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

TL;DR

This paper develops an adaptive testing method for detecting alpha in high-dimensional, time-varying factor models, effectively handling scenarios where the number of assets exceeds the time series length.

Contribution

It introduces a novel adaptive test combining maximum-type and sum-type tests, with proven asymptotic properties and demonstrated advantages in simulations and real data.

Findings

The proposed test performs well in sparse alternative scenarios.

The limit null distribution of the test statistic is established.

The adaptive test outperforms individual tests in various settings.

Abstract

This paper 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.(2020).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.