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 represent an anomaly 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-equilibrium foundations for the tests and show their properties in simulations. The tests take into account any risk disliked by risk-averse individuals, including high-order moments and tail risks. The tests do not rely on the validity of a factor model or 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