Adaptive Testing for Alphas in Conditional Factor Models with High Dimensional Assets

Abstract

This article focuses on testing for the presence of alpha in time-varying factor pricing models, specifically when the number of securities N is larger than the time dimension of the return series T. We introduce a maximum-type test that performs well in scenarios where the alternative hypothesis is sparse. We establish the limit null distribution of the proposed maximum-type test statistic and demonstrate its asymptotic independence from the sum-type test statistics proposed by Ma et al. Additionally, we propose an adaptive test by combining the maximum-type test and sum-type test, and we show its advantages under various alternative hypotheses through simulation studies and two real data applications.

Keywords:

• Alpha tests
• Conditional factor model
• High dimensionality
• Sparse alternatives
• Spline estimator

Supplementary Materials

The Supplementary materials provide some additional simulation results and the proofs of all theorems.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This research was supported by the China National Key R&D Program under grant nos. 2022YFA1003703, 2022YFA1003800, and 2019YFC1908502, the National Natural Science Foundation of China under grant nos. 12226007, 12271271, 11925106, 12231011, 11931001, and 11971247, the Fundamental Research Funds for the Central Universities under grant no. ZB22000105 and Shenzhen Wukong Investment Management Co. Ltd.