Essays in finance: aggregating distributions and detecting structural breaks

Abstract

Many quantitative analyses try to estimate an effect, which is measured by aggregating the underlying distribution in a suitable way. For many econometric models the consistency of the true model is a necessary condition, that means one does not find structural breaks within the model during the observations. The present thesis addresses these two questions. The first part of this thesis is about an accurate estimation of the covariance/correlation matrix and detecting structural breaks within these dependency structures. Chapter 2 addresses the problem of estimating the covariance/correlation matrix with limited observations. Estimators with and without the normality assumption of returns are used and the errors of covariance estimation and correlation estimation compared. It is analyzed, if estimation improvements transfer to economic improvements measured by the Sharpe ratio and annualized volatilities of minimum-variance portfolios. Significant out-performance of some shrinking estimators in the economic sense are found, which seem to depend weakly on the normality assumption. Using a shrinking estimator with a scaled identity matrix as shrinking target, the Sharpe ratio increases by a factor of about two. Chapter 3 tests for a constant correlation structure without any model assumption. These model free tests for constant parameters often fail to detect structural changes in high dimensions. In practice this corresponds to a portfolio with many assets and a reasonable long time series. The dimensionality of the problem is reduced by looking at a compressed panel of time series obtained by cluster analysis and the principal components of the data. With this procedure tests for constant correlation matrix can be extended from a sub portfolio to whole index, which we exemplify using a major stock index. The second part of this thesis deals with the general problem of aggregating distributions. Using conditional first moments, one can ask the question: am I better off than the others in the population? Chapter 4 deals with this question in the context of income distributions and proposes metrics for skewness and spread, based on this internal view. Using them, the trajectories of European countries from 2005 to 2013 are tracked in a phase plane. This movement enables a grouping into three groups of inequality risers, fallers and a mixed group. In a regression analysis determinants of the Gini coefficient are examined to check if these effects translate to the two metrics. Chapter 5 turns to one source of income, investment income and the question arising 1 from the perspective of a fund manager: How does a performance metric look like and would fund managers be ranked differently when using different performance metrics? The originated performance criterion w is more consistent with the implicit Friedman- Savage utility ordering. It weights the lower versus upper conditional expected returns, while a dual spread or dispersion metric d also exists. A point of departure is the conventional Sharpe performance ratio, with the empirical comparisons extending to a range of existing performance criteria. In contrast to existing metrics, the proposed performance metric W results in different and more embracing rankings.