This paper introduces the concept of standard risk aversion. A von Neumann-Morgenstern utility function has standard risk aversion if every risk that has a negative interaction with a small reduction in wealth also has a negative interaction with any undesirable, independent risk. It is shown that, given monotonicity and concavity, the combination of decreasing absolute risk aversion and decreasing absolute prudence is necessary and sufficient for standard risk aversion. Standard risk aversion is shown to imply not only Pratt and Zeckhauser's "proper risk aversion" (an undesirable risk always remaining undesirable in the presence of an independent undesirable risk), but also that being forced to face an undesirable risk reduces the optimal investment in a risky security with an independent return.