A Factor-Adjusted Multiple Testing Procedure With Application to Mutual Fund Selection

Abstract

In this article, we propose a factor-adjusted multiple testing (FAT) procedure based on factor-adjusted p-values in a linear factor model involving some observable and unobservable factors, for the purpose of selecting skilled funds in empirical finance. The factor-adjusted p-values were obtained after extracting the latent common factors by the principal component method. Under some mild conditions, the false discovery proportion can be consistently estimated even if the idiosyncratic errors are allowed to be weakly correlated across units. Furthermore, by appropriately setting a sequence of threshold values approaching zero, the proposed FAT procedure enjoys model selection consistency. Extensive simulation studies and a real data analysis for selecting skilled funds in the U.S. financial market are presented to illustrate the practical utility of the proposed method. Supplementary materials for this article are available online.

KEY WORDS:

• Factor model
• False discovery proportion
• Fund performance
• High-dimensional data
• Multiple testing.

ACKNOWLEDGMENTS

Wei Lan’s research was supported by National Natural Science Foundation of China (NSFC, 11401482, 71532001). Lilun Du’s research was partially supported by IGN15BM04, SBI16BM01, and Hong Kong RGC ECS26301216. The authors are grateful to the editor, the AE, and two anonymous referees for their insightful comments and constructive suggestions.