High Dimensional Factor Models with an Application to Mutual Fund Characteristics

Lettau, Martin (2021): High Dimensional Factor Models with an Application to Mutual Fund Characteristics.

Abstract

This paper considers extensions of 2-dimensional factor models to higher-dimension data that can be represented as tensors. I describe decompositions of tensors that generalize the standard matrix singular value decomposition and principal component analysis to higher dimensions. I estimate the model using a 3-dimensional data set consisting of 25 characteristics of 1,342 mutual funds observed over 34 quarters. The tensor factor model reduces the data dimensionality by 97% while capturing 93% of the variation of the data. I relate higher-dimensional tensor models to standard 2-dimensional models and show that the components of the model have clear economic interpretations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Tucker decomposition, CP decomposition, tensors, PCA, SVD, factor models, mutual funds, characteristics
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Abdallah, Emad E., A. Ben Hamza, and Prabir Bhattacharya (2007) “MPEG Video Watermarking Using Tensor Singular Value Decomposition,” in Kamel, Mohamed and Aurélio Campilho eds., Lecture Notes in Computer Science, 4633, 772–783, Springer, Berlin, Heidelberg, 10.1007/ 978-3-540-74260-9_69.

Andersen, Anders H. and William S. Rayens (2004) “Structure-Seeking Multilinear Methods for the Analysis of fMRI Data,” NeuroImage, 22 (2), 728–739, 10.1016/J.NEUROIMAGE.2004.02. 026.