Are there multiple independent risk anomalies in the cross section of stock returns?

Using multivariate portfolio sorts, firm-level cross-sectional regressions and spanning tests, we show that, in the cross section of stock returns, most commonly used risk measures in academia and in practice are separate return predictors with negative slopes. That is, in contrast to what many researchers might expect, there are multiple risk anomalies that are independent of each other. This implies that, in empirical asset pricing models, even different forms of total risk can be simultaneously relevant. Further, it suggests that investors trading based on one risk measure can obtain significant gains when also trading based on another. For example, an investor selecting stocks based on volatility can earn a significant monthly alpha by also considering the information contained in the maximum drawdown.