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Nothing is normal in nance!: On Tail Correlations and Robust Higher Order Moments in Normal Portfolio Frameworks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2012 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Abstract

This thesis project is divided in two parts. The first part examines the possibility that correlation matrix estimates based on an outlier sample would contain information about extreme events. According to my findings, such methods do not perform better than simple shrinkage methods where robust shrinkage targets are used. The method tested is especially outperformed when it comes to the extreme events, where a shrinkage of the correlation matrix towards the identity matrix seems to give the best result.

The second part is about valuation of skewness in marginal distributions and the penalizing of heavy tails. I argue that it is reasonable to use a degrees of freedom parameter instead of kurtosis and a certain regression parameter, that I develop, instead of skewness due to robustness issues. When minimizing the one period draw-down is our target, the "value" of skewness seems to have a linear relationship with expected returns. Re-valuing of expected returns, in terms of skewness, in the standard Markowitz framework will tend to lower expected shortfall (ES), increase skewness and lower the realized portfolio variance. Penalizing of heavy tails will most times in the same way lower ES, lower kurtosis and realized portfolio variance. The results indicate that the parameters representing higher order moments in some way characterize the assets and also reflect their future behavior. These properties can be used in a simple optimization framework and seem to have a positive impact even on portfolio level

Place, publisher, year, edition, pages
2012. , 79 p.
Series
Trita-MAT, ISSN 1401-2286 ; 4
Keyword [en]
Correlation Matrix, Tail Correlations, Skewness, Robust Skewness
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-102699OAI: oai:DiVA.org:kth-102699DiVA: diva2:555889
Educational program
Master of Science in Engineering -Engineering Physics
Uppsok
Physics, Chemistry, Mathematics
Examiners
Available from: 2012-09-21 Created: 2012-09-21 Last updated: 2012-09-21Bibliographically approved

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