Anomaly or Possible Risk Factor? Simple-To-Use Tests

Basic asset pricing theory predicts high expected returns are a compensation for risk. However, high expected returns might also constitute anomalies due to frictions or behavioral biases. We propose two complementary simple-to-use tests to assess whether risk can explain differences in expected returns. We provide general theoretical equilibrium foundations for the tests and show their properties in simulations. The tests take into account risks disliked by risk-averse individuals, including high-order moments and tail risks. None of the tests rely on the validity of a factor model nor other parametric statistical models. Empirically, we find risk cannot explain a large majority of variables predicting differences in expected returns. In particular, value, momentum, operating profitability, and investment appear to be anomalies.