Martin Lettau, UC Berkeley: High-Dimensional Factor Models and the Factor Zoo (8/29/2023)

This paper proposes a new approach to the “factor zoo” conundrum. Instead of applying dimension-reduction methods to a large set of portfolios that are obtained from sorts on characteristics, I construct factors that summarize the information in characteristics across assets and then sort assets into portfolios according to these “characteristic factors”. I estimate the model on a data set of mutual fund characteristics. Since the data set is 3-dimensional (characteristics of funds over time), characteristic factors are based on a tensor factor model (TFM) that is a generalization of 2-dimensional PCA. I find that parsimonious TFM capture over 90% of the variation in the data set. Pricing factors derived from the TFM have high Sharpe ratios and capture the cross-section of fund returns better than standard benchmark models.