Considerable debate persists around the definition of risk. Depending on the area of study, the concept of risk may be defined as the variance of the possible outcomes, the probability of a loss, or a combination of the loss probability and its maximum possible loss. Mounting evidence suggests the anterior cingulate cortex (ACC), including the surrounding medial prefrontal cortex (mPFC), and the anterior insula/inferior frontal gyrus (IFG) are key neural regions that represent perceived risks. Yet it remains unclear which of these formalisms best accounts for the pattern of activation in brain regions representing risk, and it is also difficult to disentangle risk from value, as both contribute to perceived utility. To adjudicate among the possible definitions, we used fMRI with a novel gambling task that orthogonalized the variance, loss probability, and maximum possible loss among the risky options, while maintaining a constant expected value across all monetary gambles to isolate the impact of risk rather than value. Here we show that when expected value is controlled for ACC and IFG activation reflect variance, but neither loss probability nor maximum possible loss. Across subjects, variance-related activation within the ACC correlates indirectly with risk aversion. Our results highlight the variance of the prospective outcomes as a formal representation of risk that is reflected both in brain activity and behavior, thus suggestive of a stronger link among formal economic theories of financial risk, naturalistic risk taking, and neural representations of risk.