Estimating the Pricing Kernel: A Simple Regression-Based Dimension-Reduction Approach

We propose a simple framework for estimating the pricing kernel in factor space by constructing the mean–variance efficient factor portfolio via an ordinary least squares formulation with least absolute shrinkage and selection operator regularization. The method accommodates high-dimensional settings in which the number of candidate factors exceeds the sample size and automatically shrinks redundant factor weights toward zero. We show theoretically that the out-of-sample Sharpe ratio of the estimated portfolio converges to the theoretical maximum at the fastest rate among existing regression-based approaches. Applying the method to 174 characteristic-based factors together with the market factor, we obtain an out-of-sample Sharpe ratio of 3.59, substantially outperforming competing strategies and delivering the smallest aggregate pricing errors. The selected factors vary over time in both composition and number, averaging about 50. We further develop a model comparison test and reject the hypothesis that eight widely used sparse factor models are sufficient to span the pricing kernel.

This paper was accepted by Kay Giesecke, finance.

Funding: This work was supported by the National Natural Science Foundation of China [Grants 72671091, 72371079, and 72501192, and Key Program 72432005] and the Science and Technology Planning Project of Guangdong Province [Grant 2023B1515020045].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2025.03608 .