Eurex Zinsderivate Fixed Income Trading Strategien

Eurex-Zinsderivate - Fixed Income Trading-Strategien Zinsderivate Fixed Income Trading-Strategien eurex Bitte beachten Sie die Definitionen der Basis und der Kosten des Trages in dieser Version der Broschüre geändert wurden. In der Vorgängerversion wurden folgende Definitionen verwendet: Basis-Futures-Preis Preis des Cash-Instrumentes Cost of Carry Basis In dieser Fassung werden folgende Definitionen verwendet: Basis-Preis von Cash Instrument Futures-Preis Cost of Carry Basis Diese Änderungen wurden in der Reihenfolge vorgenommen Um sicherzustellen, dass die Definitionen beider Positionen in allen Eurex-Materialien, einschließlich der Händlerprüfung und entsprechenden Vorbereitungsmaterialien, konsistent sind. Zinsderivate Fixed Income Trading-Strategien eurex Inhalt Broschüre Struktur und Ziele 06 Merkmale der festverzinslichen Wertpapiere 07 08 09 09 10 11 14 16 16 Anleihen Definition Lifetime und Restlaufzeit Nominaler und tatsächlicher Zinssatz (Coupon und Rendite) Aufgelaufene Zinsen Die Renditekurve Anleihebewertung Macaulay Duration Modified Duration Konvexität der Tracking-Fehler der Duration Eurex Fixed Income Derivatives 18 18 18 18 18 Merkmale von börsengehandelten Finanzderivaten Einführung Flexibilität Transparenz und Liquidität Hebelwirkung Einführung in Fixed Income Futures 19 19 20 21 22 22 23 24 26 27 28 Was sind Fixed Income Futures Definition Futures Positionen Obligationen Abrechnungs - oder Kontraktspezifikationen Eurex Fixed Income Futures Überblick Futures Spread Margin und Margin Additional Margin Variation Margin Der Futures-Preis Fair Value Cost of Carry und Basis-Umrechnungsfaktor (Price Factor) und Cheapest-to-Deliver (CTD) Bond Ermittlung der günstigsten Anleiheanleihen von Fixed Income Futures 32 32 33 35 36 37 38 40 41 41 41 42 43 43 45 47 47 Handelsstrategien Basis-Futures-Strategien Long-Positionen (Bullische Strategien) Short-Positionen (Bearish Strategies ) Spread-Strategien Zeitspanne Inter-Produkt-Spread-Hedging-Strategien Auswahl des Futures-Kontrakts Perfekte Hedge versus Cross Hedge Hedging-Überlegungen Bestimmung des Hedge-Verhältnisses Nominalwertmethode Modified Duration Method Empfindlichkeitsmethode Statisches und dynamisches Hedging Cash-and-Carry Arbitrage Einführung in Optionen auf Fixed Income Futures 49 49 50 50 51 52 54 Optionen auf Fixed Income Futures Definition Optionen auf Fixed Income Futures Rechte und Verpflichtungen Closeout Ausübungsoptionen auf Fixed Income Futures Kontraktspezifikationen Optionen auf Fixed Income Futures Prämienzahlung und Risk Based Margining Optionen auf Fixed Income Futures Übersicht Option Preis 55 55 55 56 56 56 57 Bestandteile Intrinsischer Wert Zeitwert Feststellungsfaktoren Volatilität des Basiswertes Restlaufzeit der Option Einflussfaktoren Wichtige Risikoparameter Griechen 58 60 61 61 Delta Gamma Vega (Kappa) Theta-Handelsstrategien für Optionen auf Fixed Income Futures 62 63 65 66 67 68 69 71 72 72 73 74 Long Call Kurzanruf Long Put Short Put Bull Call Spreizbär Put Verbreitung Lang Straddle Lang Strangle Einfluss der Zeit Wert Verfall und Volatilität Zeit Wert Verfall Auswirkungen der Schwankungen der Marktvolatilität Trading Volatility Maintaining Delta-Neutrale Position mit Futures-Hedging-Strategien 77 79 80 82 Hedging-Strategien für eine feste Zeit Horizont Delta Hedging Gamma Hedging Zero Cost Collar FuturesOptions Beziehungen, Arbitrage-Strategien 83 83 85 86 88 88 90 91 Synthetische Fixed Income Optionen und Futures Positionen Synthetische Long Call Synthetic Kurzanruf Synthetisch Lang Put Synthetisch Kurz Put Synthetisch Lang FutureReversal Synthetisch Kurz FutureConversion Synthetische Optionen und Futures Positionen Übersicht Glossar 92 Anhang 1: Bewertungsformeln und Indikatoren 100 100 100 101 Einzelperioden verbleibende Lebensdauer Mehrperiodenverbleibende Lebensdauer Macaulay Dauer Konvexität Anhang 2: Umwandlung Faktoren 102 102 Anleihen in Euro Anleihen in Schweizer Franken Anhang 3: Abbildungsverzeichnis 103 104 105 Kontakte Weitere Informationen Broschüre Struktur und Ziele Diese Broschüre beschreibt die an Eurex gehandelten festverzinslichen Derivate und illustriert einige ihrer bedeutendsten Anwendungen. Diese Verträge setzen sich aus Futures auf festverzinsliche Wertpapiere (Fixed Income Futures) und Optionen auf Fixed Income Futures zusammen. Um ein besseres Verständnis der beschriebenen Verträge zu schaffen, werden die grundlegenden Merkmale der festverzinslichen Wertpapiere und die Indikatoren, die zur Analyse verwendet werden, skizziert. Grundkenntnisse der Wertpapierbranche sind Voraussetzung. Die in dieser Broschüre enthaltenen Erläuterungen zu festverzinslichen Wertpapieren beziehen sich überwiegend auf solche Emissionen, auf denen Eurex festverzinsliche Derivate basieren. 6 Merkmale der festverzinslichen Wertpapiere Anleihen Definition Eine Anleihe kann als großflächige Anleihe am Kapitalmarkt bezeichnet werden, wobei die Forderungen der Gläubiger in Form von Wertpapieren zertifiziert werden. Die Wertpapiere werden als Emissionen und der jeweilige Schuldner als Emittent bezeichnet. Anleihen sind nach ihrer Lebensdauer, Emittent, Zinszahlung Details, Bonität und andere Faktoren kategorisiert. Festverzinsliche Anleihen tragen eine feste Zinszahlung, die als Kupon bekannt ist und auf dem Nominalwert der Anleihe basiert. Abhängig von den Spezifikationen ist die Zinszahlung in der Regel halbjährlich oder jährlich. An Eurex gehandelte festverzinsliche Derivate basieren auf einem Korb von deutschen oder schweizerischen festverzinslichen Staatsanleihen. Die Schweizerische Nationalbank (SNB) verwaltet in der Schweiz die Anleiheanforderungen für die Eidgenössische Finanzverwaltung. Das Kapital wird durch die Ausgabe von sogenannten Geldmarkt - bucheinträgen sowie Treasury Notes und Confederation Bonds erhöht. Nur die Bund-Anleihen mit unterschiedlichen Lebenszeiten sind frei handelbar. Andere Staatsanleihen werden nur zwischen der SNB und den Banken oder im Interbankenhandel ausgetauscht. Die Bundesrepublik Deutschland Finanzagentur GmbH ist seit Juni 2001 für die Emission deutscher Staatsanleihen (im Auftrag der Bundesregierung) zuständig. Weitere öffentlich handelbare Emissionen sind bis 1995 von der ehemaligen Treuhandanstalt und der Bundesrepublik Deutschland ausgegebene Anleihen Regierungen Spezialfonds, zum Beispiel der Deutsche Einheitsfonds. Diese Schuldverschreibungen werden durch die Übernahme der Haftung durch die Bundesrepublik Deutschland der gleichen Bonität zugerechnet. Deutsche Staatsanleihen, die für die Eurex-Fixed-Income-Derivate von Bedeutung sind, weisen die folgenden Laufzeiten und Couponzahlungen auf. Regierungsausgaben Bundesschatzanweisungen Bundesobligationen Staatsanleihen (Bundesanleihen) Laufzeit 2 Jahre 5 Jahre 10 und 30 Jahre Kuponzahlung Jährlich Jährlich Die Konditionen dieser Emissionen sehen keine vorzeitige Rückzahlung vor Oder Zeichnung 1. 1 Vgl. Deutsche Bundesbank, Der Markt fr deutsche Bundeswertpapiere, 2. Aufl., FrankfurtMain, 1998. 7 In diesem Kapitel werden für eine Reihe von Erläuterungen und Berechnungen folgende Informationen verwendet: Beispiel: Forderungsausfall. Durch den Emittenten. Zum Ausgabetag. Mit einer Lebensdauer von. Ein Rückzahlungsdatum am. Deutsch - Übersetzung - Linguee als Übersetzung von. Gutscheinzahlung. Ein Nominalwert der deutschen Bundesanleihe Bundesrepublik Deutschland 5. Juli 2001 10 Jahre 4. Juli 2011 4.5 jährlich 100 Lebensdauer und verbleibende Lebenszeit Man muss zwischen Lebenszeit und Restlebensdauer unterscheiden, um festverzinsliche Anleihen und damit zusammenhängende Derivate zu verstehen. Die Laufzeit bezeichnet den Zeitraum vom Ausgabetag bis zum Rückkauf des Nominalwerts des Wertpapiers, während die Restlaufzeit die verbleibende Restlaufzeit vom Bewertungsstichtag bis zur Rückzahlung bereits ausgegebener Wertpapiere ist. Beispiel: Die Anleihe hat am Bilanzstichtag eine Restlaufzeit von 10 Jahren 11. März 2002 (heute) 9 Jahre und 115 Tage 8 Nominaler und tatsächlicher Zinssatz (Coupon und Rendite) Der Nominalzins eines Festzinses Einkommensanleihe ist der Wert des Kupons im Verhältnis zum Nominalwert des Wertpapiers. Grundsätzlich entspricht weder der Emissionspreis noch der Handelspreis einer Anleihe ihrem Nominalwert. Stattdessen werden Anleihen unter oder über Par. Gehandelt, deren Wert unter oder über dem Nominalwert von 100 Prozent liegt. Sowohl die Couponzahlungen als auch das tatsächlich investierte Kapital werden bei der Berechnung der Rendite berücksichtigt. Dies bedeutet, dass, sofern die Anleihe nicht zu genau 100 Prozent gehandelt wird, der tatsächliche Zinssatz mit anderen Worten: die Rendite weicht von dem nominalen Zinssatz ab. Der tatsächliche Zinssatz ist niedriger (höher) als der nominale Zinssatz für einen Anleihehandel oberhalb (unterhalb) seines Nominalwertes. Beispiel: Die Bindung hat. Ein Nennwert von. Sondern handelt zu einem Preis von. Deutsch - Übersetzung - Linguee als Übersetzung von. Ein Gutschein von. Eine Rendite von 100 102,50 4,5 4,5 100 4,50 4.172 In diesem Fall ist die Rendite der Anleihen niedriger als der nominale Zinssatz. Aufgelaufene Zinsen Wenn eine Anleihe ausgegeben wird, kann sie nachträglich zwischen den vorgegebenen zukünftigen Coupon-Jubiläumsterminen gekauft und verkauft werden. Als solcher zahlt der Käufer dem Verkäufer die Zinsen bis zum Valutatag der Transaktion, da heshe den vollen Coupon zum nächsten Couponzahlungstag erhält. Die Zinsen, die bis zum Bewertungstag vom letzten Couponzahlungstag stammen, werden als aufgelaufene Zinsen bezeichnet. Beispiel: Die Anleihe wird an Der Zins wird gezahlt Der Coupon ist der Zeitraum seit der letzten Couponzahlung Dies führt zu aufgelaufenen Zinsen vom 11. März 2002 (heute) jährlich am 4. Juli 4.5 250 Tage 3 4.5 250 365 3.08 2 An dieser Stelle haben wir noch nicht genau geklärt, wie die Renditen berechnet werden: Dazu müssen wir die Konzepte des Barwerts und der aufgelaufenen Zinsen, die wir in den folgenden Abschnitten behandeln, näher untersuchen. 3 Auf der Grundlage der tatsächlichen. 9 Die Renditekurve Die Renditen der Anleihen sind weitgehend abhängig von der Bonität der Emittenten und der Restlaufzeit der Emission. Da die zugrundeliegenden Instrumente der Eurex-festverzinslichen Derivate Staatsanleihen mit erstklassigen Bonitätsbeurteilen sind, konzentrieren sich die nachfolgenden Erläuterungen auf die Korrelation zwischen Rendite und Restlebensdauer. Diese werden oft als mathematische Funktion der sogenannten Zinskurve dargestellt. Aufgrund ihrer langfristigen Kapitalbindung tendieren Anleihen mit einer längeren Restlebensdauer im Allgemeinen dazu, mehr zu erzielen als jene mit einer verkürzten Restlebensdauer. Dies wird als normale Zinsstrukturkurve bezeichnet. Eine flache Zinskurve ist, wo alle verbleibenden Lebensdauern den gleichen Zinssatz haben. Eine invertierte Zinsstrukturkurve ist durch eine abwärts gerichtete Kurve gekennzeichnet. Renditekurven Rendite Restlaufzeit Invertierte Renditekurve Renditekurve Normal Renditekurve 10 Rentenbewertung In den vorangegangenen Abschnitten haben wir gesehen, dass Anleihen eine gewisse Rendite für eine bestimmte Restlebensdauer haben. Diese Renditen können unter Zugrundelegung des Marktwertes (Kurs), Couponzahlungen und Tilgung (Cash Flows) berechnet werden. Bei welchem ​​Marktwert (Kurs) entspricht die Rendite (tatsächlicher Zinssatz) den vorherrschenden Marktrenditen In den folgenden Beispielen wird zur Klarstellung ein einheitlicher Geldmarktsatz (Euribor) verwendet, um den Marktzinssatz darzustellen Nicht wirklich die Umstände auf dem Kapitalmarkt widerspiegeln. Für diese Schritt-für-Schritt-Erläuterung wird eine Anleihe mit jährlichen Kuponzahlungen verwendet, die in genau einem Jahr fällig wird. Coupon und Nominalwert werden bei Fälligkeit zurückgezahlt. Beispiel: Geldmarktzins p. a. Anleihe Nominalwert Kupon Bewertungstag 3.63 4.5 Bundesrepublik Deutschland am 10. Juli 2003 fällige Schuldverschreibung 100 4.5 100 4.50 11. Juli 2002 (heute) Daraus ergibt sich folgende Gleichung 4: Barwert Nominalwert (n) Coupon (c) 100 4,50 100,84 1 Geldmarktsatz (r) 1 0,0363 Zur Bestimmung des Barwertes einer Anleihe werden die zukünftigen Zahlungen durch den Renditefaktor (1 Geldmarktzins) dividiert. Diese Berechnung wird als Diskontierung des Cashflows bezeichnet. Der daraus resultierende Preis wird als Barwert bezeichnet, da er zum aktuellen Zeitpunkt (heute) erzeugt wird. Das folgende Beispiel zeigt die zukünftigen Zahlungen für eine Anleihe mit einer Restlaufzeit von drei Jahren. 4 Vgl. Anhang 1 für allgemeine Formeln. 11 Beispiel: Geldmarktzins p. a. Anleihe Nominalwert Kupon Bewertungstag 3.63 4.5 Bundesrepublik Deutschland am 11. Juli 2005 fällige Schuldverschreibung 100 4.5 100 4.50 12. Juli 2002 (heute) Der Anleihekurs kann nach folgender Gleichung berechnet werden: Barwert Coupon (c1) Coupon C) Nennwert (n) Kupon (c3) Ausbeutefaktor (Ausbeutefaktor) 2 (Ausbeutefaktor) 3 Gegenwärtiger Wert 4.50 4.50 100 4.50 102.43 (1 0.0363) (1 0.0363) 2 (1 0.0363) 3 Bei der Berechnung einer Bindung für a Datum, das nicht mit dem Couponzahlungsdatum übereinstimmt, muss der erste Coupon nur für die Restlaufzeit bis zum nächsten Couponzahlungstag diskontiert werden. Die Potenzierung des Renditefaktors bis zur Reifung der Bindungen ändert sich entsprechend. Beispiel: Geldmarktzins p. a. Anleihe Nominalwert Kupon Bewertungstag Restlaufzeit für den ersten Coupon Aufgelaufene Zinsen 3,63 4,5 Bundesrepublik Deutschland am 4. Juli 2011 fällige Schuldverschreibung 100 4,5 100 4,50 11. März 2002 (heute) 115 Tage oder 115 365 0,315 Jahre 4,5 250 365 3,08 Der annualisierte Zinssatz wird anteilsmäßig für Laufzeiten von weniger als einem Jahr berechnet. Der Abzinsungsfaktor lautet: 1 1 (0,0363 0,315) Der Zinssatz muss für die Restlebensdauer über ein Jahr (1,315, 2,315,9,315 Jahre) auf eine höhere Leistung angehoben werden. Dies wird auch als Compoundierung der Zinsen bezeichnet. Dementsprechend beträgt der Anleihekurs: Barwert 4,50 4,50 4,50 100. 109,84 1 (0,0363 0,315) (1 0,0363) 1,315 (1 0,0363) 9,315 12 Der Diskontierungsfaktor für weniger als ein Jahr wird zur Vereinfachung auch auf eine höhere Macht angehoben5. Die bisherige Gleichung kann so interpretiert werden, dass der Barwert der Anleihe gleich der Summe ihrer individuellen Gegenwartswerte ist. Mit anderen Worten, sie entspricht der Summe aller Couponzahlungen und der Tilgung des Nominalwerts. Dieses Modell kann nur über einen Zeitraum verwendet werden, wenn ein konstanter Marktzins angenommen wird. Die implizite flache Zinsstrukturkurve neigt dazu, die Realität nicht zu reflektieren. Trotz dieser Vereinfachung bildet die Ermittlung des Barwertes mit einer flachen Zinsstrukturkurve die Basis für eine Reihe von Risikoindikatoren. Diese werden in den folgenden Kapiteln beschrieben. Bei der Anleihekurve ist zwischen dem Barwert (schmutziger Preis) und dem sauberen Preis zu unterscheiden. Entsprechend vorherrschender Versammlung ist der gehandelte Preis der saubere Preis. Der saubere Preis kann durch Subtraktion der aufgelaufenen Zinsen von dem schmutzigen Preis bestimmt werden. Es wird wie folgt berechnet: Sauberer Preis Barwert Abgegrenzte Saldo Sauberer Preis 109,84 3,08 106,76 Der folgende Abschnitt unterscheidet zwischen einem Anleihe-Barwert und einem gehandelten Anleihepreis (Clean Price). Eine Veränderung der Marktzinssätze wirkt sich direkt auf die Abzinsungsfaktoren und damit auf den Barwert der Anleihen aus. Basierend auf dem obigen Beispiel ergibt sich der folgende Barwert, wenn die Zinsen um einen Prozentpunkt von 3,63 Prozent auf 4,63 Prozent steigen: Barwert 4,50 4,50 4,50 100. 102,09 3,08 99,01 Eine Zinserhöhung führte zu einem Rückgang um 7,06 Prozent im Barwert von 109,84 auf 102,09. Der saubere Preis sank jedoch um 7,26 Prozent von 106,76 auf 99,01. Für die Beziehung zwischen dem Barwert oder dem sauberen Preis einer Anleihe und der Zinsentwicklung gilt folgende Regel: Die Anleihekurse und Marktrenditen reagieren umgekehrt aufeinander. 5 Vgl. Anhang 1 für allgemeine Formeln. 13 Macaulay Duration Im vorherigen Abschnitt haben wir gesehen, wie der Kurs der Anleihen von einer Veränderung der Zinssätze beeinflusst wurde. Die Zinssensitivität von Anleihen kann auch mit den Konzepten der Macaulay-Duration und der modifizierten Duration gemessen werden. Der Macaulay-Durationsindikator wurde entwickelt, um die Zinsempfindlichkeit von Anleihen oder Anleiheportfolios zur Absicherung gegen ungünstige Zinsänderungen zu analysieren. Wie bereits erläutert, ist das Verhältnis zwischen Marktzinssätzen und dem Barwert der Anleihen umgekehrt: Der unmittelbare Einfluss steigender Renditen ist ein Kursverlust. Ein höherer Zinssatz bedeutet aber auch, dass die erhaltenen Couponzahlungen zu rentableren Renditen reinvestiert werden können, wodurch der künftige Wert des Portfolios erhöht wird. Macaulay Dauer, die in der Regel in Jahren ausgedrückt, spiegelt den Zeitpunkt, an dem beide Faktoren im Gleichgewicht sind. Damit kann sichergestellt werden, dass die Sensitivität eines Portfolios einem festgelegten Anlagehorizont entspricht. (Man beachte, dass das Konzept auf der Annahme einer flachen Zinsstrukturkurve und einer Parallelverschiebung der Zinsstrukturkurve beruht, bei der sich die Renditen aller Laufzeiten in gleicher Weise ändern.) Die Macaulay-Duration wird verwendet, um die Zinsempfindlichkeit in einer einzigen Zahl zusammenzufassen : Veränderungen in der Laufzeit einer Anleihe oder Laufzeitunterschiede zwischen verschiedenen Anleihen helfen, relative Risiken abzuschätzen. Die folgenden grundlegenden Beziehungen beschreiben die Merkmale von Macaulay Dauer: Macaulay Dauer ist niedriger, q q q je kürzer die verbleibende Lebensdauer je höher der Marktzins und je höher der Coupon. Beachten Sie, dass ein höherer Coupon tatsächlich die Risikohaftigkeit einer Anleihe reduziert, im Vergleich zu einer Anleihe mit einem niedrigeren Coupon: dies wird durch niedrigere Macaulay-Duration angezeigt. Die Macaulay-Duration der Anleihe im vorigen Beispiel wird wie folgt berechnet: 14 Beispiel Bewertungstag Sicherheit Geldmarktzinssatz Anleihepreis Berechnung: 4.50 4.50 4.50 100 0.315 1.315 9.315 (1 0,0363) 0,315 (1 0,0363) 1,315 (1 0,0363) 9,315 109,84 11. März 2002 4.5 Bundesrepublik Deutschland am 4. Juli 2011 fällige Verbindlichkeiten 3,63 109,84 Macaulay Laufzeit Macaulay Laufzeit 840,51 109,84 7,65 Jahre Für die verbleibenden Laufzeiten der Coupons und die Rückzahlung des Nominalwerts gelten die 0,315, 1,315, .9,155 Faktoren . Die verbleibenden Laufzeiten werden mit dem Barwert der einzelnen Rückzahlungen multipliziert. Die Macaulay-Duration ist die Summe der verbleibenden Laufzeit jedes Cashflows, gewichtet mit dem Anteil dieses Barmittelwertes im Barwert des Barwertes. Daher wird die Macaulay-Laufzeit einer Anleihe von der Restlebensdauer dieser Zahlungen mit dem höchsten Barwert dominiert. Macaulay Duration (Durchschnittliche verbleibende Restlaufzeit gewichtet mit Barwert) 1 700 680. 140 120 100 80 60 40 20 2 3 4 5 6 7 8 9 10 Anwartschaftsbarwert multipliziert mit Laufzeit des Cashflows Jahre Gewichte einzelner Cashflows Macaulay Laufzeit 7,65 Jahre Macaulay Die Duration kann auch auf Anleiheportfolios angewendet werden, indem die Durationswerte der einzelnen Anleihen, die nach ihrem Anteil am Portfolios-Barwert gewichtet werden, akkumuliert werden. 15 Modified Duration Die modifizierte Duration basiert auf dem Konzept der Macaulay-Dauer. Die modifizierte Duration entspricht der prozentualen Veränderung des Barwertes (Clean Price plus aufgelaufener Zinsen) bei einer Änderung des Marktzinsniveaus um eine Einheit (ein Prozentpunkt). Die modifizierte Duration entspricht dem negativen Wert der Macaulay-Duration, der über einen Zeitraum abgezinst wird: Modified Duration Duration 1 Rendite Die modifizierte Duration für das obige Beispiel ist: Modified Duration 7,65 7,38 1 0,0363 Nach dem modifizierten Durationsmodell eine Prozentpunkt Zunahme des Zinssatzes zu einem 7.38 Prozent Rückgang des Barwertes führen. Konvexität der Tracking Error of Duration Trotz der Gültigkeit der im vorherigen Abschnitt genannten Annahmen ist die Berechnung der Wertänderung mittels der modifizierten Duration aufgrund der Annahme einer linearen Korrelation zwischen dem aktuellen Wert und den Zinssätzen ungenau. Im Allgemeinen ist das Preis-Rendite-Verhältnis der Anleihen tendenziell konvex, weshalb eine durch die modifizierte Duration berechnete Preiserhöhung unter - bzw. überschätzt wird. Beziehung zwischen Anleihekursen und Kapitalmarktzinssätzen P0 Gegenwartswert Marktzins (Rendite) r0 Priceyield-Beziehung mit dem modifizierten Durationsmodell Tatsächliche Priceyield-Beziehung Konvexitätsfehler 16 Im Allgemeinen gilt, je größer die Änderungen des Zinssatzes, desto ungenauer die Schätzungen für Werden die Barwertänderungen die modifizierte Duration verwenden. Im angewendeten Beispiel ergab sich aus der neuen Berechnung ein Rückgang um 7,06 Prozent im Barwert, während die Schätzung mit der modifizierten Duration 7,38 Prozent betrug. Die Ungenauigkeiten, die sich aus der Nichtlinearität bei Verwendung der modifizierten Dauer ergeben, können mit Hilfe der sogenannten Konvexitätsformel korrigiert werden. Im Vergleich zur modifizierten Durationsformel wird jedes Element der Summenbildung im Zähler mit (1 t c1) und dem gegebenen Nenner durch (1 trc1) 2 multipliziert, wenn der Konvexitätsfaktor berechnet wird. Die nachstehende Berechnung verwendet dasselbe vorhergehende Beispiel: 4.50 Konvexität (1 0.0363) 0.315 4.50 (1 0.0363) 1.315 100 4.50 (1 0.0363) 9.315 0.315 (0.315 1) 1.315 (1.315 1). Dieser Konvexitätsfaktor wird in der folgenden Gleichung verwendet: Prozentualer Gegenwartswert Modifizierte Duration Veränderung der Marktzinssätze 0,5 Konvexität (Veränderung der Marktzinssätze) 2 Wandelanleihe Eine Zinserhöhung von 3,63 Prozent bis 4,63 Prozent führen zu: Prozentsatz des aktuellen Wertes 7,38 (0,01) 0,5 69,15 (0,01) 2 0,0703 7,03 Änderung der Anleihe Im Folgenden werden die Ergebnisse der drei Berechnungsmethoden verglichen: Berechnungsmethode: Neuberechnung des Istwerts Projektion mit modifizierter Duration Projektion Unter Verwendung von modifizierter Dauer und Konvexität Ergebnisse 7.06 7.38 7.03 Dies zeigt, dass die Berücksichtigung der Konvexität ein Ergebnis ähnlich dem bei der Neuberechnung erzielten Preis ergibt, während die Schätzung mit der modifizierten Dauer signifikant abweicht. Jedoch sollte man beachten, dass ein einheitlicher Zinssatz für alle verbleibenden Lebensdauern (flache Zinskurve) in allen drei Beispielen verwendet wurde. 17 Eurex Fixed Income Derivatives Merkmale von börsengehandelten Finanzderivaten Einleitung Verträge, für die die Kurse aus zugrunde liegenden Kassamarktpapieren oder Rohstoffen (die als Basiswerte oder Basiswerte bezeichnet werden), wie Aktien, Anleihen oder Öl, werden als Derivate bezeichnet Instrumente oder einfach Derivate. Handelsderivate zeichnen sich dadurch aus, dass die Abrechnung an bestimmten Terminen (Abwicklungstag) erfolgt. Die Zahlung bei Lieferung für Kassamarktgeschäfte muss nach zwei oder drei Tagen (Abrechnungszeitraum) erfolgen, wobei börsengehandelte Futures und Optionskontrakte mit Ausnahme von Ausübungsoptionen die Abrechnung an nur vier bestimmten Terminen während des Jahres vorsehen können. Derivate werden sowohl auf organisierten Derivatemärkten wie Eurex und im Freiverkehrsmarkt (OTC) gehandelt. Die standardisierten Kontraktspezifikationen und der Markierungs - oder Marginierungsprozess über eine Clearingstelle unterscheiden börsengehandelte Produkte aus OTC-Derivaten. Eurex listet Futures und Optionen auf Finanzinstrumente. Flexibilität Organisierte Derivatemärkte bieten den Anlegern die Möglichkeit, auf der Grundlage ihrer Marktwahrnehmung und entsprechend ihrer Risikobereitschaft eine Position einzugehen, ohne jedoch Wertpapiere kaufen oder verkaufen zu müssen. Durch die Eingabe eines Zählgeschäfts können sie ihre Position vor dem Vertragsfälligkeitstermin neutralisieren (schließen). Gewinne oder Verluste aus offenen Positionen in Futures oder Optionen auf Futures werden täglich gutgeschrieben oder belastet. Transparenz und Liquidität Der Handel mit standardisierten Verträgen führt zu einer Konzentration der Auftragsströme und sichert so die Marktliquidität. Liquidität bedeutet, dass große Mengen eines Produkts jederzeit ohne übermäßige Preisauswirkungen gekauft und verkauft werden können. Der elektronische Handel von Eurex garantiert eine umfassende Transparenz von Preisen, Mengen und ausgeführten Transaktionen. Hebelwirkung Beim Abschluss eines Options - oder Termingeschäfts ist es nicht notwendig, den vollen Wert des Basiswertes nach vorne zu bezahlen. Daher ist das prozentuale Gewinn - oder Verlustpotenzial für diese Termingeschäfte im Hinblick auf das eingesetzte oder verpfändete Kapital wesentlich stärker als bei den tatsächlichen Anleihen oder Aktien. 18 Einführung in Fixed Income Futures Was sind Fixed Income Futures Definition Fixed Income Futures sind standardisierte Termingeschäfte zwischen zwei Parteien, die auf festverzinslichen Instrumenten wie Anleihen mit Coupons basieren. Sie umfassen die Verpflichtung. erwerben. Oder zu liefern. Ein gegebenes Finanzinstrument. Mit einer gegebenen Restlebensdauer in einer festgelegten Menge. Zu einem festgelegten Zeitpunkt. Zu einem bestimmten Preis Kontraktgröße Fälligkeit Futures Preis Käufer Verkäufer Basiswert Langfristig Kurzfristig künftige deutsche Staatsanleihen 8,5-10,5 Jahre 100 000 EUR Nominale 10.03.2002 106,00 Lange Zukunft Kurze künftige Eidgenossenschaft Anleihen 8-13 Jahre CHF 100'000 nominal 10. März 2002 120,50 Eurex-Fixed-Income-Derivate basieren auf der Lieferung einer zugrunde liegenden Anleihe, die eine Restlaufzeit gemäß einem vordefinierten Bereich aufweist. Die Liste der vertraglichen Lieferungen enthält Anleihen mit verschiedenen Coupons, Preisen und Fälligkeiten. Zur Vereinheitlichung des Lieferprozesses wird das Konzept einer Nominalbindung herangezogen. Weitere Details finden Sie im Abschnitt "Vertragsspezifikation und Umrechnungsfaktoren". Futures-Positionen Verpflichtungen Eine Futures-Position kann entweder lang oder kurz sein: Long-Position Kauf eines Futures-Kontrakts Die Käufer-Verpflichtungen: Bei Fälligkeit führt eine Long-Position automatisch zur Verpflichtung zum Kauf von zu liefernden Obligationen: Die Verpflichtung zum Kauf des Zinsinstruments, Vertrag zu dem am Liefertermin festgesetzten Preis. Short-Position Verkauf eines Futures-Kontrakts Die Verpflichtungen des Verkäufers: Bei Fälligkeit führt eine Short-Position automatisch zur Verpflichtung zur Lieferung solcher Schuldverschreibungen: Die Verpflichtung zur Lieferung des für den Kontrakt relevanten Zinsinstruments zu dem am Liefertermin festgesetzten Kurs. 19 Settlement oder Closeout Futures werden grundsätzlich durch Barausgleich oder physische Lieferung des Basiswertes abgewickelt. Eurex Fixed Income Futures sorgen für die physische Lieferung von Wertpapieren. Der Inhaber einer Short-Position ist verpflichtet, entweder langfristige Eidgenossen - schaften oder kurz-, mittel - oder langfristige Schuldtitel der Bundesrepublik Deutschland zu liefern, je nach dem gehandelten Kontrakt. Der Inhaber der entsprechenden Long-Position muss die Lieferung gegen Zahlung des Lieferpreises annehmen. Wertpapiere der jeweiligen Emittenten, deren Restlaufzeit am Futures-Liefertermin innerhalb der für jeden Vertrag festgelegten Parameter liegt, können ausgeliefert werden. Diese Parameter werden auch als Fälligkeitsbereiche für die Lieferung bezeichnet. Die Wahl der zu liefernden Anleihe muss mitgeteilt werden (die Mitteilungspflicht des Inhabers der Short-Position). Die Auswahl und Bewertung einer Schuldverschreibung ist im Abschnitt über die Schuldverschreibung beschrieben. Es ist jedoch erwähnenswert, dass es beim Eintritt in eine Futures-Position nicht notwendigerweise auf der Absicht beruht, die Basisinstrumente bei Fälligkeit tatsächlich zu liefern oder zu übernehmen. Beispielsweise sollen Futures die Kursentwicklung des Basiswertes während der Laufzeit des Kontrakts verfolgen. Im Falle einer Preiserhöhung im Futures-Kontrakt kann ein originärer Käufer eines Futures-Kontrakts einen Gewinn erzielen, indem er einfach eine gleiche Anzahl von Kontrakten an die ursprünglich gekauften Kontrakte verkauft. Das Gegenteil gilt für eine Short-Position, die durch den Rückkauf Futures geschlossen werden kann. Daher tritt in den Tagen vor der Fälligkeit eines Anleihe-Futures-Kontraktes eine spürbare Reduzierung des offenen Interesses (die Anzahl der offenen Long - und Short-Positionen in jedem Kontrakt) ein. Während der Vertragslaufzeit kann offene Verzinsung das Volumen der verfügbaren lieferbaren Anleihen deutlich übersteigen, diese Zahl wird erheblich sinken, sobald sich die offene Verzinsung vom kürzesten Liefermonat zum nächsten, vor der Fälligkeit (ein Vorgang, bekannt als Rollover) . 20 Kontraktspezifikationen Informationen zu den detaillierten Kontraktspezifikationen der an Eurex gehandelten Fixed Income Futures finden Sie in der Eurex-Produktbroschüre oder auf der Eurex-Homepage. Die wichtigsten Spezifikationen von Eurex-Fixed-Income-Futures sind im folgenden Beispiel auf der Basis von Euro-Bund-Futures und CONF-Futures aufgeführt. Ein Anleger kauft: 2 Kontrakte Die Futures-Transaktion basiert auf einem Nominalwert von 2 x EUR 100.000 an lieferbaren Anleihen für die Euro Bund Future oder 2 x CHF 100.000 an lieferbaren Anleihen für die CONF Future. Die nächsten drei Quartalsmonate in den Zyklus MärzJuneSeptemberDezember sind für den Handel zur Verfügung. So haben die Euro Bund und CONF Futures eine maximale Restlebensdauer von neun Monaten. Der letzte Handelstag ist zwei Börsentage vor dem 10. Kalendertag (Lieferungstag) des Fälligkeitsmonats. Das Basisinstrument für Euro-Bund-Futures ist eine 6-fach langfristige deutsche Staatsanleihe. Bei CONF Futures handelt es sich um eine Eidgenossenschaft. Der Futures-Preis wird in Prozent auf zwei Dezimalstellen des Nominalwertes der zugrunde liegenden Anleihe notiert. Die Mindestpreisänderung (Tick) beträgt EUR 10,00 bzw. CHF 10,00 (0,01). Juni 2002 Fälligkeitsmonat Euro Bund oder CONF Futures. Bei 106,00 bzw. 120,50 Bezugsinstrument Futures-Preis In diesem Beispiel ist der Käufer verpflichtet, entweder deutsche Staatsanleihen oder schweizerische Schuldverschreibungen, die in den Korb der lieferbaren Schuldverschreibungen enthalten sind, zu einem Nennwert von EUR oder CHF 200'000 zu kaufen Juni 2002. 21 Eurex-Fixed-Income-Futures-Übersicht Die Spezifikationen von festen Icome-Futures unterscheiden sich im Wesentlichen durch die Körbe der lieferbaren Anleihen, die unterschiedliche Laufzeitbereiche abdecken. Die entsprechenden Restlaufzeiten sind in der folgenden Tabelle aufgeführt: Basiswerte: Schuldverschreibungen Euro Schatz Zukunfts Euro Bobl Zukünftiger Euro Bund Zukünftiger Euro Buxl Zukünftig Basiswert: Schweizerische Eidgenossenschaft KONF Future Nominaler Kontraktwert EUR 100.000 EUR 100.000 EUR 100.000 EUR 100.000 Nominaler Kontraktwert CHF 100.000 Restlaufzeit der lieferbaren Anleihen 134 bis 2 14 Jahre 412 bis 512 Jahre 812 bis 1012 Jahre 20 bis 3012 Jahre Restlaufzeit der lieferbaren Anleihen 8 bis 13 Jahre Produktcode FGBS FGBM FGBL FGBX Produktcode CONF Futures Spread Margin Und zusätzliche Marge Bei der Erstellung einer Futures-Position wird die Eurex Clearing AG, das Eurex Clearing House, Geld oder andere Sicherheiten hinterlegt. Die Eurex Clearing AG beabsichtigt, allen Clearing-Mitgliedern eine Garantie für den Fall eines Mitgliedsausfalls zu gewähren. Diese zusätzliche Margin-Einlage dient dem Schutz der Clearingstelle gegen eine nachteilige Kursbewegung im Futures-Kontrakt. 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 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 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 contracts 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 futures position: Daily futures settlement price Futures purchase or selling price Variation margin The daily settlement price of the CONF Future in our example is 121.65. The contracts were bought at a price of 121.50. 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 121.65 121.50 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. 1,000 0.01). This is known as the tick value. Therefore the profit on the one futures trade is 15 CHF 10 1 CHF 150. 23 The same process applies to the Euro Bund Future. The Euro Bund Futures daily settlement price is 105.70. It was bought at 106.00. The variation margin calculation results in the following: Example 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 105.70 106.00 30 ticks loss multiplied by the tick value of one bund future (EUR 10) EUR 300. Calculating the variation margin during the contracts 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 Bond 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. An investor 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 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 Today Futures lifetime Futures delivery Period Futures purchase investmentvaluation Entering into a futures position (no cash outflow) Investing the equivalent value of the financing cost saved, on the money market Portfolio value Bond (purchased at the futures price) income from the money market investment of the financing costs saved Cash bond purchase investmentvaluation Bond purchase (market price plus accrued interest) Coupon credit (if any) and money market investment of the equivalent value Portfolio value Value of the bond including accrued interest any coupon credits any interest on the 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 Ct ( Ct c t t0 T t T t ) t rc c 365 360 365 Whereby: Ct: c: t0: t: t rc. Current clean price of the underlying security (at time t) Bond coupon (percent actualactual for euro-denominated bonds) Coupon date Value date Short-term funding rate (percent actual 360) Futures delivery date Futures remaining lifetime (days) T: T-t: 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 Cost of Carry and Basis The difference between the financing costs and the proceeds from 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 higher or lower than the price of the underlying instrument, depending on whether the cost of carry is negative or positive. 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 Proceeds from the cash position: Negative cost of carry Financing costs Positive cost of carry 8 Cost of carry and basis are frequently shown in literature using a reverse sign. 26 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 6 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 contracts 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 eurexchange. 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 t t0 T t T t Ct (Ct c ) t rc c CF 365 360 365 The following example describes how the theoretical price of the Euro Bund Future June 2002 is calculated. 27 Example: Trade date Value date Cheapest-to-deliver bond Price of the cheapest-to-deliver Futures delivery date Accrued interest Conversion factor of the CTD Money market rate May 3, 2002 May 8, 2002 3.75 Federal Republic of Germany debt security due on January 4, 2011 90.50 June 10, 2002 3.75 (124 365) 100 1.27 0.852420 3.63 Theoretical futures price 1 33 33 90.50 (90.50 1.27) 0.0363 3.75 0.852420 360 365 Theoretical futures price 1 90.50 0.3054 0.3390 0.852420 Theoretical futures price 106.13 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 At delivery, basis will be zero. Therefore, at this point we can manipulate the formula to achieve the following relationship: Cash bond price Conversion factor Futures price 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 5 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 5 6 7 Maturity 07152012 03042012 05132011 Conversion factor 0.925836 0.999613 1.067382 Price at 5 yield 99.99 107.54 114.12 Price divided by conversion factor 108.00 107.58 106.92 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 106.92. In reality of course only one real futures price exists at delivery. Suppose that at delivery the real futures price was 106.94. If that was the case an arbitrageur could buy the cash bond (7 051302) at 114.12 and sell it immediately via the futures market at 106.94 1.067382 and receive 114.14. This would create an arbitrage profit of 2 ticks. Neither of the two other bonds would provide an arbitrage profit, however, with the futures at 106.94. Accrued interest is ignored in this example as the bond is bought and sold into the futures contract on the same day. 29 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 fulfil 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 5 6 7 Maturity Conversion factor Price at 5 99.99 107.54 114.12 Price CF 107.99 107.58 106.92 Price at 6 92.58 99.97 106.75 Price CF 100.00 100.00 100.01 Price at 7 85.84 93.07 99.99 Price CF 92.72 93.11 93.68 07152012 0.925836 03042012 0.999613 05132011 1.067382 q 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. q If the market yield is below the notional coupon level, bonds with a shorter duration (higher coupon given similar maturities shorter maturity given similar coupons) will be preferred for delivery. q When yields are at the notional coupon level (6) the bonds are almost all equally preferred for delivery. As we pointed out above, this bias is caused by theincorrect discount rate of 6 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 6 percent. 9 Cf. chapters Macaulay Duration and Modified Duration. 30 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 07152012 106.92 100.00 92.72 5 Zero basis futures price Market yield 6 7 5 07152012 6 03042012 7 05132011 31 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 forecast 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 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). 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 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 forecast 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 investor wants to benefit from a forecast development without tying up capital in the cash market. Initial Situation The investor assumes that yields on German Federal Debt Obligations (Bundesobligationen) will fall. Strategy The investor buys 10 Euro Bobl Futures June 2002 at a price of 105.10, with the intention to close out the position during the contracts lifetime. If the price of the Euro Bobl Futures rises, the investor 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. The calculation of additional and variation margins for a hypothetical price development 33 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 selling price 105.10 Daily settlement price 104.91 Variation margin 10 profit in EUR Variation margin loss in EUR 1,900 Additional margin 11 in EUR 10,000 0311 Buy 10 Euro Bobl Futures June 2002 0312 0313 0314 0315 0318 0319 0320 Sell 10 Euro Bobl Futures June 2002 105.37 104.97 104.80 104.69 104.83 105.14 105.02 600 1,700 1,100 1,400 3,100 1,200 3,500 0321 Total 0.27 Changed Market Situation: 8,600 5,900 10,000 0 The investor closes out the futures position at a price of 105.37 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 10 contracts multiplied by the value of EUR 10: (105.37 105.10) 10 EUR 10 EUR 2,700. 10 Cf. chapter Variation Margin. 11 Cf. chapter Futures Spread Margin and Additional Margin. 34 Short Positions (Bearish Strategies) Investors who expect market yields to rise sell futures contracts. The short fixed income futures diagram illustrates the outcome of the futures price and its corresponding profit and loss potential. Profit and Loss Profile on the Last Trading Day, Short Fixed Income Futures 0 Profit and loss Bond price PL short fixed income futures Rationale The investor wishes to benefit from rising yields, but is unable to sell the actual bonds short (i. e. sell them without owning them). Initial Situation The investor expects yields for short-term (two-year) German Federal Treasury Notes (Bundesschatzanweisungen) to rise. 35 Strategy The investor decides to enter into a short position of 20 Euro Schatz Futures June 2002 contracts at a price of 102.98. After a certain period of time, heshe closes out this position by buying back the contracts. Again, the additional margin is derived by multiplying the margin parameter, as set by Eurex Clearing AG ( in this case EUR 500 per contract), by the number of contracts. Date Transaction Purchase selling price 102.98 Daily settlement price 103.00 Variation margin 12 profit in EUR Variation margin loss in EUR 400 Additional margin 13 in EUR 10,000 0311 Sell 20 Euro Schatz Futures June 2002 0312 0313 0314 0315 0318 0319 0320 Buy 20 Euro Schatz Futures June 2002 103.60 102.60 102.48 102.52 103.20 103.45 103.72 8,000 2,400 800 13,600 5,000 5,400 2,400 0321 Total 0.62 Changed Market Situation 12,800 25,200 10,000 0 The investor closes out the futures position at a price of 103.60 on March 20. The additional margin pledged is released the following day. Result The loss of EUR 12,400 is equivalent to the sum of the variation margin cash flows (EUR 12,800 EUR 25,200) calculated on a daily basis. Alternatively the net result is the sum of the futures price movement multiplied by 20 contracts multiplied by the value of EUR 10: (102.98 103.60) 20 EUR 10 EUR 12,400 Spread Strategies A spread is the simultaneous purchase and sale of futures contracts. Spread positions are designed to achieve profits on expected changes in the price difference between the long and short positions. There are various types of spreads. This section describes time spreads and inter-product spreads. 12 Cf. chapter Variation Margin. 13 Cf. chapter Futures Spread Margin and Additional Margin. 36 Time Spread A time spread comprises long and short positions in futures with the same underlying instrument but with different maturity dates. This strategy is based on one of two assumptions: the first motivation is a forecast change in the price difference between both contracts, because of expected shifts in the financing costs for different maturities. Alternatively, a spread position could be based on the perception of mispricing of one contract (or both contracts) and the expectation that this mispricing will be corrected by the market. The simultaneous establishment of long and short positions is subject to lower risks compared to outright long or short positions. Even when the expectations are not met, the loss incurred on one futures position is largely offset by the counter position. This is why Eurex Clearing AG demands reduced margin rates for time spread positions ( Futures Spread Margin instead of Additional Margin). Time Spread Purchase Simultaneous purchase of a fixed income futures contract with a shorter lifetime and the sale of the same futures contract with a longer lifetime Sale Simultaneous sale of a fixed income futures contract with a shorter lifetime and the purchase of the same futures contract with a longer lifetime. where a positive (negative) spread between. where a positive (negative) spread between the shorter and the longer maturity is expected the shorter and the longer maturity is expected to widen (narrow) or to narrow (widen) or. where the contract with the longer lifetime is overvalued in relative terms. Rationale An investor analyzes the value of the September 2002 Euro Bobl Future in April and establishes that the contract is overvalued. The investor expects the spread between the June and September Euro Bobl Futures to widen. Initial Situation Valuation date Euro Bobl Futures June 2002 Euro Bobl Futures September 2002 April 18, 2002 (today) 104.81 104.75. where the contract with the shorter lifetime is overvalued in relative terms. 37 Strategy Purchase of 5 Euro Bobl Futures JuneSeptember 2002 time spreads. Euro Bobl Futures June 2002 bought at a price of Euro Bobl Futures September 2002 sold at a price of Price of JuneSeptember spread bought 104.81 104.75 0.06 Changed Market Situation The investors expectations have come true in May. Heshe decides to close out the spread position and to realize hisher profit. Euro Bobl Futures June 2002 sold at a price of Euro Bobl Futures September 2002 bought at a price of Price of JuneSeptember spread sold 105.34 104.99 0.35 Result JuneSeptember spread entry level JuneSeptember spread closeout level Result per contract 0.06 0.35 0.29 The total profit for 5 contracts is 5 29 EUR 10 EUR 1,450.00. Inter-Product Spread Inter-product-spreads involve long and short futures positions with different underlying instruments. This type of strategy is directed at varying yield developments in the respective maturity sectors. Assuming a normal yield curve, if 10-year yields rises more than 5-year or 2-year yields, the yield curve is steepening, whereas a flattening indicates approaching short-, medium - and long-term yields. In comparison to outright position trading, inter-product spreads are also subject to lower risks. When calculating additional margin, the correlation of the price development is taken into account by the fact that the Euro Bund and the Euro Bobl Futures form part of the same margin group 14. Due to the different interest rate sensitivities of bonds with different remaining lifetimes and the corresponding futures contracts, the long and short positions (the legs of the strategy) must be weighted according to the modified duration of the contracts. Otherwise parallel shifts in the yield curve would lead to a change in the value of the spread. 14 Cf. Risk Based Margining brochure. 38 Inter-Product Spread Purchase Simultaneous purchase of a fixed income future on a shorter-term underlying instrument and sale of a fixed income future on a longer-term underlying instrument, with identical or similar maturities the yield curve is expected to steepen. Sale Simultaneous sale of a fixed income future on a shorter-term underlying instrument and the purchase of a fixed income future on a longerterm underlying instrument, with identical or similar maturities the yield curve is expected to flatten. Motive In mid-May, assuming a normal relationship between the five and ten-year sectors, the investor expects the yield curve to become steeper. This means that long-term yields will rise more (or fall less) than medium-term yields. Initial Situation Valuation date Euro Bobl Futures June 2002 Euro Bund Futures June 2002 Euro BoblEuro Bund ratio May 13, 2002 104.84 106.00 5:3 Strategy By buying in the ratio of 10 Euro Bobl Futures and simultaneously selling 6 Euro Bund Futures, the investor wants to benefit from the forecast interest rate development. Due to the different interest rate sensitivities of the respective issues, the medium-term and long-term positions are weighted differently. The strategys success depends mainly on the yield differential and not on the absolute level of market yields. Changed Market Situation 10-year yields have risen by twenty basis points, compared to ten basis points in the 5-year sector by the beginning of June. The Euro Bund and Euro Bobl Futures prices have developed as follows: Valuation date Euro Bobl Futures June 2002 Euro Bund Futures June 2002 June 6, 2002 104.40 104.52 39 The investor decides to close out hisher position, and obtains the following result: Result from the Euro Bobl position Euro Bobl Futures June 2002 bought at a price of Euro Bobl Futures June 2002 sold at a price of Loss per contract Loss incurred on the Euro Bobl position (10 contracts) Result from the Euro Bund position Euro Bund Futures June 2002 sold at a price of Euro Bund Futures June 2002 bought at a price of Profit per contract Profit made on the Euro Bund position (6 contracts) Total result in EUR The investor made a total profit of EUR 4,480. 106.00 104.52 104.84 104.40 EUR 104,840 104,400 440 4,400 EUR 106,000 104,520 1,480 8,880 4,400 8,880 4,480 Hedging Strategies Potential hedgers who hold a long (short) position in the cash bond market will seek to protect their position from short term adverse movements in yields, by using futures. Depending on the position to be hedged, they will buy or sell futures and thus, in effect, fix a future price level for their underlying position. Hedging of interest rate positions largely comprises choosing a suitable futures contract, determining the number of contracts required to hedge the cash position (the hedge ratio) and deciding on the potential adjustments to be made to the hedge ratio during the period in question. 40 Choice of the Futures Contract Ideally, a futures contract is used to hedge securities that belong to the basket of deliverable bonds. When hedging an existing portfolio, for instance, the investor is free to either close out the futures position before the last trading day (liquidating the hedge position), or to deliver the securities at maturity. Where the creation of a portfolio is planned, the long position holder can decide to either take delivery of the securities when the contract is settled or alternatively, to close out the futures position and buy them on the cash market. Where there is no futures contract corresponding to the life-time of the bonds to be hedged, or if hedging individual securities in the portfolio is too complex, contracts showing a high correlation to the portfolio are used. Perfect Hedge versus Cross Hedge A strategy where losses incurred on changes in the value of the cash position are almost totally compensated for by changes in the value of the futures position is called a perfect hedge. In practice, due to the stipulation of trading integer numbers of contracts and the incongruity of cash securities and futures, a totally risk-free portfolio is not usually feasible. Frequently there is also a difference between the remaining lifetime of the futures contracts and the hedging period. A cross hedge involves strategies where for the reasons outlined above the hedge position does not precisely offset the performance of the hedged portfolio. Hedging Considerations Basis risk the cost of hedging The performance of any hedge, however, does depend upon the correlation between the price movement of the underlying asset to be hedged and that of the futures or options contract used. With government bond futures we know that the futures price will closely track the price movement of the cheapest-to-deliver (CTD) bond. Hedging with exchange traded futures has the effect of transferring outright market risk into what is termed basis risk. Basis risk reflects the over - or underperformance of a hedge, and is due to the nature of the hedge instrument vis--vis the underlying asset to be hedged. 41 Degree of basis risk Hedgers are often prepared to tolerate a certain degree of basis risk in order to manage their bigger exposure to the market. Since exchanges provide very liquid and transparent marketplaces for government bond futures, it is not uncommon for certain hedgers to use these contracts to hedge non-CTD bonds which may even include corporate bonds. Naturally, the greater the disparity between the bond to be hedged and the actual CTD bond, the less reliable the hedge will be, creating in some cases significant basis risk. CTD and non-CTD hedges We have already seen (see chapter Conversion Factor (Price Factor) and Cheapest-toDeliver (CTD) Bond) how the hedge ratio employs the use of the price factor. When hedging a CTD bond the price factor allows for a good hedge performance provided the shape of the yield curve doesnt alter too much over time. If a change in the yield curve results in a change in the status of the CTD bond during the life of the hedge, then the success of the futures hedge may be affected. The hedger needs to monitor the situation and, if need be, alter the hedge position to reflect the changed relationship. Determining the Hedge Ratio The relationship of the futures position to the portfolio in other words, the number of futures contracts required for the hedge is referred to as the hedge ratio. Given the contract specifications, only integer multiples of a futures contract may be traded. Various procedures to determine the hedge ratio have been developed, providing differing degrees of precision. The following section outlines the most common procedures. 42 Nominal Value Method In this method, the number of futures contracts to be used is derived from the relationship between the portfolios nominal value and that of the futures contracts chosen for the hedge. While being the simplest of the methods described, the nominal value method is also the most imprecise in mathematical terms. The hedge ratio is determined as follows using the nominal value method: Hedge ratio Nominal value of the bond portfolio Nominal value of fixed income futures Nominal value of the bond portfolio Sum of nominal value of the bonds Nominal value of the fixed income futures Nominal contract size of a fixed income future (CHF 100,000 or EUR 100,000) Possible different interest rate sensitivity levels of the futures and bonds are not accounted for. Modified Duration Method The modified duration can be used to calculate the interest rate sensitivity of the cash and futures position, and to set the hedge ratio accordingly. The modified duration method uses the following given factors to calculate the hedge ratio: The cheapest-to-deliver (CTD) bond The modified duration as the underlying security of the futures15 of the individual positions and thus of the total portfolio, as a measure of their interest rate sensitivity. The modified duration of the portfolio corresponds to the modified duration of its component securities, weighted using the present value16 which standardizes the different coupons to 617. The conversion factor 15 Cf. chapter Conversion Factor (Price Factor) and Cheapest-to-Deliver (CTD) Bond. 16 Cf. chapters Macaulay Duration and Modified Duration. 17 Cf. chapter Conversion Factor (Price Factor) and Cheapest-to-Deliver (CTD) Bond. 43 The modified duration of the futures position is expressed as the modified duration (MD) of the cheapest-to-deliver bond, divided by the conversion factor (based on the assumption that futures price cheapest-to-deliverconversion factor). Using the modified duration method, the hedge ratio is calculated as follows: Hedge ratio Market value of the bond portfolio Modified duration of the bond portfolio Conversion factor Price (CTD) 1,000 Modified duration (CTD) This method is limited by the conditions of the duration model, as illustrated in the sections on Macaulay Duration and Modified Duration. However, the error of assessment in this calculation method is partly compensated for by the fact that both the numerator and the denominator are affected by the simplified assumptions in the hedge ratio calculation. Motive A pension fund manager is expecting a term deposit of CHF 10,000,000 to be repaid in mid-June. As heshe expects interest rates in all maturity sectors to fall, heshe wants to lock in the current (March) price level of the Swiss bond market. Initial Situation Market value of the bond portfolio Price of the CTD bond CONF Future June 2002 Modified duration of the bond portfolio Modified duration of the CTD CTD conversion factor Strategy A profit should be made on the futures position by buying CONF Futures June 2002 in March at a price of 120.50 and closing out at a higher price at a later date. This should largely compensate for the forecast price increase of the planned bond purchase. Hedge ratio using the modified duration method: 10,000,000 7.00 0.819391 76.84 contracts 98,740 7.56 CHF 10,000,000 98.74 120.50 7.00 7.56 0.819391 Hedge ratio The hedge is entered into in March by buying 77 CONF Futures contracts at a price of 120.50. 44 Changed Market Situation In line with expectations, market yields have fallen by 0.30 percentage points ( 30 basis points, bp) in June. The investor closes out the futures position. Market value of the bond portfolio Price of the CTD bond Price CONF Future June 2002 CHF 10,210,000 101.01 123.27 Result Date March June Bond portfolio Market value Market value Loss CHF 10,000,000 10,210,000 210,000 CONF Future 77 contracts bought at 120.50 77 contracts sold at 123.27 Profit CHF 9,278,500 9,491,790 213,290 The overall result of the investors position is as follows: CHF CHF Profit (long CONF position) Loss (higher bond purchase price) Result of the hedge 213,290 210,000 3,290 The increased investment of CHF 210,000 was more than offset by the counter position. Sensitivity Method The sensitivity or basis point value method is also based on the duration concept. Hence, the same assumptions prevail. However, interest rate sensitivity, as an indicator of the change in value of a security, is expressed as a one basis point (0.01 percent) interest rate change. Using the sensitivity method, the hedge ratio is calculated as follows 18: Hedge ratio Basis point value of the cash position Conversion factor Basis point value of the CTD bond Basis point value (sensitivity) of the cash position Market value of the bond portfolio MDbond portfolio 10,000 Basis point value (sensitivity) of the CTD bond Market value of the CTD bond MDCTD 10,000 18 The basis point value is equivalent to the modified duration, divided by 10,000, as it is defined as absolute (rather than percent) present value change per 0.01 percent (rather than 1 percent) change of market yields. 45 Motive An institutional investor wants to cut down hisher bond portfolio in the coming two months. It is valued at EUR 40,000,000 as of March. The investor fears that market interest rates could rise and prices could fall until the time of the planned sale. Initial Situation Market value of the bond portfolio Price Euro Bund Future June 2002 Price of the CTD bond Modified duration of the bond portfolio Basis point value of the bond portfolio Modified duration of the CTD CTD conversion factor Basis point value of the CTD bond EUR 40,000,000 106.00 95.12 8.20 EUR 32,800.00 7.11 0.897383 EUR 67.63 Strategy A profit is made on the futures position by selling the Euro Bund Futures June 2002 at a price of 106.00 in March and buying them back cheaper at a later date. This should compensate for the price loss incurred on the bonds. Hedge ratio using the basis point value method: Hedge ratio Basis point value of the bond portfolio Conversion factor Basis point value of the CTD bond Hedge ratio 32,800.00 0.897383 435.22 contracts 67.63 The position can be hedged by selling 435 Euro Bund Futures June 2002 in March, at a price of 106.00. Changed Market Situation Market yields have risen by 0.30 percentage points ( 30 basis points, bp) in June. The investor closes out the short futures position by buying back the Euro Bund Futures June 2002. Market value of the bond portfolio: Market value of the CTD bond: Euro Bund Future June 2002: EUR 39,016,000 EUR 93,091.10 103.73 46 Result Date March June Bond portfolio Market value Market value Loss EUR 40,000,000 39,016,000 984,000 Euro Bund Future 435 contracts sold at 106.00 435 contracts bought at 103.73 Profit EUR 46,110,000 45,122,550 987,450 The overall result of the investors position is as follows: EUR EUR EUR Profit (short Euro Bund position) Loss (loss in value of the portfolio) Result of the hedge 987,450 984,000 3,450 The profit made on the Euro Bund Futures position more than compensates for the loss incurred on the bond portfolio. Static and Dynamic Hedging Simplifying the interest rate structure upon which the hedging models are based can, over time, lead to inaccuracies in the hedge ratio. Hence, it is necessary to adjust the futures position to ensure the desired total or partial hedge. This kind of continuous adjustment is called dynamic hedging or tailing. In contrast, static hedging means that the original hedge ratio remains unchanged during the life of the hedge. Investors must weigh up the costs and benefits of an adjustment. Cash-and-Carry Arbitrage In principle, arbitrage is defined as creating risk-free (closed) positions by exploiting mispricing in derivatives or securities between two market places. The so-called cashand-carry arbitrage involves the purchase of bonds on the cash market and the sale of the relevant futures contracts. Selling bonds and simultaneously buying futures is referred to as a reverse cash-and-carry arbitrage. In each case, the investor enters into a long position in an undervalued market (cash or futures). Although these arbitrage transactions are often referred to as risk-free, their exact result depends on a variety of factors, some of which may in fact hold certain risks. These factors include the path of price developments and the resulting variation margin flows, as well as changes in the CTD during the term of the transaction. A detailed review of all influences on cash-andcarryreverse cash-and-carry positions would exceed the scope of this brochure. The theoretically correct basis can be determined by discounting the delivery price. Cashand-carry opportunities tend to arise for very short periods only and rarely exceeds the transaction costs incurred. 47 The principle of cash-and-carry arbitrage is explained below, using the valuation example taken from the section on futures pricing. Starting Scenario Valuation date CTD bond Price of the CTD bond Accrued interest Conversion factor Money market rate Theoretical futures price 19 Traded futures price Delivery date of the future May 8, 2002 (today) 3.75 Federal Republic of Germany debt security due on January 4, 2011 90.50 3.75 124 365 100 1.274 0.852420 3.63 106.12 106.46 June 10, 2002 If the futures contract trades above its theoretically correct price, the arbitrageur buys deliverable bonds and enters into a short position in the relevant futures contract. The arbitrageur carries out the following transactions, based on an individual futures contract: Transaction CTD bought Financing costs until futures maturity Total amount invested in the bonds EUR 91,774.00 301.19 92,075.19 Remarks Clean price 90,500 1,274 accrued interest 91,774.00 0.0363 (33 365) years 91,774.00 301.19 This total investment must be compared to the delivery price at the futures maturity, in addition to the profit and loss settlement during the lifetime. The delivery price is derived from the final settlement price, multiplied by the conversion factor plus the accrued interest. Transaction Futures sold Final settlement price Profit from variation margin delivery price EUR 106,460.00 106,350.00 110.00 92,267.87 106,350 0.852420 1,613.00 accrued interest Remarks Value on May 4 If the profit made on the short position is added as income to the delivery price, the profit made on the arbitrage transaction is equivalent to the difference to the capital invested. Total profit: 92,267.87 110.00 92,075.19 302.68 The price imbalance has resulted in a profit of EUR 302.68 for the investor. 19 Cf. chapter Conversion Factor and Cheapest-to-Deliver Bond. 48 Introduction to Options on Fixed Income Futures Options on Fixed Income Futures Definition An option is a contract entered into between two parties. By paying the option price (the premium) the buyer of an option acquires the right, for example. to buy. or to sell. a given fixed income future. in a set amount. for a set exercise period. at a determined price Call option Put option Underlying instrument Contract size Expiration Exercise price Calls Puts Euro Bund Future One contract May 24, 2002 106.50 If the buyer claims hisher right to exercise the option, the seller is obliged to sell (call) or to buy (put) the futures contract at a set exercise price. The option buyer pays the option price (premium) in exchange for this right. This premium is settled according to the futures-style method. In other words the premium is not fully paid until the option expires or is exercised. This means that, as with futures, the daily settlement of profits and losses on the option premium is carried out via variation margin (cf. Chapter Variation Margin). Options on Fixed Income Futures Rights and Obligations Investors may assume a position in the option market by buying or selling options: Long position An investor buying options assumes a long position. This can be a long call or a long put position, depending on the contract. Short position An investor selling an option assumes a short position. This can be a short call or a short put position, depending on the contract. 49 Buyers and sellers of options on fixed income futures have the following rights and obligations: Call option Call buyer Long call The buyer of a call has the right, but not the obligation, to buy the futures contract at an exercise price agreed in advance. Call seller Short call In the event of exercise, the seller of a call is obliged to sell the futures contract at an exercise price agreed in advance. Put option Put buyer Long put The buyer of a put has the right, but not the obligation, to sell the futures contract at an exercise price agreed in advance. Put seller Short put In the event of exercise, the seller of a put is obliged to buy the futures contract at an exercise price agreed in advance. An option position on fixed income futures can be liquidated by closing it out (see below) the buyer of the option can also close it by exercising the option. Closeout Closing out means neutralizing a position by a counter transaction. In other words, a short position of 2,000 Euro Bund Futures June 2002 calls with an exercise price of 104.50 can be closed out by buying 2,000 call options of the same series. In this way, the sellers obligations arising from the original short position have lapsed. Accordingly, a long position of 2,000 Euro Bund Futures June 2002 puts with an exercise price of 104.50 can be closed out by selling 2,000 put options of the same series. Exercising Options on Fixed Income Futures If an option on a fixed income future is exercised by the holder of the long position, the clearinghouse matches this exercise with an existing short position, using a random process. This is referred to as an assignment of the short position. When this happens, the options are dissolved and the buyer and seller enter into the corresponding futures positions. The decisive factor is the options exercise price, which is applicable as the purchase or sale price of the futures position. The corresponding futures positions opened according to the original options position are outlined in the following table: Exercising a. long call option long futures position long put option short futures position Assignment of a. short call option short futures position short put option long futures position leads to the following position being opened. Options on fixed income futures can be exercised on any exchange trading day until expiration (American-style options). The option expiration date is prior to the last trading day of the futures contract. An option holder wishing to exercise hisher right must inform the clearing house, which in turn nominates a short position holder by means of a neutral random assignment procedure. 50 Contract Specifications Options on Fixed Income Futures Eurex options are exchange-traded contracts with standardized specifications. The Eurex product specifications are set out on the Eurex website (eurexchange) and in the Eurex Products brochure. The most important terms are described in the following example. An investor buys: 20. June 2002 Options on Euro Bund Futures Expiration date One contract comprises the right to buy or sell a single futures contract. has a a limited limited lifetime lifetime and and a a set setexpiexpiry Each option has date. The expiry months available trading are ration date. The expiration months for available for the three nearest calendar months, as months, well as the trading are the three nearest calendar as following month within the March, June, Septemwell as the following month within the March, ber and December cycle i. e. lifetimes two June, September and December cycle of i. e.one, lifetimes and three months, as well as a as maximum of six of one, two and three months, well as a maximonths available. Hence, for the months mum of are six months are available. Hence, for the March, June, September and December, the months March, June, September and December, expiration months for the option and and the the maturity the expiration months for the option months for the underlying futures are identical maturity months for the underlying futures are (although the last trading differ fordiffer options identical (although the lastdays trading days for and futures). In the case of case the other contract options and futures). In the of the other months, months, the maturity month of the underlying contract the maturity month of the instrument instrument is the quarterly month following underlying is the quarterly monththe expirationthe date of the option. Hence, the option following expiration date of the option. always expires before the expires maturity of the underHence, the option always before the lying futures contract. maturity of the underlying futures contract. This is the price at which the buyer can enter into the corresponding futures position. At least nine exercise prices per contract month are always available. The price intervals of this contract are set at 0.50 points. The buyer can convert this position into a long futures position. Upon exercise the seller enters into a short position. The Euro Bund Future is the underlying instrument for the option contract. Buyers of options on fixed income futures pay the option price to the seller upon exercise, in exchange for the right. The option premium is EUR 10.00 per 0.01 points. Therefore a premium of 0.15 is really worth EUR 150. The premium for 20 contracts is 20 EUR 150 EUR 3,000. 106.50 Exercise price (also called strike price ). Call Call option. Options on the Euro Bund Future. at 0.15 Underlying instrument Option price (premium) In our example, the buyer acquires the right to enter into a long position of 20 Euro Bund Futures, at an exercise price of 106.50, and pays EUR 3,000 to the seller in exchange. Upon exercise, the seller of the option is obliged to sell 20 Euro Bund Futures June 2002 contracts at a price of 106.50. This obligation is valid until the options expiration date. 51 Premium Payment and Risk Based Margining Contrary to equity or index options, buyers of options on fixed income futures do not pay the premium the day after buying the contract. Instead the premium is paid upon exercise, or at expiration. Contract price changes during the lifetime are posted via variation margin. When the option is exercised, the buyer pays the premium to the value of the daily settlement price on this day. This method of daily profit and loss settlement is called futures-style premium posting. Additional margin equivalent to that for the underlying future has to be deposited to cover the price risk. Rationale The investor expects the price of the Euro Bund Future June 2002 to fall, and decides to enter into a put option position. In this way, the risk will be limited if the expectation should turn out to be wrong. Strategy On May 13, the Euro Bund Future June 2002 is trading at 150.78. The investor buys 10 put options on this contract with an exercise price of 106.00. The price is 0.55 points, which equals EUR 550 per option contract. Date Transaction Purchase selling in EUR Option daily settlement price in EUR 0.91 0.81 Variation margin 20 credit in EUR 3,600 1,000 Variation margin debit in EUR Additional margin 21, 22 in EUR 16,000 0513 0514 10 Put options 0.55 bought Changed Market Situation The Euro Bund Future is now trading at 105.50. The investor decides to exercise the option, which is trading at 0.70. 0515 0516 Exercise Opening of a short position in the Euro Bund Future June 2002 0.70 3,100 0 In this case, the futures additional margin rates correspond to the option 3,600 4,100 Total up to entry into futures position 20 Cf. chapter Variation Margin. 21 Cf. chapter Futures Spread Margin and Additional Margin. 22 The Additional Margin may vary because of changes in volatility or time value decay. 52 The variation margin on the exercise day (0515) is calculated as follows: Profit made on the exercise EUR 5,000 Difference between the exercise price (106.00) and the daily settlement price (105.50) multiplied by the contract value and the number of contracts. EUR 1,100 EUR 7,000 EUR 8,100 EUR 7,000 0.70 10 1,000 EUR 3,100 Change in value of the option compared to the previous day Option premium to be paid Variation margin on 05152002 Result of the Exercise These transactions result in a total loss of EUR 500 for the investor. This loss can be expressed either as the difference between the option price of EUR 5,500 (0.55 10 EUR 1,000), which was fixed when the agreement was concluded but which was not paid in full until exercise, and the profit of EUR 5,000 made from exercising or as the net balance of variation margin flows (EUR 3,600 EUR 4,100). When an option is exercised, the change in value of the option between the time of purchase and entering into the futures position has no impact on the investors end result. Additional margin for options on the Euro Bund Future is equal to that of the underlying instrument, so that no further margin call is required should the position be exercised. In this case, however, it would not be appropriate to exercise the option, since the investor can make a profit above the initial purchase price if heshe closes out, i. e. sells the put option. Result of Closeout Given the previous days settlement price of 0.81, a sale on May 15 at a price of 0.70 also prevailing during the day would only result in a variation margin debit of EUR 1,100 (0.11 10 EUR 1,000). The profit and loss calculation for the sale of the option is shown below: Date Transaction Purchase selling in EUR 0.70 3,600 Option daily settlement price in EUR Variation margin profit in EUR Variation margin loss in EUR 1,100 16,000 2,100 Additional margin in EUR 05 15 05 16 Total Sale By selling the options, the investor makes a total profit of EUR 1,500. This is derived from the difference between the selling and purchase price (0.70 0.55), multiplied by the contract value and the number of futures contracts. Additional margin is released to the investor. 53 Options on Fixed Income Futures Overview The following three option contracts on fixed income futures are currently traded at Eurex: Products Option on the Euro Schatz Future Option on the Euro Bobl Future Option on the Euro Bund Future Product code OGBS OGBM OGBL 54 Option Price Components The option price is comprised of two components intrinsic value and time value. Option value Intrinsic value Time value Intrinsic Value The intrinsic value of an option on fixed income futures corresponds to the difference between the current futures price and the options exercise price, as long as this difference represents a price advantage for the option buyer. Otherwise, the intrinsic value equals zero. For calls: Intrinsic value Futures price Exercise price of the option, if this is 0 otherwise it is zero. For puts: Intrinsic value Exercise price Futures price, if this is 0 otherwise it is zero. An option is in-the-money, at-the-money or out-of-the-money depending upon whether the price of the underlying is above, at, or below the exercise price. Calls Exercise price Futures price in-the-money (intrinsic value 0) at-the-money (intrinsic value 0) out-of-the-money (intrinsic value 0) Puts out-of-the-money (intrinsic value 0) at-the-money (intrinsic value 0) in-the-money (intrinsic value 0) An option always has intrinsic value (is always in-the-money) if it allows the purchase or sale of the underlying instrument at better conditions than those prevailing in the market. Intrinsic value is never negative, as the holder of the option is not obliged to exercise the option. Time Value Time value reflects the buyers chances of hisher forecasts on the development of the underlying instrument during the remaining lifetime being met. The buyer is prepared to pay a certain sum the time value for this opportunity. The closer an option moves towards expiration, the lower the time value becomes until it eventually reaches zero on that date. The time value decay accelerates as the expiration date comes closer. Time value Option price Intrinsic value 55 Determining Factors The theoretical price of options on fixed income futures can be calculated using different parameters, regardless of the current supply and demand scenario. An important component of the option price is the intrinsic value as introduced earlier (cf. section on Intrinsic Value). The lower (call) or higher (put) the exercise price compared to the current price, the higher the intrinsic value and hence the higher the option price. An at-the-money or out-of-the-money option comprises only time value. The following section illustrates the determining factors of time value. Volatility of the Underlying Instrument Volatility measures the propensity of price fluctuations in the underlying instrument. The greater the volatility, the higher the option price. Since an underlying instrument which is subject to strong price fluctuations provides option buyers with a greater chance of meeting their price forecast during the lifetime of the option, they are prepared to pay a higher price for the option. Likewise, sellers demand a higher return to cover their increasing risks. There are two types of volatility: Historical volatility This is based on historical data and represents the standard deviation of the returns of the underlying instrument. Implied volatility This corresponds to the volatility reflected in a current market option price. In a liquid market it is the indicator for the changes in market yields expected by the market participants. Remaining Lifetime of the Option The longer the remaining lifetime, the greater the chance that the forecasts of option buyers on the price of the underlying instrument will be met during the remaining time. Conversely, the longer the lifetime the higher the risk for the option seller, calling for a higher price for the option. The closer it moves towards expiration, the lower the time value and hence the lower the option price ceteris paribus. As the time value equals zero on the expiration date, the course of time acts against the option buyer and in favour of the option seller. The time value is relinquished when the option is exercised. This generally minimizes the investors earnings (cf. chapter Premium Payment and Risk Based Margining). 56 Influencing Factors The price of the call is higher, the higher the price of the underlying instrument the lower the exercise price the longer the remaining lifetime the higher the volatility. The price of the put is higher, the lower the price of the underlying instrument the higher the exercise price the longer the remaining lifetime the higher the volatility. The price of the call is lower, the lower the price of the underlying instrument the higher the exercise price the shorter the remaining lifetime the lower the volatility. The price of the put is lower, the higher the price of the underlying instrument the lower the exercise price the shorter the remaining lifetime the lower the volatility. 57 Important Risk Parameters Greeks An options price is affected by a number of parameters, principally changes in the underlying price, time and volatility. In order to estimate the changes in an options price, a series of sensitivities are used, which are known as the Greeks. The price calculations in this chapter are based on the assumption that the only changes that occur are those that are given and that all other influencing factors remain constant (ceteris-paribus assumption). Delta The delta of an option indicates the change in an options price for a one unit change in the price of the underlying futures contract. The delta changes according to fluctuations in the underlying instrument. With calls, the delta lies between zero and one. It lies between minus one and zero with puts. Call option deltas Put option deltas 0 delta 1 1 delta 0 The value of the delta depends on whether an option is in-, at - or out-of-the-money: Out-of-the-money Long Short Call Put Call Put 0 Spread Positions. In-the-money An option whose intrinsic value is greater than zero. Intrinsic value The intrinsic value of an option is equal to the difference between the current price of the underlying instrument and the options exercise price. The intrinsic value is always greater than or equal to zero. Leverage effect The leverage effect allows participants on derivatives markets to enter into a much larger underlying instrument position using a comparably small investment. The impact of the leverage effect is that the percentage change in the profits and losses on options and futures is greater than the corresponding change in the underlying instrument. Lifetime The period of time from the bond issue until the redemption of the nominal value. Long position An open buyers position in a forward contract. 95 Macaulay duration An indicator used to calculate the interest rate sensitivity of fixed income securities, assuming a flat yield curve and a linear priceyield correlation. Margin Collateral, which must be pledged as cover for contract fulfillment (Additional Margin, Futures Spread Margin), or daily settlement of profits and losses (Variation Margin). Mark-to-market The daily revaluation of futures positions after the close of trading to calculate the daily profits and losses on those positions. Maturity date The date on which the obligations defined in the futures contract are due (deliverycash settlement). Maturity range Classification of deliverable bonds according to their remaining lifetime. Modified duration A measure of the interest rate sensitivity of a bond, quoted in percent. It records the change in the bond price on the basis of changes in market yields. Option The right to buy (call) or to sell (put) a specific number of units of a specific underlying instrument at a fixed price on, or up to a specified date. Option price The price (premium) paid for the right to buy or sell. Out-of-the-money A call option where the price of the underlying instrument is lower than the exercise price. In the case of a put option, the price of the underlying instrument is higher than the exercise price. 96 Premium Option price. Present value The value of a security, as determined by its aggregate discounted repayments. Put option An option contract, giving the holder the right to sell a fixed number of units of the underlying instrument at a set price on or up to a set date (physical delivery). Remaining lifetime The remaining period of time until redemption of bonds which have already been issued. Reverse cash-and-carry arbitrage Creating a neutral position by exploiting mispricing on the cash or derivatives market, by simultaneously selling bonds and buying the corresponding futures contract (opposite of Cash-and-carry arbitrage). Risk based margining Calculation method to determine collateral to cover the risks taken. Short position An open sellers position in a forward contract. Spread positions In the case of options, the simultaneous purchase and sale of option contracts with different exercise prices andor different expirations. In the case of a financial futures contract, the simultaneous purchase and sale of futures with the same underlying instrument but with different maturity dates (time spread) or of different futures (inter-product spread). Straddle The purchase or sale of an equal number of calls and puts on the same underlying instrument with the same exercise price and expiration. 97 Strangle The purchase or sale of an equal number of calls and puts on the same underlying instrument with the same expiration, but with different exercise prices. Synthetic position Using other derivative contracts to reproduce an option or futures position. Time spread Spread positions. Time value The component of the option price arising from the possibility that the investors expectations will be fulfilled during the remaining lifetime. The longer the remaining lifetime, the higher the option price. This is due to the remaining time during which the value of the underlying instrument can rise or fall (a possible exception exists for options on futures and deep-in-the-money puts). Underlying instrument The financial instrument on which an option or futures contracts is based. Variation margin The profit or loss arising from the daily revaluation of futures or options on futures (mark-to-market). Volatility The extent of the actual or forecast price fluctuation of a financial instrument (underlying instrument). The volatility of a financial instrument can vary, depending on the period of time on which it is based. Either the historical or implied volatility can be calculated. Worst-case loss The expected maximum closeout loss that might be incurred until the next exchange trading day (covered by additional margin). Yield curve The graphic description of the relationship between the remaining lifetime and yields of bonds. 98 99 Appendix 1: Valuation Formulae and Indicators Single-Period Remaining Lifetime Pt N c1 (1 trc1) Pt N c1 trc1 Present value of the bond Nominal value Coupon Yield from the time period t 0 until t 1 Multi-Period Remaining Lifetime Pt c1 c2 N cn . (1 trc1) t1 (1 trc2) t2 (1 trcn) tn Pt N cn trcn Present value of the bond Nominal value Coupon at time n Average yield from the time period t 0 until t n Macaulay Duration c1 Macaulay-Duration (1 trc1)t c1 c2 cn N t c1 t c2 . t cn (1 trc1)t c2 (1 trc1)t cn Pt Pt N cn t rcn Present value of the bond Nominal value Coupon at time n Average yield from the time period t 0 until t n Remaining lifetime of coupon c n tn 100 Convexity c1 c2 cn N t c1 (t c1 1) t c2 (t c2 1) . t cn (t cn 1) (1 t rc1)t c2 (1 t rc1)t cn (1 t rc1)t c1 Convexity Pt (1 t rc1)2 Pt N cn trcn Present value of the bond Nominal value Coupon at time n Average yield from the time period t 0 until t n Payment date of coupon c n tn 101 Appendix 2: Conversion Factors Bonds Denominated in Euros Conversion factor 1 c c 1 1 c i 1,06 i e (1.06)f 100 act2 6 (1.06)n (1.06)n 100 act2 act1 ( ) ( ) Definition: e act1 i act2 f c n DD NCD NCD1y-DD NCD NCD1y, where e Publications Brochures Entrance Hall Publications Brochures Market Place Products Trading Calendar Location Market Place Clearing and Settlement Risk Based Margining The following educational tools can be ordered on CD Rom via the Learning Portal: All about Eurex Options All about Eurex Futures Eurex StrategyMaster Eurex MarginCalculator Eurex OptionAlligator (option price calculator) Members can also find the most recent legal documentation relating to membership on our website eurexchange under entrance hall information center becoming a member in the NCM Guideline or GCMDCM Guideline. 105 Entrance Hall Publications Brochures Location Entrance Hall Publications Brochures Entrance Hall Publications Brochures Entrance Hall Publications Brochures Entrance Hall Publications Brochures Zurich T 41-1-229-2435 F 41-1-229-2466 Eurex, November 2002 Published by Eurex Communications Eurex Frankfurt AG Neue Brsenstrae 1 60487 Frankfurt Main Germany Eurex Zrich AG Selnaustrasse 30 8021 Zurich Switzerland eurexchange Order Number E2E-036-1102 ARBN Number Eurex Frankfurt AG ARBN 100 999 764 Eurex , DAX, MDAX , SMI are registered trademarks. STOXX is a registered trademark of STOXX Limited. Eurex 2002 All proprietary rights and interest in this publication shall be vested in Eurex Frankfurt AG and all other rights including, but without limitation to, patent, registered design, copyright, trade mark, service mark, connected with this publication shall also be vested in Eurex Frankfurt AG. Whilst all reasonable care has been taken to ensure that the details contained in this publication are accurate and not misleading at the time of publication, no liability is accepted by Eurex Frankfurt AG for the use of information contained herein in any circumstances connected with actual trading or otherwise. Neither Eurex Frankfurt AG, nor its servants nor agents, is responsible for any errors or omissions contained in this publication, which is published for information only and shall not constitute an investment advice. This brochure is not intended for solicitation purposes but only for the use of general information. All descriptions, examples and calculations contained in this publication are for guidance purposes only and should not be treated as definitive. Eurex Frankfurt AG reserves the right to alter any of its rules or contract specifications, and such an event may affect the validity of information contained in this publication. Eurex Frankfurt AG offers services direct to members of the Eurex market. Those wishing to trade in any products available on the Eurex market or to offer and sell any such products to others should consider both their legal and regulatory positions in the relevant jurisdiction and the risks associated with such products before doing so. STOXX and Dow Jones EURO STOXXSTOXX 600 Sector Indexes are service marks of STOXX Limited andor Dow Jones Company Inc. and have been licensed for use for certain purposes by Eurex Frankfurt AG. Eurex Frankfurt AGs Dow Jones EURO STOXX STOXX 600 Sector Index Futures and Options based on the Dow Jones EURO STOXXSTOXX 600 Sector Indexes are not sponsored, endorsed, sold or promoted by STOXX or Dow Jones, and neither STOXX nor Dow Jones makes any representation regarding the advisability of trading in such product(s). In particular futures and options on the Dow Jones STOXX 600 and futures and options on the Dow Jones EURO STOXX Automobiles, Energy, Financial Services, Healthcare, Insurance, Media, Technology, Telecommunications and Utilities are currently not available for offer or sale to United States persons. Eurex Frankfurt AG Neue Brsenstrae 1 60487 Frankfurt Main Germany Eurex Zrich AG Selnaustrasse 30 8021 Zurich Switzerland eurexchangeTrading Derivatives Trading derivatives instead of the underlying equity provides a range of benefits and carries a number of risks. Derivative contracts can be used to Gain leverage Hedge Risk Speculate in various markets Trade markets where there is, in fact, no underlying equity Provide options for purchase or sale in uncertain market situations Profit from providing a kind of insurance for other traders Options and More Trading options, futures contracts, credit derivatives, forwards, foreign exchange derivatives or interest rate derivatives are all ways to reduce risk. In each case traders learn to use both fundamental and technical analysis to obtain their objective and avoid problems. Because of the high degree of leverage often used in trading derivatives it is possible to earn a large amount of money with a single trade. It is also possible to lose substantial amount of money in poorly thought out trades or over leveraged trades in which the trader does not accept and cut his losses in a timely manner. The Barings Bank disaster in 1995 is a prime example of an options trader trying to cover his losses and waiting for a market turnaround to save him from badly set up sales of options contracts. By the time the trader was picked up by police in Singapore the British bank that had been an institution for hundreds of years was bankrupt However, if in trading options you remain on the side of the buyer you will commonly limit your risk and still be able to gain handsome profits for your work of analysis and timing of trades. Interest Rate Derivatives The biggest market for trading derivatives is interest rate derivatives. An interest rate derivative is the right to receive a given amount of money at a given interest rate. There are interest rate swaps totaling hundreds of trillions of dollars each year. Primarily this market is used by large companies to control their cash flows. Just as the small trader uses technical analysis to anticipate market prices large companies use technical analysis indicators to anticipate interest rate changes.