Abstract We provide evidence supporting Rubinstein's (1973) model that if returns are not normal, measuring risk requires more than just measuring covariance. Higher‐order systematic comoments should be important to risk‐averse investors who are concerned about the extreme outcomes of their investments. Our paper shows that the Fama‐French factors [SMB (return on small stocks less the return on big stocks), HML (return on high book‐to‐market stocks less the return on low book‐to‐market stocks)] as well as the momentum and market liquidity factors can be explained by the higher‐order systematic comoments, and it lends support to the traditional covariance risk‐based theory without having to resort to behavior assumptions.