This paper investigates stable and efficient networks in the context of risk sharing, when it is costly to establish and maintain relationships that facilitate risk sharing. We find a novel trade-off between efficiency and equality: The most stable efficient networks also generate the most inequality. We then suppose that individuals can be split into groups, assuming that incomes across groups are less correlated than within a group but relationships across groups are more costly to form. The tension between efficiency and equality extends to these correlated income structures. More-central agents have stronger incentives to form across-group links, reaffirming the efficiency benefits of having highly central agents. Our results are robust to many extensions. In general, endogenously formed networks in the risk-sharing context tend to exhibit highly asymmetric structures, which can lead to stark inequalities in consumption levels.