,000 per contract), by the number of contracts. Date Transaction Purchase Daily Variation Variation Additional selling price Settlement Margin 10 Margin Margin 11 Price profit in EUR loss in EUR in EUR 0311 Buy ,900 10,000 Euro Bobl Futures June ,700 03 ,100 03 ,400 03 ,100 03 ,200 0320 Sell ,500 Euro Bobl Futures June 21 10,000 Result ,600 5,900 0 Changed Market Situation: The trader closes out the futures position at a price of on March 20. The Additional Margin pledged is released the following day. Result: The proceeds of EUR 2,700 made on the difference between the purchase and sale is equivalent to the balance of the Variation Margin (EUR 8,600 EUR 5,900) calculated on a daily basis. Alternatively the net profit is the sum of the futures price movement multiplied by ten contracts multiplied by the point value of EUR 1,000: ( ) 10 EUR 1,000 EUR 2, Cf. chapter Variation Margin. 11 Cf. chapter Futures Spread Margin and Additional Margin. 34Navigation Eurex Fixed Income Options: an opportunity not to be missed 13 Market Makers are permanently supporting liquidity in Eurex fixed income options. I HY1 2015 hadde daglig omsetning i opsjoner på Bund, Bobl og Schatz Futures over 350.000 kontrakter (pluss 70 prosent y-o-y). Av dette har 30 prosent blitt handlet via orderbok og 30 prosent via Eurex Strategy Wizard SM. Ordinære anførselstegn er kontinuerlig tilgjengelig for 1000 kontrakter. Strategi sitater varierer mellom 500 og 1000 kontrakter. Eurex-alternativer på Bund, Bobl og Schatz Futures er tilgjengelig som samtaler og setter med en rekke tenorer i en rekke treningspriser og gir dermed en høy grad av skreddersy. I tillegg kombinerer investorer ofte flere alternativer til en handel for å utføre en raffinert handelsstrategi. Handelsinteresse spredes dermed bredt i disse dimensjonene, i motsetning til rentemarkedet futures markedet hvor handel er fokusert på den svært flytende frontmånederserien. Futures drives ofte i ordrevurderte markeder, hvor likviditet er gitt av den varierende toveis ordreflyten fra den sentrale ordreboken. Optiehandel er sitat drevet ettersom likviditet ikke kan konsentreres i en enkelt kontrakt på grunn av den store spredningen av handelsinteressen over streik og utløp og de mange kombinasjonsmulighetene i opsjonsstrategier. Investorer finner prisveiledning for risikostyring og faste omsettelige priser fra spesialiserte markedsførere som leverer elektroniske sitater i bestillingsboken og telefonnotering for off-trade-handel. I skjermhandelen kan investorer handle direkte på noterte priser og benytte ytterligere kilder til likviditet når Market Maker-sitater fylles på ved utførelse. Market Maker-sitater er også viktige for grenseordrer som inngås av investorer som initierer opsjonshandler. Eurex Exchange har etablert elektronisk notering i renterett og tilbyr permanente og avanserte Markedsføringsprogrammer. Streaming sitater tilbys av over et dusin høyt spesialiserte Markedsføringsfirmaer som betjener etterspørsel etter direkte henrettelse fra institusjonelle sluttbrukere. Handler i 1000 kontrakter og mer kan enkelt utføres i punkt-og-klikk-handel av investorer med direkte markedsadgang. I HY1 2015 var daglig elektronisk handelsvolum i Bund, Bobl og Schatz Options over 90.000 kontrakter. I løpet av de siste tre årene har andelen av bokvolum i Bund Options økt fra rundt 20 prosent og i 2015 opprettholdt en andel på 33 prosent. Andelen bokvolum i Bobl Options doblet fra 10 til 20 prosent i 2014. På samme måte i 2015 blir opptil 25 prosent av volumet av Schatz Options utført elektronisk. Alternativer handler ikke bare som samtaler og setter, men også som opsjonsstrategier. I november 2013 lanserte Eurex et skreddersydd Market-Making-program for opsjonsstrategier som i økende grad tiltrekker volum direkte fra henrettelsen av ordrer mot anførselstegnene fra Market Makers. I 2015 ser vi nå et daglig gjennomsnitt på 5000 opsjoner for rentekostnadsopsjoner som handler mot Market Maker-sitater i opsjonsstrategier. Som i handel med direkte anrop og setter, er mid-market trading med grenseordrer også utbredt i opsjonsstrategier. Siden slutten av 2013 økte strategimengden både på grunn av økt bruk av strategibetingelser for blokkbransjer og høyere skjermvolumer etter introduksjonen av strategien Markedsføringsprogram. I 2015 økte daglig ordrevolum i strategier til 32 000 kontrakter i renter. Samlet handler strategiproduksjon om lag 30 prosent av volumet både i ordrebok og off-book trading. I tillegg til å sitere opsjonsstrategier, markedsfører Markedsførere også faste priser. Dermed er likviditet gitt for et vidt spekter av strategier. Strategibestemmelsesbøker er vanligvis sitert for 500 til 1000 kontrakter på det indre markedet, avhengig av risikoprofilen for opsjonsstrategien i spørsmålet. Interessant er strategiske sitater ofte strammere enn den kumulative spredningen fra enkelthåndsutførelse av bena individuelt. Dette reflekterer riktig risikoprofilen for opsjonsstrategier, og oversetter også til lavere implisitte transaksjonskostnader for investorer som bare trenger å krysse en budbudsspredning. SubnavigationInterest Rate Derivatives Fixed Income Trading Strategies. eurex 1 Interest Rate Derivatives Fixed Income Trading Strategies eurex 2 Please note The definitions of basis and cost of carry have been changed in this version of the brochure. In the previous version, the following definitions were used: Basis Futures Price Price of Cash Instrument Cost of Carry Basis In this version, the following definitions are used: Basis Price of Cash Instrument Futures Price Cost of Carry Basis These changes have been made in order to ensure that definitions of both items are consistent throughout Eurex materials, including the Trader Examination and corresponding preparatory materials. 3 Interest Rate Derivatives Fixed Income Trading Strategies eurex 4 Contents Brochure Structure and Objectives Characteristics of Fixed Income Securities Bonds Definition 08 Lifetime and Remaining Lifetime 09 Nominal and Actual Rate of Interest (Coupon and Yield) 09 Accrued Interest 10 The Yield Curve 11 Bond Valuation 14 Macaulay Duration 16 Modified Duration 16 Convexity the Tracking Error of Duration Eurex Fixed Income Derivatives 18 Characteristics of Exchange-Traded Financial Derivatives 18 Introduction 18 Flexibility 18 Transparency and Liquidity 18 Leverage Effect Introduction to Fixed Income Futures 19 What are Fixed Income Futures Definition 19 Futures Positions Obligations 20 Settlement or Closeout 21 Contract Specifications 22 Eurex Fixed Income Futures Overview 22 Futures Spread Margin and Additional Margin 23 Variation Margin 24 The Futures Price Fair Value 26 Cost of Carry and Basis 27 Conversion Factor (Price Factor) and Cheapest-to-Deliver (CTD) Bond 28 Identifying the Cheapest-to-Deliver Bond 5 Applications of Fixed Income Futures 32 Trading Strategies 32 Basic Futures Strategies 33 Long Positions ( Bullish Strategies) 35 Short Positions ( Bearish Strategies) 36 Spread Strategies 37 Time Spread 38 Inter-Product Spread 40 Hedging Strategies 41 Choice of the Futures Contract 41 Perfect Hedge versus Cross Hedge 41 Hedging Considerations 42 Determining the Hedge Ratio 43 Nominal Value Method 43 Modified Duration Method 45 Sensitivity Method 47 Static and Dynamic Hedging 47 Cash-and-Carry Arbitrage Introduction to Options on Fixed Income Futures 49 Options on Fixed Income Futures Definition 49 Options on Fixed Income Futures Rights and Obligations 50 Closeout 50 Exercising Options on Fixed Income Futures 51 Contract Specifications Options on Fixed Income Futures 52 Premium Payment and Risk Based Margining 54 Options on Fixed Income Futures Overview 6 Option Price 55 Components 55 Intrinsic Value 55 Time Value 56 Determining Factors 56 Volatility of the U nderlying Instrument 56 Remaining Lifetime of the Option 57 Influencing Factors Important Risk Parameters Greeks 58 Delta 60 Gamma 61 Vega (Kappa) 61 Theta Trading Strategies for Options on Fixed Income Futures 62 Long Call 63 Short Call 65 Long Put 66 Short Put 67 Bull Call Spread 68 Bear Put Spread 69 Long Straddle 71 Long Strangle 72 Impact of Time Value Decay and Volatility 72 Time Value Decay 73 Impact of Fluctuations in Market Volatility 74 Trading Volatility Maintaining a Delta-Neutral Position with Futures Hedging Strategies 77 Hedging Strategies for a Fixed Time Horizon 79 Delta Hedging 80 Gamma Hedging 82 Zero Cost Collar 7 FuturesOptions Relationships, Arbitrage Strategies 83 Synthetic Fixed Income Options and Futures Positions 83 Synthetic Long Call 85 Synthetic Short Call 86 Synthetic Long Put 88 Synthetic Short Put 88 Synthetic Long FutureReversal 90 Synthetic Short FutureConversion 91 Synthetic Options and Futures Positions Overview Glossary 92 Appendix 1: Valuation Form ulae and Indicators 100 Single-Period Remaining Lifetime 100 Multi-Period Remaining Lifetime 100 Macaulay Duration 101 Convexity Appendix 2: Conversion Factors 102 Bonds Denominated in Euros 102 Bonds Denominated in Swiss Francs Appendix 3: List of Diagrams Contacts 105 Further Information 8 Brochure Structure and Objectives This brochure describes the fixed income derivatives traded at Eurex and illustrates some of their most significant applications. These contracts are comprised of futures on fixed income securities ( fixed income futures ) and options on fixed income futures. To provide a better understanding of the contracts described, the fundamental characteristics of fixed income securities and the indicators used to analyze them will be outlined. Basic knowledge of the securities industry is a prerequisite. Explanations of fixed income securities contained in this brochure predominantly refer to such issues on which Eurex fixed income derivatives are based. 6 9 Characteristics of Fixed Income Securities Bonds Definition A bond can be described as large-scale borrowing on the capital market, whereby the creditor s entitlements are certified in the form of securities. The offerings of securities are known as issues and the respective debtor as the issuer. Bonds are categorized according to their lifetime, issuer, interest payment details, credit rating and other factors. Fixed income bonds bear a fixed interest payment, known as the coupon, which is based on the nominal value of the bond. Depending on the specifications, interest payment is usually semi-annual or annual. Fixed income derivatives traded at Eurex are based on a basket of either German or Swiss fixed income public sector bonds. In Switzerland, the Swiss National Bank (SNB) manages the borrowing requirements for the Swiss Federal Finance Administration. Capital is raised by issuing so-called money market book-entry claims as well as Treasury Notes and Confederation Bonds. Only the Confederation Bonds with different lifetimes are freely tradable. Other government bonds are exchanged only between the SNB and banks, or in interbank trading. The German Finance Agency (Bundesrepublik Deutschland Finanzagentur GmbH) has been responsible for issuing German Government Bonds (on behalf of the German Government) since June Other publicly tradable issues include bonds issued up until 1995 by the former Treuhandanstalt privatization agency and the German Federal Government s special funds, for example, the German Unity Fund. These bonds are attributed the same creditworthiness as a result of the assumption of liability by the Federal Republic of Germany. German government issues relevant to the Eurex fixed income derivatives have the following lifetimes and coupon payment details. Government issues Lifetime Coupon payment German Federal Treasury Notes 2 years Annual (Bundesschatzanweisungen) German Federal Debt Obligations 5 years Annual (Bundesobligationen) German Government Bonds 10 and 30 years Annual (Bundesanleihen) The terms of these issues do not provide for early redemption by calling in or drawing. 1 1 Cf. Deutsche Bundesbank, Der Markt fuumlr deutsche Bundeswertpapiere (The German Government securities market), 2nd edition, FrankfurtMain, 10 In this chapter the following information will be used for a number of explanations and calculations: Example: Debt security issue German Government Bond. by the issuer Federal Republic of Germany. at the issue date July 5, with a lifetime of 10 years. a redemption date on July 4, a fixed interest rate of 4.5. coupon payment annual. a nominal value of 100 Lifetime and Remaining Lifetime One must differentiate between lifetime and remaining lifetime in order to understand fixed income bonds and related derivatives. The lifetime denotes the time period from the time of issue until the nominal value of the security is redeemed, while the remaining lifetime is the remaining time period from the valuation date until redemption of securities already issued. Example: The bond has a lifetime of as at the valuation date the remaining lifetime is 10 years March 11, 2002 ( today ) 9 years and 115 days 8 11 Nominal and Actual Rate of Interest (Coupon and Yield) The nominal interest rate of a fixed income bond is the value of the coupon relative to the nominal value of the security. In general, neither the issue price nor the traded price of a bond corresponds to its nominal value. Instead, bonds are traded below or above par i. e. their value is below or above the nominal value of 100 percent. Both the coupon payments and the actual capital invested are taken into account when calculating the yield. This means that, unless the bond is traded at exactly 100 percent, the actual rate of interest in other words: the yield deviates from the nominal rate of interest. The actual rate of interest is lower (higher) than the nominal rate of interest for a bond trading above (below) its nominal value. Example: The bond has. a nominal value of but is trading at a price of a fixed interest rate of 4.5. a coupon of 4.5 100 a yield of 4.17 2 In this case the bond s yield is lower than the nominal rate of interest. Accrued Interest When a bond is issued, it may be subsequently bought and sold many times in between the predetermined future coupon dates. As such the buyer pays the seller the interest accrued up to the value date of the transaction, as heshe will receive the full coupon at the next coupon payment date. The interest accrued from the last coupon payment date up to the valuation date is referred to as the accrued interest. Example: The bond is purchased on March 11, 2002 ( today ) The interest is paid annually, on July 4 The coupon rate is 4.5 The time period since the last coupon 250 days 3 payment is This results in accrued interest of 4.5 250365 3.08 2 At this point, we have not yet covered exactly how yields are calculated: for this purpose, we need to take a closer look at the concepts of present value and accrued interest, which we will cover in the following sections. 3 Based on actualactual. 9 12 The Yield Curve Bond yields are largely dependent on the issuer s creditworthiness and the remaining lifetime of the issue. Since the underlying instruments of Eurex fixed income derivatives are government issues with top-quality credit ratings, the explanations below focus on the correlation between yield and remaining lifetime. These are often presented as a mathematical function the so-called yield curve. Due to their long-term capital commitment, bonds with a longer remaining lifetime generally tend to yield more than those with a shorter remaining lifetime. This is called a normal yield curve. A flat yield curve is where all remaining lifetimes have the same rate of interest. An inverted yield curve is characterized by a downwards-sloping curve. Yield Curves Yield Remaining lifetime Inverted yield curve Flat yield curve Normal yield curve 10 13 Bond Valuation In the previous sections, we saw that bonds carry a certain yield for a certain remaining lifetime. These yields may be calculated using the bond s market value (price), coupon payments and redemption (cash flows). At which market value (price) does the bond yield (actual rate of interest) correspond to prevailing market yields In the following examples, for clarification purposes, a uniform money market rate (EURIBOR) is used to represent the market interest rate, although this does not truly reflect circumstances on the capital market. A bond with annual coupon payments maturing in exactly one year s time is used for this step-by-step explanation. The coupon and the nominal value are repaid at maturity. Example: Money market interest rate p. a. 3.63 Bond 4.5 Federal Republic of Germany debt security due on July 10, 2003 Nominal value 100 Coupon 4.5 100 4.50 Valuation date July 11, 2002 ( today ) This results in the following equation: 4 Present value Nominal value (n) Coupon (c) Money market rate (r) To determine the present value of a bond, the future payments are divided by the yield factor (1 Money market interest rate). This calculation is referred to as discounting the cash flow. The resulting price is called the present value, since it is generated at the current point in time ( today ). The following example shows the future payments for a bond with a remaining lifetime of three years. 4 Cf. Appendix 1 for general formulae. 11 14 Example: Money market interest rate p. a. 3.63 Bond 4.5 Federal Republic of Germany debt security due on July 11, 2005 Nominal value 100 Coupon 4.5 100 4.50 Valuation date July 12, 2002 ( today ) The bond price can be calculated using the following equation: Present value Coupon (c1) Coupon (c2) Nominal value (n) Coupon (c3) Yield factor (Yield factor) 2 (Yield factor) Present value ( ) ( ) 2 ( ) 3 When calculating a bond for a date that does not coincide with the coupon payment date, the first coupon needs to be discounted only for the remaining lifetime up until the next coupon payment date. The exponentiation of the yield factor until the bond matures changes accordingly. Example: Money market interest rate p. a. 3.63 Bond 4.5 Federal Republic of Germany debt security due on July 4, 2011 Nominal value 100 Coupon 4.5 100 4.50 Valuation date March 11, 2002 ( today ) Remaining lifetime for the first coupon 115 days or 115 365 years Accrued interest 4.5 250365 3.08 The annualized interest rate is calculated, on a pro-rata basis, for terms of less than one year. The discount factor is: ( ) The interest rate needs to be raised to a higher power for remaining lifetimes beyond one year (1.315, 2.315, years). This is also referred to as compounding the interest. Accordingly, the bond price is: Present value ( ) ( ) ( ) 15 The discount factor for less than one year is also raised to a higher power for the purpose of simplification. 5 The previous equation can be interpreted in such a way that the present value of the bond equals the sum of its individual present values. In other words, it equals the aggregate of all coupon payments and the repayment of the nominal value. This model can only be used over more than one time period if a constant market interest rate is assumed. The implied flat yield curve tends not to reflect reality. Despite this simplification, determining the present value with a flat yield curve forms the basis for a number of risk indicators. These are described in the following chapters. One must differentiate between the present value ( dirty price ) and the clean price when quoting bond prices. According to prevailing convention, the traded price is the clean price. The clean price can be determined by subtracting the accrued interest from the dirty price. It is calculated as follows: Clean price Present value Accrued interest Clean price The following section differentiates between a bond s present value and a bond s traded price ( clean price ). A change in market interest rates has a direct impact on the discount factors and hence on the present value of bonds. Based on the example above, this results in the following present value if interest rates increase by one percentage point from 3.63 percent to 4.63 percent: Present value ( ) ( ) ( ) The clean price changes as follows: Clean price An increase in interest rates led to a fall of 7.06 percent in the bond s present value from to The clean price, however, fell by 7.26 percent, from to The following rule applies to describe the relationship between the present value or the clean price of a bond and interest rate developments: Bond prices and market yields react inversely to one another. 5 Cf. Appendix 1 for general formulae. 13 16 Macaulay Duration In the previous section, we saw how a bond s price was affected by a change in interest rates. The interest rate sensitivity of bonds can also be measured using the concepts of Macaulay duration and modified duration. The Macaulay duration indicator was developed to analyze the interest rate sensitivity of bonds, or bond portfolios, for the purpose of hedging against unfavorable interest rate changes. As was previously explained, the relationship between market interest rates and the present value of bonds is inverted: the immediate impact of rising yields is a price loss. Yet, higher interest rates also mean that coupon payments received can be reinvested at more profitable rates, thus increasing the future value of the portfolio. The Macaulay duration, which is usually expressed in years, reflects the period at the end of which both factors are in balance. It can thus be used to ensure that the sensitivity of a portfolio is in line with a set investment horizon. Note that the concept is based on the assumption of a flat yield curve, and a parallel shift in the yield curve where the yields of all maturities change in the same way. Macaulay duration is used to summarize interest rate sensitivity in a single number: changes in the duration of a bond, or duration differentials between different bonds help to gauge relative risks. The following fundamental relationships describe the characteristics of Macaulay duration: Macaulay duration is lower, the shorter the remaining lifetime the higher the market interest rate and the higher the coupon. Note that a higher coupon actually reduces the riskiness of a bond, compared to a bond with a lower coupon: this is indicated by lower Macaulay duration. The Macaulay duration of the bond in the previous example is calculated as follows: 14 17 Example Valuation date March 11, 2002 Security 4.5 Federal Republic of Germany debt security due on July 4, 2011 Money market rate p. a. 3.63 Bond price Calculation: ( ) Macaulay duration ( ) ( ) Macaulay duration 7.65 years The 0.315, 1.315, factors apply to the remaining lifetimes of the coupons and the repayment of the nominal value. The remaining lifetimes are multiplied by the present value of the individual repayments. Macaulay duration is the aggregate of remaining term of each cash flow, weighted with the share of this cash flow s present value in the overall present value of the bond. Therefore, the Macaulay duration of a bond is dominated by the remaining lifetime of those payments with the highest present value. Macaulay Duration (Average Remaining Lifetime Weighted by Present Value) Present value multiplied by maturity of cash flow Years Weights of individual cash flows Macaulay duration 7.65 years Macaulay duration can also be applied to bond portfolios by accumulating the duration values of individual bonds, weighted according to their share of the portfolio s present value. 15 18 Modified Duration The modified duration is built on the concept of the Macaulay duration. The modified duration reflects the percentage change in the present value (clean price plus accrued interest) given a one unit (one percentage point) change in the market interest rate. The modified duration is equivalent to the negative value of the Macaulay duration, discounted over a period of time: Modified duration Duration 1 Yield The modified duration for the example above is: Modified duration 7.65 7.38 According to the modified duration model, a one percentage point rise in the interest rate should lead to a 7.38 percent fall in the present value. Convexity the Tracking Error of Duration Despite the validity of the assumptions referred to in the previous section, calculating the change in value by means of the modified duration tends to be imprecise due to the assumption of a linear correlation between the present value and interest rates. In general, however, the priceyield relationship of bonds tends to be convex, and therefore, a price increase calculated by means of the modified duration is under - or overestimated, respectively. Relationship between Bond Prices and Capital Market Interest Rates P 0 16 Present value Market interest rate (yield) r 0 Priceyield relationship using the modified duration model Actual priceyield relationship Convexity error 19 In general, the greater the changes in the interest rate, the more imprecise the estimates for present value changes will be using modified duration. In the example used, the new calculation resulted in a fall of 7.06 percent in the bond s present value, whereas the estimate using the modified duration was 7.38 percent. The inaccuracies resulting from non-linearity when using the modified duration can be corrected by means of the so-called convexity formula. Compared to the modified duration formula, each element of the summation in the numerator is multiplied by (1 t c1 ) and the given denominator by (1 t r c1 ) 2 when calculating the convexity factor. The calculation below uses the same previous example: ( ) ( ) ( ) ( ) Convexity ( ) ( ) ( ) This convexity factor is used in the following equation: Percentage present value change of bond Modified duration Change in market rates Convexity (Change in market rates) 2 An increase in the interest rate from 3.63 percent to 4.63 percent would result in: Percentage present value change of bond 7.38 (0.01) (0.01) 2 7.03 The results of the three calculation methods are compared below: Calculation method: Results Recalculating the present value 7.06 Projection using modified duration 7.38 Projection using modified duration and 7.03 convexity This illustrates that taking the convexity into account provides a result similar to the price arrived at in the recalculation, whereas the estimate using the modified duration deviates significantly. However, one should note that a uniform interest rate was used for all remaining lifetimes (flat yield curve) in all three examples. 17 20 Eurex Fixed Income Derivatives Characteristics of Exchange-Traded Financial Derivatives Introduction Contracts for which the prices are derived from underlying cash market securities or commodities (which are referred to as underlying instruments or underlyings ) such as equities, bonds or oil, are known as derivative instruments or simply derivatives. Trading derivatives is distinguished by the fact that settlement takes place on specific dates (settlement date). Whereas payment against delivery for cash market transactions must take place after two or three days (settlement period), exchange-traded futures and options contracts, with the exception of exercising options, may provide for settlement on just four specific dates during the year. Derivatives are traded both on organized derivatives exchanges such as Eurex and in the over-the-counter (OTC) market. For the most part, standardized contract specifications and the process of marking to market or margining via a clearing house distinguish exchange-traded products from OTC derivatives. Eurex lists futures and options on financial instruments. Flexibility Organized derivatives exchanges provide investors with the facilities to enter into a position based on their market perception and in accordance with their appetite for risk, but without having to buy or sell any securities. By entering into a counter transaction they can neutralize ( close out ) their position prior to the contract maturity date. Any profits or losses incurred on open positions in futures or options on futures are credited or debited on a daily basis. Transparency and Liquidity Trading standardized contracts results in a concentration of order flows thus ensuring market liquidity. Liquidity means that large amounts of a product can be bought and sold at any time without excessive impact on prices. Electronic trading on Eurex guarantees extensive transparency of prices, volumes and executed transactions. Leverage Effect When entering into an options or futures trade, it is not necessary to pay the full value of the underlying instrument up front. Hence, in terms of the capital invested or pledged, the percentage profit or loss potential for these forward transactions is much greater than for the actual bonds or equities. 18 21 Introduction to Fixed Income Futures What are Fixed Income Futures Definition Fixed income futures are standardized forward transactions between two parties, based on fixed income instruments such as bonds with coupons. They comprise the obligation. to purchase Buyer Long future Long future. or to deliver Seller Short future Short future. a given financial Underlying German Swiss Confederation instrument instrument Government Bonds Bonds. with a given years 8-13 years remaining lifetime in a set amount Contract size EUR 100,000 CHF 100,000 nominal nominal. at a set point Maturity March 10, 2002 March 10, 2002 in time. at a determined Futures price price Eurex fixed income derivatives are based upon the delivery of an underlying bond which has a remaining maturity in accordance with a predefined range. The contract s deliverable list will contain bonds with a range of different coupon levels, prices and maturity dates. To help standardize the delivery process the concept of a notional bond is used. See the section below on contract specification and conversion factors for more detail. Futures Positions Obligations A futures position can either be long or short. Long position Buying a futures contract The buyer s obligations: At maturity, a long position automatically results in the obligation to buy deliverable bonds: The obligation to buy the interest rate instrument relevant to the contract on the delivery date at the pre-determined price. Short position Selling a futures contract The seller s obligations: At maturity, a short position automatically results in the obligation to deliver such bonds: The obligation to deliver the interest rate instrument relevant to the contract on the delivery date at the pre-determined price. 19 22 Settlement or Closeout Futures are generally settled by means of a cash settlement or by physically delivering the underlying instrument. Eurex fixed income futures provide for the physical delivery of securities. The holder of a short position is obliged to deliver either long-term Swiss Confederation Bonds or short-, medium - or long-term German Government debt securities, depending on the traded contract. The holder of the corresponding long position must accept delivery against payment of the delivery price. Securities of the respective issuers whose remaining lifetime on the futures delivery date is within the parameters set for each contract, can be delivered. These parameters are also known as the maturity ranges for delivery. The choice of bond to be delivered must be notified (the notification obligation of the holder of the short position). The valuation of a bond is described in the section on Bond Valuation. However, it is worth noting that when entering into a futures position it is not necessarily based upon the intention to actually deliver, or take delivery of, the underlying instruments at maturity. For instance, futures are designed to track the price development of the underlying instrument during the lifetime of the contract. In the event of a price increase in the futures contract, an original buyer of a futures contract is able to realize a profit by simply selling an equal number of contracts to those originally bought. The reverse applies to a short position, which can be closed out by buying back futures. As a result, a noticeable reduction in the open interest (the number of open long and short positions in each contract) occurs in the days prior to maturity of a bond futures contract. Whilst during the contract s lifetime, open interest may well exceed the volume of deliverable bonds available, this figure tends to fall considerably as soon as open interest starts shifting from the shortest delivery month to the next, prior to maturity (a process known as rollover ). 20 23 Contract Specifications Information on the detailed contract specifications of fixed income futures traded at Eurex can be found in the Eurex Products brochure or on the Eurex website The most important specifications of Eurex fixed income futures are detailed in the following example based on Euro Bund Futures and CONF Futures. A trader buys: 2 Contracts The futures transaction is based on a nominal value of 2 x EUR 100,000 of deliverable bonds for the Euro Bund Future, or 2 x CHF 100,000 of deliverable bonds for the CONF Future. June 2002 Maturity month The next three quarterly months within the cycle MarchJuneSeptemberDecember are available for trading. Thus, the Euro Bund and CONF Futures have a maximum remaining lifetime of nine months. The Last Trading Day is two exchange trading days before the 10th calendar day (delivery day) of the maturity month. Euro Bund or Underlying instrument The underlying instrument for Euro Bund Futures CONF Futures, is a 6 notional long-term German Government respectively Bond. For CONF Futures it is a 6 notional Swiss Confederation Bond. at or Futures price The futures price is quoted in percent, to two. decimal points, of the nominal value of the respectively underlying bond. The minimum price change (tick) is EUR or CHF (0.01). In this example, the buyer is obliged to buy either German Government Bonds or Swiss Confederation Bonds, which are included in the basket of deliverable bonds, to a nominal value of EUR or CHF 200,000, in June 24 Eurex Fixed Income Futures Overview The specifications of fixed income futures are largely distinguished by the baskets of deliverable bonds that cover different maturity ranges. The corresponding remaining lifetimes are set out in the following table: Underlying instrument: Nominal Remaining lifetime of Product code German Government debt contract value the deliverable bonds securities Euro Schatz Future EUR 100, 4 to 2 1 4 years FGBS Euro Bobl Future EUR 100, 2 to 5 1 2 years FGBM Euro Bund Future EUR 100, 2 to 10 1 2 years FGBL Euro Buxl Future EUR 100, to 30 1 2 years FGBX Underlying instrument: Nominal Remaining lifetime of Product code Swiss Confederation Bonds contract value the deliverable bonds CONF Future CHF 100,000 8 to 13 years CONF Futures Spread Margin and Additional Margin When a futures position is created, cash or other collateral is deposited with Eurex Clearing AG the Eurex clearing house. Eurex Clearing AG seeks to provide a guarantee to all clearing members in the event of a member defaulting. This Additional Margin deposit is designed to protect the clearing house against a forward adverse price movement in the futures contract. The clearing house is the ultimate counterparty in all Eurex transactions and must safeguard the integrity of the market in the event of a clearing member default. Offsetting long and short positions in different maturity months of the same futures contract are referred to as time spread positions. The high correlation of these positions means that the spread margin rates are lower than those for Additional Margin. Additional Margin is charged for all non-spread positions. Margin collateral must be pledged in the form of cash or securities. A detailed description of margin requirements calculated by the Eurex clearing house (Eurex Clearing AG) can be found in the brochure on Risk Based Margining. 22 25 Variation Margin A common misconception regarding bond futures is that when delivery of the actual bonds are made, they are settled at the original opening futures price. In fact delivery of the actual bonds is made using a final futures settlement price (see the section below on conversion factor and delivery price). The reason for this is that during the life of a futures position, its value is marked to market each day by the clearing house in the form of Variation Margin. Variation Margin can be viewed as the futures contract s profit or loss, which is paid and received each day during the life of an open position. The following examples illustrate the calculation of the Variation Margin, whereby profits are indicated by a positive sign, losses by a negative sign. Calculating the Variation Margin for a new long futures position: Futures Daily Settlement Price Futures purchase or selling price Variation Margin The Daily Settlement Price of the CONF Future in our example is The contracts were bought at a price of Example CONF Variation Margin: CHF 121,650 (121.65 of CHF 100,000) CHF 121,500 (121.50 of CHF 100,000) CHF 150 On the first day, the buyer of the CONF Future makes a profit of CHF 150 per contract (0.15 percent of the nominal value of CHF 100,000), that is credited via the Variation Margin. Alternatively the calculation can be described as the difference between 15 ticks. The futures contract is based upon CHF 100,000 nominal of bonds, so the value of a small price movement (tick) of CHF 0.01 equates to CHF 10 (i. e. 1, ). This is known as the tick value. Therefore the profit on the one futures trade is 15 CHF 10 1 CHF 26 The same process applies to the Euro Bund Future. The Euro Bund Futures Daily Settlement Price is It was bought at The Variation Margin calculation results in the following: Example Long Euro Bund Variation Margin: EUR 105,700 (105.70 of EUR 100,000) EUR 106,000 (106.00 of EUR 100,000) EUR 300 The buyer of the Euro Bund Futures incurs a loss of EUR 300 per contract (0.3 percent of the nominal value of EUR 100,000), that is consequently debited by way of Variation Margin. Alternatively 30 ticks loss multiplied by the tick value of one bund future (EUR 10) EUR 300. Calculating the Variation Margin during the contract s lifetime: Futures Daily Settlement Price on the current exchange trading day Futures Daily Settlement Price on the previous exchange trading day Variation Margin Calculating the Variation Margin when the contract is closed out: Futures price of the closing transaction Futures Daily Settlement Price on the previous exchange trading day Variation Margin The Futures Price Fair Value While the chapter quotBond Valuation focused on the effect of changes in interest rate levels on the present value of a bond, this section illustrates the relationship between the futures price and the value of the corresponding deliverable bonds. A trader who wishes to acquire bonds on a forward date can either buy a futures contract today on margin, or buy the cash bond and hold the position over time. Buying the cash bond involves an actual financial cost which is offset by the receipt of coupon income (accrued interest). The futures position on the other hand, over time, has neither the financing costs nor the receipts of an actual long spot bond position (cash market). 24 27 Therefore to maintain market equilibrium, the futures price must be determined in such a way that both the cash and futures purchase yield identical results. Theoretically, it should thus be impossible to realize risk-free profits using counter transactions on the cash and forward markets (arbitrage). Both investment strategies are compared in the following table: Time Period Futures purchase Cash bond purchase investmentvaluation investmentvaluation Today Entering into a futures position Bond purchase (market price (no cash outflow) plus accrued interest) Futures Investing the equivalent value of Coupon credit (if any) and lifetime the financing cost saved, on the money market investment of the money market equivalent value Futures Portfolio value Portfolio value delivery Bond (purchased at the futures Value of the bond including price) Income from the money accrued interest Any coupon market investment of the credits Any interest on the financing costs saved coupon income Taking the factors referred to above into account, the futures price is derived in line with the following general relationship: 6 Futures price Cash price Financing costs Proceeds from the cash position Which can be expressed mathematically as: 7 Futures price C t (C t c t t0 ) t r c T t c T t Whereby: C t Current clean price of the underlying security (at time t) c Bond coupon (percent actualactual for euro-denominated bonds) t 0 Coupon date t Value date t r c Short-term funding rate (percent actual360) T Futures delivery date T-t Futures remaining lifetime (days) 6 Readers should note that the formula shown here has been simplified for the sake of transparency specifically, it does not take into account the conversion factor, interest on the coupon income, borrowing costlending income or any diverging value date conventions in the professional cash market. 7 Please note that the number of days in the year (denominator) depends on the convention in the respective markets. Financing costs are usually calculated based on the money market convention (actual360), whereas the accrued interest and proceeds from the cash positions are calculated on an actualactual basis, which is the market convention for all euro-denominated government bonds. 25 28 Cost of Carry and Basis The difference between the proceeds from and the financing costs of the cash position coupon income is referred to as the cost of carry. The futures price can also be expressed as follows: 8 Price of the deliverable bond Futures price Cost of carry The basis is the difference between the bond price in the cash market (expressed by the prices of deliverable bonds) and the futures price, and is thus equivalent to the following: Price of the deliverable bond Futures price Basis The futures price is either lower or higher than the price of the underlying instrument, depending on whether the cost of carry is positive or negative. The basis diminishes with approaching maturity. This effect is called basis convergence and can be explained by the fact that as the remaining lifetime decreases, so do the financing costs and the proceeds from the bonds. The basis equals zero at maturity. The futures price is then equivalent to the price of the underlying instrument this effect is called basis convergence. Basis Convergence (Schematic) Negative Cost of Carry Positive Cost of Carry Price Time Price of the deliverable bond Futures price 0 The following relationships apply: Financing costs gt Proceeds from the cash position: gt Negative cost of carry Financing costs lt Proceeds from the cash position: gt Positive cost of carry 26 8 Cost of carry and basis are frequently shown in literature using a reverse sign. 29 Conversion Factor (Price Factor) and Cheapest-to-Deliver (CTD) Bond The bonds eligible for delivery are non-homogeneous although they have the same issuer, they vary by coupon level, maturity and therefore price. At delivery the conversion factor is used to help calculate a final delivery price. Essentially the conversion factor generates a price at which a bond would trade if its yield were six percent on delivery day. One of the assumptions made in the conversion factor formula is that the yield curve is flat at the time of delivery, and what is more, it is at the same level as that of the futures contract s notional coupon. Based on this assumption the bonds in the basket for delivery should be virtually all equally deliverable. Of course, this does not truly reflect reality: we will discuss the consequences below. The delivery price of the bond is calculated as follows: Delivery price Final Settlement Price of the future Conversion factor of the bond Accrued interest of the bond Calculating the number of interest days for issues denominated in Swiss francs and euros is different (Swiss francs: 30360 euros: actualactual), resulting in two diverging conversion factor formulae. These are included in the appendices. The conversion factor values for all deliverable bonds are displayed on the Eurex website The conversion factor (CF) of the bond delivered is incorporated as follows in the futures price formula (see p. 25 for an explanation of the variables used): Theoretical futures price 1 C t (C t c t t0 ) t r c T t c T t CF The following example describes how the theoretical price of the Euro Bund Future June 2002 is calculated. 27 30 Example: Trade date May 3, 2002 Value date May 8, 2002 Cheapest-to-deliver bond 3.75 Federal Republic of Germany debt security due on January 4, 2011 Price of the cheapest-to-deliver Futures delivery date June 10, 2002 Accrued interest 3.75 (124365) 100 1.27 Conversion factor of the CTD Money market rate p. a. 3.63 1 Theoretical futures price ( ) Theoretical futures price Theoretical futures price In reality the actual yield curve is seldom the same as the notional coupon level also, it is not flat as implied by the conversion factor formula. As a result, the implied discounting at the notional coupon level generally does not reflect the true yield curve structure. The conversion factor thus inadvertently creates a bias which promotes certain bonds for delivery above all others. The futures price will track the price of the deliverable bond that presents the short futures position with the greatest advantage upon maturity. This bond is called the cheapest to deliver (or CTD ). In case the delivery price of a bond is higher than its market valuation, holders of a short position can make a profit on the delivery, by buying the bond at the market price and selling it at the higher delivery price. They will usually choose the bond with the highest price advantage. Should a delivery involve any price disadvantage, they will attempt to minimize this loss. Identifying the Cheapest-to-Deliver Bond On the delivery day of a futures contract, a trader should not really be able to buy bonds in the cash bond market, and then deliver them immediately into the futures contract at a profit if heshe could do this it would result in a cash and carry arbitrage. We can illustrate this principle by using the following formula and examples. Basis Cash bond price (Futures price Conversion factor) 28 31 At delivery, basis will be zero. Therefore, at this point we can manipulate the formula to achieve the following relationship: Cash bond price Futures price Conversion factor This futures price is known as the zero basis futures price. The following table shows an example of some deliverable bonds (note that we have used hypothetical bonds for the purposes of illustrating this effect). At a yield of five percent the table records the cash market price at delivery and the zero basis futures price (i. e. cash bond price divided by the conversion factor) of each bond. Zero Basis Futures Price at 5 Yield Coupon Maturity Conversion factor Price at 5 yield Price divided by conversion factor 5 0715 0304 0513 We can see from the table that each bond has a different zero basis futures price, with the 7 05132011 bond having the lowest zero basis futures price of In reality of course only one real futures price exists at delivery. Suppose that at delivery the real futures price was If that was the case an arbitrageur could buy the cash bond (7 051302) at and sell it immediately via the futures market at and receive This would create an arbitrage profit of two ticks. Neither of the two other bonds would provide an arbitrage profit, however, with the futures at Accrued interest is ignored in this example as the bond is bought and sold into the futures contract on the same day. 29 32 It follows that the bond most likely to be used for delivery is always the bond with the lowest zero basis futures price the cheapest cash bond to purchase in the cash market in order to fulfill a short delivery into the futures contract, i. e. the CTD bond. Extending the example further, we can see how the zero basis futures prices change under different market yields and how the CTD is determined. Zero basis futures price at 5, 6, 7 yield Coupon Maturity Conversion Price Price Price Price Price Price factor at 5 CF at 6 CF at 7 CF 5 0715 0304 0513 The following rules can be deducted from the table above: If the market yield is above the notional coupon level, bonds with a longer duration (lower coupon given similar maturities longer maturity given similar coupons) will be preferred for delivery. If the market yield is below the notional coupon level, bonds with a shorter duration (higher coupon given similar maturitiesshorter maturity given similar coupons) will be preferred for delivery. When yields are at the notional coupon level (six percent) the bonds are almost all equally preferred for delivery. As we pointed out above, this bias is caused by the incorrect discount rate of six percent implied by the way the conversion factor is calculated. For example, when market yields are below the level of the notional coupon, all eligible bonds are undervalued in the calculation of the delivery price. This effect is least pronounced for bonds with a low duration as these are less sensitive to variations of the discount rate (market yield). 9 So, if market yields are below the implied discount rate (i. e. the notional coupon rate), low duration bonds tend to be cheapest-to-deliver. This effect is reversed for market yields above six percent. 9 Cf. chapters Macaulay Duration and Modified Duration. 30 33 The graph below shows a plot of the three deliverable bonds, illustrating how the CTD changes as the yield curve shifts. Identifying the CTD under Different Market Conditions CTD 7 05132011 CTD 5 0715 Zero basis futures price Market yield 6 7 5 07152012 6 03042012 7 0513 34 Applications of Fixed Income Futures There are three motives for using derivatives: trading, hedging and arbitrage. Trading involves entering into positions on the derivatives market for the purpose of making a profit, assuming that market developments are predicted correctly. Hedging means securing the price of an existing or planned portfolio. Arbitrage is exploiting price imbalances to achieve risk-free profits. To maintain the balance in the derivatives markets it is important that both traders and hedgers are active thus providing liquidity. Trades between hedgers can also take place, whereby one counterparty wants to hedge the price of an existing portfolio against price losses and the other the purchase price of a future portfolio against expected price increases. The central role of the derivatives markets is the transfer of risk between these market participants. Arbitrage ensures that the market prices of derivative contracts diverge only marginally and for a short period of time from their theoretically correct values. Trading Strategies Basic Futures Strategies Building exposure by using fixed income futures has the attraction of allowing investors to benefit from expected interest rate moves without having to tie up capital by buying bonds. For a simple futures position, contrary to investing on the cash market, only Additional Margin needs to be pledged (cf. chapter Futures Spread Margin and Additional Margin ). Investors incurring losses on their futures positions possibly as a result of incorrect market forecasts are obliged to settle these losses immediately, and in full ( Variation Margin). During the lifetime of the futures contract this could amount to a multiple of the amount pledged. The change in value relative to the capital invested is consequently much higher than for a similar cash market transaction. This is called the leverage effect. In other words, the substantial profit potential associated with a straight fixed income future position is reflected by the significant risks involved. 32 35 Long Positions ( Bullish Strategies) Investors expecting falling market yields for a certain remaining lifetime will decide to buy futures contracts covering this section of the yield curve. If the prediction turns out to be correct, a profit is made on the futures position. As is characteristic for futures contracts, the profit potential on such a long position is proportional to its risk exposure. In principle, the priceyield relationship of a fixed income futures contract corresponds to that of a portfolio of deliverable bonds. Profit and Loss Profile on the Last Trading Day, Long Fixed Income Futures 0 Profit and loss Bond price PL long fixed income futures Rationale The trader wants to benefit from a forecast development without tying up capital in the cash market. Initial Situation The trader assumes that yields on German Federal Debt Obligations (Bundesobligationen) will fall. Strategy The trader buys ten Euro Bobl Futures June 2002 at a price of. with the intention to close out the position during the contract s lifetime. If the price of the Euro Bobl Futures rises, the trader makes a profit on the difference between the purchase price and the higher selling price. Constant analysis of the market is necessary to correctly time the position exit by selling the contracts. 33 36 The calculation of Additional and Variation Margins for a hypothetical price development is illustrated in the following table. The Additional Margin is derived by multiplying the margin parameter, as set by Eurex Clearing AG (in this case EUR 1,000 per contract), by the number of contracts. Date Transaction Purchase Daily Variation Variation Additional selling price Settlement Margin 10 Margin Margin 11 Price profit in EUR loss in EUR in EUR 0311 Buy ,900 10,000 Euro Bobl Futures June ,700 03 ,100 03 ,400 03 ,100 03 ,200 0320 Sell ,500 Euro Bobl Futures June 21 10,000 Result ,600 5,900 0 Changed Market Situation: The trader closes out the futures position at a price of on March 20. The Additional Margin pledged is released the following day. Result: The proceeds of EUR 2,700 made on the difference between the purchase and sale is equivalent to the balance of the Variation Margin (EUR 8,600 EUR 5,900) calculated on a daily basis. Alternatively the net profit is the sum of the futures price movement multiplied by ten contracts multiplied by the point value of EUR 1,000: ( ) 10 EUR 1,000 EUR 2, Cf. chapter Variation Margin. 11 Cf. chapter Futures Spread Margin and Additional Margin. 34