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High Dimensional Factor Models with an Application to Mutual Fund Characteristics

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  • Lettau, Martin

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.

Suggested Citation

  • Lettau, Martin, 2021. "High Dimensional Factor Models with an Application to Mutual Fund Characteristics," MPRA Paper 112192, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:112192
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    Keywords

    Tucker decomposition; CP decomposition; tensors; PCA; SVD; factor models; mutual funds; characteristics;
    All these keywords.

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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