Enough liquidity with enough capital - And vice versa?

We study the interplay of capital and liquidity regulation in a general equilibrium setting by focusing on future funding risks. The model consists of a banking sector with long-term illiquid investment opportunities that need to be financed by short-term debt and by issuing equity. Reliance on refinancing long-term investment in the middle of the life-time is risky, since the next generation of potential short-term debt holders may not be willing to provide funding when the return prospects on the long-term investment turn out to be bad. For moderate return risk, equilibria with and without bank default coexist, and bank default is a self-fulfilling prophecy. Capital and liquidity regulation can prevent bank default and may implement the first-best. Yet the former is more powerful in ruling out undesirable equilibria and thus dominates liquidity regulation. Adding liquidity regulation to optimal capital regulation is redundant.