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Time Variation in the Tail Behaviour of Bund Futures Returns


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  • Upper, Christian
  • Werner, Thomas


The literature on the tail behaviour of asset prices focuses mainly on the foreign exchange and stock markets, with only a few papers dealing with bonds or bond futures. The present paper addresses this omission. We focus on three questions: (i) Are heavy tails a relevant feature of the distribution of BUND futures returns? (ii) Is the tail behaviour constant over time? (iii) If it is not, can we use the tail index as an indicator for financial market risk and does it add value in addition to classical indicators? The answers to these questions are (i) yes, (ii) no, and (iii) yes. We find significant heaviness of the tails of the Bund future returns. The tail index is on average around 3, implying the nonexistence of the forth moments. With the aid of a recently developed test for changes in the tail behaviour we identify several breaks in the degree of heaviness of the return tails. Interestingly, the tails of the return distribution do not move in parallel to realised volatility. This suggests that the tails of futures returns contain information for risk management that complements those gained from more standard statistical measures. -- Die Literatur über Extreme der Renditeverteilung hat sich bisher überwiegend mit Wechselkursen und Aktienkursen befasst. Die Kurse von Rentenwerten oder Terminkontrakten auf Rentenwerte haben hingegen bisher kaum Beach- tung erfahren. Das vorliegende Arbeitspapier versucht diese Lücke zu schließen. Unser Augenmerk gilt dabei insbesondere drei Fragen: (i) Haben die Ren- diteverteilungen von Terminkontrakten auf Bundeswertpapiere "fat tails"? (ii) Ist die Wahrscheinlichkeit extremer Kursbewegungen im Zeitablauf kon- stant? (iii) Kann ein Tail-Index Informationen Äuber den Grad von Marktun- sicherheit liefern, die klassische Indikatoren wie die VolatilitÄat nicht liefern können? Die Antworten zu diesen drei Fragen sind (i) ja, (ii) nein und (iii) ja. Wir finden ein signifikantes "fat tails" Phänomen in der Renditeverteilung von BUND Future Kontrakten. Ein Tail-Index von circa 3 impliziert, dass das vierte und alle höheren Momente der Verteilung nicht existieren. Mit Hilfe kürzlich entwickelter Tests finden wir Brüche der Tail-Stärke der Ren- diteverteilungen. Interessanterweise bewegt sich der Tail-Index nicht immer in die gleiche Richtung wie die Volatilität. Dies lässt vermuten, dass die Betrachtung der Tails dem Risikomanagement Informationen liefert, die mit herkömmlichen Verfahren nicht gewonnen werden kÄonnen.

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Bibliographic Info

Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2002,25.

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Date of creation: 2002
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Handle: RePEc:zbw:bubdp1:4190

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  1. Cotter, John, 2000. "Margin Exceedences for European Stock Index Futures using Extreme Value Theory," MPRA Paper 3534, University Library of Munich, Germany, revised 2001.
  2. Lux, T., . "The Limiting Extremal Behaviour of Speculative Returns: An Analysis of Intra-Daily Data from the Frankfurt Stock Exchange," Discussion Paper Serie B 436, University of Bonn, Germany, revised Jul 1998.
  3. Kim, Jeong-Ryeol, 2002. "The stable long-run CAPM and the cross-section of expected returns," Discussion Paper Series 1: Economic Studies 2002,05, Deutsche Bundesbank, Research Centre.
  4. Caers, Jef & Beirlant, Jan & Vynckier, Petra, 1998. "Bootstrap confidence intervals for tail indices," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 259-277, January.
  5. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(3), pages 399-421.
  6. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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Cited by:
  1. Straetmans, Stefan & Candelon, Bertrand, 2013. "Long-term asset tail risks in developed and emerging markets," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 1832-1844.
  2. Cotter, John & Dowd, Kevin, 2007. "Estimating financial risk measures for futures positions: a non-parametric approach," MPRA Paper 3503, University Library of Munich, Germany.
  3. Tambakis, D.N., 2008. "Feedback Trading and Intermittent Market Turbulence," Cambridge Working Papers in Economics 0847, Faculty of Economics, University of Cambridge.
  4. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.


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