Bank size and risk-taking under Basel II

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Abstract

We analyze the relationship between bank size and risk-taking under the Basel II Capital Accord. Using a model with imperfect competition and moral hazard, we show that the introduction of an internal ratings based (IRB) approach improves upon flat capital requirements if the approach is applied uniformly across banks and if the costs of implementation are not too high. However, the banks’ right to choose between the standardized and the IRB approaches under Basel II gives larger banks a competitive advantage and, due to fiercer competition, pushes smaller banks to take higher risks. This may even lead to higher aggregate risk-taking.

Introduction

Long before the current crisis and before the inception of the Basel II Accord in 2007, both academics and politicians criticized the new regulation. Many commentators were sceptical whether it would contribute to higher stability in the banking sector. The Quantitative Impact Studies conducted by the Basel Committee pointed towards a sharp reduction in capital holdings by banks adopting an internal ratings based (IRB) approach. Moreover, academics criticized that the new accord neglected the endogeneity of risk and tended to have procyclical effects (see, e.g., Daníelsson et al., 2001). In fact, all these problems appear to have contributed to the severity of the current crisis.

The Basel II regulation directly destabilized banks because it allowed them to reduce their capital buffers. However, due to the high fixed costs of implementing an IRB approach, not all banks were able to reduce capital levels to the same extent, leading to competitive distortions in the banking sector. Such concerns led the US Congress to postpone the implementation of Basel II and to develop a modified framework of capital regulation.1

We argue that these competitive distortions are worrisome not only from a competition policy perspective, but also from a financial stability perspective because they raise aggregate risk in the banking sector. Importantly, this result does not follow from the implementation of the IRB approach as such. In fact, in our model, the introduction of an IRB approach is beneficial if it is applied uniformly to all banks and the fixed costs of implementation are not too large because this approach governs banks’ risk-taking behavior more effectively by giving banks an incentive to choose efficient projects.

The problem arises from the banks’ right to choose between the standardized and the IRB approaches, which leads to an asymmetric treatment of small and large banks by the regulation. The implementation of the IRB approach requires large initial investments in risk management technologies, which may deter small banks from choosing the IRB approach. Then only large banks profit from the reduction in capital requirements (and hence marginal costs) for safe loans in the IRB approach. This gives them a competitive advantage over small banks. In our model, this leads to reduced market shares of small banks and, due to fiercer competition in the market for deposits, to an increase in small banks’ risk-taking. Hence, an optional IRB approach may reduce financial stability.2 This may also translate into undesirable changes in lending structure. If small banks specialize in extending loans to small firms, our model predicts a cutback in the lending to these borrowers, especially to the more creditworthy ones among them.3

There is by now a large literature on the Basel II Accord. Most empirical papers (too many to be reviewed here) deal with the question whether the accord assigns the correct risk weights to different risk groups. We abstract from this issue here. Several papers deal with the adverse macroeconomic effects of Basel II, especially with its procyclicality and its neglect of the endogeneity of financial risk (see, e.g., Kashyap and Stein, 2004, Daníelsson et al., 2004). Similar to the authors of those papers, we are interested in the implications of the accord for the aggregate risk in the economy. A paper by Decamps et al. (2004) is the only one to analyze the interactions among the three pillars of the accord. In contrast, we focus on pillar I, the capital regulation.

The papers most closely related to ours are those by Repullo and Suarez, 2004, Rime, 2005, which analyze the implications of the co-existence of the standardized and the IRB approaches for banks’ risk choices. Both papers argue that banks eligible for the IRB approach have a competitive advantage in the provision of low-risk loans (because the IRB approach has a lower capital requirement), while the less sophisticated banks have a competitive advantage in the provision of high-risk loans (because the standardized approach has a lower capital requirement). This leads to a sorting of borrowers: High risk borrowers receive financing from unsophisticated banks, and low-risk borrowers from sophisticated banks.4 Ruthenberg and Landskroner (2008) provide empirical support for this type of sorting, distinguishing between corporate and retail customers. In both loan segments, high-quality borrowers finance through large banks (which are likely to adopt the IRB approach), whereas low-quality borrowers tend to go to small banks (which presumably adopt the standardized approach) where they can expect to obtain more favorable loan rates.

Our paper makes a different point by starting from a setup that differs in several important respects from those used by Repullo and Suarez, 2004, Rime, 2005. First, there are no moral hazard effects in their models. Their results are entirely driven by the cost differentials between the two regulatory approaches. In our model, we emphasize moral hazard effects because we believe that one of the main purposes of capital requirements is to provide incentives for prudent bank behavior.5 Second, the other two papers model bank competition in the loan market, and ignore competition on the liabilities side. In both models, it is crucial that borrowers are actually able to switch among banks. In contrast, we model competition on the liabilities side of banks’ balance sheets and assume that large and small banks serve different clienteles in their loan business. The large empirical literature contrasting relationship and transactions loans, cited above, points to a strong segmentation in loan markets: Large banks specialize in different types of loans than smaller banks. In a context similar to ours, Berger (2006) presents empirical evidence for limited competition in loan markets among banks that are likely to adopt the IRB approach and other (smaller) banks. This suggests that it is appropriate to abstract from loan market competition for the case relevant in our model, namely the competition among large and small banks. We assume, however, that large and small banks draw from a similar pool of deposits, such that they compete in the deposit market.6 Note that a model where banks compete in loan markets and are subject to a moral hazard problem would lead to the same effects as our model. As a third difference to the above-mentioned papers, we also consider the effects of regulation on aggregate risk-taking in the economy.

Another related paper is by Berger (2006), who empirically assesses the competitive effects caused by the preferential treatment of SME loans in the IRB approach. Our theoretical idea also applies to this more specific issue because it also implies a difference in capital requirements (and hence marginal costs) across different bank groups. Note, however, that our main interest is in the asymmetric treatment of banks due to the co-existence of the standardized and the IRB approaches, which may be quantitatively much more important than the “carve-out” on SME loans. Consistent with our assumption above, Berger (2006) concludes that the competitive effects in the loan market are likely to be small because large and small banks tend to make different kinds of loans. However, our analysis suggests that considering the competitive effects on the loan market may not in itself make for a sufficient assessment of the implications of the special provisions for SME loans.

Our findings call for a reform of banking regulation that removes the asymmetric treatment of large and small banks and the resulting competitive distortion. One proposal of how to modify banking regulation in light of the current financial crisis is to subject large systemic institutions to higher capital requirements than smaller banks to make them internalize the externalities from bank failure. Such a capital surcharge would also counteract the competitive distortions of an optional IRB approach where large banks are subject to lower capital requirements, while maintaining the benefits of the IRB approach.

The paper proceeds as follows: In Section 2, we describe the features of the Basel II Capital Accord that are relevant for our theoretical model. Section 3 contains the setup of the model. In Section 4, we analyze a banking sector where all banks are regulated according to the standardized approach. Section 5 turns to the IRB approach. We first show what happens when all banks are required to adopt the internal ratings based approach. Then we analyze the situation where banks can choose between the standardized and the IRB approaches. In Section 6, we briefly analyze the effects of capital regulation in a setup where capital requirements do not reduce moral hazard, but serve as buffer against potential losses. Section 7 concludes.

Section snippets

The Basel II Capital Accord

Our analysis focuses on one particular—and arguably the most important—aspect of the Basel II Capital Accord: the enhancement of the risk sensitivity of capital requirements for credit risk.7

Banks

Consider an economy with n + 1 chartered banks. Banks have limited liability and are risk neutral. They are owned by penniless bankers (the inside equity holders), whose only wealth is the bank charter. They collect deposits and outside equity, and can invest these funds in one risky project. There are thus three stakeholders in the bank: depositors, outside equity investors, and the banker (the inside equity investor).

Each bank can invest either in a “safe” or in a “risky” project. The safe

The standardized approach

We now characterize the equilibria of the model under different types of capital regulation. In this section, we assume that all banks must adopt the standardized approach. We determine the equilibrium by using backwards induction. First, we study the banks’ risk choices for given deposit volumes, deposit rates, and capital structures (Section 4.1). Second, we derive the supply of deposits and equity (Section 4.2). Then we discuss the optimal behavior of banks in the markets for equity and

The IRB approach

So far, we have discussed an economy in which all banks use the standardized approach. Now we turn to the IRB approach. We first assume that all banks must adopt the IRB approach (Section 5.1). Then we analyze the banks’ right to choose between the two approaches, as embodied in the Basel II Accord (Section 5.2).

Capital as buffer against losses

Capital regulation also affects financial stability directly through its effect on banks’ buffers against losses. Indeed, low capital levels are seen as one of the reasons for the vulnerability of banks in the current crisis. Therefore, we now briefly analyze the effects of the Basel II regulation when capital serves as buffer against losses.24 Strictly speaking, regulatory capital is not a buffer for banks themselves because

Conclusion

Our paper presents a novel channel through which the Basel II Capital Accord harms small banks and may lead to an increase in aggregate risk in the economy. We start from the observation that the Basel II accord implicitly treats small and large banks asymmetrically: Due to the high fixed costs from implementation, it is likely that only large banks opt for the IRB approach. Then small banks do not benefit from the lower capital requirements for safe loans. This distorts competition, benefiting

Acknowledgments

We would like to thank John Boyd, Ernst-Ludwig von Thadden, Reinhard H. Schmidt, Anne van Aaken, Falko Fecht, Felix Höffler, an anonymous referee, Ike Mathur (the editor), and especially Martin Hellwig for helpful suggestions. We also thank the participants of the Econometric Society World Congress in London, the “Tor Vergata” Conference on Banking and Finance in Rome, the Congress of the Association of University Professors of Management in Kiel, the German Economic Association of Business

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