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

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 (Fama and French, 1993) is better than CAPM (Sharpe, 1964) in explaining the mean-variance efficiency of both the Chinese and US stock markets. Furthermore, our results suggest that the US stock market is more efficient in terms of mean-variance efficiency than the Chinese stock market.