Testing Alphas in Conditional Time-Varying Factor Models With High-Dimensional Assets

ABSTRACT

For conditional time-varying factor models with high-dimensional assets, this article proposes a high-dimensional alpha (HDA) test to assess whether there exist abnormal returns on securities (or portfolios) over the theoretical expected returns. To employ this test effectively, a constant coefficient test is also introduced. It examines the validity of constant alphas and factor loadings. Simulation studies and an empirical example are presented to illustrate the finite sample performance and the usefulness of the proposed tests. Using the HDA test, the empirical example demonstrates that the FF three-factor model is better than CAPM in explaining the mean-variance efficiency of both the Chinese and U.S. stock markets. Furthermore, our results suggest that the U.S. stock market is more efficient in terms of mean-variance efficiency than the Chinese stock market. Supplementary materials for this article are available online.

KEY WORDS:

• Conditional alpha test
• High-dimensional data
• Mean-variance efficiency
• Spline estimator
• Time-varying coefficient.

Funding

Wei Lan's research was supported by National Natural Science Foundation of China (NSFC, 11401482, 71532001). Ma's research was partially supported by NSF grant DMS 1306972 and a Hellman Fellowship. Su gratefully acknowledges the Singapore Ministry of Education for an Academic Research Fund under grant number MOE2012-T2- 860 2-021 and the funding support provided by the Lee Kong Chian Fund for Excellence.