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

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.