According to the local risk-neutrality theorem an agent who has the opportunity to invest in an uncertain asset does not buy it or sell it short iff its expected value is equal to its price, independently of the agent's attitude towards risk. Contrary to that it is shown that, in the context of expected utility theory with differentiable vNM utility function, but without the assumption of stochastic constant returns to scale, nondegenerate intervals of no-trade prices may exist. With a quasiconcave (...) expected utility function they do if, and only if, the agent is risk averse of order one. (shrink)