Explaining persistently small out-of-sample improvements in the energy sector after removing style factors

Investigate the cause of the observation that, in the energy sector, the maximum mosaic bi-cross validation R^2 obtained by adding an estimated sparse additional factor remains at or below 1% even after removing the twelve style factors from the BlackRock Fundamental Equity Risk model.

Background

In the model-improvement analysis, the authors propose estimating a missing factor exposure via sparse PCA on one fold and measuring out-of-sample predictive improvement via a bi-cross validation R^2 on a second fold, then assessing significance with the mosaic permutation test.

After an ablation that removes the twelve style factors, they observe that the maximal out-of-sample R^2 in the energy sector remains small (≤1%), despite highly significant p-values elsewhere, and explicitly defer understanding the reason for this phenomenon.