Efficient modeling of cross-sectional stock returns via Reduced Rank (Seemingly Unrelated) Regression

We improve on the Instrumented Principal Component Analysis (IPCA) model developed in Kelly, Pruitt and Su (2019) by providing more efficient Generalized Least Square (GLS) estimators with a closed-form limiting distribution allowing for a more consistent (mis)pricing inference. The IPCA model can be cast in a more flexible Reduced-Rank Seemingly Unrelated Regression (RRSUR) framework which can accommodate both cross-sectional and time series dependence.We find that the additional information embedded in the second moment of contemporaneous stock returns can not only improve the model fit, but also can lead to better unconditional mean-variance spanning with parsimony. Overall our results suggest that a RRSUR model can account for mispricing in the presence of fewer factors. The cross-sectional and time-series validation results confirm our findings