Agents involved in the formation of a social or economic network typically face uncertainty about the benefits of creating a link. However, the interplay of such uncertainty and risk attitudes has been neglected in the network formation literature. We propose a dynamic network formation model that builds on standard microeconomic concepts of utility maximization, incomplete information, and risk aversion. The model predicts that an agent's risk aversion is correlated with her network clustering coefficients, but not with her degree. We discover a mechanism that generates a correlation between network position and payoffs of individuals. Moreover, we show how the generated network architecture depends on the uncertainty in the environment it is embedded in.