Korkosijoitusten Kauppa Strategiat Eurex

Navigointi Eurexin kiinteätuotto-optiot: mahdollisuus, jota ei pidä hukata 13 Markkinatekijät tukevat pysyvästi likviditeettiä Eurexin kiinteäkorkoisia vaihtoehtoja. HY1 2015: ssa Bundin, Boblin ja Schatz Futuresin päivittäinen liikevaihto oli yli 350 000 sopimusta (plus 70 prosenttia y-o-y). Tästä 30 prosenttia on myyty tilauskannalla ja 30 prosenttia Eurex Strategy Wizard SM: n kautta. Suorat lainaukset ovat jatkuvasti saatavilla 1 000 sopimukselle. Strategian lainaukset vaihtelevat 500: n ja 1 000: n välillä. Bundin, Boblin ja Schatz Futuresin Eurex-vaihtoehdot ovat saatavilla puheluina ja tarjoavat useille eri käyttäjille erilaisia ​​harjoittelushintoja ja tarjoavat siten räätälöinnin korkeaa tasoa. Lisäksi sijoittajat yhdistävät usein useita vaihtoehtoja yhdeksi kau - paksi, jotta voidaan toteuttaa hienostunut kaupankäyntistrategia. Kaupankäyntikehitys jakautuu näin laajasti näihin mittasuhteisiin, toisin kuin kiinteätuottoiset futuurimarkkinat, joissa kaupankäynti keskittyy erittäin likvideihin etukuorisarjoihin. Tulevaisuudessa käytetään usein toimivat markkinat, joissa likviditeettiä tarjotaan vaihtuvasta kaksisuuntaisesta tilausvirrasta keskusjärjestyksestä. Vaihto-optiolla tarkoitetaan lainausta, koska likviditeettiä ei voida keskittää yhteen sopimukseen, koska laaja-alainen kauppa koskee yli lakkoja ja vanhoja osakkeita sekä lukuisia vaihtoehtoja strategisissa vaihtoehdoissa. Sijoittajat löytävät hintatietoja riskienhallinnasta ja kaupankäynnin kohteena olevista hinnoista erikoistuneilta markkinatalouden toimijoilta, jotka tarjoavat sähköisiä noteerauksia tilauskantaan ja puhelinluettelot off-book-kaupankäynnille. Ruudun kaupankäynnissä sijoittajat voivat käydä kauppaa suoraan noteeratuilla hinnoilla ja hyödyntää ylimääräisiä likviditeettilähteitä, kun Market Makerin tarjoukset täydennetään toteutuksen jälkeen. Market Maker-lainaukset ovat tärkeitä myös optio-kaupankäynnin aloittavien sijoittajien antamille rajatilauksille. Eurex Exchange on perustanut elektronisen noteerauksen kiinteäkorkoisiin optioihin ja tarjoaa pysyviä ja kehittyneitä markkinointiohjelmia. Streaming-lainauksia tarjoavat yli kymmenen erittäin erikoistunutta Market-Making - yritystä, jotka palvelevat kysynnän suorasta toteutuksesta institutionaalisista loppukäyttäjistä. Kauppoja 1000 sopimusta ja muuta voidaan helposti toteuttaa napsauttamalla ja napsauttamalla kaupankäynnin kohteeksi sijoittajat, joilla on suora pääsy markkinoille. HY1 2015: ssä sähköisen kaupankäynnin volyymi Bundissa, Boblissa ja Schatz Optionsissa oli yli 90 000 sopimusta. Kolmen vuoden aikana Bund Optionsin kirjanpidon osuus kasvoi noin 20 prosentista ja vuonna 2015 osuus oli 33 prosenttia. Kirjamäärän osuus Bobl Optionsissa kaksinkertaistui 10 prosentista 20 prosenttiin vuonna 2014. Samoin vuonna 2015 jopa 25 prosenttia Schatz Options - ohjelman määrästä toteutetaan sähköisesti. Valinnat eivät pelkästään käydä kaupankäynnissä kuin puhelut ja asetetaan, vaan myös vaihtoehtostrategioita. Marraskuussa 2013 Eurex lanseerasi tilausvaihtoehtoja koskevat strategiaratkaisut, jotka houkuttelevat yhä enemmän volyymia suoraan tilausten toteuttamisesta Market Makersin tarjoamien lainausten avulla. Vuonna 2015 näemme päivittäin keskimäärin 5 000 korkotuotto-optiosopimusta vaihto-optiostrategioissa Market Maker - hinnastoja vastaan. Kuten kaupankäynnin lopullisessa kaupankäynnissä ja kaupankäynnin kohteena, myös keskisuurten kaupankäynti rajoitusten kanssa on yleistä option strategioissa. Vuoden 2013 loppupuolella strategian volyymi kasvoi sekä strategisten merkintöjen käytön lisäämiseksi lohkokauppoille että suuremman näytön määrästä strategian markkinointiohjelman käyttöönoton jälkeen. Vuonna 2015 päivittäinen tilauskanta kasvoi strategioissa 32 000 sopimukseen kiinteäkorkoisista vaihtoehdoista. Kaiken kaikkiaan strategiakauppa käsittää noin 30 prosenttia volyymistä sekä tilauskannasta että kirjanpidon ulkopuolisesta kaupankäynnistä. Optio-strategioiden lainaamisen lisäksi markkinataloudet tekevät myös pysyviä hintoja. Siten likviditeettiä tarjotaan monille strategioille. Strategia-tilauskannat ovat tyypillisesti 500-1000 sopimusta sisämarkkinoilla riippuen kyseessä olevan optiostrategian riskiprofiilista. Mielenkiintoista on, että strategian lainaukset ovat usein tiukempia kuin kumulatiivinen leviäminen yksitellen jalkojen suorittamisesta erikseen. Tämä kuvastaa oikein optiostrategioiden riskiprofiilia ja johtaa myös pienempiin epäsuoraan transaktiokustannuksiin sijoittajille, jotka tarvitsevat vain ylittää yhden bidoffer-levityksen. SubnavigationInterest Rate Johdannaiset Kiinteiden tulojen kaupankäyntistrategiat. eurex 1 Korko Johdannaiset Kiinteäkorkoiset kaupankäyntistrategiat eurex 2 Huomio Kannen perusteiden ja kustannusten määrittelyä on muutettu esitteen tässä versiossa. Edellisessä versiossa käytettiin seuraavia määritelmiä: Basis Futures Price Rahamääräisen instrumentin hinta Carry Basis Tässä versiossa käytetään seuraavia määritelmiä: Rahoitusinstrumenttien käteisrahan hinnan perushinta Kulutuksen perustekorotukset Nämä muutokset on tehty järjestyksessä että molempien esineiden määritelmät ovat johdonmukaisia ​​koko Eurex-materiaalin, mukaan lukien Trader-tutkimukset ja vastaavat valmistelevat materiaalit. 3 Korko Johdannaiset Kiinteäkorkoiset kaupankäyntistrategiat eurex 4 Sisältö Esite Rakenne ja tavoitteet Kiinteäkorkoisten arvopaperien arvopaperiominaisuudet Määritelmä 08 Elinikäinen ja jäljellä oleva elinikä 09 Nimellis - ja reaalikorko (kuponki ja tuotto) 09 Kertynyt korko 10 Tuottokäyrä 11 Arvonmääritys 14 Macaulay Kesto 16 Muokattu kesto 16 Convexity Kesto Eurex Korkosijoitusten johdannaiset 18 Pörssissä kaupankäynnin kohteena olevat rahoitusjohdannaiset 18 Johdanto 18 Joustavuus 18 Transparenssi ja likviditeetti 18 Vastuuvakuutus Johdanto kiinteän tuoton futuureihin 19 Mitä ovat kiinteätuottoiset futuurit Määritelmä 19 Tulevaisuuspositiot Velvoitteet 20 Settlement tai Closeout 21 Sopimussisältö 22 Eurex Fixed Income Futures Yleisnäkymä 22 Tulevaisuuden spread marginaali ja lisämarginaali 23 Vaihtoramarginaali 24 Futuurien hinta Fair Value 26 Kulujen ja perustarpeiden 27 Conversion Factor (Price Factor) ja Cheapest-to-Deliver ( CTD) Joukkovelkakirja 28 Edullisin toimittama joukkovelkakirjalaina 5 Korkosijoitusten futuurit 32 Kaupankäyntistrategiat 32 Futuurisidonnaiset strategiat 33 Pitkäaikaiset positiot (härät strategiat) 35 Lyhyet asemat (kartoitustrategiat) 36 Levinneet strategiat 37 Aikataulut 38 Keskinäisen tuotannon leviäminen 40 Suojausstrategiat 41 futuurisopimus 41 Täydellinen suojaus ristiinsaajalle 41 Suojausominaisuudet 42 Suojaosuuden määrittäminen 43 Nimellisarvomenetelmä 43 Muunnettu kesto Menetelmä 45 Herkkyysmenetelmä 47 Staattinen ja dynaaminen suojaus 47 Rahavirtalaskelma Kiinteiden tuottojen futuurivertailuvaihtoehdot 49 Vaihtoehdot Kiinteä tuotto futuurit Määritelmä 49 Kiinteäkorkoiset tuotot Tulevaisuuden oikeudet ja velvoitteet 50 Lähes 50 Kiinteäuudekesäätiöiden käyttötilanteet 51 Sopimussäännöt Kiinteän tuoton rahastoihin liittyvät vaihtoehdot 52 Premium-maksu - ja riskiperusteinen marginaali 54 Kiinteän tuoton rahastoihin liittyvät optiot 6 Vaihtoehtoinen hinta 55 Osat 55 Luontainen arvo 55 Ajan arvo 56 Tunnisten määrittäminen 56 U: n volatiliteetti Vaihtoehtoinen instrumentti 56 Jäljellä oleva optio-oikeus 57 Vaikutus tekijöihin Tärkeät riskiparametrit Kreikkalaiset 58 Delta 60 Gamma 61 Vega (Kappa) 61 Theta-kaupankäynnin strategiat kiinteän tuoton futuurivalikoiman osalta 62 Pitkäaikainen kutsu 63 Lyhyt puhelu 65 Pitkä sijoitettu 66 Lyhyt sali 67 Bull Call Spread 68 Bear Put Spread 69 Long Straddle 71 Long Strangle 72 Aikavälin arvon heikkeneminen ja volatiliteetti 72 Aikavälin decade 73 Vaihteluiden vaikutukset markkinavaihteluihin 74 Kaupankäynnin epävakaisuus Delta-neutraalin positiivisuuden ylläpitäminen tulevaisuuden suojausstrategioilla 77 Suojausstrategiat kiinteän ajan horisonttiin 79 Delta Hedge 80 Gamma Hedge 82 Zero Cost Collar 7 FuturesSuosteet Suhteet, Arbitraasi Strategiat 83 Synteettinen Pitkä Call 85 Synteettinen Lyhyt Call 86 Synteettinen Pitkä Pitkä 88 Synteettinen Short Put 88 Synteettinen Pitkä FutureReversal 90 Synteettinen Lyhyt FutureConversion 91 Synthetic Optiot ja tulevaisuussijoitukset Yleiskuvaus Sanasto 92 Liite 1: Arvostuslomake ulot ja indikaattorit 100 Yksittäisen jakson jäljellä oleva elinikä 100 Moniajan jäljellä oleva elinikä 100 Macaulay Kesto 101 Convexity Liite 2: Muuntokerroin 102 Euroissa noteeratut joukkovelkakirjalainat 102 Sveitsin frangiin merkittyjä joukkovelkakirjoja Liite 3: Luettelo kaavioista Yhteystiedot 105 Lisätietoja 8 Esitteiden rakenne ja Tavoitteet Tässä esitteessä kuvataan Eurexissa kaupattavat kiinteätuottoiset johdannaiset ja kuvataan joitakin merkittävimpiä sovelluksia. Nämä sopimukset koostuvat kiinteäkorkoisten arvopapereiden futuurista (kiinteätuottoiset futuurit) ja kiinteätuottoisten futuurien optioista. Jotta voitaisiin selkeyttää kuvattuja sopimuksia, määritellään kiinteätuottoisten arvopapereiden perusominaisuudet ja niistä analysoitavat indikaattorit. Arvopaperiteollisuuden perustiedot ovat edellytys. Tässä esitteessä olevat kiinteätuottoisten arvopapereiden selitykset viittaavat pääosin sellaisiin asioihin, joihin Eurexin korkosijoitusten johdannaiset perustuvat. 6 9 Kiinteäkorkoisten arvopaperien joukkovelkakirjalainojen ominaispiirteet Määritelmä Joukkovelkakirjalainaa voidaan kuvata pääomamarkkinoilta laaja-alaiseksi lainaksi, jolloin velkojan oikeudet on sertifioitu arvopapereina. Arvopapereiden tarjonta tunnetaan liikkeeseenlaskijana liikkeeseenlaskijana ja liikkeeseenlaskijana. Joukkovelkakirjat luokitellaan niiden elinajan, liikkeeseenlaskijan, korkomaksun, luottoluokituksen ja muiden tekijöiden mukaan. Kiinteäkorkoisilla joukkovelkakirjalainoilla on kiinteä koronmaksu, joka tunnetaan kuponkina, joka perustuu joukkovelkakirjalainan nimellisarvoon. Korvauskorvaukset ovat eritelmien mukaan yleensä puolivuosittain tai vuosittain. Eurexin kaupassa olevat kiinteätuottoiset johdannaiset perustuvat joko Saksan tai Sveitsin korkotuottoisten julkisen sektorin joukkovelkakirjalainoista. Sveitsissä Sveitsin keskuspankki (SNB) hallinnoi Sveitsin valtiovarainhallinnolle lainanottovaatimuksia. Pääomaa korotetaan antamalla ns. Rahamarkkinavarausvaateita sekä rahasto-osuuksia ja valuuttamääräisiä obligaatioita. Vain eri elinaikaisten liittohallituksen liput ovat vapaasti vaihdettavissa. Muut valtion obligaatiot vaihdetaan vain SNB: n ja pankkien välillä tai pankkienvälisessä kaupankäynnissä. Saksan valtiovarainministeriö (Bundesrepublik Deutschland Finanzagentur GmbH) on vastuussa Saksan valtionhallinnon liikkeeseen laskemisesta Saksan hallituksen puolesta kesäkuusta alkaen. Muut julkisesti kaupankäynnin kohteena olevat liikkeeseenlaskut sisältävät mm. Entisen Treuhandanstaltin yksityistämisviraston ja Saksan liittohallituksen esimerkiksi erityisrahastoja, Saksan yhtenäisrahastosta. Näistä joukkovelkakirjoista on sama luottokelpoisuus, joka johtuu Saksan liittotasavallan vastuun ottamisesta. Eurexin korkotuottojohdannaisten kannalta merkityksellisillä Saksan hallituksilla on seuraavat eliniät ja kuponkimaksutiedot. Saksan liittovaltion velkasitoumukset Kahden vuoden vuosipalkkio Saksan liittovaltion velkasitoumukset 5 vuotta vuosittain (Bundesobligationen) Saksan valtion obligaatiot 10 ja 30 vuotta vuodessa (Bundesanleihen) Näiden asioiden ehtoihin ei sisälly ennakonpidätystä tai piirustus. 1 1 Ks. Deutsche Bundesbank, Saksan valtion arvopaperimarkkinat, 2. painos, Frankfurt am Main, 10 Tässä luvussa käytetään seuraavia tietoja useisiin selityksiin ja laskelmiin: Esimerkki: Saksan valtion velkasitoumusmääräys. liikkeeseenlaskija Saksan liittotasavalta. julkaisupäivänä 5. heinäkuuta ja kestoikä 10 vuotta. lunastuspäivä 4. heinäkuuta, kiinteä korko on 4,5. kuponkikorvaus vuosittain. 100 elinkaaren ja jäljellä olevan elinajan nimellisarvon on erotettava toisistaan ​​elinikä ja jäljellä oleva elinikä kiinteätuottoisten joukkolainojen ja niihin liittyvien johdannaisten ymmärtämiseksi. Elinii tarkoittaa ajanjaksoa liikkeeseenlaskun ajankohdasta, kunnes arvopaperin nimellisarvo on lunastettu, ja jäljellä oleva elinikä on jäljellä oleva ajanjakso arvopäivästä aina liikkeeseen laskettujen arvopapereiden lunastukseen. Esimerkki: Joukkovelkakirjalla on elinikä kuin arvopäivällä jäljellä oleva elinikä on 10 vuotta 11. maaliskuuta 2002 (nykyään) 9 vuotta ja 115 päivää 8 11 Nimellis - ja reaalikorko (kuponki ja tuotto) Korkotuotto on arvopaperin arvo suhteessa vakuuden nimellisarvoon. Yleensä joukkovelkakirjalainan liikkeeseenlaskuhinta tai kauppahinta ei vastaa sen nimellisarvoa. Sen sijaan joukkovelkakirjoja käydään kauppaa alle tai yli, eli niiden arvo on alle 100 prosentin nimellisarvo. Sekä kuponkimaksut että todellinen sijoitettu pääoma otetaan huomioon laskettaessa tuottoa. Tämä tarkoittaa sitä, että jollei joukkovelkakirjalainaa käydä kauppaa täsmälleen 100 prosentilla, todellinen korko on toisin sanoen: tuotto poikkeaa nimellisarvosta. Todellinen korko on alhaisempi (korkeampi) kuin nimellisarvon mukainen korko (yli) sen nimellisarvosta. Esimerkki: Lippu on. nimellisarvo, mutta käy kauppaa kiinteällä korolla 4,5. kuponki 4,5 100 sato 4,17 2 Tässä tapauksessa joukkovelkakirjan s tuotto on alempi kuin nimellinen korko. Kertynyt korko Kun joukkovelkakirjalaina annetaan, se voidaan myöhemmin ostaa ja myydä monta kertaa ennalta määrättyjen kuponkipäivien välillä. Sellaisenaan ostaja maksaa myyjälle koron, joka on kertynyt tapahtuman arvopäivämäärään, koska hän saa täyden kuponki seuraavan kupongin maksupäivänä. Viimeisestä kupongin maksupäivästä kertynyt korko arvostuspäivään asti kutsutaan kertyneeksi koroksi. Esimerkki: Joukkovelkakirjalaina ostetaan 11.3.2002 (nykyään) Korko maksetaan vuosittain 4. heinäkuuta Kuponkikorko on 4.5 Kauden viimeisen kuponin jälkeen 250 päivää 3 maksu on Tämän vuoksi kertynyt korko on 4,5 250365 3,08 2 Tässä vaiheessa emme vielä ole täsmentäneet täsmällisesti, miten tuotokset lasketaan: tätä tarkoitusta varten meidän on tarkasteltava lähemmin nykyisiä arvoja ja kertynyttä etua koskevia käsitteitä, joita käsitellään seuraavissa osissa. 3 Perustuu todelliseen tilanteeseen. 9 12 Tuottokäyrän joukkolainojen tuotot ovat suurelta osin riippuvaisia ​​liikkeeseenlaskijan luottokelpoisuudesta ja jäljellä olevasta laina-ajasta. Koska Eurex-korkosijoitusten taustalla olevat instrumentit ovat korkealuokkaisia ​​luottoluokituksia hallitseviin julkisiin kysymyksiin, alla olevat selitykset keskittyvät tuoton ja jäljellä olevan elinajan väliseen korrelaatioon. Näitä matemaattisia funktioita kutsutaan usein niin sanottuun tuottokäyrään. Pitkäaikaisen pääoman sitoutumisen ansiosta joukkovelkakirjat, joilla on pidempi elinikä, yleensä tuottavat yleensä enemmän kuin ne, joiden elinikä on lyhyempi. Tätä kutsutaan normaaliksi tuottokäyräksi. Tasainen tuottokäyrä on, jos kaikilla jäljellä olevilla elineillä on sama korko. Käänteisellä tuottokäyrällä on luonteenomaista alaspäin suuntautuva käyrä. Tuottokäyrät Tuotto Jäljellä oleva elinikä Taitettu tuotto-käyrä Tasainen käyräraja Normaali tuottokäyrä 10 13 Arvonmääritys Edellisissä jaksoissa näimme, että joukkovelkakirjoilla on tietty saanto tietyn jäljellä olevan käyttöiän ajan. Nämä tuotot voidaan laskea käyttämällä joukkolainan markkina-arvoa (hintaa), kuponkimaksuja ja lunastusta (rahavirrat). Millä markkina-arvolla (hinta) joukkovelkakirjalainan tuotto (todellinen korko) vastaa vallitsevaa markkina-arvoa. Seuraavissa esimerkeissä selkeyttämiseen käytetään yhtenäistä rahamarkkinakorkoa (EURIBOR) markkinoiden koron edustajana, vaikka tämä ei todellakaan kuvasta pääomamarkkinoiden olosuhteita. Tässä vaiheittaisessa selityksessä käytetään eräpäivään asti erääntyvää vuosittaista kuponkikorvausta. Kuponkikorko ja nimellisarvo palautetaan eräpäivänä. Esimerkki: Rahamarkkinakorko p. a. 3.63 Bond 4.5 Saksan liittotasavallan velkapaperi, joka erääntyy 10.7.2003 Nimellisarvo 100 Kuponki 4,5 100 4,50 Arvostuspäivämäärä 11.7.2002 (nykyään) Tämä johtaa seuraaviin yhtälöihin: 4 Nykyarvo Nimellisarvo (n) Kuponki c) Rahamarkkinakorko (r) Joukkolainan nykyarvon määrittämiseksi tulevat maksut jaetaan tuottokerroin (1 Rahamarkkinakorko). Tätä laskemista kutsutaan diskonttaamalla kassavirta. Tuloksena olevaa hintaa kutsutaan nykyarvoksi, koska se syntyy nykyisellä hetkellä (nykyään). Seuraavassa esimerkissä esitetään tulevat maksut joukkovelkakirjalainalle, jonka jäljellä oleva elinikä on kolme vuotta. 4 Ks. Lisäys 1 yleisten kaavojen osalta. Esimerkki: Rahamarkkinakorko p. a. 3.63 Obligaatio 4.5 Saksan liittotasavallan velkapaperi, joka erääntyy 11.7.2005 Nimellisarvo 100 Kuponki 4,5 100 4,50 Arvostuspäivämäärä 12.7.2002 (tänään) Laina-arvo voidaan laskea käyttäen seuraavaa yhtälöä: Nykyarvo Kuponki (c1) Kuponki ( c2) Nimellisarvo (n) Kuponki (c3) Tuotto (Tuotto) 2 (Tuotto) Nykyinen arvo () () 2 () 3 Laskettaessa joukkovelkakirjalainaa päivämäärälle, joka ei ole sama kuin kupon - ensimmäinen kuponki on diskontattava vain jäljellä olevan elinajan osalta seuraavaan kupongin maksupäivään saakka. Tuottotekijän eksponentiointi, kunnes sidos kypsyy, muuttuu vastaavasti. Esimerkki: Rahamarkkinakorko p. a. 3.63 Bond 4.5 Saksan liittotasavallan velkaanturisumma 4. heinäkuuta 2011 Nimellisarvo 100 Kuponki 4,5 100 4,50 Arvostuspäivämäärä 11.3.2002 (tänään) Ensimmäisen kuponjan jäljellä oleva käyttöaika 115 päivää tai 115 365 vuotta Kertynyt korko 4,5 250365 3,08 Vuotuinen korko lasketaan suhteellisesti, alle vuoden pituisilla ehdoilla. Diskonttauskerroin on: () Korkoa on korotettava suuremmalla voimalla jäljellä oleville elinvuoroille yli vuoden (1.315, 2.315, vuotta). Tätä kutsutaan myös yhdistelemiseksi kiinnostuksesta. Näin ollen joukkovelkakirjalainan hinta on: Nykyarvo () () () 15 Alennuskerroin alle vuodeksi nostetaan myös suuremman tehon yksinkertaistamiseksi. 5 Edellistä yhtälöä voidaan tulkita siten, että joukkovelkakirjalainan nykyarvo on yksittäisten nykyisten arvojen summa. Toisin sanoen se on yhtä suuri kuin kaikki kuponkimaksut ja nimellisarvon palauttaminen. Tätä mallia voidaan käyttää vain useamman kuin yhden ajanjakson aikana, jos oletetaan jatkuvan markkinakoron. Implisiittinen tasainen tuottokäyrä ei tue todellisuutta. Tästä yksinkertaistamisesta huolimatta nykyisen arvon määrittäminen tasaisella tuottokäyrällä muodostaa perustan useille riski-indikaattoreille. Näitä kuvataan seuraavissa luvuissa. On erotettava nykyarvo (likainen hinta) ja puhdas hinta noteerattaessa joukkolainojen hintoja. Vallitsevan sopimuksen mukaan kauppahinta on puhdas hinta. Puhdas hinta voidaan määrittää vähentämällä kertynyt korko likainen hinta. Se lasketaan seuraavasti: Puhdas hinta Käypä arvo Kertynyt korko Puhdas hinta Seuraavassa jaksossa erotetaan joukkovelkakirjalainan nykyarvo ja joukkovelkakirjalainan kaupankäyntihinta (puhdas hinta). Markkinakorkojen muutoksella on suora vaikutus alennustekijöihin ja siten joukkolainojen nykyarvoon. Edellä esitetyn esimerkin perusteella seuraa nykyinen arvo, jos korot nousevat prosenttiyksiköllä 3,63 prosentista 4,63 prosenttiin: Nykyarvo () () () Puhdas hinta muuttuu seuraavasti: Puhdas hinta Korot nousevat laski 7,06 prosenttiin joukkovelkakirjalainan nykyarvoon Puhdasta hintaa kuitenkin laski 7,26 prosentilla seuraavaan sääntöön Seuraavassa pätee kuvaamaan joukkovelkakirjalainan nykyarvon tai puhtaan hinnan ja koron välistä suhdetta Kehitys: Lainamaksut ja markkinatuotot reagoivat käänteisesti toisiinsa. 5 Ks. Lisäys 1 yleisten kaavojen osalta. 13 16 Macaulay Kesto Edellisessä osiossa näimme, kuinka korkojen muutos vaikutti joukkolainan hintaan. Joukkovelkakirjojen korkoherkkyyttä voidaan myös mitata käyttämällä Macaulayn kestoa ja muunneltua kestoa. Macaulay-kestoindikaattoria kehitettiin analysoimaan joukkovelkakirjojen tai joukkovelkakirjalainojen korkoherkkyyttä suojautumalla epäsuotuisilta korkomuutoksilta. Kuten aiemmin on selitetty, markkinakorkojen ja joukkovelkakirjalainojen nykyarvon välinen suhde on käännetty: nousevien tuottojen välitön vaikutus on hintatappio. Korkeammat korot merkitsevät kuitenkin sitä, että saadut kuponimaksut voidaan sijoittaa uudelleen kannattaviin korkoihin, mikä lisää salkun tulevaisuutta. Macaulayn kesto, joka ilmaistaan ​​yleensä vuosia, heijastaa ajanjaksoa, jonka lopussa molemmat tekijät ovat tasapainossa. Sitä voidaan siten käyttää sen varmistamiseen, että salkun herkkyys on asetetun investointikehityssuhteen mukainen. Huomaa, että käsite perustuu tasoittaisen tuottokäyrän olettamukseen ja rinnakkaiseen siirtymiseen tuottokäyrässä, jossa kaikkien maturiteettien tuotot muuttuvat samalla tavalla. Macaulayn kestoa käytetään tiivistämään korkoherkkyys yhdellä luvulla: joukkovelkakirjan keston pituiset muutokset tai eri joukkolainojen kestoerot helpottavat suhteellisten riskien mittaamista. Seuraavat perustavanlaatuiset suhteet kuvaavat Macaulayn keston ominaisuuksia: Macaulayn kesto on alhaisempi, sitä lyhyempi jäljellä oleva elinikä on sitä suurempi markkinakorko ja sitä korkeampi kuponki. Huomaa, että korkeampi kuponki todella vähentää joukkovelkakirjojen riskiä suhteessa joukkovelkakirjalainaan, jolla on alhaisempi kuponki: tämä on osoitettu alhaisemmalla Macaulay-kestolla. Edellisen esimerkin joukkovelkakirjalainan Macaulayn kesto lasketaan seuraavasti: 14 17 Esimerkki Arvostuspäivämäärä 11.3.2002 Turvallisuus 4.5 Saksan liittotasavallan velkapaperi 4. heinäkuuta 2011 Rahamarkkinakorko p. a. 3.63 Lainamaksut Laskelma: () Macaulay-kesto () () Macaulay-kesto 7,65 vuotta 0,315, 1,315, tekijät vaikuttavat kuponkien jäljellä oleviin elimiin ja nimellisarvon takaisinmaksuun. Loput elinajat kerrotaan yksittäisten takaisinmaksujen nykyarvolla. Macaulayn kesto on kullakin rahavirralla jäljellä oleva kesto, painotettu kassavirran tämänhetkisen arvon osuuden kanssa joukkovelkakirjalainan kokonaisarvon hetkellä. Tämän vuoksi joukkovelkakirjalainan Macaulayn kestoa hallitsevat näiden maksujen jäljellä oleva elinikä, jolla on korkein nykyarvo. Macaulay-kesto (keskimääräinen jäljellä oleva elinajan painotettu nykyarvo) Nykyinen arvo kerrottuna kassavirran kypsyydellä Vuotta Yksittäisten kassavirtojen paksuus Macaulayn kesto 7,65 vuotta Macaulayn kestoa voidaan soveltaa myös joukkovelkakirjalainoissa keräämällä yksittäisten joukkovelkakirjojen kesto-arvot, jotka on painotettu niiden osuus salkun nykyisestä arvosta. 15 18 Muokattu kesto Modifioitu kesto perustuu Macaulayn keston käsitteeseen. Muutettu kesto kuvaa nykyarvon prosentuaalista muutosta (puhdas hinta ja kertynyt korko), kun otetaan huomioon markkinakoron yhden yksikön (yhden prosenttiyksikön) muutos. Muutettu kesto vastaa Macaulayn keston negatiivista arvoa, diskontattu ajan kuluessa: Muunnettu kesto Kesto 1 Yield Edellä esitetyn esimerkin muutettu kesto on: Muokattu kesto 7,65 7,38 Modifioidun kestoajan mallin mukaan yhden prosenttiyksikön korkojen nousun pitäisi johtaa 7,38 prosentin laskuun nykyarvoon. Kavitaation keston jäljitysvirhe Vaikka edellisessä jaksossa tarkoitettujen oletusten pätevyydestä huolimatta arvon muutoksen laskeminen muokatun keston avulla on yleensä epätäsmällinen oletetun lineaarisen korrelaation välillä nykyarvon ja korkojen välillä. Yleensä kuitenkin joukkovelkakirjojen hintahyvyyssuhde on yleensä kupera, ja siksi hinnanmuutos, joka on laskettu muokatun keston avulla, on aliarvostettu tai yliarvioitu. Bond-hintojen ja pääomamarkkinoiden korkojen välinen suhde P 0 16 Nykyarvo Markkinakorko (tuotto) r 0 Hintavastuun suhde muokatun kestoaikamallin mukaan Todellinen hintajohdon suhde Convexity error 19 Yleisesti ottaen mitä suurempi korkotason muutos, sitä epätarkempi nykyarvon muutosten arviot käyttävät muokattua kestoa. Käytetyllä esimerkillä uusi laskelma johti 7,06 prosentin laskuun joukkovelkakirjalainan nykyarvoon, kun taas arvio, joka käytti modifioitua kestoa oli 7,38 prosenttia. Epätarkkuudet, jotka johtuvat epälineaarisuudesta muunneltua kestoa käytettäessä, voidaan korjata ns. Konvexity-kaavalla. Verrattuna modifioituun kestoaikatauluun laskennan summauksen jokaisen elementin kerrotaan (1 t c1) ja annetulla nimittäjällä (1 t r c1) 2 konveksitustekijää laskettaessa. Alla olevassa laskelmassa käytetään samaa edeltävää esimerkkiä: () () () () Convexity () () () Tätä kaventuvuustekijää käytetään seuraavassa yhtälössä: Prosentuaalinen nykyarvo joukkovelkakirjalainan muutos Muuttunut kesto Markkinakorot Muunneltavuus Markkina-korot) 2 Korkojen nousu 3,63 prosentista 4,63 prosenttiin johtaisi seuraaviin: Lainan prosenttiosuuden muutos 7,38 (0,01) (0,01) 2 7,03 Kolmen laskentamenetelmän tuloksia verrataan alla: Laskentamenetelmä: Tulokset Nykyisen arvon laskeminen uudelleen 7.06 Suunnittelu muunnellulla kestoajalla 7.38 Projisointi muokatun keston ja 7.03 kavennuksen avulla Tämä osoittaa, että kavennuksen huomioon ottaminen tuottaa samanlaisen tuloksen kuin uudelleenlaskennassa saavutettu hinta, kun taas muutetun keston mukainen arvio poikkeaa merkittävästi. On kuitenkin huomattava, että kaikissa kolmessa esimerkissä käytettiin yhtenäistä korkoa kaikille jäljellä oleville elineille (tasainen tuottokäyrä). 17 20 Eurexin kiinteätuottoiset johdannaiset Pörssijohdannaisten tunnusmerkit Johdanto Hankinnat, joista hinnat perustuvat taustalla oleviin käteisvaroihin kuuluviin arvopapereihin tai hyödykkeisiin (joihin viitataan taustalla olevina instrumentteina tai alarahastoina), kuten osakkeisiin, joukkovelkakirjoihin tai öljyyn, tunnetaan johdannaisinstrumentit tai yksinkertaisesti johdannaiset. Kaupankäynnin johdannaiset eroavat siitä, että selvitys tapahtuu tiettyinä päivinä (selvityspäivä). Maksu käteismarkkinoilla tapahtuvasta toimituksesta on suoritettava kahden tai kolmen päivän kuluttua (selvitysajankohta), valuutanvaihtosopimukset ja optiosopimukset, lukuun ottamatta optio-oikeuksien käyttämistä, voi olla mahdollista suorittaa vain neljä erityistä päivämäärää vuoden aikana. Johdannaisilla käydään kauppaa sekä järjestäytyneillä johdannaispörsseillä kuin Eurex ja OTC-markkinoilla. Suurin osa standardoiduista sopimusten eritelmistä ja markki - nointiprosessista markkinoilta tai raja-arvoltaan selvitysyhteisön kautta erottaa pörssissä vaihdetut tuotteet OTC-johdannaisista. Eurexin mukaan rahoitusinstrumentteihin kuuluvat futuurit ja optiot. Joustavuus Järjestäytyneen johdannaispörssi tarjoaa sijoittajille mahdollisuuden päästä markkina-asemaansa ja riskialttiutensa mukaisesti, mutta ei tarvitse ostaa tai myydä arvopapereita. Liittymällä vastatoimiin ne voivat neutralisoida (sulkea) asemansa ennen sopimuksen eräpäivää. Tulevaisuuksina tai futuurisopimusten avoimissa positioissa syntyneet voitot tai tappiot kirjataan tai veloitetaan päivittäin. Avoimuus ja likviditeetin kaupankäynnin standardisoidut sopimukset johtavat tilausvirtojen keskittymiseen, mikä takaa markkinoiden likviditeetin. Likviditeetti tarkoittaa, että suuria määriä tuotetta voi ostaa ja myydä milloin tahansa ilman liiallista vaikutusta hintoihin. Sähköinen kaupankäynti Eurexilla takaa hintojen, volyymien ja toteutettujen transaktioiden avoimuuden. Vipuvaikutus Vaihtoehtojen tai futuurikauppojen tekemiseen ei ole välttämätöntä maksaa kohde-etuuden täysi arvo eteenpäin. Näin ollen sijoitetun tai pantattavan pääoman suhteen prosenttimääräinen voitto tai tappio potentiaali näille termiinisopimuksille on paljon suurempi kuin varsinaisille joukkovelkakirjalainoille tai osakkeille. 18 21 Johdanto kiinteätuottoisiin futuureihin Mitä on kiinteäuottopäivärahasto Määritelmä Kiinteätuottoiset futuurit ovat vakioituja termiinikauppoja kahden osapuolen välillä, jotka perustuvat kiinteäkorkoisiin instrumentteihin, kuten velkakirjoihin. Ne ovat velvoite. ostaa ostajaa Pitkä tulevaisuus Pitkä tulevaisuus. tai myydä Myyjä Lyhyt tulevaisuus Lyhyt tulevaisuus. tietyn taloudellisen taustalla Saksan Sveitsin valaliiton instrumenttihallitus Valtion joukkovelkakirjalainat. tietyn vuoden ajan 8-13 vuotta jäljellä olevan käyttöikä määrätyllä määrällä Sopimuskoko 100 000 EUR 100 000 CHF nimellistä nimellistä. eräpäivänä Maturiteetti 10. maaliskuuta 2002 10. maaliskuuta 2002 ajoissa. määrätyllä futuurihinnalla Eurexin korkosijoitusten johdannaiset perustuvat kohde-etuutena olevan joukkovelkakirjalainan luovuttamiseen, jonka jäljellä oleva maturiteetti on ennalta määritelty. Sopimuksen toimittamisluettelo sisältää joukkovelkakirjalainoja, joilla on useita eri kuponintasoja, hintoja ja erääntymispäiviä. Tavoitteena on toimitusprosessin standardisoimiseksi käyttää nimellissidoksen käsitettä. Katso tarkemmat tiedot sopimuksen erittelystä ja muuntokertoimista. Tulevaisuuden positioihin liittyvät velvoitteet Futuuripaikka voi olla pitkä tai lyhyt. Pitkä asema Ratkaisusopimuksen ostaminen Ostajien velvoitteet: Pitkä asema syntyy automaattisesti erääntymishetkellä velvollisuudesta ostaa toimitettavia joukkovelkakirjalainoja: Velvoite hankkia sopimuksen mukaiset korkoinstrumentit toimituspäivänä ennalta määritettyyn hintaan. Lyhytaikaisessa asemassa Futuurisopimuksen myyminen Myyjän velvoitteet: Lyhytaikaisessa asemassa syntyy velvoite toimittaa tällaiset joukkovelkakirjat erikseen: Velvoite toimittaa sopimuksen kannalta merkityksellisen korkovälineen toimituspäivänä ennalta määrättyyn hintaan. 19 22 Settlement tai Closeout Tulevaisuuden maksut suoritetaan yleensä käteissuorituksena tai fyysisesti toimittamalla kohde-etuus. Eurexin kiinteätuottoiset futuurit tarjoavat arvopapereiden fyysistä toimitusta. Lyhytaikaisen sijoittajan haltija on velvollinen toimittamaan joko pitkäaikaisia ​​Sveitsin valuutanantajapakkauksia tai lyhytaikaisia, keskipitkän tai pitkän ajan Saksan valtion velkainstrumentteja kaupan kohteena olevan sopimuksen mukaan. Vastaavan pitkäaseman haltijan on hyväksyttävä toimitus toimitusmaksua vastaan. Kunkin liikkeeseenlaskijan arvopaperit, joiden jäljellä oleva käyttöaika futuurien toimitushetkellä on kunkin sopimuksen mukaisten parametrien puitteissa, voidaan toimittaa. Nämä parametrit tunnetaan myös toimituksen kypsyysalueina. Toimitettavan joukkovelkakirjalainan valinta on ilmoitettava (lyhytaikaisen sijoittajan ilmoitusvelvollisuus). Joukkovelkakirjalainan arvostus on kuvattu joukkovelkakirjalainan osassa. On kuitenkin syytä huomata, että futuurisopimukseen siirtymisen ei välttämättä perustu aikomukseen tosiasiallisesti toimittaa tai ottaa käyttöön kohde-etuutena olevat instrumentit maturiteetiltaan. Esimerkiksi futuurit on suunniteltu seuraamaan taustalla olevan instrumentin hintakehitystä sopimuskauden aikana. 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. 34Navigation Eurex Fixed Income Options: an opportunity not to be missed 13 Market Makers are permanently supporting liquidity in Eurex fixed income options. In HY1 2015, daily turnover in options on Bund, Bobl and Schatz Futures totalled over 350,000 contracts (plus 70 percent y-o-y) Thereof, 30 percent have been traded via orderbook and 30 percent via Eurex Strategy Wizard SM . Outright quotes are continuously available for 1,000 contracts. Strategy quotes range between 500 and 1,000 contracts. Eurex options on Bund, Bobl and Schatz Futures are available as calls and puts with a range of tenors in a variety of exercise prices and thus offer a high degree of tailoring. In addition, investors often combine multiple options into one trade to execute a refined trading strategy. Trading interest is thus broadly spread out in these dimensions, in contrast to fixed income futures market where trading is focused on the highly liquid front month series. Futures are often operated in order driven markets, where liquidity is provided by the varying two-way order flow from the central order book. Option trading is quote driven as liquidity cannot be concentrated in one single contract due to the widely-spread trading interest over strikes and expiries and the numerous combination possibilities in options strategies. Investors find price guidance for risk management and firm tradable prices from specialized Market Makers who provide electronic quotes in the order book and phone quotes for off-book trading. In screen trading, investors can trade directly on quoted prices and utilize additional sources of liquidity when Market Maker quotes are replenished upon execution. Market Maker quotes are also important for limit orders entered by investors initiating options trades . Eurex Exchange has established electronic quotation in fixed income options and offers permanent and advanced Market-Making programs. Streaming quotes are provided by over a dozen highly specialized Market-Making firms who service demand for direct execution from institutional end-users. Trades in 1,000 contracts and more can easily be executed in point-and-click trading by investors with direct market access. In HY1 2015, daily electronic trading volume in Bund, Bobl and Schatz Options was over 90,000 contracts. Over the past three years, the share of book volume in Bund Options increased from about 20 percent and in 2015 maintained a share of 33 percent. The share of book volume in Bobl Options doubled from 10 to 20 percent in 2014. Likewise, in 2015. up to 25 percent of volume of Schatz Options is executed electronically. Options not only trade as calls and puts, but also as options strategies. In November 2013, Eurex launched a bespoke Market-Making program for option strategies that is increasingly attracting volume directly from the execution of orders against the quotes provided by Market Makers. In 2015, we now see a daily average of 5,000 fixed income option contracts trading against Market Maker quotes in option strategies. As in trading outright calls and puts, mid-market trading with limit orders is also prevalent in option strategies. Since the end of 2013, strategy volume increased both due to higher usage of strategy entries for block trades as well as higher screen volumes following the introduction of the strategy Market-Making program. In 2015, daily order book volume in strategies rose to 32,000 contracts in fixed income options. Overall, strategy trading comprises about 30 percent of volume both in order book and off-book trading. In addition to quoting option strategies, Market Makers also stream permanent prices. Thus liquidity is provided for a vast range of strategies. Strategy order books are typically quoted for 500 to 1,000 contracts on the inside market depending upon the risk profile of the option strategy in question. Interestingly, strategy quotes are frequently tighter than the cumulative spread from single-handedly executing the legs individually. This correctly reflects the risk profile of option strategies, and also translates into lower implicit transaction costs for investors who only need to cross one bidoffer spread. 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