DISS. ETH NO MANAGERIAL INCENTIVES FOR RISK MITIGATION AND THE MODERATION OF CREDIT CYCLES FROM A MACROPRUDENTIAL PERSPECTIVE

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1 DISS. ETH NO MANAGERIAL INCENTIVES FOR RISK MITIGATION AND THE MODERATION OF CREDIT CYCLES FROM A MACROPRUDENTIAL PERSPECTIVE A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by ELIAS APTUS M.Sc. in Applied Mathematics, ETH Zurich born on citizen of Germany accepted on the recommendation of Prof. Dr. Hans Gersbach (ETH Zurich), examiner Prof. Dr. Antoine Bommier (ETH Zurich), co-examiner 2014

2 Abstract This thesis investigates two macroprudential tools for banking regulation and analyzes two approaches to modeling moral hazard. After an introductory chapter that motivates the thesis, in the second chapter we examine the impact of so-called Crisis Contracts on bank managers risk-taking incentives and on the probability of banking crises. Under a Crisis Contract, managers are required to contribute a pre-specified share of their past earnings to finance public rescue funds when a crisis occurs. This can be viewed as a retroactive tax that is levied only when a crisis occurs and that leads to a form of collective liability for bank managers. We develop a game-theoretic model of a banking sector whose shareholders have limited liability, so that society at large will suffer losses if a crisis occurs. Without Crisis Contracts, the managers and shareholders interests are aligned, and managers take more than the socially optimal level of risk. We investigate how the introduction of Crisis Contracts changes the equilibrium level of risk-taking and the remuneration of bank managers. We establish conditions under which the introduction of Crisis Contracts will reduce the probability of a banking crisis and improve social welfare. We explore how Crisis Contracts and capital requirements can supplement each other and we show that the efficacy of Crisis Contracts is not undermined by attempts to hedge. In the third chapter we analyze several extensions of the paper Aggregate Investment Externalities and Macroprudential Regulation by Gersbach and Rochet (2012A). First, we show how Gersbach and Rochet s results are affected when a macroeconomic shock hits both sectors of the economy, instead of one sector only. We provide an intuition why capital shifts between the sectors still occur in the competitive equilibrium and we analytically confirm this intuition. Furthermore, we show that the regulation of capital adjustments which can be realized via the regulation of short-term debt can increase social welfare. Second, we show that the results of Gersbach and Rochet with regard to the existence and uniqueness of a competitive equilibrium do not depend on the authorship of the contracts between the bankers and the investors. However, we show that the efficacy of the regulation of capital adjustments does crucially depend on the authorship of the contracts. In fact, when investors write the contracts, the regulation of capital adjustments cannot increase welfare. Third, we show that the results of Gersbach and Rochet i

3 ii continue to hold qualitatively when the bankers moral hazard is modeled by an effort cost instead of a leisure benefit. Thus, we continue Gersbach and Rochet s investigation of the macroeconomic consequences of the introduction of a Net Stable Funding Ratio as in Basel III. The two mentioned approaches to modeling moral hazard are standard ones in the literature. In the fourth chapter we consider a principal-agent problem with agent-moralhazard, in which the allocation is determined by the Generalized Nash Bargaining Solution. In this framework, we show that the two ways to model moral hazard may yield different qualitative results and are biased quantitatively into opposite directions regarding the resulting allocations. We point out the limitations of our results and illustrate how our findings may be used to build and assess models involving agent moral hazard in bargaining situations.

4 Zusammenfassung Diese Dissertation untersucht zwei makroprudentielle Instrumente der Bankenregulierung und analysiert zwei Ansätze, Moral Hazard zu modellieren. Nach einem einleitenden Kapitel, welches eine Motivation für diese Dissertation enthält, analysieren wir im zweiten Kapitel den Einfluss von so genannten Crisis Contracts auf die Risikoanreize der Bankmanager und auf die Wahrscheinlichkeit von Bankenkrisen. Unter einem Crisis Contract sind Manager verpflichtet, einen bestimmten Anteil ihrer Einnahmen aus der Vergangenheit beizusteuern, um öffentliche Rettungsschirme zu finanzieren, wenn eine Krise eintritt. Das kann als rückwirkende Steuer angesehen werden, die nur im Krisenfall erhoben wird, und die zu einer kollektiven Haftung für Bankmanager führt. Wir entwickeln ein spieltheoretisches Modell eines Bankensektors, dessen Aktionäre nur beschränkt Haftung tragen, sodass im Falle einer Krise die gesamte Gesellschaft Schaden erleidet. Ohne Crisis Contracts sind die Interessen der Manager und diejenigen der Aktionäre angeglichen, und Manager riskieren mehr als sozial optimal wäre. Wir untersuchen, wie die Einführung von Crisis Contracts das Gleichgewichts-Level des Risikoverhaltens und die Entlöhnung der Bankmanager beeinflusst. Wir leiten Bedingungen her, unter denen die Einführung von Crisis Contracts die Krisenwahrscheinlichkeit reduzieren und die soziale Wohlfahrt steigern wird. Wir untersuchen, wie Crisis Contracts und Kapitalanforderungen einander ergänzen können und wir zeigen, dass die Effektivität der Crisis Contracts durch Hedgingversuche nicht untergraben werden kann. Im dritten Kapitel analysieren wir verschiedene Erweiterungen des Papiers Aggregate Investment Externalities and Macroprudential Regulation von Gersbach und Rochet (2012A). Als Erstes zeigen wir, in welcher Weise es die Resultate von Gersbach und Rochet beeinflusst, wenn ein makroökonomischer Schock statt nur eines Sektors beide Sektoren der Ökonomie trifft. Wir liefern eine Intuition dafür, warum Kapital-Reallokationen im wettbewerblichen Equilibrium weiterhin vorkommen, und bestätigen diese Intuition analytisch. Des Weiteren zeigen wir, dass die Regulierung von Kapitalanpassungen welche durch die Regulierung von kurzfristigen Schulden umgesetzt werden kann die soziale Wohlfahrt steigern kann. Als Zweites zeigen wir, dass Gersbach und Rochets Resultate bezüglich der Existenz und Eindeutigkeit eines wettbewerblichen Equilibriums nicht von der Autorschaft der Verträge zwischen den Bankern und den Investoren iii

5 iv abhängen. Allerdings zeigen wir auch, dass dass die Effektivität der Regulierung von Kapitalanpasungen entscheidend von dieser Autorschaft abhängt. In der Tat, wenn Investoren die Verträge schreiben, kann die besagte Regulierung nicht die soziale Wohlfahrt steigern. Als Drittes zeigen wir, dass Gersbach und Rochets Resultate weiterhin qualitativ gelten, wenn der Moral Hazard der Banker mit Arbeitsaufwandkosten anstatt mit Freizeitbenefits modelliert wird. Wir führen also Gersbach und Rochets Untersuchung der makroökonomischen Konsequenzen der Einführung eines Net Stable Fundung Ratio wie in Basel III um einen Schritt weiter. Die beiden erwähnten Ansätze zur Modellierung von Moral Hazard entsprechen dem Standard in der Literatur. Im vierten Kapitel betrachten wir ein Principal-Agent-Problem mit Moral Hazard des Agenten, in welchem die Allokation durch die Generalized Nash Bargaining Solution bestimmt wird. In diesem Rahmen zeigen wir, dass die zwei Ansätze zur Modellierung von Moral Hazard qualitativ unterschiedliche Resultate liefern können und quantitativ in entgegengesetzte Richtungen verzerrt sind im Bezug auf die resultierenden Allokationen. Wir legen die Grenzen unserer Resultate dar und zeigen auf, wie unsere Ergebnisse verwendet werden können, um Modelle zu entwerfen und einzuschätzen, die Moral Hazard von Agenten in Verhandlungssituationen beinhalten.

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