Bayesian Portfolio Regularization

• Applicant: Professor Dr. Winfried Franz Xaver Pohlmeier
• Subject Area: Statistics and Econometrics
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 321011636

• Final Report Year: 2020

Final Report Abstract

This project has demonstrated the improvements of computationally intensive Bayesian methods and machine learning when applied to high-dimensional portfolio choice problems. The classical portfolio weight shrinkage methods were reformulated into a regression framework, which allowed for application of Bayesian regularization methods. Moreover, in the project a generalization of asymptotic theory for the newly developed statistical learning technique, sparse approximate factor models, was developed and shown to outperform the existing approaches. Furthermore, the project contributed to the literature by providing and explanation for the puzzling empirical findings of the naive equally weighted portfolio. Portfolio evaluation procedures commonly used in the literature has been shown to have low power and thus the the null hypothesis of equal performance of the equally weighted portfolio compared to many theoretically superior strategies cannot be rejected in many out-of-sample horse races. Finally, the drawbacks of the considered methods were shown to be mitigated with the help of machine learning tools applied to the high-dimensional portfolio choice. This project has contributed to a better understanding of the statistical properties of highdimensional portfolio models and provided the literature with extensive empirical comparisons of the proposed methods to the commonly used approaches.

Publications

• Bayesian Shrinkage of Portfolio Weights
  Frey, Christoph
  
• “Bayesian Shrinkage of Portfolio Weights,” Working Paper. Available at SSRN
  Frey, Christoph
  
• (2017): Three Essays on Bayesian Shrinkage Methods, Ph.d. thesis, University of Konstanz, Konstanz
  Frey, C.
  
• (2019): Three Essays on Covariance Matrix Estimation and Factor Models in High Dimensions, Ph.D. thesis, University of Konstanz, Konstanz
  Zagidullina, A.
  
• (2019): Three Essays on Robust Inference in Economics and Finance, Ph.D. thesis, University of Konstanz, Konstanz
  Kazak, E.
  
• (2019): “Testing out-of-sample Portfolio Performance,” International Journal of Forecasting, 35 (2), 540–554
  Kazak, Ekaterina & Pohlmeier, Winfried
  
• (2019): “Widened Learning of Index Tracking Portfolios,” 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA), Boca Raton, FL, USA, pp. 1800–1805
  Gavriushina, Iuliia; Sampson, Oliver; Berthold, Michael R.; Pohlmeier, Winfried & Borgelt, Christian
  
• “Sequential Stock Return Prediction Through Copulas,” DEA Working Papers 91, Universitat de les Illes Balears, Departament d'Economía Aplicada
  Audrone Virbickaite & Christoph Frey & Demian N. Macedo
  
• “The CAPM with Measurement Error: There?s life in the old dog yet!” Jahrbücher für Nationalökonomie und Statistik - Journal of Economics and Statistics, 240 (4), 417–453
  Simmet, Anastasia & Pohlmeier, Winfried
  
• (2020): Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices
  Daniele, M., Pohlmeier, W., & Zagidullina, A.
  
• (2020): Three Essays on Regularization Methods in High-Dimensional Factor Models, Ph.D. thesis, University of Konstanz, Konstanz
  Daniele, M.
  
• (2020): “Valid Inference for Treatment Effect Parameters under Irregular Identification and Many Extreme Propensity Scores,” Journal of Econometrics
  Heiler, Phillip & Kazak, Ekaterina