A working paper published on April 3, 2017 by the US Federal Reserve attempts to quantify the costs and benefits of bank capital to arrive at an estimate of the optimal capital ratio for U.S. banks. In their paper, authors Simon Firestone, Amy Lorenc, and Ben Ranish begin their analysis by estimating to what extent the probability of financial crises falls as bank capital rises and calculate the output costs of a financial crisis. Against this cost, the authors then balance the cost of equity, a more expensive source of funding for banks than debt.
The authors conclude that interest rates would rise by around seven basis points if banks pass on all of the increase in the cost of capital to borrowers. Balancing the difference between costs and benefits, they estimate that the optimal level of capital is between 13% and 26%.
The range is merely an estimate, however. The authors caution that “The reported range reflects a high degree of uncertainty and latitude in specifying important study parameters that have a significant influence on the resulting optimal capital level, such as the output cost of a financial crisis.”
The study also discusses a range of considerations and factors beyond the cost-benefit framework that could have substantial effects on estimated optimal capital levels.
 Firestone, Simon, Amy Lorenc and Ben Ranish (2017). “An Empirical Economic Assessment of the Costs and Benefits of Bank Capital in the US,” Finance and Economics Discussion Series 2017-034. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2017.034.