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High-Dimensional Factor Models with an Application to Mutual Fund Characteristics

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  • Martin Lettau

Abstract

This paper considers extensions of two-dimensional factor models to higher-dimensional data 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 three-dimensional data set consisting of 25 characteristics of 1,342 mutual funds observed over 34 quarters. The tensor factor models reduce the data dimensionality by 97% while capturing 93% of the variation of the data. I relate higher-dimensional tensor models to standard two-dimensional models and show that the components of the model have clear economic interpretations.

Suggested Citation

  • Martin Lettau, 2022. "High-Dimensional Factor Models with an Application to Mutual Fund Characteristics," NBER Working Papers 29833, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:29833
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    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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