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Value-at-Risk-Limitstrukturen zur Steuerung und Begrenzung von Marktrisiken im Aktienbereich

Author

Listed:
  • Beeck, Helmut
  • Johanning, Lutz
  • Rudolph, Bernd

Abstract

Ein Value-at-Risk-Limit wird als DM-Betrag gekennzeichnet, der von den tatsächlichen Handelsverlusten innerhalb einer bestimmten Zeitdauer nur mit geringer Wahrscheinlichkeit überschritten werden darf. Da der Bankvorstand i.d.R. Jahres-Value-at-Risk-Limite beschließt, im Handelsbereich die Geschäfte aber für einen kurzfristigen - unterstellt wird ein eintägiger - Planungshorizont abgeschlossen werden, ist zu klären, wie Jahres-Limite in Tages-Limite umgerechnet und während des Jahres realisierte Gewinne und Verluste auf die Limite angerechnet werden können. Auf der Grundlage des Umrechnungsverfahrens nach der Quadratwurzel-T-Formel lassen sich drei Verfahren für die Ermittlung des Tages-Limits unterscheiden: 1. Realisierte Gewinne und Verluste werden nicht angerechnet (starres Limit). 2. Bei Verlusteintritt vermindert sich das Tages-Limit für die Restperiode, realisierte Gewinne machen Kürzungen rückgängig (Verlustbegrenzungslimit). 3. Tages-Limite werden um Gewinne und Verluste angepaßt, wodurch eine Erweiterung des Handlungsspielraumes möglich ist (dynamisches Limit). Die drei Limite werden in einem Simulationsmodell gegeneinander abgewogen, wobei unterstellt wird, ein Händler handle nur eine einzige Aktie und antizipiere in 55% der Fälle die Kursrichtung. Die Simulationsergebnisse sind bei den unterstellten Renditeprozessen (geometrische Brownsche Bewegung und reale Renditen von 77 deutschen Aktien für die Zeit vom 01.01.1974 bis 31.12.1995) weitgehend identisch. Das dynamische Limit produziert deutlich höhere durchschnittliche Ergebnisse als das starre Limit und das Verlustbegrenzungslimit. Überschreitungen des Jahres-Limits treten nur beim starren Verfahren auf, die Häufigkeit ist allerdings wesentlich geringer als die zulässige Wahrscheinlichkeit von 1 %.

Suggested Citation

  • Beeck, Helmut & Johanning, Lutz & Rudolph, Bernd, 1997. "Value-at-Risk-Limitstrukturen zur Steuerung und Begrenzung von Marktrisiken im Aktienbereich," CFS Working Paper Series 1997/02, Center for Financial Studies (CFS).
    • Handle: RePEc:zbw:cfswop:199702
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    References listed on IDEAS

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    1. Darryll Hendricks, 1996. "Evaluation of value-at-risk models using historical data," Economic Policy Review, Federal Reserve Bank of New York, vol. 2(Apr), pages 39-69.
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    4. Johanning Lutz, 1996. "Value-at-Risk-Modelle zur Ermittlung der bankaufsichtlichen Eigenkapitalunterlegung beim Marktrisiko im Handelsbereich," Zeitschrift für Bankrecht und Bankwirtschaft (ZBB) / Journal of Banking Law and Banking (JBB), RWS Verlag, vol. 8(4), pages 287-303, December.
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