Identifying improvements to BFRE when violations are significant but adding estimated factors degrades out-of-sample performance

Determine how to modify or augment the BlackRock Fundamental Equity Risk model in cases where the mosaic permutation test detects statistically significant violations of residual independence, yet adding an estimated additional factor yields negative out-of-sample bi-cross validation R^2, indicating that current approaches do not improve predictive fit.

Background

The authors propose an out-of-sample diagnostic: estimate candidate missing exposures via sparse PCA on a training period, construct predictions of residuals using those exposures on a test period, and summarize improvement via a bi-cross validation R^2, with significance assessed by their mosaic test.

They report instances—particularly in healthcare post-COVID—where the mosaic test’s p-values are significant but the added factor worsens out-of-sample fit (negative R^2), and explicitly state they do not know how to improve the model in these cases.