The GSIB (global systemically important bank holding company) capital surcharge requires GSIBs to maintain higher capital ratios than banks that aren’t GSIBs.  When the Fed announced the surcharge, it explained that the surcharge was designed to achieve “equal expected impact” of the systemic costs of the failure of a GSIB and a reference not-quite GSIB.  In a nutshell, they seek to have the odds of failure times the systemic costs of failure equated for the two types of firms.  Since the systemic costs of failure of the GSIB are higher, the GSIB holds more capital to reduce its odds of failure proportionately. 

Setting aside significant problems with how the Fed actually calibrated the capital charge (some of which we discuss in a previous research note), there are reasons to be skeptical about the equal expected impact objective itself.  Usually economic conditions for optimality equate marginal costs and marginal benefits.  In this case, the marginal social cost of becoming more systemic (contagion, moral hazard if viewed as TBTF, etc.) should equal the marginal social benefit of being more systemic (returns to scale to becoming larger, ability to provide global services, etc.).  If there are no economic gains to a bank being more systemic, then the correct policy is to reduce the size of all systemic banks to a level where they are no longer systemic.

In this note we show that in a simple model of banking, socially optimal bank size does not, in fact, equate the expected systemic impact of banks of different sizes. We are not aware of an economic model, or even a compelling rationale, where the socially optimal distribution of bank size has the characteristic that the expected systemic cost of failure is equal across sizes.