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Quantitative Financial Risk Management: Theory and Practice by ConstantinZopounidis and Emilios Galariotis

QuantitativeFinancial RiskManagement

Theory and Practice

CONSTANTIN ZOPOUNIDISEMILIOS GALARIOTIS

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Copyright © 2015 by Constantin Zopounidis and Emilios Galariotis. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

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Library of Congress Cataloging-in-Publication Data

Zopounidis, Constantin.Quantitative financial risk management : theory and practice / Constantin Zopounidis, Emilios Galariotis.

pages cm. – (The Frank J. Fabozzi series)Includes index.ISBN 978-1-118-73818-4 (hardback)

1. Financial risk management. I. Galariotis, Emilios. II. Title.HD61.Z67 2015332–dc23

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

This work is dedicated to our families for theirsupport and encouragement, as well as for their

understanding.

More specifically, Constantin Zopounidis wishes todedicate this to his wife, Kalia, and children,

Dimitrios and Helene.

Emilios Galariotis wishes to dedicate this to his wife,Litsa, his children, Irini and Vasileios, and his

parents, Christos and Irini.

Contents

Preface xvii

About the Editors xix

SECTION ONESupervisory Risk Management

CHAPTER 1Measuring Systemic Risk: Structural Approaches 3Raimund M. Kovacevic and Georg Ch. Pflug

Systemic Risk: Definitions 4From Structural Models to Systemic Risk 6Measuring Systemic Risk 10Systemic Risk and Copula Models 15Conclusions 20References 20

CHAPTER 2Supervisory Requirements and Expectations for Portfolio-LevelCounterparty Credit Risk Measurement and Management 22Michael Jacobs Jr., PhD, CFA

Introduction 22Review of the Literature 25Supervisory Requirements for CCR 26Conceptual Issues in CCR: Risk versus Uncertainty 41Conclusions 44References 44

xi

xii Contents

CHAPTER 3Nonperforming Loans in the Bank Production Technology 46Hirofumi Fukuyama and William L. Weber

Introduction 46Selective Literature Review 47Method 51Empirical Application 57Summary and Conclusion 65Appendix 3.1 Bank Names and Type 66References 67

SECTION TWORisk Models and Measures

CHAPTER 4A Practical Guide to Regime Switching in Financial Economics 73Iain Clacher, Mark Freeman, David Hillier, Malcolm Kempand Qi Zhang

A Brief Look at Markov Regime Switching in AcademicEconomics and Finance 74

Regime Switching and Interest Rate Processes 75Regime Switching and Exchange Rates 76Regime Switching, Stock Returns, and Asset Allocation 77Single-Asset Markov Models 79Two-State Estimation 82Three-State Estimation 84Markov Models for Multiple Assets 85Practical Application of Regime Switching Models for

Investment Purposes 87Intuitive Appeal of Such Models 87Implementation Challenges 89Selecting the “Right" Model Structure 89Calibrating the Selected Model Type to Suitable Data 90Drawing the Right Conclusions from the Model 93References 95

CHAPTER 5Output Analysis and Stress Testing for Risk Constrained Portfolios 98Jitka Dupacová and Miloš Kopa

Introduction 98Worst-Case Analysis 107

Contents xiii

Stress Testing via Contamination 110Conclusions and New Problems 122References 122

CHAPTER 6Risk Measures and Management in the Energy Sector 126Marida Bertocchi, Rosella Giacometti and Maria Teresa Vespucci

Introduction 126Uncertainty Characterization via Scenarios 128Measures of Risks 132Case Studies 137Summary 147References 147

SECTION THREEPortfolio Management

CHAPTER 7Portfolio Optimization: Theory and Practice 155William T. Ziemba

Static Portfolio Theory 155Importance of Means 163Stochastic Programming Approach to Asset Liability

Management 167Siemens InnoALM Pension Fund Model 182Dynamic Portfolio Theory and Practice: The Kelly Capital

Growth Approach 194Transactions Costs 199Some Great Investors 201Appendix 7.1: Estimating Utility Functions and Risk

Aversion 206References 208

CHAPTER 8Portfolio Optimization and Transaction Costs 212Renata Mansini, Wlodzimierz Ogryczak and M. Grazia Speranza

Introduction 212Literature Review on Transaction Costs 215An LP Computable Risk Measure: The Semi-MAD 221

xiv Contents

Modeling Transaction Costs 223Non-Unique Minimum Risk Portfolio 232Experimental Analysis 234Conclusions 237Appendix 238References 239

CHAPTER 9Statistical Properties and Tests of Efficient Frontier Portfolios 242C J Adcock

Introduction 242Notation and Setup 245Distribution of Portfolio Weights 247Empirical Study 255Discussion and Concluding Remarks 267References 268

SECTION FOURCredit Risk Modelling

CHAPTER 10Stress Testing for Portfolio Credit Risk: Supervisory Expectationsand Practices 273Michael Jacobs Jr.

Introduction and Motivation 273Conceptual Issues in Stress Testing: Risk versus Uncertainty 276The Function of Stress Testing 277Supervisory Requirements and Expectations 280Empirical Methodology: A Simple ST Example 281Conclusion and Future Directions 291References 293

CHAPTER 11A Critique of Credit Risk Models with Evidence from Mid-Cap Firms 296David E. Allen, Robert J. Powell and Abhay K. Singh

Introduction 296Summary of Credit Model Methodologies 297Our Empirical Methodology 302

Contents xv

Critique 303Conclusions 310References 310

CHAPTER 12Predicting Credit Ratings Using a Robust Multicriteria Approach 312Constantin Zopounidis

Introduction 312Credit Scoring and Rating 315Multicriteria Methodology 319Empirical Analysis 325Conclusions and Future Perspectives 330References 331

SECTION FIVEFinancial Markets

CHAPTER 13Parameter Analysis of the VPIN (Volume-Synchronized Probability ofInformed Trading) Metric 337Jung Heon Song, Kesheng Wu and Horst D. Simon

Introduction 337Definition of VPIN 341Computational Cost 346Optimization of FPR 348Uncertainty Quantification (UQ) 353Conclusion 360References 362

CHAPTER 14Covariance Specification Tests for Multivariate GARCH Models 364Gregory Koutmos

Introduction 364Covariance Specification Tests 365Application of Covariance Specification Tests 367Empirical Findings and Discussion 368Conclusion 370References 370

xvi Contents

CHAPTER 15Accounting Information in the Prediction of Securities Class Actions 372Vassiliki Balla

Introduction 372Literature Review 375Methodology 376Data 378Results 387Conclusions 394References 395

About the Contributors 399

Glossary 413

Index 421

Preface

The book Quantitative Financial Risk Management: Theory and Practiceprovides an invaluable forum for creative and scholarly work on financial

risk management, risk models, portfolio management, credit risk modeling,portfolio management, and financial markets throughout the world.

Quantitative financial risk management consists of economics, account-ing, statistics, econometrics, mathematics, stochastic processes, andcomputer science and technology. The tools of financial management aremore frequently being applied to manage, monitor, and measure risk, espe-cially in the context of globalization, market volatility, and economic crisis.

The main objectives of this book are to advance knowledge relatedto risk management and portfolio optimization, as well as to generatetheoretical knowledge with the aim of promoting research within varioussectors wherein financial markets operate. Chapters will relate to one ofthese areas, will have a theoretical and/or empirical problem orientation,and will demonstrate innovation in theoretical and empirical analyses,methodologies, and applications.

We would like to thank the assistant editors Georgios Manthoulis andStavroula Sarri for their invaluable help. We extend appreciation to theauthors and referees of these chapters, and to the editors at John Wiley &Sons, Inc., for their assistance in producing this book.

The editors,Constantin Zopounidis

Emilios Galariotis

xvii

About the Editors

Constantin Zopounidis is professor of Financial Engineering and Opera-tions Research at Technical University of Crete in Greece, distinguished

research professor at Audencia Nantes, School of Management (EQUIS,AMBA, AACSB) in France, senior academician of the Royal Academyof Doctors and the Royal Academy of Economics and Financial Sciencesof Spain, and elected president of the Financial Engineering and BankingSociety (FEBS).

His research interests include financial engineering, financial risk man-agement, and multiple-criteria decision making. He has edited and authoredmore than 70 books in international publishers and more than 450 researchpapers in scientific journals, edited volumes, conference proceedings, andencyclopedias in the areas of finance, accounting, operations research, andmanagement science. Prof. Zopounidis is editor-in-chief and member of theeditorial board of several international journals. In recognition of his scientificwork, he has received several awards from international research societies.

Emilios Galariotis is professor of Finance at Audencia Nantes Schoolof Management (AMBA, EQUIS, AACSB) in France. He is the founder anddirector of the Centre for Financial and Risk Management (CFRM) and headof research in the area of Finance, Risk, and Accounting Performance atAudencia.

His academic career started at Durham University and head of researchin the area of Finance, Risk, and Accounting Performance as well asco-chair of the department of Accounting and Finance at Audencia. UK.There, beyond his academic role. His academic career started at DurhamUniversity, UK (Top 100 in the world, 3rd oldest in England), he was alsodirector of Specialized Finance Masters Programs. His research interestsinclude behavioral finance and market efficiency, contrarian and momentuminvestment strategies, and liquidity.

His work has been published in quality refereed journals, such as(to mention only the most recent) the European Journal of OperationalResearch, the Journal of Banking and Finance, as well as the Wiley Encyclo-pedia of Management. Professor Galariotis is associate editor and memberof the editorial board of several international journals, and member of theboard of directors of the Financial Engineering and Banking Society anddistinguished researcher at various research centers.

xix

SECTION

OneSupervisory Risk

Management

CHAPTER 1Measuring Systemic Risk:

Structural ApproachesRaimund M. Kovacevic

ISOR, Department of Statistics and OR,University of Vienna, Austria

Georg Ch. PflugISOR and IIASA, Laxenburg

“Systemic risks are developments that threaten the stability of thefinancial system as a whole and consequently the broadereconomy, not just that of one or two institutions.”

—Ben Bernanke, ex-chairman of the US Federal Reserve Bank.

The global financial crisis of 2007–2008, often considered as the worstfinancial crisis since the Great Depression of the 1930s, resulted in a

change of paradigms in the financial and banking sector. These crisis yearssaw collapses of large financial institutions, bailouts of banks by govern-ments, and declines of stock markets. Triggered by the U.S. housing bubble,which itself was caused by giving easy access to loans for subprime bor-rowers, financial distress spread over the banking sector and led to failureof key businesses and to the 2008–2012 global recession. Finally, this alsocontributed to the European sovereign-debt crisis, with lots of aftereffects inour present times.

3

4 SUPERVISORY RISK MANAGEMENT

Uncertainties about bank solvency, declines in credit availability,and reduced investor confidence had an impact on global stock markets.Governments responded with fiscal measures and institutional bailouts,which in the long term resulted in extreme public debts and necessary taxincreases.

This negative experience demonstrates that the economy as a whole,but especially the financial sector is subject to risks, which are groundedin the interdependencies between the different economic actors and not inthe performance of individual actors. This type of risk is generally calledsystemic risk. While aspects of systemic risk (e.g., bank run and contagion)were always an issue in discussions about the financial system, the recentcrises have increased the interest in the topic, not only in academic circles,but also among regulators and central banks.

SYSTEMIC RISK: DEFINITIONS

If one aims at measuring—and in a further step managing and mitigating—systemic risk, it is important to start with a definition. However, despite theconsent that systemic risk is an important topic, which is reflected by anincreasing number of related papers and technical reports, there is still nota single generally accepted definition.

As a first step, one should distinguish between systemic and systematicrisk. Systematic risks are aggregate (macroeconomic) risks that cannot bereduced by hedging and diversification. Systemic risk, on the other hand, isa different notion. It refers to the risk of breakdown or at least major dys-function of financial markets. The Group of Ten (2001) gave the following,often cited definition:

Systemic financial risk is the risk that an event will trigger a loss of eco-nomic value or confidence in, and attendant increases in uncertainly about,a substantial portion of the financial system that is serious enough to quiteprobably have significant adverse effects on the real economy. Systemic riskevents can be sudden and unexpected, or the likelihood of their occurrencecan build up through time in the absence of appropriate policy responses.The adverse real economic effects from systemic problems are generally seenas arising from disruptions to the payment system, to credit flows, and fromthe destruction of asset values.

This formulation describes many aspects related to systemic risk but canhardly be called a definition in the technical sense, as it is very broad andhard to quantify. In addition, it seems to confuse cause (confidence) andconsequence (breakdown).

Measuring Systemic Risk: Structural Approaches 5

As an alternative, Kaufmann and Scott (2003) introduced the followingdefinition:

Systemic risk refers to the risk or probability of breakdowns in an entiresystem, as opposed to breakdowns in individual parts or components, andis evidenced by co-movements among most or all the parts.

In similar manner, but naming the cause and again considering largerconsequences, the European Central Bank (2004) defines systemic risk asfollows:

The risk that the inability of one institution to meet its obligations whendue will cause other institutions to be unable to meet their obligations whendue. Such a failure may cause significant liquidity or credit problems and,as a result, could threaten the stability of or confidence in markets.

All discussed definitions focus on the banking or financial system as awhole, and relate systemic risk to the interconnectedness within the system.Often, they stress the risk of spillovers from the financial sector to the realeconomy and the associated related costs. This effect is emphasized evenmore after the financial crisis as described in the following definition of sys-temic risk from Adrian and Brunnermeier (2009):

The risk that institutional distress spreads widely and distorts the supply ofcredit and capital to the real economy.

A similar definition can be found in Acharya et al. 2009.Given the described diversity of definitions, which are similar but also

different with respect to their focus, it is hard to develop universally acceptedmeasures for systemic risk. Different definitions refer to different importantnuances of systemic risk, which means that on the operational level a robustframework for monitoring and managing systemic risk should involve a vari-ety of risk measures related to these different aspects. See Hansen (2012)for a deeper discussion of the basic difficulties in defining and identifyingsystemic risk.

We will focus on the first part of the definition by Kaufmann and Scott(2003), which summarizes the most important aspect of systematic risk infinancial systems, without addressing more general economic aspects. Suchan approach could be seen as “systemic risk in the narrow sense” and westate it (slightly modified) as follows:

Systemic risk is the risk of breakdowns in an entire system, as opposedto breakdowns in individual parts or components.

Three issues have to be substantiated, if one wants to apply such a defi-nition in concrete situations: system, breakdowns, and risk.

6 SUPERVISORY RISK MANAGEMENT

System

In financial applications, the focus lies on parts of the financial system (likethe banking system, insurance, hedge funds) or the financial system as awhole. Any analysis has to start with describing the agents (e.g., banks inthe banking system) within the analyzed system. This involves their assetsand liabilities and the main risk factors related to profit and loss.

For a systemic view, it is important that the agents are not isolated enti-ties at all. Systematic risk can be modeled by joint risk factors, influencing allprofit and losses. Systemic risk in financial systems usually comes by mutualdebt between the entities and the related leverage.

Breakdowns

In single-period models, breakdown is related to bankruptcy in a technicalsense—that is, that the asset value of an agent at the end of the period doesnot reach a certain level (e.g., is not sufficient to pay back the agents debt). Alower boundary than debt can be used to reflect the fact that confidence intoa bank might fade away even before bankruptcy, which severely reducesconfidence between banks. In a systemic view, it is not sufficient to lookat breakdowns of individual agents: Relevant are events that lead to thebreakdown of more than one agent.

Risk

Risk is the danger that unwanted events (here, breakdowns) may happenor that developments go in an unintended direction. Quantifiable risk isdescribed by distributions arising from risk. For financial systems this mayinvolve the probability of breakdowns or the distribution of payments nec-essary to bring back asset values to an acceptable level. Risk measures sum-marize favorable or unfavorable properties of such distributions.

It should be mentioned that such an approach assumes that a good distri-butional model for the relevant risk factors can be formulated and estimated.During this chapter, we will stick to exactly this assumption. However, it isclear that in practice it is often difficult to come up with good models, anddata availability might be severely restricted. Additional risk (model risk) isrelated to the quality of the used models and estimations; see Hansen (2012)for a deeper discussion of this point.

FROM STRUCTURAL MODELS TO SYSTEMIC RISK

Structural models for default go back to Merton (2009) and build on the ideathat default of a firm happens if the firm’s assets are insufficient to cover

Measuring Systemic Risk: Structural Approaches 7

contractual obligations (liabilities). Simple models such as Merton (2009)start by modeling a single firm in the framework of the Black–Scholes optionpricing model, whereas more complex models extend the framework to mul-tivariate formulations, usually based on correlations between the individualasset values. A famous example is Vasicek’s asymptotic single factor model(see Vasicek 1987; 1991; and 2002), which is very stylized but leads to aclosed-form solution.

In most structural default models, it is not possible to calculate the port-folio loss explicitly; hence, Monte Carlo simulation is an important toolfor default calculations. Even then, the models usually make simplifyingassumptions.

Consider a system consisting of k economic entities (e.g., banks), andlet A1(t),A2(t),… ,Ak(t) denote the asset processes—that is, the asset valuesat time t for the individual entities. Furthermore, for each entity i a limit Di,the distress barrier, defines default in the following sense: default occurs ifthe asset value of entity i falls below the distress barrier:

Ai(t) < Di. (1.1)

The relation between asset value and distress barrier is usually closelyrelated to leverage, the ratio between debt and equity.

Finally, let X1(t),X2(t),… , Xk(t) with

Xi(t) = Ai(t) − Di (1.2)

denote the distance to default of the individual entities. Note that alter-natively the distance to default can also be defined in terms of Xi(t) as apercentage of asset value, divided by the asset volatility (see e.g., Crosbieand Bohn 2003).

In a one period setup—as used throughout this chapter—one isinterested at values Ai(T),Xi(T) at time T, the end of the planninghorizon. Analyzing systemic risk then means analyzing the joint distri-bution of the distances to default Xi(t), in particular their negative partsXi(T)− = max{−Xi(T),0}, and the underlying random risk factors aredescribed by the joint distribution of asset values Ai(T).

Many approaches for modeling the asset values exist in literature. Ina classical finance setup, one would use correlated geometric Brownianmotions resulting in correlated log-normal distributions for the asset valuesat the end of the planning horizon. Segoviano Basurto proposes a Bayesianapproach (Segoviano Basurto 2006); for applications, see also Jin andNadal de Simone (2013). In this chapter, we will use copula-based models,as discussed later.

8 SUPERVISORY RISK MANAGEMENT

The second component of the approach, the distress barrier, is in the sim-plest case (Merton 2009), modeled just by the face value of overall debt foreach entity. Other approaches distinguish between short-term and long-termdebt (longer than the planning horizon). Usually, this is done by adding somereasonable fraction of long-term debt to the full amount of short term debt;see, for example, Servigny and Renault (2007).

Still, such classical credit default models (see, e.g., Guerra et al. 2013),although classified as systemic risk models, neglect an important aspect:Economic entities like banks are mutually indebted, and each amount ofdebt is shown as a liability for one entity but also as an asset for anotherentity. Default of one entity (a reduction in liabilities) may trigger subse-quent defaults of other entities by reducing their asset values. We call suchmodels systemic models in the strict sense.

Such approaches with mutual debt have been proposed, such as inChan-Lau et al. (2009a; 2009b). Models neglecting this aspect are systemicmodels in a broad sense; in fact, they are restricted to the effects ofsystematic risk related to asset values.

The basic setup of systemic models in the strict sense can be describedas follows: Let H0

ij denote the amount of debt between entities i and j —thatis, the amount of money borrowed by entity i from entity j. We also includedebt to the nonbank sector, denoted by Hi for each entity i and credit Ci tothe nonbanking sector, both repayable (including interest) at the end of theplanning horizon, time T. Furthermore, Si(T) is the value at time T of otherfinancial assets held by entity i. Then the asset value of entity i at the end ofthe planning horizon is given by

A0i (T) = Si(T) +

∑j∶j≠i

H0ji + Ci, (1.3)

the distress barrier (in the simplest case) is

D0i =

∑j∶j≠i

H0ij + Hi, (1.4)

and the distance to default can be written as

X0i (T) = Ai(T) − D0

i = Si(T) + Ci +∑j∶j≠i

H0ji −

∑j∶j≠i

H0ij − Hi . (1.5)

The random factors are the values Si(T) of financial assets, and (in anextended model) the credits Ci from outside the system, payable back at time.

Again, one could stop at this point and analyze the distances todefault X0

i , respectively the sum of all individual distances to default in the