Abstract We examine asset prices in a representative-agent model of general equilibrium. Assuming only that individuals are risk averse, we determine conditions on the changes in asset risk that are both necessary and sufficient for the asset price to fall. We show that these conditions neither imply, nor are implied by the conditions for second-degree stochastic dominance. For example, if the payoff on an asset becomes riskier in the sense of second-degree stochastic dominance, the equilibrium price of the asset need not necessarily fall. We further demonstrate how our results can be imbedded into a market that is incomplete in the sense of containing an uninsurable background risk, such as a risk on labor income. We extend our model to show how a miscalibration of the asset risk can lead to a partial explanation of high equity premia (i.e., the “equity premium puzzle”).