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Sample Kovarianz-/Korrelationsmatrizen und ihre robusten Schätzer by Saffaf, Tarek

Sample Kovarianz-/Korrelationsmatrizen und ihre robusten Schätzer

by Tarek Saffaf
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Book cover type: Paperback
  • ISBN13: 9783656525455
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 30
  • Original Price: USD 25.5
  • Language: German
  • Edition: 1. Auflage
  • Item Weight: 50 grams
  • BISAC Subject(s): Reference

Studienarbeit aus dem Jahr 2004 im Fachbereich Mathematik - Angewandte Mathematik, Note: 2,7, Technische Universität München, Sprache: Deutsch, Abstract: Seit der bahnbrechenden Arbeit von Markowitz, ist die Portfolio Theorie aus dem Asset Management nicht mehr wegzudenken. Wichtige Bestandteile seiner Theorie sind die erwartete Aktienrendite und das Risiko, das durch die Kovarianzmatrix ausgedrückt wird. Das Schätzen der Kovarianzmatrix kann zu grö eren Problemen führen. Wenige Ausrei er reichen aus, um die Schätzer zu verzerren und somit unbrauchbar zu machen. Kapitel 1 zeigt welche Auswirkungen einzelne Ausrei er haben und wie diese durch die "blo e" Anwendung von robusten anstatt klassischen Schätzverfahren vermieden werden können. Doch auch diese haben Nachteile; darum wurden andere Verfahren entwickelt, wie z.B. die sog. "paarweisen" Schätzmethoden, bei der anstatt der gesamten Matrix die einzelnen Einträge der Matrix geschätzt werden. Eine weitere Schätzmethode ist das Shrinkage-Verfahren, das in Kapitel 2, ausgehend von einem quadratischen Optimierungsproblem, gezeigt wird. Des Weiteren wird eine praktische Anleitung der Alpharegel vorgestellt, bei der ein aktiver Portfoliomanger, der von einer Benchmark abweichen will, sog. Alphaprognosen erhält, die den Input seiner Arbeit darstellen. Kapitel 3 beschäftigt sich mit empirischen Korrelationsmatrizen und der Annahme, dass diese zufällig verteilt sind. Die Ergebnisse führten dazu, dass die Portfoliotheorie von Markowitz zunächst in Frage gestellt wurde, durch die Erkenntnisse in Kapitel 4 aber wieder verworfen werden konnte.

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