Testing portfolio alpha against a linear factor model can be interpreted as a mean-variance efficiency test of the optimal portfolio of factors. For ambiguity neutral investor, adding active portfolio with statistically significant alpha always implies efficiency gain relative to the optimal...

We examine the connection between tail risk — as measured in Kelly and Jiang (2014) — and the cross-section of expected returns. In conditional predictive regression systems and vector-autoregressions of the market portfolio and the long- and shoresides of the Fama-French factor portfolios,...