How much capital should banks hold?

How do banking crises occur and how can bank capital requirements and other macroprudential policies help reduce the frequency and severity of these crises? Since the global financial crisis in 2008-2009, the field of macroeconomics has made big strides in integrating banking and financial frictions into standard analytical frameworks. This has helped deliver new quantitative insights into this question. Nevertheless, more than a decade after the financial crisis, the optimal level of bank capital requirements remains an open question. 

To assess the optimal level of capital requirements, it is crucial to quantify their benefits and costs. Higher capital requirements reduce the probability of banking crises at the expense of restricting the supply of bank credit in normal times. To evaluate this trade-off we provide a framework that captures well the behaviour of the economy not only in normal times but also during periods of banking crises driven by bank equity declines (Baron et al. 2019).

One specific challenge that has not been addressed in the current debate is to properly quantify the channels via which borrower defaults lead to bank insolvency. In Mendicino et al. (2020), we develop a structural general equilibrium model of bank default risk and undertake a quantitative exploration of the role of borrower defaults in generating rare but severe episodes of bank failures, which are associated with large output losses. We show that underestimating the impact of borrower defaults on bank solvency biases downwards the optimal level of bank capital requirements.

The mechanism 

In our framework, banks’ solvency problems arise endogenously from high default rates among their borrowers. Loans have limited upside potential because healthy borrowers merely repay the contractually agreed amount including interest. However, they carry significant downside risk due to the possibility of default. Although we are not the first to point out this asymmetry in returns (e.g. Nagel and Purnanandam 2019), we explore its implications in a quantitative general equilibrium model. The asymmetric returns on bank loans lie at the heart of our mechanism.

Figure 1 shows how this insight operates in a simple model of a bank holding a portfolio of loans. The left panel shows the return on the loan portfolio as a function of the average productivity of the borrowing firms. We can clearly see how the return on the portfolio is insensitive to borrower productivity when the latter is high, but it deteriorates sharply as productivity falls. The right panel of Figure 1 shows the distribution of the rates of return banks receive on loans. They are highly skewed to the left, which means that the most likely outcome is that most borrowers repay fully, but there is a long left tail of very low returns due to high borrower defaults. The key observation is that this left skewness in the distribution of bank loan portfolio returns arises endogenously due to the non-linear returns of bank loans (or, more generally, debt contracts), even when the shocks to the productivity of borrowing firms have a standard log-normal distribution. In other words, bank returns are asymmetric even if the shocks that affect borrowers are fully symmetric.

The asymmetry shown in the chart arises endogenously in our model and implies that bank balance sheets are more sensitive to recessions than to booms. Most of the time, therefore, banks are very stable and safe, but a sufficiently deep recession can push them to insolvency. Capturing this fact allows our model to match the economy’s behaviour in normal times while generating rare but severe ‘twin default’ crises – i.e. episodes of high firm defaults that result in bank solvency problems and deep recessions. During such episodes, bank solvency is much more sensitive to the…