Maximum Conditional Alpha Test for Conditional Multi-Factor Models

Abstract

In this paper, a novel test, called the maximum conditional alpha (MCA) test, which enhances the testing power for detecting alpha in linear multi-factor models, is proposed. This test is specifically designed for conditional multi-factor models with time-varying coefficients, where the number of test assets (N ) exceeds the number of observations (T ) and the alternative hypothesis is a sparse vector, meaning that only a few components violate the null hypothesis.By carefully studying the estimation error derived from the B-spline estimation, we rigorously demonstrate that the proposed test converges to a type-I extreme value distribution when min(T, N ) tends to infinity, subject to mild conditions. Furthermore, the proposed MCA test was extended to incorporate latent factors within conditional multi-factor models. The small-sample properties of the