Problems related to disaster management are strongly influenced by random outcomes, which indicates the importance of using a mathematical tool that can coherently take into account the stochasticity associated with humanitarian logistics problems. However, stochastic models can lead to decisions that consider solely expected values and thus neglect the eventual damage associated with the worst-case scenarios of a disaster. Two-stage stochastic optimization can lead to solutions that present relief supply shortages that could be often prevented. Bearing this in mind, models with risk aversion have been proposed to make decisions that are better suited to humanitarian operations. In this paper, we propose a model for pre-positioning, location and distribution that uses the measure of Conditional Value at Risk (CVaR) to better attend to affected people in a disaster. A post-optimization analysis is conducted to evaluate the quality of the solution. The results indicate that a risk-aversion profile can lead to a 100% reduction of shortages that can be avoided.