Estimating the Required Amount of a Bank’s Loss-Absorbing Capacity

ABSTRACT

The issue of banks’ loss-absorbing capacity (LAC) has been extensively discussed in recent years. That debate was triggered by the idea of a “bail in”: the use of certain bank’s liabilities to cover losses and recapitalization when it is failing or likely to fail. The objective of this article is to determine the volume of a bank’s equity and liabilities available for bail in that would ensure a feasible resolution. To determine that amount, we propose a general quantitative model, considering that the troubled bank must cover its losses (in any resolution path) and restore both its equity and LAC (in the event of recapitalization). One novelty of our approach is that it accounts for the decline in a bank’s size as a result of the resolution process and the time-varying regulatory regime (capital requirements). The approach presented in this article makes it possible to determine the amount of LAC required as well as the importance of capital constraints and buffers, which might play a key role in determining the best resolution path. The calculations based on the model under Basel II and Basel III regimes confirm the importance of the time-varying capital buffers to enhance bank resilience. However, if the losses are large, other regulatory actions are required to increase bank LAC.

KEYWORDS:

• Bail in
• bank resolution
• capital requirement
• loss-absorbing capacity
• resolution tools

JEL:

• E42
• G21
• G28
• H12

Notes

1. Losses are first absorbed by the bank capital. If it is insufficient, the remainder become liabilities that are subject to the bail-in (in increasing order of maturity).

2. P&A is a transaction in which a healthy bank purchases assets from an unhealthy bank and assumes its liabilities.

3. An institution created by a regulator to operate a failed bank until a buyer for it can be found.

4. The off-balance-sheet position can be reflected using conversion factors.

5. This justifies the use of comparative statics.

6. Considering that the loss can gradually rise over time, the required LAC is related to the specific trigger of the resolution. It may depend on the current total asset value (i.e., loss amount), as well as the current equity level or the respective indicator, whose breach triggers the resolution process. The earlier the resolution is launched, the more equity there is that can be used in the bank resolution, and, as a consequence, the scale of the bail in is expected to be smaller.

7. This article implicitly assumes that the loss is proportionate to the bank’s total assets. The alternative assumption is that the loss is proportionate to $\mathrm{R}\mathrm{W}\mathrm{A}$.

8. This assumption follows Acharya and Yorulmazer (2007) and White and Yorulmazer (2014), who believe that a “misallocation cost” can arise if the bank is liquidated or its assets are transferred to another entity in the course of the resolution process.

9. The value of α seems to depend on the resolution path. Considering that assets that remain in the banking system are expected to retain their value better, the misallocation costs in the event of a bank’s liquidation ${\alpha }_{\mathrm{L}}$ are higher than when P&A or the bridge bank resolution tool are applied, ${\alpha }_{\mathrm{P}\mathrm{A}}$. So, we can apply the following condition: $0\le {\alpha }_{\mathrm{P}\mathrm{A}}<{\alpha }_{\mathrm{L}}$.

10. Alternatively, the same conclusion can be presented as follows. If P&A (or a bridge bank) is considered the optimal resolution tool, the resolution authority must step in earlier (i.e., when the loss is lower) than in event of an open bank bail in.

11. The first of these equations follows the one derived in Section 2 for P&A and the required LAC is a linear function of ε, but with the required leverage ratio $w_1{\rho }_1$in place of α. At the same time, the second equation precisely follows the quadratic, concave function derived in Section 2 in the event of recapitalization (see Figure 2).

12. The Basel Accords are three sets of recommendations on banking regulations (Basel I, II, and III) set by the Basel Committee on Bank Supervision (BCBS) as the regulatory framework specifically, concerning capital adequacy with respect to the risk borne by a bank.

13. And without severe systemic disruptions.

14. Total liabilities and own funds.