Universität zu Köln

Hansen, Philipp Christian (2023). Statistical Methods for the Analysis of Financial Risk. PhD thesis, Universität zu Köln.

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Abstract

The thesis contains three self-contained essays on statistical methods for the analysis of financial risk. First, we compare alternative estimation approaches for factor augmented panel data models that are also relevant in the field of financial risk. Our focus lies on panel data sets where the number of panel groups (N) is large relative to the number of time periods (T). The Principal Component (PC) and Common Correlated Effects (CCE) estimators were originally developed for panel data with large N and T, whereas two considered GMM approaches assume that T is fixed in the asymptotic analysis. Our comparison of existing methods addresses three different issues. First, we analyze the possibility of an inappropriate normalization of the factor space (the so-called normalization failure). In particular we propose a variant of the CCE estimator that avoids the normalization failure by adapting a weighting scheme inspired by the Mundlak approach. Second, we analyze the effects of estimating versus fixing the number of factors in advance. Third, we demonstrate how the design of the Monte Carlo simulations favors some estimators, which explains the conflicting findings from existing Monte Carlo experiments. Second, we consider empirical challenges that are relevant for portfolio selection. Portfolio selection according to Markowitz requires reliable estimates of the expected returns and the covariance matrix of returns. Estimating these moments via their sample analogs (the so-called plug-in method) yields extreme portfolio weights that excessively fluctuate over time and typically perform poorly out-of-sample. Obtaining reliable estimates is particularly problematic in case the number of investable assets is of similar magnitude as the available amount of time series data. A common procedure is to ignore information on the first moment, resulting in the estimation of the global minimum variance (GMV) portfolio, which generally improves the out-of-sample performance. In practice, it is important to cope with negative estimates of the weights. The corresponding shorting strategy implies excessive leverage, risk exposure and turnover costs. We argue that suitable put option strategies typically perform much more desirable and limit the risk exposure and turnover of the portfolio. In an empirical application, we demonstrate how alternative regularization approaches, such as LASSO or other shrinkage methods, help to improve the performance of the portfolio allocation in practice. The third essay focuses on the analysis of the two risk measures Value at Risk (VaR) and Expected Shortfall (ES) with regard to their theoretical differences and practical estimation. This comparison is particularly relevant, since ES replaces VaR as the regulatory risk measure for calculating capital requirements according to the Basel III Accords. ES is often considered as the theoretically superior risk measure. Nevertheless, both risk measures have to be estimated in practice. This leaves the question whether the more complex estimation of ES provides any additional insights with regard to the quantification of risk. In a simulation study and empirical applications, both risk measures are examined with respect to various estimation methods. In addition, there exists a relationship between the two risk measures under certain distributional assumptions. The study investigates whether this relationship can be utilized to improve the estimation of ES.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Hansen, Philipp Christian p.c.hansen3@gmail.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-719178
Date:	2023
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Faculty of Management, Economics and Social Sciences > Economics > Econometrics and Statistics > Professorship for Statistics and Econometrics
Subjects:	General statistics Economics
Uncontrolled Keywords:	Keywords Language Factor Models, Panel Data, CCE, Principal Components, GMM, Portfolio Optimization, Shrinkage, LASSO, High-dimensionality, Value at Risk, Expected Shortfall, Coherence, Subadditivity, Elicitability English UNSPECIFIED English UNSPECIFIED English
Date of oral exam:	21 December 2023
Referee:	Name Academic Title Breitung, Jörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/71917