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Asset Management & Portfolio Optimierung

A Semi-Infi nite Approach to Portfolio Optimization

Master Thesis in "Mathematical Finance", Oxford (2015)

The main goal of this thesis is to tackle some known drawbacks of an established state-of-the-art portfolio optimization technique, the so-called Resampled Efficient Frontier by Michaud. This technique is based on the observation that the classical Mean-Variance optimization as introduced by Markowitz is based on the strong assumption that the input parameters are known which is unrealistic in practice. To circumvent this issue, Michaud uses a finite number of Monte Carlo simulated return time series to produce statistically equivalent scenarios and hence takes uncertainty of the input parameters into account. [...] 

 

Stability of Allocation Weights from Bayesian Networks: The Role of Ambiguity Aversion

Master Thesis in "Mathematical Finance", Oxford (2013)

This work applies the asset allocation model, introduced by Rebonato & Denev to a real-life example, where the tail distribution of the returns is constructed based on the hypothetical stress scenario of a sovereign crisis. The expected utility optimization is performed for the power utility function and the Mean-Variance approach calibrated to locally approximate each other. The focus of the analysis is on the stability of the allocation weights with respect to changes in the uncertain input parameters. 

 

Asset Allocation under a Conditional Diversification Measure

Master Thesis in "Mathematical Finance", Oxford (2011)

In this thesis we consider the problem of diversifying investments in common market securities under certain restrictions, such as budget constraints, etc. Therefore we adapt the entropy diversification measure as well as the conditional principal component decomposition, both proposed by Meucci (2009). We derive a rigorous and powerful theoretical framework describing the geometry of the conditional principal components, which particularly allows us to prove the existence of such decompositions. Furthermore, we apply numerical tests to selected index securities, compare two approaches of portfolio selection (mean-variance vs. mean-diversification) and illustrate the differences that arise between the efficient frontiers. A propagated aim in this thesis is the asset allocation of mutually uncorrelated portfolios, which are naturally given by the principal components. Thus, finally, we back-test several rebalancing strategies based on a principal component decomposition and verify whether the resulting portfolios are closely uncorrelated.