Even 30 years after Rothschild and Stiglitz's () seminal work on competitive insurance markets with adverse selection, existence and characterization of the equilibrium outcome are still an open issue. We model a basic extension to the Rothschild and Stiglitz () model: we endogenize up‐front capital of insurers. Under limited liability, low up‐front capital gives rise to an aggregate endogenous insolvency risk, which introduces an externality among customers of an insurer (Faynzilberg, 2006). It is shown that an equilibrium with the second‐best efficient Miyazaki–Wilson–Spence allocation always exists.