Macrofinancial Risk Analysis

Dale F. Gray and Samuel W. Malone

Macrofinancial Risk Analysis For other titles in the Wiley Finance series please see www.wiley.com/finance Macrofinancial Risk Analysis

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Gray, Dale, 1953– Macrofinancial risk analysis / Dale F. Gray and Samuel W. Malone. p. cm. — (Wiley finance series) Includes bibliographical references and index. ISBN 978-0-470-05831-2 (cloth) 1. Macroeconomics. 2. Risk management. I. Malone, Samuel W. II. Title. HB172.5.G73 2008 339—dc22 2008003729 British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library ISBN 978-0-470-05831-2 (HB) Typeset in 10/12pt Times by Integra Software Services Pvt Ltd, Pondicherry, India Printed and bound in Great Britain by TJ International Ltd, Padstow, Cornwall, UK This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. I dedicate this book to Cheryl, Ryan, Marie, and Colin. DFG

I dedicate this book to the memory of my father and greatest friend, John Malone. SWM

Contents

Foreword xv

Preface xix

1 Introduction 1

PART I OVERVIEW OF FINANCE, MACROECONOMICS, AND RISK CONCEPTS 7 2 An Overview of Macroeconomics, and Why the Theory of Asset Pricing and Contingent Claims Should Shape its Future 9 2.1 An overview of macroeconomics 10 2.2 How uncertainty is incorporated into macroeconomic models 13 2.3 Missing components in macro models: balance sheets with risk, default, and (nonlinear) risk exposures 15 2.4 Asset-pricing theory, financial derivatives pricing, and contingent claims analysis 17 2.5 Autoregression in economics vs. random walks in finance 19 2.6 Asset price process related to a threshold or barrier 21 2.7 Relating finance models and risk analytics to macroeconomic models 23 2.8 Toward macrofinancial engineering 24 2.9 Summary 25 References 26

3 Macroeconomic Models 29 3.1 The Hicks–Hansen IS-LM model of a closed economy 29 3.2 The Mundell–Fleming model of an open economy 33 3.3 A dynamic, stochastic, five-equation, small open economy macro model 38 3.4 Summary 42 References 42 viii Macrofinancial Risk Analysis

4 Stochastic Processes, Asset Pricing, and Option Pricing 43 4.1 Stochastic processes 43 4.2 Itô’s lemma 46 4.3 Asset pricing: Arrow–Debreu securities and the replicating portfolio 47 4.4 Put and call option values 48 4.5 Pricing the options using the Black–Scholes–Merton formula 50 4.6 Market price of risk 52 4.7 Implications of incomplete markets for pricing 54 4.8 Summary 55 Appendix 4A Primer on relationship of put, call, and exchange options 55 Appendix 4B Physics, Feynman, and finance 57 References 57

5 Balance Sheets, Implicit Options, and Contingent Claims Analysis 59 5.1 Uncertain assets and probability of distress or default on debt 59 5.2 Probability of distress or default 60 5.3 Debt and equity as contingent claims 61 5.4 Payoff diagrams for contingent claims 62 5.5 Understanding why an implicit put option equals expected loss 63 5.6 Using the Merton model and Black–Scholes–Merton formula to value contingent claims 64 5.7 Measuring asset values and volatilities 68 5.8 Estimating implied asset value and asset volatility from equity or junior claims 68 5.9 Risk measures 71 5.10 Summary 72 References 72

6 Further Extensions and Applications of Contingent Claims Analysis 73 6.1 Extensions of the Merton model 73 6.2 Applications of CCA with different types of distress barriers and liability structures 74 6.3 Risk-adjusted and actual probabilities using the market price of risk, Sharpe ratios, and recovery rates 78 6.4 Moody’s-KMV approach 80 6.5 CCA using skewed asset distributions modeled with a mixture of lognormals 81 6.6 Maximum likelihood methods 84 6.7 Incorporating stochastic interest rates and interest rate term structures into structural CCA balance sheet models 85 6.8 Other structural models with stochastic interest rates 86 6.9 Summary 87 Appendix 6A Calculating parameters in the Vasicek model 87 References 88 Contents ix

PART II THE MACROFINANCE MODELING FRAMEWORK 91

7 The Macrofinance Modeling Framework: Interlinked Sector Balance Sheets 93 7.1 Contingent claim balance sheets for sectors 93 7.2 Measuring asset values and volatilities 98 7.3 Measuring risk exposures 100 7.4 Linkages in a simple four-sector framework 100 7.5 Integrated value and risk transmission between sectors 101 7.6 Policy effectiveness parameters in implicit options 105 7.7 Advantages of an integrated balance sheet risk approach 106 7.8 Summary 106 References 107

8 The Macrofinance Modeling Framework: A Closer Look at the Sovereign CCA Balance Sheet 109 8.1 CCA balance sheet for the government and monetary authorities 109 8.2 Sovereign distress 111 8.3 Calculating implied sovereign assets and implied sovereign asset volatility using CCA for the public sector balance sheet 111 8.4 Applications of the macrofinancial risk framework to sovereigns 115 8.5 Sovereign risk-neutral and estimated actual default probabilities on foreign-currency-denominated debt 117 8.6 Spreads on sovereign foreign currency and local currency debt 118 8.7 Breaking down sovereign assets into key components 122 8.8 Risk-based scenario and policy analysis using calibrated sovereign CCA related to spreads on foreign currency debt 123 8.9 Short-term and long-term government CCA balance sheets with monetary authority 124 8.10 Summary 126 Appendix 8A Value and volatility of local currency liabilities and base money 126 References 127

9 The Macrofinance Modeling Framework: Linking Interest Rate Models in Finance and Macroeconomics 129 9.1 Overview of interest rate term structure models in finance 129 9.2 Two early theories: liquidity preference and the market for loanable funds 131 9.3 Monetary policy, Taylor rules, and interest rates 131 9.4 Reconciling different perspectives on interest rate behavior 133 9.5 What to do when the monetary authority is linked closely to the government balance sheet 135 9.6 Summary 136 References 137 x Macrofinancial Risk Analysis

10 Macrofinance Modeling Framework: Financial Sector Risk and Stability Analysis 139 10.1 Calculating risk indicators for individual banks or financial institutions 139 10.2 Time series of financial system risk indicators 140 10.3 Snapshot of system risk 145 10.4 Expected loss as a portfolio of implicit put options 146 10.5 Using a structural Merton model with stochastic interest rates for capital adequacy estimates 149 10.6 Factor model to assess key drivers of system risk and for scenario analysis 150 10.7 Multifactor risk analysis using copulas 152 10.8 Household balance sheet risk 152 10.9 Linking banking sector loans to corporate, household, and other borrowers 153 10.10 Foreign-currency-denominated loans and the impact of the presence of foreign banks on banking system risk 154 10.11 CCA models, financial stability indicators and links to macro models 155 10.12 Summary 159 Appendix 10A CCA model for banks and borrowers with foreign-currency-denominated debt and lending spreads based on credit risk 160 References 161

11 Macrofinancial Modeling Framework: Extensions to Different Exchange Rate Regimes 163 11.1 Floating exchange rate regimes, interest rates, and the sovereign balance sheet 163 11.2 Fixed exchange rate regimes, interest rates and the sovereign balance sheet 167 11.3 The impact of capital flows on the CCA sovereign balance sheet 172 11.4 Role of quasi-public entities in exchange rate management 173 11.5 Summary 174 References 174

PART III LINKING MACROFINANCIAL AND MACROECONOMIC FRAMEWORKS 175 12 Sovereign Reserve, Debt, and Wealth Management from a Macrofinancial Risk Perspective 177 12.1 Reserves adequacy and asset allocation: moving from simple rules to a national framework 177 12.2 CCA for a firm with a subsidiary and its wealth management 179 12.3 Constructing contingent claim balance sheets for the national economy 180 12.4 Macro risk and wealth management 181 12.5 Summary 184 References 185 Contents xi

13 Macrofinancial Modeling Framework: Relationship to Accounting Balance Sheets and the Flow of Funds 187 13.1 Economy-wide macro contingent claim balance sheets and risk exposures 187 13.2 Recovering traditional macroeconomic budget constraints and flow identities from CCA valuation equations when volatility is zero 191 13.3 Interlinkages between CCA balance sheets, flows, and risk premiums 195 13.4 Using the production function to link corporate and household assets 197 13.5 Macrofinance, macroeconomic flows, and the business cycle 198 13.6 Summary 199 Appendix 13A Cross-holding by households and financial sectors of contingent claims in other sectors 200 Appendix 13B Contingent claim values and returns of different sectors 201 References 202

14 Macrofinancial Risk Framework Linked to Macroeconomic Models 203 14.1 Adding risk analytics to the spectrum of macroeconomic models 203 14.2 The Mundell–Fleming model and default risk 204 14.3 Linking macrofinance outputs to DSGE models 206 14.4 Linking macrofinance outputs to dynamic, stochastic macroeconomic policy models 208 14.5 Linking macrofinance outputs to macroeconometric VAR models 215 14.6 An integrated policy framework 216 14.7 Summary 217 References 217

PART IV CRISIS AND DISTRESS IN ECONOMIES 219

15 Macroeconomic Models vs. Crisis Models: Why Nonlinearity Matters 221 15.1 Recent financial crises and crisis models 222 15.2 Summary 229 References 229

16 Sensitivity Analysis, Destabilization Mechanisms, and Financial Crises 231 16.1 Sensitivity analysis, the “Greeks”, and the valuation multiplier effect 232 16.2 The volatility leverage effect 236 16.3 Feedback between the forward rate and domestic interest rates on local currency debt 237 16.4 Feedback between local currency debt issuance and local currency spreads in the presence of contingent liability constraints 241 16.5 Summary 244 References 245

17 The Case of Thailand, 1996–1999 247 17.1 Background 247 17.2 A macrofinance analysis of the Thai crisis 249 xii Macrofinancial Risk Analysis

17.3 Scenario analysis 253 17.4 Summary 255 Appendix 17A Banking and corporate sector risk analysis with scenarios 257 References 258 18 The Brazil Crisis of 2002–2003 259 18.1 Background 259 18.2 A macrofinance analysis of the Brazil crisis 261 18.3 Summary 266 References 266

PART V MACROFINANCIAL MODEL APPLICATIONS AND ANALYTICAL ISSUES 267 19 International Shocks, Risk Transmission, and Crisis Prevention: Backdrop for Understanding the 2007–08 Global Financial Credit Turmoil 269 19.1 Changing global environment and global risk 270 19.2 Types of global shocks and the interaction with macrofinancial risk models 277 19.3 The international financial system and crisis prevention 281 19.4 Structuring an effective risk-management hierarchy from the international level down to the country authorities 282 19.5 Summary 283 References 283 20 Macro Risk Management: Ways to Mitigate, Control, and Transfer Risk in the Economy 285 20.1 Overview of ways to manage risk 285 20.2 Direct change in financial structure 287 20.3 Risk transfer 288 20.4 Management of guarantees 290 20.5 Longer-term risk management via institutional and policy change 293 20.6 Summary 294 References 294 21 Integrated Framework for Corporate and Sovereign Relative Value and Capital Structure Arbitrage 297 21.1 Capital structure arbitrage for firms and financial institutions 297 21.2 Credit and equity cycles 299 21.3 Sovereign capital structure relative value 300 21.4 Summary 302 References 302 22 Conclusions and New Directions for Macrofinance 303 22.1 Summary of conceptual issues 303 22.2 The roadmap for an integrated contingent claims analysis-macroeconomic Model 306 Reference 309 Contents xiii

Appendix A Mundell–Fleming with a Risk Premium 311 A.1 The model 311 A.2 Equilibrium 315 A.3 Monetary and fiscal policy 317 A.4 Summary 321 References 322

Index 323

Foreword

The arrival of Macrofinancial Risk Analysis, with its new perspective on how investors, bankers, risk managers, economic overseers and policymakers can measure and analyze risk in both emerging market and developed economies, could not have been better timed. We are amidst a perplexing financial crisis of banking and credit risk which is directly affecting the United States, United Kingdom and Europe. At the same moment, many emerging market countries, often the sources of financial crisis, appear remarkably strong, with large reserves and trade surpluses. How it will play out in the impending future, we do not know. But what we do know is that over the past five to ten years, the interconnected risks among emerging and developed market countries have become significantly greater, reactions in financial markets across geopolitical borders are considerably more rapid, and the complexity of the risk structures in every domain has increased dramatically. Happily, the collection of market-proven risk measurement and risk management techniques has also become proportionally richer. Dale Gray and Samuel Malone provide a prime exemplifying case by applying the financial engineering tools of contingent claims analysis (CCA) to create an innovative and substantial addition to the measurement, analysis, and management of the financial risks of a national economy. From its 1970s origins in measuring the risk and pricing of derivative securities, CCA has continuously found ever broader applications in the mainstream of finance and risk management. This book extends this type of analysis to help us better understand and evaluate risk flows among sectors and across economies and links this new approach to traditional macroeconomic analysis. The core analytical tool employed is the CCA risk-adjusted balance sheet, which quantifies the risk sensitivity of a country or sector’s assets and liabilities to external “shocks.” At the national level, the corporate, financial and governmental sectors of an economy are viewed as interconnected portfolios of assets, liabilities, and guarantees – some explicit and others implicit. Traditional sovereign-risk models have difficulty in analyzing how risk exposures can be rather benign at a point in time and then without any apparent change in asset or liability holdings, those exposures increase rapidly and erupt into a full-blown crisis. Such behavior is however well-understood by risk managers of a derivatives book in which the non-linear nature of the derivative prices relative to the underlying fundamentals can cause rapid and radical changes in the risk characteristics of the book without any changes in the actual positions held. Both the assets and liabilities of the various macro-sectors exhibit nonlinear derivative-like structures. The CCA approach is well-suited to capturing the impact of such non-linearity and quantifying the risk effects of asset-liability mismatches within and across institutions. Gray and Malone apply CCA at the level of the government sector to develop risk measures that help gauge the probability of systemic crises. Risk-adjusted CCA balance sheets are used to facilitate simulations and stress testing to evaluate the potential impact of policies to manage systemic risk. This approach to evaluating risk on the xvi Macrofinancial Risk Analysis balance sheets of the macroeconomic sectors represents an enhanced framework for macro risk analysis distinct from, and complementary to, traditional macroeconomic analysis based primarily on flow variables. The approach also applies modern risk management and finance techniques to the macroeconomy to achieve a richer method of assessing country vulnerability, as well as the valuation of sovereign debt, contingent liabilities, equity and other contingent claims on sector assets. It can be used to help formulate relative-value investing and trading strategies, including sovereign capital structure arbitrage and cross-sector and cross-country arbitrage. In addition, the framework can enrich analysis and management of sovereign wealth funds and to inform the design of new instruments and contracts to control or transfer risk between economies. Section I begins with two chapters that provide an overview of the evolution of selected models from macroeconomics and finance, and make the case for why a new generation of macrofinance models are needed that integrate the two types of models. Chapter 3 reviews a few core macroeconomic models used for evaluating policy. Chapter 4 proceeds to explain the basic analytical tools used in finance, including a primer on stochastic processes and option pricing models. Chapters 5 and 6 describe contingent claims analysis and its extensions that are used throughout the book. Section II begins by laying out the basic macrofinance framework with contingent claims balance sheets of interlinked sectors (sovereign, financial, corporate, and household) and the risk transmission between sectors in Chapter 7. Chapter 8 discusses how sovereign contingent claim balance sheets can be calibrated using current financial market prices and used to calculate sovereign credit risk indicators. It describes how this new tool can be used for policy analysis, including debt and reserves management as well as fiscal policy. Chapter 9 discusses the relationship between models of interest rates in macroeconomics, as in the Taylor rule in macroeconomic policy models, and term structure of interest rates models in finance, with a view towards reconciling these different approaches. In Chapter 10, financial stability indicators are developed that are linked into macroeconomic models in the chapters to follow. Chapter 11 discusses the adaptation of the macrofinance framework to fixed and floating exchange rate regimes. Section III begins with Chapter 12 on new applications of macrofinance to sovereign reserve, debt, and sovereign wealth management, which is certainly a hot topic at the moment and promises to continue to be so into the indefinite future. Chapter 13 shows how to relate the risk-adjusted, contingent claims balance sheets of macrofinance to the standard flow- of-funds and national accounting balance sheets used in macroeconomic analysis. Among other things, it shows how traditional macroeconomic flow-of-funds can be derived as a special case of contingent claims pricing relationships in the limit as uncertainty disappears. Chapter 14 discusses several ways to link macrofinance outputs to monetary policy models, Dynamic Stochastic General Equilibrium (DSGE) models, and macroeconometric Vector Autoregression (VAR) models. Section IV focuses on analyzing financial distress and crisis in economies, beginning with an overview in Chapter 15 of the existing economics literature on financial crises. Chapter 16 discusses four important “destabilization mechanisms”, or potentially danger- ous interactions of nonlinear effects, that can cause crises to occur in the context of the macrofinance model. These mechanisms rely on the valuation formulas of contingent claims analysis applied to the macroeconomic sectors, and as such, are contributions to the theory of financial crises. Chapters 17 and 18 are devoted to an empirical application of the Foreword xvii macrofinance model to study the Asian crisis of 1997–98 and the Brazilian crisis of 2002, respectively. Section V applies the insights of the macrofinance approach to selected topics relevant to senior managers in international financial institutions, staffs of finance ministries, and global investors. Chapter 19 uses the macrofinance model to focus on the new international global environment and the potential impact of international shocks and risk transmission. Chapter 20 looks at alternative policies, contracts, and tools that can be used to transfer and mitigate risk on the sovereign balance sheet and the economy. It points out how the modern techniques of Alternative Risk Transfer (ART) can be adapted and applied at the sector, economy, and international level. Chapter 21 offers several ideas for investment and trading strategies, including sovereign capital structure arbitrage using relative-value techniques based on contingent claims and macrofinance model. Chapter 22 closes the book with a summary look at the “bigger picture” surrounding macrofinance and lays out several suggestions for future research ideas, which will surely be of interest to those working in both macroeconomics and finance. Macrofinancial Risk Analysis is a bold and largely self-contained offering of an integration of finance and macroeconomic modeling to help us to better understand, measure and manage risk in the evolving global economic system. Whether prime researcher, experienced public policy maker, or seasoned private-sector practitioner, the reader is in for a treat: Bon Appétit!

Robert C. Merton Harvard Business School

Preface

The initial sense of the need to bring finance and risk management insights to bear on macroeconomics, as described in this book, was the outcome of one author’s (Dale Gray’s) experience in the International Monetary Fund (IMF) during the Asian and Russian crises. The failure of traditional macroeconomic flow and stock models to deal with the credit risk and balance sheet aspects of the Asian and Russian crises was so evident that it was clear that a new framework blending risk analysis and balance sheets with macroeconomics was long overdue. When we first met and worked together in the International Capital Markets (ICM) department of the IMF, during the summer of 2005, we decided to write this book. It is the product of years of work and fascination, on both our parts, with the idea that concepts from finance and risk management can, and should, be applied to improve our understanding of important issues and policy questions in macroeconomics – in particular those relating to financial crises as well as sovereign risk and wealth management. A related motivation for this work is the belief of the authors that finance and macroeconomics can be unified within an appropriate overarching mathematical framework. Several people deserve thanks for their many helpful and insightful conversations related to this material during the past several years. In particular we would like to thank Robert Merton and Zvi Bodie for all their help and support. We would also like to thank Carlos Medeiros, Matthew Jones, Mike Gapen, Cheng Hoon Lim, Ying-bin Xiao, Mark Swinburne, Chris Towe, Andrea Maechler, and John Odling-Smee of the IMF, Dan Russell and Simon Jiang (Moody’s Investors Service), David Vines (Oxford), Gustavo García (IESA), Enrique ter Horst (IESA), Stephen Kealhofer (MKMV), Joe Zou (Taconic), Emanuel Derman (Columbia University), Pijus Verkitus and Ben Heller (HBK), and Erwin Martens (TIAA-CREF) whose support and confidence in this project has helped to make it possible. Additionally, we would like to express our appreciation for the hard work of the team at John Wiley & Sons, including Samantha Hartley, Aimée Dibbens, Caitlin Cornish, Pete Baker, and Sunita Jayachandran at Integra. Finally, we would like to thank those macroeconomists (primarily in the IMF) who were so certain that finance has absolutely nothing to offer macroeconomics, on the level of theory or practice, that it gave an added impetus to carry this work forward for the sake of both.

1 Introduction

In this book we will: • Provide a new framework for risk and policy analysis using quantitative risk-based tools for: — evaluation of financial institution risk and financial system stability; — improving ratings and vulnerability analysis for firms, banks, and sovereigns; — reserve, fiscal, and debt management; — assessing benefits of risk mitigation policies and transfer contracts; — linking macroeconomics with finance in a more unified framework. • Apply modern risk management and finance techniques to the macroeconomy so as to better assess country vulnerability, and the valuation of debt, contingent liabilities, equity, and other contingent claims on sector assets. • Analyze the impact of shocks, both domestic and external, on the macroeconomy using a framework based on the analysis of risk-adjusted, interlinked balance sheets of the major economic sectors. The new framework measures non-linear risk transmission between the sectors of the economy and from abroad. • Provide a new framework for relative valuation, investing, and trading, including sovereign capital structure arbitrage and cross-sector and cross-country arbitrage. The framework allows for analysis and management of sovereign wealth funds and the design of new instruments and contracts to control or transfer sovereign risk. The fields of macroeconomics and finance have both experienced great innovations during the past thirty-five years. Unfortunately, some of the most important advances during that period are only just beginning to percolate between the two fields. Despite their apparent differences in subject matter, the two fields have a substantial natural area of overlap. Both are concerned with interest rates and the determination of prices. Finance focuses on the prices of assets, whereas macroeconomics focuses on the prices of goods. The major entities that make up the economy – households, governments, firms, and banks – hold portfolios consisting of both types of assets, however, and must be concerned with both asset and goods prices. Moreover, the entities in the economy are linked by the fact that the assets of one entity form part of the assets of other entities. Changes in the value of assets induce changes in the fair value of the liabilities backed by those assets, and this, in turn, changes the market value of the assets and liabilities of the entity that owns those liabilities. These valuation linkages are crucial in the macroeconomy, especially when default on liabilities is a real possibility. Most current macroeconomic models, and especially those used for policy analysis, however, routinely ignore both valuation linkages and the possibility of default. One major goal of this book is to provide a framework that can be used to help overcome these limitations in our analysis of the macroeconomy. 2 Macrofinancial Risk Analysis

The directionality of our contribution in this book, in theoretical terms, will be first from finance and risk management to macroeconomics. As we will see later in the book, the integration of these two fields provides new insights for financial activities – investing, trading, risk mitigation, and risk transfer arrangements. The results we believe will be of interest to finance professionals and macroeconomists alike. Our framework is based on the method of contingent claims, which was pioneered by Robert Merton in the early 1970s. The “Merton model”, as it is popularly known in finance, is a structural model of the firm built upon the observation that the value of a firm’s liabilities, whether debt or equity, is linked directly to the value of the firm’s assets. Debt and equity are different types of claims, and because of their different payoff structures, will share differently the value of the firm’s assets, depending on the level and volatility of those assets, the interest rate, and the face value of the debt, among other factors. Adapting risk management and contingent claims analysis to the sectors of the macroeconomy, and linking it with macroeconomics, requires considerable work; to do it properly requires nothing less than a book. With that said, the reader will see clearly that several parts of what follows contain a variety of ideas for future research. Our goal in this work is to lay out the basics of the “macrofinance” approach, as we like to call it, in a very clear way that can be adapted for policy-making, for a course on this or a related subject in economics departments, and for courses in business schools. We believe that an analytical framework that takes into account both balance sheets and risk exposures is a necessary part of any analysis of macroeconomic and sectoral vulnerability. We make the argument on a theoretical and empirical level that such an analytical platform is well suited to explaining a variety of past crises, and could be invaluable in anticipating and diffusing new ones. The book is organized into five parts. Part I begins with Chapter 2, which lays out an overview of macroeconomics and finance. It discusses how shocks and volatility are handled in macroeconomic models but not uncertainty and risk. A conspicuous omission in macroeconomic models has been risk exposures, in particular default risk, as well as risk transmission between sectors and the behavioral nonlinearities to which these features give rise. Finance, and the closely related field of risk management, contain the appropriate tools to quantify and measure risks in the macroeconomy, as well as risk transmission within and between economies. It points out the need for a new generation of macrofinance models that combine the two types of models into an integrated system – a system of equations which are part macroeconomic equations and part finance/option-based equations. Chapter 3 provides an exposition of three types of models that are instrumental for evaluating macroeconomic policies. The three models are the IS-LM model of the closed economy, the Mundell–Fleming model of the open economy, and a dynamic macroeconomic model, which is a simplified DSGE model used to guide monetary policy in many central banks today. We will make reference to these models later in the book, in the generalized macrofinance framework incorporating stochastic interest rates, and when discussing ways to incorporate the outputs of the macrofinance framework into monetary policy models. Part I then proceeds to explain basic analytical tools used in finance, including stochastic processes, the Black–Scholes–Merton option pricing formula, and related concepts in Chapter 4. Chapter 5 describes the contingent claims theory that will be used throughout the book. The contingent claims approach provides a framework for formulating risk-adjusted balance sheets of interlinked sectors in an economy and a way to measure risk exposures and risk transmission. It overcomes the limitations of statistical crisis prediction models in Introduction 3 the policy arena that rely heavily on “vulnerability ratios”, such as debt-to-GDP or debt- to-exports, that are drawn from the national accounting and income statements published by country authorities. We make the analogy between these sorts of measures and the well-known accounting-based Altman Z-score measures developed in the 1960s by Edward Altman to aid in the prediction of firm bankruptcies. Over the last two decades, since the early 1990s, the cutting edge of finance has moved forward to the commercial adaptation of the Merton model to assess default probabilities of firms and financial institutions around the world (commercial applications were pioneered by KMV in the 1990s, and KMV has since been bought by the rating agency Moody’s to form Moody’s-KMV). Chapter 6 describes extensions and applications of the contingent claims approach, which is in widespread use for credit risk modeling, vulnerability assessment, and relative value capital structure investment strategies. The benefits of this structural method are harnessed throughout the book to produce better results in the analysis of macro risk, vulnerability of economies, and valuation. Part II begins with Chapter 7, which lays out the basic macrofinance framework with contingent claims balance sheets of key sectors (sovereign, financial, corporate, and household) and the risk transmission between sectors. The rest of Part II is then devoted to a closer examination of various important aspects of the framework. Chapter 8 provides a closer look at the sovereign balance sheet, how sovereign contingent claim balance sheets can be calibrated, and the calculation of useful credit risk indicators for sovereign foreign currency and local currency debt, as well as other public sector risk exposures. It describes how this new tool can be used for policy and vulnerability analysis (debt and reserves management as well as fiscal policy). Chapter 9 discusses the relationship between models of interest rates in macroeconomics, as in the Taylor rule in macroeconomic policy models, and term structure models of interest rates in finance, with a view towards reconciling these different approaches. Chapter 10 focuses on the analysis of financial sector risk and linkages to firms and households. Financial stability indicators are developed, which can be used for vulnerability assessments and which will be linked into macroeconomic models in following chapters. Chapter 11 discusses the adaptation of the macrofinance framework to fixed and floating exchange rate regimes for the sovereign, and looks at the impact of capital flows and problems that can arise from the use of quasi-public entities to hide contingent liabilities on the sovereign balance sheet. Part III contains three chapters, each of which treats one facet of how to relate the macrofinance framework to the framework of macroeconomics. Chapter 12 discusses sovereign reserve, debt, and wealth management from the macrofinancial risk perspective. Chapter 13 shows how to relate the risk-adjusted, contingent claims balance sheets of macrofinance to the standard flow-of-funds and national accounting balance sheets used in macroeconomic analysis. Among other things, we show how the traditional budget constraint of macroeconomics can be derived as a special case of contingent claims pricing relationships when volatility goes to zero. Chapter 14 discusses several ways to link macrofinance outputs to monetary policy models, DSGE models, and macroeconometric vector autoregression (VAR) models. The four chapters that comprise Part IV focus on distress and crisis in economies. Chapter 15 provides a relatively brief, guided tour of the economics literature on financial crises that highlights the recognition that balance-sheet-based vulnerabilities have been crucial in past crisis episodes. More generally, this chapter also takes care to discuss why an explicit accounting for crucial nonlinear effects in economic models is necessary if those 4 Macrofinancial Risk Analysis models are to be reasonable crisis models. The models in the crisis literature make clear that this is so, and we note the relationship of our work to that literature. Chapter 16 discusses four important “destabilization mechanisms”, or potentially dan- gerous interactions of nonlinear effects, that can cause crises to occur in the context of the macrofinance model. These theoretical mechanisms rely on the valuation formulas of contingent claims analysis applied to the macroeconomic sectors, and in particular to the sovereign, and, as such, are contributions to the theory of financial crises. Chapters 17 and 18 are devoted to an application of the macrofinance model to the Asian crisis of 1997–98, and the more recent crisis episode in Brazil in 2002, respectively. We discuss how, in both of these episodes, the destabilization mechanisms analyzed in Chapter 16 are real and can be very important in provoking or exacerbating crises. Part V, which concludes the book, applies the insights of the macrofinance approach to three topics highly relevant to international financial institutions, finance ministries, and international investors. Chapter 19 focuses on the new international global environment and the potential impact of international shocks and risk transmission using the macrofinance model. It looks at the impact of both high-frequency shocks and low-frequency shocks. Chapter 20 looks at alternative policies, contracts, and tools that can be used to transfer and mitigate risk on the sovereign balance sheet. Chapter 21 lays out several ideas for corporate and sovereign investment and capital structure arbitrage using the relative value tool of the contingent claims and macrofinance model. This is written in particular for those in the private sector who may be interested in using our ideas to generate trades and investment

Macrofinancial risk analytics

Vulnerability Risk analysis Policy Sophisticated and ratings and analysis macro models of entities, management Monetary, RBC, GE, sectors, Integrated financial DSGE, MPM, sovereign economy-wide sector, VAR CCA model fiscal, debt, reserve, SWF

Investors • Asset management (long only) • Sovereign wealth fund managers • Hedge fund, relative value, sovereign capital structure arbitrage (long and short strategies) • ART – alternative risk transfer

Figure 1.1 Applications of the tools provided by the macrofinance perspective. SWF – sovereign wealth funds; RBC – real business cycle; GE – general equilibrium; DSGE – dynamic stochastic general equilibrium; MPM – monetary policy models; VAR – vector autoregression Introduction 5 strategies. Chapter 22 closes the book with a look at the “bigger picture” surrounding macrofinance, and lays out a summary of the book accessible to a wide audience, along with several suggestions for future research ideas based on the material, which we hope will be of interest to those working in both macroeconomics and finance. The main applications of the tools provided by the macrofinance perspective are summarized in Figure 1.1. The ability of macrofinancial risk analysis to improve vulnerability analysis, risk management, and policy is also highly relevant to investors, whether those on the asset management side or hedge fund managers interested in taking advantage of arbitrage opportunities based on assessments of relative value. In addition, the outputs of the macrofinance model have the potential to inform and improve the state of the art of macroeconomic and macroeconometric modeling.

Part I Overview of Finance, Macroeconomics, and Risk Concepts