Universität zu Köln

Reh, Laura Annabelle ORCID: 0000-0002-8083-0535 (2022). Dynamic Modeling and Forecasting of Financial Portfolio Weights. PhD thesis, Universität zu Köln.

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Abstract

This thesis addresses the modeling and prediction of portfolio weights in high-dimensional applications to returns on a set of risky financial assets with a particular emphasis on Global Minimum Variance Portfolio (GMVP) allocations. In total, it comprises three self-contained essays on modeling and predicting dynamic portfolio weights for financial asset returns. The first essay is a joint paper with Prof. Dr. Roman Liesenfeld and Jun.-Prof. Dr. Fabian Krüger. The second essay is a joint work with Prof. Dr. Roman Liesenfeld and Prof. Dr. Guilherme Valle Moura. The third essay is a single authored project. In the first essay a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP) for the conditional covariance matrix of asset returns is proposed. Building on a representation in which the GMVP weights obtain as population coefficients of a linear regression of a benchmark return on a vector of return differences, a consistent loss function is derived from which the GMVP weights can be inferred without imposing any distributional assumptions on the returns. In order to capture time variation in the returns' conditional covariance structure, the portfolio weights are modeled through a recursive least squares (RLS) scheme as well as by generalized autoregressive score (GAS) type dynamics. These models are applied to daily stock returns, and it is found that they perform well compared to existing static and dynamic approaches in terms of both the expected loss and unconditional portfolio variance. In the second essay, again the regression representation of the GMVP weights is the starting point, from which a linear state space model with time-varying parameters and stochastic volatility is derived. This specification allows to address both the time variation in the assets' conditional covariance structure and the heteroscedasticity in the market. Using Bayesian regularization techniques, the portfolios are robustified against estimation risk. Bayesian inference techniques with LASSO type priors provide data driven shrinkage to alleviate overfitting and to automatically identify time-invariant coefficients. The approach allows for scalability to high dimensional applications and performs well in application in which the number of observations per asset is low. The applicability and robustness of our approach, particularly under challenging concentration ratios, are demonstrated through comprehensive simulation and empirical analysis. In the third essay, it is proposed to use a Gaussian time-varying graphical LASSO (TVGL) approach for inferring financial precision matrices. The model is developed based on theoretical and practical insights from high-dimensional financial portfolio applications, addressing particularly the challenges of achieving the optimal degree of model flexibility and temporal stability for predictive performance. To solve the problem in an efficient manner, the Alternating Direction Method of Multipliers (ADMM) is used, which allows to incorporate tailored constraints on the precision matrices and their dynamic evolution that complement $L_1$-type regularization induced by the LASSO. It is shown how to directly constrain gross exposure of the GMVP weights within the estimation process of the inverse covariances exploiting that they are directly related to the portfolio weights through a scaled linear link function. Moreover, a dynamic recalibration scheme for the penalty parameters that allows for rapid adjustment to changing economic conditions is proposed. Using applications to daily financial returns, it shows that the proposed approach leads to consistently good performance over a 40-year out-of-sample period.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Reh, Laura Annabelle reh@statistik.uni-koeln.de orcid.org/0000-0002-8083-0535 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-617788
Date:	2022
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
Uncontrolled Keywords:	Keywords Language Portfolio Optimization English High-dimensionality English Shrinkage English Loss Function English Bayesian Econometrics English Graphical Models English
Date of oral exam:	1 June 2022
Referee:	Name Academic Title Liesenfeld, Roman Prof. Dr. Breitung, Jörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/61778