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Bank Risk Taking and Competition Revisited: New Theory and New Evidence John Boyd, Gianni De Nicolò and Abu Al Jalal The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF or the Federal Reserve System.

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Questions Is there a trade-off between competition and stability in banking? Is there a trade-off between competition and stability in banking? The existing empirical evidence is mixed and theory has produced conflicting predictions. The existing empirical evidence is mixed and theory has produced conflicting predictions. What are the implications of market structure for bank asset allocations? What are the implications of market structure for bank asset allocations? To date, neither theory nor evidence To date, neither theory nor evidence We address these important policy questions bringing to bear new theory and new evidence. We address these important policy questions bringing to bear new theory and new evidence.

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New Theory: bank asset allocation Banks face both a portfolio allocation problem and an optimal contracting problem Banks face both a portfolio allocation problem and an optimal contracting problem They acquire bonds and other traded securities (they are price takers) and they lend in environments with private information. They acquire bonds and other traded securities (they are price takers) and they lend in environments with private information. A causal relationship from market structure to asset portfolio allocation is of more than theoretical interest (what is special about banks?) A causal relationship from market structure to asset portfolio allocation is of more than theoretical interest (what is special about banks?)

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New Theory: bank asset allocation We model both decisions by allowing banks to invest in a default-risk- free government bond. We model both decisions by allowing banks to invest in a default-risk- free government bond. We get a good deal of increased complexity for two reasons: We get a good deal of increased complexity for two reasons: A) Banks investment in bonds can be viewed as a choice of collateral (indeed, the risk-free bond becomes a risky asset....) B) The asset allocation between bonds and loans becomes a strategic variable

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Two New Models The (CVH) model : a) competition in deposit, but not in loan, markets, and b) no contracting problem (e.g. Keeley, 1990, Hellman, Murdoch and Stiglitz, 2000, Repullo, 2004). The (CVH) model : a) competition in deposit, but not in loan, markets, and b) no contracting problem (e.g. Keeley, 1990, Hellman, Murdoch and Stiglitz, 2000, Repullo, 2004). Our model (BDN): a) competition in both loan and deposit markets, and b) contracting problem (Boyd and De Nicolo (2005). Our model (BDN): a) competition in both loan and deposit markets, and b) contracting problem (Boyd and De Nicolo (2005). In both models, lower concentration (more banks) means more competition In both models, lower concentration (more banks) means more competition

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New Theory: Predictions Both models yield a negative relationship between loan-to-asset ratios and concentration... Both models yield a negative relationship between loan-to-asset ratios and concentration... BUT BUT CVH model : negative relationship between concentration and banks probability of failure CVH model : negative relationship between concentration and banks probability of failure BDN model: positive relationship between concentration and banks probability of failure BDN model: positive relationship between concentration and banks probability of failure

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New Evidence We explore the predictions of the models empirically using two data sets: We explore the predictions of the models empirically using two data sets: U.S. sample: 2003 cross-sectional sample of about 2,500 U.S. banks U.S. sample: 2003 cross-sectional sample of about 2,500 U.S. banks International sample: panel data set with bank-year observations ranging from 13,000 to 18,000 in 134 non-industrialized countries for the period 1993-2004. International sample: panel data set with bank-year observations ranging from 13,000 to 18,000 in 134 non-industrialized countries for the period 1993-2004.

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Empirical Results A measure of bank probability of failure is positively and significantly related to concentration. A measure of bank probability of failure is positively and significantly related to concentration. The risk implications of the CVH model are rejected, those of the BDN model are not. The risk implications of the CVH model are rejected, those of the BDN model are not. The implications of both models for asset allocations are not rejected, as loan-to-asset ratios are negatively and significantly associated with concentration. The implications of both models for asset allocations are not rejected, as loan-to-asset ratios are negatively and significantly associated with concentration.

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Implications No trade-off between banking stability and competition No trade-off between banking stability and competition The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking Many positive and normative analyses of regulation based on CVH-type models should be re-examined. Many positive and normative analyses of regulation based on CVH-type models should be re-examined.

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CVH Model (1) Bank Problem Bank Problem NMH and MH strategies NMH and MH strategies

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CVH Model (2) No-moral-hazard (NMH) strategy (max{.}>0) No-moral-hazard (NMH) strategy (max{.}>0) Moral-hazard (MH) strategy (max{.}=0) Moral-hazard (MH) strategy (max{.}=0) Banks may or may not endogenously choose to be default risk-free even though they have the option of risk shifting. Banks may or may not endogenously choose to be default risk-free even though they have the option of risk shifting. Focus on symmetric Nash equilibria in pure strategies Focus on symmetric Nash equilibria in pure strategies

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CVH Model (3) Proposition 1 Proposition 1 (a) Either the unique equilibrium is MH (loans/assets=1) or (a) Either the unique equilibrium is MH (loans/assets=1) or (b) Unique NMH if N N(2) (b) Unique NMH if N N(2) Risk of failure increases in N Risk of failure increases in N In (b), loans/assets move from 0 to 1 as N increases In (b), loans/assets move from 0 to 1 as N increases

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BDN Model (1) Entrepreneurs: Given a loan rate, entrepreneurs solve: Entrepreneurs: Given a loan rate, entrepreneurs solve: Banks: Each bank solves Banks: Each bank solves

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BDN model (2) As before, NMH and MH strategies As before, NMH and MH strategies But NOW, NMH strategies need to be distinguished in two categories: But NOW, NMH strategies need to be distinguished in two categories: No provision of credit (if this is an equilibrium outcome, we have CREDIT RATIONING) No provision of credit (if this is an equilibrium outcome, we have CREDIT RATIONING) Some provision of credit Some provision of credit

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BDN Model (3) Propositions 2, 3 and 4 Propositions 2, 3 and 4 (a): There exists economies for which for N

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Evidence: Theory and Measurement Measure of Bank Risk Measure of Bank Risk Theory: probability of bank failure Theory: probability of bank failure Measurement: Z-score (distance-to-default) Measurement: Z-score (distance-to-default) Measure of Competition Measure of Competition Theory: Number of banks (homogenous firms) Theory: Number of banks (homogenous firms) Measurement: Hirschmann-Hirfendahl Indices (HHIs). Measurement: Hirschmann-Hirfendahl Indices (HHIs).

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Evidence: U.S. Sample About 2500 U.S. banks that operate only in rural non- Metropolitan Statistical Areas About 2500 U.S. banks that operate only in rural non- Metropolitan Statistical Areas Cross-section for one period only, June, 2003. Cross-section for one period only, June, 2003. The FRB defines a competitive market as a county and maintains and updates HHI Indices The FRB defines a competitive market as a county and maintains and updates HHI Indices Within each market area the FRB defines a competitor as a banking facility, which could be a bank or a bank branch. Within each market area the FRB defines a competitor as a banking facility, which could be a bank or a bank branch.

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U.S. sample The U.S. sample has an important, interesting and unique feature. We asked the FRB to delete from the sample all banks that operated in more than one market area. The U.S. sample has an important, interesting and unique feature. We asked the FRB to delete from the sample all banks that operated in more than one market area. Thus, we are able to better match up competitive market conditions as represented by the HHI and individual bank asset allocations as represented by balance sheet data. Thus, we are able to better match up competitive market conditions as represented by the HHI and individual bank asset allocations as represented by balance sheet data. Disadvantage : exclusion of many banks (all in HHI) Disadvantage : exclusion of many banks (all in HHI)

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International sample Panel data set of about 2700 banks in 134 countries excluding major developed countries over the period 1993 to 2004 (Bankscope). (Bank-year observations range from more than 13,000 to 18,000, depending on variables availability). Panel data set of about 2700 banks in 134 countries excluding major developed countries over the period 1993 to 2004 (Bankscope). (Bank-year observations range from more than 13,000 to 18,000, depending on variables availability). Disadvantage: bank market definitions are necessarily imprecise, since it is assumed that the market for each bank is defined by its home nation. Disadvantage: bank market definitions are necessarily imprecise, since it is assumed that the market for each bank is defined by its home nation. We did not include in the sample banks from the U.S., Western Europe and Japan, since defining the nation as a market is problematic. We did not include in the sample banks from the U.S., Western Europe and Japan, since defining the nation as a market is problematic.

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U.S. Sample Regressions Dependent variables: Dependent variables: a) Z-score, b) loans/assets, and c) Z-score components, regressed on: county HHI, county/state specific and bank specific controls regressed on: county HHI, county/state specific and bank specific controls Robust OLS and GMM IV estimation Robust OLS and GMM IV estimation

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Results Bank risk of failure positively related with concentration Bank risk of failure positively related with concentration The ratio of loans to assets negatively related to concentration The ratio of loans to assets negatively related to concentration The positive relationship between bank risk of failure and concentration mainly driven by the positive relationship between concentration and ROA volatility The positive relationship between bank risk of failure and concentration mainly driven by the positive relationship between concentration and ROA volatility

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Z-score regressions

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Loans/Assets regressions

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ROA regressions

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Equity/Asset regressions

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ROA volatility regressions

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International Sample Regressions Z-score is defined at each date Z-score is defined at each date Panel regressions with a) Z-score, b) loans/assets and c) Z-score components as dependent variables, regressed on: Panel regressions with a) Z-score, b) loans/assets and c) Z-score components as dependent variables, regressed on: countrys HHIs (Asset, Loans, Deposits) countrys HHIs (Asset, Loans, Deposits) country-specific and bank-specific controls. country-specific and bank-specific controls. Robust country fixed effects and firm fixed effects panel regressions Robust country fixed effects and firm fixed effects panel regressions All explanatory variables are lagged one year All explanatory variables are lagged one year

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Results Bank risk of failure positively related with concentration Bank risk of failure positively related with concentration The ratio of loans to assets negatively related to concentration The ratio of loans to assets negatively related to concentration The positive relationship between bank risk of failure and concentration driven by the negative relationship between capitalization and concentration, and the positive relationship between ROA volatility and concentration The positive relationship between bank risk of failure and concentration driven by the negative relationship between capitalization and concentration, and the positive relationship between ROA volatility and concentration

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Dependent Variable: Z-score(t)

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Dependent Variable: LGLTA(t)

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Components of the Z-score(t)

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Conclusion No trade-off between banking stability and competition No trade-off between banking stability and competition The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking The positive relationship between competition and willingness to lend suggests an important dimension policy makers should consider to evaluate costs and benefits of competition in banking Many positive and normative analyses of regulation based on CVH-type models should be re-examined. Many positive and normative analyses of regulation based on CVH-type models should be re-examined.

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Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Return and Risk: The Capital Asset Pricing Model (CAPM) Chapter.

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