The Paris Agreement’s goals cannot be achieved without sufficient funding, but the funding has been extremely inadequate. Addressing this problem innovatively, John Broome and Duncan Foley offer economic and political arguments in favor of establishing a new international institution, a World Climate Bank (WCB). The economic case for a WCB appears strong insofar as the bank’s main function would be to scale up mobilization of the financial resources needed for decarbonizing the world economy. However, Broome and Foley problematically assert that a WCB must buy up fossil fuel assets. I argue that this could lead to disastrous consequences and must be ruled out. Claims by Broome and Foley about realism play important roles in their proposal, although it is not clearly based on any particular form of realist political theory. I argue that a realistic proposal would include sound arguments, and I show that the political arguments offered by Broome and Foley involve equivocation, vagueness, and self-contradiction. I sketch a provisional political case for a World Climate Bank for Mitigation, Adaptation, and Resilience (WCB-MAR) satisfying certain desiderata. In the course of critiquing and revising the Broome-Foley proposal, I begin to develop a new conception of political realism. Here I aim to motivate political scientists and theorists focusing on international institutions and global justice to help develop and assess political responses to the climate crisis, including my proposal for a WCB-MAR. When doing such work, they should take full account of the gravity and urgency of the crisis. This requires them to be politically realistic in the sense discussed herein.