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© Hélyoth Hessou, 2020

Essays on financial institutions capital and liquidity

regulation

Thèse

Hélyoth Hessou

Doctorat en sciences de l'administration

Philosophiæ doctor (Ph. D.)

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Essays on financial institutions capital and liquidity regulation

Thèse

Hélyoth T. S. Hessou

Sous la direction de :

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ii Résumé

Cette thèse comprend quatre articles résumés qui vont comme suit :

Le premier essai étudie le comportement d’ajustement au capital réglementaire dans un régime de capital réglementaire multiple. La présence de cet essai est motivée par le fait que les modèles d’ajustement au capital bancaire existants déjà dans la littérature ne modélisent que l’ajustement à une seule mesure de capital et ne tiennent donc pas compte de l’importante corrélation entre les différentes normes de capital. Les résultats issus de ce travail sont de deux ordres. Premièrement, il est montré que la réglementation de deux ratios de capital (ajusté ou non au risque) est assimilable à la réglementation d’un ratio unique de capital (non ajusté au risque) dont la limite est assimilable à la valeur d’une option d’achat avec comme sous-jacent le taux de risque (réglementaire) des actifs bancaires. Une analyse de l’expérience du Canada et des États-Unis offre une justification supplémentaire à la résilience relative des banques canadiennes lors de la dernière crise des subprimes des années 2007.

Le deuxième essai se consacre à l’analyse de la norme de coussin contracyclique introduite sous Bâle III. Cette norme vise à lisser les fluctuations cycliques indésirables dans le capital bancaire qui affectaient négativement l’octroi de crédit par les banques surtout en période de crise. Ce travail vise à quantifier le niveau de coussin requis en tenant compte des composantes cycliques du capital bancaire. Une analyse de l’implication des nouvelles normes de liquidité est également abordée.

Le troisième essai analyse l’adéquation de l’application des nouvelles normes de capital contracycliques de Bâle III avec les coopératives de crédit canadiennes. En se basant sur les données des bilans comptables des coopératives canadiennes entre la période 1996 et 2014, Cet essai démontre que, contrairement aux institutions bancaires, les coopératives possèdent déjà une stratégie de gestion contracyclique pour leur coussin de capital. À cet effet, une introduction des nouvelles normes de coussin contracycliques n’affectera pas leur comportement d’ajustement. L’analyse révèle que le coussin de capital des coopératives de crédit sous-capitalisées sont procycliques et donc qu’une attention particulière de la part des régulateurs à l’endroit de ces coopératives serait nécessaire.

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Le quatrième essai est une extension de celui qui le précède ce sens où il analyse l’effet du capital réglementaire sur l’activité d’intermédiation des coopératives de crédit canadiennes. Nos résultats suggèrent que la croissance du portefeuille de prêt croît positivement avec le niveau de capitalisation des coopératives de crédit. À l’inverse, la croissance du portefeuille est négativement liée aux changements ou ajustements dans le capital réglementaire. Cette observation suggère que les coopératives de crédit devraient être encouragées via l’implémentation et le respect d’exigences de coussin de capital (de conservation et contracyclique) qui viseraient à détenir des niveaux suffisants de capitalisation.

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iv Abstract

The review of the articles included in this thesis can be summarized as follows:

The first essay examines the behavior of regulatory capital adjustment in a multiple capital requirement regime such as the Basel III one. This essay is motivated by the fact that the existing bank capital adjustment models are designed to address adjustment towards a single capital ratio. Our findings are numerous. Firstly, it appears that the joint regulation of two capital ratios (adjusted and unadjusted for risk) is assimilated to the regulation of a single capital ratio (not adjusted to risk), whose limit is assimilated to the value of a call option written on (regulatory) asset risk ratio. An analysis of both the Canadian and US experiences in the joint capital regulation provides further justification for the relative resilience of Canadian banks (in comparison with their US counterparts) during the last subprime crisis of late 2007.

The second essay is devoted to the analysis of the counter-cyclical buffer standard introduced under Basel III. This standard aims to smooth undesirable cyclical fluctuations in bank capital as this negatively affect the granting of credit by banks, especially in times of crisis. This work aims to quantify the required level of cushion by taking into account the cyclical components of bank capital. The implications of the new liquidity standards are also discussed.

The third essay analyzes the appropriateness of the new counter-cyclical capital standards of Basel III to Canadian credit unions regulation. Based on data extracted from Canadian financial cooperatives balance sheets over the period between 1996 and 2014, this essay shows that unlike banking institutions, credit union capital is already countercyclical, and therefore the introduction of the countercyclical buffer would not alter their intermediation activities. However, the analysis also reveals that the capital cushion of under-capitalized credit unions is pro-cyclical, and therefore these credit unions need close monitoring from regulators regarding their adjustment behaviors following countercyclical measures’ adoption.

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The fourth essay is an extension of the previous one in that it analyzes the effect of regulatory capital on lending by Canadian credit unions. Our findings suggest that the growth in the Canadian credit unions loan portfolio is positively associated with the level of capitalization. In contrast, we uncover a negative relation between change in credit union capital and the growth of their lending portfolio. This finding suggests that credit unions should be encouraged to hold adequate levels of capital. This can be achieved through the implementation of conservative and countercyclical capital requirements as advocated for banks.

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vi Table des matières

Résumé ... ii

Abstract ... iv

Table des matières ... vi

Liste des figures ... viii

Liste des tableaux ... ix

Liste des appendices ... x

Remerciements ... xii

Avant-propos ... xiv

Introduction ... 1

Essai 1: Risk-based capital and leverage ratios adjustments by banks: Canadian and the US experience ... 3

1.1 Résumé ... 3

1.2 Abstract ... 3

Introduction ... 4

1.4 Overview of the leverage ratio regulated in Canada and US prior to Basel III ... 8

1.4.1 Overview of the new Basel III leverage requirement... 9

1.4.2 Overview of the leverage ratio regulated in Canada ... 9

1.4.3 Overview of leverage ratio regulated in the US ... 10

1.5 Adjustment to multiple capital ratio: Implications, stylized facts and hypotheses ... 11

1.5.1 A conceptual framework... 11

1.5.2 Stylized facts and hypothesis development ... 14

1.6 Data and empirical analysis ... 16

1.6.1 Empirical analysis of banks adjustment to capital ratios ... 16

1.6.2 Empirical analysis of banks adjustment to capital ratios ... 18

1.6.4 Description of control variables ... 23

1.7 The econometric estimation framework ... 26

1.8 Empirical results ... 28

1.8.1 Descriptive analysis ... 28

1.8.2 Econometric Analysis ... 32

1.9 Robustness check analysis ... 36

1.9.2 The 2007 subprime crisis and the US and Canadian government supports ... 37

1.9.3 Additional controls: M&A and regulatory regime changes in Canada ... 39

1.10 Conclusion and policy implications... 40

References... 42

Essai 2: The countercyclical capital buffer under the LCR regulation ... 70

2.1 Résumé ... 70

2.2 Abstract ... 70

Introduction ... 71

2.4 The model set-up ... 77

2.4.1 The representative bank ... 78

2.4.2 The regulator ... 78

2.4.3 The bank objective function ... 79

2.5 The equilibrium equity-to-loan ratio ... 80

2.5.1 Solution to the banker problem ... 80

2.5.2 The cyclical behavior of the equilibrium equity-to-loan ratio ... 81

2.6 The banker problem under the CCyB requirement ... 83

2.6.1 An overview of the Basel III CCyB ... 83

2.6.2 The equilibrium equity-to-loan ratio under the CCyB requirement... 84

2.6.3 Adequate CCyB requirement (𝒎𝒂) ... 85

2.7 Potential impact of the LCR requirement on CCyB... 86

2.7.1 The liquidity coverage ratio (LCR) requirement ... 86

2.7.2 The optimal equity-to-loan ratio under the LCR requirement ... 88

2.8 Calibration and empirical evidence ... 90

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vii

2.8.2 Estimation of the required CCyB levels ... 92

2.9 Why is the CCyB higher under the LCR requirement? ... 94

2.10 The Basel III CCyB as an option on the credit cycle variable ... 96

2.11 Conclusion, policy implications and future research ... 97

References... 105

Essai 3: Basel III capital buffer requirements and credit union prudential regulation: Canadian evidence .... 108

3.1 Résumé ... 108

3.2 Abstract ... 108

Introduction ... 109

3.4 Credit unions regulation in Canada ... 112

3.5 Literature review ... 116

3.5.1 Determinants of capital buffer in banks and credit unions ... 116

3.5.2 Capital buffer and the business cycle in banks and credit unions ... 118

3.6 The empirical model ... 119

3.6.1 The partial adjustment model and hypotheses ... 119

3.6.2 Estimation methodology ... 122

3.6.3 Dependent variables ... 123

3.7 Data and descriptive analysis ... 128

3.7.1 Data ... 128

3.7.2 Credit union asset and liability structure ... 129

3.7.3 Descriptive statistics of variables used in the regression analysis ... 130

3.8 Regression analysis ... 132

3.9 Robustness check ... 134

3.10 Policy Implications ... 134

3.11 Conclusion ... 136

References... 137

Essai 4: Basel III capital buffers and Canadian credit unions lending: Impact of the credit cycle and the business cycle ... 160

4.1 Résumé ... 160

4.2 Abstract ... 160

Introduction ... 161

4.4 Literature review: The role of capital structure on lending ... 168

4.5 Data ... 170

4.6 The empirical model ... 171

4.6.1 Capital buffer and lending in credit unions ... 171

4.6.2 Risk-based capital buffers and the credit cycle ... 172

4.6.3 Estimation methodology ... 174

4.6.4 Variables and their description ... 175

4.6.6 Descriptive statistics of variables used in the regression analysis ... 182

4.7 Regression analysis ... 183 4.8 Robustness checks ... 186 4.9 Policy Implications ... 187 4.10 Conclusion ... 188 References... 190 Conclusion ... 205

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viii Liste des figures

Figure 1.1 : Leverage ratio (LR) by Bank Size ... 63

Figure 1.2 : Risk-based capital ratio (RBC) by Bank Size... 63

Figure 1.3 : Risk weighted assets density (RWAD) by Bank Size ... 64

Figure 1.4: The dynamic between the leverage ratio and the risk-weighted assets density ... 64

Figure 1.5: The dynamic between the leverage ratio and the risk-weighted assets density ... 65

Figure 1.6: The risk-weighted assets density (RWAD) and market measure of bank risk ... 66

Figure 3.7: Credit unions’ asset distribution by year ... 154

Figure 3.8: Basel risk-based capital buffer and GDP growth, smallest credit unions ... 154

Figure 3.9: Largest credit unions’ risk-based capital buffer and GDP growth, ... 155

Figure 3.10: Basel risk-based capital buffer and GDP growth ... 157

Figure 3.11: Basel risk-based capital buffer and GDP growth by capitalization ... 157

Figure 4.12: Asset distribution by year... 195

Figure 4.13: The credit-to-GDP (CGDP) gap and the Canadian GDP growth (CYCL_C) ... 195

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ix Liste des tableaux

Table 1.1 : Description of variables ... 49

Table 1.2 : Descriptive statistics for the variables used in the main study ... 49

Table 1.3 : Wilcoxon test statistics on large versus small and medium banks. ... 51

Table 1.4 : RWAD density for the 6 largest Canadian banks ... 51

Table 1.5 : Correlation matrix ... 52

Table 1.6 : Correlation matrix between the LR, the RBC and others covariates ... 54

Table 1.7 : Correlation matrix between the LR, the RBC and the RWAD ... 54

Table 1.8 : Regression of the leverage ratio on the risk-weighted density for Canadian banks ... 55

Table 1.9 : Regression of the leverage ratio on the risk-weighted density for the US banks ... 57

Table 1.10 : Leverage ratio and the risk-weighted assets density: Assets side versus liabilities side ... 59

Table 1.11 : Endogeneity analysis of the RWAD in the US sample: 3SLS approach ... 60

Table 1.12 : Leverage ratio and the RWAD: Analysis around the 2007 financial crisis ... 61

Table 2.13: The bank balance sheet at date 0 ... 78

Table 2.14: The bank balance sheet at date 0 ... 84

Table 2.15: Value of the calibrated parameters ... 92

Table 2.16: The required levels of the CCyB ... 93

Table 3.17: Breakdown by provinces of the 100 largest cooperatives ... 140

Table 3.18: List of regulators by province ... 140

Table 3.19: List of the 100 largest credit unions in alphabetical order ... 141

Table 3.20: List of the 100 largest credit unions in alphabetical order (continued) ... 142

Table 3.21: List of the 100 largest credit unions ranked by average asset size ... 143

Table 3.22: List of the 100 largest credit unions ranked by average asset size (continued) ... 144

Table 3.23: Average assets and liabilities, major components in 1000s of $CAD ... 145

Table 3.24: Balance Sheet components and financial ratios ... 145

Table 3.25: Regulatory capital ratios and risk-weighted assets (in 1000s of $CAD) ... 146

Table 3.26: Total assets, distribution by year (1000s $CAD)... 146

Table 3.27: Definition of the variables ... 147

Table 3.28: Descriptive statistics for the business cycle indicator ... 148

Table 3.29: Descriptive statistics by capitalization ... 149

Table 3.30: Comparing credit unions actual buffers to the minimum Basel III buffer requirement ... 149

Table 3.31: Descriptive statistics on the dynamic of capital buffers ... 150

Table 3.32: Correlation matrix ... 150

Table 3.33: Dynamic GMM and 3SLS estimation of the capital buffers ... 151

Table 3.34: Dynamic GMM estimation of capital ratio components and the benefit to members ... 152

Table 3.35: Dynamic GMM estimation of capital buffer in absence of the crisis period ... 153

Table 4.36: Average assets and liabilities, major components in 1000s of $CAD ... 197

Table 4.37: Assets and liabilities, major components in proportions ... 197

Table 4.38: Average and median of regulatory capital, capital ratios and risk-weighted assets ... 198

Table 4.39: Total assets, distribution by year (1000s $CAD)... 198

Table 4.40: Definition of the variables ... 199

Table 4.41: Descriptive statistics ... 200

Table 4.42: Correlation matrix ... 201

Table 4.43: Fixed Effects estimation of the risk-based capital buffer on loan growth portfolio ... 202

Table 4.44: Dynamic GMM estimation of capital buffer adjustment over the cycle ... 203

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x Liste des appendices

Appendix1.1: List of Canadian banks included in the sample and their activities status by 2014 ... 68 Appendix1.2: Canadian banks listed on stock markets ... 69 Appendix 3.3: Regulation of credit unions in Canada: A synthesis by province ... 158

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xii Remerciements

Mes premières pensées vont à l’endroit du Professeur Van Son Lai qui a été pour moi bien plus qu’un directeur de thèse.

Au point de vue de l’encadrement à la rédaction, son soutien à la fois financier, moral et intellectuel a été d’une contribution fondamentale pour l’écriture de cette thèse. De plus, sa maîtrise (intégrée) de la théorie financière, sa générosité intellectuelle et sa disponibilité ont été pour moi un repère important dans le long tunnel du processus de rédaction. J’ai également beaucoup appris des conférences annuelles de haut calibre qu’il organise chaque année sous la bannière du Fonds Conrad Leblanc.

Au point de vue de l’insertion professionnelle, Van Son a une connaissance parfaite des réalités du marché du travail et n’hésite pas à partager son point de vue. Son soutien indéfectible m’a permis de décrocher des entretiens dans des institutions prestigieuses comme l’université de Sherbrooke (mon employeur actuel), la Banque Mondiale («short list» entrevue à Washington D.C.), le Fonds Monétaire International («short list» entrevue à Washington D.C.), l’université Carlton, l’université de Saskatchewan, l’université de l’île-du-Prince-Édouard, et bien d’autres. Je souhaite que mon témoignage serve de signal pour la qualité de son encadrement.

Ma reconnaissance profonde aux membres de mon comité de soutenance de thèse, à savoir les Professeurs Jean-Marie Gagnon, Georges Dionne (examinateur externe) et Michäel Bourdeau-Brien, pour avoir pris le temps de lire cette thèse et d’accepter de l’évaluer. Je voudrais aussi remercier les Professeurs Marie-Claude Beaulieu et Issouf Soumaré pour leurs commentaires sur les ébauches préliminaires du projet de cette thèse.

Toute ma reconnaissance aussi au département de finance assurance et immobilier et à ses responsables passé (Pre Marie-Claude Beaulieu) et actuel (Pr Philippe Grégoire) pour les efforts fournis pour enrichir l’expérience des étudiants au doctorat, au travers des séminaires et rencontres avec les chercheurs. Aussi, la disponibilité des ressources comme les bases de données WRDS et la salle de marché ont grandement contribué à la rédaction de la thèse. Je remercie aussi mes anciens collègues au doctorat en autres : Éric Ékpinda, Ali Ghali, Alaa

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Guidara, Charli Tandja et Denis-Alexandre Trottier, pour les échanges fructueux sur certains des articles de cette thèse.

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xiv Avant-propos

L’ensemble des quatre essais qui composent cette thèse sont co-écrits avec le Professeur Van Son Lai.

Article 1: Risk-based capital and leverage ratios adjustments by banks: Canadian and the US experience

Article 2: The countercyclical capital buffer under the LCR regulation

Article 3: Hessou, H., Lai, V. S. (2017). Basel III capital buffer requirements and credit union prudential regulation: Canadian evidence, Journal of Financial Stability, 30, 92-110. Article 4: Hessou, H., Lai, V. S. (2018). Basel III capital buffers and Canadian credit unions lending: Impact of the credit cycle and the business cycle, International Review of Financial Analysis, 57, 23-39.

J’ai le rôle de premier auteur dans l’ensemble des articles. J’ai rédigé les articles, collecté les données, construit les modèles et effectué les analyses. Pour les articles publiés, j’ai également travaillé à satisfaire les exigences des éditeurs et arbitres desdits journaux. La contribution du professeur Lai a consisté essentiellement à son implication dans la définition de la ligne de recherche, l’orientation sur la revue de littérature, la production de critiques et commentaires, les discussions sur la pertinence des résultats, les suggestions d’études additionnelles et les discussions pour la formulation des politiques économiques. Pour les articles publiés, il a aussi investi un temps inestimable pour le polissage. Les articles ont été aussi présentés plusieurs fois dans des conférences et congrès de 2015 à aujourd’hui et ont bénéficié de commentaires avisés.

Les deux derniers articles de la thèse ont été rédigés et publiés dans le cadre du projet AMF- SC-1968 avec le Professeur Lai comme chercheur principal. La mise en œuvre du projet AMF- SC-1968 a bénéficié de l’assistance de recherche d’anciens étudiants au « Master of Business Administration » (MBA) tels Jean-Philippe Allard-Desrochers, Amine Arfaoui, Houa Balit, Gino Biaou, Olivier Côté-Lapierre, Gérald Gnambodé et Cyrille Tiendaka qui ont été associés à diverses tâches mais ont principalement contribué à la collecte manuelle des données comptables sur les sites des coopératives de crédit.

La première publication (Article 3) est aussi parue dans un rapport conjoint de Filène Research Institute et le CCUA (« Canadian Credit Union Association ») et a été sollicitée pour présentation à l’AMF (l’Autorité des Marchés Financiers) ainsi que dans des congrès scientifiques où il a bénéficié de commentaires judicieux.

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1 Introduction

Au lendemain de la crise financière des années 2008, d’importantes réformes ont été introduites afin d’accroître la résilience du secteur bancaire. Au rang de ces mesures figurent le renforcement des normes de capital existantes et l’introduction de nouvelles normes de liquidité. Cette thèse offre une analyse critique de ces mesures en quatre essais. Les deux premiers essais sont consacrés à l’analyse de ces mesures dans le secteur bancaire nord-américain alors que les deux derniers essais (publiés dans des revues à comité de lecture) traitent de l’application de ces réformes aux coopératives de crédit canadiennes. Le premier essai étudie le comportement d’ajustement au capital réglementaire dans un régime de capital réglementaire multiple. La présence de cet essai est motivée par le fait que les modèles d’ajustement au capital bancaire existants déjà dans la littérature ne modélisent que l’ajustement à une seule mesure de capital et ne tiennent donc pas compte de l’importante corrélation entre les différentes normes de capital. Les résultats issus de ce travail sont de deux ordres. Premièrement, il est montré que la réglementation de deux ratios de capital (ajusté ou non au risque) est assimilable à la réglementation d’un ratio unique de capital (non ajusté au risque) dont la limite est assimilable à la valeur d’une option d’achat avec comme sous-jacent le taux de risque (réglementaire) des actifs bancaires. Une analyse de l’expérience du Canada et des États-Unis offre une justification supplémentaire à la résilience relative des banques canadiennes lors de la dernière crise des subprimes des années 2007.

Le deuxième essai se consacre à l’analyse de la norme de coussin contracyclique introduite sous Bâle III. Cette norme vise à lisser les fluctuations cycliques indésirables dans le capital bancaire qui affectaient négativement l’octroi de crédit par les banques surtout en période de crise. Ce travail vise à quantifier le niveau de coussin requis en tenant compte des composantes cycliques du capital bancaire. Une analyse de l’implication des nouvelles normes de liquidité est également abordée.

Le troisième essai analyse l’adéquation de l’application des nouvelles normes de capital contracycliques de Bâle III avec les coopératives de crédit canadiennes. En se basant sur les données des bilans comptables des coopératives canadiennes entre la période 1996 et

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2014, cet essai démontre que, contrairement aux institutions bancaires, les coopératives possèdent déjà une stratégie de gestion contracyclique pour leur coussin de capital. À cet effet, une introduction des nouvelles normes de coussin contracycliques n’affectera pas leur comportement d’ajustement. L’analyse révèle que le coussin de capital des coopératives de crédit sous-capitalisées est procyclique et donc qu’une attention particulière de la part des régulateurs à l’endroit de ces coopératives serait nécessaire.

Le quatrième essai est une extension de celui qui le précède en ce sens où il analyse l’effet du capital réglementaire sur l’activité d’intermédiation des coopératives de crédit canadiennes. Nos résultats suggèrent que la croissance du portefeuille de prêts évolue positivement avec le niveau de capitalisation. À l’inverse, la croissance du portefeuille est négativement liée aux changements ou ajustements dans le capital réglementaire. Cette observation suggère que les coopératives de crédit devraient être encouragées via l’implémentation et le respect d’exigences de coussin de capital (de conservation et contracyclique) qui viseraient à détenir des niveaux suffisants de capitalisation.

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3

Essai 1: Risk-based capital and leverage ratios adjustments by banks:

Canadian and the US experience

1.1 Résumé

Les réformes de Bâle III s'accompagnent d'une nouvelle règle sur les fonds propres (non ajusté au risque) qui sera réglementée parallèlement au ratio de fonds propres ajusté au risque qui existait sous Bâle II. Cet article étudie les implications de la réglementation d’un double ratio de capital (ajusté ou non ajusté au risque). Premièrement, il est montré que la réglementation de deux ratios de capital (ajusté ou non au risque) est assimilable à la réglementation d’un ratio unique de capital (non ajusté au risque) dont la limite est comparable à la valeur d’une option d’achat avec comme sous-jacent le taux de risque (réglementaire) des actifs bancaires. Il s'avère que les banques canadiennes ont été soumises à une limite plus stricte sur leur ratio non ajusté au risque contrairement à leurs homologues américaines. Ainsi, elles ont maintenu un ratio de levier proportionnel à leur risque d'actifs bien avant la crise des subprimes de 2007. Inversement, la limite du ratio de levier américain était moins contraignante. En conséquence, le ratio de levier était moins sensible ou parfois négativement relié au risque des actifs bancaires. Ces résultats fournissent une explication supplémentaire de la résilience relative des banques canadiennes pendant la dernière crise financière de 2007. Le message principal de cet article est que le bon calibrage des limites associées aux ratios de fonds propre (ajusté ou non ajusté au risque) est essentiel à la stabilité financière et à une prise de risque responsable des banques.

1.2 Abstract

Basel III reforms come with a new leverage capital rule that will be regulated alongside the existing Basel II risk-based capital ratio. We investigate the implication of this double capital rule for banks capital adjustment. We find that the mix of the two-capital rules can be assimilated in a single leverage ratio with a “hockey stick” limit equals to the value of a call option on the risk-weighted density (the ratio of asset risk over total assets). Given that Canada and the US have adopted similar double capital rules prior to Basel III, we analyze banks capital adjustment in these countries. It comes out that Canadian banks have been subjected to a tighter limit on their "combined" leverage ratio compared to their US counterparts. Accordingly, Canadian banks have maintained a leverage ratio that was proportional to their asset risk well before the 2007 subprime crisis. Meanwhile, the limit on the US leverage ratio was loosening resulting into a leverage ratio that was irresponsive or negatively related to banks’ asset risk. Additional robustness checks suggest that the risk-weighted asset density is strongly correlated with market asset risk. These findings provide another reason for the Canadian banks relative resilience during the global financial crisis of 2007. Hence, a proper calibration of the limits on the capital rules is a major driver of both financial stability and sensible risk-taking in banks.

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4 Introduction

Since the seminal study of Modigliani and Miller (1958), capital structure has become a core topic in financial economic research. In the banking literature though, capital structure has been distinctively analyzed due to the high-powered regulated environment in which banks operate. Unlike traditional firms, banks provide liquidity to the economy and their liabilities are insured against runs in order to preserve financial system stability. In return, banks capital structure is regulated to ensure that banks do not socialize their costs by taking excessive risk (see Saunders and Wilson, 1999). While the analysis of banks capital structure has significantly borrowed from the traditional corporate theory, the existing literature seems to converge toward the tradeoff theory against other competing theories such as pecking order and market timing. This is because banks cannot free ride their capital structure because of minimum capital requirements (see Haubrich, 2020, among others). This theory has extensively been tested in the literature with some success1 for

financial institutions (Ediz et al., 1998; Jokipii and Milne, 2008; Berger et al., 2008; Flannery and Rangan 2008; Memmel and Raupach, 2010; Stolz and Wedow, 2011; De Jonghe and Őztekin, 2015; Hessou and Lai, 2017) as well as non-financial firms (Marsh, 1982; Hovakimian et al. 2001, Fama and French, 2002; Flannery and Rangan, 2006; Xu, 2007; Flannery and Őztekin, 2012; Flannery and Hankins, 2013).

While the existence of capital limits is well rooted in banks capital structure analysis and favored the tradeoff theory, the issue regarding the existence of multiple capital limits has received less or no attention at all. Unlike non-financial firms, banks should adjust their capital structure in order to meet various and interrelated capital limits. This interrelation between capital rules, complicates the analysis of the adjustment towards a specific capital rule, since any adjustment aiming for a target capital rule will passively affect other capital rules. Given that regulators are continuously interested in the effect of the capital regulation on banks’ balance sheet, we provide a framework to accommodate the existing of multiple capital ratios. Considering the introduction of a new capital limit, namely the leverage ratio

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5

(under Basel III) which will be implemented and regulated jointly with the existing Basel II risk-based capital ratio by 2022, this study is particularly important.

The new Basel III leverage is motivated by the excessive build-up of (on- and off- balance sheet) assets by financial institutions in the year preceding the 2007 financial crisis. According to post-crisis literature, this excessive leverage was pinpointed as the major cause of the crisis. For example, on the eve of the 2007-2009 Global Financial Crisis (GFC), the top 25 American and European banks had maintained adequate buffer in ‘risk-based’ capital ratio, but had reached very high leverage ratio (e.g., Chami and Cosimano, 2010 and Hildebrand, 2008).2 During the crisis, banks were forced to deleverage quickly, notably by reducing lending, which exacerbated the real effect of the crisis (Global Financial Stability Report; 2008). Accordingly, following the crisis episode, in an effort to contain banks excessive asset expansion during booms in the future, a new leverage limit was set to complement the existing regulatory capital ratio. Notwithstanding the COVID-19 pandemic outbreak in 2020, the Financial Stability Board (FSB)3 on November 2015

had issued its final regulatory capital standards, by setting higher capital ratio limits that must be implemented by 1st January 2022 (FSB, 2019). The required limits are at least 16%

for the capital-to-risk weighted assets ratio (‘risk-based’ capital ratio), and 6% for the capital-to-asset ratio (‘non-risk-based’ capital ratio called leverage ratio) and should be implemented by 2019.4 Banks then have to comply with two different capital requirements under the new Basel III regulation: the ‘risk-based’ capital ratio and the ‘non-risk based’ leverage ratio.

The understanding of banks capital structure choice and their adjustment toward their target is of great interest to regulators. Firstly, this helps regulators to monitor its effects on monetary policy (see Berrospide and Edge, 2010; Van den Heuvel, 2001) and the possible

2 Tier 1 capital ratio of 8.3% and 8.1%, while the total capital ratio was 11.4% and 11.6% respectively for top 25 United States and Europe banks.

3http://www.investmentexecutive.com/-/fsb-updates-list-of-banks-too-big-to-fail-

4 Those level quite double Basel III standards and raise concern about their intended consequences. The FSB argue that those levels may induce increase in lending spreads by 2 to 2.8 basis points but may induce 15 to 20 basis points gain in annual GDP due to low probability of future crisis.

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undesirable effect of banks capital adjustment on the real activities.5 A well-documented example lays in the procyclical effect of banks capital (e.g., Peek and Rosengren, 1997; Ayuso et al., 2004; Gambacorta and Mistrulli, 2004; Jokipii and Milne, 2008; Stolz and Wedow, 2011; Guidara et al., 2013; Behn et al. 2016). Secondly, change in capital rules can also be accompanied by abrupt adjustments form banks with negative consequence on real activities. As a matter of fact, history shows us that changes in capital rules have been followed by unintended consequences. For instance, the introduction of the risk-based capital ratio requirement in 1988 on top of the already existing leverage ratio, seems to have triggered the credit crunch of the 1990s (e.g., Brinkmann and Horvitz, 1995 and Thakor, 1996). Thirdly, the study of capital adjustment allows regulators to access how costly capital is for banks and the extent to which, the cost associated in terms of banks adjustment (see Baker and Wurgler, 2013) balance with the benefice in term of a stable financial system (Van den Heuvel, 2008, 2019). For example, DeAngelo and Stulz (2015) show that banks fail to endogenize the social cost of their capital and are then better off operating with lower capital ratios than those of non-financial firms. Fourthly, the new leverage ratio is expected to fulfill a different mission, which has to be analyzed through the banks’ adjustment towards it. These objectives are to complement the risk-based capital ratio by inducing banks to truthfully communicate their risk (Jokivuolle et al. 2014) and to reduce the undesirable procyclicality of the Basel II risk-based capital ratio which has been pointed out to have exacerbated the last 2007-2009 subprime credit crisis.

This study builds on the experiences of countries which have regulated bank leverage ratio6 prior to Basel III in the aim, to provide guidance for policy makers regarding the interrelation between both ratio and their effects on banks risk taking. While the international adoption of the leverage ratio by the Basel committee is new, some countries have regulated leverage ratios, like the one advocated by the Basel III, and can then provide a semi-natural experimental environment to the analysis of the capital ratios. Three

5 In addition, to prevent undesirable outcome and provide warning tools to regulators, the Basel Committee on Banking Supervision (BCBS) planned in his agenda to study the nexus between the ratios to see if the intended objectives will be met. This is a clear evidence that the potential effects of the proposed joint capital requirement on banks’ decisions are not understood fully.

6 The leverage ratios regulated in Canada and the U.S. are not identical to the new Basel III leverage ratio but share some similarities with it.

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countries with large international banking systems have regulated the leverage ratios (Canada, United States and Switzerland). The first two have maintained a leverage ratio alongside the risk-based capital adequacy requirement since the 1990s, while Switzerland has announced its introduction only recently (Bank of England, 2014; Hildebrand, 2008). Since Switzerland’s experience is still very young, merely American and Canadian experiences deserve greater attention, as they are amongst the few in the developed World to have had long-standing limits on leverage ratio.

Our contribution to the literature is threefold. Firstly, we explicitly document the adjustment behavior of banks in Canada and the US, considering the interrelation between the two ratios, namely the risk-based capital ratio and the leverage ratio. In such regard, we build a "unique" or "combined" capital rule as a mix of the two ratios. Secondly, we study how the banks adjust to this "unique" capital rule. Thirdly, we follow Memmel and Raupach (2010), Cohen and Scatigna (2016) and Hessou and Lai (2017) by breaking down the adjustment process in order to distinguish numerator-based and denominator-based adjustments through which banks can adjust their capital (via earnings retention or new claims issuance) or assets (via risky asset reduction or cutting back new assets).

Our findings show that the joint regulation of the leverage ratio and the risk-based capital ratio can be reduced to a "unique" leverage ratio with a limit having a "hockey stick" dynamic which can be interpreted as the value of a call option on banks’ asset risk (measured by the share of banks’ risk-weighted assets (RWA) over total assets, also called "RWA density"). The exercise price being the ratio of the limits on the leverage ratio over the limit on the risk-based capital ratio. Using the long-standing regulation of risk-based capital ratios measures and leverage ratio in Canada and the US, we have documented that Canadian banks have been subject to a tighter dynamic limit in comparison to their American counterparts. The tightness of this limit has been stricter by the Canadian regulator in 2000, seven years prior to the last financial crisis. Our empirical and econometric analysis provide evidence that Canadian banks leverage ratio is positively associated with their assets risk suggesting that they hold more equity per unit of assets when their asset risk increases. Oppositely, the regulatory limits on the leverage and the

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risk-based capital ratios in the US case has induced a loosening limit turning the American leverage ratio less responsive and even negatively sensitive to their asset risk. These findings provide support to the relative resilience of Canadian banks regarding the GFC. This paper main takeaway is with the imposition of higher capital limits on banks, the ensuing relationship between the limits imposed on various capital limits have an important impact on the responsiveness of their leverage ratio to their asset risk.

Our work relates to studies on the relationship between leverage ratio and regulatory capital ratio (Cathcart et al., 2015; Estrella, 2004 and Blum 1999, 2008, among others). Cathcart et al. (2015) investigate the correlation pattern between the two-capital rule and find evidence that changes in the correlation pattern between the two capital rules, somehow, was one of the causes of banks vulnerability during the last 2007 financial crisis. In line with our findings, the latter show that a proper calibration of both ratios is vital to a stable financial system.

We are also close to the literature on the determinants of banks capital (or capital buffer) with different objectives such as their cyclical behavior (Ayuso et al., 2004; Guidara et al., 2013), their adjustment process and their motive (Flannery and Rangan, 2008; Memmel and Raupach, 2010; Berger et al., 2008 and De Jonghe and Őztekin, 2015).

The paper is organized as follows. Section 1.4 describes the historical leverage ratio regulated in Canada and the US and compares it to the new Basel III leverage ratio. Section 1.5 develops our analysis of the joint regulation of the two capital ratio and provides stylized facts as well as hypotheses. Section 1.6 describes the data and discusses the empirical framework. Sections 1.7 and 1.8 present respectively the econometric framework and empirical results. Robustness checks are performed in section 1.9 and the last section concludes.

1.4 Overview of the leverage ratio regulated in Canada and US prior to Basel III In this section, we present the new Basel III leverage ratio and draw some parallel with the leverage ratio regulated in Canada and the United States prior to Basel III.

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1.4.1 Overview of the new Basel III leverage requirement

The new Basel III framework comes with a new leverage ratio which will be regulated jointly with the existing Basel II risk-based capital ratio. The new leverage ratio is computed as the ratio of Tier 1 capital7 to total exposures (total on balance and certain off-balance sheet items) and banks are expected to hold a minimum of 3% of such a ratio (BCBS, 2014). While the measure is internationally adopted, there are some variabilities in the way it is implemented across countries.

1.4.2 Overview of the leverage ratio regulated in Canada

Prior to Basel III, the leverage ratio regulated in Canada was known as the asset-to-capital multiple (ACM). The tradition of leverage regulation started in 1981, when the banking system experienced an excessive increase in leverage, just as the one experienced during the last 2007 financial crisis (see Bordeleau et al. 2009). The leverage ratio is calculated as the ratio of total assets topped with the certain off-balance sheet items and divided by total capital. We consider this ratio’s inverse which better compares to the Basel ratio. The inverse of the ACM, namely the Canadian leverage ratio, is very similar to the newly introduced Basel III leverage ratio. The only difference with the new Basel III leverage ratio is the former includes every source of bank capital (core and tier 2 capital) while it is only the core capital which is eligible with the Basel III leverage ratio. Regarding the limits applied to the Canadian leverage, it was 5% (i.e. ACM=20) from 1996 to 2000 and 4.34% (i.e., ACM=23) from 2000 until the recent introduction of the new Basel III leverage ratio.

The traditional adherence to a rigorous leverage ratio requirement is believed to be one of the main reasons for which Canadian banking system remained resilient to the 2007-2009

7 Tier 1 capital is composed of common equity Tier 1 Capital (CET 1) and additional Tier 1 capital instruments. According to FDIC (2013), CET1 is composed of « qualifying common stock and related surplus net of treasury stock; retained earnings; certain accumulated other comprehensive income (AOCI) elements if the institution does not make an AOCI opt-out election (refer to opt-out election discussion in next paragraph), plus or minus regulatory deductions or adjustments as appropriate; and qualifying common equity tier 1 minority interests ». Additional Tier 1 capital includes « qualifying noncumulative perpetual preferred stock, bank-issued Small Business Lending Fund and Troubled Asset Relief Program instruments that previously qualified for tier 1 capital, and qualifying tier 1 minority interests, less certain investments in other unconsolidated financial institutions’ instruments that would otherwise qualify as additional tier 1 capital. »

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subprime credit crisis (e.g., Bordeleau et al. (2009) and Guidara et al. (2013)). Thus, the Canadian experience offers a unique laboratory to study how the combined "risk-based" capital ratio and "non-risk-based" leverage ratio requirements can limit bank excessive risk taking under this new Basel III rule.

In addition to its rigorous leverage regulation, the Canadian regulator has also implemented the risk-based capital measure. It imposes a minimum capital requirement on banks as a buffer against their risk-weighted assets. However, the two capital requirements were effective throughout Canada since the introduction of 1988 Basel capital rule. Starting from 1988, the Basel I Accords require banks to hold regulatory capital against their credit risk-weighted assets. More specifically, banks were required to hold 4% as Tier 1 capital ratio (Tier 1 Capital8 / Risk Weighted Assets) and 8% as total regulatory capital ratio (Total Capital9 / Risk Weighted Assets). In 1996, the first amendment to the Basel I Accord introduced market risk as an additional risk category and was enforced in 1998. In 2000, the Canadian regulator increased the minimum regulatory capital ratio to 10% and the Tier 1 capital ratio to 7%. Since 2004 and the advent of Basel II Accords, banks are required to hold capital against operational risk fully implemented in Canada by 2008. Given this historical regulation of the risk-based capital ratio alongside to the leverage ratio, Canadian banks experience is henceforth a valid candidate to investigate capital ratios.

1.4.3 Overview of leverage ratio regulated in the US

Prior to the implementation of Basel III, American banks were required to hold a ratio of leverage ratio (Tier 1 capital to total assets) of respectively 4 and 5% to be considered as adequately and well-capitalized (see Shim, 2013). Therefore, the US leverage ratio shares with the new Basel III leverage the same numerator (the Tier 1 capital). The denominator however differs since the new Basel III leverage include some off-balance sheet elements in the exposure calculation. Under Basel III regime, the American regulator will maintain the existing leverage ratio and will apply the new Basel III leverage ratio (designated as

8 Majors components of Tier 1 capital are: common shares, contributed surplus and retained earnings.

9 Total capital is composed of the Tier 1 capital plus additional capital instruments such as preferred shares and subordinated debt.

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supplemental leverage ratio) to banks using the advanced approach. The limit varies between 5 and 6% for bank holding companies with more that 700 billion of assets (FDIC, 2013).

In addition to the leverage ratio, the US regulator has also implemented two risk-based capital ratios following the advent of Basel I capital requirements10 in the late eighties. US

banks11 were y required to hold at least 4 and 8% as minimum as leverage and risk-based capital ratio to be considered as adequately capitalized. These limits need to respectively reach of 6% and 10% in order to be considered as well capitalized, accordingly to the Federal Deposit Insurance Corporation Improvement Act (FDICIA) adopted by the US Congress in 1991. Following Basel III, American regulators have been pursuing its risk-based capital ratio monitoring with the following ratios and limits:

• Common equity Tier 1 capital (CET 1) to total risk-weighted assets ratio of 4.5 %; • Tier 1 capital to total risk-weighted assets ratio of 6 %; and

• Total capital to total risk-weighted assets ratio of 8 %.

1.5 Adjustment to multiple capital ratio: Implications, stylized facts and hypotheses

1.5.1 A conceptual framework

The previous section provides evidence that prior to Basel III, both Canadian and American banks have been subjected to the leverage ratio and other different measures of the risk-based capital ratio. Given that the two ratios share more or less the same numerator (bank capital in the form of Tier 1 capital or total capital) and related denominator (total assets or risk-weighted assets), any adjustment by banks to address a capital shortfall in one or the other ratio will affect both ratios. Therefore, we hereby analyze the relationship between atio to investigate the joint regulation’s implication and the net effect of banks’ adjustment.

10 Prior to Basel III, banks were required to hold at least 3.25% and 7.25% of their risk weighted assets in the form of tier one capital and total capital respectively during the period between December 1990 and 1991.

11Unlike Canada’s, the larger US’ investment bank holding companies and their subsidiaries were regulated by the Securities and Exchange Commission and thus were not subject to a leverage limit.

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We can express the relation between the leverage ratio (LR) and the risk-based capital ratio (RBC) as follows: 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 ⏟ LR =𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑊𝐴 ⏟ RBC × 𝑅𝑊𝐴 𝐴𝑠𝑠𝑒𝑡𝑠 ⏟ δ = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑊𝐴 × 𝛿 (1) where:

• capital is the total regulatory capital of the bank;

• assets represent the bank total assets (plus certain off-balance sheet items as in the Canadian or the Basel III case);

• RWA are the risk-weighted assets abbreviation; and

• 𝛿 stands for the risk-weighted assets density or the ratio of RWA to total assets. Let’s assume that each quarter the bank must simultaneously comply with the two ratios, i.e.,: 𝐿𝑅: 𝑅𝐵𝐶: 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 ≥ 𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑊𝐴 ≥ 𝑐 , (1.1.1)

with l and c, respectively, the leverage ratio and capital ratio limits. Using equation (1.1) in (1.1.1) yields: 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 ≥ 𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑊𝐴 = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠×𝛿≥ 𝑐 or 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 𝑨𝒔𝒔𝒆𝒕𝒔 ≥ 𝒍 𝑪𝒂𝒑𝒊𝒕𝒂𝒍 𝑨𝒔𝒔𝒆𝒕𝒔 ≥ 𝒄 × 𝜹 (1.1.2)

We can clearly see from the above equation that the second ratio, which is the risk-based capital ratio, can be transformed in order to produce a second constraint on the leverage ratio. Therefore, both capital constraints are transformed in one leverage constraint (𝐶𝑎𝑝𝑖𝑡𝑎𝑙

𝐴𝑠𝑠𝑒𝑡𝑠)

with two different limits (𝑙 𝑜𝑟 𝑐 × 𝛿 ). The question, then, is: which of the two limits will, the banks comply to? The answer to this question depends on the choice of the level of the asset risk parameter 𝛿 =𝐴𝑠𝑠𝑒𝑡𝑠𝑅𝑊𝐴, qualified as the “RWA density” of the bank. Two situations may occur.

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In the first scenario, 𝑙 < 𝑐 × 𝛿. In that case, the leverage ratio limit constraining the bank is 𝐶𝑎𝑝𝑖𝑡𝑎𝑙

𝐴𝑠𝑠𝑒𝑡𝑠 ≥ 𝑐 × 𝛿. This ensues only if the bank chooses 𝛿 such that 𝛿 > 𝛿

= 𝑙

𝑐. Under this

case, the limit on the leverage ratio is an increasing function of the bank 𝛿. In other words, one-point increases in the bank RWA density 𝛿 implies a marginal increase in the leverage constraint in a proportion of the capital ratio limit c. When a bank’s asset risk is in this region, the capital ratio limit acts as the binding minimum capital requirement.

In the second scenario, 𝑙 ≥ 𝑐 × 𝛿. Here, the binding constraint is 𝐶𝑎𝑝𝑖𝑡𝑎𝑙

𝐴𝑠𝑠𝑒𝑡𝑠 ≥ 𝑙, which

occurs only if the bank chooses 𝛿 such that 𝛿 ≤ 𝛿∗ = 𝑙

𝑐. Under this assumption, the

leverage ratio limit remains independent of the bank’s asset risk movement proxied by its RWA density. Hence, the leverage ratio limit acts as the binding minimum capital requirement. This marks a clear difference with the case where only the “risk-based” capital ratio regulation is in effect. Here, we observe that in absence of a leverage ratio limit, the minimum capital ratio does not bind, and the bank may keep on either reducing the regulatory capital level or increasing the asset size simply by adding more non-risk sensitive assets. This may be done by RWA arbitrage via securitization, hedging with derivatives, and so on.

Based on the previous analysis, the combination of the risk-based capital rule (RBC) and the leverage rule (LR) delivers a leverage ratio (LR) with a non-linear limit which goes as follows: 𝐿𝑅 ≥ 𝑙 𝑖𝑓 𝜹 ≤ 𝛿∗ = 𝑙 𝑐 𝐿𝑅 ≥ 𝑐 × 𝛿 𝑖𝑓 𝜹 > 𝛿∗ = 𝑙 𝑐 (1.2)

The limit on the leverage ratio under the joint regulation is constant and equals the leverage limit l if 𝛿 is below the threshold but become a linear-increasing function of 𝛿 (𝑐 × 𝛿) for riskier banks, when 𝛿 lingers above the threshold. Therefore, the joint regulation of the leverage and the risk-based capital ratio can be assimilated to the regulation of a unique leverage ratio with a non-linear limit. The limit has the form of a call option payoff (or a hockey-style shape) on the risk-weighted density (𝛿) with 𝛿 = 𝑅𝑊𝐴

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for low risk-banks and increases for banks where asset risk hovers above a certain threshold.

The analysis provided below is only valid if the two-capital rules share the same numerator. Therefore, our analysis solely considers the risk-based capital measure which shares the same numerator with the leverage ratio. Accordingly, for the Canadian case, we use the total risk-based capital ratio as the risk-based measure and consider the total risk-based capital ratio. In the US, however, we use the Tier 1 risk-based capital ratio since it shares the same numerator as the Tier 1 leverage ratio.

1.5.2 Stylized facts and hypothesis development

Based on the historical limits applied in the United States and Canada, we can then infer which of the leverage and the risk-based capital ratio matters the most for each jurisdiction or the ratio that is most likely to be the binding one and build testable hypothesis of the conceptual framework.

Based on the conceptual framework presented previously, it appears that the joint regulation of the risk-based and the leverage ratio can be reduced to a "unique" leverage ratio which limit is non-linear in banks risk-weighted assets density as follows:

𝐿𝑅 ≥ 𝑙 𝑖𝑓 𝜹 ≤ 𝛿∗ = 𝑙 𝑐

𝐿𝑅 ≥ 𝑐 × 𝛿 𝑖𝑓 𝜹 > 𝛿∗ = 𝑙

𝑐

(1.3)

The limit depends on the regulatory limits (𝑙 𝑎𝑛𝑑 𝑐) applied by the different regulators and the risk-weighted assets density (𝛿).

In the Canadian case, the leverage limit (𝑙) and the risk-based capital ratios (𝑐) are respectively of 5% and 8% prior to 2000 and of 4.34% and 10% after 2000. Therefore, and

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accordingly to Equation (3), the risk-weight density threshold is 𝛿∗ = 𝒍

𝒄= 0.625 for the

period prior to year 2000 and 𝛿∗ = 𝒍

𝒄= 0.434 for the period afterwards.

Under the American Prompted corrective Action (PCA), banks are required to hold a minimum of 5 and 6% in their leverage and risk-based capital ratios to be considered as well capitalized. Based on this, the threshold for the well-capitalized limit is 𝛿∗ = 𝑙

𝑐=

5%

6%= 0.833. This limit can increase up to 1 when one considers the required limit to be

considered as adequately capitalized which is 4% on both capital ratios (the Tier 1 risk-based capital ratio and the leverage ratio.

This graphic plots the limit on the "unique" leverage ratio, respectively in Canada and the United States. As may be noticed, the limit of the "unique" leverage ratio is flat for values of the risk-weighted assets density (RWAD) below the RWAD threshold. The latter is theoretically around 0.434 for Canadian banks and 0.833 for their American peers (in the post year 2000 period).

4.34%

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The comparison between the asset risk thresholds 𝛿∗(Canada vs. the U.S.) suggests that

Canadian banks are more likely to target a leverage ratio that is more responsive to their asset risk compared to their American peers. This is because they have the lowest threshold 𝛿∗ = 0.434 compared to 𝛿∗ = 0.833 in the U.S. case. Following this, we formulate and test the following hypotheses.

H0a: Canadian banks are more likely (compared to their U.S. counterparts) to target a

leverage ratio that is an increasing function of their risk-weighted assets density.

H0b: US banks are more likely (compared to their Canadian counterparts) to target a

leverage ratio that is less or not sensible to their risk-weighted assets density.

This sensibility of the leverage ratio to the RWAD is the main change suggested for the estimation of banks adjustment to their internal leverage target. In the following section, we start with the description of a traditional model of capital adjustment.

1.6 Data and empirical analysis

1.6.1 Empirical analysis of banks adjustment to capital ratios

We collected data on both American and Canadian banks. Data on Canadian banks are extracted and merged from the Office of the Superintendent of Financial Institutions (OSFI) website12 on quarterly basis for the balance sheet, income statements and capital

adequacy-components, over the period 1996Q1-2014Q1. Most of the Canadian banking sector studies only focus on the six (6) largest banks: The National Bank of Canada (NB), The Canadian Imperial Bank of Commerce (CIBC), The Bank of Montreal (BMO), The Bank of Nova-Scotia, The Toronto-Dominion bank (TD) and the Royal Bank of Canada (RBC). These banks are designated by the national banking regulator as systemically important financial institutions (SIFI) and are amongst the few banks listed on the stock market. However, these six banks only represent 70% of the total banking sector. Accordingly, we collect data on roughly all domestic banks and include some major foreign 12https://www.osfi-bsif.gc.ca/Fra/wt-ow/Pages/FINDAT.aspx

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banks subsidiaries.13 Thereby, our Canadian database consists of a panel of 66 banks14 and foreign banks subsidiaries15 with 3,195 bank-quarter observations which accounts for more

than 97% of the whole banking sector assets. From these banks, we designate the top 10 banks as large banks (other ones include the HSBC Bank of Canada (HSBA), the Tangerine Bank, The Laurentian Bank of Canada (LB) and The Manulife Bank). This choice is based on the sharp decline in total assets following the tenth largest banks. The rest of the sample is labelled as small and medium banks. Macroeconomic data is obtained from Statistics Canada and the Bank of Canada. There is no public information regarding mergers and acquisition on Canadian banks. Accordingly, we manually collect data from the Canadian Payments association (2017) and other news journal on change of status of some Canadian banks which become inactive and discussed the finding in the robustness section. We also collect stock market data on listed Canadian banks from Bloomberg database for the robustness check analysis. The list of the banks included in the sample can be found in Appendix 1.2.

Regarding the American banks, we extracted and merged quarterly data (balance sheets, income statements and performance ratios) for all of the insured US commercial banks spanning the period from 1996Q1 to 2013Q4. The data used in the study come from various sources: financial data is collected from the Federal Deposit Insurance Corporation (FDIC) website16 while FDIC data is downloaded in separated files containing financial information (balance sheets, income statements, performance and condition ratios and others) on a quarterly basis. We merged all information in one file to enable our analysis.17 There is evidence that the top 1% American banks concentrate more than 79% of the total assets, by the fourth quarter of 2010 (see Kim and Sohn, 2017). Therefore, the close monitoring of the capital adjustment behavior of these banks should be of paramount importance for regulators. Accordingly, we consider banks in the last decile of asset

13 According to the annual ranking of the top 25 banks in Canada by PwC.

14 In this regard, we depart from existing papers on Canadian banks analysis which rely on the six largest Canadian banks (see Guidara et al., 2013 among others). Finally, 64 banks are included in the regression because of data availability for two banks.

15 Banks operating in Canada can be categorized in Schedule I banks (domestic banks), Schedule II banks (foreign bank

subsidiaries) and Schedule III banks (branches of foreign banks). These three categories contain respectively, 36, 18 and 32 banks according to OSFI.

16 https://www5.fdic.gov/sdi/download_large_list_outside.asp.

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distribution as large banks.18 The remaining banks are treated as small and medium banks.

Macroeconomic variables such as the average quarterly gross domestic product (millions of chained 2012 dollars) and the total employment growth rate (part-time and full-time jobs) as well as GDP growth rate and the annual employment growth rate are obtained through the Bureau of Economic Analysis (BEA) website. We also collected information on mergers and acquisitions from the WRDS Merger and Acquisition data and the FDIC database on failed banks. Finally, we collected the stock return of 605 banks holding companies for which we successfully matched the PERMCO to the unique RSSD identifier, as provided in the CRSP-FRB Link.19 These data come from the WRDS CRSP database.

1.6.2 Empirical analysis of banks adjustment to capital ratios

In section 1.5, we showed that depending on the RWA density, banks can either be bounded by a constant or increasing limit on the leverage ratio. Given this capital adjustment dynamic over time, we hereby explore existing models of capital adjustment towards a long-term target. The existing literature holds numerous competing theories to explain non-financial firms’ capital structure choice, amongst which the pecking order theory, the market timing, the inertia theory and the tradeoff theory. For banks, the existence of regulatory capital target makes the pecking order, the market timing and the inertia theories less relevant to explain banks capital structure (e.g., Huang and Ritter, 2009 and Welch, 2004). This is explained by the fact that banks cannot be passive in the adjustments of their capital ratio due to regulatory compliance. Hence, the tradeoff theory which assumes that adjustment is costly and that firms may target a long-term capital structure and slowly adjust to reach the target which makes more sense for banks.

Contrary to the previous works, which only addresses the adjustment towards one of the two capital rules, we postulate that banks should either simultaneously comply the two-18 Various limits have been employed in the literature to define large banks based on the value of total book assets. Shrieves and Dahl (1992) considers in their analysis banks with assets above $100 million from which those with assets above $ 1 billion are considered as large banks. In the same vein, Cornett et al. (2011) consider large banks as the one with total assets above 1 billion. Kim and Sohn (2017) consider banks in the last decile of assets distribution as large.

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capital or simply the "unique" leverage previously shown. We start with the description of the one capital rule adjustment model widely used in the literature, and then provide an extension to take into account the "unique" leverage ratio which was found to be an equivalent of the joint leverage and capital ratio regulation.

1.6.2.1 Model of capital adjustment to one capital target

In a frictionless environment, banks would constantly maintain their desirable target leverage or capital ratio. By doing so, they would presumably tradeoff the adjustment costs against the costs of operating with sub-optimal leverage. The proposed model permits incomplete or partial adjustments of the bank’s capital and leverage ratios towards their desirable level. The typical partial adjustment model goes as follows:

∆𝑌𝑖𝑡 = 𝛼(𝑌𝑖𝑡∗ − 𝑌𝑖𝑡−1) + 𝜀𝑖𝑡, (1.4)

where 𝑌𝑖𝑡 is either the risk-based capital ratio or the leverage ratio of bank i at time t. 𝜀𝑖𝑡 is assumed to be a one-way error component containing the bank fixed effects (𝜀𝑖𝑡 = 𝜃𝑖+ 𝜗𝑖𝑡). The fixed effect 𝜃𝑖 may captured unobservable individual banks characteristics such

as governance culture, board structure, etc.). The error term 𝜗𝑖𝑡 is assumed to be distributed

according to a weak stationary process with zero mean and constant variance. Equation (1.4) assumes that each time t, the typical bank i closes a proportion 𝛼 of the gap between its actual ratio 𝑌𝑖𝑡−1 (or the ratio realized the previous period) and its desired target ratio

𝑌𝑖𝑡∗ in the current period. The desired target ratio being unobservable, we assume it can be predicted using observed banks’ characteristics and economic conditions (e.g., Jokipii and Milne, 2008; Berger et al., 2008; Flannery and Rangan, 2008 and De Jonghe and Őztekin, 2015). Hence, the unobservable target ratio is expressed as follows:

𝑌𝑖𝑡∗ = 𝛽𝑋𝑖𝑡−1, (1.5)

where 𝑋𝑖𝑡−1 is a vector of banks’ predetermined characteristics, macroeconomic

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𝑋𝑖𝑡−1 is well chosen, if the tradeoff theory of capital structure choice holds, then we should have 𝛽 ≠ 0. We replace expression (5) in equation (4) to obtain:

∆𝑌𝑖𝑡 = 𝛼(𝛽𝑋𝑖𝑡−1− 𝑌𝑖𝑡−1) + 𝜀𝑖𝑡

= −𝛼𝑌𝑖𝑡−1+ 𝛼𝛽𝑋𝑖𝑡−1+ 𝜀𝑖𝑡. (1.6)

We can therefore decompose the adjustment process in the short-term adjustment measured by the coefficient 𝛼 and the long-term adjustment vector of coefficient 𝛽.

1.6.2.2 An extension to the context of multiple capital rule

As shown in section 1.5, the joint regulation of the leverage and risk-based capital ratio may be reduced to a single leverage ratio with a dynamic nonlinear target which is the function of banks’ risk-weighted assets density (𝛿). This suggests that we should include the risk-weighted assets density as a major determinant of the leverage ratio adjustment for our analysis of Canadian and American leverage. Therefore, we adopt a simple leverage ratio dynamic model which includes the risk-weighted assets density as covariate as follows:

Specification (weak form): Banks’ target leverage ratio is a function of their risk-weighted assets, depending on their risk-weighted asset density.

∆𝐿𝑅𝑖𝑡 = 𝛼(𝐿𝑅𝑖𝑡∗ − 𝐿𝑅𝑖𝑡−1) + 𝜀𝑖𝑡, (1.7) with 𝐿𝑅𝑖𝑡∗ = 𝛽𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1] + 𝛾𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]

Equation (1.7) could be rewritten as:

𝐿𝑅𝑖𝑡 = (1 − 𝛼)𝐿𝑅𝑖𝑡−1+ 𝛼(𝛽𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1] + 𝛾𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]) + 𝜀𝑖𝑡

where 𝐿𝑅𝑖𝑡∗ would be the desirable target leverage ratio, and 𝛿𝑖𝑡 the bank i’s ‘RWA density’ defined as bank i’s RWA divided by its total assets. It is assumed that, at the beginning of each period, the bank targets its desired leverage ratio based on its expectation regarding

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its attainable risk level (𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]) and expectation of its characteristics,

macroeconomics and regulatory variables ( 𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1]) under the information set 𝐼𝑡−1.

Equation (1.7) is our weak specification form for which we expect that banks on average to operate above the risk-weighted threshold and thus, obtain a positive relationship with the risk-weighted assets density. Conversely, the relationship might be flat or even negative if banks have already accumulated large leverage buffer and simultaneously invest in risk management to reduce their risk-weighted assets and increase their flexibility in taking future profitable risk.

Specification (strong form): Given that the limit on the "unique" leverage ratio in section 1.5 has a non-linear (hockey-stick) relationship to the risk-weighted assets, banks with leverage ratios which behave like their target (mainly the one operating closely to the regulatory target) are likely to exhibit a non-linear adjusting behavior (threshold-like) in the risk-weighted assets density. Accordingly, we test for the following specification:

∆𝐿𝑅𝑖𝑡 = 𝛼(𝐿𝑅𝑖𝑡∗ − 𝐿𝑅𝑖𝑡−1) + 𝜀𝑖𝑡, (1.8)

with 𝐿𝑅𝑖𝑡∗ = 𝛽𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1] + 𝛾1𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]𝟏𝜹𝒊𝒕≤ 𝜹∗+ 𝛾2𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]𝟏𝜹 𝒊𝒕> 𝜹∗

We rewrite the Equation (1.8) as follows:

𝐿𝑅𝑖𝑡 = (1 − 𝛼)𝐿𝑅𝑖𝑡−1

+ 𝛼(𝛽𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1] + 𝛾1𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]𝟏𝜹𝒊𝒕≤ 𝜹∗

+ 𝛾2𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]𝟏𝜹𝒊𝒕> 𝜹∗) + 𝜀𝑖𝑡

where 𝐿𝑅𝑖𝑡∗ would be the desirable target leverage ratio, and 𝛿𝑖𝑡 is bank i’s ‘RWA density’ defined as bank i’s RWA divided by its total assets. We assume that at the beginning of each period, the bank targets its desirable leverage ratio based on its expectation around its attainable risk level (𝐸𝑡−1[𝛿𝑖𝑡|𝐼𝑡−1]) and expectation about its characteristics,

macroeconomics and regulatory variables ( 𝐸𝑡−1[𝑋𝑖𝑡|𝐼𝑡−1]) under the information set 𝐼𝑡−1.

Figure

Table 1.2 : Descriptive statistics for the variables used in the main study
Table 1.3 : Wilcoxon test statistics on large versus small and medium banks.
Table 1.6 :  Correlation matrix between the LR, the RBC and other covariates
Table 1.8 : Regression of the leverage ratio on the risk-weighted density for Canadian banks
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