Ambiguity Aversion and Portfolio Efficiency Tests

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 portfolio of factors. In contrast, for ambiguity averse investor, the efficiency gain must be above a threshold which depends on the uncertainty about the factors' and active portfolio's expected returns. Building on the theoretical framework developed in Garlappi, Uppal and Wang (2007), we propose a new method to test portfolio efficiency relative to a factor model by using asset exclusion conditions from the optimal portfolio of the ambiguity averse investor. The asset exclusion threshold is an F-statistic that is non-redundant with significance of alpha under the ambiguity-neutral test. Active portfolios with statistically significant alpha but weak efficiency gain may be excluded from the optimal portfolio. We apply this criterion empirically to screen active portfolios ("anomalies'') and find that some anomalies do not pass our exclusion test under statistically reasonable ambiguity about their expected return