The common folklore that giving options to agents will make them more willing to take risks is false. In fact, no incentive schedule will make all expected utility maximizers more or less risk averse. This paper finds simple, intuitive, necessary and sufficient conditions under which incentive schedules make agents more or less risk averse. The paper uses these to examine the incentive effects of some common structures such as puts and calls, and it briefly explores the duality between a fee schedule that makes an agent more or less risk averse, and gambles that increase or decrease risk.