Testing Alphas in Linear Factor Models: A Portfolio Approach

This paper develops a test for evaluating linear factor models in high-dimensional settings. The proposed Maximum Random Sparse Portfolio (MRSP) test generates L random sparse portfolios, each obtained through K random draws, and then selects the hardest-to-price portfolio to assess factor model performance. By evaluating multiple randomly generated sparse portfolios, the MRSP test retains a portfolio-based economic interpretation while avoiding reliance on a single hardest-to-price asset. Under the null hypothesis and the stated regularity conditions, the centered MRSP statistic converges to a type I extreme value distribution. Monte Carlo simulations show stable finite-sample performance. In the empirical application, model fit generally improves in recent years, although the evidence varies across factor models and test assets. The 3-factor model of Daniel, Hirshleifer, and Sun (2020, Review of Financial Studies) performs best among the models considered.