Finance and Banking Developments [1 ed.] 9781611229288, 9781608763290

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Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

BANKING AND BANKING DEVELOPMENTS

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

FINANCE AND BANKING DEVELOPMENTS

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BANKING AND BANKING DEVELOPMENTS

FINANCE AND BANKING DEVELOPMENTS

CHARLES V. KARSONE

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

EDITOR

Nova Science Publishers, Inc. New York

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Finance and banking developments / editor, Charles V. Karsone. p. cm. Includes index. ISBN H%RRN 1. Finance. 2. Banks and banking. I. Karsone, Charles V. HG173.F4875 2009 332--dc22 2009050564

Published by Nova Science Publishers, Inc.

New York

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CONTENTS

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Preface

vii

Chapter 1

Credit Rating Modelling by Neural Networks Petr Hájek

Chapter 2

Sticky Credit Spreads, Macroeconomic Activity and Equity Market Volatility Yan Li and James M. Steeley

43

Chapter 3

Profitability Determinants: An Empirical Study of Portuguese SMEs Zélia Serrasqueiro

75

Chapter 4

Derivatives and Debt: The Market as God and Marketing as Proselytizing Niccolo Caldararo

99

Chapter 5

Assessing Household Vulnerability to Climate Change: The Case of Farmers in the Nile Basin of Ethiopia T.T. Deressa, R.M. Hassan and R. Claudia

119

Chapter 6

The Effects of Asymmetric Volatility Shocks on Equity and Foreign Exchange Rate Interactions Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis and Deren Unalmis

137

Chapter 7

Banking Regulation and Procyclicality – Cross-Country Analysis in EMU Tamás Isépy

159

Chapter 8

Can a Financial Information Distortion Event Facilitate a Revision in the Independent Directors Institution Cheng Xin-sheng, Li Hai-ping and Luo Yan-mei

169

Chapter 9

Managerial Methods to Control Derivatives Losses Patrick L. Leoni

179

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1

vi

Contents

Chapter 10

Asymptotic Expansion Approaches in Finance: Applications to Currency Options Akihiko Takahashi and Kohta Takehara

185

Chapter 11

An Analysis of the Determinants of Credit Default Swap Spread Changes before and during the Subprime Financial Turmoil Antonio Di Cesare and Giovanni Guazzarotti

233

Chapter 12

The Expenses Problem of Personal Financial Planning Oliver Braun and Marco Spohn

267

Chapter 13

The Subprime Mortgage Crisis and Its Connections with Bank Bailouts M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen, B. de Waaland S. Thomas

289

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Index

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PREFACE This book presents original research results on the leading edge of finance and banking research. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Chapter 1 presents the modelling possibilities of neural networks on a complex realworld problem, i.e. credit rating process modelling. First, current approaches in credit rating modelling are introduced. Second, previous studies on corporate and municipal credit rating modelling are analyzed. Based on this analysis, the model is designed to classify US companies and municipalities into credit rating classes. The model includes data preprocessing, the selection process of input variables, and the design of various neural networks’ structures for classification. The selection of input variables is realized using genetic algorithms. The objective of this process is to select only significant variables in order to improve the performance of neural networks. Input variables are extracted from financial statements and capital markets in line with previous studies. These variables represent the inputs of neural networks, while the rating classes stand for the outputs. The credit rating classes have been obtained from the rating agencies Standard & Poor’s and Moody’s. Except for exact credit rating classes, data are also labelled by investment or non-investment grades. As a result, the classification accuracies and the contributions of input variables are studied for the different number of classes. The results show that the rating classes assigned to bond issuers can be classified with a high accuracy rate using a limited subset of input variables. In Chapter 2 the authors uncover high persistence in credit spread series that can obscure the relationship between the theoretical determinants of credit risk and observed credit spreads. The authors use a Markov-switching model, which also captures the stability (low frequency changes) of credit ratings, to show why credit spreads may continue to respond to past levels of credit risk, even though the state of the economy has changed. A bivariate model of credit spreads and either macroeconomic activity or equity market volatility detects large and significant correlations that are consistent with theory but have not been observed in previous studies. As ecplained in Chapter 3, the increasing importance of service SMEs for employment and for the wealth of the Portuguese economy motivates the current study that seeks to verify if profitability determinants of service SMEs are different from the profitability determinants of manufacturing SMEs. For the period 1999–2006, the authors use data collected for two research samples: 1) 610 unlisted service SMEs; and 2) 381 unlisted manufacturing SMEs. As determinants of firm profitability the authors consider: 1) profitability of the previous

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Charles V. Karsone

period; 2) firm size; 3) firm age; 4) liquidity; 5) long-term debt; 6) R&D intensity; 7) asset tangibility; and 8) default risk. To control for possible data bias the authors use a two-step procedure, an innovative estimation method in the context of the study of profitability determinants of SMEs. In the first step, the authors estimate probit regressions, for service and manufacturing SMEs, considering profitability determinants as explanatory variables, and obtain the inverse Mill’s ratio. In the second step, the authors introduce the inverse Mill’s ratio as an additional explanatory variable, in the regressions performed for the profitability determinants of services and manufacturing SMEs. The empirical evidence obtained indicate that there are strong significant differences between the profitability determinants of service SMEs and those of manufacturing SMEs: 1) size, liquidity, long-term debt; R&D intensity are the factors fostering the profitability of service SMEs, but they are unimportant factors for the profitability of manufacturing SMEs; 2) the default risk is a factor inhibiting the profitability of the service SMEs, but it is unimportant as a factor of profitability of manufacturing SMEs; 3) asset tangibility is a determinant promoting, whereas age is a determinant inhibiting, the profitability of manufacturing SMEs; these two determinants are unimportant for the profitability of service SMEs; and 4) the persistence of profitability verifies greater magnitude in the context of SMEs belonging to the manufacturing sector in comparison with that verified by SMEs of the service sector. As a general overview of the results, the service SMEs are more dependent on liquidity and long-term debt, and they are more vulnerable regarding default risk compared to the manufacturing SMEs. Furthermore, R&D intensity is the most important determinant fostering the profitability of service SMEs, whereas tangibility assets are the most important determinant fostering the profitability of manufacturing SMEs. As discussed in Chapter 4, most religions have images of their gods or spirits. There is often a preferred “veronica” or true image. The function of images is, according to the Catholic Church, to provide a focus for contemplation and the reflection of faith (McCrone, 1996). Often the image of the sacred is shrouded from human view, destructive to gaze upon or an imperfect reflection. Aspects of divinity are often perceived by some peoples in the spread of a disease through a population or its natural history in the signs and symptoms it creates in a body. Here the authors see an image of the god of capitalism (Figure 1). The authors can produce it from a variety of data, on the value of stock, prices of a variety of goods and services, and other means. But in general, the image is very similar. It traces the behavior of man’s faith in the value of his creations and in his future wealth. It is the single most important representation of the health of the world economy. In a Durkheimian sense, it gives as a representation of the sum total of society’s active mood and reflects, as some economists have said, the attitude and character of humanity. In a sociobiological sense, it represents the pushing and shoving of the actors involved, each trying to capture a greater share of the wealth available now and in the future, like ants (described by E.O. Wilson, 1976) trying to individually seize a piece of food, their common actions can be argued to be a tide of social consequence increasing the fitness of all concerned as they result in the arrival of the food in the nest. Objects of wealth and prestige motivate people to action in modern society and it has long been held in economic debates that contracts and money were modern phenomenon. In Figure 3 the authors see an image of Chinese “knife money” and its evolution to coinage (“Pu” money was earlier), cerca 700 BCE perhaps to CE 680. Figure 2 is the acknowledgement of a loan from CE 122 in Egypt from a woman, Tamystha to Heraclides, a

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Preface

ix

man. This is a check of sorts undermining the idea that checks were invented in the 17th century by the Dutch as receipts for gold. And in Figure 4 are images of tunny fish of Cyzicus and Cowrie Shells, Dentalium shells, Wampum and a coin of Thurii, all are pre-modern examples of money. We should keep in mind that the idea of exchange was divided by economists, and later by some anthropologists into modern and pre-modern periods. This neat division allowed for strict ideological definitions in historical context of a unilinear description of history with Capitalism and Communism (this includes its various forms, socialism, Marxism, etc.) contending for supremacy as ultimate successors in human social organization. Due to this cosmology of the time, Herskovits suffered severe criticism over his uniformitarian view that all human societies practiced similar forms of economic behavior. The cosmology of the 20th century, held that there was a vector or direction in time in which events could be placed. Both Communism and Capitalism were based on ideologies that firmly conceived that society of the 20th century was characterized by elements that differentiated it from all other social contexts in the past. They called this “modernity.” Recently a book by Jack Goody (2004) criticized this view, arguing that modernity was a worldview of hegemony created in each period of political and economic dominance. As such, modern man could be compared in terms of economic behavior with earlier periods. While he recognized that technology had changed, the basic foundations of human behavior remained the same, thus while no economic system in the past was exactly like that which exists today, comparisons were valid. Further, while some economists and social scientists had argued that modern man was guided by rational thought while primitive society was a context in which man’s behavior was embedded in irrational beliefs that permeated economic behavior, this contrast was not supported by all the evidence. I have described this argument in more detail in a recent book (Caldararo, 2004). Details, like the fact that early guild members of European free cities and towns paid taxes to buy weapons and soldiers to train them to protect them from the ravages of the knights and feudal lords who constantly raided their towns for runaway serfs and wealth, were ignored. By banning together they could defend themselves and they came to wear their tax receipts, as Henry Pirenne (1925) tells us, on their shirts as badges of honor proving they were free men. Then there was the banking and investment activity of people like Crassus in the Early Roman Republic. Or, the Roman examples of unions in late Republican and Imperial times of free tradesmen not associated with the clients system as Marsh and other historians have noted. This ideological position required there be but one future, defined by one struggle and the production of one inevitable victor. And eventually a Capitalist historian, Francis Fukuyama would proclaim victory in the collapse of the Soviet Block in 1989 only to recant this past year as a new struggle, that of resurgent Islam proved to be a viable challenge to the neat scenario followed by the implosion of the main components of modern finance during the past 18 months. In my opinion, the most useful and comprehensive book on economics today is Herskovits’ 1940 (1952 revised text), Economic Life of Primitive Peoples. It describes a uniformitarian view across space and time demonstrating the unity of mankind’s abilities and creativity in production and exchange. As Evans-Pritchard argued in 1965 there is no primitive vs modern mentality.

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In neither anthropology nor economics did the authors find total agreement with the primitive/modern distinction so epitomized byKarl Polanyi’s (1957) analysis. Some distinct variations occurred in theory as in the work of Ludwig von Mises(1949) who argued that the various price doctrines were really circular arguments and not theories at all. He placed emphasis on the changes in mutual relations between those buying and selling. Thus relationships, like the focus of Herskovits and Daryl Forde (1949), are the central factor to von Mises in the function of the market. But von Mises could hardly be called a uniformitarian in the manner I have defined, and most certainly would have rejected such an idea being that he was a Capitalist economist. If the authors are to look at the specialized knowledge at the core of our economic system they might profess that bankers are the priesthood and that the mystery is the creation of credit. This goes beyond people understanding the complex terms of their credit card agreements, or car loans, rather it is lodged in the central conceptions of how banks work, why value appears to increase in the stock market and then disappear. This mystery will be the subject of the authors’ inquiry. Chapter 5 measures the vulnerability of farmers to climatic extremes such as droughts, floods and hailstorms, by employing the “vulnerability as expected poverty” approach. This approach is based on estimating the probability that a given shock or set of shocks will move household consumption below a given minimum level (such as the consumption poverty line) or force the consumption level to stay below the given minimum if it is already below this level. The utilized data come from a household survey of farmers performed during the 2004/2005 production year in the Nile Basin of Ethiopia. The results show that the farmers’ vulnerability is highly sensitive to their minimum daily requirement (poverty line). For instance, when the daily minimum income is fixed at 0.3 United States dollars (USD) per day, only 12.4% of farmers are vulnerable to climate extremes, whereas 99% of farmers are vulnerable when the minimum requirement is fixed at 2 USD per day. The results further indicate that farmers in kola agro-ecological zones (which are warm and semi-arid) are the most vulnerable to extreme climatic events. Policy-wise, these preliminary results indicate that, keeping other factors constant, increasing the incomes of farmers (with special emphasis on those in kola agro-ecological zones) and enabling them to meet their daily minimum requirements will reduce their vulnerability to climatic extremes. In Chapter 6 the authors investigate the transmission of financial turbulence across domestic markets by analyzing the responses of the conditional variances of foreign exchange and equity returns and their conditional covariance following a shock to either market. The authors estimate an asymmetric bi-variate GARCH model and generate Volatility Impulse Response Functions (VIRFs) to evaluate the importance of the dynamic interactions between these two markets within a number of East Asian emerging economies. The authors’ results show strong evidence of volatility spillovers between domestic financial markets. Exchange rate returns are particularly sensitive to shocks and both markets exhibit higher reaction to adverse shocks. In general, shocks from either source tend to increase market co-movement. The main critique is in connection with Basel II. regulation, that the New Capital Accord raises the procyclicality of banking system. In EMU-wide cross-country comparative analysis the author tested evolution of the capital buffers, the output gap and the financial structure index. In Chapter 7 the author searched answers for the following questions: what factors are influencing the measure of capital buffers held by the bank above the minimum capital adequacy ratio (BIS ratio 8%), how level of the capital buffers worked out by country, what

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Preface

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relationship is between measure of capital buffers and business cycle? Is there any relation between the extent of capital buffers and financial structure? The independence of the Board has an important and direct impact on the quality of information disclosure. To a large extent, the proportion of Independent Directors reflects the independent characteristics of the board. A common understanding of the effect of the actual operation on the Independent director has been lacking in China. In Chapter 8, 92 listed companies were selected from 2003 to 2005 to be defined as the sample group, which have distorted financial information, and the paired-sample companies were chosen to be defined as the control group, according to factors such as profession, property and so on. The author analyzes the proportion’s change in the listed company, whose Independent Directors proportion is less than 1/3 in the distortion sample group and the control group, and the change rate of Independent Directors proportion in the sample group and the control group. The research discovered that a financial information distortion incident will prompt companies to increase the proportion of Independent Directors, and due to the mandatory effect of the policy, distortion and matching the company will increase the independent Directors proportion, but the rate in distortion companies was significantly higher than that in the paired companies. The study provided evidence to support the view that increasing the proportion of independent directors will help to prevent distortion of financial information. The long history of financial disasters caused by derivatives has triggered a significant interest to control their downside risk, both from portfolios’ managers and regulators. In Chapter 9, in a non-technical manner, the authors first describe the managerial methods currently used in practice for this purpose and their relative cost. The authors then show that those common methods either aggravate the downside risk or are too costly. The authors then argue that selecting underlyings satisfying some specific statistical and easily identifiable properties is a natural way to significantly reduce the downside risk without involving costly managerial interventions. Chapter 10 presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; the authors do not model a foreign exchange rate’s variance such as in Heston [27], but its volatility that follows a general timeinhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market. Chapter 11 analyzes the determinants of credit default swap spread changes for a large sample of US non-financial companies over the period between January 2002 and March 2009. In the authors’ analysis the authors use variables that the literature has found to have an impact on CDS spreads and, in order to account for possible non-linear effects, the theoretical CDS spreads predicted byMerton model. The authors show that their set of variables is able to explain more than 50% of CDS spread variations both before and after July 2007, when the current financial turmoil had its onset. The authors also document that since the beginning of the crisis CDS spreads have become much more sensitive to the level of leverage while volatility has lost its importance. Using a principal component analysis they also show that since the beginning of the crisis CDS spread changes have been increasingly driven by a

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common factor, which cannot be explained by indicators of economic activity, uncertainty, and risk-aversion. In Chapter 11 the authors regard financial goals with different height, time, and type preferences which allow to reduce or to postpone the goals to a certain degree. Additionally, the authors show how these preferences can be determined in interaction with the decision maker and how to use the Analytic Hierarchy Process (AHP) for this purpose. Furthermore, the authors include the possibilty of taking out loans and to add some financial ratios which can serve as a means to indicate or to prevent from bankruptcy. Finally, the authors provide a Mixed Integer Program (MIP) to derive a financial plan that maximizes a person’s value of financial goals with respect to her preferences. The subprime mortgage crisis (SMC) and subsequent global financial crisis (GFC) have made a better understanding of bank bailouts an imperative. Since the onset of the SMC in 2007, bailout packages have been implemented on an unprecedented scale throughout the world. In the U.S. this culminated in an intervention known as the Troubled Assets Relief Program (TARP) that enabled the purchase of toxic assets such as subprime residential mortgage loans (RMLs) and residential mortgage-backed securities (RMBSs) as well as common and preferred equity from financial institutions. Even though many other countries approved more general rescue packages, the crises demonstrated that the largest banks were considered to be too-big-to-fail by their respective governments. Although there has been very little opposition to these bailout measures, it is important to assess the effects of bailouts in terms of the risktaking and -shifting. In Chapter 13, some of the SMC-related issues that the authors probe include the reason for and efficiency of government bailouts, liquidity and its relationship with debt market efficiency as well as the comparative effectiveness of government purchases of preferred and common equity as well as toxic RMBSs. This is done separately for the special cases involving subprime RMLs that default, refinance and fully amortize. The authors find that the defaulting of such RMLs is less likely to lead to bailouts than the buying of toxic RMBSs.

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Chapter 1

CREDIT RATING MODELLING BY NEURAL NETWORKS Petr Hájek* Institute of System Engineering and Informatics, Faculty of Economics and Administration, University of Pardubice, Studentská 84, 532 10 Pardubice, Czech Republic

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Abstract The chapter presents the modelling possibilities of neural networks on a complex real-world problem, i.e. credit rating process modelling. First, current approaches in credit rating modelling are introduced. Second, previous studies on corporate and municipal credit rating modelling are analyzed. Based on this analysis, the model is designed to classify US companies and municipalities into credit rating classes. The model includes data preprocessing, the selection process of input variables, and the design of various neural networks’ structures for classification. The selection of input variables is realized using genetic algorithms. The objective of this process is to select only significant variables in order to improve the performance of neural networks. Input variables are extracted from financial statements and capital markets in line with previous studies. These variables represent the inputs of neural networks, while the rating classes stand for the outputs. The credit rating classes have been obtained from the rating agencies Standard & Poor’s and Moody’s. Except for exact credit rating classes, data are also labelled by investment or non-investment grades. As a result, the classification accuracies and the contributions of input variables are studied for the different number of classes. The results show that the rating classes assigned to bond issuers can be classified with a high accuracy rate using a limited subset of input variables.

Keywords: Credit rating analysis, corporate credit rating, municipal credit rating, neural networks, support vector machines, classification.

*

E-mail address: [email protected].

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1. Introduction Credit rating is an independent evaluation whose aim is to find out how an object is capable and willing to meet its payable obligations, specifically based on complex analysis of all the known risk factors of the assessed object. The capability and willingness to meet obligations is called creditworthiness. More precisely, the probability of the repayment of principal and interest of an obligation is measured by means of credit rating. A higher credit rating shows a low credit risk. The assessment is realized by a rating agency. According to the assessed object, credit ratings of the state, company, municipality, financial institution, single bond, etc. exist. Credit rating is a result of a credit rating process. It is represented by the j-th rating class ωi,j∈Ω, Ω={ω1,j,ω2,j, … ,ωi,j, … ,ωn,j}, where n stands for the number of objects and Ω is a rating scale. The rating class ωi,j∈Ω is assigned to the i-th assessed object oi∈O, O={o1,o2, … ,oi, … ,on}. Based on the above, the credit rating modelling is considered to be a classification problem with the aim of classifing the i-th object oi∈O into the j-th rating class ωi,j∈Ω. Credit ratings are used by bond investors, debt issuers, and governmental officers as a measure of the risk of a company. They provide a means of determining risk premiums and marketability of bonds, allowing firms issuing debt to estimate the likely return investors require. Bankers and companies considering providing credit rely on credit ratings to make important investment decisions, many regulatory requirements for financial decisions are based on credit ratings, and some companies are restricted to investment grade bonds. Credit ratings are costly to obtain because rating agencies invest large amount of time and human resources to perform the credit rating process. Therefore, there has a large much effort made in order to simulate the credit rating process of rating agencies through statistical (e.g. [49], [50]), and soft-computing methods (e.g. [13], [45]). The difficulty in designing such models lies in the subjectivity of the credit rating process. This subjectivity is emphasized as the mode in which complex relations between financial and other variables are evaluated. Such a complex process makes it difficult to classify rating classes through statistical methods. However, soft-computing methods (neural networks [13], fuzzy systems [5], evolutionary algorithms [12], artificial immune systems [20], and hybrid systems [53]) can be applied for the modelling of such complex relations. Therefore, soft-computing methods, so far, have been used for corporate credit rating modelling [45], [51]. As a result, high classification accuracy has been achieved by neural networks [13], [33] and support vector machines (SVMs) [45], [60]. In economics and finance, neural networks (including SVMs) are usually applied in such cases where variables are in non-linear relations. This is reported to be typical for economic and financial data [37]. Neural networks make it possible to model these relations as they learn the dependencies in training data. As a result, gained knowledge is stored in synapse weights. Moreover, the knowledge can also be applied for unknown input data which were not used in the training process. This is also known as generalization ability of neural networks. The disadvantage of neural networks lies in the fact that neural networks are usually designed as so-called “black boxes”, i.e. it is difficult to extract understandable knowledge from them. Therefore, prior studies in modelling credit rating are aimed at quantifying the effect of input variables for classification, i.e. to find out which input variables are crucial for credit rating process. Mostly, sensitivity analysis has been employed for this purpose. Based on the mentioned

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Credit Rating Modelling by Neural Networks

3

facts, it is possible to state that the methods capable of processing and learning the expert knowledge, enabling their user to generalize and properly interpret, have proved to be most suitable for credit rating modelling. The chapter is structured as follows. First, basic components of credit rating process will be introduced. Further, current methods used for corporate and municipal credit rating modelling will be reviewed. Statistical and soft-computing methods will be reported. Then, basic notions of neural networks will be presented with an emphasis on neural networks’ models suitable for classification problem realization. The models will be used for the modelling of corporate and municipal credit rating. Using a number of neural networks (NNs) for credit rating modelling has so far not been reported in prior studies. Using probabilistic NNs, GMDH NNs, or cascade correlation NNs is novel in credit rating modelling. Moreover, the modelling of municipal credit rating process has only been previously realized through statistical methods. The input variables for the modelling are designed based on all the aspects of economic and financial performance of companies and municipalities. Most input variables used in this study have also been used in previous works. However, there are financial markets indicators applied for the first time in this study. In order to get an optimum set of input variables, a novel two-step approach is proposed. First, the original sets of input variables are optimized by genetic algorithms (GAs). Then the contribution of selected input variables is studied using sensitivity analysis, with the intention to compare the relative importance of the variables. As a result, interpretable models will be obtained. The contribution analysis of input variables for different numbers of rating classes has also not been previously realized. As a result, credit rating models will be designed in order to achieve high classification accuracy on testing data and, at the same time, to study the contribution of input variables. Finally, the gained results will be compared across selected models of neural networks (NNs).

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2. Credit Rating Modelling Credit rating modelling is regarded as a classification problem, i.e. as supervised learning. For its realization, rating classes assigned by a rating agency should be known in advance. The rating classes represent a result of credit rating process. Therefore, credit rating process and credit rating modelling is introduced in this subchapter. Further, the relations between credit rating modelling and default modelling are reported. The overview of prior studies concerning corporate and municipal credit rating modelling is also presented.

2.1. Credit Rating Process As presented above, credit rating process represents a subjective assessment of both quantitative and qualitative factors of a particular object (company, municipality, etc.) as well as industry and market factors. The credit rating process begins with an application to the rating agencies by the issuer (object). The object contacts a rating agency and requests an issue of credit rating to the new debt or to the object. Documentations like financial statements, the preliminary official statement, a prospectus for the debt issue, other non-financial information, etc. are provided to the rating agencies.

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Discussions take place between the rating agency and management of the object, and a rating report is prepared by the credit analysts examining the object. Key analytical factors are discussed in the rating report. The credit analyst provides a recommendation for credit rating to a rating committee. The committee decides the credit rating to be assigned to the object. The result of this process is represented by an assignment of a rating class ωi,j∈Ω to the object oi∈O. The assignment is based on an evaluation of relevant economic, financial, and management factors. Finally, the rating is released to the issuer, followed by a publication of a full credit report. Of course, the assessed objects pays a fee to the rating agencies for the credit rating. Rating agencies emphasise that the credit rating process involves consideration of financial, as well as non-financial, information about the object, and also considers industry and market-level factors. The precise factors, and related weights of these factors used in determining a credit rating, are not publicly disclosed by the rating agencies. As a result, credit ratings issued by different rating agencies need not to be the same. In a comparison of the ratings of Standard & Poor’s and Moody’s [54], it was found that in a sample of 1,607 US bond ratings of investment grade, the two rating agencies differed in 836 credit ratings. In the cases where the rating classes differed, the difference was more than one rating class in 111 cases. Rating agencies should preserve independency and objectivity in their evaluation. Nevertheless, they are criticised for their prejudice and unsatisfactory evaluation accuracy [83]. Credit ratings of individual assessed objects (companies, municipalities, banks, etc.) can also be distinguished as short-term and long-term credit ratings. A short-term credit rating is designed to evaluate the up-to-one-year expiration obligations; a long-term credit rating is designed to evaluate the over-one-year obligations. All public credit ratings are monitored on an ongoing basis. It is common to schedule an annual review with management. Subsequent to the initial credit rating, an object may be re-rated upwards (upgrade) or downwards (downgrade) if the object or environmental circumstances change. The effect of an object being assigned a lower rather than a higher credit rating is that its riskiness is considered to be higher, and consequently the required interest yield of the bonds rises. Credit rating can be defined as the process of a rating class assignment to an object according to expected default probability. From a mathematical point of view, credit rating is represented as a mapping of each object oi∈O into a set of rating classes ωi,j∈Ω so that:

∀o i ∈O → ∃ω i, j∈Ω 

(1)

where oi stands for the i-th object, O is a set of object, ωi,j is rating class, j=1,2, … ,q, and Ω is a rating scale. Rating class ωi,j indicates the probability that the given object will be capable to meet its payable obligations. It is defined on the rating scale Ω [69]. Rating classes ωi,j∈Ω are ranked in the rating scale Ω according to credit risk rate. If the credit risk changes, the object oi is assigned to different rating class ωi,j’∈Ω, j≠j’. Although the precise notation used by individual rating agencies to denote the creditworthiness of an object varies, in each case, the credit rating is primarily denoted by a ‘letter’.

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Table 1. Rating scales Ω of selected rating agencies.

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Moody's Aaa Aa A Baa Ba,B Caa,Ca,C C

S&P’s/Fitch AAA AA A BBB BB,B CCC,CC,C D

Grade Investment Investment Investment Investment Non-investment/Junk Non-investment/Junk Non-investment/Junk

Credit risk Highest quality High quality Strong Medium grade Speculative Highly speculative In default

Rating scales Ω of notable rating agencies are presented in Table 1. Rating agencies such as Standard & Poor’s, Moody’s, and Fitch belong to the most important ones. Taking the rating scale Ω of Standard & Poor’s as an example, the credit ratings are broken down into 10 broad rating classes. The strongest rating class is denoted as AAA, and the rating classes then decrease in the following order, AA, A, BBB, BB, B, CCC, CC, C, and D. Therefore, credit ratings are typically conveyed to investors by means of a discrete, mutually exclusive, letter grade. Rating classes between AAA and BBB (inclusive) are considered by investors to represent ‘investment grade’, with lower quality rating classes considered to represent debt issues with significant speculative (risky) characteristics (non-investment grade or ‘junk’ bonds). A ‘C’ grade represents a case where a bankruptcy petition has been filed, and a ‘D’ rating represents a case where the borrower is currently in default on its financial obligations. Ratings from AAA to CCC can be modified by the addition of a ‘+’ or a ‘-’, to indice at which end of the rating class the credit rating falls. Credit rating cuts the costs of assessed object, investors and banks. For the assessed object, good rating classes are reflected in lower interest rates, and they can represent an impetus to new business contracts. The significant influence of credit ratings on interest rates has been confirmed in several studies, e.g. [14], [62]. A good credit rating supports an object with everyday commercial activities with third parties: to secure favourable credit terms and when negotiating long-term leases and outsourcing contracts. A credit rating may enable an object to manage its borrowing costs by potentially diversifying the funding base, since it is healthy for both banks and objects to avoid high exposures to only one financing partner. As rating agency compares key features of the accounts, budget, etc. with benchmarks derived from assessing similar objects’ operations in the country or internationally, the rating process helps the management to identify areas that need improvement. In similar structures, a stronger credit rating may often mean better financial management. Credit ratings also serve as an external validation of financial health. The rating report typically comments on factors that support or constrain the rating. Thus, it can assist management in the formulation of action plans to address shortcomings in areas such as investment management. For investors and banks, credit rating makes decision-making more effective and faster, mainly due to lower transaction and personal costs necessary for information acquisition about the business partners. Banks and other investors do not like uncertainty and will charge higher interest rates when they are less certain about the reliability of the person, business, or municipality to whom they are lending. Commercial banks may have the skills and willingness to assess the credit quality of an object. However, investors rarely have the

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specialist skills to investigate the financial health and management competence of a borrower, so they tend to rely on experts (rating agencies) to do this for them. The reasons for credit rating applications of objects have been studied in prior studies [71], [96]. This decision is affected mostly by both the size of debt and the expected rating class. The size of costs saving is dependent on these factors. The difference between the costs saving and the costs of credit rating serves as the decision-making mechanism.

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2.2. Credit Rating and Default Prediction Default prediction can be understood as: a special case of objects’ classification into rating classes. When predicting default, the objects are classified into two classes, i.e. either as non-default (i.e. with rating class different from default D) or default (with rating class D). Thus, the relation between credit rating modelling and default modelling is evident. Default models are based on the assumption that future financial distress can be predicted by observing the level and the development of financial and non-financial indicators. They are designed to inform about the forthcoming financial difficulties. Being in default means that the object is not able to pay off its obligations. Bankruptcy represents a special case of default for companies. Therefore, some authors have studied the problems of default prediction and bankruptcy prediction, e.g. [3], [73], which are also representatives of classification problem. Similar variables and methods were used in such studies as for credit rating modelling. The first attempts at predicting company bankruptcy were made by [7], as a significant difference in the financial ratios of failing and prosperous companies was observed. The proposed model could be used as an early indicator of corporate bankruptcy. Thirty financial ratios were tested stepwise in order to determine those giving the highest classification accuracy in the classification of failing and non-failing firms. This univariate approach was followed by multiple discriminant analysis (MDA), making it possible to use more input variables at the same time. The Z-score model developed by [3] represents the most famous example. Weighted values of five financial ratios were used to sum up a Z-score. One year prior to bankruptcy the prediction accuracy of this model was 95%, with 72% for two years prior to bankruptcy, and 48% for three years before. Regression models were also constructed by e.g. [34], [73], [97] with the view of improving the classification accuracy of bankruptcy firms. Recently, models based on soft-computing methods were developed for bankruptcy prediction such as NNs [56], rough sets [21], genetic algorithms [55], grammatical evolution [12], and hybrid genetic algorithms [11]. A low number of defaulted municipalities makes it difficult to propose default models for municipalities. The differences between failed and non-failed municipalities were tested only in [41] using multiple disciminant and regression analysis. However, only 45 US municipalities were analyzed. The following input variables showed a significant effect on municipal default: total debt/taxable properties, uncollected taxes/total taxes, total debt/population, population growth, total debt/collected taxes, and collected taxes/taxable properties. Using these input variables, a classification accuracy CAtrain=76% was obtained for the training data, respectively CAtest=56% on testing data.

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Table 2. Rating transition matrix. ωi,j‘ ωi,j AAA AA A BBB BB B CCC D

AAA

AA

A

BBB

BB

B

CCC

D

pAAA,AAA pAA,AAA pA,AAA pBBB,AAA pBB,AAA pB,AAA pCCC,AAA 0

pAAA,AA pAA,AA pA,AA pBBB,AA pBB,AA pB,AA pCCC,AA 0

pAAA,A pAA,A pA,A pBBB,A pBB,A pB,A pCCC,A 0

pAAA,BBB pAA,BBB pA,BBB pBBB,BBB pBB,BBB pB,BBB pCCC,BBB 0

pAAA,BB pAA,BB pA,BB pBBB,BB pBB,BB pB,BB pCCC,BB 0

pAAA,B pAA,B pA,B pBBB,B pBB,B pB,B pCCC,B 0

pAAA,CCC pAA,CCC pA,CCC pBBB,CCC pBB,CCC pB,CCC pCCC,CCC 0

pAAA,D pAA,D pA,D pBBB,D pBB,D pB,D pCCC,D 1

Legend: ωi,j stands for an initial rating class, ωi,j∈{AAA, AA, A, BBB, BB, B, CCC, D}, ωi,j‘ stands for a rating class after t years, ωi,j‘∈{AAA, AA, A, BBB, BB, B, CCC, D}, pj,j’ denotes the probability of rating class ωi,j change in rating class ωi,j‘, and D is default.

Table 3. Rates of default by initial rating classes (1986-2001).

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Initial rating class AAA AA A BBB BB B CCC

pi,D (%) 0.52 1.31 2.32 6.64 19.52 35.76 54.38

The default model based on rating transition matrix [23] combines the rating classes of assessed objects with the probabilities of change and default of individual rating classes ωi,j. It can be constructed comparing the changes in rating classes ωi,j in consecutive years. The example of rating transition matrix is shown in Table 2. The probabilities pj,j’ of rating class ωi,j change into rating class ωi,j are presented in rating transition matrix. A default model can be created based on the rating transition matrix so that the probabilities of default pj,D are assigned to each rating class ωi,j. As would be expected, the probability of default pj,D strongly depends on the initial rating class ωi,j which a bond or issuer receives (Table 3) [90]. Reduced form models [23] result from rating transition matrix as they use conditional default probabilities of an object in a certain time period.

2.3. Corporate Credit Rating Modelling Methods used for corporate credit rating modelling include statistical methods and artificial intelligence methods. Except for the used methods, prior studies also differ in assessed objects, input variables, and in the number of rating classes.

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Statistical Methods The first attempts attemps at credit rating modelling were realized by ordinary least squares (OLS) [43], [79], [94]. In [43], the top six bond rating classes were predicted, for both Moody's and Standard & Poor’s, employing a multiple regression model. About 200 bonds were studied with unchanged ratings in the 1959-64 time period and, from a model estimated on this population, both the credit ratings of newly issued bonds and the changes in bond ratings were predicted for the 1961-64 period. It was concluded that a model containing six input variables could predict approximately 58% of Moody's ratings and 52% of Standard & Poor’s ratings. In [94], the model developed by [31] was used to classify the first six Moody's bond rating classes. The same dependent variable was used by [43] but the equation was estimated in logarithmic form. The logarithmic form allows the impact of each independent variable to be a function of the levels of the other independent variables, thus allowing for some interaction effects among the independent variables. By employing four variables in a multiple regression model, it was possible to classify approximately 62% of the actual rating classes. The predictive ability of the model by [94] was about the same as in [43]. A regression model was employed in [79] with a dichotomous (0-1) dependent variable to predict which of two rating classes (i.e., Aaa or Baa) a bond should be assigned. Limiting the analysis to investment grade bonds (Aaa, Aa, A or Baa), as rated by Moody's, a model was developed employing five different input variables. This model was proposed to classify a number of subsets of bonds, with particularly good results when they paired high (Aaa) and low (Baa) rated bonds. In a holdout sample, a procedure, based on the estimated functions for the three adjacent paired comparisons, correctly classified 8 out of 10 bonds with the two misclassifications by having an error of only one rating class. Advanced statistical methods followed such as multiple discriminant analysis (MDA) [4], [8], [77], [78], logistic regression analysis (LogR) [25], [47], [49], and probit analysis [35], [48], [50]. The details of selecting financial ratios were discussed in [77] for the model using factor analysis. Unlike the previous studies, a population from newly issued industrial bonds was drawn. An estimating sample of 132 bonds, and a holdout sample of 48 bonds issued in 196768, with bond credit ratings in the five Moody's rating classes from Aa down to B, were selected. In the holdout sample, 65% were correctly classified and no bond was in error by more than one rating class. In a sample of 48 bonds, newly issued in 1969, 27 (56%) were correctly classified. A subsequent study by [78] used a more sophisticated classification rule. This process improved the classification of Baa bonds but worsened the classification of bonds in other rating classes. Multiple discriminant analysis was applied in [4] to the credit ratings of companies in the electric public utility industry. Unlike [77], no priori screening of independent variables was done by [4]. Starting from an initial list of 30 input variables, a series of ad hoc procedures produced a set of 14 input variables, many of them still highly intercorrelated, for the discriminant function. A potential defect of MDA is the inability to screen out insignificant variables through significance tests on individual coefficients. The extensive fitting of the data with the model, enabled to correctly classify 80%-90% of the bonds in their estimation sample. On a complex holdout sample technique which still had some upward bias (in the selection of independent variables), the model correctly classified about 76% of the bonds

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correctly. Opposed to only two rating classes used by [4], a multiclass problem was modelled by [8] using MDA with a 65.9% classfication accuracy. A simple model developed by [50], using only four input variables, could correctly classify about two-thirds of a holdout sample of newly issued bonds. No bond was predicted more than one rating class away. The robustness of the ordered probit model (OPM) was tested in comparerason with the more appropriate N-probit technique. The conclusion was that OPM seems robust and does not cause the equation to be bias. In the study by [25], the OPM method was compared to MDA and LR models. As a result, classification accuracy of 78% was obtained by OPM, while only 69% for MDA, and 65% for LR. The gained conclusions have been confirmed by further studies, e.g. [35] observing 41% classification accuracy on testing data using OPM. Different financial variables have been used in the studies. Given the limited number of objects in the training set, only a limited number of input variables were used for corporate credit rating modelling in the first works. The financial variables typically selected included: measures of size, financial leverage, long-term capital intensiveness, return on investment, short-term capital intensiveness, earnings stability, and debt coverage stability [70], [77]. Table 4. The list of prior studies using statistical methods. Study [43] [94] [77], [78] [50]

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[4] [79] [49]

[47]

Method LR LR MDA OPM LR MDA LR OLR OLR MDA MDA LR LR OLR

q 9 9 5 6 6 2 2 6 6 6 6 6 6 3

Data set 200 ? 180 207 207 ? 113 89 265 89 265 89 265 736

m 6 4 6 10 10 14 5 5 5 5 5 5 5 24

CAtest [%] 56.0 62.0 64.6 66.0 55.0 77.0 CAtrain = 80.0 58.4 47.5 62.9 41.9 52.8 38.9 72.8

Legend: MDA is multiple discriminant analysis, LR is linear regression, OLR is ordered logistic regression, OPM is ordered probit model, q is the number of rating classes, m is the number of input variables, CAtest is classification accuracy on testing data, and CAtrain is classification accuracy on training data.

In paper [49] ordered logit regression (OLR) methods were combined to form a consensus forecast from differing individual forecasts to predict credit ratings in the transportation and industrial sectors. In a data set of 265 observations, an ordered logit forecast combination of credit ratings yields statistically significant, quantitatively meaningful, improvements in classification over other statistical methods (MDA, LR). It was also shown that in a second data set of only 89 observations the OLR method perform well, albeit outperformed by MDA. Recently, the OLR method has been used for a three-class (above BBB, BBB, below BBB) corporate credit rating classification by [47]. As substantionally larger data set of 736 observations (504 estimation companies and 232 holdout companies) was provided for the OLR model design. Such an amount of data made it

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possible to use more input variables (24) than in previous studies. As a result, classification accuracy of 72.8% was achieved. The results from the stepwise selection procedure showed that the final list of the selected predictors in the model contains industry effects, two marketdriven variables, and three accounting variables. They were considered being important predictors of Standard & Poor’s credit rating process. The results of the studies comparing traditional statistical methods showed that OLR and OPM outperformed methods such as LR and MDA in the problem of corporate credit rating modelling. The reason for this consists, among others, in the fact that OLR and OPM can incorporate the fact that rating classes are ordered ordinally. The list of studies using statistical methods is presented in Table 4. The statistical models are succinct and easy to explain [45]. However, the problem with applying these methods to the credit rating classification problem is that the multivariate normality assumptions for independent variables are frequently violated in financial data sets [19], which makes these methods theoretically invalid for finite samples.

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Artificial Intelligence Methods Recently, artificial intelligence (AI) methods such as neural networks (NNs) [13], [45], [70], support vector machines (SVMs) [45], [60], artificial immune systems (AISs) [20], evolutionary algorithms such as grammatical evolution (GE) [11], and case based reasoning (CBR) [53], [60], [85] have been used for corporate credit rating modelling. Usually, AI methods are compared to statistical methods such as MDA and OLR. As stated by [45], the major difference between traditional statistical methods and AI methods is that statistical methods usually require researchers to impose structures to different models, such as the linearity in the multiple regression analysis, and to construct the model by estimating parameters to fit the data or observation, while AI methods allow learning the particular structure of the model from the data. As a result, the structures of the models used in statistical methods are relatively simple and easy to interpret, while models obtained by AI methods are usually very complicated and hard to explain. For an example of credit scoring modelling, [32] used model size to differentiate statistical methods from AI methods. For a given training sample size, there is an optimal model size. The models used in statistical methods are usually too simple and tend to under-fit the data while AI methods generate complex models and tend to over-fit the data. Thus, a trade-off between prediction accuracy and generalizability and interpretability of the model was observed. The most frequently used AI method is represented by feed-forward neural networks (FFNNs). For example, a model was developed by [24] to recognize if a given object is rated AA or non-AA by Standard & Poor’s. The experiments were realized with NNs having zero or one hidden layer with varying number of hidden neurons and 6 or 10 inputs, but did not give a precise account of the network architecture used. Data for 47 firms were used, 30 exemplars were used for training and 17 for testing. Note that for the models considered, one suspects that the number of parameters exceeded the number of training exemplars. Accordingly, a model with 10 inputs and one hidden layer gave the best performance on the training set, 92.4% correct, whereas a smaller model with 10 inputs and no hidden layer had the best testing set performance, 88.3% correct. A regression model for this problem correctly classified only 64.7%.

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A NN was used by [87] to classify bonds of the 18 Bell Telephone companies. Fifty six exemplars were available consisting of data from 1982-1985. The task was to classify a bond as being rated either Aaa or one of A1, A2, or A3 by Moody’s. The experiments were realized with NNs with one or two hidden layers. The best network had 7 inputs, 10 hidden neurons in the first hidden layer, 5 hidden neurons in the second, and 2 output neurons. It classified 88% of the testing set correctly. In a later study [87] the experiments were extended using more data and hold-out-one cross-validation to correctly classify 73% of the bonds into the Standard & Poor’s ratings, and 97% into Moody‘s ratings. However, these results must be understood in the context of a very homogeneous set of firms. Also, the model failed if the rating classes were extended to include the agencies’ subclassifications the NN did not converge. The proposed model was also compared with MDA, and it was demonstrated that NNs achieved better performance in predicting direction of a bond rating than MDA could. Counter-propagation neural networks were developed by [33] for the simulation of the Standard & Poor’s rating system. The study considers 87 input variables for each of 797 companies; 156 exemplars were used for training and 641 for testing the model. The data were unevenly distributed among the rating classes. The NNs had 17 outputs representing 17 rating classes; the number of hidden neurons varied from 156 to 425. No overall average classification results are given, instead the classification accuracy for each of the 17 rating classes is listed separately and for the best model (156 hidden neurons) classification accuracy varies from 55.6% to 8.0%. Classification results for cases where only three broad rating classes (Investment, Speculative, and Poor Quality) are considered were 92.3%, 68.3% and 32.3% correct. In a later paper, an average classification accuracy of only 11% for a network with 170 hidden neurons is given. It was recognized that the NN was overfitting the data, increasing the proportion of the data used for training, and decreasing the number of hidden neurons. The best result was obtained by NN with 51 hidden neurons trained using 415 observations, the classification accuracy increased to 22% on the testing set. The approach based on NNs was compared with linear regression, discriminant analysis, logistic analysis, and a rule-based system for bond rating by [51]. Neural networks achieved best results in terms of classification accuracy. The data set used in this study was prepared using Standard & Poor’s Compustat financial data covering 228 corporations in eight critical financial variables, the same input variables as suggested by [8]. Similarly, NNs were applied by [70] to classify 16 rating classes of Standard & Poor’s, rating ranging from ‘‘B-’’ and below (3) to ‘‘AAA’’ (18). The model classified the rating classes of 36.2% of the firms correctly. This credit rating study has shown that non-linear networks can outperform a multiple linear regression model. The results demonstrated that substantial benefits in performance can be obtained using the principled architecture selection methods proposed in this study. The systems with 5-class and 3-class classification were also tested, and classification accuracies of 63.8% and 85.2% were obtained. Despite using input financial data drawn from companies in a variety of industrial sectors, the NNs’ models proposed by [13] demonstrated a capability to discriminate between bond rating classifications with classification accuracy, 84% in two-class and 53% in a fiveclass problem. It was also noted that there is no clear support for the hypothesis that financial statements were exceptionally ‘noisy’ during the late 1990s, as the obtained classification accuracies are broadly comparable with those of earlier studies. In [65] the performance of feed-forward neural networks (FFNNs) was compared with that of MDA and logistic regression. Data from Moody’s Annual Bond Record and Standard

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& Poor’s Compustat financial data were used. The best performance obtained was nearly 70% for the six-class credit rating problem using only five input financial variables. FFNNs were also compared with radial basis function neural networks (RBFNNs), learning vector quantization neural networks (LVQNNs) and logistic regression in [16]. This study revealed that FFNNs and the logistic regression model obtained the best performances. However, the two methods only achieved an accuracy of 51.9% and 53.3%, respectively. RBFNNs and LVQNNs were outperformed, mainly because only 120 observasions were used for the models design. Small data sets do not make it possible to set and tune the topological and learning parameters of the RBFNNs and the LVQNNs. The study by [52] has shown that corporate credit ratings of Standard & Poor’s could be assessed using publicly available financial and non-financial data (COMPUSTAT diabase, Dun and Bradstreet database, and Standard & Poor’s bond manuals). The data set of 1080 objects excluded utilities, transportation, and financial companies because their financial structures are quite different from the rest of the companies. Next, the sample was randomly divided into a group for training (75%) and another group for testing the model (25%). High classification accuracy on testing data (84%) was achieved by adaptive learning networks for a four-class classification problem. Since individual industries have thein own common characteristics in financial structure, it can be conjectured that the model performance could be enhanced significantly. This fact has been confirmed by [45] for financial companies. The data set covered financial variables and ratings from 1991 to 2000. After filtering data with missing values, 265 cases were obtained from the 10-year data for 36 commercial banks. Five rating classes appeared in the data set, including AA, A, BBB, BB, and B. Two sets of input variables, 5 and 12 financial variables, were used as the inputs of the models. Nevertheless, similar results have been obtained for both sets of variables. A relatively new machine learning technique, SVMs, was introduced to the credit rating problem in an attempt to provide a model with a better explanatory power. FFNNs were used as a benchmark method. Classification accuracy of around 80% was observed for both FFNNs and SVMs for the US and Taiwan markets. Only a slight improvement was observed using SVMs. In summary, previous literature has consisted of extensive efforts to apply NNs and other AI methods for the modelling of corporate credit rating. The results have been mostly compared to other statistical methods. The general conclusion has been that AI methods outperformed conventional statistical methods in most prior studies. The results of the previous studies are strongly affected by the number of rating classes, as low classification accuracies were obtained for multiple rating classes. Further, the availability of data has limited the obtained results in some cases [24], [86], [87]. A low number of companies makes it difficult to generalize the results. Moreover, the size of data sets determines also the number of input variables, as only several variables could be used in most studies. The highest classification accuracy (more than 80%) was achieved for two (investment and noninvestment grade) and three rating classes. However, the results obtained by [86] can be hardly considered as being relilable, due to a low number of companies. The higher the number of rating classes, the lower classification accuracy was achieved. For five or six rating classes, a classification accuracy of less than 60% was obtained. The study by [45] also shows good results for five rating classes. However, the data set of only 36 companies (for 10 years) from financial industry was used.

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Input variables are mostly represented by financial ratios. They usually include the size of the company, profitability, leverage, asset management, liquidity, cash, and value ratios. Input variables differ for financial industry and other industries. The review of used input variables will be provided in the next subchapter concerning the design of input variables for experiments. Further, it is clear that larger data sets have been available in more recent studies. Larger data sets make it possible to train the classifiers properly. At the same time, generalization ability on testing data can be improved in this way. Moreover, larger data sets allow applying more input variables. Table 5. The list of prior studies using AI methods. Study [70]

[24] [86], [87] [13] [20] [11]

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[33] [52] [65]

[45]

[51]

[16]

Method FFNN FFNN FFNN MLRM FFNN MLRM FFNN MDA FFNN FFNN AIS GE FFNN MDA FFNN ALN FFNN MDA OLR FFNN FFNN SVM SVM FFNN RBES LR MDA OLR FFNN RBFNN LVQNN

q 16 5 3 16 2 2 2 2 2 5 2 2 2 2 3 4 6 6 6 5 5 5 5 6 6 6 6 6 6 6 6

Data set 196 196 196 196 47 47 18 18 600 791 791 791 791 791 797 1080 299 299 299 265 265 265 265 228 228 228 228 228 120 120 120

m 10 10 10 10 10 10 8 8 8 8 8 8 8 8 87 26 5 5 5 5 12 5 12 8 8 8 8 8 8 8 8

CAtest [%] 36.2 63.8 85.2 21.4 83.3 64.7 88.0 39.0 84.0 52.7 72.5 84.9 83.3 85.2 84.9 83.8 66.7 61.0 61.7 80.0 79.3 78.9 80.0 55.2 31.0 36.2 36.2 43.1 56.7 38.3 36.7

Legend: OPM is ordered probit model, FFNN is feed-forward NN, ALN is adaptive learning network, SVM is support vector machine, RBFNN is radial basis function neural network, LVQNN is learning vector quantization neural network, RBES is rule based expert system, GE is grammatical evolution, q is the number of rating classes, m is the number of input variables, and CAtest is classification accuracy on testing data.

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Given the results of the studies using NNs and earlier studies using statistical methods, it appears that the level of information available in financial data is bounded [13]. Although NNs are capable of detecting non-linear structures in input data, it does not appear that this has noticeably improved the results, as the classification power of NNs is only slightly better than that recorded by traditional statistical methods. This suggests that additional inputs are required to obtain significantly better results. This is in line with the claims of rating agencies who emphasise the importance of qualitative factors in their rating decisions. It is also noted that there are problems which can emerge when using accounting data as an input for models for bond ratings or bankruptcy prediction. Managers may attempt to utilise creative accounting practices to manage earnings and disguise signs of distress [13], [88]. In addition to NNs, AISs, GAs and CBR have been also applied for corporate credit rating modelling. The suitability of AISs was investigated by [20] for the financial problems of credit rating and corporate failure prediction. The focus was placed on the negative selection algorithm and the recently proposed variable detector modification. However, the obtained results so far show that AISs have not outperformed other AI methods. Nevertheless, the classification algorithms based on AISs are still beeing developed. Grammatical Evolution (GE) used by [11] represents a novel data driven, model induction tool, inspired by the biological geneto-protein mapping process. This study demonstrates the metodology by applying it to model the corporate credit rating process, using information drawn from the financial statements of 791 bond-issuing firms drawn from the year 1999-2000. The best developed model was found to be able to discriminate out-ofsample between investment grade and non-investment bond ratings, with an average accuracy of 84.9% across a five-fold cross validation. Prior literature that applied AI methods for the corporate credit rating modelling is summarized in Table 5. The methodology and the results of the studies are presented as only studies using data on US companies, are referred. The rating classes provided by the two rating agencies Standard & Poor’s and Moody’s were used as output variables in the mentioned studies. The factors of credit rating provided by these agencies are similar. However, as stated in [71], significant differences were observed based on statistical testing. This means that these rating agencies stress different input variables. Though previous sudies have been focused on US data, there are also several works concerning other countries and rating agencies in prior literature. Many companies assessed by Korean rating agencies make it possible to realize a number of experiments on Korean data sets. Artificial intelligence methods have been used in these studies, such as: NNs, SVMs, CBR, ordinal pairwise partitioning (OPP), and hybrid methods combining AI methods, see Table 6. Case-based reasoning (CBR) systems were used to classify corporate credit ratings by [85]. Better user interpretability was provided this way. The basic principle of CBR is to match a new problem with the closest previous cases and try to learn from experiences to solve the problem. Inductive learning for case indexing and used nearest-neighbor matching algorithms were used to retrieve similar past cases. It was demonstrated that the proposed model has a higher prediction accuracy (75.5%) than the MDA (60%) and ID3 (59%) methods for five-class credit rating problem. The research data consisted of 168 financial ratios and corresponding credit ratings of Korean companies. The ratings have been performed by the National Information and Credit Evaluation Inc. The total number of

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Credit Rating Modelling by Neural Networks

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samples available included 3,886 companies whose commercial papers have been rated from 1991 to 1995. Ordinal pairwise partitioning (OPP) approaches were applied to FFNNs by [58]. The main idea of the OPP approach is to partition the data set in the ordinal and pairwise manner according to the output classes. Then, each FFNN is trained by using each partitioned data set and is separately used for classification. They demonstrated that FFNNs with OPP had the highest level of classification accuracy (71–73%), followed by conventional FFNNs (66– 67%), and then MDA (58–61%). The data set used by [53] consisted of 167 input variables and corresponding credit ratings (5 rating classes) issued by National Information and Credit Evaluation Inc. The total number of assessed objects included 2,971 issues of bonds rated from 1992 to 1996. The companies were attached with financial data from 1992 to 1995. Case-based reasoning and its variants optimized by SOMs and LVQNNs were applied for the classification problem. These methods outperformed MDA, as best results were obtained by LVQ-indexing CBR (69.1%). Table 6. The list of prior studies on Korean data. Study [85]

[58]

[53]

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[2]

[60]

Method MDA CBR GA-CBR FFNN+OPP FFNN MDA MDA CBR SOM+CBR LVQ+CBR MDA OLR CBR FFNN SVM MDA CBR FFNN SVM

q 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 5 5 5 5

Data set 3886 3886 3886 126 126 126 2971 2971 2971 2971 1295 1295 1295 1295 1295 3017 3017 3017 3017

m 168 168 168 24 24 24 329 329 329 329 14 14 14 14 14 297 297 297 297

CAtest [%] 60.0 62.0 75.5 73.0 67.0 61.6 55.0 61.1 67.1 69.1 63.1 65.4 51.4 65.7 68.0 58.8 63.4 59.9 67.2

Legend: GA is genetic algorithm, OPP is ordinal pairwise partitioning, and SOM is self-organizing map.

The study by [2] proposed Ordinal Multiclass SVMs which applied OPP to conventional SVMs in order to handle ordinal multiple classes efficiently and effectively. The suggested model used fewer classifiers but predicted more accurately because it utilizes additional hidden information, the order of the rating classes. The Ordinal Multiclass SVMs outperformed other statistical (MDA, OLR) and AI methods (FFNNs, CBR), with the classification accuracy of 68% on testing data. Support vector machines were applied by [60] to the corporate credit rating problem in an attempt to suggest a new model with better explanatory power and stability. A grid-search technique was applied using 5-fold cross-validation to find out the optimal parameter values

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of RBF kernel function of SVM. In addition, to evaluate the classification accuracy of SVM, the performance of SVMs was compared to those of MDA, CBR, and FFNNs. The experimental results showed that SVM outperformed the other methods with the classification accuracy CAtest=67.2%. An extensive number of 297 financial ratios were used for the experiments together with the corresponding credit ratings (5 rating classes) of 3,017 Korean companies, whose commercial papers were rated from 1997 to 2002. Considerably less attention has been given to develop models explaining or replicating the rating process of specialized and regional agencies [22], [59]. The data set studied by [59] consisted of 35 input variables from 3,200 Finnish companies. In a binary classification problem, the differences in performance between the OLR and LR models were insignificant, provided that the LR model is rotated. Both of the models give a classification accuracy of 90% in the training sample and 96% in the test sample. The objective of the study by [22] was also to fill in the gap by exploring the potentials for developing models to replicate the credit ratings of a regional agency using publicly available data. The analysis was based on the credit ratings issued by Qui Credit Assessment Ltd., a UK credit rating agency. The rating of this agency is expressed in a numerical scale, between 0 and 100, measuring the likelihood of failure in the 12 months following the date of calculation. On the basis of this rating scale, the firms were classified into five credit risk groups. The analysis is based on a multicriteria decision model with the classification accuracy of 72.9%. Moreover, the comparison of classification results is provided to other method such as FFNNs, probabilistic NNs (PNNs), MDA, and LR. The Taiwanese data set of 74 cases with bank credit rating and 21 financial variables, which covered 25 financial institutes from 1998 to 2002, were used by [45]. Five rating classes appeared in the data set, and the best results were obtained by SVM (79.7%), followed by FFNN (75.7%), and then OLR (73%).

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2.4. Municipal Credit Rating Modelling The specific position of municipalities associated with their financial management, requires the use of different input variables than for companies. Municipalities dispose, same as companies, of internal and external financial resources. Internal financial resources come mostly from municipal taxes, while loans and bonds represent external resources. Moreover, the share in central government taxes and grants rank among key financial resources of municipalities. The objectives of municipalities consist in providing public services (in sufficient quantity and quality). It is obvious that the mentioned facts influence the credit rating process of municipalities. Specific financial indicators are beeing monitored by rating agencies, as well as other socio-economic and management information. Further, municipalities have rarely financial resources to pay for the credit rating. As a result, there have been less attention paid to municipal credit rating modelling in the literature. Small data sets make it impossible to get consistent results. Therefore, only convention statistical methods have been used for the modelling so far. The use of MDA was reported by [15] to study those variables affecting municipal credit rating. A set of four key input variables was used from which a discriminant function was generated. Although significant coefficients were obtained, only 50% of testing sample was classified correctly. The same database as in [15] was used by [44] in an attempt to improve the results. Regression analysis was employed instead of MDA. Only two rating classes

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(investment and non-investment grade) represented the outputs of the regression model. A sample of 150 municipalities, nationwide, was used as 75 of them had investment grade ratings. The rating classes’ proportion was the same for testing data (50 municipalities). The study was superior to that one of [15] as 80% of testing data was classified correctly. Regression analysis was also used by [81] in order to derive a rating index based on Moody’s four highest credit ratings for New England municipalities. Unlike previous studies, the issue he addressed was to determine the input variables that led to an Aaa credit rating. The Aaa rating class was the function of eight input variables. The model correctly classified 67% of training data. However, testing data were not used to support the conclusions. In the study by [91], the modeling was confined only to credit ratings issued in Oklahoma and rated late in 1970s by the Municipal Rating Committee of Oklahoma. Four highest rating classes were examined. The classification accuracy achieved by MDA of the holdout sample was 71%. The aim of the study by [80] consisted in trying to replicate changes in either direction from Moody’s A rating class (1975-1979) nationwide for thirty cities with population of 50,000 or more. Multiple discriminant analysis was applied to twelve input variables. Upgraded and downgraded rating classes were examined with several stages used to test the stability of the results. The testing of the models was realized by Lachenbruch’s U method. However, the results could be hardly validated due to small set of training data. The timeliness and reliability of financial accounting data were examined by [17] in predicting changes in Moody’s credit ratings. Multiple discriminant analyses was also applied to a set of 28 financial variables thought to influence municipal credit ratings. The input variables were calculated for each 168 cities nationwide for the period from 1975 to 1977. Through credit rating change, 35 cities experienced downgrades, 77 received upgrades, and 56 experience no change. Two models were constructed. One model with eight input variables was used to test the data one year prior to the rating change. Another model with seven input variables was used to test the data one year after the rating change. The classification accuracy of the prior-year model for the entire sample was 79% (55% for testing data) while 83% (70% for testing data) for the post-year sample. As a result, the authors concluded that financial variables can reflect past changes in credit ratings but may not be sufficiently reliable to predict credit rating changes. The study by [29] questioned the results obtained in previous studies in three ways. First, some data sets were too small or were confined to a single region. Thus, general inferences drawn form these studies were held to be suspect. Second, classification accuracy has varied according to the number of rating classes used. Third, the input variables used in previous studies were criticized. Attempting to overcome these weaknesses, a sample of 680 municipalities, nationwide, was used that had Moody’s credit ratings from Baa and higher for 1977. Four groups of input variables were created, namely financial, debt, economic base, and administrative. Out of 680 observations, 205 served as testing data set. Classification accuracy for the testing data ranged from 62% to 68%. In [30] Moody’s credit ratings of 976 municipalities and Standard & Poor’s credit ratings of 271 municipalities were used in order to compare the credit rating criteria between the two agencies. A special form of regression analysis was designed to more accurately measure the importance of input variables than MDA and OLR. Only four of the total 23 input variables were represented by financial variables. The remaining input variables were either socioeconomic or geographical.

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The changes in credit ratings assigned by Moody’s were examined by [63]. The extent to which credit rating upgrades could be explained by socio-economic variables was tested by the designed regression model. No financial accounting variables were employed with respect to their unreliability addressed in previous studies [17], [68]. The changes in credit ratings for 117 municipalities between 1971 and 1980 were examinied. It was concluded that future studies on municipal credit ratings needed to give greater weight to economic base variables and less weight to financial accounting variables. A similar theme was examinied by [64] with the intent to find factors affecting Aaa rating class provided by Moody’s rating agency. A classification accuracy of 80% was reported for the on holdout sample. So far only a small effort has been done to employ AI methods for municipal credit rating modelling. A model based on fuzzy logic was employed by [5]. In this case a fuzzy set with three triangle membership functions was created for each input variable. Membership functions and a rule base was designed by experts. The rule base was beeing modified during the learning process so that maximum classification accuracy was obtained. However, only 30 municipalities were used as training sample to develop the model. Thus, doubts of the generalization ability of such a model rise. Table 7. Prior studies on municipal credit rating modelling.

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Study [15] [44] [81] [72] [68] [6] [91] [80] [17] [29] [30] [63] [64] [84] [5]

Method MDA LR LR MDA MDA MDA MDA MDA MDA MDA MDA OLR OLR LR LR MDA MDA FRBS

q 5 2 2 5 5 2 2 4 2 3 4 ? ? 2 2 3 3 12

Rating agency Moody's Moody's Moody's Moody's S&P´s Moody's Moody's MRCO Moody's Moody's Moody's Moody's S&P’s Moody's Moody's Moody's S&P´s Moody's

Data set 691 398 155 266 266 40 24 152 30 168 680 976 271 117 ? 203 203 30

m 4 4 8 ? ? ? ? ? 12 28 ? 23 23 4 4 ? ? ?

CAtest[%] 50 80 CAtrain = 67 46 63 58 CAtrain = 96 71 CAtrain = 83 55 62 ? ? ? 80 66 64 CAtrain = 53

Legend: FRBS is fuzzy rule based system and MRCO is Municipal Rating Committee of Oklahoma

The overview of previous studies concerning the modelling of municipal credit rating is presented in Table 7. It is obvious that the rating classes, the same as for companies, were assigned mostly by Standard & Poor’s or Moody's rating agency. According to [72] Moody's emphasizes financial variables, while Standard & Poor’s gives priority to economic factors. However, most studies used both economic and financial variables. Concerning methods, regression models and MDA prevail. Similarly, as for companies, less attention has been given to develop models replicating the municipal rating process for non-US objects. Municipalities

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from European countries (Italy, Sweden, France) have so far been studied only by [84]. The reason lies in the small data sets available. Moreover, fiscal systems of different countries are rather specific, which implies other input variables used for credit rating process. As a result, only about two thirds of testing data were classified correctly by [84] using three rating classes as output. There have been several attempts made to overcome the problem concerning small data sets in the literature. One of the possibilities consists in the design of an expert system based on the knowledge acquired from the rating agencies’ experts [75]. Further, it is possible to extend the training and testing set using unsupervised methods. In this case only low proportion of municipalities are labelled with rating classes a priori. The other municipalities can be then labelled with the rating classes belonging to the most similar labelled municipality. Then it is possible to apply supervised methods like NNs [38], [39] on such preprocessed data sets. If the information about the unlabelled municipalities is beeing used during the learning process, then this approach represents a combination of supervised and unsupervised methods.

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3. Neural Networks for Classification Neural networks [40], [42] are defined as massively parallel processors, which tend to preserve the experimental knowledge and enable their further use. They simulate the human brain with the intent to collect the empirical evidence during the learning process, and interneural connections (synapses) are used to store the knowledge. An important feature of NNs, in addition to the ability of learning, is the ability to generalize knowledge learned. Currently, there exist many structures and learning algorithms of NNs, including a number of their applications. In the economic field, NNs are used primarily in problems where the variables are in non-linear relationships. An extensive overview of NNs’ applications in the economic field can be found in [42], [95]. Among others, NNs are suitable for time series predictions. They have been used in the prediction of stocks [67], GDP [74], sales [57], etc. Except for credit rating modelling and bankruptcy prediction, NNs have been also applied for other classification problems such as corporate financial analysis [26], credit applicants classification [66], customers segmentation [9], products development [92], etc. As the credit rating modelling represent a classification problem, the classification problem will be characterized in general, and the NNs suitable for its realization will be introduced consequently.

3.1. Classification Problem Credit rating modelling represents a classification problem. The model of credit rating should simulate the decision-making process of rating agencies in order to correctly classify the objects into rating classes. The classification process is based on data matrix X that includes the values of selected input variables x1,x2, ... ,xm and rating classes ωi,j∈Ω for assessed objects oi∈O, O={o1,o2, … ,oi, … ,on}. The data matrix X can be defined in this way:

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Petr Hájek

o1 ...

X = oi ... on

x1

...

x 1,1

... x 1, k

xk

xm ... x 1, m ω1, j

...

...

...

...

x i,1

...

x i, k

...

... ... ... x n,1 ... x n, k

...

... ... x i, m ω i, j , ... ... ... ... x n, m ω n, j

(2)

where xk is the k-th input variables, k=1,2, ... ,m, xi,k is the value of the input variable xk for the i-th object oi∈O, xi =(xi,1,xi,2, … ,xi,k, … ,xi,m) is the i-th pattern, x=(x1,x2, … ,xk, … ,xm) is the vector of input variables. Generally, the classification problem [93] can be defined as follows. Let F(x) be a function defined on a set O which assigns picture xˆ œΩ, where Ω={AAA,AA, ... ,D} is the set of classes, to each element xœO. A classifier (machine realizing the classification problem) xˆ =F(x)œΩ represents then the projection F : O → Ω . Further, let G(x,w) be a function with arguments from the finite set Otrain={x1,x2, … ,xr}ÕO, and w is the parameter (or parameters) of projection G. Then, xˆ =G(x,w)œΩtrainÕΩ. The complement of the set Otrain to the set O presents a testing set Otest. Let for each xiœOtrain be the required picture xˆ i . The goal of the classification consists in finding the parameters w of the function G(x,w) so that the functional values of the arguments from the training set Otrain are as close as possible to the pictures of the function F(x). Further, let the objective function be as follows:

E(w ) =

1 r ∑ (G(x i , w ) − xˆ i ) 2 2

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i =1

.

(3)

Then the goal lies in the minimization of this function. Global minimum is achieved as the values of parameters w are optimal. Then, the function G(x,w) is adapted. Let w be the optimal value of the parameter w. Then, the adapted function G(x, w ) is used for the classification of training (testing) set Otrain (Otest). It is assumed that the adapted function approximates well the original function F(x) also outside the training set Otrain. Thus, classification error E and classification accuracy CA are usually evaluated on testing data. Classification accuracy is defined as follows: CA[%]=(CC/n)*100, where CC is the number of correctly classified objects.

(4)

3.2. Feed-Forward Neural Networks A FFNN [40] uses neurons connected among themselves in layers. The neurons of adjoining layers are connected so that the output of one neuron is distributed into the inputs of the neurons in the following layer. As a result, the input values only move from input to hidden layers and, at the same time, from hidden to output layers.

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A vector x of input values is presented to the input layer. This pattern is then expanded (transformed) through the FFNN using synapse weights wij and activation functions f up to the outputs of the FFNN. The values of potentials ξ are computed consecutively from input to output layer as follows: ξ j = ∑ w ij * y i ,

(5)

i

where wij are synapse weights between the i-th and the j-th neuron, i and j stand for indices passing through neurons of two adjoining layers, and yi is the output of the i-th neuron. The resulting weighted values are added together producing a weighted sum given to a transfer function. The outputs of the transfer function are distributed to the output layer. They are multiplied by a weight wjk, and based on the resulting weighted values, the weighted sum is put to a transfer function, which outputs a value ωk representing a class. The FFNNs are based on supervised learning. The objective of the learning lies in obtaining such a setting of synapse weights wij that the deviation (error) E between actual and target outputs of the FFNN is minimum for the given training patterns. The partial derivative of the error E, with respect to the synapse weights, represents the minimization of the error E by gradient method. Backpropagation algorithm is a standard learning algorithm of the FFNNs [40]. Since the FFNN uses the gradient method in the learning process, it is possible that the learning algorithm gets stuck in local minimum within the error function. This can be solved, for example, by adding noise to the equation for synapse weights adaptation, adding neurons, setting the learning rate, or adding momentum.

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3.3. Radial Basis Function Neural Networks Radial basis function neural networks (RBFNNs) [40], [76] are a popular alternative to the FFNNs. They are also good at modeling nonlinear data and can be trained in one stage, rather than using an iterative process as in FFNNs, and also learn the given application quickly. The RBFNN means any kind of FFNN that uses RBF as a activation function. Using RBFNN for classification is suitable, since in most cases a specific group of input vectors xi belongs to one of classes ωij∈Ω, which are sought by RBFNN. It is therefore possible to pick a group representative, and consider the set within output of required class ωij∈Ω its surroundings. Radial basis function neural networks are, in term of approximation [76] natural, because approximation is done by functions, which influence the final function only in the center surroundings ci of the RBF neuron and not in the whole function range. The j-th output fj(x,H,w) RBF of neural network can be defined this way: q

f j (x, H, w ) = ∑ w ji * h i (x) ,

(6)

i =1

where H={h1(x),h2(x), … ,hi(x), … ,hq(x)} is a set of activation functions RBF of neurons (of RBF functions) in the hidden layer and wj,i are synapse weights. Each m components of vector x=(x1,x2, … ,xk, … ,xm) is an input value for q activation functions hi(x) of RBF neurons.

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This NN includes exactly one hidden layer. The reason for a hidden layer number limitation is the fact that each from m input vector values x=(x1,x2, … ,xk, … ,xm) is used as an activation function parameter H={h1(x),h2(x), … ,hi(x), … ,hq(x)} RBF neurons, where q is a number of neurons in the hidden layer. Activation function hi(x) of RBF neurons in the hidden layer is a special class of mathematical functions, whose main characteristics is the monotonous rising or falling, with increasing distance from center ci, of activation function hi(x) of RBF neuron. For the classification problem, Gaussian activation function hi(x) is preferred. Neurons of the output layer represent only the weighted sum of all inputs coming from the hidden layer. In RBF neural network learning process [40], it is required to set a number of centres ci of activation function hi(x) of RBF neurons, and to find the most suitable positions for RBF centres ci. Other parameters are radiuses of centres ci, rate of activation functions hi(x) of RBFs, and synapse weights wqn setup between hidden and output layer.

3.4. Probabilistic Neural Networks

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Probabilistic neural networks (PNNs) [89] are based on Bayes classifiers. They learn to approximate the probability density function of the training objects (i.e. underlying objects’ distribution). The PNN consists of neurons allocated in three layers. The hidden layer has one neuron for each case in the training data set. The neuron stores the values of the input variables for the case along with the target value. When presented with the xi vector of input values from the input layer, a hidden neuron computes the Euclidean distance of the test case from the neuron’s center, and then applies the RBF kernel function using the sigma value. There is one neuron for each class in the class layer. The actual target class of each training object is stored with each hidden neuron. The neurons add the values for the class they represent (hence, it is a weighted vote for that class). The decision layer compares the weighted votes for each target classs and uses the largest vote to predict the the target class.

3.5. Cascade Correlation Neural Networks Cascade correlation neural networks (CCNNs) [27] combine two key ideas. The first is the cascade architecture, in which hidden units are added to the network one at a time and do not change after they have been added. The second is the learning algorithm for each new hidden neuron. The magnitude of the correlation between the new neuron’s output and the residual error is maximized. Every input neuron is connected to every output neuron by a synapse with an adjustable weight wij. The learning algorithm begins with no hidden neurons. The direct input-output synapses are trained over the entire training set. Then any of the learning algorithms for single-layer NNs can be applied. The CCNN has three layer (input, hidden, and output layer). Each output neuron representing class ωj receives values from all of the input neurons (including the bias) and all of the hidden layer neurons. Each value presented to an output neuron is multiplied by a weight wij, and the resulting weighted values are added together producing a combined value.

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3.6. GMDH Polynomial Neural Networks Group Method of Data Handling (GMDH) polynomial NNs [28] are self-organizing networks, which means that the synapses between neurons in the network are not fixed but rather are selected during training to optimize the network. The network begins with only input neurons. During the training process, neurons are selected from a pool of candidates and added to the hidden layers in the similar matter as in CCNNs. The number of layers in the network is selected automatically to produce maximum accuracy without overfittin. Neurons in the hidden layers are selected based on their contribution to the mean squared error during the process of learning. Each neuron in the second layer draws its inputs from two of the input variables. The neurons in the third layer draw their inputs from two of the neurons in the previous layer; this progresses through each layer. The final layer draws its two inputs from the previous layer and produces a single value which is the output of the network. Inputs to neurons in GMDH networks can skip layers and come from the original variables, or from earlier layersr. Traditional GMDH NNs use complete quadratic polynomials of two variables as transfer functions in the neurons. These polynomials have the form: y = p0 + p1*x1 + p2*x2 + p3*x12 + p4*x22 + p5*x1*x2.

(7)

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3.7. Support Vector Machines Support Vector Machines (SVMs) [1], [18] are affiliated to NNs and create the category of so-called kernel machines. They represent an essential kernel-based method. Using kernel functions SVMs are an alternative learning method for the RBFNNs and FFNNs. During the SVMs learning process, the decision boundaries are derived directly from the data. Thus, separating margins are maximized in multidimensional feature space. This learning strategy minimizes the classification errors in training (testing) data Otrain (Otest). Hence, the generalization ability of SVMs differs from other methods significantly, especially, when the training set Otrain is small [46]. It is possible to separate data in the event of classification. In this context, the main principle of SVMs consists in the creation of the decision hyperplane between classes ωj so that the margin between positive and negative patterns is maximized. This feature of SVMs comes from statistical learning theory [93]. More precisely, SVMs represent the approximate implementation of the structural risk minimization method [1]. This principle is based on the fact that the testing error is limited by the sum of training error and by the expression depending on Vapnik-Chervonenkis dimension. The central point in the construction of SVMs algorithm is the inner product kernel between support vector xi and vector x from input space. Support vectors xi consist of a small subset of training data Otrain extracted by the algorithm. Depending on how the inner product kernel is generated, different learning machines can be constructed which are characterized with their own non-linear decision hyperplane. The design of SVMs depends on the non-linear projection of the input space Ξ into multidimensional space Λ, and on the construction of an optimal hyperplane. This operation is dependent on the estimation of inner product kernel referred to as kernel function k(x,xi).

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Based on the given facts, it is possible to find linear separators in the q-dimensional space Λ, so that (x,xi) is replaced by kernel function k(x,xi). Accordingly, the process of learning can be realized so that only kernel functions k(x,xi) can be computed instead of full list of attributes for each data point. Evidently, the found linear separators can be transformed back into the original space Ξ. This way any non-linear boundaries between the positive and negative patterns can be obtained. Various kernel functions k(x,xi) representing different spaces can be used for modelling, e.g. linear, polynomial, RBF and sigmoid kernel function [18]. Then the output f(xt) of SVMs is defined this way: N

f(xt)=

∑α i =1

i

* y i * k (x i , x t ) + b ,

(8)

where xt is the evaluated pattern, N is the number of support vectors, xi are support vectors, αi are Lagrange multipliers determined in the optimization process, and k is the actual kernel function k(x,xi). Support vectors xi represent the component of classifiers’ structure, and their number N is cut during the optimization process [1].

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4. Data Sets US data are used for both the corporate and municipal credit rating modelling. Data sets cover input variables for 852 companies and 150 municipalities in the year 2007. The sets of input variables for the modelling are designed based on all the aspects of economic and financial performance of companies and municipalities. The input variables selection is based on the review of prior literature. The variables proposed in this subchapter will be optimized in further process of modelling. Credit ratings of two rating agencies represent the output variable. Companies are labelled with Standard & Poor’s rating classes, while municipalities are labelled with Moody’s rating classes.

4.1. Corporate Credit Rating Data Rating agencies do not give publicity to their credit rating factors. Thus, when selecting input variables for corporate credit rating modelling, one can result from prior studies. The list of input variables used by them is presented in Table 8, their description is provided in Table 9. The main factors considered in assigning a credit rating are industry risk (e.g. each industry has an upper limit rating – no issuer can have a higher rating regardless of how conservative its financial posture), size (usually provides a measure of diversification and market power), management skills, profitability, capital structure, cash flow, and others. The first group of input variables is concerned with the business position of a company. The size of the capital determines the ability of a company to pay off its loans. It can be measured in several ways such as market capitalization, assets, equity, etc. A company should also be capable to generate sufficient cash flow. Character (reputation) of a company results from its willingness to meet obligations. Holders are mostly responsible for this factor.

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Character is difficult to evaluate, however, some information is hidden in insiders’ and institutional holdings. Conditions (circumstances) designate external factors of business. Companies in different industries and markets are sensitive to the changes in the economy in varying degrees. In prior literature the size of companies were mostly measured by TA. Market values of companies were used only sporadically, e.g. [94]. Other factors like reputation or industry have not been involved so far, or have been realized only partially. Table 8. Overview of the input variables used for corporate credit ratings in prior studies.

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Study [77], [78] [50] [4] [79] [94] [8] [43] [47] [49] [11] [20] [65] [24] [86], [87] [13] [51] [52] [45] [16]

Input variables DIV yrs, IS, (NI+I)/I, SS, LD/TA, NI/TA CF/I, CF/TD, LD/TA, LD/NW, NI/TA, TA, BI, TA var, NI var, SS IC, IC var, CF, E var, ROI, DA/OR TD/TC, NI/TA, NI var/TA, TA, (NI+I)/I E var, WL, MV/TD, MV, TA, TD, LD/TC, CuA/TL, (NI+I)/I, PD, P, SS TA, NW/TD, OM, WC/S, S/NW, SS KMV, MEV, E, TA, TD/(EBIT+DA), TA/Eq, LD/TC, SD/TC, IC, (EBIT+DA)/I, CF, I, NI, ROC, ROE, ROA, OM, RE/TA, CR, QR, CaR TA, SS, ROA, TD/TA, IC CR, RE/TA, IC, TD/TA, NM, MBV, TA, ROA CR, RE/TA, IC, TD/TA, NM, MBV, TA, ROA TA, TD/TA, NI/TA, SS, Beta TL/CA, TD/TA, S/NW, ROS, FS, E/FC, 5-yr RGR, WC/S, SPC, TRR LD/TC, IC, ROI (ROE), 5-yr ROE var, TA, CC/CF CR, RE/TA, IC, TD/TA, NM, MBV, TA, ROA TA, TD, LD/TC, CR, (NI+I)/I, PD, P, SS TA, CR, ROA, TD/TA, S/FA, OM, IC, LD/TC, CF/CL TA, TL, LD/TC, TD/TA, OM, ROE TA, TD, LD/TC, SD/TC, CR, (NI+I)/I, TD/TA, ROS

Financial indicators represent the other important factors of corporate credit rating process. Profitability, activity, liquidity, leverage and market value ratios are usually included into financial ratios. Profitability ratios reflect the positive and negative influence of assets management, financing, and liquidity on the profit of a company. Except the absolute size of profit, the effect of ROA, ROE, ROS, OM, and NM on credit rating was analyzed. Profitability ratios are closely related to activity ratios. Activity ratios inform on the effectiveness of asset management. Asset management belongs to common financial decision-making areas, which means that its influence on the creditworthiness of a company is rather indirect. Therefore, only ratios S/NW and S/FA heve been used in prior literature. Liquidity ratios show the capability of companies to pay off short-term obligations. Though, liquidity is determined by the whole economy and industry. The use of CR prevail in the presented studies, QR and CaR were rarely applied. Leverage ratios show the indebtedness of a company, and thus have an effect on ROE and business risk. They represent crucial input variables in all corporate credit rating models. The indebtedness is mostly measured as TD/TA or LTD/TA. Besides, it is also important to assess the capability of a company to pay off debt from the generated profit, i.e. by IC. Further, debt is ussually

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classified according to SS because subordinated debt is repayable only after other debts have been paid, they are more risky for the lender of the money. Market value ratios reflect how markets assess the past activity of companies, as well as their future outlook. Recovery of investment results from both dividends and share fluctuations. Share fluctuations show the risk of investment reliably. Market risk was monitored only by [65] using Beta coefficient. In other studies, priority was given to other indicators of business risk, such as TA variation or NI variation. For foreign companies, the aggregate risk of the country can be also considered. In particular, foreign companies are usually assigned a lower rating than their governments, the most creditworthy entity in a country. However, this factor is redundant when classifying only US companies. Table 9. Description of input variables BD BI BV

book debt size of bond issue book value

I IC IH

CA

cash assets

InH

CaR

cash ratio

IO

CC CF

donstruction costs cash flow

IS KMV

CL

current liabilities

Cor

correlation of stock returns with market index current ratio current assets depreciation plus amortization dividends years of consecutive dividends earnings earnings before interest and taxes

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CR CuA DA DIV DIV yrs E EBIT EBITDA

interest interest coverage number of shares held by mutual funds number of shares held by insiders net income form operations

QR RE RGR

quick ratio retained earnings revenue growth rate

ROA ROC ROE

LD

issue size KMV-Merton default probability long-term debts

return on total assets return on capital return on equity

MBV

market to book value

ROS

return on investment return on sales

MC MD IA

market capitalization market debt intangible assets

TRR S SC

total revenue ratio sales size class

MEV NCWC

market equity value non-cash working capital

SD SIC

short-term debts SIC code

NG NI

net gearing net income

P SPC

stock price subjective prospect of company subordination status

ROI

NM

net margin

SS

EPS Eq ETR EV FA FC FCFF

EBIT increased by depreciation and amortization earnings per share equity effective tax rate enterprise value fixed assets fixed costs free cash flow to firm

NW OM OR P/E P/CF PBV PD

net worth operating margin operating revenue stock price/earnings stock price/cash flow price/book value preferred dividends

TA TC TD TL var WC WL

FS HiLo

financial strenght high/low stock price

PS PR

price/sales payout ratio

total assets total capital total debts total liabilities variation working capital without loss in years

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Table 10. Input variables for corporate credit rating modelling.

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3-yr Pvar BD/TC Beta BV/E Cor CaR CF

CR DA Div Div/P EPS EPS growth EV/S

EBIT ETR EV EV/EBITDA FA/TA FCFF HiLo

IA/TA IH InH MBV MC/TD MD/TC NCWC

NCWC/S NG NI NM OR/TA OM P

P/CF P/E PR PS RE ROA ROC

ROE S S growth S/NW S/TA SC SIC

TA TC WC/TA

From the given facts, it can be concluded that key input variables of corporate credit rating are represented by the size of a company, its profitability, liquidity, and leverage ratios. However, some factors have either not been monitored yet (industry, reputation), or so far only little attention have been paid to them (asset management, market value ratios). Therefore, the design of input variables is realized as presented in Table 10. The original set contains 52 input variables. The size of companies is characterized by TA, TC, S, CF, EBIT, EV, NI, and SC. Corporate reputation (character) is expressed as the number of shares held by mutual funds (IH) and insiders (InH). Besides the industry risk, specific financial characteristics of each industry should also be considered. Therefore, information about the industries are incorporated using the SIC code. The financial ratios ROA, ROE, ROC, OM, NM, and EV/EBITDA point to the profitability of the company while S/NW, S/TA, and OR/TA represent activity ratios. Besides, the ETR is involved as it is a measure of the average rate at which a corporation is taxed on its pre-tax profits. Business situation is further represented by S growth. Trends in ETR over time can provide information about corporate operating performance and income. The asset structure of companies is specified with the share of fixed assets (FA/TA) and intangible assests (IA/TA). It is however obvious that the asset structure is affected by particular industry. Concerning the asset structure, the measures of working capital are monitored as well (NCWC, NCWC/S, WC/TA). Liquidity ratios are represented by CR and CaR, while BV/E, BD/TC, MC/TD, MD/TC, and NG stand for leverage ratios. Compared to previous studies, much more attention is paid to market value ratios. Market risk indicators play an important role as 3-year P var, Beta, Cor, and HiLo are their representatives. Moreover, several other market value ratios are monitored such as Div, Div/P, EPS, EPS growth, P, P/CF, P/E, RE, PR, and PS.

Figure 1. The frequencies of rating classes in corporate credit rating data set.

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As a result, the data set covers 52 financial and non-financial variables on 852 US companies. They were drawn from the Value Line Database and Standard & Poor’s database. The companies are labelled with rating classes obtained from the Standard & Poor’s rating agency. The rating classes with their frequencies f in the data set are presented in Figure 1. Moreover, original rating classes (AAA, AA, … , D) are merged into two rating categories (investment and non-investment rating). The investment grade involves rating classes AAA,AA, ... ,BBB, while the non-investment grade comprises rating classes BB,B,... ,D.

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4.2. Municipal Credit Rating Data Municipal credit rating is based on the analysis of four categories of variables, namely: economic, debt, financial, and administrative [64]. Economic variables include socioeconomic conditions such as population, unemployment, and local economy concentration. These variables affect the revenue and expenditure of a municipal budget. Higher population entails higher municipal tax revenue. At the same time, more populated municipalities have higher spending for infrastructure and other public goods. Higher population also guarantees future municipal revenue for the creditors. Thus, it decreases the credit risk. The change in the number of inhabitants is reported as good criterion for the economic vitality of a municipality [29], [61]. Economic growth of the municipality leads to the growing number of its inhabitants. Sudden growth of the parameter should be assessed prudently, because real trend is not needed. The income of population has an impact on the demand for public services. Populations with higher incomes requires better public goods and services. A municipality may receive additional funds resulting from taxes and higher fees for services provided. On the other hand, it is necessary to invest in better social and technical infrastructure. Municipalities with more diversified economy and more favourable social and economic conditions are better prepared for the economic recession. Debt variables include the size and structure of the debt. Ratios are often used to measure both the debt of the municipality and its ability to pay off a debt service. However, using the ratios is only effective if the parameters for comparable municipalities are available. The comparison between the municipalities illustrates the current debt and financial situation of a given municipality. Debt service (especially related to total revenue) is a crucial debt factor measuring the ability of the municipality to pay off the debt service from budget revenues. The debt service includes yearly interest and annuity payment. The value of DS/TR above a certain level can be considered a signal of the imminent debt trap. Total debt represents a gross measure of the municipality indebtedness, i.e. the extent of the accrued debt per inhabitant. Financial variables inform about the scope of budget implementation. Their values are extracted from the municipality budget. The ratio of total revenue to total expenditure reports on the quality of the budget implementation. If it is constantly greater than 1, i.e. total budget is in excess, and at the same time a growing trend is indicated, the municipality is in good financial state. The same fact holds for the current budget. Good financial standing enables the municipality to use surplus to finance its engagements. US minicipalities dispose of a high fiscal autonomy. This allows the municipalities to influence their revenues through local taxation and fees for municipal services. Municipal management chooses a combination of

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own revenue and the debt on public goods financing. The higher the fiscal autonomy of the municipality is, the smaller is the need for the debt as a financing tool. Tax collectible determins the tax capacity of municipality. Administrative factors are comprise of qualitative variables concerning office organization, qualification of employees, municipal strategy, etc. They are, however, difficult to quantify. There are several variables that inform about municipal management, e.g. tax collection rate shows municipal management quality. Municipalities can be also devided into four forms of government (i.e. selectman–town meeting, council-manager, mayor–council, and other forms of government). Consequently, the forms of government can be expressed as nominal variables. The mentioned input variables were used, in varying degrees, in prior studies. Especially, administrative variables have not been analyzed hithereto. The overview of statistically significant variables obtained in these studies is presented in Table 11. The design of input variables for the used data set is based on these results. Economic, debt, financial, and administrative categories are proposed in order to include all aspects of municipal credit rating process as presented in Table 12.

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Table 11. Statistically significant input variables for municipal credit rating in prior studies. Study [68] [6] [91] [80] [17] [29] [84] [44] [30] [81] [64]

Significant input variables TD/PO, TR/PO, UCTAX/DS BPO/PO TD, PO TR/PO, SD/TR, GP, CF SD, RPTR, OR/TR PO, OH, PV, GP GDP/PO, U, DS/CR, CR/CE, CR-CE, TR-TE PO, TD, GP TD/PO, PV, OCH, OUS TD, FI, GP ED, ATT, ENE, POG

Legend: ATT is economic attractivity, BPO is black population, CE is current expenditure, CF is cash flow, CR is current revenue, DS is debt service, ED is economic diverzification, ENE is dependence on energy, FI is agerage family income, GP is geographical position, OH is the share of old houses [%], OR is own revenue, OOH is the share of owner occupied houses [%], OUS is the share of one-unit structures [%], PO is population, POG is population growth, PV is property value, RPTR is real property tax revenue, SD is short-term debt, TD is total debt, TR is total revenue, TE is total expenditure, U is unemployment [%], and UCTAX are uncollected taxes.

Table 12. The design of input variables for municipal credit rating modelling. Economic Financial Debt Administrative

Input variables PO, POG, FI, U TR/TE, TAXR/TR, TR/PO, CR-CE, TAXC/PO DS, DS/TR, TD/PO, LD/PO TAXCR, FoG

Legend: TAXR is tax revenue, FoG is form of government, LD is long-term debt, TAXCR is tax collection rate, and TAXC is tax collectible.

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The values of the proposed input variables were obtained for 150 US municipalities. Rating classes from Moody’s rating agency are assigned to these municipalities. Frequencies of municipalities in rating classes are presented in Figure 2.

Figure 2. The frequencies of rating classes in municipal credit rating data set.

Figure 3. Model for corporate and municipal credit rating classification.

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5. Experimental Results As we know the rating classes ωi,j∈Ω, Ω={AAA, AA, ... , D}, it is possible to realize the classification problem by supervised methods. Therefore, the supervised NNs presented previously can be applied for both corporate and municipal credit rating modelling. Based on the presented facts, the model is designed for the classification of objects (corporates and municipalities) oi∈O into classes ωi,j∈Ω, Figure 3. The modelling is realized on three data sets, i.e. corporate credit rating data with both two classes (investment vs. non-investment grade) and nine classes (AAA, AA, ... , D), and municipal credit rating with four classes (Aaa, Aa, Aa, Baa). For all the models of NNs it is suitable to pre-process the data. For both data sets, data pre-processing is carried out by means of data standardization. Thereby, the dependency on units is eliminated. The preprocessed data represent the inputs of the proposed structures of NNs. Neural networks work more effectively if the input variables influence their output [66], [95]. Therefore, it is suitable to optimize the set of input variables before they are used as inputs of NNs. An easy method used previously [45] lies in selecting optimal sets of input variables following a step-wise procedure. One starts from a simple model, and then each remaining variable is added in the model. During this process, the model is modified if any classification accuracy improvement is observed. The process is iterated with the modified model until no improvement is observed. Besides, there are several other more sophisticated methods addressed to realize this optimization process, e.g. principal component analysis, gain ratio, information gain, SVMs, GAs, etc. GAs have worked well recently [46].

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Therefore, the original sets of input variables are optimized using GAs so that only significant input variables remained in the data sets. The GA optimizes the set of input variables so that it evaluates the worth of a subset of attributes by considering the individual predictive ability of each input variable along with the degree of redundancy between them. The selected input variables for all the data sets are presented in Table 13. The selected input variables are surprising for corporate credit rating, in particular. As stated above, financial variables performed best in prior studies. Key input variables of corporate credit rating have been represented by the size of a company (TA), its profitability (ROA, ROE, OM), liquidity (CR), and leverage ratios (TD/TA, LD/TA). However, the obtained results show that it is better to explain the size of companies by SC and MC. Both the number of employees (SC) and the size of capital (MC) determine the capacity of companies. Corporate reputation (character) is represented by the number of shares held by mutual funds (IH) for corporate credit rating with 9 rating classes, while the effect of conditions, or industry respectivelly (SIC), seems to be more important when classifying companies into two rating categories (investment and non-investment grade). Profitability ratios are represented only indirectly by ETR. Moreover, liquidity ratios are not presented at all. The structure of assets (FA/TA, IA/TA) is related to industry (sector). For 9 rating classes, they proved to be more effective than the nominal input variable SIC. The input variable MD/TC stands for leverage ratios. The rest of the input variables are associated with financial markets. The input variables Beta and Cor show the relation between corporate and market risk. The risk of stocks is further represented by HiLo, while the dividend yield Div/P shows the return of shareholders. This variable seems to be more importatnt than e.g. P/E or P/CF. Table 13. Optimized sets of input variables.

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Credit rating data set Corporate (9 rating classes) Corporate (2 rating classes) Municipal

Input variables SC, MC, IH, ETR, FA/TA, IA/TA, MD/TC, Beta, HiLo, Cor, Div/P SC, SIC, MD/TC, HiLo, Cor, Div/P PO, FI, TAXR/TR

Table 14. Mean values of input variables for corporate credit rating . Rating Class AAA AA A BBB BB B CCC CC D

SC

MC

10.00 255859 9.74 64325 9.49 33625 9.00 10660 8.30 4201 6.98 2006 5.41 909 6.00 5082 5.57 376

FA/TA IA/TA 0.186 0.243 0.255 0.316 0.301 0.332 0.255 0.288 0.385

0.161 0.153 0.187 0.187 0.237 0.236 0.251 0.264 0.120

IH 0.543 0.630 0.667 0.662 0.583 0.519 0.448 0.659 0.550

ETR MD/TC Beta HiLo Div/P

Cor

0.280 0.319 0.296 0.298 0.306 0.229 0.100 0.188 0.220

0.741 0.752 0.744 0.718 0.587 0.515 0.378 0.462 0.447

0.140 0.160 0.175 0.232 0.253 0.431 0.662 0.893 0.705

0.857 0.948 0.986 1.022 1.158 1.171 1.160 1.333 1.130

0.119 0.147 0.188 0.210 0.286 0.338 0.476 0.495 0.570

0.025 0.024 0.021 0.02 0.008 0.007 0.006 0.013 0.023

The mean values for the input variables of corporate credit rating data sets are shown in Table 14. The higher the size of company (SC, MC) is the better is the credit rating. On contrary, higher debt MD/TC and financial risk (Beta, HiLo, Cor) indicate worse credit rating. The effect of other input variables is ambiguous. Besides, the frequencies of

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companies in industries is shown in Table 15. Manufacturing, services and transportation industries prevail in the data set. Table 15. Frequencies of companies according to industries (SIC). Industry Construction Finance Manufacturing Mining Public Administration Retail Trade Services Transportation Wholesale Trade

Frequency 14 79 432 48 32 65 169 179 3

Concerning municipalities, only three input variables are left in the data set, i.e. the size of municipality (PO), wealth of municipality (FI), and the fiscal autonomy (TAXR/TR). Neither the debt variables nor the balance of budget played an important role for the used data set. According to the mean values for each rating class (Table 16), a better credit rating is linked with the wealth and fiscal autonomy of the municipality. Table 16. Mean values of input variables for municipal credit rating.

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Rating Class AAA AA A BBB

PO 40208.92 25333.71 16018.96 39811.38

FI 55754.85 32260.37 26425.14 25071.38

TAXR/TR 0.84 0.79 0.67 0.65

The results for the two-class corporate credit rating problem are presented in Table 17. With a two-class problem it is possible, except for the classification accuracy CA, to follow also other indicators of classification quality, such as sensitivity, specificity, and ROC (Receiver Operating Characteristic) curve, where the area under ROC curve shows the classification quality. For this case, best results were obtained using PNNs and SVMs, while statistical methods (LDA, LR) and FFNNs were significantly outperformed. The classification accuracy, higher than 88%, can be held as superior to previous studies for the two-class credit rating problem. Moreover, these results were obtained using only 6 input variables. The classification accuracies 83.3% to 88% were achieved using FFNNs by [11], [13], [24], [86], [87]. Nevertheless, the classification realized by [86], [87] was negatively infuenced by a low number of companies in the testing set. For FFNNs, we can conclude that the results obtained here (CAtest=83.74%) are in line with other studies reported above. The experiments were realized for different settings of NNs’ parameters. As a result, optimum values of parameters were found as follows: FFNN (5 neurons in the hidden layer, logistic activation functions, learning rate of 0.05), PNN (Gaussian kernel function), RBFNN (50 neurons in the hidden layer), SVM (RBF kernel function, C=70.7, Gamma=0.86, 317 support vectors), GHMD (quadratic function with two variables), and CCNN (2 Gaussian neurons in the hidden layer, 1 output neuron).

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Table 17. Classification results for two-class corporate credit rating problem. Model FFNN PNN RBF SVM GHMD CCNN LDA LR

CAtest 83.74 88.54 85.60 87.37 84.92 84.72 83.35 83.35

Sensitivity 83.77 87.50 84.87 86.84 83.55 82.02 84.65 84.65

Specificity 83.22 89.38 86.19 87.79 86.02 86.90 82.30 82.30

ROC 0.889 0.936 0.929 0.932 0.923 0.922 0.913 0.913

Legend: CAtest is classification accuracy on testing data and ROC is area under ROC curve.

Further, it is obvious that similar classification accuracy was obtained for both rating classes by the PNN (89.4% for investment grade and 88.5% for non-investment grade) as presented in the confusion matrix in Table 18. Here, actual and predicted classes are compared. The model classifies both classes correctly. Table 18. Confusion matrix of PNN for two-class corporate credit rating problem.

Actual

IG NG Total

Predicted IG NG Total CA [%] 505 60 565 89.4 57 399 456 87.5 562 459 1021 88.5

Legend: IG stands for investment grade and NG is non-investment grade.

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Table 19. Classification accuracy CAtest for nine-class corporate credit rating. Data set Corporate (9-class)

FFNN 51.71

PNN 58.47

RBF 58.28

SVM 55.63

GHMD 54.46

CCNN 57.69

LDA LR 55.83 53.28

We can expect that the classification accuracy CAtest will be lower for credit rating problems with more classes than it is for the two-class problem. Again, PNN show best results concerning classification accuracy (CAtest=58.47%) for corporate credit rating, see Table 19. Similar results are obtained also for RBFNNs as a classification accuracy of higher than 58% was obtained. A considerably worse classification was realized by the FFNN model (CAtest=51.71%). The rating scale Ω with more than nine rating classes was used only by [70] with the classification accuracy of CAtest=36.2%. Furthermore, in the case of six-class credit rating problem, the classification accuracies of 66.7% [65], 56.7% [16], and 55.2% [51] (see Table 4) were obtained. Compared to these results, a similar classification quality was achieved for nine-class rating problem in this study. Again, the optimum values of NNs’ parameters are reported: FFNN (10 neurons in hidden layer, logistic activation functions, learning rate of 0.05), PNN (Gaussian kernel function), RBFNN (100 neurons in hidden layer), SVM (RBF kernel function, C=12.8, Gamma=0.11, 902 support vectors), GHMD (quadratic function with two variables), and CCNN (2 Gaussian neurons in hidden layer, 1 output neuron).

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The classification results for the best model (PNN) is presented in the confusion matrix (Table 20). The results show that the model correctly classifies rating classes BBB, BB, B, and CCC, while the results become worse facing the extreme rating classes. In this case the model classifies only a low percentage of companies correctly (28.6% for AAA, 14.3% for D). Default of company D is obviously difficult to predict. The model does not keep necessary data at disposal to distinguish these rating classes. The results are also affected by the fact that the distribution of data into rating classes is unbalanced, i.e. the numbers of companies in the rating classes vary significantly. The comparison of these results with the studies concerning default prediction, is difficult to realize as they used only balanced classes, i.e. the distribution of defaulted and non-defaulted firms was even. Classification accuracy of more than 80% is obtained using SVM with municipal credit rating data set, see Table 21. The comparison to prior studies can be realized only with the MDA method, as it was mostly used for municipal credit rating modelling. For a three-class problem, classification accuracy on testing data CAtest ranges from 55% [17] to 66% [84], for four-class problem 62%-71% [29], [91], and for five-class problem 46%-63% [15], [72]. The results obtained using statistical methods (69.68% for MDA, 70.32% for LR) correspond to previous results, while NNs achieve significantly better classification quality. Table 20. Confusion matrix of PNN for nine-class corporate credit rating problem. Rating Class

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Actual

AAA AA A BBB BB B CCC CC D

AAA 2 1 1 1 0 0 0 0 0

AA 2 9 2 1 0 0 0 0 0

A 2 10 67 29 4 3 0 0 0

Predicted BBB BB 1 0 7 0 65 1 197 50 72 173 14 85 1 1 0 1 0 2

B 0 0 0 7 31 141 16 1 4

CCC 0 0 0 1 0 4 7 1 0

CC 0 0 0 0 0 0 1 0 0

D 0 0 0 0 0 1 1 0 1

CA [%] 28.6 33.3 49.3 68.9 61.8 56.9 25.9 0.0 14.3

Table 21. Classification accuracy CAtest for four-class municipal credit rating problem. Data set Municipal (4-class)

FFNN 76.13

PNN 76.13

RBF 73.55

SVM 80.65

GHMD 77.42

CCNN 72.90

LDA 69.68

LR 70.32

The settings of NNs’ parameters are as follows: FFNN (2 neurons in hidden layer, logistic activation functions, learning rate of 0.05), PNN (Gaussian kernel function), RBFNN (100 neurons in hidden layer), SVM (RBF kernel function, C=71.3, Gamma=0.14, 103 support vectors), GHMD (quadratic function with two variables), and CCNN (2 Gaussian neurons in hidden layer, 1 output neuron). Again, detailed information on the classification by SVM can be presented using the confusion matrix (Table 22). It is evident that the SVM model classified rating classes Aaa, Aa, and A correctly, while all municipalities in Baa rating class were classified incorrectly. This evidence confirms the results obtained for corporate credit rating problem. Usually, classification results are supplemented with an one-away credit rating classification. It is important to classify both companies and municipalities into the closest

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rating class. The classification with one class error is presented in Table 23. Regarding this classification, the best results are obtained using RBFNNs and FFNNs for companies, and by PNNs and CCNNs for municipalities. Table 22. Confusion matrix of SVM for four-class municipal credit rating problem. Rating Class

Actual

Aaa Aa A Baa

Aaa 8 0 0 0

Predicted Aa A Baa CA [%] 4 1 0 61.5 38 11 0 77.6 6 79 0 92.9 3 5 0 0.0

Table 23. One-away classification accuracy CAtest for corporate and municipal credit rating data sets.

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Data set Corporate Municipal

FFNN 94.71 97.42

PNN 94.61 99.35

RBF 95.30 98.71

SVM 93.44 97.42

GHMD 91.87 98.71

CCNN 93.24 99.35

MDA 91.67 98.06

LR 92.26 96.77

For a user, it is also important to get information about the process of classification, i.e. how the NNs obtain the results. However, the possibilities of the interpretation of NNs are bounded. The knowledge stored in synapse weights are represented by figures ranging from 0 to 1. Thus, it is difficult to interpret them in a way understandable to a user. The goal of the model’s interpretation consists in the evaluation of input variables’ effects on the results of classification. In previous studies on credit rating modelling, this issue was addressed only by [45]. The simplest way to solve this problem is a step-wise procedure constisting in successive extraction of input variables and, at the same time, in monitoring its effect on classification accuracy. There are however more sophisticated methods for the realization of this problem. For example, [45] tried to find out the relative importance of selected financial variables to the credit rating problem using Garson’s measure of relative strength of inputs to the NNs. It is also possible to extract the IF-THEN rules from the NNs [38]. Interpretation capability of NNs can be improved in this way. In this work, sensitivity analysis is used for the evaluation of input variables’ contribution. The method works as follows. First, the misclassification accuracy for the model is calculated using the actual data values for all input variables. Then for each input variable, it randomly permutes (rearranges) the values of the input variable and computes the misclassification accuracy for the model using the permuted values. The difference between the misclassification accuracy with the correctly ordered values and the misclassification accuracy for the permuted values is used as the measure of importance of the input variable. As a result, the contribution of the most important input variable is 100, and the contribution of other input variables is related to this variable. The resulting contributions of input variables on corporate and municipal credit rating data sets are presented in Table 24 for two-class corporate credit rating, Table 25 for nineclass corporate credit rating, and Table 26 for municipal credit rating. The most important variable for both the two-class and the nine-class corporate credit rating problem is the size class (SC). It is obvious that the SC is more significant than the MC in most cases, as both

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Petr Hájek

input variables measure the size of company. In the two-class corporate credit rating, other input variables have similar contribution, i.e. the indebtedness measure MD/TC, the dividend yield DIV/P, the risk measures HiLo and Cor, as well as the industry expressed as the SIC code. For the nine-class corporate credit rating problem, the size of the company is the most important input variable (SC, MC). Further, the input variables MD/TC and SIC play important roles. As a result, we can conclude that the size of companies, their debt, and industry are the most important factors in corporate credit rating process realized by Standard & Poor’s rating agency. However, there are several other factors including asset management, shareholder structure, profitability, and financial risks which serve for improving credit rating evaluation process. Table 24. Contributions of input variables for two-class corporate credit rating. FFNN PNN RBF SVM GHMD CCNN MDA LR

SC 100 100 100 100 100 100 100 100

MD/TC 53.2 61.8 55.9 44.2 10.3 36.2 40.5 29.0

HiLo 66.6 25.7 25.5 50.3 10.9 76.4 44.3 39.7

Div/P 48.0 35.2 42.4 38.1 45.6 63.8 17.7 29.7

Cor 54.6 66.8 44.6 37.4 29.1 28.2 54.4 46.5

SIC 58.3 31.0 43.7 57.1 0.0 74.8 30.4 43.6

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Table 25. Contributions of input variables for nine-class corporate credit rating. SC FFNN 90.7 PNN 100 RBF 100 SVM 62.2 GHMD 74.2 CCNN 100 MDA 100 LR 100

MC FA/TA IA/TA 48.8 55.1 35.0 23.4 10.0 1.5 23.0 10.8 10.8 100 19.6 25.2 100 3.1 1.0 51.7 13.9 5.3 58.6 19.5 25.2 38.9 9.7 11.6

IH ETR MD/TC Beta HiLo Div/P Cor SIC 45.9 49.4 54.1 51.6 59.8 26.2 49.7 100 3.7 16.7 54.4 14.5 10.1 41.7 28.1 41.3 10.8 13.7 57.6 6.5 21.6 12.9 32.4 69.1 11.9 27.7 31.2 19.7 17.1 31.0 24.4 35.1 0.2 25.9 16.4 3.9 11.1 10.4 31.9 10.1 3.7 16.3 70.0 17.6 27.6 4.1 36.7 69.4 3.5 17.2 55.2 17.2 0.0 0.0 48.3 59.9 5.8 19.3 47.4 26.7 6.5 9.6 56.8 48.5

Table 26. Contributions of input variables for municipal credit rating. FFNN PNN RBF SVM GHMD CCNN MDA LR

PO 100 100 100 100 91.3 100 76.2 46.7

FI 51.1 50.8 97.6 82.8 100 70.0 100 89.4

TAXR/TR 94.7 48.4 16.5 48.3 12.4 45.4 57.1 100

In the case of municipalities, the rating process of Moody’s rating agency can be simulated using only three input variables presented in Table 26. The size of the municipality represented by its population (PO), and the wealth of its population (FI) show the highest

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contribution. However, municipal financial autonomy and the capability of collecting taxes is also important in municipal credit rating process.

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6. Conclusion The chapter introduces the problem of corporate and municipal credit rating process. This process is presented as a classification problem. Prior studies were reported in order to get an overview of obtained results and input variables used. The results showed that there are several crucial problems in the credit rating process modelling. First, data availability was a critical point of concern in prior studies. Sufficient number of subjects assessed by rating agencies and, at the same time, values of important input variables must be at hand when modelling credit rating process. Without a large data set, the use of input variables is also limited. Next point lies in the selection of input variables as rating agencies do not publish the details on their credit rating process as they stress out the subjectivity of the evaluation process. Further, the appropriate method has to be applied in order to model the complex relations among the input variables. Neural networks worked well in previous works. Finally, the model should be intrepreted in a suitable way which is difficult when using NNs. The different models of neural networks were designed in the chapter in order to realize the presented problems. Data were collected for US companies and municipalities, and the assessed subjects were labelled by rating classes from Standard & Poor’s and Moody’s rating agencies. The selection of input variables was realized as a two-step procedure. First, the original sets of input variables were proposed based on previous studies. Then genetic algorithms were eployed with the aim of reducing the original sets. These input variables were used for training and testing NNs’ models. The goal of the modelling consisted in achieving the highest classification accuracy on testing data. From the presented results it is evident that different models of NNs are appropriate for different data sets. The PNNs and SVMs showed best results for the two-class corporate credit rating problem, while the PNNs and the RBFNNs worked best for the nine-class corporate credit rating problem. Best classfication results were obtained by SVMs in the case of municipal credit rating data set. Moreover, the contribution of input variables was studied for each model and, at the same time, for different numbers of rating classes. This way, the gained results can be compared across all models of NNs as the contributions of input variables show their relative importance in the models. The models present an easier conception of the corporate and municipal credit rating evaluation for corporate and public administration managers, banks, investors, or rating agencies.

Acknowledgements This work was supported by the scientific research of Czech Science Foundation, under Grant No: 402/09/P090 with title Modelling of Municipal Finance by Computational Intelligence Methods.

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References [1] Abe, S. (2005). Support vector machines for pattern classification. London: SpringerVerlag. [2] Ahn, H. & Kim, K. J. (2005). Combining pairwise SVM classifiers for bond rating. In KMIS International Conference, (586-590). [3] Altman, E. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The Journal of Finance, 9, 589-609. [4] Altman, E. & Katz, S. (1976). Statistical bond rating classification using financial and accounting data. In M. Schiff, & G. Sorter (Eds.), Topical research in accounting. NYU Press. [5] Ammar, S., Duncombe, W. & Hou, Y. (2001). Using fuzzy rule-based systems to evaluate overall financial performance of governments: An enhancement to the bond rating process. Public Budgeting and Finance, 21, 91-110. [6] Aronson, J. R. & Mardsen, J. R. (1980). Duplicating Moody's municipal credit ratings. Public Finance Quarterly, 8, 97-106. [7] Beaver, W. (1966). Financial ratios as predictors of failures. Journal of Accounting Research, 5, 71-111. [8] Belkaoui, A. (1980). Industrial bond rating: A new look. Financial Management, 9, 44-51. [9] Boone, D. S. & Roehm, M. (2002). Evaluating the appropriateness of market segmentation solutions using artificial neural networks and the membership clustering criterion. Marketing Letters, 13, 317-333. [10] Brabazon, A. & Keenan, P.B.(2004). A hybrid genetic model for the prediction of corporate failure. Computational Management Science, 1, 293-310. [11] Brabazon A. & O’Neill M. (2006). Credit classification using grammatical evolution. Informatica, 30, 325-335. [12] Brabazon, A., O’Neill M. & Matthews R. (2002). Grammatical evolution and corporate failure prediction. Proc. Genetic and Evolutionary Computation Conf. (1011-1019). New York, USA: Morgan Kaufmann. [13] Brennan, D. & Brabazon, A. (2004). Corporate bond rating using neural networks. In Proc. of the Conf. on Artificial Intelligence (161-167). Las Vegas, USA. [14] Capeci, J. (1991). Credit risk, credit ratings and municipal bond yields : A panel study. National Tax Journal, 44, 42-56. [15] Carleton, W. T. & Lerner, E. M. (1969). Statistical scoring of municipal bonds. Journal of Money, Credit and Banking, 11, 750-764. [16] Chaveesuk, R. & Srivaree-Ratana, C. (1999). Alternative neural network approaches to corporate bond rating. Journal of Engineering Valuation and Cost Analysis, 2, 117-131. [17] Copeland, R. M. & Ingram, R. W. (1982). The association between municipal accounting information and bond rating changes. Journal of Accounting Research, 20, 275-289. [18] Cristianini, N. & Shawe-Taylor, J. (2000). An introduction to support vector machines and other kernel-based learning methods. Cambridge: Cambridge University Press. [19] Deakin, E. (1972). A discriminant analysis of predictors of business failure. Journal of Accounting Research, 1, 167-179.

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Credit Rating Modelling by Neural Networks

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[20] Delahunty, A. & OCallaghan, D. (2004). Artificial immune systems for the prediction of corporate failure and classification of corporate bond ratings. Dublin: University College Dublin. [21] Dimitras, A., Slowinski, R. & Susmaga, R. (1999). Business failure prediction using rough sets. European Journal of Operational Research, 114, 263-280. [22] Doumpos, M. & Pasiouras, F. (2005). Developing and testing models for replicating credit ratings: A multicriteria approach, Computational Economics, 25, 327-341. [23] Duffie, D. & Singleton, K. J. (2003) Credit risk: Pricing, management, and measurement. Princeton: Princeton University. [24] Dutta, S. & Shekhar, S. (1988). Bond rating: A non-conservative application of neural networks. Proc. of the IEEE International Conf. on Neural Networks, (443-450). [25] Ederington, H. L. (1985). Classification models and bond ratings. Financial Review, 20, 237-262. [26] Eklund, T., Back, B. & Vanharanta, H. (2003). Using the self-organizing map as a visualization tool in financial benchmarking. Information Visualization, 2, 171-181. [27] Fahlman, S. E. & Labiere, Ch. (1990). The cascade-correlation learning architecture. Advances in Neural Information Processing Systems, 2, 524-532. [28] Farlow, S. J. (1984) Self-organizing methods in modelling - GMDH type algorithms. New York: Marcel Dekker. [29] Farnham, P. G. & Cluff, G. S. (1982). Municipal bond ratings: New directions, new results. Public Finance Quarterly, 26, 427-455. [30] Farnham, P. G. & Cluff, G. S. (1984). Standard and Poor's vs. Moody's: Which city characteristics influence municipal bond ratings? Quarterly Review of Economics and Business, 24, 72-94. [31] Fisher, L. (1959). Determinants of risk premiums on corporate bonds. Journal of Political Economy, 217-237. [32] Galindo, J. & Tamayo, P. (2000). Credit risk assessment using statistical and machine learning: Basic methodology and risk modelling applications. Computational Economics, 15, 107-143. [33] Garavaglia, S. (1991). An application of a counter-propagation neural networks: Simulating the Standard & Poor’s corporate bond rating system. Proc. of the First International Conference on Artificial Intelligence on Wall Street, (278-287). [34] Gentry J., Newbold P. & Whitford D. (1985). Classifying bankrupt firms with funds flow components. J. Account. Res., 23, 146-160. [35] Gentry, J. A. & Whitford, D. T. (1988). Predicting industrial bond ratings with a probit model and funds flow components. Financial Review, 23, 269-286. [36] Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. New York: Addison-Wesley. [37] Granger, C. W. J. (1991). Developments in the nonlinear analysis of economic series. Scandinavian Journal of Economics, 93, 263-281. [38] Hajek, P. & Olej, V. (2008). Municipal creditworthiness modelling by Kohonen’s selforganizing feature maps and fuzzy logic neural networks. In V. Kurkova, R. Neruda, & J. Koutnik (Eds.), Lecture Notes in Artificial Intelligence (533-542). Heidelberg, Germany: Springer-Verlag.

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[39] Hajek, P. & Olej, V. (2007). Municipal creditworthiness modelling by clustering methods. In Margaritis, Illiadis (Eds.), Proc of the 10th International Conf. on Engineering Applications of Neural Networks, (168-177). Thessaloniky, Greece. [40] Haykin, S. (1999). Neural networks: A comprehensive foundation. New Jersey: Prentice-Hall. [41] Hempel, G.H. (1973). Quantitative borrower characteristics associated with defaults on municipal general obligations. Journal of Finance, 28, 523-530. [42] Herbrich, R., Keilbach, M. & Graepfel, T. (1999). Neural networks in economics. Advances In Computational Economics, 11, 169-196. [43] Horrigan, J. L. (1966). The determination of long term credit standing with financial ratios, empirical research in accounting: selected studies. Journal of Accounting Research, 4. [44] Horton, J. J. (1970). Statistical classification of municipal bonds. Journal of Bank Research, 3, 29-40. [45] Huang, Z. & Chen, H. (2004). Credit rating analysis with support vector machines and neural networks: A market comparative study. Decision Support Systems, 37, 543-558. [46] Huang, Ch. L., Chen, M. Ch. & Wang, Ch. J. (2007). Credit scoring with a data mining approach based on support vector machines. Expert Systems with Applications, 33, 847-856. [47] Hwang, R. Ch. & Cheng, K. F. (2008) On multiple-class prediction of issuer credit ratings. Applied Stochastic Models in Business and Industry, Wiley Interscience. [48] Jackson, J. D. & Boyd, J. W. (1988). A statistical approach to modelling the behavior of bond raters. The Journal of Behavioral Economics, 17, 173-193. [49] Kamstra, M., Kennedy, P. & Suan, T. K. (2001). Combining bond rating forecasts using logit. The Financial Review, 37, 75-96. [50] Kaplan, R. S. & Urwitz, G. (1979). Statistical models of bond ratings: a methodological inquiry. The Journal of Business, 52, 231-261. [51] Kim, J. W. (1993). Expert systems for bond rating: A comparative analysis of statistical, rule-based and neural network systems. Expert Systems, 10, 167-171. [52] Kim, K. S. (2005). Predicting bond ratings using publicly available information. Expert Systems with Applications, 29, 75-81. [53] Kim, K. S. & Han, I. (2001). The cluster-inndexing method for case-based reasoning using self-organizing maps and learning vector quantization for bond rating cases. Expert systems with applications, 21, 147-156. [54] Kish, R. J., Hogan, K. M. & Olson, G. (1999). Does the market perceive a difference in rating agencies? The Quarterly Review of Economics and Finance, 39, 363-377. [55] Kumar, N., Krovi R. & Rajagopalan B. (1997). Financial decision support with hybrid genetic and neural based modelling tools. Europ. J. Oper. Res., 103, 339-349 [56] Kun, C. L. & Ingoo, H. (1996). Hybrid neural network models for bankruptcy predictions. Decision Support Systems, 18, 63-72. [57] Kuo, R. J. (2001). A sales forecasting system based on fuzzy neural network with initial weights generated by genetic slgorithm. European Journal of Operational Research, 129, 496-517. [58] Kwon, Y. S. & Han, I. G. (1997). Ordinal pairwise partitioning (OPP) approach to neural networks training in bond rating. Intelligent Systems in Accounting, Finance and Management, 6, 23-40.

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Credit Rating Modelling by Neural Networks

41

[59] Laitinen, E. K. (1999). Predicting a corporate credit analyst’s risk estimate by logistic and linear models. International Review of Financial Analysis, 8, 97-121. [60] Lee, Y. Ch. (2007). Application of support vector machines to corporate credit rating prediction. Expert Systems with Applications, 33, 67-74. [61] Lipnick, L. H. & Rattner, Y. (1999). The determinants of municipal credit quality. Government Finance Review, 12, 35-41. [62] Liu, P. & Seyyed, F. J. (1991). The impact of socioeconomic variables and credit ratings on municipal bond risk premia. Journal of Business Finance and Accounting, 18, 735746. [63] Loviscek, L. A. & Crowley, F. D. (1990). What is in a municipal bond rating? The Financial Review, 25, 25-53. [64] Loviscek, L. A. & Crowley, F. D. (2003). Municipal bond ratings and municipal debt management. New York: Marcel Dekker. [65] Maher, J. J. , & Sen, T. K. (1997). Predicting bond ratings using neural networks: a comparison with logistic regression. Intelligent Systems in Accounting, Finance and Management, 6, 59-72. [66] Marose, R. A. (1990). A financial neural network application. AI Expert, 5, 50-53. [67] Michalak, K., Lipinski, P. (2005). Prediction of high increases in stock prices using neural networks. Neural Network World, 15, 359-366. [68] Michel, A. J. (1977). Municipal bond rating: Discriminant analysis approach. Journal of Financial and Quantitative Analysis, 12, 587-598. [69] Miller, G. J. (2003). Handbook of debt management. New York: Marcel Dekker. [70] Moody, J. & Utans, J. (1995). Architecture selection strategies for neural networks application to corporate bond rating. In A. Refenes (Ed.), Neural Networks in the Capital Markets (277–300). Chichester, UK: Wiley. [71] Moon, Ch. G. & Stotsky, J. G. (1993). Municipal bond rating analysis: Sample selectivity and simultaneous equations bias. Regional Science and Urban Economics, 29, 29-50. [72] Morton, T. G. (1975). A comparative analysis of Moody’s and Standard and Poor’s municipal bond ratings. Review of Business and Economic Research, 1, 74-81. [73] Ohlson, J., (1980). Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 1, 109-131. [74] Olej, V. (2002). Prediction of gross domestic product development by frontal neural networks with learning process on the basic genetic and eugenic algorithms. Neural Network World, 12, 279-292. [75] Olej, V. & Hajek, P. (2007). Hierarchical dtructure of fuzzy inference systems design for municipal creditworthiness modelling. WSEAS Transactions on Systems and Control, 2, 162-169. [76] Park, J. & Sandberg, I. W. (1993). Approximation and radial basis function network. Neural Comput., 5, 305-316. [77] Pinches, G. E. & Mingo, K. A. (1973). A multivariate analysis of industrial bond ratings. Journal of Finance, 28, 1973 1-18. [78] Pinches, G. E. & Mingo, K. A. (1975). The role of subordination and industrial bond ratings. The Journal of Finance, 30, 201-206. [79] Pogue, T. F. , & Soldofsky, R. M. (1969). What’s in a bond rating? Journal of Financial and Quantitative Analysis, 4, 201-228.

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Petr Hájek

[80] Raman, K. K. (1981). Financial reporting and municipal bond rating changes. The Accounting Review, 56, 911-926. [81] Rubinfield, D. (1973). Credit ratings and the market for general obligation municipal bonds. National Tax Journal, 26, 17-27. [82] Saeys, Y, Inza, I, & Larrañaga, P, (2007). A review of feature selection techniques in bioinformatics. Bioinformatics, 23, 2507-2517. [83] Sender, H. (2003). Moody’s swings, so why are some analysts cautious? The Wall Street Journal, January, 6, C1-C3. [84] Serve, S. (2001). Assessment of local financial risk: The determinants of the rating of european local authorities - An empirical study over the period 1995-1998. Lugano: EFMA Lugano Meetings. [85] Shin, K. S. & Han, I. (2001). A case-based approach using inductive indexing for corporate bond rating. Decision Support Systems, 32, 41-52. [86] Singleton, J. C. & Surkan, A. J. (1990). Neural networks for bond rating improved by multiple hidden layers. Proc. of the IEEE International Conf. on Neural Networks, (163168). [87] Singleton, J. C. & Surkan, A. J. (1995). Bond rating with neural networks. In A. Refenes (Ed.), Neural Networks in the Capital Markets (301-307). Chichester: Wiley. [88] Smith, T. (1992). Accounting for Growth. London: Century Business. [89] Speckt, D. F. (1990). Probabilistic neural networks. Neural Networks, 3, 109-118. [90] Standard and Poor’s (2002). Statement at US SEC public hearing on the role and function of credit rating agencies in the US securities markets. New York: Standard and Poor’s Rating Services. [91] Stock, D. & Robertson, T. (1981). Improved techniques for predicting municipal bond ratings. Journal of Bank Research, 12, 153-160. [92] Thieme, R. J., Song, M. & Calantone, R. J. (2000). Artificial neural network decision support systems for new product development project selection. Journal of Marketing Research, 37, 499-507. [93] Vapnik, V. N. (1995). The nature of statistical learning theory. New York: SpringerVerlag. [94] West, R. R. (1970). An alternative approach to predicting corporate bond ratings. Journal of Accounting Research, 8, 118-125. [95] Wong, B. K., Lai, V. S. & Lam, J. A. (2000). Bibliography of neural network business applications research: 1994-1998. Computers And Operations Research, 27, 1045-1076. [96] Ziebell, M. T. & Rivers, M. J. (1992). The decision to rate or not to rate: The case of municipal bonds. Journal of Economics and Business, 44, 301-316. [97] Zmijewski, M. (1984). Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 59-82.

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Chapter 2

STICKY CREDIT SPREADS, MACROECONOMIC ACTIVITY AND EQUITY MARKET VOLATILITY Yan Li1 and James M. Steeley2,* 1

2

BNP Paribas, Hong Kong Aston Business School, Aston University, Birmingham, UK

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Abstract We uncover high persistence in credit spread series that can obscure the relationship between the theoretical determinants of credit risk and observed credit spreads. We use a Markovswitching model, which also captures the stability (low frequency changes) of credit ratings, to show why credit spreads may continue to respond to past levels of credit risk, even though the state of the economy has changed. A bivariate model of credit spreads and either macroeconomic activity or equity market volatility detects large and significant correlations that are consistent with theory but have not been observed in previous studies.

Introduction Explaining the variation in credit spreads is one of the major concerns in the current research and practitioner literature devoted to credit risk. Theoretically, macroeconomic conditions and equity market volatility should both make a strong contribution. Bernanke and Gertler (1995) and Bernanke and Lown (2000) suggest that there is an intimate relation between economic activity and the credit condition of households and firms. Asset prices rise during an economic boom and banks extend credit at more favourable rates. Recessions that lead to declining asset prices and a deterioration of corporate balance sheets lead banks to restrict credit and so credit spreads rise. In Merton’s (1974) corporate bond pricing model (1974), which falls within the theoretical framework of the Black-Scholes-Merton option pricing model, high volatility increases credit spreads and low volatility reduces spreads. Despite the force of these theoretical models, empirical research has had surprising difficulty in linking credit spreads with their theoretical determinants. Variables such as equity volatility and macroeconomic activity have displayed rather limited explanatory

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power, especially for high rating firms. Collin-Dufresne, Goldstein and Martin (2001) show that default probability, equity volatility, and the debt/equity ratio can only explain a small part of the variation of credit spreads. A subsequent principal components analysis of the regression residuals showed that they were driven by a single common factor, but the authors were unable to attribute it to known systematic variables such as the Fama-French (1993) factors, the VIX index and a default premium index. Elton, Gruber, Argawal and Mann (2001) find that a measure of expected default accounts for a surprisingly small fraction of the credit spreads, but the residuals can, in part, be explained by the Fama-French factors. The adjusted R² of their regressions using these factors are, however, very low, typically between zero and ten percent for high rating bonds. Huang and Huang (2003) calibrate a set of structural models and find that credit risk can only account for 20-30 percent of the variation of credit spreads with high ratings. They attribute the residuals to liquidity risk. Duffie and Singleton (2002) explore the dynamic impact of an index of consumer confidence, the S&P500 index and interest rates to the level of a credit spread index (the BAA yield over the Treasury rate). Even though the credit spread reacts negatively to the shocks of all of these systematic factors, the response function is within the two-standard-deviation band for a measure of consumer confidence and only slightly beyond the band for the S&P500 variable. Liu, Longstaff and Mandell (2000) also show that liquidity dominates the variations of credit spreads in swap market. Research that is more recent finds that some other proxies for equity volatility and macroeconomic activity increase their contribution to explaining credit spreads. Huang and Kong (2003) examine a range of credit spread indices. They show that systematic factors, such as the Russell 2000 historical return volatility and the Conference Board composite leading and coincident indicators have a significant impact on the contemporaneous changes in credit spreads, especially for high-yield corporate bonds. For high rating credit spreads, the adjusted R² can be as high as 27.13%. Campbell and Taksler (2003) decompose a firm’s equity volatility into market-wide and idiosyncratic components and find that the latter can explain as much as one third of the variations of credit spreads. There are several potential weaknesses of the methods pursued in above research that, as we shall argue, could explain the difficulty in finding strong empirical support for the structural theoretical models of credit spreads. First, most of the papers analyze credit spreads at daily, weekly or monthly frequencies, yet the credit quality of high rating firms is remarkable for its stability. The probability of remaining in the same rating in one year’s time for a typical AAA rating firm is 90.81%, for an AA firm is 90.65% and for an A firm is 91.05% (J. P. Morgan, Inc., 1995). The high probability of remaining in the same rating within one year time does not mean, of course, that the credit quality of the firm will remain the same; immediate bankruptcy and downgrade could occur even to the highest rating firms. However, substantial changes to the credit quality of high rating firms are likely to be relatively low frequency events with a short time period. Over such short time periods, the small changes of credit spreads that are observed are more likely to be dominated by high frequency factors, such as liquidity and other non-credit risk related events. Therefore, it may prove difficult to identify the contribution of credit quality, and its structural economic determinants, to changes in credit spread using an implicitly high-frequency approach. Second, many researchers, including Elton, Gruber, Argawal and Mann (2001) and Collin-Dufresne, Goldstein and Martin (2001), Huang and Kong (2003), have examined the change, rather than the level of credit spreads. By contrast, the theoretical models refer to the

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latter rather than the former. Baxter (1994) shows that a first-difference filter can remove nearly all of the trend components and most of the cyclical variations in levels data. What one may end up with after taking first differences, therefore, is the irregular movement of the data. The limited contribution of the structural economic variables to the change of credit spread that has been observed is to be expected. Third, the sample periods that have been examined are usually very limited. If the structural variables have a slow moving influence over credit spreads it will be important to use as long a sample period as possible. For example, Elton, Gruber, Argawal and Mann (2001) and Collin-Dufresne, Goldstein and Martin (2001) use monthly data over the period 1986-1997, during which only one short economic recession happened. In Huang and Kong (2003), the sample period of their weekly data is even shorter, covering only 1997-2002. Although this further shortening of the sample period might be expected, given our line of reasoning, to reduce the influence of economic conditions on credit spreads, Huang and Kong (2003) found an increase in explanatory power. This is, however, likely to be a sample specific result arising from the clustering of low frequency credit quality related events such as the financial crisis of 1998, the economic recession of 2001 and the economy slow down in 2002 within this short sample period. The purpose of this paper, therefore, is to examine the low frequency movements of credit spreads of high credit ratings and their relation with those of the structural economic variables, such as the industrial output and the market volatility, and to do so over a relatively long sample period. We conjecture that a firm's credit status is relatively stable but may experience infrequent changes of credit quality. At this low frequency credit risk may play a more important role in the credit spreads than at a high frequency (weekly or monthly) when actually there are no changes of credit quality and the variations of credit spreads are dominated by liquidity risk premium, the temporary change of demand and supply and other non-credit components. We note there is some research into credit spreads in this direction. For example, Koopman and Lucas (2003) examine business and credits spread cycles and find a cocyclicity (negative relation) at frequencies of both 6 years and 11 years. The lengths of the business and credit cycle however are assumed to be fixed in that study, implying that credit spreads change at fixed time points and at equal time intervals. This is in contrast to the possibility of immediate default or immediate deterioration of credit quality, even for high quality firms. Fama (1989) and Guha and Hiris (2002) have also shown that there is a correlation between credit spreads and the business cycle. Fama (1989) studies the default premiums proxied by the difference between the forward rates of CD's and T-bills. He finds that, graphically, there is some corresponding increases in credit spread level when the economy is in NBER defined business recession periods. Guha and Hiris (2002) examine the equality of credit spread level, the difference between Moody's BAA yield and the long term Treasury rate in economic recession and boom. Using a Wilcoxon signed rank-sum test they find that the credit spread narrows during economic expansion and widens during contractions. However, neither of these two papers modelled the dynamics of the credit spreads and the associated macroeconomic variables. In this paper, we employ Markov switching models to analyze the cyclical movement of credit spreads. The advantage of these models is that they describe not only the dynamics of the observed data but also that of the low frequency phase variable that underlies the observed data. The low frequency phase variable is stochastic and unobservable but one can make inferences

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Yan Li and James M. Steeley

about it. We expect that the low frequency variable underlying credit spreads contains more information about the firm’s credit quality than the observed high frequency data. We construct credit spread data by taking the difference between Moody's corporate BAA yield and the 10 year Treasury rate (BAA spread thereafter), and that between the AAA and the 10 Treasury rate (AAA spread thereafter). The sample ranges from 04/1953-07/2004, covering major events in both the real economy and the equity market. We expect that more than 50 years of data will contain the systematic information about the low frequency events affecting credit spreads and their relation with those of equity volatility and the industrial output. We find that credit spreads show cyclical patterns with durations of more than one year. The long run mean credit spread at one phase is significantly higher than at the other phase. We show that this important cyclical information is lost within the change of the credit spread, which has been the measure mostly examined in the literature. Studying the level of credit spreads, however, may also provide limited information unless these important low frequency cycles are also identified. We find a very high persistence in the credit spread series, which means that the convergence to the long run mean in the new phase is very slow, many times longer than the duration of a phase. Thus, credit spreads will display very sticky behaviour, such that even though the economy has moved into , for example, the low long run mean state, the observed level of the credit spread could still be more strongly reflecting the high long run mean state. This would naturally obscure, if not breakdown, the relationship between the phases, and so their economic determinants, and the level of credit spreads. So, without modelling the low frequency behaviour of the credit spreads, it will be difficult even to link the level of the spread to its economic determinants. In addition, a spurious trend in the level of credit spreads might also arise due to the slow rate of mean reversion. If the credit quality of an underlying firm suddenly becomes worse and then stabilizes at that level, the level of the credit spread may not also rise and then stay high, but instead climb gradually towards the high long run mean. Campbell and Taksler (2003) study the increasing trend in credit spreads in the late 1990s and find that a rise in idiosyncratic volatility corresponds to the rise the spreads. Our results, suggest that this may instead, or in part, reflect the slow rate of mean reversion in credit spreads. Having identified the existence and potential importance of the low frequency cycles in credit spreads, we explore the relationship between these and the cyclical movement of the economic variables, specifically the growth rate of industrial output and equity market volatility, now using a bivariate Markov switching model. Our results show that the correlation between the spreads and their structural economic determinants is much higher than has previously been identified. The unconditional correlation of the state variable for the growth rate of industrial output with that of the AAA (BAA) spread is -0.4473 (-0.3316). For equity market volatility, the correlation is 70.93% for the AAA spread and 0.7981 for the BAA spread. These results are found to be robust to small changes in the sample size, and use model specifications that are tested both in and out of sample. Further robustness analysis suggests that allowing independent cycles for the intercept and volatility of the credit spreads may slightly reduce these correlations, but that they will still be much higher than that observed using only high frequency methods. The rest of the paper is organized as follows. In section I, we describe the data and report on some preliminary analysis of the data. Section II, presents the univariate Markov switching analysis for the credit spreads and the economic variables. In Section III, we describe the modelling of the cyclical relationship for a bivariate system of each credit spread with, in

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turn, industrial output and equity volatility. In section IV, report the results of a check of the robustness of our results to a common state variable for both the intercept and volatility of the credit spread. In section V, we provide a conclusion..

I. Data Description

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Credit spreads are the difference between corporate yields and the otherwise equivalent Treasury yield. To capture successfully low frequency dynamics in credit spreads, we need a relatively long sample history of both corporate yield and Treasury yield data. We therefore use the Moody’s monthly corporate yields, which start from 01/1919, and the Federal Reserve 10 year constant maturity Treasury rate, available from 04/1953.1 The sample period for the effective credit spread begins therefore also in 04/1954, and then runs until 07/2004. We construct two measures of high rating credit spreads, using the AAA and the BAA corporate yield data. In obtaining a time series that is considerably longer than that used in prior work, we have no choice but to use yield data that, during the period until the mid-1980s, have been constructed from a set of bonds that could contain special features such call provisions and sinking funds. To avoid the inclusion of such features, or to use other maturities, would render the sample size too small for our analysis. Since both the corporate yield data and the Treasury yield data were constructed from bonds that may have had special features and as the former is an average across many bonds, there may be, at least in part, some offset within our measure of credit spreads. The sample period covers the US business recessions of 1957-1958, 1960-1961, 19691970, 1973-1975, 1979-1982, 1990-1991 and 2001, as dated by NBER2. To proxy macroeconomic activity, we use monthly industrial output from the Conference Board3. This data series is first differenced to obtain a growth measure (DIP hereafter). For the equity return series, we use the Fama-French monthly market excessive return ( rt hereafter) which is the value-weighted return on all NYSE, AMEX, and NASDAQ stocks (from CRSP) minus 2

the one-month Treasury bill rate.4 We measure equity volatility rt as the squared deviation of

rt from its sample mean. Summary statistics of the data are given in Table 1. As would be expected both the mean and standard deviation of the BAA spread are greater than the AAA spread. The null hypothesis of non-stationarity in each of the spread series is rejected by both an ADF and Phillips-Perron test at a 5% level. While non-stationarity is rejected, both series display relatively high first order autocorrelation, which can be a source of spurious correlations. Both DIP and rt, by contrast, have very small first autocorrelation and therefore we should not expect problems, similar to spurious regression in a linear regression, when we examine 1

The data source is the Federal Reserve statistical release H15, available at www.federalreserve.gov/releases/h15. The data are averaged daily data so the chance of ending up with a regime shift caused by an erratic change of the observations will be small. 2 The data source is www.nber.org/cycles. 3 The data are available from www.conference-board.org/economics/bci/data-search.cfm. 4 The data source is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library .html. We did not use the S&P500 index as it has relatively shorter history, starting only from 02/1965, and over the common period it has a correlation of 0.94 with the rt .

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Yan Li and James M. Steeley

correlations between these economic factors and the spread series. The kurtosis of 4.8730 in the equity return series is an indication of regime dependent or time varying volatilities. The kurtosis values of the AAA spread and BAA spread are 3.2438 and 2.5800 respectively, neither suggestion non-constant variance. It is possible, however, that short run dynamics in the spread series could mask this characteristic, and so we examine the errors from an autoregression, using 3 lags. The kurtosis figures for the error series from these autoregressions are 6.2633 (AAA spread) and 7.1959 (BAA spread), which does point to nonconstant variances. Table I. Summary Statistics.

Mean Std Skewness Kurtosis ADF PP

AAA

BAA

DIP

rt

0.7521 0.5045 2.4600 3.2438 0.0476 0.0141

1.7000 0.7177 0.4215 2.5800 0.0362 0.0204

0.1494 0.4533 -0.2655 4.7960 0.0000 0.0000

0.5836 4.3202 -0.4866 4.8730 0.0000 0.0000

AAA denotes AAA spread, BAA denotes BAA spread, DIP is the first difference of industrial output,

rt

is

the market returns from Fama-French factor. The credit spread data are annualized rates of return (in percent), while the equity return is a monthly rate of return (percent per month). This difference is scaling, which will not affect the correlation analysis, facilitates the numerical calculations as it makes the data similar in magnitude. The last two rows are the p-values of ADF and PP unit root tests. ADF and PP are the p-value of ADF and PP tests. The lag length in the ADF tests is 2 for all variables. This is selected using a SBIC with maxlag=18. The sample period is 04/53 to 07/04.

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Table II. Correlation Matrix.

rt 2

AAA

BAA

DIP

AAA BAA DIP

1 0.8179 -0.0367

1 -0.1287

1

2

0.1287

0.1585

-0.0126

1

0.1314 0.0949

0.1058 0.1164

-0.1101 -0.1711

0.1163 0.1522

rt

DAAA DBAA

DAAA

DBAA

1 0.1522

1

This table reports the correlation matrix of the variables over the period 04/53 to 07/04. AAA denotes AAA spread, BAA denotes BAA spread, DIP is the first difference of industrial output, rt is the returns from Fama-French market factor. The prefix D on a spread variable indicates first differences.

Table 2 reports the correlation matrix for the spread variables, the change in industrial production, equity volatility and also the differenced spread series. The differenced spread series will be used to demonstrate how differencing may disconnect the credit spread series with their economic determinants under certain data generating processes for the levels of the spread series. The matrix of estimated correlation coefficients conform to the findings in previous studies that have been unable to explain credit spreads with measures of macroeconomic activity and equity volatility. The AAA spread has very low correlation

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2

49

(0.1287). For the BAA spread, the

corresponding correlation coefficients are 0.1287 and 0.1585. The result is similar in the case of the differenced spreads, denoted DAAA and DBAA.

II. Markov Switching Models and Credit Spreads As was reported in Section I, the credit status of high rating firms is stable, with firms having greater than 90% probability of remaining in the rating class from one year to the next. It is very rare that firms face serious financial problems and go bankrupt. By contrast, credit spreads contain liquidity risk premium and can be very volatile, see, for example, Liu, Longstaff and Mandell (2000). The explicit modelling of cyclical behaviour within Markov switching models provides a convenient way to investigate both the low frequency components of credit spreads and their potential determinants, and also accommodate the high frequency movements. In this section, we identify separately appropriate Markov switching models for credit spreads, macroeconomic activity and equity volatility. To begin, we make an important distinction between two, apparently similar, specifications of Markov switching models, that is critical to the correct identification of the low frequency movement of credit spreads.

A. Two Specifications of Markov Switching Models The original Markov switching model of Hamilton (1989) was proposed to describe the cyclical behaviour of the economy. Specifically, the growth rate of GDP was shown to follow a specific form of the general process

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m

yt − μ ( st ) = ∑ φi ( yt −i − μ ( st −i )) + ε t

(1)

i =1

where φi are the autoregressive coefficients and ε t ~ N ( 0, σ 2 ) or ε t | st ~ N ( 0, σ 2 ( st ) ) . The unobservable state variable st , which is assumed to take on the values of 0 or 1, controls difference phases of economic cycle. Thus, for example, the mean of the growth rate of GDP,

μ ( st ) say, can take on different values in different intervals of time, so characterizing the

cyclical behavior of the economy. The dynamics of the state variable st , which describe the transition between different phases of the economic cycle, are assumed to be governed by a K-state Markov (switching) chain, described by the probability relations

P ( st = j | st −1 = i ) = pij j=K

∑ P(s j =1

t

= j | st −1 = i ) = 1

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Yan Li and James M. Steeley

in which i, j, = 1,2,..., K , K is the number of states, and P ( st = j | st −1 = i ) is the probability of transition from state i to state j . This form of dynamics is, therefore, low frequency, while the residual ε t | st ~ N ( 0, σ 2 ( st ) ) accommodates the high frequency dynamics. In applications to interest rate data, Gray (1996), Ang and Bekaert (1998) and Garcia and Perron (1996) have all modified the specification of the observable variable to m

y t = ν ( st ) + ∑ φi y t −i + ε t

(2)

i =1

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They find interest rates are characterised by two different phases: high level/high volatility and low level/low volatility. This positive relation between the level and volatility of interest rates is a feature of standard theoretical models of the yield curve, such as Cox, Ingersoll and Ross (1985). Although the specifications in equations (1) and (2) are identical in the absence of regime switching, they display an important difference when combined with switching behavior. Krolzig et al (1996) observe that, after a change of regime in the mean, μ ( st ) , the original specification implies an immediate jump in the process to the new mean, while in the latter, m the process smoothly approaches a long run mean, v( st ) / ⎛1 − ∑ φi ⎞ , with the adjustment ⎜ ⎟ ⎝ i =1 ⎠ speed determined by the sum of the autoregressive coefficients. The former model, therefore, is known as the Markov Switching Mean (MSM) model, and the latter is known as the Markov Switching Intercept (MSI) model. We can demonstrate the difference between the two specifications by simulating the response of an AR(1) variable, with different levels of the autoregressive coefficient, after a change of regime in its mean. We set the Gaussian noises to be zero and, for direct comparison purposes, scale the MSM mean after the regime change, to equal the long run mean of the MSI model. The variable is initialized at the low regime level and, at time 1, a regime change is assumed to occur. In Figure 1, it can be seen that the variable, under the MSM specification, jumps immediately to the high level at time 1, (the dashed line). By contrast, the response under the MSI specification depends on the persistence of the process, measured by φ . One can see that it takes more than 100 months to get to the long run high level (the solid line in the bottom panel) when φ = 0.97 , about 40 months when φ = 0.9 (middle panel), and is almost the same as under the MSM specification when φ = 0.3 (the upper panel). The two specifications become equivalent when when

φ is close to zero and differ the most

φ is close to unity. So, for a highly persistent variable with a DGP of MSI, its

responses to regime changes will be very slow. Within a short period of time or when it is subject to frequent regime changes, it will be very difficult therefore to observe the true phases of the variable from its observed level. This will naturally confound attempts to explain the causes of these phases and, if credit spreads display such behaviour, can explain why economic variables have had little success in explaining them.

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Figure 1. This figure displays the response of an AR(1) variable with different autoregressive coefficient ( φ = 0.3, 0.9, 0.97 ) after a change of regime in the intercept (solid line) and in the mean (dashed line) at time t=1. The intercept in the two regimes are set to be 0.000 and 0.0200 respectively.

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Both the MSI and MSM specifications can be estimated using Hamilton (1994)’s maximum likelihood estimation algorithm. The conditional likelihood function of the MSI model depends on past values of the state variable st , and one needs to consider K

m +1

states,

where K is the number of states and m is the lag order. By contrast, the estimation is much simpler for the MSM model as the likelihood function only depends on the number of states. Although in both cases, we can not obtain for sure the value of the state variable st on a specific date, the smoothed probabilities obtained from the estimation procedure provide the best inference of the unobservable state variable st .

B. Cyclical Movement of Credit Spreads In this section, we estimate and compare four possible specifications that could describe the dynamics of credit spreads. These are: (a) MSI; (b) Equation (1) with a constant mean

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(MSC); (c) MSM; and (d) a linear AR(m) model. The conditional variance

σ 2 ( st ) in the

Markov switching models (a), (b), (c), is allowed to be regime dependent in order to capture the heteroscedasticity in credit spreads. The MSC model is nested in the MSI model and so a LR test can be used to detect whether the intercepts, and therefore the implied long run means, are different in the two regimes. Similarly, the LR test can be applied to detect whether there is an immediate jump in the mean of the process (MSM against MSC). To compare the MSI and MSM models, which are not nested in each other, we use AIC, BSIC and both in-sample and out-of-sample fitting performance to help us choose the proper specification for the credit spread data. The linear AR(m) model is used to test whether the cyclical specification is appropriate or not for the data. Autoregressive coefficients at lags larger than three turn out to be insignificant in all models, and therefore so only the 3 lag specifications are reported here. We estimate the models using maximum likelihood estimation. To account for potential misspecification of the normality assumption of the within-regime error terms, we calculate quasi-maximum likelihood standard errors (see White, 1980). We reserve the last three years of data for a comparison of out-of-sample forecasting performance of the alternative models. The estimation was carried out therefore on the sample from 04/1953 to 06/2001, leaving most of the latest 2001 recession period out of the sample period. Table 3 contains the results for the AAA and BAA spreads. Table III. Markov Switching models of Credit Spread Series.

μ0 μ1 φ1 φ2

AAA （04/1953-07/2001） MSI MSM MSC Linear 0.0013 0.3517 0.0071 0.0242 [0.0070] [0.2692] [0.0074] [0.0100] 0.0422 0.4017 [0.0173] [0.2689] 1.0130 1.0493 1.0560 1.0359 [0.0561] [0.0508] [0.0492] [0.0526] -0.2291 -0.2408 -0.2436 -0.2549 [0.0613] [0.0640] [0.0621] [0.0731]

MSI 0.0375 [0.0181] 0.1043 [0.0453] 1.1564 [0.0657] -0.3558 [0.0916]

BAA (04/1953-07/2001) MSM MSC Linear 1.2101 0.0208 0.0521 [0.2003] [ 0.0140] [0.0165] 1.2861 [0.2310] 1.1923 1.2034 1.1963 [0.0603] [ 0.0641] [0.0654] -0.3747 -0.3947 -0.4451 [0.0865] [ 0.0924] [0.0973]

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Table III. Continued

φ3 σ 02

σ 12

AAA （04/1953-07/2001） MSI MSM MSC Linear 0.1873 0.1727 0.1661 0.1885 [0.0502] [0.0480] [0.0468] [0.0533] 0.0033 0.0035 0.0036 0.0157 [0.0010] [0.0009] [0.0013] [0.0015] 0.0258 0.0261 0.0269 [0.0051] [0.0062] [0.0088]

MSI 0.1623 [0.0504] 0.0073 [0.0015] 0.0546 [0.0139]

BAA (04/1953-07/2001) MSM MSC Linear 0.1570 0.1736 0.2188 [0.0468] [ 0.0462] [0.0540] 0.0073 0.0078 0.0268 [0.0015] [ 0.0015] [0.0029] 0.0511 0.0582 [0.0151] [ 0.0144]

p11

0.9211

0.9417

0.9398

-

0.9461

0.9637

0.9598

-

p22

0.9306

0.9501

0.9448

-

0.9155

0.9511

0.9330

-

Loglik LR Davies MAE RMSE MAE* RMSE* AIC SC

451.7050 447.1100 446.3317 378.0447 314.5828 310.3091 310.2598 224.6597 10.7466 147.3206 8.6460 179.8462 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0889 0.0892 0.0890 0.0898 0.1140 0.1143 0.1142 0.1151 0.1242 0.1260 0.1260 0.1254 0.1619 0.1646 0.1645 0.1637 0.1007 0.0981 0.0972 0.0971 0.0990 0.1027 0.1026 0.1029 0.1482 0.1491 0.1477 0.1486 0.1268 0.1309 0.1309 0.1324 -1.5398 -1.5239 -1.5246 -1.0629 -1.0480 -1.0513 -1.4717 -1.4557 -1.4640 -0.9947 -0.9799 -0.9908

This table reports the estimation results of the four specifications of AAA and BAA spread models. The column MSI is for the model of regime dependent intercept and volatility. The column MSM is for the model of immediate jump of mean. The column MSC is for the constant intercept. Volatility is allowed to be regime dependent for these three models. The column Linear is for the linear model. The lag order of all the three models is 3. The coefficients

μ 0 , μ1

are in percent and

σ 02 , σ 12

are in squared

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percent, and the subscripts distinguish between the two regimes. In brackets are the White heteroscadasticity- consistent standard errors. The LR tests are against the MSI model. Davies is the pvalue of Davies bound test. MAE and RMSE denote the in-sample and out-of-sample mean absolute errors and the root mean squared errors respectively.

Considering first the AAA spread, the results from the MSI model (in column 2) show that, in regime one, this spread has a low and insignificant intercept 0.0013. The conditional variance is also low with a value of 0.0033. In regime two, the intercept is 0.0422, significant and higher than that in regime one. The conditional variance is also high with a value of 0.0258. Thus, the dynamics of the AAA credit spread display two clear-cut phases: low intercept, low variance and high intercept, high variance. The constant mean model, MSC (in column 3), has a log-likelihood value of 446.3317, which is much lower than that of the MSI model (451.7050), yet there is only one less parameter. Not surprisingly, the LR test strongly rejects this constant mean model against model MSI at the level of 99.75% confidence. The log-likelihood value for the MSM model (447.1100) is only slightly higher than that of the constant mean model and the LR test cannot reject the constant mean model. Clearly, the LR tests appear to select the MSI model as the appropriate specification of the AAA spread. The AIC and BSIC values support the LR tests: the MSI model has the smallest AIC and SC values. The in-sample forecast errors of model MSI are also the smallest, in term of MAE and RMSE, among the three competing Markov switching models. The out-of-sample forecast performance however appears to choose the constant mean model, a result that might not be surprising, as a more complicated model can have poorer out-of-sample performance.

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The test of a Markov switching model against linear alternatives is not trivial, as under the null hypothesis of no regime switching, the parameters associated with the additional

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regime ( μ1 , σ 1 ) are not identified. The presence of the nuisance parameters

μ0 and σ 0

under the null hypothesis gives the likelihood surface sufficient freedom such that the scores associated with parameters of interest under the alternative may be identically zero under the null. To avoid this complication, we resort to the upper bound test of Davis (1977, 1979). This test strongly rejects the one regime hypothesis. We also note that the in-sample MAE and RMSE of the MSI model are smaller than for the linear model, and that the out-of-sample RMSE is also smaller than that of the linear model. Finally, to ensure that the model describes the data well and does not miss features in the out-of-sample data, we re-estimate the model over the full sample period. Again the LR test, the AIC and SBIC values, and the in-sample forecast support MSI as the underlying data generating process.5 We conclude, therefore, that the AAA spread is characterized by a two regime process, giving a low intercept and low volatility in one regime and a high intercept and high volatility in the other one. We now consider the implications of this specification. The AAA spread features two distinct intercepts, 0.0013 and 0.0422. Under the MSI specification, the respective implied long run means are 0.0451 and 1.4653, which are much farther apart than the intercepts. This means that, for example at the time of a switch to the high regime, although the intercept of the credit spread rises from 0.0013 to 0.0422, the credit spread level only receives a small initial push towards the long run mean. Moreover, the m persistence coefficient, ⎛⎜ ∑ φi ⎞⎟ , is very high at 0.9712, implying that the time to reach the ⎝ i =1 ⎠ high long run mean is very long (about 140 months). Over a short period of time, therefore, the observed spread will still be at the proximity of the current low level. The relation between the credit spread level and the determinants of the regimes (such as output and equity market volatility variables, which have strong theoretical support) may therefore appear to be very weak. This is indeed what we found in Table 2 and was also reported in previous studies. We will see later that the relation is strongly supported when the low frequency movements of credit spreads are well specified. To further confound the explanation of credit spreads, the estimated parameters of the MSI model indicate that the duration of the two regimes is about 12 months. This means that, for example, long before the spread reaches the high long run mean and fully reflects the current regime or the credit status of the firm, the financial situation might have improved, asset volatility might have decreased, and the spread will begin to revert back towards the low long run mean. The observed level however may have already reached a relatively high level, so that in a short period of time the higher credit spread level will not be able to reflect the improvement of credit status. This will further impede the identification of a relationship between the observed credit spread and the determinants of the regimes. In Figure 2, it can be seen that AAA spread data behaves consistently with the stylized description of the properties of the MSI model. The spread is around its low long run mean at the beginning of the sample period. The regime changes in 1957-1958 and 1960-1961 do not last long and therefore the spread stays at relatively low levels. From the late 1960s up to the early 1990s the high long run mean regime dominates the sample and the spread keeps 5

These results are in the appendix.

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increasing, while temporary switches to the low long run mean regime drag it down once in a while. From the mid-1990s, there occurs a long period of the low long run mean regime and the spread is pulled down. However it can be seen that the observed level of the spread is still higher than it was during the high long run mean regime in the 1950s and 1960s, due to the slow mean reversion from the high level. From 1995 to 2003 there is an apparent increasing trend in the spread. Campbell and Taksler (2003) found a similar pattern in several investment rating spreads. This again might be the result of the slow transition from the low regime to the high regime. The occurrence of the low long run mean regime after 1999 is relatively short and the reversion to the low long run mean does not last long. The subsequent long duration of the high long run mean regime starting at the beginning of the new century however keeps the spread crawling up, resulting in an increasing trend-like pattern of the spread from 2002 to 2003. Again the MSI model uncovers the importance of the regimes, which are responsible for this trend pattern of the spread, rather than the trend itself, in the investigation of the determinants of the credit spread.

Figure 2. This figure displays the raw data of AAA spread (left) and the smoothed probabilities of regime 1(high intercept, high volatility) over 04/1953-07/2004. The dashed lines in the top right graph are the NBER dated troughs.

Within-regime high frequency noise adds volatility along the path of the cyclical movement. When the credit spread moves towards its high long run mean it becomes more volatile and when the credit spread moves down to its low long run mean it is relatively stable. The variance of the high long run mean regime is 0.0283, which is 7.8 times that in the low long run mean regime. It is interesting that this positive relation between the variance of the high frequency noise and the low frequency long run mean is different from what is predicted by the widely applied CIR (1985) process in modelling the dynamics of credit spread (Duffee, 1999; Duffie and Singleton, 1999). These specify a positive relation between the level of credit spread (rather than its mean) and its volatility. The results for the BAA spread are quite similar to those for the AAA spread. The LR tests, the AIC and SBIC values, and the in-sample forecast performance all support the MSI specification. For this spread, the MSI also has the best out-of-sample performance. The full

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sample estimation, adding back the hold-out sample, again show a supporting pattern of results. The Davies test strongly rejects the linear model against the switching alternatives. Therefore, the BAA spread also possesses regimes featuring high intercept/high volatility and low intercept/low volatility. The implied long run means of BAA spread in the two regimes are 1.0108 and 2.8113 respectively, higher than the corresponding values for the AAA spread. p

The mean reverting rate is slightly less slow than for the AAA spread ( ∑ ϕi = 0.9629 ). The i =1

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duration of the low long run mean regime is about 19 months and of the high long run mean regime 12.5 months, both much lower than 120 months, the time to reach the mean.

Figure 3. This figure displays the raw data of BAA spread (left), the smoothed probabilities of regime 1(high intercept, high volatility) over 04/1953-07/2004. The dashed lines in the top right graph are the NBER dated troughs.

Figure 3 displays the raw data and the smoothed regime probabilities of the BAA spread. Similar to AAA spread, the level of the spread is low and relatively flat from 1953 to 1965. From 1988 to 1998 the spread slowly moves down towards the low long run mean from the high observed level. Again this downward movement does not reach the low long run mean and the level of spread during this period is higher than that in the high long run mean regime in 1950s and 1960s. From 1998 to 2003, the BAA spread experiences two high long run mean regimes, resulting in a trend-like pattern. There is also a positive relationship between the long run mean and the variance of the spread. The variance of the high long run mean regime is 0.0523, 7.16 times which of the low long run mean regime. While regime switching appears to represent credit spread behaviour well, it does not indicate the determinants of the regimes. According to Bernanke and Gertler (1995) and Bernanke and Lown (2000), credit spreads vary with macroeconomic conditions. Better economic condition increases asset prices and therefore firms have less default risk and lower credit spreads. In the graphs of the smoothed probabilities of the high long run mean regime we plot the NBER dated recessions. The visual impression is that there appears a close relationship between regime one and the economic recessions. For almost every occurrence of

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economic recession, the spreads are in the high long run means regimes. The high long run mean regime usually starts earlier and lasts longer, an indication that the spreads are correlated with the economic condition and may even have some predictability of it. Later, in Section III, we will investigate this relationship in the framework of bivariate Markov switching models.

C. The Change of Credit Spreads Due to the close-to-unit-root characteristics of credit spreads, many studies including Elton, Gruber, Argawal and Mann (2001), Collin-Dufresne, Goldstein and Martin (2001) and Huang and Kong (2003) examine the change rather than the level of credit spreads in order to avoid ending up with spurious regression. However economic theories such as Merton (1974) and Bernanke and Gertler (1995) involve the level of credit spreads, not the change in the spreads. In this section, we show that differencing persistent variables will lose regime information, and consider the implications for modelling credit spreads. Suppose that the observed variable y t follows the simple switching process

yt = α 0 + α1st + φ yt −1 + ε t where α 0 = μ 0 ,

(3)

α 0 + α1 = μ1 , and other terms are as defined earlier. On lagging one period

and take the first difference, we obtain

Δyt = α1 ( st − st −1 ) + φΔyt −1 + ε t − ε t −1

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In equation (3), when st −1 = st = 0 , yt is in the regime with low intercept

(4)

α 0 = μ0 and

when st −1 = st = 1 , yt is in the other regime with intercept α 0 + α1 = μ1 . When there is no regime switching in equation (4), st − st −1 = 0 , equation (5) becomes

Δyt = φΔyt −1 + ε t − ε t −1 , which is a linear ARMA process with intercept and mean as zero, while when a regime change takes place, i.e. st −1 = 1, st = 0 or st −1 = 0, st = 1 , equation (4) becomes

Δyt = ±α1 + φΔyt −1 + ε t − ε t −1 Therefore the change of regime of yt −1 periodically injects an immediate impulse of size ±α1 into the process of Δyt = φΔyt −1 + ε t − ε t −1 , and the response is just the impulse response of

a linear model. There is no sustained regime in the DGP of Δyt and the dynamics of Δyt are fundamentally different from the regime switching model like (4) and it is not appropriate to

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Yan Li and James M. Steeley

apply Markov switching models in the change of credit spreads. Thus, if there is Markov switching in the level of a variable, there cannot be Markov switching in the first differences of the variable. If Markov switching is detected in first differences of such a series, then it is spurious and reflects the high persistence in the variable. Table IV. Markov Switching models of changes in Credit Spreads.

μ0 μ1 φ1 φ2 φ3 σ 02 σ 12

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p11

MSI -0.0120 [0.0062] 0.0170 [0.0158] 0.0614 [0.0517] -0.1892 [0.0464] 0.0512 [0.0431] 0.0036 [0.0011] 0.0269 [0.0071] 0.9319

DAAA (04/1953-07/2001) MSM MSC Linear -0.0110 -0.0054 0.0031 [0.0056] [0.0045] [0.0052] 0.0152 [0.0152] 0.0641 0.0792 0.0581 [0.0515] [0.0477] [0.0544] -0.1863 -0.1823 -0.2084 [0.0462] [0.0452] [0.0529] 0.0558 0.0610 0.0404 [0.0423] [0.0443] [0.0524] 0.0037 0.0036 0.0159 [0.0011] [0.0012] [0.0015] 0.0270 0.0265 [0.0074] [0.0084] 0.9326 0.9436 -

MSI -0.0078 [0.0062] 0.0194 [0.0185] 0.2181 [0.0641] -0.2032 [0.0502] 0.0495 [0.0464] 0.0075 [0.0017] 0.0567 [0.0140] 0.9556

DBAA (04/1953-07/2001) MSM MSC Linear -0.0080 -0.0042 0.0031 [0.0064] [0.0050] [0.0068] 0.0191 [0.0192] 0.2202 0.2275 0.2258 [0.0643] [0.0634] [0.0652] -0.2024 -0.2035 -0.2478 [0.0502] [0.0506] [0.0551] 0.0524 0.0518 0.0499 [0.0456] [0.0464] [0.0617] 0.0076 0.0077 0.0271 [0.0017] [0.0014] [0.0029] 0.0566 0.0574 [0.0140] [0.0134] 0.9563 0.9597 -

p22 Loglik

0.9358

0.9360

0.9511

-

0.9306

0.9318

0.9358

-

447.837 0

447.634 2

444.917 1

375.415 2

310.168 2

310.017 8

309.032 7

221.306 2

LR

-

-

5.8398

144.843 2.2710 177.724 6 0 Davies 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 MAE 0.0897 0.0897 0.0891 0.0898 0.1149 0.1149 0.1146 0.1147 RMSE 0.1254 0.1254 0.1263 0.1260 0.1645 0.1646 0.1650 0.1647 MAE* 0.1114 0.1061 0.1013 0.1060 0.1152 0.1102 0.1072 0.1105 RMSE* 0.1637 0.1569 0.1544 0.1579 0.1474 0.1365 0.1341 0.1375 AIC -1.5264 -1.5257 -1.5197 -1.2884 -1.0475 -1.0470 -1.0471 -0.7524 SC -1.4582 -1.4575 -1.4591 -1.2505 -0.9794 -0.9789 -0.9865 -0.7145 This table reports the estimation results of the four specifications of the change of AAA and BAA spread models. The column MSI is for the model of regime dependent intercept and volatility. The column MSM is for the model of an immediate jump in the mean. The column MSC refers to the constant intercept model. Volatility is allowed to be regime dependent for these three models. The fourth column is for the linear model. The lag order of all the three models is 3.

μ 0 , μ1

are in percent and

σ 02 , σ 12

are in squared percent, and the subscripts distinguish between the two regimes. In brackets are the White heteroscadasticity-consistent standard errors. The LR tests are against the MSI model. Davies is the pvalue of Davies bound test. MAE and RMSE denote the in-sample mean absolute errors and the root mean squared errors respectively.

To confirm our conjecture that modelling the spreads will lose potentially valuable regime information, we apply the four model specifications to the change of AAA and BAA spreads, denoted DAAA and DBAA respectively. The results are reported in Table 4. For the AAA spread changes, all the specifications indicate that the data are highly mean reverting

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p

with ∑ φi = -0.0766 , -0.0664, -0.04210 and -0.1099 for the MSI, MSM, MSC and linear i =1

models, respectively. The MSI and MSM models have almost equal log-likelihood values, but the MSM model performs slightly better in out-of-sample forecasting. There is a hint that DAAA experiences regime dependent intercept or means, with the LR statistics against the MSC model being 5.8398 and 5.4342 for MSI and MSM respectively, and significant at 2.5% level. This result is likely spurious and due to the slow response of AAA spread level p

( ∑ φi = 0.9629 ). This possibility is confirmed by the results for the BAA spread, which has a i =1

p

slightly persistence rate ( ∑ φi = 0.9582 ). Here, the pattern of Markov switching in i =1

mean/intercept in the change of spread (DBAA) disappears. The log-likelihood values of MSM, MSI and MSC are 310.1682, 310.0178 and 309.0327 respectively, almost equivalent and LR tests cannot reject the constant mean hypothesis. DBAA also appears to be highly p

mean reverting ( ∑ φi = 0.0758 in the case of MSC). i =1

D. Cyclical Movement in Macroeconomic Activity and Equity Volatility

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We also apply the Markov switching models to the industrial output and equity return data. For the changes in industrial output, the results in Table 5 show that the MSM specification overwhelmingly dominates the MSI and linear models in terms of in-sample and out-of-sample forecasting performance. The smoothed probabilities of the low growth rate regime also match the NBER dated recession, see Figure 4. It appears that regime changes in the macro-economy are more likely to take effect immediately rather than gradually. Table V. Markov Switching models of macroeconomic activity variables.

rt

DIP

σ 02

MSI -0.3928 [0.2677] 0.1581 [0.1187] 0.1588 [0.1217] 0.0971 [0.0836] 0.0878 [0.0741] 0.1435 [0.0219]

σ 12

-

-

-

p11

0.7907

0.7934

-

μ0 μ1 φ1 φ2 φ3

MSM -0.5450 [0.1458] 0.2482 [0.0479] 0.1592 [0.0810] 0.1724 [0.0613] 0.1612 [0.0545] 0.1289 [0.0148]

Linear 0.0681 [0.0217]

MSC 0.7744 [0.1842]

Linear 0.6043 [0.1908]

-

-

-

0.2754 [0.0568] 0.1532 [0.0477] 0.1133 [0.0465] 0.1679 [0.0154]

0.0319 [0.0390] 10.1303 [1.3564] 31.8629 [6.6757] 10.1303 [1.3564] 31.8629 [6.6757]

0.0518 [0.0481] 18.3664 [1.5467]

0.9642

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-

60

Yan Li and James M. Steeley Table V. Continued

rt

DIP MSI

MSM

Linear

MSC

Linear

0.9727

0.9695

-

0.9417

-

-296.3034

-289.9762

-302.9055

-1632.1683

-1652.6648

Davies

0.0039

0.0000

-

0.0000

-

MAE

0.2987

0.2982

0.2988

3.2769

3.2843

RMSE

0.4103

0.4095

0.4098

4.2893

4.2856

MAE*

0.4109

0.4036

0.4093

3.5532

3.5533

RMSE*

0.4886

0.4766

0.4912

4.5744

4.5546

AIC

1.0584

1.0364

1.0710

5.6980

5.7588

SC

1.1190

1.0970

1.1088

5.7434

5.7816

p22

Loglik

This table reports the estimation results of DIP and

rt

for the sample period of 04/1953-07/2001. The

column MSI is for the model of regime dependent intercept and volatility. The column MSM is for the model of immediate jump of mean. The column MSC is for the constant intercept. The lag order of all the three models is 3.

μ 0 , μ1

are in percent and

σ 02 , σ 12

are in squared percent. Davies is the p-value

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of Davies bound test. The MAE*, RMSE* are the out-of-sample MAE and RMSE. In brackets are the White heteroscadasticity consistent standard errors.

Figure 4. This figure displays the smoothed probabilities of regime 1(negative mean) of DIP over the sample period of 04/1953-07/2004. The dashed lines are the NBER dated recessions.

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For the equity returns, we use the process p

rt = μ + ∑ φi rt −i + ε t

(5)

i =1

where ε t | st ~ N ( 0, σ 2 ( st ) ) . This constant within-regime volatility model is nested in the

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Hamilton and Susmel (1994)’s SWARCH model. A preliminary application of the SWARCH model did not find significant ARCH effects. The smoothed probabilities also do not show any difference from the constant conditional volatility model. This is consistent with both Hamilton and Susmel (1994) and Kim, Nelson and Startz (1998) who find that an ARCH process may not be necessary in modeling monthly stock returns. The model is specified with only one lag, which is sufficient to pick up index autocorrelation arising from nonsynchronous trading, yet also meets the desire to maintain a small parameter space. This is a similar specification to that used by Hamilton and Lin (1996) in their model of equity returns and business cycles.

Figure 5. This figure displays the smoothed probabilities of regime 1(high volatility) of

rt

over the

sample period of 04/1953-07/2004. The dashed lines are the NBER dated recessions.

The model identifies two volatility regimes; the results are reported in Table 5. The variance in one regime is 31.4555 while the variance in the other regime is 9.9998. The smoothed probabilities, in Figure 5, display some coincidence with the economic recessions, such that high volatility is correlated with economic recessions. By contrast to Hamilton and Lin (1996), however, the high volatility periods appear to last longer than both the NBER

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dated recessions and also our estimated recessions using the industrial output series. This difference could reflect the inclusion of both earlier and more recent sample periods within our dataset. During the 1950s, there were recessions that had little impact on equity market volatility, while during the late 1990s and early 2000s, equity market volatility increased ahead of the recession of 1999 and continues.

III. Correlation Between Cycles of Credit Spreads and the Industrial Output, and Equity Volatility A. Model Specification In this section, we examine the correlation between the cyclical movements of credit spreads and those of macroeconomic conditions and equity volatility. The correlation between the cyclical movements is modelled using the bivariate Markov switching model of Hamilton and Lin (1996). So, we specify a bivariate system in which one equation is the dynamics of credit spread (equation 4) and the other one, either that of the growth rate of the industrial output (equation 2) or the equity return (equation 5). Now, in this bivariate system, the state variable st is defined by

st = 1 if s1,t = 0, s2,t = 0

st = 2 if s1,t = 0, s2,t = 1 st = 3 if s1,t = 1, s2,t = 0

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st = 4 if s1,t = 1, s2,t = 1 where s1,t denotes the binary state variable of the credit spread and s2,t the state variable of either industrial output or equity returns. The transition matrix of this bivariate system can be written as

⎡ p11 ⎢p P = ⎢ 12 ⎢ p13 ⎢ ⎣ p14

p21

p31

p22 p23

p32 p33

p24

p34

p41 ⎤ p42 ⎥⎥ p43 ⎥ ⎥ p44 ⎦

where the only restriction is that the each element of the matrix is a probability 0 < pij < 1 and each column is sum to unity. This specification nests the independent estimation of each series, which was undertaken in the previous section, as a special case in which each element of the unrestricted transition matrix is the product of two elements from the individual transition matrix. Thus, under the hypothesis of regime independence, the transition matrix becomes

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Sticky Credit Spreads, Macroeconomic Activity and Equity Market Volatility 1 ⎡ p11 p112 ⎢ 1 2 p p11 P = ⎢ 12 1 ⎢ p11 p122 ⎢ 1 2 ⎢⎣ p12 p12

p121 p112 p122 p112 p121 p122 p122 p122

1 2 p11 p21 1 2 p12 p21 1 2 p11 p22 1 2 p12 p22

63

2 ⎤ p121 p21 1 2 ⎥ p22 p21 ⎥ 2 ⎥ p121 p22 2 ⎥ p122 p22 ⎥⎦

1

2

where pij denotes the transition probability for one series in the bivariate system and pij for the second series. This nesting means that we can use a conventional likelihood ratio statistics to test whether the low frequency changes of the two variables in the bivariate system are independent of each other. The LR statistics has

χ 2 ( k ) distribution with k the number of

restrictions. In our case, k = 8 . The LR test does not, however, directly test the correlation of the two variables, nor does it indicate the magnitude of correlation. In order to gauge the numerical value and significance of the correlation, we can calculate the ergodic correlation of the two state variables which is σ ( s1 = 0, s2 = 0 ) (6) ρ* = σ ( s1 = 0 ) σ ( s2 = 0 ) The covariance and the standard deviations in the above expression can be obtained from the ergodic probabilities of the new state variable st p ( s1 = 1) = p ( s1 = 1, s2 = 1) + p ( s1 = 1, s2 = 0) = p( s = 4) + p ( s = 3)

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p ( s2 = 1) = p ( s1 = 1, s2 = 1) + p ( s1 = 0, s2 = 1) = p ( s = 4) + p ( s = 2) The covariance of two 0-1 variables is (1 − p ( s1 = 1))(1 − p ( s2 = 1)) and the variance is p ( si = 1) (1 − p ( si = 1) ) where i = 1, 2 . The ergodic correlation

ρ * is a function of probability

parameters and therefore we can easily calculate the white heteroscedasticity-consistent standard error of it. Although we assume that the only correlation within the bivariate system is through the state variables s1,t and s2,t , we try to avoid biases arising from missing correlation at high frequency, by allowing for linear contemporaneous correlation through the off-diagonal elements of variance-covariance matrix ⎡ σ 2 ( s ) σ 122 ( st ) ⎤ Ω ( st ) = ⎢ 12 t ⎥ 2 ⎣σ 12 ( st ) σ 2 ( st ) ⎦

We expect any high frequency linear contemporaneous correlation to be small, however, as shown in table 2 of section 2, and therefore have an insignificant impact on the low frequency regime correlation. Finally, we note that although our method can identify and quantity the correlation between the low frequency, or cyclical, components of credit spreads and the economic variables, it does not explicitly filter out the cycles. This approach is

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therefore different to that of Baxter (1994), who studied cyclical components of real interest rates, and calculated the correlation between cycles extracted using approximate band-pass filters. Our method identifies the correlation simultaneously with the cycles.

B. Credit Spreads and the Growth Rate of the Industrial Output We estimate the bivariate system of credit spreads and the growth rate of the industrial output, both with and without the contemporaneous with-regime correlation. Table 6 reports the estimation results for the two spread measures, without the contemporaneous withinregime correlation, over the sample of 04/1953-07/2004. The parameter estimates are similar to those for the series individually. For the AAA spread series, the LR statistic of 19.1403 strongly rejects the null hypothesis of independent cycles of the two variables. The magnitude of the ergodic correlation coefficient is -0.4473 with standard error of 0.1694, suggesting a significant counter-cyclical relationship between AAA spread and the growth rate of industrial output. We also re-estimated this bivariate system allowing for (high-frequency) contemporaneous linear correlation, but found that none of the correlation coefficients were significantly different from zero and that the likelihood value was only slightly higher, indicating that the model without contemporaneous linear correlation was preferred.

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Table VI. Bivariate Markov Switching models of Credit Spread Series and Changes in Industrial Production. AAA

DIP

BAA

DIP

0.0010 [0.0065]

-0.4675 [0.0725]

0.0431 [0.0148]

-0.5069 [0.1285]

0.0490 [0.0135]

0.2711 [0.0310]

0.1287 [0.0612]

0.2592 [0.0436]

1.0547 [0.0398]

0.1173 [0.0463]

-0.3124 [0.0814]

0.1258 [0.0721]

-0.2632 [0.0538]

0.1623 [0.0500]

-0.3392 [0.0635]

0.1689 [0.0605]

0.1779 [0.0360]

0.1697 [0.0480]

0.1493 [0.0421]

0.1749 [0.0546]

σ 02

0.0034 [0.0006]

0.1269 [0.0089]

0.0076 [0.0018]

0.1292 [0.0145]

σ 12

0.0281 [0.0032]

-

0.0546 [0.0148]

0.0897 0.1262

0.3014 0.4100

0.1135 0.1604

μ0 μ1 φ1 φ2 φ3

MAE RMSE

Loglik

0.3008 0.4079

LR

166.0505 19.1403

26.4961 10.8767

ρ*

-0.4473 [0.1694]

-0.3317 [0.1290]

This table reports the estimation results for the general bivariate system of AAA (BAA ) spread and DIP (without contemporaneous linear correlation) over the period of 04/1963-07/2004. percent and

σ σ 2 0 ,

2 1

are in squared percent.

ρ*

μ 0 , μ1

are in

is the ergodic correlation of regimes. Column 2-3 are

for the bivariate system of AAA and DIP and column 4-5 are for the bivariate system of BAA and DIP. In brackets are the White heteroscadasticity consistent standard errors. The estimates of the transition probabilities have many close to zero values and are not reported here.

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Figure 6. This figure displays the smoothed probabilities of regime 1-4 of the bivariate system of AAA spread and the change of industrial output over the sample period of 04/1953-07/2001. The dashed lines are the NBER dated recessions.

Figure 7. This figure displays the smoothed probabilities of regime 1-4 of the bivariate system of BAA spread and the change of industrial output over the sample period of 04/1953-07/2004. The dashed lines are the NBER dated recessions.

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The smoothed probabilities, in Figure 6, show that for the most part the sample period is categorized into two counter-cyclical regimes: low growth rate, high spread (regime 3, in the bottom left graph) and high growth rate, low spread (regime 2, in the top right graph). The low growth rate, high spread regime almost match those of the NBER dated recession. There are almost no occurrences of the low growth rate, low spread regime (regime 1). The bottom right figure of the graph shows that the pro-cyclical regime (regime 4) of a high growth rate and a high spread has larger number of occurrences. The results for the BAA spread and industrial output are also displayed in Table 6. Although the BAA spread represents a higher level of default risk, it appears to be relatively less sensitive to the economic cycle. The ergodic regime correlation is -0.3317 with a standard error 0.1290, significantly different from zero but less than the magnitude of the AAA spread. However, the LR statistics is only 10.8767 and we cannot reject the null hypothesis of regime independence. The inclusion of the linear contemporaneous correlation structure does not change this result. The smoothed regime probabilities, in Figure 7, are broadly similar to the estimates for the AAA spread, but with rather more potential procyclical (low growth, low spread) regime occurrences.

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C. Credit Spreads and Equity Volatility The results from the estimation of the bivariate systems of the credit spreads with equity return volatility, over the sample period of 04/1953-07/2004, are displayed in Table 7. For the AAA spread, the ergodic correlation with the cycles in equity returns is 0.7093, with a standard error of 0.2916, suggesting equity volatility regimes and credit spread regimes overlap most of the time. The LR statistics is 16.6436, rejecting the null hypothesis of regime independence at 5% level. The BAA spread and equity returns also shows a strong regime correlation. The LR statistics is 34.6035, strongly rejecting the null of independent regime correlation at 1% level. The ergodic correlation coefficient is 0.7981, with a standard error of 0.1160, strongly significant at 1% level. Table VII. Bivariate Markov Switching models of Credit Spread Series and Equity market volatility. General Models

μ0 μ1 φ1 φ2 φ3 σ 02 σ 12

Common Regime Models

AAA

rt

BAA

rt

AAA

rt

BAA

rt

0.0079 [0.0091] 0.0537 [0.0200] 1.0572 [0.0567] -0.2601 [0.0985] 0.1702 [0.0626] 0.0046 [0.0012] 0.0324 [0.0066]

0.7851 [0.2635]

0.0437 [0.0124] 0.1330 [0.0273] 1.1126 [0.0527] -0.3141 [0.0733] 0.1574 [0.0408] 0.0072 [0.0012] 0.0546 [0.0095]

0.7747 [0.1720]

0.0108 [0.0078] 0.0589 [0.0190] 1.0649 [0.0472] -0.2728 [0.0657] 0.1742 [0.0420] 0.0054 [0.0008] 0.0358 [0.0053]

0.7421 [0.1841]

0.0474 [0.0116] 0.1402 [0.0288] 1.1123 [0.0525] -0.3075 [0.0735] 0.1501 [0.0410] 0.0082 [0.0011] 0.0576 [0.0093]

0.7519 [0.1792]

0.0324 [0.2254] 9.6981 [1.5462] 32.6472 [5.8135]

0.0356 [0.0396] 10.2999 [1.1350] 34.3713 [4.6428]

0.0455 [0.0458] 11.2329 [1.1672] 32.9571 [4.9582]

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0.0465 [0.0448] 11.0396 [1.0247] 33.5694 [4.8085]

Sticky Credit Spreads, Macroeconomic Activity and Equity Market Volatility

67

Table VII. Continued General Models

Common Regime Models

AAA

rt

BAA

rt

AAA

rt

BAA

rt

MAE

0.0901

3.3064

0.1133

3.3065

0.0901

3.3072

0.1132

3.3069

RMSE

0.1264

4.3239

0.1599

4.3231

0.1263

4.3211

0.1599

4.3214

Loglik LR

-1259.1186

-1385.5611

-1263.4291

-1390.5822

-16.6436

-34.6035

-

-

0.7094 0.7981 ρ* [0.2404] [0.1035] This table reports the estimation results for the general and common regime bivariate system of AAA (BAA) spread and

rt (without contemporaneous linear correlation) over the period of 04/1963-07/2004. μ 0 ,

μ1 are in percent and σ 02 , σ 12 are in squared percent. ρ * is the ergodic correlation of regimes. Column

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2-5 are for the general bivariate system when the state variable takes 4 values while column 6-9 are for the common regime cases (state variable takes 2 values). In brackets are the heteroscadasticity consistent standard errors. The MAE*, RMSE* are the out-of-sample ME and RMSE. In brackets are the White heteroscadasticity consistent standard errors. The estimates of the transition probabilities have many close to zero values and are not reported here.

Figure 8 and 9 display the smoothed probabilities of each regime for the two bivariate systems. It appears that both the AAA and BAA spread have almost the same phases with equity returns: when the equity volatility is high, so are the BAA spread level and volatility; and when the equity volatility is low, the same occurs for BAA spread level and volatility. This result, of correlated regime changes, does not change when linear contemporaneous correlation is taken into account. The LR test rejects the independent regime null.6 This closely matched phase prompts us to specify a common regime model for the spread and the equity volatility. In this case, the phases of the (AAA or BAA) spread and the equity volatility are determined by the same 0-1 state variable st .In the general case estimated earlier, the state variable st takes on four values. The results of the bivariate systems under this restriction are also reported in Table 7. On inspection of the likelihood values, the common regime model appears superior to the general model. The common regime model has 10 fewer parameters than the general model but the reduction of log-likelihood value is only 4.3105 for AAA and equity, and for BAA and equity 5.0211. Though the LR statistics does not have the conventional distribution and a formal test comparison is not trivial due to the nuisance parameter problem, it does strongly supports the common regime models in an informal way. The MAE and RMSE of the common regime models are roughly the same as more complicated models.

6

The contemporaneous correlation coefficients did appear significant in regime 3, where there AAA spread and equity volatility are in opposite phase, but there were only a few observations in that regime.

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Yan Li and James M. Steeley

Figure 8. This figure displays the smoothed probabilities of regime 1-4 of the bivariate system of AAA spread and

rt

over the sample period of 04/1953-07/2004. The dashed lines are the NBER dated

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recessions.

Figure 9. This figure displays the smoothed probabilities of regime 1-4 of the bivariate system of BAA spread and

rt

over the sample period of 04/1953-07/2004. The dashed lines are the NBER dated

recessions.

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Sticky Credit Spreads, Macroeconomic Activity and Equity Market Volatility

69

Table VIII. Correlation matrix of smoothed probabilities of intercept regimes. AAA

BAA

DIP

AAA BAA DIP

1 0.7241 -0.2419

1 -0.2823

1

2

0.4238

0.6092

-0.2116

rt

rt 2

1

This table displays the sample correlation matrix of the smoothed probabilities of the intercept regimes for 2

AAA spread, BAA spread, the change of industrial output (DIP) and the equity volatility ( rt ). The smoothed probabilities of the intercept regimes are obtained by summing up the probabilities of all volatility regimes that might occur in each intercept regime.

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IV. Robustness Analysis In the Markov Switching models employed above, both the intercept and the volatility of a measure of credit spread are assumed to be driven by the same state variable. This means that the correlation between the cycles in spreads and their determinants could be being driven by cycles in spread volatility rather than by cycles in spread intercept. Since the latter is the measure of interest and that permits appropriate comparisons to be drawn to earlier research, it is important to ensure that the switching behaviour in spread volatility is not biasing the findings. While the LR tests of the individual spread series in Section 3 broadly support the assumption that there is a single state variable, in a statistical sense, they do not necessarily imply that the intercept and the volatility move together on every occasion. And if they do not, then the regime correlation results in the above section can be smaller or larger than those of interest, that is, between the regimes of the intercept and those of the economic variables. To investigate this potential source of bias, we allow the low frequency movement of the intercept and the volatility to be driven by two different state variables such that p

yt = μ ( s1,t ) + ∑ φi yt −i + ε t

(

where ε t | s2,t ~ N 0, σ

i =1

2

( s ) ) . As in the previous sections, the movement of the two state 2,t

variables can be fully characterized by a new state variable st defined as

st = 1 if s1,t = 0, s2,t = 0 st = 2 if s1,t = 0, s2,t = 1 st = 3 if s1,t = 1, s2,t = 0 st = 4 if s1,t = 1, s2,t = 1 This four-state MSI specification allows for both co-movement ( st = 1 , st = 4 ) as well as counter-movement ( st = 2 , st = 3 ) of the intercept and

volatility.

We measure the

smoothed probability of an intercept regime, independent of volatility regime, as the sum of

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Yan Li and James M. Steeley

the smoothed probabilities of regimes 1 and 2. We then correlate this with the smoothed probability of the corresponding regime with the other variables. The results are given in Table 8. The sample correlation coefficient between equity volatility and the spreads are 0.4238 for AAA spread and 0.6092 for BAA spread. Although these are lower than the ergodic correlations measured in the previous sections, they are still much higher than has been found in the previous studies that adopted only high frequency modelling approach. The correlations with the growth rate for the spreads are also much higher than has been observed with high frequency methods. It should also be noted that, since the sample correlation is based on the probabilities filtered from a univariate estimation that effectively assumes independence between the variables, these correlations may therefore underestimate the real correlation if the variables are indeed correlated.

V. Conclusion

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In this paper we conjecture that the low frequency movement of high rating credit spreads may reveal more information about a firm’s changing credit quality than can be observed using high frequency methods and therefore there should be higher correlation with some of the theoretical credit spread determinants. We test the conjecture by applying Markov switching models to analyze the low frequency movement of high rating credit spreads, and the relationship between the low frequency movement of credit spreads and that of the two macroeconomic variables: industrial output and the equity market volatility. We find evidence of strong low frequency correlation between credit spreads and equity volatility. This is consistent with Merton’s (1974) corporate bond pricing model. However, we find that the low frequency movement to the long run mean is very slow and the relatively short duration of the regimes can distort the relation between credit spread determinants and the observed spread level. Thus, one may easily end up with a spuriously weak influence of credit spread determinants, which could explain the relatively poor results of previous studies.

Appendix: Tables of Estimation Results over Sample Period 04/1953-07/2001 Table A1 contains the estimation results of the bivariate system of credit spreads (AAA or BAA) and the growth rate of the industrial output (DIP) over sample period 04/195307/2001. The model is specified as p

y1,t = μ1 ( st ) + ∑ φ1,i y1,t −i + ε1,t i =1

(1)

p

y2,t − μ 2 ( st ) = ∑ (φ2,i y2,t −i − μ 2 ( st −i ) ) + ε 2,t i =1

Where (1) is for credit spreads and (2) is for the growth rate of the industrial output.

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(2)

Sticky Credit Spreads, Macroeconomic Activity and Equity Market Volatility

71

Table A1. AAA

BAA

μ0

DIP

DIP

-0.0008 [0.0067]

-0.4786 [0.0766]

0.0389 [0.0165]

μ1

0.0453 [0.0131]

0.1122 [0.0423]

φ1 φ2

1.0165 [0.0423]

0.2654 [0.0327] 0.1478 [0.0496]

1.1447 [0.0639]

-0.5239 [0.1398] 0.2477 [0.0430] 0.1472 [0.0706]

0.1603 [0.0520] 0.1500 [0.0494] 0.1256 [0.0092]

-0.3379 [0.0893]

0.1550 [0.0654]

0.1543 [0.0473]

0.1495 [0.0571]

0.0075 [0.0017]

0.1310 [0.0156]

φ3

0.1880 [0.0391]

σ 02

0.0031 [0.0004]

σ 12

-

0.0557 [0.0151]

-

MAE

0.0257 [0.0026] 0.0885

0.2964

0.1137

0.2952

RMSE MAE* RMSE*

0.1237 0.1001 0.1485

0.4071 0.3981 0.4739

Loglik

167.7653

0.1615 0.0993 0.1281 26.4961

LR

12.0734 -0.3976 [0.1272]

10.8767 -0.3317 [0.1290]

ρ Notes:

-0.2344 [0.0559]

ρ*

*

0.4044 0.4005 0.4762

is the ergodic correlation of regimes. The MAE*, RMSE* are the out-of-sample MAE and

RMSE. In brackets are the White heterscadasticity consistent standard errors.

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Table A2 is the estimation results of the bivariate system of credit spreads and equity returns over sample period 04/1953-07/2001. The model is specified as p

y1,t = μ1 ( st ) + ∑ φ1,i y1,t −i + ε1,t i =1

(1)

p

rt = μ2 + ∑ φ2,i rt −i + ε 2,t

(2)

i =1

Table A2. AAA

rt

BAA

rt

μ0

0.0050 [0.0093]

0.8219 [0.1811]

0.0414 [0.0134]

0.7903 [0.1752]

μ1 φ1

0.0516 [0.0169]

-

0.1239 [0.0289]

-

1.0231 [0.0485]

0.0202 [0.0673]

1.1264 [0.0545]

0.0217 [0.0438]

φ2

-0.2330 [0.1785]

-

-0.3316 [0.0778]

-

φ3

0.1785 [0.0425]

-

0.1631 [0.0440]

-

σ

2 0

0.0043 [0.0009]

9.8627 [1.3103]

0.0072 [0.0014]

10.2040 [1.2103]

σ 12

0.0299 [0.0045]

33.2565 [5.1521]

0.0565 [0.0107]

34.1332 [5.1038]

0.1137

0.2952

0.1135

3.2767

MAE

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72

Yan Li and James M. Steeley Table A2. Continued

RMSE MAE* RMSE*

Loglik LR

ρ

*

AAA

rt

BAA

rt

0.1615 0.0993 0.1281

0.4044 0.4005 0.4762

0.1610 0.0987 0.1262

4.2908 3.5672 4.5802

-1174.5024

-1301.7660

10.4572 0.6231 [0.2916]

-31.639 0.7825 [0.1160]

ρ*

Notes: is the ergodic correlation of regimes. The MAE*, RMSE* are the out-of-sample MAE and RMSE. In brackets are the White heterscadasticity consistent standard errors. The estimates of the transition probabilities have many close to zero values and are not reported here.

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References [1] Ang, A. & Bekaert, G. Regime switches in interest rates, working paper 6508, NBER. [2] Altman, L. & A. Saunders (2003), A survey of cyclical effects in credit risk measurement models, Technical report, BIS Working paper, 126. [3] Bansal, R. & H. Zhou (2002), Term structure of interest rates with regime shifts, Journal of Finance, 57, 1997-2043. [4] Barnhill, Joutz & Maxwell (2000), Factors Affecting the Yield on Noninvestment Grade Bond Indices, Journal of Empirical Finance, 57-86. [5] Basle Committee on Banking Supervision (2003), The new Basle capital accord, report, Bank of International Settlements, Basle. [6] Baxter, (1994). Real exchange rates and real interest differentials, Have we missed the business-cycle relationship?, Journal of Monetary Economics, 33, 5-37. [7] Bekaert, G., Hodrick, R. J. & Marshall, D. A. (1998). Peso problem Explanation for the term structure anomalies, NBER working paper. [8] Bernanke, B., Gertler, M. & Gilchrist, S. (1999). The financial accelerator in a quantitative business cycle framework, Handbook of Marcroeconomics (Edited by J. Taylor, & M. Woodford), Volume 1, 1341-1393, Elsevier. [9] Campbell, J. & Taksler, G. B (2003), Equity volatility and corporate bond yields, Journal of Finance, 58, 2321-2349. [10] Chen, N. F. (1991), Financial investment opportunities and the macroeconomy, Journal of Finance, 46, 529-554. [11] Collin-Dufresne, P. & Goldstein, R. (2001). The determinants of credit spread change, Journal of Finance, 56, 2177-2208. [12] Duffee, G. (1998). The relation between Treasury yields and corporate bond yield spreads, Journal of Finance, 53, 2225-2242. [13] Duffee, G. (1999). Estimating the price of default risk, Review of Financial Studies, 12, 197-226. [14] Duffie, D. & Singleton, K. (1999). Modeling the term structure of defaultable bonds, Review of Financial Studies, 12, 687-720.

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73

[15] Elton, E., Gruber, M., Agrawal, D. & Mann, C. Explaining the rate spread on corporate bonds, Journal of Finance, 56, 247-277. [16] Fama, E. F. & French, K. R. (1989). Business conditions and expected returns on stocks and bonds, Journal of Financial Economics, 25, 23-49. [17] Gertler, M. & Lown, C. S. (2000). The information in the high yield bond spread for the business cycle: evidence and some implications, Working paper, NBER. [18] Gorton, G. B. & He, P. (2003), Bank credit cycles, Working paper, University of Pennsylvania. [19] Gray, S. F. (1996), Modeling the conditional distribution of interest rates as a regimeswitching process, Journal of Financial Econometrics, 42, 27-62. [20] Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and business cycle, Econometrica, 57, 357-384. [21] Hamilton, J. D. (1994). Time Series Analysis, Princeton University Press, Princeton, NJ. [22] Hamilton, J. D. & Susmel, R. (1994), Autoregressive conditional heteroskedasticity and changes in regimes, Journal of Econometrics, 64, 307-333. [23] Hamilton, J. D. & Lin, G. (1996), Stock market volatility and the business cycle, Journal of Applied Econometrics, 11, 573-593. [24] Hansen, B. E. (1992). The likelihood ratio test under non-standard conditions: testing the Markov switching model of DNP, Journal of Applied Econometrics, 7, S61-S82. [25] Hansen, B. E. (1996). Erratum: The likelihood ratio test under non-standard conditions: testing the Markov switching model of DNP, Journal of Applied Econometrics, 11, 195198. [26] Huang, J. Z. & Huang M. (2003), How much of the corporate-Treasury yield spread is due to credit risk, Working paper, Standard University. [27] Hunag, J. Z. & Kong W. P. (2003). Explaining credit spread change: new evidence from option-adjusted bond indexes, Journal of Derivatives. [28] Jarrow, R. A., Land, D. & Yu, F. (2000). Default risk and diversification: Theory and application, Working paper, Cornell University. [29] Morgan, J. P. (1997). Inc. RiskMetrics, 4th ed. Technical document. New York: J.P.Morgan, Inc. [30] Morgan, J. P. (1995). Inc. CreditMetrics, Technical Document, New York: J. P. Morgan, Inc. [31] Kim, H. J. & Charles, R. (1998). Nelson, and Richard Atartz, Testing for mean reversion in heteroskedastistic data based on Gibbs-sampling-augmented randomization, Journal of Empirical Finance. [32] Koopman, S. J. & Lucas, A. (2003). Business and default cycles for credit risk, Working paper, Universiteit Amsterdam, the Netherlands. [33] Krolzig, H. M., Marcellino, M. & Mizou, G. E. (2002). A Markov-switching vector equilibrium correction model of the UK labor market, Empirical Economics, 27, 233-254. [34] Lam, P. (1990). The Hamilton model with a general autoregressive component: estimation and comparison with other models of economic time series, Journal of Monetary Economics, 36, 607-630. [35] Leland, H. E. & Toft, K. (1996). Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads, Journal of Finance, 51, 987-1019.

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[36] Liu, J., Longstaff, F. & Mandell, (2000). The market price of credit risk: an empirical analysis of interest rate swap spreads, working paper, University of California. [37] Longstaff, F. & Schwartz, E. (1995). A simple approach to valuing risky fixed and floating rate debt, Journal of Finance, 50, 789-821. [38] Lopez, J. A. (2002). The empirical relationship between average asset correlation, firm probability of default and asset size, Working Papers in Applied Economic Theory, Federal Reserve Bank of San Francisco. [39] Merton, R (1974). On the pricing of corporate debt: The risk structure of interest rates, Journal of Finance, 29, 449-470. [40] Morris, C., Neal, R. & Rolph, D.(1998), Credit spreads and interest rate: a cointegration approach, Working paper, Federal Reserve Bank of Kansa City. [41] Nickell, P. W. Perraudin, & Varotto, S. (2000), Stability of rating transitions, Journal of Banking and Finance, 29, 449-470. [42] Stock, J. H. & Waston, M. (1989). New indexes of coincident and leading economic indicators, NBER Macroeconomics Annual, 4, 351-394. [43] White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica, 48, 817-838.

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In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 75-97

ISBN: 978-1-60876-329-0 © 2010 Nova Science Publishers, Inc.

Chapter 3

PROFITABILITY DETERMINANTS: AN EMPIRICAL STUDY OF PORTUGUESE SMES Zélia Serrasqueiro* Management and Economics Department, Beira Interior University and Researcher of CEFAGE- Évora University, Portugal

Abstract

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The increasing importance of service SMEs for employment and for the wealth of the Portuguese economy motivates the current study that seeks to verify if profitability determinants of service SMEs are different from the profitability determinants of manufacturing SMEs. For the period 1999–2006, we use data collected for two research samples: 1) 610 unlisted service SMEs; and 2) 381 unlisted manufacturing SMEs. As determinants of firm profitability we consider: 1) profitability of the previous period; 2) firm size; 3) firm age; 4) liquidity; 5) long-term debt; 6) R&D intensity; 7) asset tangibility; and 8) default risk. To control for possible data bias we use a two-step procedure, an innovative estimation method in the context of the study of profitability determinants of SMEs. In the first step, we estimate probit regressions, for service and manufacturing SMEs, considering profitability determinants as explanatory variables, and obtain the inverse Mill’s ratio. In the second step, we introduce the inverse Mill’s ratio as an additional explanatory variable, in the regressions performed for the profitability determinants of services and manufacturing SMEs. The empirical evidence obtained indicate that there are strong significant differences between the profitability determinants of service SMEs and those of manufacturing SMEs: 1) size, liquidity, long-term debt; R&D intensity are the factors fostering the profitability of service SMEs, but they are unimportant factors for the profitability of manufacturing SMEs; 2) the default risk is a factor inhibiting the profitability of the service SMEs, but it is unimportant as a factor of profitability of manufacturing SMEs; 3) asset tangibility is a determinant promoting, whereas age is a determinant inhibiting, the profitability of manufacturing SMEs; these two determinants are unimportant for the profitability of service SMEs; and 4) the persistence of profitability verifies greater magnitude in the context of SMEs belonging to the manufacturing sector in comparison with that verified by SMEs of the service sector. As a general overview of the results, the service SMEs are more dependent on liquidity and long-term debt, and they are more vulnerable regarding default risk compared to the manufacturing SMEs. Furthermore, R&D intensity is the most important determinant *

The author gratefully acknowledges partial financial support from FCT, program POCTI.

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Zélia Serrasqueiro fostering the profitability of service SMEs, whereas tangibility assets are the most important determinant fostering the profitability of manufacturing SMEs.

Keywords: Dynamic Panel Estimators; Profitability SMEs; Service Sector; Manufacturing; Two Step Estimation Method.

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1. Introduction The study of the determinants of firm profitability has warranted prominence in various studies concerning industrial economics, strategic management and financial management. In industrial economics, researchers (Bain, 1956; Mueller, 1977; Porter, 1980; Slater and Olsen, 2002), focus firstly upon the persistence of profitability, and secondly on the influence of firm characteristics such as size and age on profitability. Researchers in the field of strategic management (Teece, 1981; Peteraf, 1993; Levinthal, 1995; Barney, 2001) study the influence of heterogeneity of firm resources on profitability, and these authors give great emphasis to the influence of tangible and intangible assets on firm profitability. Finally, researchers in the area of financial management (Little and Rayner, 1966; Ball and Watts, 1972; Callen et al., 1993; Chan et al., 2003) have focused their studies on the influence of financial resources, namely firm liquidity and levels of debt, as well as risk, on profitability. According to Galbreath and Galvin (2008) profitability is influenced by various aspects: 1) firm specific characteristics; 2) specificity of the markets where the firm operates; and 3) specific characteristics of the sectors where the firm operates. It is particularly relevant to highlight the importance of industry sector as a possible determinant of profitability, since firms’ specific characteristics as well as the specificity of the markets where they operate can clearly be influenced by industry sector. Although the study of profitability determinants has been amply dealt with in the literature, specific studies comparing determinants of firm profitability of the service and manufacturing sectors are scarce, with the exceptions of the studies by Goddard et al. (2005) of Belgian, Spanish, French, Italian and British firms, and the study by Galbreath and Galvin (2008) of Australian firms. Market liberalization and deregulation on a world scale in general, and on the European Union in particular, lead to considerable reduction of the legal and economic barriers firms face. On the one hand, this allows firms greater capacity for diversification of activities and products, which allows increased profitability, but on the other hand, the increased competition and convergence of the technology that firms use is an obstacle to take advantage of investment opportunities that may lead to diminished firm profitability. Study of profitability determinants is particularly relevant in the context of SMEs. The higher level of risk associated with SME activities, contributing to greater likelihood of bankruptcy, can lead to restrictions to obtain finance, which inhibits these firms from making efficient use of investment opportunities with negative consequences on profitability. The service sector is especially prominent in the European economy, namely for economic growth and for job creation, with service SME activity being extremely relevant in this particular context. In Portugal, SMEs account for around 99.6% of businesses (IAPMEI, 2008). The number of SMEs in the service sector has been growing, compared to what has happened in the context of manufacturing SMEs. Between 2000 and 2005, the number of

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Profitability Determinants: An Empirical Study of Portuguese SMEs

77

service SMEs grew by 10.1%, employment grew by 8.6% and business volume was up 7.3%. As for manufacturing SMEs, the same period recorded growth of only 4.5% in number, with a reduction in employment of 0.2%, and business volume down by 0.3%. Given the scarcity of studies comparing the profitability of service SMEs and manufacturing SMEs, and considering the growing importance of service SMEs in the context of the Portuguese economy, this study has two main objectives: 1) to contribute to the empirical literature on the study of determinants of firm profitability, comparing the profitability determinants of service and manufacturing SMEs; and 2) in the Portuguese context, ascertain if possible differences in the profitability determinants of service and manufacturing SMEs justify distinct economic policies, according to the sector of activity to which SMEs belong. We take a wide set of determinants usually considered in the specialized literature. As profitability determinants usually considered by researchers in the area of industrial economics, we take: 1) profitability in the previous period; 2) size; and 3) age. As profitability determinants usually used by researchers in the area of strategic management, we consider: 1) asset structure; and 2) Research and Development (R&D) intensity. Finally, as profitability determinants usually used by researchers in the area of financial management, we consider: 1) liquidity; 2) long-term debt; and 3) risk. To control for the sample bias problem, we use the two-step estimation procedure introduced by Heckman (1979). In step one, a firm survival model for the full sample (both surviving and existing firms) is estimated, using a probit regression, from which we determine the inverse Mill’s ratio variable which is added as a correcting factor in step two when estimating profitability determinants. At the second stage, we use dynamic panel estimators in order to estimate suitably the persistence of profitability in Portuguese service and manufacturing SMEs. The two-step estimation method is original for studying the profitability determinants of firms in general and SMEs in particular. The empirical evidence obtained in this study lets us conclude there are statistically significant differences in the profitability determinants of Portuguese service and manufacturing SMEs. The empirical evidence also suggests that economic policies to support Portuguese SMEs should be of a different nature according to the sector of activity to which they belong. After this introduction, the study is structured as follows: 1) section 2 presents the research hypotheses; 2) section 3 presents the methodology used in this study, namely the database, variables and estimation method used; 3) section 4 presents the results obtained in this study; 4) section 5 discusses the results; and 5) finally, section 6 presents the conclusions and implications of this study.

2. Research Hypotheses According to Mueller (1986) and Goddard et al. (2005), there is a propensity for firm profitability to be persistent over time. The breaks of persistence of profitability, which may occur at certain times, are filled by firms entering or leaving the market. Persistence of profitability is expected to be less for SMEs than for large firms, given the greater level of business risk associated with their activities and the lower level of economies of scale (Picot and Dupuy, 1998; Mueller, 1990).

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Greater firm size can contribute to increased profitability for multiple reasons (Winter, 1994; Hardwick, 1997; Wyn, 1998; Gschwandtner, 2005): 1) greater size allows more efficient use of economies of scale; 2) large firms are more able to diversify the activities and products that they offer, which lets them cope more successfully with changes of the markets where they operate; and 3) greater firm size allows them to increase market power, as a consequence of raised barriers to the entry of possible competitors. In the context of SMEs, greater capacity to diversify can be especially important for increased profitability, given the special ability of SMEs to take advantage of good growth opportunities generated by their greater organizational flexibility (Rogers, 2004). In addition, Davidson (1989), Delmar et al. (2003) and Wiklund et al. (2003) state that greater SME size can be a motivational factor for all agents participating in firm’s activities, which contributes to increased profitability. The effect of learning over time can be fundamental for firms to cope more easily with the multiple challenges that they face, whether internal challenges of increased productive efficiency or external challenges forced by changes in their markets. Therefore, greater firm age can contribute to increased profitability (Johnsen and McMahon, 2005). In this context, Lu and Beamish (2006) conclude that greater SME age allows the learning effect of efficient management of internal resources. However, Rogers (2004) refers that younger SMEs, with consequently greater entrepreneurial ability, are more able to diversify and to respond to the multiple challenges imposed by market conditions, and this may result in considerable increases of profitability in this type of firm. Audretsch et al. (2004) claim that service firms find more easily a minimum level of efficiency that allows them to achieve survival, compared to manufacturing firms. This happens because of the lower level of investment necessary in fixed capital, lower level of sunk costs, and consequently lower level of economies of scale corresponding to the minimum level of efficiency. We can expect service SMEs to have greater persistence of profitability, and that size and age are less important for increased profitability, compared to the case with manufacturing SMEs, by two fundamental reasons: 1) they find more easily a minimum level of efficiency that allows them to survive; and 2) they have greater organizational flexibility and are more able to change the composition of their assets. Based on the above arguments, we formulate the following research hypotheses: H1: The persistence of profitability of service SMEs is greater than that one of manufacturing SMEs. H2: Size and age are more important for increased profitability in manufacturing SMEs than in service SMEs. Various authors (Teece, 1998; Barney, 2001; Hitt et al., 2001) claim that tangible assets are of little relevance for increased firm profitability. The reasons pointed out by the authors are basically two: 1) the great majority of tangible assets are normally acquired in the market, creating the same benefits for all firms with capacity to acquire them; and 2) if competing firms are willing to pay, it is relatively easy for competitors to use tangible assets similar to those used by a firm at a given time.

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However, Johnsen and McMahon (2005) mention that in business activities characterized by considerable levels of tangible assets and economies of scale, tangible assets, given the nature of firms’ activities, can be a relevant characteristic for increased profitability. According to Johnsen and McMahon (2005), tangible assets can be particularly important for increased profitability of manufacturing SMEs. One of the most relevant intangible assets in the context of firm activities is R&D expenditure (Rogers, 2004). According to Beise-Zee and Rammer (2006), Rickne (2006) and Andries and Debackere (2007), R&D expenditure can take on special importance for SME activity. This happens because R&D is closely associated with greater innovative capacity of firms, contributing decisively for diversification of their activities. Diversification of activities can contribute to mark relative positions in the markets where SMEs operate, as well as allowing expansion into new markets, and may contribute decisively to increased profitability. While tangible assets are important in the total assets of the manufacturing firms, intangible assets are closely linked to service firms’ activities. Based on the above arguments, we formulate the following research hypotheses:

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H3: Tangible assets take on greater importance for increased profitability in manufacturing SMEs than in service SMEs. H4: R&D intensity takes on greater importance for increased profitability in service SMEs than in manufacturing SMEs. According to Deloof (2003), a higher level of liquidity in SMEs increases the possibility of firm to accomplish its short-term commitments, reducing the financial stress SMEs are subject to. For Fagiolo and Luzzi (2006) and Honjo and Harada (2006), the reduction of financial stress is a fundamental aspect for SMEs to be able to increase profitability, since this can contribute to greater capacity to make efficient use of good investment opportunities. According to Jensen and Meckling (1976), there are relevant conflicts of interest between owners/managers and creditors regarding firms’ recourse to debt. Owners/managers may be interested to finance projects with debt that, despite the expected high profitability, may equally have a high level of associated risk. When investment projects are successful, it is above all the firms that enjoy the benefits, but in cases of failure it is the creditors who bear almost all the costs. In this respect, Myers (1977) concludes that when creditors grant shortterm, rather than long-term, debt contributes to diminish the conflicts of interest between firm owners/managers and creditors. This occurs, since it is easier for creditors to monitor repayment of the debt, given the need for firms to do so over a shorter period of time. Conflicts of interest between owners/managers and creditors can be exacerbated in the context of SMEs, due to the level of risk associated with these firms’ activities. Consequently, SMEs may become excessively dependent on short-term debt, and the possible financial stress of paying off the debt over a very short period contributes to the failure to take advantage of good investment opportunities. In this context, when internal finance is insufficient, Fagiolo and Luzzi (2006) conclude that access to long-term debt by SMEs can contribute to increased profitability, given the greater capacity to make efficient use of good investment opportunities. According to Pettit and Singer (1985), the high operational risk of SMEs may contribute to diminished levels of profitability, as a consequence of the more restricted conditions they

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face in accessing credit. For SMEs is easier to change their assets compositions, due to greater flexibility of their organizational structure, which increases the difficulty for creditors to assess the exact nature of SMEs’ asset structure. Given the relevance of tangible assets for SMEs to obtain external finance, and considering the lower level of tangible assets of service firms, compared to the case of manufacturing firms, we can expect on one hand that liquidity and long-term debt are more relevant for increased profitability in service SMEs than in manufacturing SMEs. On the other hand, we can expect that the higher level of risk means a sharper fall in the profitability of service SMEs compared to what the case of manufacturing SMEs. Based on the above, we formulate the following research hypotheses: H5: Liquidity and long-term debt are more important for increased profitability in service SMEs than in manufacturing SMEs. H6: Risk is more important for diminishing profitability in service SMEs than in manufacturing SMEs.

3. Methodology

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3.1. Database This study uses the SABI (System Analysis of Iberian Balance Sheets) database supplied by Bureau van Dijk´s, for the period from 1999 to 2006. We select SMEs based on the recommendation of the European Union L124/36 (2003/361/CE). According to this recommendation, a firm is considered SME when it meets two of the following criteria: 1) fewer than 250 employees; 2) annual balance sheet total that does not exceed 43 million euros; and 3) annual turnover not exceeding 50 million euros. Seeking to test the differences between profitability determinants in Portuguese service SMEs and Portuguese manufacturing SMEs, we select: 1) 610 unlisted SMEs from the service sector1; and 2) 381 unlisted SMEs from the manufacturing sector2. Table 1. Sample Description Firms present in the entire period 1999 – 2006 Firms entering in the period 1999 – 2006 Firms exiting in the period 1999 – 2006 Total number of firms

Services 468 66 76 610

Manufacturing 287 45 49 381

Notes: 1. Services Include: Real Estate Activities; Renting of Machinery and Equipment Without Operator and Personal and Household Goods; Computer and Related Activities; and Other Business Activities. 2. Manufacturing Include: Manufacture of food products; Manufacture of textiles; Manufacture of products of wood and paper related products; Manufacture of chemicals and chemical products; Manufacture of basic metals; Manufacture of machinery and equipment 1

Services Include: Real Estate Activities; Renting of Machinery and Equipment Without Operator and Personal and Household Goods; Computer and Related Activities; and Other Business Activities. 2 Manufacturing Includes: Manufacture of food products; Manufacture of textiles; Manufacture of wood and paperrelated products; Manufacture of chemicals and chemical products; Manufacture of basic metals; Manufacture of machinery and equipment.

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So as to avoid possible bias in the samples used, and also seeking to have research samples that are more representative of the industry sector structure of Portuguese SMEs, we consider three types of service and manufacturing SMEs: 1) SMEs that belong to the market for the entire period of analysis (468 belonging to the service sector and 287 belonging to the manufacturing sector); 2) SMEs that enter in the market during the period of analysis (66 belonging to the service sector and 45 belonging to the manufacturing sector); and 3) SMEs that leave the market during the period of analysis (76 belonging to the service sector and 49 belonging to the manufacturing sector). Table 1, shows the research sample structure of the service and manufacturing SMEs used in this study.

3.2. Variables In Table 2 we present the variables used in this study, together with their corresponding measures. Table 2. Measurement of Variables Variables Dependent variable Profitability ( PROFi ,t )

Measurement Ratio between Earnings before Interest and Taxes and Total Assets

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Independent variables Size ( SIZE i ,t )

Logarithm of Total Assets

Age ( AGEi ,t )

Logarithm of the Number of Years of Firm Existence

Asset Structure ( TANGi ,t )

Ratio between Fixed Assets and Total Assets

Research and Development ( R & Di ,t )

Ratio Between Research and Development Expenses and Total Assets

Liquidity ( LIQi ,t )

Ratio between Short Term Debt and Current Assets

Long Term Debt ( LLEVi ,t )

Ratio between Long Term Liabilities and Total Assets

Risk ( EVOLi ,t )

Absolute Value of Percentage Change of Earnings Before Interest and Taxes

The dependent variable is profitability. As independent variables, we consider: 1) size; 2) age; 3) liquidity; 4) long-term debt; 5) asset structure; 6) research and development intensity; and 7) risk.

3.3. Econometric Method The study of determinants of SME profitability without correcting possible sample bias, as a consequence of missing the firms that left the market during the period of analysis, could lead to bias of the results, given the omission of firms with survival difficulties, a situation which could be different from that of firms with good possibilities to survive.

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The best way to solve this problem is to use the two-step estimation method proposed by Heckman (1979). In the first stage, all firms are considered, both surviving and nonsurviving, we estimate a probit regression, where the dependent variable has the value of 1 if the firm is in the market and the value of 0 if it has left the market. As independent variables, we consider the determinants of profitability used in this study. At the second stage, for the estimations of regressions regarding to profitability determinants, we only consider surviving firms, and we add the inverse Mill’s ratio as one more explanatory variable, so as to control for possible data bias as a consequence of survival. The probit regression estimated in the first step allows us to calculate the additional explanatory variable of the inverse Mill’s ratio, a variable that permits control of possible sample bias. The probit regression to estimate, corresponding to the first step, is given by: 7

Pr(δ i ,t = 1) = τ 0 + κPROFi ,t −1 + ∑ τ K X K ,i ,t + d t + z i ,t ,

(1)

K =1

where: PROFi ,t −1 is profitability in the previous period; X K ,i ,t is the vector of the K 3

determinants of profitability considered in this study ; d t are annual dummy variables that measure the impact of alterations in the economic situation on the likelihood of bankruptcy; and z i ,t is the error.

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4

For each of the observations, we consider the inverse Mill’s ratio as an additional explanatory variable of profitability. At the second stage, in order to estimate regressions referring to profitability determinants, we use dynamic panel estimators. Advantages of dynamic estimators are the elimination of firms’ non-observable individual effects, the greater control of endogeny and the greater control of collinearity between explanatory variables. Use of dynamic panel models has also the advantage of allowing determination of the persistence of profitability according to the dynamic approach of profitability changes over time. Therefore, the regressions to estimate, using various dynamic panel estimators, can be expressed as follows: 7

PROFi ,t = β 0 + δPROFi ,t −1 + ∑ β K X k ,i ,t + β λ λi ,t + d t + vi + ei ,t ,

(2)

K =1

in which:

λi,t is the inverse Mill’s ratio; vi are the non-observable individual effects; and

ei ,t is the error, assumed to have normal distribution. Estimation of equation (2) using static panel models, with or without correlation between non-observable individual effects and profitability determinants, leads to biased and inconsistent estimates of the parameters, since as well as there is correlation between vi and

PROFi ,t −1 , correlation also exists between ei ,t and PROFi ,t −1 . Correlation of non3

As already mentioned, we consider as profitability determinants of Portuguese service and manufacturing SMEs: 1) size; 2) age; 3) liquidity; 4) long-term debt; 5) asset structure; 6) R&D intensity; and 7) risk. 4 For more details of the way to calculate the inverse Mill’s ratio, consult Heckman (1979).

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observable individual effects and the error with the lagged profitability has the consequence of bias and inconsistency of the estimated parameters. Arellano and Bond (1991) recommend estimation of equation (2) with the variables in first differences, and the use of profitability lags and their determinants at level as instruments. Estimation of equation (2) in first differences allows for elimination of nonobservable individual effects ( vi ), therefore it eliminates the correlation between vi and

PROFi ,t −1 . Use of profitability lags and their determinants as instruments allows the creation

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of orthogonal conditions between eit and PROFi ,t −1 , eliminating correlation. Nevertheless, Blundell and Bond (1998) conclude that when the dependent variable is persistent, with high correlation between its values in the current and previous periods, and the number of periods is not very high, the General Method of Moments (GMM, 1991) estimator is inefficient, as a rule the instruments used being weak. In these circumstances, Blundell and Bond (1998) extend the GMM (1991) estimator, considering a system with variables at level and in first differences. For variables at level in equation (2) the instruments are the lagged variables in first differences. In the case of the variables in first differences in equation (2) the instruments are those lagged variables at level. However, the GMM (1991) and GMM system (1998) estimators can only be considered valid on two conditions: 1) if the restrictions created, a consequence of the used instruments, are valid; and 2) there is no second order autocorrelation. The Sargan test assesses the validity of the restrictions in the case of the GMM (1991) estimator and the Hansen test does so in the case of the GMM system (1998) estimator. In both cases, the null hypothesis indicates that the restrictions imposed by use of the instruments are valid, thus the alternative hypothesis indicates that the restrictions are not valid. By rejecting the null hypothesis, the conclusion is that the estimators are not robust. We test for the existence of first and second order autocorrelation. The null hypothesis is that no autocorrelation exists, thus the alternative hypothesis refers to the existence of autocorrelation. By rejecting the null hypothesis of non-existence of second order autocorrelation, the conclusion is that the estimators are not robust. Bruno (2005) concludes that in situations where the number of cross-sections is not very high, and consequently nor is the number of observations very high, use of dynamic estimators, given the number of instruments generated, can lead to bias of the estimated parameters. Given the number of observations, the study uses the Bruno (2005) LSDVC estimator, regression of convergence of corrected fixed effects, so as to test the robustness of the results. Seeking to test for differences in the relationships between determinants and profitability for service and manufacturing SMEs, we use the Chow5 test. We test for possible differences in each of the determinants considered in this study, as well as the overall difference for the set of determinants considered. The null hypothesis is that there are no differences in the estimated parameters referring to the relationships between determinants and profitability for service and manufacturing SMEs, the alternative hypothesis relates to the existence of differences in the estimated parameters. 5

We also use the Chow test to test for differences in survival determinants for Portuguese service and manufacturing SMEs.

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Table 3. Descriptive Statistics – Services and Manufacturing Services

Manufacturing

Variable

N

Mean

S.D.

Min.

Max.

N

Mean

S. D.

Min.

Max.

PROFi ,t

3933

0.05211

0.08089

-0.35539

0.62002

2354

0.05305

0.08317

-0.29832

0.60445

SIZE i ,t

3933

15344804

17300884

36112.3

42879223

2354

16178498

18089384

38509.9

42941134

AGEi ,t

3933

15.0792

6.24914

2

98

2354

16.09348

6.78487

2

104

TANGi ,t

3933

0.29778

0.21899

0.00358

0.98933

2354

0.35098

0.24176

0.02698

0.99461

R & Di ,t

3933

0.01579

0.04337

0

0.79662

2354

0.01023

0.03876

0

0.68804

LIQi ,t

3933

1.48984

1.30938

0.040581

30.7932

2354

1.58932

1.337463

0.042834

33.3697

LLEVi ,t

3933

0.12011

0.14338

0

0.73098

2354

0.16738

0.17839

0

0.76618

EVOLi ,t

3933

1.64564

2.89843

0.00056

22.8394

2354

1.47583

2.6678

0.00078

20.0993

Profitability Determinants: An Empirical Study of Portuguese SMEs

85

4. Results 4.1. Descriptive Statistics The following table presents the descriptive statistics of the dependent and independent variables1 used in this study, for service and manufacturing SMEs. We find that the average profitability of manufacturing SMEs is slightly above of that of Portuguese service SMEs, although the difference cannot be considered very significant. On average, the size2 and age of manufacturing SMEs is greater than the size and age of service SMEs, the same occurring with liquidity and long-term debt. As could be expected, manufacturing SMEs have a higher average level of tangible assets than service SMEs, the opposite verified by the average values of R&D intensity. Finally, we find that the average level of risk is higher in service SMEs than in manufacturing SMEs.

4.2. Survival Analysis Table 4 presents the results of the probit regressions for service and manufacturing SMEs. Table 4. Survival Analysis – Service and Manufacturing SMEs Dependent Variable: Pr(δ i ,t = 1) Independent Variables PROFi ,t −1

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SIZEi ,t AGEi ,t TANGi ,t R & Di ,t LIQi ,t

LLEVi ,t EVOLi ,t PseudoR 2

Services 0.54838*** (0.05647) 0.11389*** (0.02098) 0.09765*** (0.02765) 0.17677*** (0.05476) 0.41435*** (0.10432) 0.17829*** (0.04472) 0.23453*** (0.05845) -0.04673*** (0.01508) 0.48839

Manufacturing 0.19283*** (0.04774) 0.06228*** (0.01458) 0.05854*** (0.01963) 0.08674** (0.04264) 0.09123 (0.09674) 0.08637** (0.04289) 0.11454** (0.05508) -0.00534 (0.01786) 0.39657

1

We opt to present the descriptive statistics of the size and age variables not as logarithms, so that the information about Portuguese SMEs is more understandable. However, in the regressions we use the variables as logarithms, an identical procedure to that used in the literature. 2 Average business turnover for Portuguese manufacturing SMEs is 26489813, the average number of employees being 134. As for Portuguese service SMEs, average business turnover is 25583942, and average number of employees is 123. We find that just as in the case of assets, Portuguese manufacturing SMEs have on average greater business volume and number of employees than Portuguese service SMEs.

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Zélia Serrasqueiro Table 4. Continued Dependent Variable: Pr(δ i ,t = 1) Independent Variables Log Likelihood Companies Observations

Services -806.67

Manufacturing -749.51

610 3097

381 1952

Notes: 1. Robust standard deviations in parentheses 2. *** significant at 1% level. 3. Year – dummies are included, but not shown.

Table 5. Chow Test – Differences of Survival Determinants – Service and Manufacturing SMEs Dependent Variable: Pr(δ i ,t = 1) Independent Variables ( PROFi ,t −1 ) α SERV − α MANUF = 0

χ 2 (1) ( SIZEi ,t ) τ 1SERV − τ 1MANUF = 0 χ 2 (1) ( AGEi ,t ) τ 2 SERV − τ 2 MANUF = 0 χ (1) 2

( TANGi ,t ) τ 3 SERV − τ 3 MANUF = 0

χ (1) 2

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χ 2 (1) ( LIQi ,t ) τ 5 SERV − τ 5 MANUF = 0

χ 2 (1) ( LLEVi ,t ) τ 6 SERV − τ 6 MANUF = 0

χ 2 (1) ( EVOLi ,t ) τ 7 SERV − τ 7 MANUF = 0

χ 2 (1) Global Difference χ 2 (8)

27.07*** (0.0000) 21.85*** (0.0000) 18.91*** (0.0000) 22.54*** (0.0000) 36.33*** (0.0000) 23.45*** (0.0000) 25.06*** (0.0000) 24.41*** (0.0000) 29.38*** (0.0000)

Notes: 1. *** significant at 1% level. 2. Probabilities in parentheses

The empirical evidence obtained lets us conclude that: 1) profitability of the previous period, size, age, liquidity, long-term debt, tangible assets, and R&D intensity all contribute positively to greater probability of survival of service SMEs, and the variable risk is a restrictive factor of survival probability in service SMEs; and 2) profitability of the previous period, size, age, liquidity, long-term debt and tangible assets all contribute positively to

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greater probability of survival of manufacturing SMEs, while R&D intensity and risk do not contribute positively or negatively to the probability of survival of these SMEs. Table 5 below presents the results of the Chow test of possible differences between the survival determinants of service and manufacturing SMEs. For each of the profitability determinants considered in this study, the results of the Chow test indicate rejection of the null hypothesis of equality of estimated parameters regarding relationships between profitability determinants and survival probability of service and manufacturing SMEs. The result of the overall Chow test confirms there are significant differences between profitability determinants and survival probability in service and manufacturing SMEs.

4.3. Dynamic Estimators Table 6 below presents the results of the relationships between determinants and profitability of service and manufacturing SMEs, considering for this purpose use of the GMM (1991), GMM system (1998) and LSDVC (2005) estimators. Table 6. Determinants of Profitability—Service and Manufacturing SMEs Dependent Variable: Independent variables

PROFi ,t −1 SIZEi ,t Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

AGEi ,t TANGi ,t R & Di ,t LIQi ,t LLEVi ,t EVOLi ,t

λi,t CONS Firms Observations

Wald ( χ 2 ) F (N (0,1)) Sargan

(χ 2 )

PROFi ,t

Services Manufacturing GMM GMM system LSDVC GMM GMM system LSDVC (1991) (1998) (2005) (1991) (1998) (2005) 0.05647 0.33652*** 0.32838*** 0.11928** 0.55662*** 0.58929*** (0.05097) (0.05377) (0.05182) (0.05782) (0.06283) (0.06721) 0.00786 0.02529** 0.03473*** -0.02738* 0.00543 -0.01623 (0.01332) (0.01245) (0.00701) (0.01407) (0.01379) (0.01675) 0.01298 0.01234 0.01078 -0.08732*** -0.04087*** -0.03723*** (0.01987) (0.01788) (0.01563) (0.02189) (0.00956) (0.00834) -0.07821** -0.01234 -0.02349 0.06832* 0.08098** 0.11778*** (0.03705) (0.03114) (0.03778) (0.04012) (0.03783) (0.03371) 0.17362*** 0.28729*** 0.24531*** -0.00783 -0.02839 -0.04536 (0.05076) (0.06089) (0.05821) (0.05631) (0.06088) (0.07827) 0.11889*** 0.07998*** 0.07453*** -0.00984 0.01342 0.00982 (0.03006) (0.02366) (0.02112) (0.03118) (0.03749) (0.03440) 0.02832 0.07983*** 0.08631*** -0.00654 0.00768 -0.01778 (0.03098) (0.01665) (0.01774) (0.01449) (0.02009) (0.02344) -0.01678* -0.02117*** -0.01672** 0.02298 0.01982 0.00783 (0.09031) (0.05687) (0.00789) (0.04415) (0.03844) (0.03223) -0.10983*** -0.12837*** -0.16374*** -0.14783*** -0.13047*** -0.17005*** (0.02738) (0.02879) (0.03098) (0.02873) (0.02534) (0.03228) 0.01234 0.02346 0.02839** 0.02773* (0.03829) (0.04092) (0.01367) (0.01409) 534 534 534 332 332 332 2531 3097 3097 1598 1952 1952 169.43*** 156.04*** 97.04*** 41.02***

81.12*** 38.49***

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Zélia Serrasqueiro Table 6. Continued Dependent Variable:

Independent variables Hansen

GMM (1991)

Services GMM system (1998) 135.10

-6.04*** -0.37

(χ 2 )

m1 ( N (0,1)) m2 ( N (0,1))

PROFi ,t

GMM (1991)

Manufacturing GMM system (1998) 126.61

-6.35***

-5.32***

-5.11***

-0.25

-0.32

-0.48

LSDVC (2005)

LSDVC (2005)

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Notes: 1. Robust standard deviations are reported parentheses. 2. *** indicates significance at 1% level, ** indicates significance at 5% level, and * indicates significance at 10% level. 3. The estimates include time dummy variables.

Whether considering service or manufacturing SMEs as the unit of analysis, the results of the Sargan test indicate rejection of the null hypothesis of validity of the instruments used3. Given the non-validity of the instruments used, we cannot consider the results obtained with the GMM (1991) estimator as robust, and consequently open to interpretation. The results of the Hansen test, referring to the GMM system (1998) estimator, indicate that, regardless of considering service or manufacturing SMEs as the unit of analysis, we cannot reject the null hypothesis of validity of the instruments used. In addition, the results of the second order autocorrelation test also indicate that regardless of considering service or manufacturing SMEs as unit of analysis, we cannot reject the null hypothesis of absence of second order autocorrelation. Based on the results of the Hansen and second order autocorrelation tests, we can consider the results obtained with the GMM system (1998) estimator as robust, and consequently open to interpretation. Regarding the empirical evidence obtained with the LSDVC (2005) estimator, we conclude that, whether taking service or manufacturing SMEs as the unit of analysis, the parameters obtained for the relationships between determinants and profitability are similar to those obtained with the GMM system (1998) estimator, regarding sign, magnitude, and statistical significance of the estimated parameters. Therefore, we take as our reference the results obtained with the GMM system (1998) and LSDVC (2005) estimators to interpret the empirical evidence regarding the relationships between determinants and profitability of service and manufacturing SMEs. Regarding the relationships between determinants and profitability of service SMEs, we can conclude that: 1) profitability in the previous period, size, liquidity, long-term debt and R&D intensity influence positively profitability; 2) risk influences negatively profitability; and 3) age and tangible assets have neither a positive nor negative influence on profitability. As for the relationships between determinants and profitability of manufacturing SMEs, we can conclude that: 1) profitability of the previous period and tangible assets influence 3

The correlation coefficients between profitability in the present and previous periods are 0.7770 for Portuguese service SMEs and 0.7942 for Portuguese manufacturing SMEs. The high correlation coefficients between profitability in the present and previous periods indicate that profitability in Portuguese service and manufacturing SMEs is persistent. The rather low number of cross-sections together with the high correlation between profitability in the present and previous periods may contribute decisively to non-validity of the instruments when using the GMM (1991) estimator, corroborating what is forecast by Blundell and Bond (1998).

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positively profitability; 2) age influences negatively profitability; and 3) size, liquidity, longterm debt, R&D intensity and risk have neither a positive nor negative influence on profitability. Besides the above, it is worth highlighting that whether considering service or manufacturing SMEs as the unit of analysis, there is a statistically significant relationship between the inverse Mill’s ratio and profitability. Based on these results, we can conclude that use of the inverse Mill’s ratio is shown to be appropriate in order to rule out possible data bias as a consequence of the problem of survival of service and manufacturing SMEs. Table 7. Chow Test - Determinants of Short and Long Term Debt – Services and Manufacturing Dependent Variable: PROFi ,t Independent variables ( PROFi ,t −1 ) δ SERV − δ MANUF = 0

χ 2 (1) ( SIZE i ,t ) β 1SERV − β 1MANUF = 0

χ 2 (1) ( AGEi ,t ) β 2 SERV − β 2 MANUF = 0

χ 2 (1)

(TANGi ,t ) β 3 SERV − β 3MANUF = 0 χ 2 (1) ( R & Di ,t ) β 4 SERV − β 4 MANUF = 0

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χ 2 (1) ( LIQi ,t ) β 5 SERV − β 5 MANUF = 0

χ 2 (1) ( LLEVi ,t ) β 6 SERV − β 6 MANUF = 0

χ 2 (1) ( EVOLi ,t ) β 7 SERV − β 7 MANUF = 0

χ 2 (1) Global Difference χ 2 (8)

GMM system (1998) LSDVC (2005) 22.78*** 24.55*** (0.0000) (0.0000) 17.89*** (0.0000)

20.43*** (0.0000)

19.78*** (0.0000)

18.98*** (0.0000)

26.88*** (0.0000)

30.08*** (0.0000)

32.67*** (0.0000)

30.77*** (0.0000)

24.54*** (0.0000)

23.12*** (0.0000)

25.99*** (0.0000)

27.53*** (0.0000)

17.58*** (0.0000)

15.67*** (0.0000)

28.53*** (0.0000)

29.81*** (0.0000)

Notes: 1. *** significant at 1% level. 2. Probabilities in parentheses.

Table 7 below presents the results of the Chow test referring to differences in the relationships between determinants and profitability of service and manufacturing SMEs. For each of the determinants, the results of the Chow test indicate rejection of the null hypothesis of equality of estimated parameters regarding the relationships between determinants and profitability of service and manufacturing SMEs. The result of the overall Chow test confirms there are significant differences in the relationships formed between determinants and profitability of service and manufacturing SMEs.

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5. Discussion of the Results The empirical evidence indicates that the persistence of profitability in service SMEs varies between δ SERV = 0.32838 , when estimated with the LSDVC (2005) estimator, and

δ SERV = 0.33652 , when using the GMM system (1998) estimator. In the case of manufacturing SMEs, we find that persistence of profitability varies between δ MAN = 0.55662 , when

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estimated with the GMM system (1998) estimator, and δ MAN = 0.58929 , when using the LSDVC (2005) estimator. We find that the persistence of profitability of manufacturing SMEs is considerably greater than that one of service SMEs. On basis of the empirical evidence we cannot accept the hypothesis H1, since the persistence of profitability of service SMEs is less than that one recorded for manufacturing SMEs. The fact that as a general rule service SMEs find more easily a minimum level of efficiency that permits survival, compared to the case of manufacturing SMEs (Audretsch et al. 2004), does not mean, as was expected, greater persistence of profitability of Portuguese service SMEs than of Portuguese manufacturing SMEs. The empirical evidence suggests that possible market instability, as a consequence of competition (Mueller, 1986; Goddard et al., 2005), affects more severely the persistence of profitability in Portuguese service SMEs than in manufacturing SMEs. When presenting the descriptive statistics, we find that on one hand service SMEs have higher average levels of R&D intensity and risk than manufacturing SMEs, and on the other hand, average level of tangible assets is higher for manufacturing SMEs than for service SMEs. Compared to what happens for manufacturing SMEs, the greater risk associated with the activities of service SMEs, in the form of a higher average level of R&D intensity and a higher average level of operational risk, together with the lower level of economies of scale of service SMEs, may contribute decisively to less persistence of profitability of service SMEs and higher persistence of profitability of manufacturing SMEs. The conclusions of Picot and Dupuy (1998) and Mueller (1990), about the persistence of profitability in SMEs seem to be particularly relevant to explain the difference of persistence of probability in Portuguese service and manufacturing SMEs. The comparison of empirical evidence regarding persistence of profitability in Portuguese service and manufacturing SMEs with that obtained by Goddard et al. (2005), despite the authors’ study do not take SMEs specifically as its unit of analysis, we can conclude that except for the profitability of Belgian firms (0.4708), the figures for persistence of profitability in Spanish (0.3697), French (0.3350), Italian (0.3698) and British (0.3408) service firms are almost identical to those obtained for Portuguese service SMEs. Regarding the figures for persistence of profitability in Belgian (0.3928), Spanish (0.3854), French (0.3547), Italian (0.4518) and British (0.3227) manufacturing firms, these are considerably lower than those obtained for Portuguese manufacturing SMEs. The empirical evidence obtained suggests that the effects of competition have considerably more influence on the persistence of profitability in firms in general in other countries than on persistence of profitability in Portuguese manufacturing SMEs. Contrary to what was expected, the empirical evidence obtained here indicates that size and age are no more important for increased profitability in manufacturing SMEs than for

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increased profitability in service SMEs. Therefore, on basis of the empirical evidence we cannot accept the previously formulated hypothesis H2. Greater size of service SMEs contributes positively to increased profitability, whereas it has a negligible effect on the profitability of manufacturing SMEs. The positive effects of size on firm profitability, forecast by Winter (1994), Hardwick (1997), Wyn (1998) and Gschwandtner (2005): 1) more efficient use of economies of scale; 2) greater capacity to diversify the activities and products offered; and 3) increased market power, and consequently the barriers to the entry of possible competitors only seem to be important for the profitability of Portuguese service SMEs, having negligible importance for the profitability of Portuguese manufacturing SMEs. The fact that service firms find more easily a minimum level of efficiency that allows them to survive, and their greater organizational flexibility, are not sufficiently relevant factors to diminish the dependence on size for increased profitability. Contributing to this result could be the considerable competition faced by Portuguese service SMEs, given the lower barriers to the entry of new competitors, compared to what happens in the context of Portuguese manufacturing SMEs. Therefore, the size of Portuguese service SMEs appears to be especially important for the effects of diversification (Rogers, 2004), and increased motivation of all agents participating in firm activities (Davidson, 1989; Delmar et al., 2003; Wiklund et al., 2003), which may contribute for increased profitability. While not specifically about SMEs, Goddard et al. (2005) find a negative relationship between size and profitability in the context of service and manufacturing firms in Belgium, Spain, France, Italy and the United Kingdom. The authors conclude there are no significant differences between sectors and countries concerning the relationship between size and profitability. Galbreath and Galvin (2008), although also not specifically about SMEs, find statistically insignificant relationships between size and profitability in Australian service and manufacturing firms. Size appears to have greater importance for increased profitability of Portuguese service SMEs than for firms of other countries. Age has a negative effect on the profitability of Portuguese manufacturing SMEs, with a negligible effect on profitability of Portuguese service SMEs. The experience effect that firms can acquire over time (Johnsen and McMahon, 2005), and the capacity to retain profits, the learning effect and efficient management of internal resources (Lu and Beamish, 2006), as a consequence of firms’ greater age, does not seem to be important for increased profitability of Portuguese service and manufacturing SMEs. Regarding Portuguese manufacturing SMEs, the arguments of Rogers (2004) seem to be important, since greater age of Portuguese manufacturing SMEs means diminished profitability, and so the entrepreneurial capacity of younger SMEs can contribute to greater capacity for diversification, this leading to increased profitability. Also, as when we analyze the relationships between size and profitability of Portuguese service and manufacturing SMEs, the empirical evidence suggests that the fact of service firms reaching more easily a minimum level of efficiency that permits survival, together with greater organizational flexibility, does not mean less importance of age for increased profitability of service SMEs compared with what happens in the case of manufacturing SMEs. Galbreath and Galvin (2008), although not specifically about SMEs, state that age is not relevant in explaining the profitability of Australian service and manufacturing firms. The

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entrepreneurial capacity seems to be more relevant for increased profitability of younger manufacturing Portuguese SMEs than for Australian firms in general. Tangible assets contribute to increased profitability of Portuguese manufacturing SMEs, with negligible importance in explaining the profitability of service SMEs. Concerning the relationships between tangible assets and profitability, the empirical evidence show that tangible assets have greater relevance for increased profitability for manufacturing SMEs than for service SME, thus we accept the hypothesis H3. The argument that most tangible assets can be acquired in the market, as long as firms are financially able to do so, and is not important for increased profitability (Teece, 1998; Barney, 2001; Hitt et al., 2001), only seems to be relevant for Portuguese service SMEs. For this effect may contribute the fact that tangible assets of service SMEs are less onerous than those used by manufacturing SMEs, which means that the various competitors are able to use the same technology more easily. On the contrary, the positive relationship between tangibility and profitability for Portuguese manufacturing SMEs corroborates the arguments of Johnsen and McMahon (2005), since the considerable amount of required tangible assets, given the nature of the activities of SMEs in the manufacturing sector, may be decisive to increased profitability. Galbreath and Galvin (2008), although not specifically about SMEs, conclude that tangible assets for Australian service and manufacturing firms have negligible importance for firm profitability. The empirical evidence obtained in this study suggests that tangible assets are less important for increased profitability of Portuguese manufacturing SMEs than for Australian manufacturing firms as a whole. R&D intensity contributes positively to profitability in Portuguese service SMEs, but is negligible in explaining the profitability of manufacturing SMEs. This being so, we can accept the hypothesis H4, since R&D intensity is more important for increased profitability for service SMEs than for manufacturing SMEs. The greater capacity of innovation and diversification of activities, as a consequence of R&D expenditure (Beise-Zee and Rammer, 2006; Rickne, 2006; Andries and Debackere, 2007), appears to be especially important for increased profitability for Portuguese service SMEs. This result is particularly important since efficient use of R&D expenditure by service SMEs can let them diversify their activities, winning relative positions in new markets, which contributes to increased profitability and, consequently, to SME survival. Tangible assets take on special relevance in the context of manufacturing firms’ activities, while intangible assets are especially relevant for service firms’ activities, which seems to contribute to tangible assets being associated with increased profitability of manufacturing SMEs, whereas R&D intensity is associated with increased profitability of service SMEs. While liquidity and long-term debt contribute to increased profitability for service SMEs, they have negligible importance in explaining the profitability of manufacturing SMEs. Based on this empirical evidence, we can accept the hypothesis H5, since liquidity and long-term debt are more important for increased profitability of service SMEs than for increased profitability of manufacturing SMEs. Greater liquidity, and consequently greater capacity to accomplish short-term commitments (Deloof, 2003; Fagiolo and Luzzi, 2006; Honjo and Harada, 2006) only appears to be important for increased profitability of Portuguese service SMEs. In addition, long-term

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debt is also a determinant factor for increased profitability of Portuguese service SMEs, but is negligible in explaining the profitability of Portuguese manufacturing SMEs. When analyzing the descriptive statistics of the variables, we find that service SMEs have lower levels of liquidity and long-term debt than manufacturing SMEs. Greater dependence on short-term debt, and the consequent need to pay off the debt and its charges over a short and constant period, may contribute decisively to the importance of liquidity and long-term debt for increased profitability of Portuguese service SMEs, corroborating the conclusions of Fagiolo and Luzzi (2006) in the context of SMEs. The lower level of tangible assets in Portuguese service SMEs may contribute decisively to less liquidity and less access to longterm debt. Given the lower level of tangible assets, creditors make access to long-term debt difficult, so as to monitor repayment of the debt more easily, something which is easier when granting short-term debt (Myers, 1977). Given the higher level of tangible assets, Portuguese manufacturing SMEs may have easier access to long-term debt, and so avoid such excessive use of short-term debt, in such a way that liquidity and long-term debt have relatively less importance for increasing their profitability, compared to the case of Portuguese service SMEs. Although not specifically about SMEs, for service and manufacturing firms in Belgium, Spain, France, Italy and the United Kingdom, Goddard et al. (2005) identify a positive relationship between liquidity and profitability, but a negative one between debt and profitability, whatever the country and industry sector considered. We find that liquidity is less relevant for increased profitability of Portuguese manufacturing SMEs compared to that found for manufacturing firms as a whole in other countries, whereas long-term debt is more important for increased profitability of Portuguese service SMEs than it is for service firms as a whole in other countries. We find that risk influences the profitability of service SMEs negatively, but is of negligible importance in explaining the profitability of manufacturing SMEs. Therefore, we can accept the hypothesis H6, since risk is a more restrictive factor for the profitability of Portuguese service SMEs than for the profitability of Portuguese manufacturing SMEs. The possible worsening of credit terms, as a consequence of greater operational risk (Pettit and Singer, 1985), appears to influence negatively the profitability of Portuguese service SMEs, but does not seem to influence the profitability of Portuguese manufacturing SMEs. The nature of service SME activities, with greater level of intangible assets, may contribute decisively to creditors to aggravate the conditions of credit for these firms. The more adverse terms of credit that service SMEs may face contribute to diminished profitability, as a consequence of the unbearable financial stress they may be subject to at certain times. The empirical evidence obtained from the survival analysis reinforces the greater importance of liquidity and long-term debt in the context of service SMEs, compared to the case of manufacturing SMEs, since liquidity and long-term debt are more relevant for the survival of service SMEs than for manufacturing SMEs. Besides, we find that risk contributes negatively to the likelihood of survival of service SMEs, being of negligible importance for the likelihood of survival of manufacturing SMEs. The greater importance of tangible assets and R&D intensity for the survival of service SMEs should also be highlighted, compared to the case of manufacturing SMEs. While tangible assets can allow service SMEs greater access to long-term debt, reducing the financial stress they are subject to, R&D can mean greater diversification of activities, and

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these two factors can contribute decisively to increased probability of survival of service SMEs. Finally, we find that the persistence of profitability, size and age are more important for greater probability of survival for service SMEs than for manufacturing SMEs. This empirical evidence corroborates the idea explained earlier that the competitive environment can have a more negative effect on service SMEs than on manufacturing SMEs.

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6. Conclusion Based on a sample of 610 service Portuguese SMEs and on another sample of 381 Portuguese manufacturing SMEs, using various dynamic panel estimators, this study seeks to analyze if determinants of profitability of service SMEs are different from those of manufacturing SME, for the period 1999–2006. The empirical evidence obtained lets us conclude there are considerably significant differences between the profitability determinants of service and manufacturing SMEs: 1) size, liquidity, long-term debt and R&D intensity are determinants that promote profitability in service SMEs, but are not relevant for the profitability of manufacturing SMEs; 2) risk is a factor that restricts the profitability of service SMEs, but is not important for the profitability of manufacturing SMEs; 3) tangibility of assets is a positive determinant, and age a negative determinant, of profitability of manufacturing SMEs, but neither determinant is important for profitability of service SMEs; and 4) persistence of profitability is of a greater magnitude for manufacturing SMEs than for service SMEs. Contrary to what was expected, service firms’ greater ease to achieve a minimum level of efficiency that allows them to survive does not mean, for one thing, greater persistence of profitability, and for another, less importance of size and age for increased profitability. Instead, the empirical evidence suggests that service SMEs are more vulnerable to the possibly competitive environment of the markets where they operate, compared to the case of manufacturing SMEs. As was expected, tangible assets are more relevant for increased profitability for manufacturing SMEs than for increased profitability for service SMEs. On the contrary, and also as expected, R&D intensity is more relevant for increased profitability for service SMEs than for manufacturing SMEs. The different nature of the activities of service and manufacturing firms may clearly contribute to these results. While the activities of manufacturing firms are based more on tangible assets, the activities of service firms place special importance on intangible assets R&D. On one hand, greater liquidity and long-term debt are more relevant for increased profitability for service SMEs than for manufacturing SMEs. On the other hand, risk is a more restrictive factor for the profitability of service SMEs than for profitability of manufacturing SMEs. This empirical evidence obtained agrees with what was expected, since SMEs’ difficulty to obtain debt can be aggravated in the case of service SMEs, given the greater risk associated with their activities based on intangible assets and a lower level of tangible assets. Use of the two-step estimation method, an innovative approach in the context of empirical studies of profitability determinants in general, and in the specific context of the study of profitability determinants of SMEs, let us ascertain the survival determinants of

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service and manufacturing SMEs. The results indicate there are considerably significant differences in the survival determinants of service and manufacturing SMEs. Also in these circumstances, the empirical evidence suggests that financial stress and a competitive environment have a greater effect on service SMEs than on manufacturing SMEs. Overall, the empirical evidence suggest different orientations of economic policy for Portuguese service and manufacturing SMEs. In the Portuguese economy, service SMEs have special prominence due to their potential to create employment and economic growth. Given the empirical evidence obtained in the context of Portuguese service SMEs, the following economic policy guidelines are suggested: 1) creation of special lines of credit with relatively long repayment periods, so that excessive dependence of short-term debt does not lead to excessive financial stress in paying off the debt, which jeopardizes efficient use of firms’ good investment opportunities; and 2) given the relevance of R&D for profitability of Portuguese service SMEs, and considering the expensive nature of this type of activity, it would be advisable to give specific financial support to young, entrepreneurial SMEs with clearly limited internal finance and whose activities involve high levels of R&D intensity. In terms of economic policy, guidelines for Portuguese manufacturing SMEs, we suggest that: 1) given the current reduced dynamism of Portuguese manufacturing SMEs, and considering that the younger of these firms have higher levels of profitability, then financial incentives would be advisable for firms with a culture of quality and efficiency; and 2) considering the low importance of R&D intensity in the context of Portuguese manufacturing SMEs, strong incentives are recommended to promote the innovation in these firms, so that greater capacity to diversify products and activities contributes to the development and sustainability of the manufacturing sector in Portugal. In future researches, we intend to study the effect of various types of financing, namely of public financing for investment in R&D, on the profitability of SMEs of different industry sectors, to verify if that effect depends on the industry sector in which SMEs operate.

References Andries, P. & Debackere, K. (2007). Adaptation and Performance in New Businesses: Understanding the Moderating Effects of Independence and Industry. Small Business Economics, Volume 29, 81-99. Arellano, M. & Bond, S. (1991). Some Tests of Specification For Panel Data: Monte Carlo Evidence and Applications to Employment Equations. Review of Economic Studies, Volume 58, 277-297. Audretsch, D., Klomp, L., Santarelli, E. & Thurik, A. (2004). Gibrat´s Law: Are the Services Different?. Review of Industrial Organization, Volume 24, 301-324. Bain, J. (1956). Barriers to New Competition. Harvard University Press, Cambridge, MA. Ball, R. & Watts, R. (1972). Some Time Series Properties of Accounting Income. Journal of Finance, Volume 27, 663-681. Barney, J. (2001). Resource-Based Theories of Competitive Advantage: A Ten Year Retrospective on the Resource Based View. Journal of Management, Volume 27, 643-650.

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Zélia Serrasqueiro

Beise-Zee, R. & Rammer, C. (2006). Local User-Producer Interaction in Innovation and Export Performance of Firms. Small Business Economics, Volume 27, 207-222. Blundell, M. & Bond, S. (1998). Initial Conditions and Moment Restrictions in Dynamic Panel Data Models. Journal of Econometrics, Volume 87, 115 - 143. Bruno, G. (2005). Approximating the Bias of LSDV Estimator for Dynamic Unbalanced Panel Data Models. Economic Letters, Volume 87, 361 - 366. Callen, J., Cheung, C., Kwan, C. & Yip, R. (1993). An Empirical Investigation of the Random Character of Annual Earnings. Journal of Accounting, Auditing and Finance, Volume 8, 151-162. Chan, L. Karceski, J. & Lakonishok, J. (2003). The Level and Persistence of Growth Rates. Journal of Finance, Volume 58, 643-684. Davidson, P. (1989). Entrepreneurship-and After? A Study of Growth Willingness in Small Firms. Journal of Business Venturing, Volume 4, 211-226. Delmar, F., Davidson, P. & Gartner, W. (2003). Arriving at the High-Growth Firm. Journal of Business Venturing, Volume 18, 189-216. Deloof, M. (2003). Does Working Capital Management Affect Profitability of Belgian Firms?. Journal of Business Finance and Accounting, Volume 30, 573-588. Fagiolo, G. & Luzzi, A. (2006). Do Liquidity Constraints Matter in Explaining Firm Size and Growth? Some Evidence From the Italian Manufacturing Industry. Industrial and Corporate Change, Volume 15, 1-39. Galbreath, J. & Galvin, P. (2008). Firms Factors, Industry Structure and Performance Variation: New Empirical Evidence to a Classic Debate. Journal of Business Research, Volume 61, 109-117. Goddard, J., Tavakoli, M. & Wilson, J. (2005). Determinants of Profitability in European Manufacturing and Services: Evidence From a Dynamic Panel Data. Applied Financial Economics, Volume 15, 1269-1282. Gschwandtner, A. (2005). Profit Persistence in the ´Very` Long Run: Evidence From Survivors and Exiters. Applied Economics, Volume 37, 793-806. Hardwick, P. (1997). Measuring Cost Inefficiency in the UK Life Insurance Industry. Applied Financial Economics, Volume 7, 37-44. Heckman, J. (1979). Sample Selection Bias as a Specification Error. Econometrica, Volume 47, 153-161. Hitt, M., Bierman, L., Shimizu, K. & Kochhar, R. (2001). Direct and Moderating Effects of Human Capital on Strategy and Performance in Professional Services Firms: A ResourceBased Perspective. Academy Management Journal, Volume 44, 13-28. Honjo, Y. & Harada, N. (2006). SME policy, financial structure and firm growth: evidence from Japan. Small Business Economics, Volume 27, 289-300. IAPMEI, (2008). Sobre as PMEs em Portugal. Instituto de Apoio à Pequena e Média Empresa (IAPMEI), Lisboa, Portugal. Jensen, M. & Meckling, W. (1976). Theory of the Firm: Managerial Behaviour, Agency Costs and Ownership Structure. Journal of Financial Economics, Volume 3, 306-360. Johnsen, P. & McMahon, R. (2005). Cross-Industry Differences in SME Financing Behaviour: An Australian Perspective. Journal of Small Business and Enterprise Development, Volume 12, 160-177.

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97

Levinthal, D. (1995). Strategic Management and the Exploration of Diversity. In C. A. Montgomery (Ed.), Resource-Based and Evolutionary Theories of the Firm, Kluwer, Norwell, MA. Little, I. & Rayner, A. (1966). Higgledy-Piggledy Growth Again: An Investigation of the Predictability of Firm Earnings and Dividends in the UK, Basil Blackwell, Oxford. Lu, J. & Beamish, P. (2006). SME Internationalization and Performance: Growth vs. Profitability. Journal of International Entrepreneurship, Volume 4, 27-48. Mueller, D. (1977). The Persistence of Profits Above the Norm. Economica, Volume 44, 369380. Mueller, D. (1986). Profits in the Long-Run, Cambridge University Press, Cambridge. Mueller, D. (1990). The Persistence of Profits in the United States. In: D. C. Mueller (Ed.), The Dynamics of Firm Profits: An International Comparison, Cambridge University Press, Cambridge. Myers, S. (1977). The Determinants of Corporate Borrowing. Journal of Financial Economics, Volume 5, 147-176. Pettit, R. & Singer, R. (1985). Small Business Finance: A Research Agenda. Financial Management, Volume 14, 47-60. Peteraf, M. (1993). The Cornerstones of Competitive Advantage: A Resource Based View. Strategic Management Journal, Volume 14, 179-191. Picot, G. & Dupuy, R. (1998). Job Creation by Firm Size Class: The Magnitude, Concentration and Persistence of Job Gains and Losses in Canada. Small Business Economics, Volume 10, 117-139. Porter, M. (1980). Competitive Strategy: Techniques for Analysing Industries and Competitors. The Free Press, New York. Rickne, A. (2006). Connectivity and Performance of Science-Based Firms. Small Business Economics, Volume 26, 393-407. Rogers, M. (2004). Networks, Firm Size and Innovation. Small Business Economics, Volume 22, 141-153. Slater, S. & Olsen, E. (2002). A Fresh Look at Industry and Market Analysis. Business Horizons, sp suppl., 15-22. Teece, D. (1981). Internal Organization and Economic Performance: An Empirical Analysis of the Profitability of Principal Firms. Journal of Industrial Economics, Volume 30, 173-179. Teece, D. (1998). Capturing Value From Knowledge Assets: The New Economy, Markets For Know-How, and Intangible Assets. California Management Review, Volume 40, 55-79. Wiklund, J., Davidson, P. & Delmar, F. (2003). Expected Consequences of Growth and Their Effect on Growth Willingness in Different Samples of Small Firms. Entrepreneurship Theory & Practice, Volume 27, 247-269. Winter, R. (1994). The Dynamics of Competitive Insurance Markets. Journal of Financial Intermediation, Volume 3, 379-415. Wyn, J. (1998). The Fourth Wave. Best’s Review, Volume 99, 53-57.

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Chapter 4

DERIVATIVES AND DEBT: THE MARKET AS GOD AND MARKETING AS PROSELYTIZING Niccolo Caldararo San Francisco State University, San Francisco, California “That which distinguishes man from other animals is lying and literature.” Anatole France

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Abstract Most religions have images of their gods or spirits. There is often a preferred “veronica” or true image. The function of images is, according to the Catholic Church, to provide a focus for contemplation and the reflection of faith (McCrone, 1996). Often the image of the sacred is shrouded from human view, destructive to gaze upon or an imperfect reflection. Aspects of divinity are often perceived by some peoples in the spread of a disease through a population or its natural history in the signs and symptoms it creates in a body. Here we see an image of the god of capitalism (Figure 1). We can produce it from a variety of data, on the value of stock, prices of a variety of goods and services, and other means. But in general, the image is very similar. It traces the behavior of man’s faith in the value of his creations and in his future wealth. It is the single most important representation of the health of the world economy. In a Durkheimian sense, it gives as a representation of the sum total of society’s active mood and reflects, as some economists have said, the attitude and character of humanity. In a sociobiological sense, it represents the pushing and shoving of the actors involved, each trying to capture a greater share of the wealth available now and in the future, like ants (described by E.O. Wilson, 1976) trying to individually seize a piece of food, their common actions can be argued to be a tide of social consequence increasing the fitness of all concerned as they result in the arrival of the food in the nest. Objects of wealth and prestige motivate people to action in modern society and it has long been held in economic debates that contracts and money were modern phenomenon. In Figure 3 we see an image of Chinese “knife money” and its evolution to coinage (“Pu” money was earlier), cerca 700 BCE perhaps to CE 680. Figure 2 is the acknowledgement of a loan from CE 122 in Egypt from a woman, Tamystha to Heraclides, a man. This is a check of sorts undermining the idea that checks were invented in the 17th century by the Dutch as receipts for gold. And in Figure 4 are images of tunny fish of Cyzicus and Cowrie Shells, Dentalium shells, Wampum and a coin of Thurii, all are pre-modern examples of money.

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Niccolo Caldararo We should keep in mind that the idea of exchange was divided by economists, and later by some anthropologists into modern and pre-modern periods. This neat division allowed for strict ideological definitions in historical context of a unilinear description of history with Capitalism and Communism (this includes its various forms, socialism, Marxism, etc.) contending for supremacy as ultimate successors in human social organization. Due to this cosmology of the time, Herskovits suffered severe criticism over his uniformitarian view that all human societies practiced similar forms of economic behavior. The cosmology of the 20th century, held that there was a vector or direction in time in which events could be placed. Both Communism and Capitalism were based on ideologies that firmly conceived that society of the 20th century was characterized by elements that differentiated it from all other social contexts in the past. They called this “modernity.” Recently a book by Jack Goody (2004) criticized this view, arguing that modernity was a worldview of hegemony created in each period of political and economic dominance. As such, modern man could be compared in terms of economic behavior with earlier periods. While he recognized that technology had changed, the basic foundations of human behavior remained the same, thus while no economic system in the past was exactly like that which exists today, comparisons were valid. Further, while some economists and social scientists had argued that modern man was guided by rational thought while primitive society was a context in which man’s behavior was embedded in irrational beliefs that permeated economic behavior, this contrast was not supported by all the evidence. I have described this argument in more detail in a recent book (Caldararo, 2004). Details, like the fact that early guild members of European free cities and towns paid taxes to buy weapons and soldiers to train them to protect them from the ravages of the knights and feudal lords who constantly raided their towns for runaway serfs and wealth, were ignored. By banning together they could defend themselves and they came to wear their tax receipts, as Henry Pirenne (1925) tells us, on their shirts as badges of honor proving they were free men. Then there was the banking and investment activity of people like Crassus in the Early Roman Republic. Or, the Roman examples of unions in late Republican and Imperial times of free tradesmen not associated with the clients system as Marsh and other historians have noted. This ideological position required there be but one future, defined by one struggle and the production of one inevitable victor. And eventually a Capitalist historian, Francis Fukuyama would proclaim victory in the collapse of the Soviet Block in 1989 only to recant this past year as a new struggle, that of resurgent Islam proved to be a viable challenge to the neat scenario followed by the implosion of the main components of modern finance during the past 18 months. In my opinion, the most useful and comprehensive book on economics today is Herskovits’ 1940 (1952 revised text), Economic Life of Primitive Peoples. It describes a uniformitarian view across space and time demonstrating the unity of mankind’s abilities and creativity in production and exchange. As Evans-Pritchard argued in 1965 there is no primitive vs modern mentality. In neither anthropology nor economics did we find total agreement with the primitive/modern distinction so epitomized byKarl Polanyi’s (1957) analysis. Some distinct variations occurred in theory as in the work of Ludwig von Mises(1949) who argued that the various price doctrines were really circular arguments and not theories at all. He placed emphasis on the changes in mutual relations between those buying and selling. Thus relationships, like the focus of Herskovits and Daryl Forde (1949), are the central factor to von Mises in the function of the market. But von Mises could hardly be called a uniformitarian in the manner I have defined, and most certainly would have rejected such an idea being that he was a Capitalist economist. If we are to look at the specialized knowledge at the core of our economic system we might profess that bankers are the priesthood and that the mystery is the creation of credit. This goes beyond people understanding the complex terms of their credit card agreements, or car loans, rather it is lodged in the central conceptions of how banks work, why value appears to increase in the stock market and then disappear. This mystery will be the subject of our inquiry.

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1. Introduction Currently, investors, auditors and accountants are having a great deal of difficulty assessing the value of assets and the underlying veracity of financial statements. It stands at the center of the storm threatening the financial system of world Capitalism at present. Since the scandals of Worldcom and Enron this problem has exploded as many accountancy firms have been caught up in a considerable degree of culpability in hiding or distorting asset value and profitability. This is only part of a wider debate in economics, one which was reflected in William H. Beaver’s calling efforts to increase information on the net worth of companies in the 1970s and 80s, a “revolution” (Beaver 1989), by investors and employees. It also impinges on a much wider discussion of value and credit in theories concerning the evolution of human economic behavior. The invention and acting out of various behavioral strategies by financial professionals can produce significant rewards or deficits for themselves and individuals who follow these strategies. A number of innovations have recently been made to hedging devices known from the 19th century like options and futures, puts, etc. and given new roles, often they are classed as derivatives as they are forms of bets or insurance-like contracts derived from real assets (Abolafia, 1996a &b Arditti, 1996 ). The use of these strategies and the models behind them has drastically changed financial markets today. Billions in profits have been produced by their use, while some of these innovators failed to produce positive returns for themselves, like Robert Merton in the Long Term Capital Management firm collapse (Lowenstein, 2000); a central question has arisen as to whether they introduce new stresses in the economy or reduce its volatility and make it more stable. In the context of products, however, and how selling advice to clients and molding their financial behavior brings up questions as to whether the selling of such instruments functions like religious proselytizing (Caldararo, 2004) where the production of converts changes the system, is demonstrated in the acceptance of new financial devices in the market today. The desire of investors to know the values of financial devices and assets increases in times of cyclical markets, and yet there are cyclical aspects to environmental conditions affecting the survival of most life on the planet (Wilson, 1975). We see animal behavior in many species structured around saving food for the future (caching), as humans have done in the past, and people do today mainly in forms of wealth (savings, retirement, pensions, etc.) in modern human societies. Yet this behavior of projecting present wealth into future action is often defined as a specifically human, and essentially modern aspect, certainly where interest and transfers of wealth between individuals are concerned. However, we find many parallels with modern financial behavior in traditional societies, as Lorraine Baric has noted regarding the indigenous pre-European economy of Rossel Island in Melanesia (1964). She states, “…the island was covered with a network of debtor and creditor relationships of great complexity, in which loans were manipulated so as to provide the greatest advantage that was possible under the circumstances. In the course of this,.. a great deal of calculation, discounting and careful allocation of resources was exercised.” Fixation on buying and selling to the detriment of the individual or kin group is seen by some societies as a disease, like that of pathological gambling, while mass responses to economic news can become as stereotyped as herding behavior in other vertebrates and has

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been defined as a pathological mass psychogenic event. While in some traditional societies these “panics” occur regularly and have the effect of wealth transfer devices.

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Figure 1.

Economic systems are guided by central core values in most societies, while being explained within the general cosmological outlook of the culture. As already mentioned in 1940 Melville Herskovits’, The Economic Life of Primitive Peoples, initiated a debate between economists and anthropologists on the nature of economic behavior in modern societies. Another approach, led by Michel Callon (1998), follows a line of questioning by Alfred Marshall in 1920 that economic theory became reduced to a study of market prices and not the marketplace itself. This emphasizes von Mises’ position, but shows that it was not an original thought but a continuation of earlier knowledge. Callon’s theory, the “performativity of economics,” focuses on the creativity that brings an economy into being, and notes the specific roles of actors in the process. Critics of this approach, for example, MacKenzie & Millo (2003) instead give more emphasis on the underlying “embedding” of values in which commercial exchanges are seen as cultures and moral communities. This is also reinforced by research cited in Baker (1984) and Granovetter (1985). In MacKenzie & Millo’s view the Chicago exchanges (CBOE & CBT) memberships came to be passed from father to son, a characteristic of a kin-based society at first glance. Likewise, violations of procedures (“out trades”) are dealt with by social informalities like shunning, typical of traditional societies. Also like traditional societies, MacKenzie & Millo (2003) found that reciprocity is practiced in the exchanges intergenerationally. The behavior of some members was that of the proselytizing activist, to the extent that some lent newcomers the money to join (initially $10,000), similar to “fronting” a stake in a poker game: “…not just in the hope of personal reward.” stated one early member. In the creation of the CBOE, members participated in an ethos of group recognition and personal investment beyond the financial where, “This (contributions) was part of the concept that was inculcated into all of us: ‘You owe it to your community.’”(MacKenzie & Milo, 2003).

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Figure 2.

Economists like Knight (1941) and social historians like Polanyi (1957) attacked Herskovits on the social nature of traditional exchange, arguing that non-Western societies’ economies were not constructed on rational determinations of value but on kinship and that modern ones were based on rational maximizing instead. They attempted to support this assertion by examples that contrasted the translation of value from objects (food, housing, manufactured items) to abstract carriers of value (stock, letters of credit, checks, “money”).

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Their essential point centered on the belief that such abstract carriers could always be translated into objects by different actors in Western societies, but that such abstract carriers did not exist in non-Western societies. Exchange in such societies was established by haggling or mediated by custom. The economy was seen as “embedded” by culture in each actor limiting the choice and goals available (Cohen, 1967), much like that described for the Chicago exchanges just noted. But modern mass media certainly limits choices by conditioning the responses of economic actors to perhaps an even greater degree as shown by the work of Packard (1957), Henry (1963) and Wagner (1975). The attitude of modern markets as efficient and rational is to be expected as the market is central to the exchange system of our society, but to make it an essential focus of modernity may be ethnocentric. Lorraine Baric (1964) demonstrates that on Rossel Island goods and services were exchanged not primarily via markets but by adjudication and the resolution of claims. Markets therefore, are not the only legitimate social device of exchange. This rigid distinction was partially breached, for example, in critiques of rational actors in market economies, by the rise of a number of schools of behavioral economics (e.g., Becker, 1975) in the 1960s to the 1990s, but none took a uniformitarian position as did Herskovits.

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2. Money & Value, Primitive & Modern In a 2005 article, in the Financial Times, Fearnley & Sunder state that the main problem accountants have with the drive for accounting standards is that it is difficult for accountants to produce equal determinations of value when one steps outside the simple audit of cash accounts. This was made clear in reference to insurance accounting in an interview with Sir David Clementi in the Financial Times (Felsted & Jopson, 2006). When value is to be assigned to assets of different classes, then accountants have no reliable yardsticks to arrive at uniform translations into money. The same difficulty has beset the back offices of hedge funds over the value of CDOs (collateral debt obligations) and hedges of risk, e.g., over bonds and settlement of contracts. This dilemma of the auditors certainly justifies Herskovits (1940, 1952) and shows that the convertibility of units of value in non-Western societies, like the wheels of Yap are a universal in human society. I made this comparison in a comment in the Financial Times (Caldararo, 2005). In fact, the wheels are much more like Western money than any of these devices (Einzig, 1966), contradicting modern economists, such as Greenspan’s assertion about primitive money and credit systems (1966, 1967), since the stone wheels of Yap, as money, could readily be translated into products or services. Many credit devices traditionally used in non-Western ‘primitive societies’ are very much like the paper promises and wagers of CDOs (Firth & Yamey, 1964). Baker (1984) found that consideration of a financial asset as being close to money in industrial society, depended on the social position of the holders. The “piles of paper,” and the vast interpretations of lawyers discussed by Robert Bruce (2004) in his description of the clearing of obligations contained in derivative contracts reflect kindly on the “haggling” in traditional societies so depreciated by Knight (1941) and Dalton (1969). Since Bruce’s article the situation has only gotten worse where now in the midst of the liquidity crisis begun by the Subprime loan collapse many derivatives cannot be assigned value (Hughes & Tett, 2008). Resolution of the derivative contracts originated or related to the Lehman Bros. accounts have been reported as settled, but many are being challenged in the courts. This parallels Baric’s

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(1964) conclusions on Rossel Island, and we see that the market is only one half of our economic legitimacy process. The creation of credit devices, such as derivatives, depreciate other forms of money in one sense, but only reshuffle control over wealth, as in many former primitive economies as Raymond Firth described (Firth, 1964). This process is being demonstrated today with the several trillion dollars in bonds and contracts based on the collapsed Subprime loan markets being assumed by taxpayer supported entities (especially America’s Federal Home Loan Banking System, Fannie Mae and Freddie Mac) in both the USA and Europe governed by the Federal Reserve Bank and Europe’s central banks (Guha & Scholtes, 2008).

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Later Chinese knife money: 7-22 A.D.; showing the development from the knife money in the Cash.

Chinese Cash: 680 A.D.; weight 59 g.

Chinese knife money: length 7 in.; weight 740 g.

These pictures show how the round chinese money, with which we are familiar today, has evolved from the earlier “knife” form. The blade of the knife has disappeared into the end of the handle.

Figure 3.

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3. Magical Economic thought in the 20th Century Comprehensive studies of human mass action were the subject of a number of psychologists and sociologists in the late 19th and 20th centuries (e.g., Canetti, 1960). Many focused on the nature of the crowd, its makeup in sex, age, socio-economic and cultural background, etc. Other studies analyzed the psychology of the motivator (in religion, what Paul Radin, [1937] called the “religious formulator”). On a more general level, however, innovators (whether in technology or business or politics, etc.), like celebrities, motivate people through the pathos of their lives, but usually as models for life. In the realm of finance we find the same factor of the impact of individual egos, not only in the “get rich quick” “seminars” led by celebrities like Donald Trump, but also in the case of Fischer Black whose mathematics describing the nature of derivatives and risk did not reflect reality very well when he first proposed them in the late 1970s early 1980s (see Mehrling, 2005), derived partly, as it was, on his idea of monetary policy which differed from Keynsians (who recognized the instability of the market with booms and busts) and Monetarists like Milton Friedman (who saw central bank interference in the money supply as the problem). Black supported a capital pricing model from which the risk of market variations could be avoided. Despite the divergence of his projections and the market, he and a number of other economists continued to proselytize, to promote their relevance by the distribution of printed explanations (called “theoretical option values”), and, like magic charms, the behavior of traders and bankers began to change, (recall here von Mises’ emphasis on relationships and Callon’s performativity) resulting in a shift in the market until there was a correspondence of theory and market movement. This is like the action of preachers described by Adam Smith which is discussed elsewhere (Caldararo, 2004) in regards to the compatibility of capitalism and Christianity. But the correspondence of Black’s method and the market has degraded significantly today and endangers the stability of the financial basis of our system (Mackenzie, 2005; Larsen, 2006). Black’s formulae and the math behind them do not provide a scientific description of reality but simply verify the existence of human belief. Another example would be Fibonacci sequences which have been found to be useful in studying patterns in biology. They have long been used in a number of theoretical applications to market trends, but Batchelor & Ramyar (2006) have shown that they have nothing to do with predicting market movements. The use of these numbers is based on belief, like magic charms, providing users with a degree of confidence. The fact that stock options and futures were part of 19th century exchanges and gained considerable condemnation as a business practice after the Depression, the speculation in derivatives, wrote one regulator in the 1940s “…looked like wagers on price movements (MacKenzie & Millo, 2003)” and this attitude continued into the 1960s. What changed this climate was the election of Richard Nixon and the appointment of tax lawyer William Casey to the SEC. The Chicago Board of Trade, which was the vehicle for this change, as mentioned earlier, was not a hierarchical organization, but more horizontal in structure, electing its officials. This structure could be interpreted differently, however. The idea of “fronting” individuals money, and the kin-based nature of many of the relationships, has many aspects of generalized reciprocity found in many primitive (Traditional) economic systems (Cohen, 1967). Of course, biological kinship does not make up the basis for social membership or exchange in all human societies, as we see in cognatic societies (Stone, 2006) an example is

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the Huli of New Guinea, where group membership is in flux and by free association (Glasse, 1965, 1968). When one takes into consideration the nature of the clearing-house for settlement of stock and bond transactions, we find more support for this idea of a similarity with forms of traditional societies. Efforts to establish a central and uniform international clearing house for derivative transactions have gained momentum through 2008 but thus far failed. The Depository Trust and Clearing Corporation, as one such organization, is a monopoly, but it is also owned by its industry customers, a collective of sorts. Thus, at the top of our modern economic system, where new financial devices are created and risk theoretically abated, we have one of the most primitive forms of economic structures, a modified generalized reciprocity. It would also be consonant with the idea that futures, options and derivatives, and hedging in general, distributes risk and reduces the overall danger of loss. In that sense, the theory of hedges would be parallel with primitive economics where the community is the basis of growth and renewal. The proliferation of these devices is amazing as Tett notes (2006a). Some new variations include LCDS (loan credit default swaps), CDS of CDOs (credit default swaps of collateralized debt obligations), CFDs (contracts for difference) and dispersion swaps. These have increased the total in the market said to be above 65,000 billion dollars in value (although the total value of derivative-like devices has risen to notional values of over $415,000bn by the Bank of International Settlements in its Dec. 2007 report, there is no general agreement of value). While pension funds, corporations and banks are suspected to be the biggest users, tax avoidance is also a potential use (Tett, 2006a). Stephen Kingsley, managing director of Bearing Point, a financial consultancy, points out that most financial products today are virtual, existing in cyberspace. They bolster banking profits but also are an example of great creativity, but also represent an increasing desire by the financial world to chance profits (gamble) and avoid risk at the same time. The present level of hedging and derivative leveraging has created destabilizing conditions as with Long Term Capital Management (Lowenstein, 2000), where a very small investment could influence a quite remarkable segment of the market. This has been often felt in “shorting the market” where a combination of “borrowed” stocks by hedge funds and rumor have caused substantial falls in the stock of some companies producing large profits for hedge funds. Where can we find the origin of all the liquidity that has been created by derivatives and like synthetic products? It is in asset inflation that essentially comes down to human faith in value, that is like a belief in Mana. The difference from what Keynes proposed in 1923 and what has become practice in current innovations, can be seen in the lack of information and its distribution among investors, as Keynes states in 1921, “The terms “certain” and “probable” describe various degrees of rational belief about a proposition which different amounts of knowledge authorize us to entertain.” Without knowledge all is luck and Mana. It is a mystery to most. The social effect of hedging behavior was reported in Traditional economies by anthropologists. Barth (1967) described how hedging – taking advantage of minor discrepancies in prices – operated in the economy of the Mountain Fur people of Darfur. The process had the effect of profits for a few speculators but also undermined the traditional economic relations associated with kinship and neighborhood obligations based on ceremonial labor exchange. Thus we can see that derivatives and hedging are not new, nor is

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the behavior without risk of damage to the underlying economy and social relations that sustain it.

Figure 4.

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4. Risk and Cycles In an article in the Financial Times of July 17th 2006, Partnoy and Skeel argue that credit derivates create a “moral hazard” in that they allow banks to shift risk, encouraging people to take on more debt because they believe they are insured. Credit derivatives leave borrowers unmonitored fueling credit expansion, as well as increasing the lack of knowledge people have about financial transactions they are involved in due to the complexity of the contracts and related agreements. Also, as Davies and Tett reported (FT 5/17/07), a new version of loan instruments was created as brokers of derivatives and hedge fund managers found they could control consumers need for cheap credit by demanding no risk to themselves, these devices called “cov-lites” were being produced in the past five years in which most of the traditional protections lenders received are removed. These traditional covenants, even when they are retained are weakened and nearly unenforceable. The unwinding of these positions as defaults have occurred has resulted in legal challenge not only to the contract language, but remarkably, to the intent of the institutions who have been the originators (van Duyn & Mackenzie, 2008). Buying and possessing these devices conforms to a number of aspects of consumer behavior related to other purchases made today based on advertising. There is a similar aspect of the totem, belonging to a group very similar to tribal identification seen in branding efforts in commercials. There is a considerable effort that goes into the design of these financial instruments, but what is most compelling is the consumers’ contradictory desire to achieve substantial profits with no risk. This pursuit seems irrational and brings up a trend noted by Robert Shiller in his book, Irrational Exuberance where he notes that there has been a 60 fold rise in gambling in the USA since 1962. He suggests that this desire to engage in risky behavior has spilled over into the investment world. MacKenzie and Milo (2003) argue that the emergence of the skew in the market represents a stability due to generational experience in the 1987 crash and thus can be explained as a form of rational learning. They propose that actor networks perform to reduce tendencies that would return instability. But the facts of 1987, where they imply that 3 minutes separated the collapse of the economic system and survival, seem to argue otherwise. As the collapse accelerated Leo Melamed is called by Allan Greenspan to acknowledge the ability of markets to open. This history belies Greenspan’s pleas before Congress that he misjudged the risks involved in his deregulation policy. Only transfers of credit, especially by the Federal Reserve to Continental Illinois, provided the necessary liquidity in 1987. But where this “liquidity” came from is the essential question, just as in yesterday’s tremendously liquid worldwide financial system we are seeing today a shrinkage of liquidity in response to the Subprime loan crisis. Are we dealing with Mana? Dark Matter? As the value of the paper contracts disappeared, like the ectoplasm of 19th century spiritualists, the debt was assumed by the taxpayer. “Eaten” in the sense of the old Celtic “sin-eater,” taken on by the commons. All this relates to the pursuit of certainty and is an interesting aspect of modern culture in the contradictory nature of risk and guaranteed unusual profits. Mary Douglas (1966 & 1985) addressed the issue of risk and reward in two insightful books and with Aaron Wildavsky (1982) investigated variations in application of risk assessment and perception in a variety of cultures. In Purity and Danger (1966) she found clear distinctions in how people in different cultures come to “…pay attention to a particular pattern of disasters, treating them as omens or punishments. On this argument there would always be a mutual adaptation of views about

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natural dangers and views of how society works: rewards and punishments are stored in the environment.” This is undoubtedly how people in modern economies view the market. We are accustomed to its vagaries, economic actors therefore should not be considered irrational or pathological, their views are not privately formed. As Douglas (1985) argues, “…irrationality tends to be invoked to protect the too narrow definition of rationality.”

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5. Motivation: Need & Spirit In primitive or Traditional societies that are often juxtaposed with our modern context, motivational forces are often attributed to supernatural forces; to gods, spirits, or general essences like Mana. While the idea of Mana as an impersonal force in the world was originally derived from Codrington’s research in Melanesia (1897), it has taken on a variety of forms in the century since he wrote, especially as a foundation for a proposed earliest form of religion known as animatism. Codrington describes it as, “It is a power or influence, not physical and in a way supernatural; but it shows itself in physical force, or in any kind of power or excellence which a man possesses. This mana is not fixed in anything, and can be conveyed in almost anything…. All Melanesian religion consists, in fact, in getting this mana for one’s self, or getting it used for one’s benefit.” In a way we have taken on the strategy of the Traditional society's idea of "limited good," (Foster, 1965) and in so doing, attempt to cushion ourselves from the inevitable fall by spreading the risk, hoping that the damage will be limited and manageable, since we are incapable of understanding ourselves and controlling it. We do have regulation, however, but it is seen by some investors as an impediment to extracting profit by manipulating risk. Hedging, futures and options are all derived from the common human desire to provide alternative resources, should central investment fail (crops, herds, etc.). Where these strategies depart is when the probability of return (gambling) is so low that losses must be transferred from the common store (note the government bailout of LTCM investors). How can we characterize the market then? It responds to all the influences placed upon it, each buy or sell, each pronouncement by experts or charlatans, each new theory or system to work it makes it different, as it is the sum total of the desires, frustrations and hopes of all who watch it. Better than any other image of divinity, it gives or withholds its bounty. Its actions are seldom predictable, like a distant but all powerful immortal, they are mysterious and unexplainable. More striking is the conclusion reached by Harvard University’s Ricardo Hausmann and Federico Sturzenegger, concerning the US deficit (Financial Times, 8 December 2005). They invoke the idea of “Dark Matter” from Astrophysics to make the US deficit disappear. The existence and movement of this “Dark Matter” of value is very much like the concept of Mana. This conception might be viewed from a different perspective, that of a change in paradigm. For example, Baric (1964), using Armstrong’s (1928) original data from Rossel Island, argues that, “…despite great activity in the economic sphere, aggregate capital is largely maintained at the same level although individuals may become wealthy.” Here is reflected the idea described by George Foster (1965) in, “Peasant society and the image of limited good.” But in the present usage, one might say, in terms of mentality as described by

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Levy-Bruhl (1923), a primitive or traditional conception, somewhat akin in physics to the idea of the conservation of matter, it cannot be created anew or destroyed in the balance of the universe, only transformed back and forth into energy. In the new view of Western modernity (in Physics and finance), one might say that from Dark Matter we get both the mysterious creation of multiple worlds and universes as well as new wealth.

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7. Productivity and a Standard of Living In Gillian Tett's interview with Robert Merton (in the Financial Times, May 21st 2007), we find some insights to the problem of performance in the market. In a very similar exposition of Nassin Nicholas Taleb's life since the publication of his book, The Black Swan we are subject to some surprising comments. Just as Taleb's performance as a hedge fund manager has been spotty at best, Prof Merton made the claim, following the LTCM collapse, that derivatives protect us from crashes which seems remarkable. It would be like Lord Treasurer Robert Hartley, the inventor of the South Seas Bubble in 1711, asserting that his scheme had protected England from economic panics in 1720. Or John Law, who produced the great French economic bubble and collapse in 1719-1720 by securitizing French debt in a startlingly similar pattern to that of the current Subprime American debacle (Macdonald, 2008), arguing the same. Prof. Merton's view of a world of controllable risk by mathematics in the face of his admission that in the case of LTCM people did not behave in ways predicted by his model, based on his model's assumptions, that is, that people act rationally, is unconvincing. Instead of acting as the model predicted, people behaved, first as a group under conversion, and then as a herd in panic. Canetti described such patterns in 1962 and a number of scholars from Krondratieff and Schumpeter (1939) to Sornette (2003) have attempted to develop an understanding of such panics and their role in economics. Recent actions of the Fed and EU central banks buying or accepting distressed debt as collateral from banks without producing the stigma for specific institutions of applying for support, parallels Traditional societies’ means of maintaining authority in times of stress. Usually in Traditional society, the cause of failure is expressed in terms of supernatural intervention, and the parallels with forms of magic and sorcery are obvious. Credit was created that has turned “bad,” though the people responsible for this “bad” credit are not punished, official institutions will act to “purify” such credit and make it “good.” The essential element here is to produce sufficient signs of authority and consensus and demonstrate it through ritual to enforce and entice the general public to accept the terms and consequences of these acts. The slow and partial release of the subprime “infection” has so far contained panic within the financial community, whether it spreads from there will be determined by the recognition of the public of the symbols utilized to communicate the correction, and their perception that they are not being victimized in the process. I think that Mary Douglas (1966 & 1985), in her works on risk in various cultures, has shown how risk functions varies in different cultures at different times. As in 1929, a slow collapse of financial institutions and products is taking place in the context of an economy that is seemingly functioning with solid fundamentals. Of course we wish to know what must be done and at present we find that the central banks, both in Europe in the USA, are providing easy credit to try to ease the illiquidity which is seen as the major

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problem. As Ellis U. Hawley describes in his book, The New Deal and the Problem of Monopoly (1966), the roots of the 1930s collapse were to be found in the control of business activity and finance that had developed during WWI. The business associations and the product planning and distribution advantages businesses enjoyed during the war years carried over into the 1920s and resulted in the suppression of competition and the growth of large monopolies who determined prices and the resulting profits encouraged speculation without regulation. The size of institutions to monitor mega corporations is a central problem and no matter what the intent of Congress, unless funding and direction are given to such agencies, unless they are free of political influence, we will continue to repeat these cycles of boom and bust. A related problem to that of lack of regulation and the size of corporations, is that of information. Robert Eccles’ studies of audits and accounting information from 1980 to 1983, demonstrated that information on actual value produced and costs in internal audits were more accurate than external ones but that both kinds failed to reflect reality (1985). There were systematic errors produced in accounting and audits to benefit management at various levels. For investors to have any degree of confidence in audits there must be more controls on the relationships between accounting firms and the companies they examine. The Savings and Loan debacle and the Enron and Worldcom frauds and the current Madoff findings all point out that no effective changes have taken place. This is why we need more transparency in reporting banking assets not less. The fact that many banks and financial organizations are eager to repay bail-out funds rather than submit to curbs on salaries and bonuses and audits only increases the skepticism investors must have. There can be no real return to the market until we can be sure that they system is sound. Undermining mark to market will not help restore confidence. However, while establishing the image of stability, essentially the atmosphere that no recession or depression is at hand, the heads of these institutions are incapable of dealing with the underlying problem that is driving the present spread of uncertainty throughout the economic system. Here we see the advance of the destruction of faith in relationships, at its core is the idea that things have gotten out of hand, but what is worse is the erosion of social credit (foundation of belief in common action, demonstrated in trust and support for social institutions, cooperation, etc.) that has been undermined and is what supports the system in bad times. The agent of this process is moral hazard, the actions of some have produced an environment where the populace of consumers and investors feel taken advantage of and in this milieu we cannot expect social credit to sustain the financial system. A creeping decay has set in, the evaporation of Mana is afoot and only efforts to restore confidence in fairness can reduce its loss. After Enron this was accomplished by the investigations and arrests of “those responsible.” But today there is no target for such expression and as a result the unfolding process is taking hold. This is especially true as a general feeling of distrust is apparent expressed by the public in the current Presidential campaign. It is difficult, however, for it to be focused as some of the central investment bankers from Goldman Sachs are leading the Federal government’s actions and reports from the lawsuits over both Bear Sterns and Lehman Brothers contain charges of unfair actions by these individuals. The uniformitarian perspective outlined here for economics should be seen in the context of other discussions, like Toynbee’s on modernity and that recently produced by Maier (2008) in assessing the nature of empire and American political and social behavior, both domestic and international. The essential question now is, if banks will not lend and the government

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cannot make them lend will the global economy settle into depression because it rejects the prospect of governmental agencies originating loans? If all the banking players feel the contamination of each other can governmental replacement of private lending (uncontaminated Mana?) break the paranoia of private finance? It seems unlikely that a permanent solution could be arrived at even with ritual constraints as I have described in traditional societies. It is possible that these crises are ritual components of modern society as organized around the market mechanism and its traditions. They may be channeled or restrained but a transformation may be necessary and possible as Mead (1964) describes for the Manus and their customary economic mania.

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References Abolafia, M. M. (1996a). Making Markets: Opportunism and Restraint on Wall Street, Cambridge, Harvard University Press. Abolafia, M. M. (1996b). “Hyper-rational Gaming,” Journal of Contemporary Ethnography, v. 25, n. 2, 226-250. Arditti, Fred, D. (1996). Derivatives: A Comprehensive Resource for Options, Futures, Interest Rate Swaps, and Mortgage Securities, Harvard Business School Press, Boston. Armstrong, W. E. (1928). Rossel Island, An Ethnographical Study, Cambridge U. Press, Cambridge. Baker, Wayne E. (1984). “The social structure of a national securities market,” American Journal of Sociology, v. 89, n. 4, 775-811. Baric, Lorraine, (1964). “Some aspects of credit, saving and investment in a ‘non-monetary’ economy (Rossel Island)” in Capital, Saving and Credit in Peasant Societies, eds., Raymond Firth & B. S. Yamey, Aldine Publishing Chicago, 35-52. Barth, F. 1967. Economic spheres in Darfur, in Themes in Economic Anthropology, Edited by R. Firth, 149-74. London: Tavistock. Batchelor, Roy & Ramyar, Richard, (2006). “Magic numbers in the Dow,” Cass Business School, JEL Classifiation: C15, C53, G10, September. Beaver, W. H. (1989). Financial Reporting: An Accounting Revolution, 2nd Edition, PrenticeHall, Englewood Cliffs. Becker, Gary, (1975). Human Capital: A Theoretical and Empirical Analysis with special reference to Education, National Bureau of Economic Research. Boas, Franz, (1888). The Central Eskimo, 6th Annual Report of the Bureau of Ethnology, Smithsonian Institution, Washington. Boulding, Kenneth, E. (1966). Economic Analysis: Volume One Microeconomics, New York, Harper & Row. Bowe, C. & Cookson, C. (2006). “High anxiety: what ails the world’s big spender on health,” Financial Times, 1 September. Bruce, Robert, “Piles of paper,” 2004, Financial Times, March 29. Caldararo, Niccolo, (2004). Sustainability, Human Ecology and the Collapse of Complex Societies: Economic Anthropology in the 21st Century, The Edwin Mellen Press, Lewiston. Caldararo, Niccolo, 2005. Global standards seen in light of history of economic theory. The Financial Times, (October 31).

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Niccolo Caldararo

Callon, Michel, (1998). The Laws of the Markets, Oxford, Blackwell. Canetti, Elias, 1960 (1966), Crowds and Power, Viking Press, N.Y. Codrington, R. H., 1897 (1957), The Melanesians: studies in their anthropology and folk-lore. New Haven, HRAF Press. Coggin, Philip, (2006). “Tossing a coin could well be as insightful to investors as a fund manager,” Financial Times, July 1. Cohen, Percy, S. (1967). Economic analysis and Economic Man: some comments on a controversy,” in Themes in Economic Anthropology, ed. By Raymond Firth, Tavistock, London, 91-118. Cribb, Joe, ed., (1986). Money: from Cowrie Shells to Credit Cards, London, British Museum. d’ Andrade, R. (1995). The Development of Cognitive Anthropology, Cambridge U. Press. Dalton, G., (1969). “Theoretical issues in Economic Anthropology,” Current Anthropology, v. 20, n. 1, 63-102. Douglas, Mary, (1954). 1963 (2002 ed.). The Lele of the Kasai, Routledge, London. Douglas, Mary, (1966). Purity and Danger; an Analysis of Concepts of Pollution and Taboo. London: Routledge & Kegan Paul. Douglas, Mary & Isherwood, B., (1978). ed., The World of Goods: Towards an Anthropology of Consumption, Routledge, London. Douglas, M. & Wildavsky, A. (1982). Risk & Culture; an Essay on the Selection of Technological and Environmental Dangers. Berkley: University California Press. Douglas, Mary, (1985). Risk Acceptability According to the Social Sciences. New York: Russell Sage Foundation. Durkheim, Emile, (1915). The Elementary Forms of The Religious Life, Free Press, New York. Eccles, Robert G. (1985). The Transfer Pricing Problem: A Theory for Practice. New York. Einzig, Paul, (1949, 1966 ed.), Primitive Money, Pergamon Press, Oxford. Eliade, Mircea, (1964). Shamanism: Archaic Techniques of Ecstasy, Bolligen Series, 76, Pantheon, N.Y. Evans-Pritchard, E. E. (1965). Theories of Primitive Religion, Oxford, Clarendon Press. Felsted, A. & Jopson, B. (2006). “Scoring the dark art of insurance accounting,” Financial Times, July, 24. Firth, Raymond, (1964), “Capital, saving and credit in peasant societies: a viewpoint from economic anthropology,” In R. Firth, & B. S. Yamey (Eds.), Capital Saving and Credit in Peasant Societies, Aldine Publishing, Chicago, 15-34. Firth, Raymond, (1967). “Themes in economic anthropology,” In Themes in Economic Anthropology, ed. Raymond Firth, Tavistock Publications, London, 1-28. Firth, Raymond, (1996). Religion, A Humanist Interpretation, Routledge, London. Firth, R. & Yamey, B. S., eds., (1964). Capital, Saving and Credit in Peasant Societies, Aldine Publishing, Chicago. Forde, Daryl C. (1949). Habitat, Economy and Society, London, Methuen. Foster, George, (1965). “Peasant society and the image of limited good,” American Anthropologist, v. 67, 293-315. Freud, S. (1927 )(1954 ed.), The Future of an Illusion, Anchor Books, N.Y. Fukuyama, Francis, (1992). The End of History and the Last Man, Free Press, N.Y.

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115

Glasse, R. M. (1965). “The Huli of the Southern Hightlands,” in Gods, Ghosts and Men in Melanesia: Some Religions of Australian and New Guinea and the New Hebrides. Edited by P. Lawrence, & M. J. Meggitt, 27-49. London: Oxford University Press. Glass, R. M. (1968). The Huli of Papua: A Cognatic Descent System. Paris/The Hague: Mouton & Company. Goody, Jack, (2004). Capitalism and Modernity: The Great Debate, Wiley-Blackwell, N.Y. Granovetter, M. (1973). “The strength of weak ties,” American Journal of Sociology, v. 78, 1360-1380. Granovetter, M. (1985). “Economic action and social structure: the problem of embeddedness,” American Journal of Sociology, v. 91, 481-510. Greenspan, Alan, (1967). “Gold and economic freedom,” Objectivist Newsletter, 1966 and reprinted in Rand, Ayn, Capitalism: The Unknown Ideal. Guha, K. & Scholtes, S. (2008). Fed takes leap towards the unthinkable. The Financial Times, (March 12). Henry, J. (1963). Culture Against Man. New York: Vintage Books. Herskovits, Melville, (1940). Economic Life of Primitive Peoples, (1952 the title was changed to Economic Anthropology). Hughes, J. & Tett, G. (2008). An unforgiving eye. The Financial Times. (March 14). Jackson, J. W. (1917). Shells as Evidence of Migration of Early Culture, U. of Manchester Manchester. James, E. O. (1957). Prehistoric Religion, Barnes & Noble, New York. Jung, Carl, 1960 (1954). Answer to Job, Meridan Books, New York. Kahneman & Tversky, eds., (2000). Choices, Values & Frames, Cambridge, Cambridge U. Press. Khaldun, Ibn, 1377 (1967 ed.), The Muqaddimah, Bollingen Series, Princeton. Keynes, J. M. (1921). A Treatise on Probability, London, Macmillan. Keynes, J. M., (1923). “Some aspects of commodity markets,” Manchester Guardian Commercial, Reconstruction Supplement 29, March. Knight, F. H., (1941). “Anthropology & Economics: a review of The Economic Life of Primitive Peoples, “ Journal of Political Economy, April, v. 49, n. 2, 1-16. Konishi, A. & Dattatreya, R. E., Eds., (1991). The Handbook of Derivative Instruments, Probus Publishing, Chicago. Kroeber, A. L., (1917). “The Superorganic,” American Anthropologist, v. 19, n. 2, 116-123. Kuhn, Thomas S., (1967). The Structure of Scientific Revolutions, 2nd ed., Univesity of Chicago Press, Chicago. Lacombe, Frank, (2006). “Modeling swarm behavior,” Apple Science Profile, July 17, 1-2. Larson, Peter Thal, (2006). “Oil price leaps over fraud in bankers’ fear list,” The Financial Times, June 28. Levy-Bruhl, L. (1923). (1966 ed.), Primitive Mentality, Beacon Press, Boston. Lowenstain, Roger, (2000). When Genius Failed: The Rise and Fall of Long Term Capital Management, New York, Random House. Macdonald, J. (2008). How the French invented subprime in 1719. The Financial Times. (March 7). MacKenzie, Donald, (2005). “Earning from risks,” Science, v. 309, 9 September, 1678-9.

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Niccolo Caldararo

MacKenzie, D. & Millo, Yuval, (2003). “Constructing a market, Performing Theory: the historical sociology of a financial derivatives exchange,” American Journal of Sociology , V. 109, n. 1, July, 107-145. Maier, Charles, (2007). “America among empires? Imperial analogues and imperial syndrome,” Bulletin of the German Historical Institute, n. 41, Fall:21-32. Malinowski, B. (1938). “Introduction,” in J. Kenyatta, Facing Mount Kenya, Vintage Edition. Malinowski, B. 1916 (1954 ed.), Magic, Science and Religion, Anchor Books, N.Y. Mandelbrot, B. B. (1997). Fractals and Scaling in Finance, Springer, Berlin. Marsh, F. B. (1927). The Founding of the Roman Empire, (2nd ed.) Barnes & Noble, N.Y. Marshall, Alfred, 1920 (1961), “On Markets,” In Principles of Economics, ed. Alfred Marshall, London, MacMillan, & Co., 323-330. Marshall, Alfred, (1923). Money, Credit, and Commerce, (Reprints in Economic Classics, August Kelly, New York, (1960 ed.). McCrone, Walter, (1996) Judgement Day for the Turin Shroud, McCrone Institute, Chicago. Mead, Margaret, (1964). Mehrling, Perry, (2005). Fischer Black and the Revolutionary Idea of Finance, Wiley, Hoboken, N, J. Meyer, Eduard, (1924). “Die wirtschaftliche Entwicklung des Altertums,” in his, Kleiner Schriften, Halle. Moore, Omar Kayam, (1957). “Divination- a new perspective,” American Anthropologist, v. 59, n. 1, 69-74. Nuttall, Chris, (2006). “Watch this space as network sites vie for youth market,” The Financial Times, May, 30. Packard, Vance, (1957). The Hidden Persuaders, Pocket Books, N.Y. Pareto, V. (1917-1919). Trait de sociologie generale, Payot et Cie, Lausanne. Partnoy, Frank & Skeel, D. (2006). “Credit derivatives play a dangerous game,” Financial Times, July, 17. Philips, G. & Connolly, K. (1992). Japanese Warrant Markets, Palgrove, Houndmills. Pirenne, Henri, (1925). Medieval Cities, (1956 ed.) N.Y., Doubleday. Polanyi, K. (1957). “Marketless trading in Hammurabi’s time,” in Trade and Market in the Early Empires, In K. Polanyi, C. M. Arensberg, & H. K. Pearson (Eds.), The Free Press, Glencoe, 12-26. Radin, Paul, 1937 (1957), Primitive Religion, Dover, N.Y. Rappaport, R. A. (1967). Pigs for Ancestors: Ritual in the Ecology of a New Guinea People, Yale U. Press, New Haven. Redfield, Robert, (1953). The Primitive World and Its Transformations, Cornell U. Press, Cornell. Rostovtzeff, Michael Ivnovitch, (1953). The Social and Economic History of the Hellenistic World, Oxford, The Clarendon Press. Rostovtzeff, M. I. (1957). The Social and Economic History of the Roman Empire, Oxford, The Clarendon Press. Rothschild, Michael L. (1990). Bionomics, Holt, N.Y. Sabloff, J. A. & Lamberg-Karlovsky, C. C. (1974). The Rise and Fall of Civilizations, Cummings Publishing, Menlo Park. Sahlins, Marshal, (1988). “Notes on the original affluent society (1968),” in Tribal Peoples and Development Issues, J. H. Bodley (Ed.), Mayfield, Mountain View, 15-22.

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Sahlins, Marshall, (1972). Stone Age Economics, Chicago, Aldine-Atherton. Schumpeter, J. A. (1939). Business Cycles, Porcupine Press, Philadelphia, 1989ed. Schumpeter, J. A. 1989 (1939), Business Cycles. Philadelphia: Porcupine Press. Schurr, Stephen, (2006). “Performance of hedge funds steadies but the fears persist,” Financial Times, 10 July. Shiller, Robert, (2000). Irrational Exuberance, Princeton U Press, Princeton. Smith, Adam, 1776, (1965 ed.), The Wealth of Nations, Arlington House, N.Y. Sornette, D. (2003). Why Stock Markets Crash: Critical Events in Complex Financial Systems, Princeton U. Press, Princeton. Stone, Linda, (2006). Kinship and Gender: An Introduction, 3rd ed., Westview Press, Cambridge, Ma. Tainter, J. A. (1988). The Collapse of Complex Societies, New Studies in Archaeology, Cambridge U. Press, Cambridge. Tett, Gilllian, (2006). “The Dream Machine,” Financial Times, Weekend Section, March, 25. Tett, Gillian, (2006a). “The innovation combat zone,” Financial Times, July, 19. Tett, Gillian, (2006b). “Japan’s ‘death spiral’ bonds under scrutiny,” Financial Times, July, 21. Toynbee, Arnold, (1948). Civilization on Trial, Meridan Books, N.Y. Van Duyn, A. & Mackenzie, M. (2008). ‘Tranche warfare’ breaks out over CDOs. The Financial Times. (April 15). Von Mises, Ludwig, (1949). Human Action, Lodge & Co. London. Wagner, Roy, (1975). The Invention of Culture, Prentice Hall, Englewood Cliffs. Weller, Paul, Ed., (1992). The Theory of Futures Markets, Blackwell, Oxford. White, Leslie, (1947). “The locus of mathematical reality: an anthropological footnote,” Philosophy of Science, v. 14, n. 4, October, 289-303. Wilson, E. O. (1975). The New Synthesis, Sociobiology, Belnap Press, Harvard U. Press, Cambridge. Wilson, Peter, (1988). The Domestication of the Human Species, New Haven, Yale U. Press. Woit, Peter, (2006). Not Even Wrong, Jonathan Cape, London.

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In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 119-136

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Chapter 5

ASSESSING HOUSEHOLD VULNERABILITY TO CLIMATE CHANGE: THE CASE OF FARMERS IN THE NILE BASIN OF ETHIOPIA T.T. Deressaa,∗, R.M. Hassana and R. Claudiab a

Center for Environmental Economics and Policy in Africa, University of Pretoria, South Africa. b International Food Policy Research Institute, Washington, D.C.

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Abstract This study measures the vulnerability of farmers to climatic extremes such as droughts, floods and hailstorms, by employing the “vulnerability as expected poverty” approach. This approach is based on estimating the probability that a given shock or set of shocks will move household consumption below a given minimum level (such as the consumption poverty line) or force the consumption level to stay below the given minimum if it is already below this level. The utilized data come from a household survey of farmers performed during the 2004/2005 production year in the Nile Basin of Ethiopia. The results show that the farmers’ vulnerability is highly sensitive to their minimum daily requirement (poverty line). For instance, when the daily minimum income is fixed at 0.3 United States dollars (USD) per day, only 12.4% of farmers are vulnerable to climate extremes, whereas 99% of farmers are vulnerable when the minimum requirement is fixed at 2 USD per day. The results further indicate that farmers in kola agro-ecological zones (which are warm and semi-arid) are the most vulnerable to extreme climatic events. Policy-wise, these preliminary results indicate that, keeping other factors constant, increasing the incomes of farmers (with special emphasis on those in kola agro-ecological zones) and enabling them to meet their daily minimum requirements will reduce their vulnerability to climatic extremes.

Keywords: Vulnerability to climate extremes, Nile Basin of Ethiopia, minimum daily income.

∗

E-mail address: [email protected]. (Corresponding author)

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1. Introduction Ethiopia has a population of 70 million, but remains one of the least developed countries in the world. Agriculture, which is the main sector of the Ethiopian economy, contributes about 52% of the country’s Goss Domestic Product (GDP), generates more than 85% of the foreign exchange earnings and employs about 80% of the population. The real per capita Gross National Product (GNP) is about 100 United States dollars (USD) in Ethiopia, and most residents find it hard to meet their daily basic needs. About 50% of the population lives under absolute poverty, and the average life expectancy in the country is about 43 years (CSA 2005). The agricultural sector is dominated by small-scale mixed crop-and-livestock production with very low productivity. The major factors responsible for this low productivity include: reliance on obsolete farming techniques; soil degradation caused by overgrazing and deforestation; poor complementary services such as extension services, credit, markets and infrastructure; and climatic factors such as drought and flood (Deressa 2007). These factors reduce the farmers’ adaptive capacity and/or increase their vulnerability to future changes, negatively affecting the performance of the already weak agricultural sector. Despite the fact that Ethiopia has a long history of drought, studies have shown that the frequency and spatial coverage of droughts have increased over the past few decades (Lautze et al. 2003). Moreover, over the past 50 years, the average annual minimum and maximum temperatures across the country have increased by about 0.25oC and about 0.1oC, respectively, per decade, and precipitation has shown a decreasing trend throughout the country (NMSA 2001). This trend of increasing temperature, decreasing precipitation and increasingly frequent drought is predicted to continue in the tropics (which include Ethiopia) through the future (World Bank 2003; Mitchell and Tanner 2006; IPCC 2001). Thus, the country’s agricultural sector should be considered vulnerable to future climate change. Attempts have been made to analyze the vulnerability of Ethiopian farmers to climatic and non-climatic shocks in studies using panel datasets (Dercon 2004; Dercon et al. 2005; Skoufias and Quisumbing 2003; Dercon and Krishnan, 2000), and policy options have been suggested to reduce vulnerability. The studies by Dercon (2004), Dercon et al. (2005) and Dercon and Krishnan (2000) used ex ante vulnerability assessment approaches to analyze the vulnerability of Ethiopian farmers by taking maximum of only 15 villages. The Skoufias and Quisumbing (2003) study used an ex post approach to analyze vulnerability in the same 15 villages. While these studies are informative and methodologically sound, their use of a relatively small data pool means that they are unlikely to accurately represent the vast agroecological and socio-economic diversity of the country. This represents an important limitation, since the results from these studies cannot be generalized to farming communities that do not share the same socio-economic and environmental attributes. The present study addresses this knowledge gap by using a cross-sectional dataset collected from 162 villages in the Nile Basin of Ethiopia, representing diverse socioeconomic and environmental settings. The paper is organized as follows. Section 2 reviews the literature on approaches to vulnerability assessment. Section 3 describes the empirical method employed in this study. Section 4 discusses the results, and Section 5 provides conclusions.

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2. Review of Literature

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2.1. Definitions of Vulnerability The term “vulnerability” has no universally accepted definition, largely because different disciplines use the term differently to explain their areas of concern. Studies on natural hazards and epidemiology define vulnerability as the degree to which an exposed unit is susceptible to being harmed by exposure to a perturbation or stress, in conjunction with its ability (or lack thereof) to cope, recover or fundamentally adapt (become a new system or go extinct) (Kasperson et al. 2001). In contrast, the poverty and development literature, which focuses on social, economic and political conditions, defines vulnerability as an aggregate measure of human welfare that integrates environmental, social, economic, and political exposure to a range of harmful perturbations (Bohle et al. 1994). According to Yamin et al. (2005), the disaster community defines vulnerability as conditions that are determined by physical, social, economic, and environmental factors or processes, and that increase the susceptibility of a community to the impact of a hazard. In the resilience community, vulnerability is defined as a loss of resilience (Franklin and Downing 2004). Adger (1999) defines social vulnerability as the exposure of groups or individuals to stress as a result of social and environmental change, where “stress” refers to unexpected changes and disruptions to livelihoods. Reilly and Schimmelpfennig (1999) define vulnerability as a probability-weighted mean of damages and benefits, and give examples of crop yield vulnerability, farmer or farm sector vulnerability, regional sector vulnerability, regional economic vulnerability, and vulnerability to hunger. The Intergovernmental Panel on Climate Change (IPCC 2001) defines vulnerability to climate change as: “The degree to which a system is susceptible, or unable to cope with adverse effects of climate change, including climate variability and extremes, and vulnerability is a function of the character, magnitude and rate of climate variation to which a system is exposed, its sensitivity, and its adaptive capacity.”

2.2. Approaches to Estimating Vulnerability Two types of analytical methods for measuring vulnerability are discussed in this section, namely indicator and econometric approaches.

2.2.1. Indicator Approaches The indicator approaches are based on developing a wide range of indicators and selecting some of them through expert judgment (Kaly and Pratt 2000; Kaly et al. 1999), principal component analysis (Easter 1999; Cutter et al. 2003), or correlation with past disaster events (Brooks et al. 2005). Each of these selection procedures is used to choose the indicators that account for the largest proportion of vulnerability. The selected indicators may be used at the local (Adger 1999; Leon-Vasquez et al. 2003; Morrow 1999), national (O’Brien et al. 2004), regional (Leichenko and O’Brien, 2001; Vincent 2004) or global (Brooks et al. 2005; Moss et al. 2001) scales. According to Luers et al. (2003), the indicator approaches are valuable for monitoring trends and exploring conceptual frameworks.

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However, these approaches are limited by: 1) considerable subjectivity in the selection of variables and their relative weights, 2) the availability of data at various scales, and 3) the difficulty of testing or validating the different metrics.

2.2.2. Econometric Approaches The econometric methods, which use household-level socio-economic survey data to analyze the vulnerability levels of different social groups, include three assessments: vulnerability as expected poverty (VEP), vulnerability as low expected utility (VEU) and vulnerability as uninsured exposure to risk (VER) (Hoddinott and Quisumbing 2003). All of these methods construct measures of welfare loss attributed to shocks, but differ in that VEP and VEU measure the ex ante probability of a household’s consumption or utility falling below a given minimum level in the future due to current or past shocks, while VER measures ex post welfare loss due to shocks. The most commonly cited shocks resulting in welfare loss include climatic, economic, political, social, legal, crime and health shocks (Hoddinott and Quisumbing 2003).

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2.2.2.1. Vulnerability as Expected Poverty In the expected poverty framework, an individual’s vulnerability is the prospect of that person becoming poor in the future if currently not poor, or the prospect of him/her continuing to be poor if currently poor (Christiaensen and Subbarao 2004). Thus, vulnerability is seen as expected poverty, while consumption (income) is used as a proxy for well-being. This method is based on estimating the probability that a given shock or set of shocks will move household consumption below a given minimum level (such as a consumption poverty line) or force the consumption level to stay below the minimum if it is already below this level (Chaudhuri et al. 2002). Using this method on cross-sectional survey data obtained in 1998, Chaudhuri et al. (2002) found that while only 22% of the Indonesian population was poor, as much as 45% of the population could be considered vulnerable to poverty. Tesliuc and Lindert (2002) examined cross-sectional survey data obtained from Guatemala in 2000 and showed that three-quarters of the total poor had a vulnerability index in excess of 0.67, indicating that two out of three of the then-poor households would still be poor in the coming period. Similarly, Sarris and Karfakis (2006) measured the vulnerability of rural households in Tanzania, and found that poorer regions were considerably more vulnerable to poverty. One of the disadvantages of this method, however, is that the use of estimations made across a single cross-section requires the strong assumption that the cross-sectional variability captures temporal variability (Hoddinott and Quisumbing 2003). 2.2.2.2. Vulnerability as Low Expected Utility Ligon and Schechter (2002, 2003) defined vulnerability as the difference between the utility derived from some level of certainty-equivalent consumption (at and above which the household would not be considered vulnerable) and the expected utility of consumption. Ligon and Schechter (2003) applied this method to a panel dataset obtained from Bulgaria in 1994, and found that poverty and risk played roughly equal roles in reducing welfare. The disadvantage of this method is that it is difficult to account for an individual’s risk preference,

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given that individuals are ill-informed about their preferences, especially those related to uncertain events (Kanbur 1987). 2.2.2.3. Vulnerability as Uninsured Exposure to Risk This method is based on as ex post assessment of the extent to which a negative shock causes welfare loss (Hoddinott and Quisumbing 2003). Here, the shock impact is assessed by using panel data to quantify shock-induced changes in consumption. Skoufias (2003) employed this approach to analyze the impact of shocks on Russia. In the absence of riskmanagement tools, shocks impose a welfare loss that materializes through reductions in consumption. The amount of loss incurred due to shocks equals the amount paid as insurance to keep a household as well off as it had been prior to any shock. This approach, which is mainly based on regressions of panel datasets containing the consumption levels of specific households before and after a specific shock, analyzes how households mange to smooth their consumptions over time, and categorizes households as vulnerable or less vulnerable. In the absence of panel data, it is typically impossible to measure the impact of shocks such as droughts, floods and hailstorms, as ex ante and ex post consumption and income data are generally not included in cross-sectional household-level datasets. Moreover, an attempt to compare the predicted incomes between households that did and did not experience shocks will result in a biased estimate of the shock impacts, largely because household income levels do not vary only due to shocks. Instead, households vary across many different attributes and hence may have different income levels even in the absence of shock. Thus, these exercises cannot precisely quantify shock-specific losses.

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3.1. Empirical Model Here, the probability of a farmer falling below a given consumption (income) level due to climatic shocks (droughts, floods or hailstorms) was measured with the vulnerability as expected poverty approach. This allows estimation of the proportion of people that are vulnerable to shocks, and hence may be used to support policies aimed at implementing safety nets or adaptation strategies. Following Chaudhuri et al. (2002), the stochastic process generating the consumption of a household h is given by:

ln C h = X h β + eh

(1)

where Ch is per capita consumption1 expenditure, Xh represents a bundle of observable household characteristics (household size, location, educational attainment of the household head, etc.) and climatic shocks (droughts, floods and hailstorms), β is a vector of parameters,

1

This study considers farmers’ incomes rather than their consumption. In poor countries, including Ethiopia, it is assumed that most or all of the farmers’ incomes are consumed, and the farmers do not save.

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and eh is a mean-zero disturbance term. The dependent and independent variables are described in Table 6. We assume that the variance of eh is given by:

σ

e,h

2=Xθ h

(2)

where β and θ are parameter estimates obtained from the three-step feasible generalized least squares (FGLS) procedure suggested by Amemiya (1977). Using the estimates β and θ, the expected log of consumption and the variance of log consumption for each household h are, respectively, estimated as: ^

^

E [ln C h | X h ] = X h β

(3)

^ ^ ⎡ ⎤ V ⎢ln C h | X h = σ ^ 2 e ,h = X h θ ⎥ ⎣ ⎦

(4)

By assuming that consumption is log-normally distributed (i.e. that lnCh is normally distributed), the above equations allow us to estimate the probability that a household with characteristics Xh will be poor (i.e., the household’s vulnerability level). If Φ (.) denotes the cumulative density of the standard normal, the estimated probability will be given by: ^ ⎛ ⎜ ln z − X h β V h = Pr (ln C h < ln z | X h ) = Φ⎜ ^ ⎜ Xhθ ⎝

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^

^

⎞ ⎟ ⎟ ⎟ ⎠

(5)

where ln z is the log of the minimum consumption/income level beyond which a household would be called vulnerable. This analysis is based on the assumption that experiencing climatic shocks such as a drought, flood and/or hailstorm will increase the probability of a farmer falling below a given consumption/income level, or force him/her to stay under such a level if already below it.

3.2. Study Area The study area for this research is the Nile basin of Ethiopia. The Nile basin of Ethiopia covers a total area of about 358,889 km2, which is equivalent to 34% of Ethiopia’s total geographic area, and contains about 40% of the country’s population. Portions of six different regional states of Ethiopia are contained within the basin, namely: 38% of the total land area of Amhara, 24% of Oromiya, 15% of Benishangul-Gumuz, 11% of Tigray, 7% of Gambella and 5% of Southern Nations Nationalities and Peoples (SNNP) (MoWR 1998).

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Table 1. Climatic zones and their physical characteristics. Zone

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Wurch (cold and moist) Dega (cool and humid) Weynadega (cool and sub-humid) Kola (warm and semi-arid) Berha (hot and arid)

Altitude (meters)

Rainfall (mm/year)

Average annual temperature (oC)

3200 plus

900 – 2200

>11.5

2300 – 3200

900 – 1200

17.5/16.0 – 11.5

1500 – 2300

800 – 1200

20.0 – 17.5/16.0

500 – 1500

200 – 800

27.5 – 20

under 500

under 200

>27.5

Figure 1. Nile Basin of Ethiopia with its agro-ecological classifications and survey districts.

The basin contains three major rivers: the Abbay River, which originates from the central highlands; the Tekeze River, which originates from the north-western parts of the country and the Baro-Akobo River, which originates from the south-western part of the country. The total annual surface runoff of the three rivers is estimated at 80.83 billion cubic meters per year, which amounts to nearly 74% of the total runoff from Ethiopia’s 12 river basins (MoWR 1998). Of the five agro-ecological zones found in Ethiopia (Table 1), the surveyed districts all fall under three: namely dega, weynadega and kola (Figure 1).

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3.3. Data The data used for this study come from a farmers’ household survey performed during the 2004/2005 production year in the Nile Basin of Ethiopia. The International Food Policy Research Institute (IFPRI) conducted this cross-sectional survey in collaboration with the Ethiopian Development Research Institute (EDRI). The sampled districts were selected to represent the different attributes of the basin, including the typologies of the regions’ agroecological zones (dega, weynadega and kola), the degree of irrigation activity (percent of cultivated land), the average annual rainfall, the rainfall variability, and the vulnerability (food aid-dependent population). Peasant associations (administrative units lower than districts) were also purposively selected to include households that irrigate their farms. One peasant association was selected from each of 20 sampled districts, for a total of 20 sampled peasant associations. Once the peasant associations were chosen, 50 farming households were randomly selected from each peasant association (Peasant associations have more than one village) for a total of 1000 interviewed households. Table 2 lists the surveyed districts and peasant associations Table 2. Surveyed districts and peasant associations.

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Regional state

Zone

Tigray

East Tigray

Amhara

South Tigray North Gondar

Oromiya

South Gondar East Gojam West Gojam West Wellega East Shoa East Shoa East Wellega

Benishangul Gumuz

SNNP Total

Jimma Metekel Asosa Kamashi Zone 1

District Hawzein Atsbi Wonberta Endamehoni Debark Chilga Wogera Libo Kemkem Bichena Quarit Gimbi Haru Bereh Aleltu Hidabu Abote Limu Nunu Kumba Kersa Wonbera Bambasi Sirba Abay Gesha Daka

Peasant association Selam Felege Woinie Mehan Mekara Teber Serako Sak Debir Angot Aratband Bichena Gebez Were Sayo Genti Abo Welgewo Sira marase Areb Gebeya Bachu Merewa Addis Alem Sonka Koncho Kicho

Number of households 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 1,000

The collected dataset includes the following: household characteristics; the incidence of different climatic and other shocks over the previous five years; food aid; land tenure; machinery ownership; rain-fed and irrigated agriculture; livestock production; access to credit, markets and extension services; income and food expenditures; perceptions of climate change; adaptation options; and social capital. Moreover, temperature and rainfall data for the surveyed households during the relevant production seasons were obtained from IFPRI.

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4. Results and Discussion 4.1. Descriptive Statistics The average income of the sampled farmers was equal to Ethiopian Birr 4356.20 per year (about 1.2 USD per day). The percentages of households that reported droughts, floods and hailstorms over the prior five years were 31%, 12% and 18%, respectively (Table 3). The relatively high frequency of drought-affected households is consistent with Ethiopia being a drought-prone country. These shocks resulted in a variety of reported losses, primarily consisting of crop yield declines and asset/income losses (Table 4). The majority of farmers did nothing to respond to these shocks, mainly due to poverty. Those farmers who attempted to cope with the negative impacts of the shocks responded mainly by selling their livestock, borrowing from their relatives, participating in food-for-work programs, and/or obtaining food aid (Table 5). Table 3. Major shocks encountered by surveyed farmers. Shock Drought Hailstorm Flood Animal disease Pest damage to crops before harvest Illness of family member

Number of farmers 380 225 142 112 84 71

Percent of farmers 31.0 18.3 11.6 9.1 6.8 5.8

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Table 4. Effects of shocks by surveyed farmers. Result Decline in crop yield Loss of assets Loss of income Food insecurity/shortage Death of livestock Decline in consumption

Number of farmers 403 213 201 140 128 124

Percent of farmers 32.8 17.4 16.4 11.4 10.4 10.1

Table 5. Coping strategies by surveyed farmers. Response to shocks Did nothing Sold livestock Borrowed from relatives Participated in food-for-work Received food aid Ate less Sought off-farm employment

Number of farmers 503 438 106 34 21 35 18

Percent of farmers 41.0 35.7 8.6 2.8 1.7 2.9 1.5

Closer examination of the coping strategies used to deal with the major environmental shocks (droughts, floods and hailstorms) reveals that most of the surveyed farmers who reported taking action to deal with shocks experienced over the prior five years coped by

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selling livestock. This suggests that in addition to serving as source of power for farming (e.g., oxen) and manure for fertilizing soil, livestock can serve as assets and insurance against shocks (Yirga, 2007). The other utilized coping strategies include borrowing from relatives, eating less, depending on food aid and food-for-work, and looking for off-farm employment. Figure 2 describes the types of coping strategies employed under different climatic shocks by percent of farmers who used a coping strategy.

50.0 45.0 40.0 35.0 30.0

Percent

25.0 20.0 15.0 10.0 5.0 0.0 Flood

Drought

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Did nothing Received food aid Ate less

Sold livestock Participated in food -for -work Applied soil conservation schemes

Hailstorm Borrowed from relatives Sought off-farm employment

Figure 2. Coping strategies used to deal with major environmental shocks.

Table 6. Description of the utilized dependent and independent variables.

Farm income Explanatory variables Drought

Mean value 4356.169 Mean 0.3099511

7276.695 Std. dev. 0.4626619

Flood

0.1158238

0.3201441

Hailstorm

0.1835237

0.3872532

Years of education for household head Size of household Gender of household head Age of household head

1.7035

2.7777

6.1493 0.8963

2.2206 0.3051

44.2915

12.6248

Dependent variable

Std. dev.

Description Continuous Description Dummy, takes the value of 1 if occurred during the prior five years, and 0 otherwise Dummy, takes the value of 1 if occurred during the prior five years, and 0 otherwise Dummy, takes the value of 1 if occurred during the prior five years, and 0 otherwise Continuous Continuous Dummy, takes the value of 1 if male and 0 otherwise Continuous

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Table 6. Continued Mean value 0.9488

0.2205

Use of crop and livestock extension services Credit access

0.5455

0.4982

0.2191

0.4138

Farm size in hectares Distance to output market in kilometers Amhara region

2.02 5.70

1.18 4.14

0.4380098

0.4963448 0.4595754

Dependent variable Livestock ownership

Oromia region

Std. dev.

0.3026101 Beneshangul region 0.1272431 South Peoples’ region

0.333381 0.1494494

0.0228385 Average temperature

2.578172 18.63101

Average rainfall

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Local agro-ecology is Kola Local agro-ecology is Weynadega Local agro-ecology is Dega

36.58814 111.4413 0.25

0.43

0.50

0.50

0.25

0.43

Description Dummy, takes the value of 1 if owned and 0 otherwise Dummy, takes the value of 1 if visited and 0 otherwise Dummy, takes the value of 1 if there is access and 0 otherwise Continuous Continuous Dummy, takes the value of 1 if Amhara region and 0 otherwise Dummy, takes the value of 1 if Oromia region and 0 otherwise Dummy, takes the value of 1 if Beneshangul region and 0 otherwise Dummy, takes the value of 1 if South Peoples’ region and 0 otherwise Continuous, annual average over the 2004– 2005 survey period Continuous, annual average over the 2004– 2005 survey period Dummy, takes the value of 1 if Kola and 0 otherwise Dummy, takes the value of 1 if Weynadega and 0 otherwise Dummy, takes the value of 1 if Dega and 0 otherwise

Across the household survey, 90% of the households were male-headed; the average years of education for the household head was 1.7 years; the average age of the household head was 44.3 years; and the average household size was 6.15 individuals. As indicated in the previous section (section 3.1), the logarithm of farm income has been used as a dependent variable where as different socio-economic and environmental factors have been used as independent variables. Table 6 gives the means and standard deviations of the dependent and independent variables included in the analysis from the surveyed households.

4.2. Model Results Using the procedures discussed in Section 3 (applied through the STATA software), we estimate the probability of a household falling below a given level of income (poverty line), and perform a sensitivity analysis by examining this probability using four different minimum levels of income (poverty lines). The choice of minimum levels of income is based on different assumptions such as the international poverty line of 1.25 US per day (World Bank, 2008), average income of the surveyed households and arbitrary values above and below the average income of the surveyed households.

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.5

.6

Vulnerability .7 .8

.9

1

The results are plotted in Figures 3 to 6. The x-axis shows the observed and imputed values for the natural log of income, while the y-axis shows the computed estimates of vulnerability. Each graph is broken in to four sections. Those in the upper left are poor today and likely to be poor tomorrow, and those in the bottom left are poor today, but have characteristics suggesting they have a less than 50 ( 0.5 probability level is taken as a cutoff point) percent chance of being poor in the future. Those in the upper right corner are not below the income threshold at present, but are likely to become so in the future, while those in the bottom left are above the income threshold and are likely to remain above it in the future.

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4

6

8

10

Ln(Income)

Figure 3. Vulnerability (income at 2 USD per day or 6570 Ethiopian Birr per year) plotted against Ln (income).

Table 7. Sensitivity analysis at the agro-ecological level: percent of farmers in each agro ecology. Agro-ecological zone Kola Dega Weynadega

2 USD per day p > 0.5 p < 0.5 100.00 0.00 100.00 0.00 99.73 0.27

1.5 USD per day p >0.5 p< 0.5 99.64 0.36 97.69 2.31 93.57 6.43

1.25 USD per day P > 0.5 p < 0.5 98.57 1.43 88.65 11.35 93.98 6.02

0.3 USD per day p > 0.5 p < 0.5 17.20 82.80 9.26 90.74 12.72 87.28

In figure 3, where the poverty line is fixed at 2USD per day, most farmers are poor today and more likely to be poor tomorrow. As Figure 6 shows, when the poverty line is fixed at 0.3USD per day, most people have the characteristics that they are not poor today and are likely to remain above the poverty line in the future. Figures 4-6 depict that the number of

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.2

.4

Vulnerability .6

.8

1

people poor today and likely to be poor in the future increases with increasing the minimum income level required to sustain daily life.

4

6

8

10

Ln(Income)

.8 Vulnerability .4 .6 .2 0

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1

Figure 4. Vulnerability (income at 1.5 USD per day or 4928 Ethiopian Birr per year) plotted against Ln (income).

4

6

8

10

Ln(Income)

Figure 5. Vulnerability (income at 1.25 USD per day or 4471 Ethiopian Birr per year) plotted against Ln (income).

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T.T. Deressa, R.M. Hassan and R. Claudia

0

.2

Vulnerability .4 .6

.8

1

132

4

6

8

10

Ln(Income)

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Figure 6. Vulnerability (income at 0.3 USD per day or 900 Ethiopian Birr per year) plotted against Ln (income).

The analysis undertaken to compare the vulnerability of households across different agroecologies over different scenarios of poverty line indicate that farmers living in kola are the most vulnerable to climatic extremes. Percent of farmers vulnerable under each agro-ecology in conjunction with the different scenarios is presented in Table 7. Out of the total households surveyed in kola, 99.4 percent of the farmers are vulnerable at present or will be vulnerable in the future (fall above the 50 % cutoff line); whereas the remaining 0.36 percent of the farmers are not vulnerable at present or will not be vulnerable in the near future when the scenario of minimum daily income is fixed at 1.25 USD per day. The same line of explanation also holds for the rest of the scenarios across different agroecologies as depicted in Table 7. Table 8. Sensitivity analysis at the regional-state level: percent of farmers in each region. Regional state Amhara Oromia Beneshangul Gumz SNNP Tigray

2 USD per day p > 0.5 p < 0.5 100.00 0.00 99.46 0.54 100.00 0.00 100.00 0.00 100.00 0.00

1.5 USD per day p> 0.5 p< 0.5 99.63 0.37 87.33 12.67 100.00 0.00 100.00 0.00 97.01 2.99

1.25 USD per day 0.3 USD per day p > 0.5 p < 0.5 p > 0.5 p 1 4

(7)

⎡1 0 ⎤ where L = ⎢0 0⎥ . ⎢ ⎥ ⎢⎣0 1⎥⎦ Before presenting our empirical results, we briefly describe the behavior of the VIRF. First of all, let Rs = [ rij ,s ] where i=1,2,3 and j=1,2. The following two cases are of interest:

Case I: Diagonal BEKK model (i.e. a12 = a 21 = b12 = b21 = d12 = d 21 = 0 ) In this case, r12 , s = r21, s = r22, s = r31, s = 0 (s=1,2,…) and thus there are no volatility spillovers for either positive or negative shocks. Specifically, 2 ⎧ r = a 2 , r ,1 = a 22 , positive shock R1 = ⎨ 11,1 2 11 32 2 2 2 , negative shock ⎩r11,1 = a11 + d11 , r32,1 = a 22 + d 22 d2 d2 2 2 r11, s = (a112 + b112 + 11 ) s −1 r11,1 , r32, s = (a 22 + b22 + 22 ) s −1 r32,1 , 2 2

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(8)

s >1

The Effects of Asymmetric Volatility Shocks on Equity…

143

Case II: ( a12 = b12 = d12 = 0 ), while ( a21 ≠ 0 and/or b21 ≠ 0 and/or d 21 ≠ 0 ) In this case, r12 , s = r22 , s = 0 and thus there are unidirectional volatility spillovers from the first to the second variable of the system. If any of a 21 , b21 and d21 is non-zero, there are still volatility spillovers from the first to the second variable of the system. It is also easy to show that r11, s and r32, s (that is the reaction of the variables to their own volatility shock) are still given by equation (8). It is clear that the opposite situation of unidirectional spillovers from the second to the first variable of the system occurs when a 21 = b21 = d 21 = 0 , while

a12 ≠ 0 and/or b12 ≠ 0 and/or d 12 ≠ 0 .

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2.3. Data Our analysis is conducted on the dollar exchange rate and equity markets of a group of East Asian emerging markets. In particular, we focus on Korea, Indonesia, the Philippines, Singapore and Thailand. We select these countries due to the fact that they have a sufficiently long time series of floating exchange rates to undertake the analysis.4 We employ weekly returns for both markets with FX returns computed as the log change in the US dollar exchange rate, with the exchange rate expressed as the US dollars price of the local currency. Similarly, equity returns are computed as the log change in the value of the domestic stock market index. These indices are value-weighted and expressed in local currency. They were obtained from Datastream International; with the Datastream codes having the following structure: TOTMKXX, where XX represents the country code, i.e. KO (Korea), ID (Indonesia), PH (Philippines), SG (Singapore) and TH (Thailand). Our sample begins as soon as the exchange rate floats against the dollar and extends to February 2008, yielding over ten years of data for each series. Table 1 presents some summary statistics. Panels A and B relate to equity and currency markets respectively. Mean equity returns are larger than foreign exchange returns for all markets. However, they are also more risky. Equity returns are positive over the sample, with Korea recording the highest mean return of 0.214%. However, it is noteworthy that in many instances, the median return is far from the mean, implying that the overall distribution of returns is nonnormal. With the exception of Singapore, average currency returns are negative, indicating that the value of the domestic currency has fallen against the dollar over the sample period. Both asset returns exhibit significant skewness and kurtosis, with the Jarque Bera test decisively rejecting normality for all series. For most currencies, there is huge negative skewness present in the distribution of returns, indicating the presence of a number of extreme observations in the data.

4

The full effects of the shock will not be observable if the exchange rate is fixed or if there is frequent intervention from a monetary authority.

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al. Table 1. Panel A. Summary Descriptive Statistics-Equity Returns. Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque Bera

Indonesia 0.186 0.302 22.72 -20.43 4.743 0.065 6.631 305.8 (0.000)

Korea 0.214 0.528 16.95 -19.57 4.878 -0.216 4.787 78.3 (0.000)

Philippines Singapore 0.023 0.109 0.108 0.255 14.74 11.74 -21.13 -18.28 3.417 2.921 -0.411 -0.508 7.801 6.826 549.8 363.1 (0.000) (0.000)

Thailand 0.086 0.064 25.27 -17.58 4.598 0.330 6.068 228.1 (0.000)

Panel B. Summary Descriptive Statistics-Foreign Exchange Returns Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque Bera

Indonesia Korea -0.239 -0.012 -0.017 0.064 38.62 13.60 -56.86 -33.05 4.758 2.215 -3.401 -5.848 56.654 97.409 67764.0 209656.7 (0.000) (0.000)

Philippines -0.078 -0.012 7.67 -12.78 1.431 -1.683 21.048 7808.6 (0.000)

Singapore 0.003 0.016 7.93 -4.45 0.858 1.081 18.892 5959.1 (0.000)

Note: P-values for the null hypothesis of normality are reported in the parentheses.

Thailand -0.040 0.043 9.68 -11.88 1.706 -1.001 16.939 4594.0 (0.000)

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3. Empirical Results We estimate our model for each country and results are presented in Table 2. Initially, the model is estimated without restrictions but a number of important parameters are not statistically different from zero (see Cases I and II above), so we re-estimate the model imposing zero restrictions where appropriate. The estimated restricted models are reported in Table 3. In all cases, likelihood ratio tests support these restrictions. Table 2. Estimated parameters of the conditional variance –covariance matrix (unrestricted models). Indonesia Korea Philippines Singapore Thailand Standard Standard Standard Standard Standard Estimate Estimate Estimate Estimate error error error error error

Estimate

ω11 ω21 ω22 α11 α12 α 21 α22

0.2696

0.0736

0.2329

0.0426

0.1304

0.0261

0.1553

0.0343

0.2028

0.0355

0.8827

0.7372

0.1482

0.1797

0.5169

0.1650

0.1601

0.0818

0.2855

0.0717

1.1257

0.6834

0.2263

0.1593

0.1644

0.2946

0.0948

0.0978

-0.0743

0.1897

0.3330

0.0665

0.4080

0.0670

0.3284

0.0498

0.1429

0.0647

0.4821

0.0559

-0.0763

0.0213

-0.0176

0.0149

0.0062

0.0160

-0.0030

0.0180

-0.0209

0.0128

-0.1725

0.0818

0.2404

0.1149

-0.0112

0.1755

-0.1777

0.1869

0.0199

0.1494

-0.0441

0.0861

0.1000

0.0482

0.0796

0.0694

0.2403

0.0453

0.0289

0.0585

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Table 2. Continued Indonesia Korea Philippines Singapore Thailand Standard Standard Standard Standard Standard Estimate Estimate Estimate Estimate error error error error error

Estimate

b11 b12 b21 b22 d11 d12 d21 d22

0.9269

0.0153

0.8785

0.0216

0.9291

0.0181

0.9300

0.0221

0.8507

0.0236

-0.0161

0.0229

0.0028

0.0033

-0.0009

0.0071

0.0007

0.0036

0.0098

0.0036

0.0568

0.0288

-0.0525

0.0526

0.0572

0.0623

-0.0258

0.0768

0.0336

0.0662

0.8899

0.0368

0.9895

0.0056

0.9672

0.0152

0.9694

0.0099

0.9900

0.0063

0.2437

0.0993

0.3073

0.1221

0.0046

0.2350

0.2455

0.0795

0.0655

0.2475

0.0323

0.0452

-0.0449

0.0208

0.0068

0.0422

0.0382

0.0182

0.0106

0.0444

0.0811

0.1124

0.0960

0.1073

0.1443

0.1745

0.2364

0.2495

0.3516

0.1329

0.0870

-0.1142

0.0663

0.1644

0.0819

0.0620

0.0940

-0.0532

0.1075

0.6312

6.4859

1.1789

5.0624

0.8007

6.9842

1.3027

6.7746

1.4619

0.3784

df 4.0311 Likelihood -2629.57 function

-2348.06

-2029.12

-1829.42

-2243.12

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Table 3. Estimated parameters of the conditional variance –covariance matrix (restricted models)

ω11 ω21 ω22 α11 α12 α 21 α22 b11 b12 b21 b22 d11 d12 d21 d22

Indonesia Korea Philippines Singapore Thailand Standard Standard Standard Standard Standard Estimate Estimate Estimate Estimate Estimate error error error error error 0.2191

0.0477

0.2302

0.0403

0.1348

0.0238

0.1547

0.0345

0.6844

0.0457

1.1789

0.2651

---

---

0.5069

0.1546

0.1407

0.0789

0.3938

0.1360

0.6777

0.2442

0.2470

0.0771

0.1573

0.0994

0.0907

0.0424

---

---

0.3144

0.0527

0.3651

0.0541

0.3337

0.0401

0.2299

0.0592

0.9283

0.0838

-0.0718

0.0201

---

---

---

---

---

---

0.0191

0.0121

-0.2035

0.0688

0.0944

0.0424

---

---

---

---

---

---

---

---

0.1292

0.0410

---

---

0.2140

0.0326

0.1533

0.0570

0.9259

0.0114

0.8924

0.0177

0.9282

0.0132

0.9259

0.0213

---

---

---

---

---

---

---

---

---

---

0.0643

0.0643

0.0633

0.0225

---

---

0.0816

0.0251

---

---

---

---

0.8994

0.0312

0.9848

0.0043

0.9684

0.0117

0.9748

0.0072

0.9833

0.0076

0.2806

0.0585

0.2713

0.1092

---

---

0.1696

0.0847

---

---

---

---

-0.0441

0.0198

---

---

0.0360

0.0203

---

---

---

---

---

---

---

---

---

---

-0.3622

0.1038

0.0687

-0.1061

0.0575

0.1975

0.0467

---

---

---

---

0.6345

6.3348

1.1111

4.9582

0.7320

6.9937

1.2795

3.9761

0.5018

0.3720

df 4.0965 Likeli-2630.59 hood function

-2349.90

-2031.03

-1830.76

-2295.45

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al. A Positive Shock in Exchange Rate

A Positive Shock in Stock Market .0052 .0051

.112

Effect on Exchange Rate

Effect on Exchange Rate

.116

.108

.104

.100

.096

.0050 .0049 .0048 .0047 .0046

25

50

75

100

25

Weeks

.00000

-.01

-.00004 Effect on Covariance

Effect on Covariance

100

A Positive Shock in Stock Market

.00

-.02 -.03 -.04 -.05

-.00008 -.00012 -.00016 -.00020

-.06 -.07

-.00024 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.045

.0020

.040

.0016 Effect on Stock Market

Effect on Stock Market

75

Weeks

A Positive Shock in Exchange Rate

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50

.035 .030 .025 .020 .015

.0012

.0008

.0004

.0000 25

50 Weeks

75

100

25

50

75

100

Weeks

Figure 1. Volatility Impulse Response Functions for Indonesia Panel A – a positive shock.

The unrestricted estimation of our model produces a number of noteworthy features. Firstly, in the majority of cases, there is evidence of bi-directional volatility spillovers between FX and equity markets. The exceptions to this pattern are the Philippines and Singapore where the transmission of shocks is uni-directional. In the Philippines, volatility flows from FX to equity markets but not in reverse, while the opposite is true for Singapore, with stock market shocks affecting FX markets but not vice-versa. Secondly, there is strong

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support for our modeling approach in that all market pairs exhibit asymmetric responses to good and bad news events. Many of the elements of the D matrix are statistically significant; implying that ignoring this channel would be costly in understanding the cross-market effects of volatility propagation. Finally, our results suggest that it is important to adopt a t(ν ) − distribution for the innovations as our estimated ‘df’ parameter is not consistent with the assumption of normally distributed errors. A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.192

.011 .010 Effect on Exchange Rate

Effect on Exchange Rate

.190 .188 .186 .184 .182 .180 .178 .176

.009 .008 .007 .006 .005

25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.00

.0000

-.01 Effect on Covariance

Effect on Covariance

-.0001 -.02 -.03 -.04 -.05

-.0002

-.0003

-.07

-.0005 25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.065

.14

.060

.12 Effect on Stock Market

Effect on Stock Market

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-.0004 -.06

.055 .050 .045 .040 .035

.10 .08 .06 .04 .02

.030

.00 25

50 Weeks

75

100

25

50

75

Weeks

Figure 1. Volatility Impulse Response Functions for Indonesia Panel B – a negative shock.

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al.

We report our findings in greater detail by presenting the VIRFs for each country in Figures 1-5. These graphs have the same format with Panels A and B depicting the response to a positive shock and negative shock respectively. Each panel is divided into two columns with the left hand (right-hand) column showing the responses to a FX market (stock market) shock. A Positive Shock in Stock Market .00030

.12

.00025 Effect on Exchange Rate

Effect on Exchange Rate

A Positive Shock in Exchange Rate .14

.10 .08 .06 .04

.00020 .00015 .00010 .00005

.02 .00

.00000 25

50

75

100

25

Weeks

.0005

.04

.0004 Effect on Covariance

Effect on Covariance

100

A Positive Shock in Stock Market

.05

.03

.02

.01

.0003

.0002

.0001

.00

.0000 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.07

.017 .016 Effect on Stock Market

.06 Effect on Stock Market

75

Weeks

A Positive Shock in Exchange Rate

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50

.05 .04 .03 .02 .01

.015 .014 .013 .012 .011 .010 .009

.00

.008 25

50 Weeks

75

100

25

50

75

Weeks

Figure 2. Volatility Impulse Response Functions for Korea Panel A – a positive shock.

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The Effects of Asymmetric Volatility Shocks on Equity… A Negative Shock in Exchange Rate

149

A Negative Shock in Stock Market

.24

.0020

Effect on Exchange Rate

Effect on Exchange Rate

.20 .16 .12 .08 .04 .00

.0016

.0012

.0008

.0004 25

50

75

100

25

Weeks A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.004 Effect on Covariance

Effect on Covariance

100

.005

.05 .04 .03 .02

.003

.002

.001

.01 .00

.000 25

50

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25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.09

.030

.08

.028

.07

Effect on Stock Market

Effect on Stock Market

75

Weeks

.06

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

50

.06 .05 .04 .03 .02

.026 .024 .022 .020 .018 .016

.01 .00

.014 25

50 Weeks

75

100

25

50

75

Weeks

Figure 2. Volatility Impulse Response Functions for Korea Panel B – a negative shock.

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al. A Positive Shock in Stock Market .0011

.8

.0010

.7

Effect on Exchange Rate

Effect on Exchange Rate

A Positive Shock in Exchange Rate .9

.6 .5 .4 .3 .2

.0009 .0008 .0007 .0006 .0005 .0004

.1 .0

.0003 25

50

75

100

25

Weeks

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.028

.0032

.024

.0028 Effect on Covariance

Effect on Covariance

50

.020 .016 .012 .008

.0024 .0020 .0016 .0012

.004 .000

.0008 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.36

.024

.32 Effect on Stock Market

Effect on Stock Market

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.022 .28 .24 .20 .16 .12 .08

.020 .018 .016 .014

.04 .00

.012 25

50 Weeks

75

100

25

50

75

100

Weeks

Figure 3. Volatility Impulse Response Functions for Thailand Panel A – a positive shock.

Figures 1-3 exhibit similar patterns and refer to Indonesia, Korea and Thailand respectively. For each of these countries, we observe strong bi-directional volatility spillovers between FX and equity markets. Interestingly, shocks to the exchange rate - both positive and negative – exert a larger influence on domestic financial markets than those to the stock market. These shocks may arise due to unanticipated international capital flows as foreign investors buy or sell the domestic currency to increase or decrease their holdings of physical or financial assets. As a result, changes in investors’ perceptions of and appetite for risk may

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lead to these unanticipated events. For example during the Asian crisis, the Bank of International Settlements report a sharp reversal in capital flows between 1996 and 1997 for Indonesia, Thailand, Korea, Malaysia and the Philippines. Net capital inflows of US$95 billion turned to a net capital outflow of US$12 billion as the crisis deepened. Interestingly, the effects of FX shocks are more persistent for stock markets than FX markets, suggesting that the latter suffers more prolonged declines than currencies. A Negative Shock in Stock Market .0011

.8

.0010

.7

Effect on Exchange Rate

Effect on Exchange Rate

A Negative Shock in Exchange Rate .9

.6 .5 .4 .3 .2

.0009 .0008 .0007 .0006 .0005 .0004

.1 .0

.0003 25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.036

.0032

.032 Effect on Covariance

Effect on Covariance

.0028 .028 .024 .020 .016 .012 .008

.0024 .0020 .0016 .0012

.000

.0008 25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.48

.024

.44 .022 .40

Effect on Stock Market

Effect on Stock Market

Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

.004

.36 .32 .28 .24 .20

.020 .018 .016 .014

.16 .12

.012 25

50 Weeks

75

100

25

50

75

Weeks

Figure 3. Volatility Impulse Response Functions for Thailand Panel B – a negative shock.

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al. A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.12

1.0

Effect on Exchange Rate

Effect on Exchange Rate

.10 .08 .06 .04 .02 .00

0.5

0.0

-0.5

-1.0 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.06

1.0

Effect on Covariance

Effect on Covariance

.05 .04 .03 .02

0.5

0.0

-0.5

.01 .00

-1.0 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

.16

1.0

.12

Effect on Stock Market

Effect on Stock Market

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.14

.10 .08 .06 .04

0.5

0.0

-0.5

.02 .00

-1.0 25

50 Weeks

75

100

25

50

75

100

Weeks

Figure 4. Volatility Impulse Response Functions for the Philippines Panel A – a positive shock.

Secondly, both FX and equity market returns exhibit an asymmetric response to favorable and adverse innovations. In particular, bad news events generate relatively more volatility. This may be due to the contagious effects documented in the literature e.g. Dungey, et al. (2004), Chiang et al. (2007) and Flavin et al. (2008) among others. Thirdly, unanticipated events of either sign, and regardless of origin, tend to increase market co-movement, except

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in Indonesia where there is a weak tendency for a fall in correlation. This suggests that there are common factors affecting both markets and factor loadings are of the same sign. A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.12

1.0

Effect on Exchange Rate

Effect on Exchange Rate

.10 .08 .06 .04 .02 .00

0.5

0.0

-0.5

-1.0 25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.06

1.0

Effect on Covariance

Effect on Covariance

.05 .04 .03 .02

0.5

0.0

-0.5

.01 .00

-1.0 25

50

75

100

25

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.16

.04

.14 .12

Effect on Stock Market

Effect on Stock Market

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Weeks

50

.10 .08 .06 .04

.03

.02

.01

.02 .00

.00 25

50 Weeks

75

100

25

50

75

100

Weeks

Figure 4. Volatility Impulse Response Functions for the Philippines Panel B – a negative shock.

The Philippines and Singapore exhibit different behavior and their VIRFs are presented in Figure 4 and 5.

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al. A Positive Shock in Stock Market .00035

.05

.00030 Effect on Exchange Rate

Effect on Exchange Rate

A Positive Shock in Exchange Rate .06

.04 .03 .02 .01

.00025 .00020 .00015 .00010 .00005

.00

.00000 25

50

75

100

25

Weeks

1.0

0.5

0.5

Effect on Covariance

Effect on Covariance

100

A Positive Shock in Stock Market

1.0

0.0

-0.5

-1.0

0.0

-0.5

-1.0 25

50

75

100

25

Weeks

50

75

100

Weeks

A Positive Shock in Exchange Rate

A Positive Shock in Stock Market

1.0

.048

.044

0.5

Effect on Stock Market

Effect on Stock Market

75

Weeks

A Positive Shock in Exchange Rate

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50

0.0

-0.5

-1.0

.040

.036

.032

.028 25

50 Weeks

75

100

25

50

75

100

Weeks

Figure 5. Volatility Impulse Response Functions for Singapore Panel A – a positive shock.

The markets of both these countries display uni-directional volatility spillovers but differ in the transmission of both shocks. In the Philippines volatility flows from FX markets to equity markets while in Singapore, the flow is in the opposite direction, i.e. equity to FX markets. Otherwise the patterns are similar with exchange rate shocks having relatively larger effects. Singapore displays relatively little evidence of volatility propagation or shock

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persistence and differs from its regional neighbors in this respect. It may suggest that Singapore is better developed than the other Asian economies in our sample and consequently, contagion effects are limited due to the higher confidence of the investment community in the ability of this market to deal with surprise events. A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

.09

.0014

.08 Effect on Exchange Rate

Effect on Exchange Rate

.0012 .07 .06 .05 .04 .03 .02

.0010 .0008 .0006 .0004

.01 .00

.0002 25

50

75

100

25

Weeks

1.0

0.5

0.5

Effect on Covariance

Effect on Covariance

100

A Negative Shock in Stock Market

1.0

0.0

-0.5

-1.0

0.0

-0.5

-1.0 25

50

75

100

25

Weeks

50

75

100

Weeks

A Negative Shock in Exchange Rate

A Negative Shock in Stock Market

1.0

.048

.044

0.5

Effect on Stock Market

Effect on Stock Market

75

Weeks

A Negative Shock in Exchange Rate

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50

0.0

-0.5

-1.0

.040

.036

.032

.028 25

50 Weeks

75

100

25

50

75

Weeks

Figure 5. Volatility Impulse Response Functions for Singapore Panel B – a negative shock.

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Thomas J. Flavin, Ekaterini Panopoulou, Theologos Pantelidis et al.

These results are important for international investors who hold the equities of these countries. In essence, equity holdings are affected by their own shocks but also by shocks to the exchange rate. The greater impact on the exchange rate provides a cautionary tale for foreign investors as the proceeds of any asset liquidation may be eroded by adverse movements in the exchange rate. If possible, the predictable component of equity returns should be hedged to avoid exchange rate fluctuations. The effects on currency traders are relatively small but may still be important in the context of portfolio formulation. Policy makers should also take account of our findings as they bid to curb the spread of adverse effects due to volatility spillovers. Specifically, the strong dynamic interactions of domestic financial markets show that policy focused on one particular market is unlikely to be successful as shocks transmit between markets. A more holistic approach needs to be adopted to smooth over episodes of financial turbulence.

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4. Conclusions We analyze the dynamic interactions of domestic financial markets for a number of East Asian emerging economies. In particular, we focus on the relationship between FX and equity markets and assess their behavior in the aftermath of a shock to either market. We adopt the existing econometric methodology to take account of potentially asymmetric reaction to favorable and adverse unanticipated events and generate Volatility Impulse Response Functions (VIRFs) to assess the dynamics of the relationship. Our results produce a number of important findings. Firstly, a feature our sampled countries is the presence of bi-directional volatility spillovers between domestic financial markets. The majority of markets share this characteristic; though for Singapore and the Philippines, the transmission of volatility occurs in one direction only. However, all market pairs experience some episodes of spillovers, suggesting that shocks are not contained within the ‘source’ market but increase the risk in both markets. We also find that the conditional covariances also increase in response to either type of shock This may be due to common shocks or ‘pure contagion’ whereby a previously idiosyncratic shock becomes an additional common factor during periods of high volatility. Our results are consistent with those of Flavin et al. (2008). Secondly, exchange rate returns are relatively more sensitive to financial turmoil than equity market returns but the effects are less persistent. Thirdly, both markets exhibit asymmetric behavior in response to good and bad news with evidence that the latter generates relatively more volatility. Adverse shocks therefore increase market risk and volatility spillovers become more important, which is again consistent with the presence of contagion documented in the extant literature, i.e. that large adverse shocks increase the co-movement of market pairs above ‘normal’ levels. These findings have important implications for equity investors and currency traders who operate in these countries. For stock market participants, both components of total return, i.e. equity returns and FX returns, appear to have common driving forces, which produce volatility spillovers in the aftermath of a shock. Given the greater reaction to negative events, investors have high risk exposure in both markets. This is further exacerbated by increasing co-movements. The two components of return do not provide a hedge against each other but rather reinforce the effects of the original shock. Policy makers also need to account for these dynamic interactions. Policy responses to surprise events must be designed to support the entire financial system and not just the market where the shock originated.

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References Bollerslev, T. (1987). A conditional heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics, 69, 542-547. Chiang, T. C., Jeon, B. N. & Li, H. (2007). Dynamic correlation analysis of financial contagion: evidence from Asian markets. Journal of International Money and Finance, 26, 1206-1228. Dungey, M., Fry, R. & Martin, V. (2004). Currency market contagion in the Asia-Pacific region. Australian Economic Papers, 43(4), 379-395. Engle, R. F. & Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11, 122-150. Flavin, T. J., Panopoulou, E. & Unalmis, D. (2008). On the stability of domestic financial market linkages in the presence of time-varying volatility. Emerging Markets Review, 9, 280-301. Granger, C. W. J., Huang, B. & Yang, C. (2000). A bivariate causality between stock prices and exchange rates: evidence from recent Asian flu. Quarterly Review of Economics and Finance, 40, 337-354. Hafner, C. & Herwartz, H. (2006). Volatility Impulse Response Functions for Multivariate GARCH Models: An Exchange Rate Illustration. Journal of International Money and Finance, 25(5), 719-740. Herwartz, H. & Lutkepohl, H. (2000). Multivariate volatility analysis of VW stock prices. International Journal of Intelligent Systems in Accounting, Finance & Management, 9, 35-54. Ito, T. & Hashimoto, Y. (2005). High-frequency contagion between exchange rates and stock prices during the Asian currency crisis. In Dungey, M., Tambakis, D.M. (Eds) Identifying International Financial Contagion: Progress and Challenges, Oxford University Press, NY. Lee, J. (2002). Federal funds rate target changes and interest rate volatility. Journal of Economics and Business, 54, 159-191. Lin, W. L (1997). Impulse response function for conditional volatility in GARCH models. Journal of Business and Economics Statistics, 15(1), 15-25. Meneu, V. & H. Torro (2003). Asymmetric covariance in spot-futures markets. The Journal of Futures Markets, 11, 1019-1046. Pan, M. S., Fok, R. & Liu, Y A. (2007). Dynamic linkages between exchange rates and stock prices: evidence from East Asian markets. International Review of Economics and Finance, 503-520. Panopoulou, E. & Pantelidis, T. (2008). Integration at a cost: evidence from volatility impulse response functions. Applied Financial Economics, 19, 917-933. Pavlova, A. & Rigobon, R. (2007). Asset prices and exchange rates. Review of Financial Studies, 20(4), 1139-1181. Susmel, R. & Engle, R. F. (1994). Hourly volatility spillovers between international equity markets. Journal of International Money and Finance, 13(1), 3-25.

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Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 159-168

ISBN: 978-1-60876-329-0 © 2010 Nova Science Publishers, Inc.

Chapter 7

BANKING REGULATION AND PROCYCLICALITY – CROSS-COUNTRY ANALYSIS IN EMU Tamás Isépy* University of Pannonia, Departement of International Economics, Egyetem u. 10, 8200 Veszprém, Hungary

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Abstract The main critique is in connection with Basel II. regulation, that the New Capital Accord raises the procyclicality of banking system. In EMU-wide cross-country comparative analysis I tested evolution of the capital buffers, the output gap and the financial structure index. In my study I searched answers for the following questions: what factors are influencing the measure of capital buffers held by the bank above the minimum capital adequacy ratio (BIS ratio 8%), how level of the capital buffers worked out by country, what relationship is between measure of capital buffers and business cycle? Is there any relation between the extent of capital buffers and financial structure?

Keywords: Banking regulation, EMU, procyclicality, financial structure, Basel II. JEL codes: F30, G21.

1. Introduction Request of banking supervision shall have reached back by long time. Initially assurance of the liquidity meant the principal task in case of the bankruptcy, market panics. Definition of the minimum reserve ratio served primarilly liquidity of the individual banks and the banking system' maintenance. This regulation later got a complementary instrument of the monetary policy. With application of the capital adequacy ratio also the asset structure of bank balance-sheet were examined. With refining of methodics with more precise and efficient quantification of risk is definable that measure of capital, which need to prudent *

E-mail address: [email protected], Telephone: +36-88-624894.

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operation of the bank. Financial markets globalization increased remarkably the risk of spreading of the crises. Both international- and the national authorities interested in definition and measuring of assumed risks taken by banks. In New Capital Accord there is a possibility to evaluate the risk with internal models, besides the market risks also the credit- and operational risk. The liberalization, consequently because of quick international spread of the crises, the blame of the supervisory authority increases significantly at appreciation of the internal models. Many researchers of international financial institutions and of the national authorities handle with examination of the Basel II's estimated results. One of the principal research areas is to define and measure the procyclicality of New Capital Accord and to analise the dimming facilities. In according to the Modigliani-Miller thesis, in case of perfect market the determination of capital leverage of the individual companies is irrelevant and has not any effects on it's efficiency. The banks at reckoning of capital adequacy ratio need to hold minimum guarantee capital, which is 8 percentage off balance-sheet total corrected by on- and off balance sheet items' riskiness. On one hand this is reflected a minimum measure of capital to be ordered to the assets, on the other hand in some extent the regulator can determines a capital leverage of an individual bank or the banking system. To be more precise through definition of minimum capital adequacy regulators effect on evolution of equity capital/ total liabilities ratio. The aim of Basel I. signed in 1988 was to solve the debt crisis and appreciated as a directive to the international payment system. There is not documentation from fixing process about measure of capital adequacy ratio, which is explainable by the fact, that the primary target was to establish an entire requirement for every bank. In international comparison the average value of the banks BIS ratio had grown steadily from the level of 8.7% in 1990 to 12% in 2001. Bikker, Metzenmakers (2004).

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2. About the Role of the Capital Buffer In spite of the fact, that in the New Capital Accord is not changing the minimum extents 8% of the capital adequacy ratio, the question occurs, why the banks and the banking system hold significantly higher guarantee capital than minimum one. The measure of capital buffer can be interpreted as a ratio, where in nominator is corrected guarantee capital hold by bank above the prescribed smallest quantity of capital requirements and in denominator either the total assets corrected by risk or the prescribed smallest quantity of capital requirements. The Basel II. can be equated more risk sensitive regulation compared to Basel I. signed in 1988 and also to the amendment with market risk approach signed in 1996. The new regulation enables mitigation of the gap between regulatory (prescribed by banking supervision/ regulating authority) capital and economic (economically required) capital. With application of the internal models the volatility of the bank's portfolio appears in minimum capital requirements and as a result the volatility of bank's capitals and capital buffers increases significantly.From point of regulator's view high capital buffers held by banks are beneficial, because they can contribute to the fulfillment of the additional capital requirements from the operational risk, moreover the banks at holding of risky portfolio can conform better to the more risk sensitive approach. In the absence of this, the capital

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adequacy ratio of banks in case of shock could fall with higher probability under the minimum level. The literature explains holding of bank's capital buffer with market discipline and avoidance of supervisory intervention. Borio, Furfine, Lowe (2001) The undercapitalised banks can lose confidence of the market and jeopardise their reputation. Above the smallest amount of a capital buffer can be considered consequently as insurance of a certain kind in relation to those cost, which would incur in case of CAR fall at the forced capital increase. Price of the new capital, namely yield of capital or interest of subordinated debt can be interpreted as price of this insurance. The increasing insurance costs have negative effect on capital buffer. Value of the insurance is depending on bank uncertainty, namely what is the probability of an extent in CAR, at which the original ratio can not restore without significant difficulties. Credit losses can emerge in case of unexpected shock or due to informational asymmetry of creditor-debtor relationship. In the latter case the bank can raise its knowledges related with risk exposure with ongoing monitoring of the individual projects. This monitoring is expensive, which profit and loss can be opposed with cost of capital buffer's holding. Due to the economies of scale big banks are less substituting monitoring activity for capital buffer, namely the larger the extent of credit portfolio of an individual bank the smaller the capital hold by bank above the minimum BIS ratio. The portfolio diversification can also reduce the probability of steep fall of capital adequacy ratio, which opportunity is proportionally growing with size of the bank. Linquist K.-G. (2004) If the big banks can rely on assistance of the government (too a big a to a fail) - which opportunity for the small banks are not available in crisis -, then it serves as further explanation of decreasing capital buffer proportionally with size of the bank. Presumably there is a positive relationship between thorough examination of banking supervision and bank's capital buffer. In the market competition the extent of overcapitalisation can be defined as a signal of bank's solvency. His extent is depending on how much the given bank disposed to spend to this in severe competition, moreover how are positioning the individual banks themselves compared to their market competitors. Berger, Herring, Szegő (1995) emphasize one of further possible aspect of capital buffer’s holding, namely with the help of this can exploit the unexpected investings opportunities. If a bank has capital buffer, than it can either deal with riskier business or strengthen his aquisition strategy. There is an alternative opportunity for the banks to decrease their capital, namely they can refund the capital for the owners, if they can use that more profitable out of banking system. A several british bank, which applied the strategy of shareholders value, utilise this opportunity in a given advantageous time (Llewellyn 2005). Those countries, in which dominate the arm's length type deals, proved to be better at exploitation of the new growth facilities due to better resource allocation. IMF (2006). The extent of capital held by banks above the minimum level can form depending on costs of additional fund raisings. In period of substantial economic growth the fall of the capital buffer can be estimated, because more encouraging investments project can realise in this term. So the banks capital buffer are affording chance for the market participants to blunt or enhance the procyclical effects of the regulations (both Basel I. and Basel II.).

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Table 1. National minimum level of capital adequacy ratio (also where prescriptions is different from 8% in EU) minimum date of reason CAR introduction Great-Britain 9% 1979 Cyprus 8% 1997 10% 2001 change in market structure Czech Republik 8% 1992 Estonia 10% 1997 quick incresease in banks assets and change in operational circumstances Hungary 8% 1991 Latvia 10% 1997 8% 2004 Lituana 10% 1997 8% 2005 Malta 8% 1994 Poland 8% 1992 Slovak Republik 8% 1997 Slovenia 8% 2002

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Source: Jokipii, Milne (2006)

Due to Basel II. the procyclicality of banking capital adequacy ratio and capital buffer rise to presumably only certain extent. The second pillar of New Capital Record specify supervisory revision in connection with the internal models applied, in addition stress tests, by means of this in case of recession the negative effects of macro circumstances on bank portfolio can be estimated. Such a model can determine more precise the riskiness of portfolio and be appropriate for definition of requested capital buffer. Creditworthiness of the debtors worsens on period of recession. Average downgrading on the one is due to the worse growth outlooks, however on the other in the light of a longer time horizon the ratings would not have to move in the same direction with the business cycles. At time of boom the individual national supervisory institutions could order for the banks a targeted capital adequacy ratio. It is known, that in European Union and within that also in EMU the scope of action of the national supervisory institution is large - based also on the new directive in European Union (CRD) -, so the national authorities can impose special regulations on their own market. In all countries of EMU the requirement is the 8%, so equals BIS ratio. It would be estimated with the help of an applicable model, which is the common CAR band, which would be fit at given periods of the business cycles. I think on a band, where the stress CAR would also remain above the minimumly prescribed 8%. The central banks in their stability reports calculate stress CAR considering negative effects of different macro variables, which refers to the banking system. In the case of individual banks this value could work out variously. With this would it be also justifiable an ideal CAR above the ratio of 8%. The holding of higher amount of capital can serve a signal for the market and strengthen negotiation positions. This recommendation conserning to holding of more capital than the minimum could embrace both micro - and a macro prudencial elements. Jokipii, Milne (2006)

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pointed out that the capital buffers of New Member Staates move with the same direction with the business cycles, while in the Old Member Staates they are anticylically. In my opinion this movement is more a spontaneous, and not a conscious behaviour characterising the banking system. In the New Member States the external shocks can cause higher amount of losses, so the difference between the banking system's average CAR and stress CAR is much higher.

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3. Relationship between the Capital Buffer and the Output Gap Suyter (2004) examined the relationship between change of equity capital requirement and nominal GDP of Germany between 1997 and 2003. He pointed out an inverse relation between them, which means, that the capital requirement is decreasing (is rising) if the nominal GDP is rising (is decreasing). This examination also strenghtens the hypothesis, that first pillar of Basel II. based on PD (probability of default) intensifies the procyclical behaviour of the banking system. Ayuso, Pérez, Saurina (2002) found in their study a significant negative relationship between the business cycle and the capital buffer in the term examined with regard to the spanish institutions. The correlation is tighter at term of the upturn, than on time of recession. 1% up in the GDP occured fall of 17% in the capital buffer. In the former studies the authors analysed banks of a given countries, while Jokipii, Milne (2006) focused on 486 banks in EU in order to find relevant features in different bank types and country type in the period 19982004. They classified the groups of countries and in addition the banks by size and type and attained the following results. The capital buffers of the big banks as well as the commercialand the savings banks moved anticyclical while the small banks and cooperative bank in the same direction with business cycle. Jokipii, Milne (2006). They analised the following groups of countries EU25, EU15, group of countries from Denmark, Sweden, Great Britain and the New Member States. The authors pointed out, that in the former three group of countries the correlation between capital buffer and output gap (or GDP growth) is negative, namely they moved anticyclical. In case of New Member States the correlation is positive, namely at term of upturn the banks are extending capital above the minimum level, which they use for covering the increased credit risk on time of recession. In that sense, authors consider the banking system of the country joined to the EU in 2004 more prudent than the OMS ones. In my opinion in this countries the rising capital buffer emerged by combined effects of more factor. The less efficiemt banks hold more capital than necessary, the market signal’s value of the capital buffers in these countries are more remarkable, the credit supply is much lower in these countries, in addition the bank's GDP-proportional credit portfolio remained much under the level of EU15. In these countries therefore are expected the widening of banking intermediation. In this case, namely increasing of capital level can be interpreted as preparation of a credit expansion in the future. Table 2. contains correlation coefficient between bank's individual ratios and the output gap. There are a negative relations between provision and output in the examined countries (removing the USA) as long as at evolution of the profitability and the stock price vs output gap the relationships are positive. While at the capital (capital/total assets) the indications of a correlation coefficient are changing in the countries in examined term (1980-2001).

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Tamás Isépy Table 2. Correlation between output gap and different ratios of banking system. Australia Finland Germany Italy Japan Norway Spain Sweden United Kingdom USA

Provision Profitability Equity price Equity capital -0,88 0,71 0,47 -0,39 0,81 0,43 0,04 -0,21 -0,42 0,18 0,20 -0,21 0,25 0,10 -0,25 -0,43 0,22 0,30 -0,25 -0,35 0,54 0,03 0,41 -0,41 0,84 0,32 0,06 -0,83 0,60 0,26 -0,16 -0,38 0,12 0,26 0,26 0,14 0,24 0,12 -0,04

Source: Borio, Furfine, Lowe (2001)

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4. Comparative Analysis of Capital Buffer, Output Gap and Financial Structure in EMU I prepared comparative analysis with datas of 12 countries from Economic and Monetary Union with regard to term between 1997-2004 between the output gap and the capital adequacy ratio. The average negative correlation between output gap and CAR means, that if the output gap is rising (is decreasing), then the banks capital adequacy ratio is decreasing, namely this is the procyclicality of banking system. The output gap is the difference of actual GDP and potential GDP divided by potential GDP. The relationship is a clear negative correlation (with the exception of Greece), from which in case of four countries (Austria, Finland, Spain and Netherlands) this relation is significant.The notions of procyclically (anticyclically) I am using to the effect that, whether the specific variable move in the same direction or reverse direction with the busines cycle, in contradistinction to the Basel II., where the notion procyclicality describe the amplification of business cycle. Stolz , Wedow (2005) mean on anticyclical behaviour of capital buffers, that the banks average capital buffer are moving oppositely with the economic cycles . In national financial systems we can make distinction between market-based- and bankbased financial structures, moreover between arm's length and relationship-based deals. Arm's length deals are predominantly characteristic of the market-based financial structures, while the relationship-based deals are feature of bank-based financial structures. However the two approaches can be treated as a synonym only in incomplete extent. The venture capital can be classified to the relationship-based deals, while it is typical in countries with market-based financial structure. New credit syndication can be classified to the arm's lengh deals, while it is typical in bank-based countries. In the examined period there is a significant positive correlation between financial structure index (stock market capitalisation divided by deposit money bank assets) and capital adequacy ratio. With regard to the fact, that I used average figures by country, so the varition inside the country are not in place.

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Table 3. Correlation between CAR and output gap in EMU (1997-2004). Austria Belgium Germany Spain Finland France Greece Ireland Italy Luxembourg Netherland Portugal

correlation coefficient -0,796* -0,2900 -0,4500 -0,775* -0,830* -0,3500 0,0700 -0,3100 -0,5910 -0,6440 -0,711* -0,1400

R2 0,63 0,09 0,2 0,65 0,69 0,12 0,01 0,1 0,33 0,42 0,51 0,02

significance 0,018 0,481 0,275 0,024 0,011 0,409 0,874 0,454 0,123 0,085 0,048 0,746

t-value -3,222 -0,751 -1,2 -3,003 -3,64 -0,888 0,166 -0,8 -1,793 -2,062 -2,48 -0,34

* Correlation is significant at the 0,05 level (2-tailed) Author’s calculations Data sources: IMF Financial Stability Report, Bankscope, OECD

21

Capital adequacy ratio

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19 17

y = 2.0391x + 10.197 R2 = 0.5472

15 13 11 9 7 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Financial structure index

Author’s calculations Data souces: Worldbank: Financial structure database, Bankscope

Figure 1. Correlation between capital adequacy ratio and financial structure index in EMU (1990-2001).

The correlation (R2: 0,5472, significance level: 0,006, t-value: 3,246) shows a remarkable relation, namely in those countries, where the financial structure is more market-based, the CAR is higher. Does the question occur, whether between the change of bank's totel asset and evolution of CAR are there any correlation? I investigated the tightness of relationship between the mentioned variables in the following. In my cross-country (cross-sectional) analysis I applied average datas of CAR (weighted by bank assets), financial structure index and deposit money bank assets between 1990 and 2001.

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Capital adequacy ratio

21 19 17 y = -0.1341x + 12.005 R2 = 0.426

15 13 11 9 7 0

5

10

15

20

Deposit money bank assets (mrd EUR)

Author’s calculation Sources: Worldbank: Financial Structure Database, Bankscope, Deutsche Bundesbank

Figure 2. Relationship between CAR and deposit money bank assets in EMU (1990-2001).

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In regression analysis I pointed out, that there is an inverse relation between CAR and deposit money bank asset. This result confirms implicit the fact, that the big banks have smaller CAR than the small banks (here examining countries and apart from bank market concentration of the individual countries), or to be more precise their CAR is decreasing with increasing of their balance sheet total. At examination of deposit money bank assets it is statable, that the CAR is decreasing significantly with expansion of bank assets (R2:0,426, significance: 0,015, t-value: -2,736). Obviously the total bank credits are connected to the extent of credit risk, and this is the main element of required capital (for market risk US banks hold only 2% of their total required BIS capital).

5. Conclusion The results strenghten the findings of previous studies concerning the anticyclical behaviour of capital buffer partly, however attain to new outcome. Examining the period between 1997 and 2004 in EMU I found negative correlation coefficient (with exeption of Greece) between output gap and capital adequacy ratio, in four countries of which (Austria, Spain, Finland, Netherlands) the correlation is significant. I pointed out analising the period between 1990-2001 in EMU, that there is a significant positive correlation between CAR and financial structure index. On the one this can come from that fact, that in the countries with market-based financial structure dominate the arm'slength type deals, while in bank-based financial structure henceforward due to strong bankcustomer connection the deals (relationship-based transactions) are following less the market prices. On the other also the composite of banking system are different and in bank-based financial structure the proportion of those banks (cooperative banks, savings banks) are higher, which are able to smooth the business cycle due to their lending activity.

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References [1] Ayuso, J., Pérez, D. & Saurina, J. (2002). Are Capital Buffers Pro-Cyclical? Evidence from Spanish panel data. Documento de Trabajo n.v 0224, Banco de Espan˜a. [2] Barrios, V. E. & Blanco, J. M. (2003). The effectiveness of bank capital adequacy regulation: A theoretical and empirical approach. Journal of Banking and Finance, 27, 1935-1958. [3] BCBS, (2003). Review of Procyclicality. Research Task Force, Mimeo. [4] BCBS, (2003). Consultative Document – Overview of the New Basel Capital Accord, [5] BCBS, (2004). International Convergence of Capital Measurement and Capital Standards, June. [6] BCBS, (2006). Results of the fifth quantitative impact study (QIS 5). [7] Berger, A. N., Herring, R. J. & Szegő,G. P. (1995). The role of capital in financial institutions. Journal of Banking and Finance, 19, 393-430. [8] Bikker, J. (2004). Metzemakers, Is bank capital procyclical? A cross-country analysis, Working Paper No. 009/2004 De Nederlandsche Bank NV [9] Borio, C., Furfine, C. & Lowe, P. (2001). Procyclicality of the financial system and financial stability: issue and policy options. BIS Papers, 1, 1-57. [10] Borio, C. (2003). Towards a macroprudential framework for financial supervision and regulation? BIS Working Papers No. 128, February. [11] Danielsson, J., Embrechts, P., Goodhart, C., Keating, C., Muennich, F., Renault, O. & Shin, H. S. (2001). An Academic Response to Basel II. Special Paper, 130, Financial Market Group, London School of Economics. [12] Daníelsson, J., Jorgensen, B. N. & Vries, C. G. (2002). Incentives for effective risk management, Journal of Banking and Finance, 26. [13] Decamps J. P. & Rochet, J. (2004). Ch., Roger B. The three pillars of Basel II: optimizing the mix, Journal of Financial Intermediation, 13, 132-155. [14] Detken, A. & Ott-Laubach, P. (2002). Die Entwicklung der Kreditneuzusagen, Wirtschaftsdienst 2002/10 618.-625. [15] ECB The New Capital Adequacy Regime—the ECB Perspective. 2001. ECB Monthly Bulletin May, 59-74. [16] Hofmann, B. (2005). Procyclicality: The Macroeconomic Impact of Risk-Based Capital Requirements, Swiss Society for Financial Market Research, 179-200. [17] Illing, M. & Paulin, G. (2004). The New Basel Capital Accord and the Cyclical Behaviour of Bank Capital, Bank of Canada Wroking Paper, 30. [18] IMF, (2006). How do financial systems affect economic cycles? Global Financial Stability Report, Chapter, 4., 1-34. old. [19] Jokipii, T. & Milne, A. (2006). Understanding European Banks Capital Buffer Fluctuations, Bank of Finland. [20] Kerkhof, J. & Melenberg, B. (2004). Backtesting for risk-based regulatory capital, Journal of Banking and Finance, 28. Februar. [21] Lindquist, K. G. (2004). Banks’ buffer capital: how important is risk, Journal of International Money and Finance, 23. [22] Llewellyn, T. D. Whither European Banking: Convergence or Diversity? Paper for ECB Seminar 2005a.

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[23] Llewellyn, T. D. (2005b). Competition and Profitability in European Banking: Why are British Banks so profitable? [24] Mérő, K. (2002). A pénzügyi közvetítés mélysége és a prociklikusság, MNB Műhelytanulmányok, 23, Tanulmányok a bankszektor tevékenységének prociklikusságáról [25] OECD, (2006). Risk Capital in OECD Countries: Past Experience, Current Situation and Policies for Promoting Entrepreneurial Finance in Financial Market Trends, No. 90, April (Paris: Organization for Economic Cooperation and Development). Ongena, [26] Suyter, A. (2004). Risikomanagement Aktuelle Entwicklungen und Auswirkungen auf Banken und Unternehmen, Fritz Knapp Verlag 422. [27] Stolz, S. & Wedow, M. (2005). Banks’ regulatory capital buffer and the business cycle: evidence for German savings and cooperative banks, Deutsche Bundesbank Discussion Paper Series 2: Banking and Financial Studies No 07. [28] Zsámboki, B. (2002). A prudenciális szabályozás hatása a bankok prociklikus viselkedésére, MNB Műhelytanulmányok 23, Tanulmányok a bankszektor tevékenységének prociklikus viselkedéséről.

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Chapter 8

CAN A FINANCIAL INFORMATION DISTORTION EVENT FACILITATE A REVISION IN THE INDEPENDENT DIRECTORS INSTITUTION Cheng Xin-sheng, Li Hai-ping and Luo Yan-mei Business School of Nankai University / Center for Corporate Governance Research, Tianjin 300071, China

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Abstract The independence of the Board has an important and direct impact on the quality of information disclosure. To a large extent, the proportion of Independent Directors reflects the independent characteristics of the board. A common understanding of the effect of the actual operation on the Independent director has been lacking in China. In this paper, 92 listed companies were selected from 2003 to 2005 to be defined as the sample group, which have distorted financial information, and the paired-sample companies were chosen to be defined as the control group, according to factors such as profession, property and so on. The author analyzes the proportion’s change in the listed company, whose Independent Directors proportion is less than 1/3 in the distortion sample group and the control group, and the change rate of Independent Directors proportion in the sample group and the control group. The research discovered that a financial information distortion incident will prompt companies to increase the proportion of Independent Directors, and due to the mandatory effect of the policy, distortion and matching the company will increase the independent Directors proportion, but the rate in distortion companies was significantly higher than that in the paired companies. The study provided evidence to support the view that increasing the proportion of independent directors will help to prevent distortion of financial information.

Keywords: Financial information; information distortion; Independent Directors Institution.

1. Introduction With the exposure of financial corruption practices at some domestic and foreign big corporations, the financial information distortion problems, such as a distorted financial

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Cheng Xin-sheng, Li Hai-ping and Luo Yan-mei

report, offending the accounting standards, punishment from supervision organization etc., have received wide attention. Many research studies of financial information distortion have been proposed in order to detect the reason for the occurrence and the influencing factors. However, some studies have been based on the corporate governance. Meanwhile, the influence of the structural feature of the board of directors on the financial information is important in the empirical studies of the relation between the corporate governance and the financial report distortion. The ratio of the independent directors to the whole board of directors is an important index, which indicated the independent characteristic. The independent directors can offer safe corporate governance methods. Now that the independent directors can improve the financial information quality, then the ratio of the independent directors should be increased. However, the real effect of the independent directors can not be recognized consistently either in the practical realm or in the academic circle. In this paper, 92 listed companies with distorted financial information from 2003 to 2005 were selected—defined as a sample group— and the paired sample companies were chosen to be defined as a control group, according to factors such as profession, property and so on. The author analyzes the proportion’s change in the listed company, whose independent directors’ proportion is less than 1/3 in distortion sample group and the control group, and the change rate of independent directors’ proportion in the sample group and the control group.

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2. Hypotheses Development From the proxy theory, it is concluded that agents are authorized to manage the company and undertake the corresponding responsibility. Shleifer et al.（1997）has pointed out that, residual control rights were usually given to managers because managers have the specialized managerial technique and more insider information. Then the managers can possibly show opportunistic behavior after they get the control rights. It is essential to establish the effective governance mechanism to restrain the opportunism and protect the investors’ benefit. Once the independent directors are introduced into the board of directors, the managers’ opportunistic behavior, like capturing property and seeking private gain by the board of directors, can be obviously decreased and the opportunism can be controlled（Fama et al., 1983. The original intention of the independent director institution was to cut off the beneficial relationship between the independent directors and the company. The independent directors can be independent of the listed company and managers and protect the company’s and investors’ benefits. Because the independent directors are not controlled by the holding shareholder and managers like inside directors, it is possible to judge the company issues fairly and independently. Furthermore, the specialized knowledge of the independent directors can promote the decision-making scientific style. Therefore, in the main marketing country, the ratio of the independent directors in the board of directors has received more and more attention. It is generally thought that the board of directors having a high ratio of independent directors can easily get rid of external interference, reduce financial cheating and confirm the reliability of financial information (Wang Yuetang, Zhu Lin, 2008). It is thought that if the idea of the high ratio of independent directors to help prevent financial information distortion is supported, the corporation which had the financial

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information distortion will receive more attention by investors and the supervision organization. The independent directors institution will be employed to improve the financial report. Based on above analysis, some hypotheses will be proposed as follows: Hypothesis 1: the occurrence of the financial information distortion will prompt the company to increase the ratio of independent directors. Hypothesis 2: after the financial information distortion, the ratio of the affected company’s independent directors will be more than the other company.

3. Research Design 3.1. Sample Data In this paper, the non-finance listed companies which had financial information distortion were selected as the research sample. Then, corresponding paired samples were selected by the following steps: the first one was the professional classification standard proposed by China Securities Regulatory Commission. The second one was the company which had the closest property would be selected under a premise of satisfying the professional pair standard. The third one was that the company should have good prestige and have no negative report and criticism of financial information distortion. Year Sample Number Total

2003 30

2004 29 92

2005 33

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Figure 1. Sample year distribution.

Variable name Ratio of independent directors (OUTDIR) Whether distorted finical information (FALSE) Ratio change of independent directors (△OUTDIR)

Definition The number of Independent Directors /total number of board of directors Financial information distortion was defined for 1 and no distortion was defined for 0. The ratio Differential value between the first year and the second year which have the Financial information distortion

Figure 2. Variables and definitions.

The data are taken from Juchao Information Network, the database CCER and Corporate Governance Database of Nankai University. Some data have been supplemented from the listed companies annual reports and SINA finance and economics network（http://finance.sina. com.cn/） by this paper’s authors. In the research period, concerning a company which only had one information distortion, the year in which it was punished or condemned publicly by the supervising organization was regarded as the information distortion occurring year. As for a company which had two or more cases if information distortion, the year in which it was firstly punished or condemned was regarded as the information distortion occurring year. In

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Cheng Xin-sheng, Li Hai-ping and Luo Yan-mei

this paper, 92 samples—not including the paired samples—were estimated and Figure 1 gives the year distribution results.

3.2. Variable Definition Figure 2 gives the main variables and their definitions.

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3.3. Descriptive Statistics The year, in which the company found financial information distortion, was assumed T year, and the next and the last year was then T-1 and T+1 year. Then, in view of the samples between 2003 and 2005, the data of T-1 , T and T+1 year was selected to be employed for a significance examination. However, there are two companies that had no data for 2004 in the pair sample companies of 2003, and there was one company that had no data for 2006 in the pair sample companies of 2005. Figure 3 and Figure 4 give the descriptive statistics result of distortion samples and pair samples. Figure 3 gives the independent directors’ ratio change results of T-1 and T+1 year of the sample and control group companies. It is concluded from Figure 3 that the independent directors’ ratio did not pass the significance examination in 2004. However, in other years the independent directors’ ratio passed the significance examination either in the sample orcontrol group companies. In other words, the independent directors’ ratio had a significant change either in the sample or control group companies. There are two actions. The first one is the independent directors’ ratio was compulsively changed under the pressure of the policy of the supervision organization, such as in the listed company before the 30, June 2003 there were at least 1/3 independent directors in the total board of directors. The other one is the occurrence of the financial information distortion. Because the independent directors’ ratio also had a significant change in the control group, it is concluded that the influence of the policy must exist. The influence of the occurrence of the financial information distortion will be discussed in the fourth part of this paper. In that part, the change range before and after the occurrence of the financial information distortion in the companies, in which the independent directors’ ratio is smaller than 1/3 in the sample and control group, will be studied. Figure 4 gives the average value results of the independent directors’ ratio in the sample and controlled group. It is concluded that all the average values did not pass the nonparameter test either in the sample or controlled group. In other words, the independent directors’ ratio had no significant change before and after the occurrence of the financial information distortion. However, compared to the minimum and maximum before and after the occurrence of the financial information distortion, we find that: (1) In T-1 year, the minimum of independent directors’ ratio in the sample group is less than the controlled group. For example, for the sample companies of 2005, the minimum of sample and controlled group are 0.182 and 0.231 in 2004, respectively. And the maximum of independent directors’ ratio in the sample group is more than the controlled group in each year. For example, for the sample companies of 2004, the maximum of sample and controlled group are 0.425 and 0.429 in 2003, respectively. (2) In T+1 year, the maximum of independent directors’ ratio in sample

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group is more than or equal to the controlled group in each year, and the minimum of the sample group is bigger than the controlled group in 2003 and 2004. This shows that differences may exist. Distortion year

Year

Group Average Z1 Asymp. Sig. 2002 0.236 Sample group -3.560 0.000*** 2004 0.318 2003 2002 0.219 Control group -3.303 0.000*** 2004 0.326 2003 0.331 Sample group -2.388 0.017** 2005 0.358 2004 2003 0.329 Control group -0.510 0.610 2005 0.326 2004 0.347 Sample group -1.739 0.082* 2006 0.370 2005 2004 0.343 Control group -2.345 0.019** 2006 0.364 ***、**、* individually expressed by 1%, 5% and 10% level. (Similarly hereinafter)

Figure 3. Descriptive Statistics and Non-parameter Test (1). Distortion year

Year 2002

2003 2004 2003 Copyright © 2010. Nova Science Publishers, Incorporated. All rights reserved.

2004 2005

2005

2004 2006

Group

Minimum

Maximum

Average

Standard deviation

Sample group

0.000

0.364

0.236

0.096

Control group

0.000

0.400

0.219

0.090

Sample group

0.133

0.429

0.318

0.133

Control group

0.000

0.429

0.326

0.075

Sample group

0.182

0.425

0.331

0.054

Control group

0.143

0.429

0.329

0.054

Sample group

0.286

0.444

0.358

0.047

Control group

0.000

0.429

0.326

0.076

Sample group

0.182

0.600

0.347

0.067

Control group

0.231

0.444

0.343

0.040

Sample group

0.273

0.600

0.370

0.069

Z

Asymp. Sig.

-1.052

0.293

-0.692

0.489

-0.186

0.852

-1.544

0.123

-0.214

0.830

-0.332

0.740

Figure 4. Descriptive Statistics and Non-parameter Test (2).

4. Empirical Results In order to distinguish whether the occurrence of the financial information distortion will enhance the independent directors’ ratio, a binomial test was employed to analysize the change range in the proportion of listed companies, which the independent directors’ ratio was smaller than 1/3, and in independent directors’ ratio in the sample and controlled group. Independent directors’ ratio change was indicated as follows: △OUTDIR=OUTDIR (T－1) + OUTDIR (T＋1). In above formula, subscript stands for the different year such as T-1 and T+1.

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4.1. Changes in the Proportion of Listed Companies in which the Independent Directors’ Ratio Is Smaller than 1/3 Consider that there was a policy which required that the listed company before the 30, June 2003 had to have more than 1/3 independent directors in the total board of directors. According to the above policy, 0.33 was adopted to be a threshold value. We separately analyzed that changes in the smallest proportion of listed companies, in which the independent directors’ ratio was smaller than 1/3, between T-1 and T+1 year in the sample and controlled group. Distortion year

Group

Sample group

2002 2004b

2003 Control group

Sample group

2002 2004 2003 2005

2004

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Control group

Sample group

2003 2005 2004 2006

2005 Control group

Category

Sample number

Observed Prop

Group 1

≤ 0 .33

23

0.767

Group 2

＞ 0.33

7

0.233

Group 1

≤ 0 .33

10

0.357

Group 2

＞ 0.33

18

0.643

Group 1

≤ 0 .33

26

0.867

Group 2

＞ 0.33

4

0.133

Year

2004 2006b

Group 1

≤ 0 .33

3

0.100

Group 2

＞ 0.33

27

0.900

Group 1

≤ 0 .33

6

0.207

Group 2

＞ 0.33

23

0.793

Group 1

≤ 0 .33

3

0.103

Group 2

＞ 0.33

26

0.897

Group 1

≤ 0 .33

7

0.241

Group 2

＞ 0.33

22

0.759

Group 1

≤ 0 .33

8

0.276

Group 2

＞ 0.33

21

0.724

Group 1

≤ 0 .33

7

0.212

Group 2

＞ 0.33

26

0.788

Group 1

≤ 0 .33

4

0.121

Group 2

＞ 0.33

29

0.879

Group 1

≤ 0 .33

3

0.091

Group 2

＞ 0.33

30

0.909

Group 1

≤0 .33

4

0.125

Group 2

＞ 0.33

28

0.875

Test Prop

Asymp. Sig.

0.770

0.553a

0.400

0.399a

0.870

0.559a

0.100

0.647a

0.210

0.591a

0.110

0.602a

0.250

0.557 a

0.280

0.574 a

0.220

0.556 a

0.120

0.571 a

0.100

0.577 a

0.130

0.596 a

a. Alternative hypothesis states that the proportion of cases in the first group < Test Prop.；b. Sample data are missing

Figure 5. Binomial Test Result(1).

In Figure 5, divided by the column of category 0.33, the sample and controlled group was divided into two groups, such as group 1 and group 2. In group 1, the independent directors’ ratio was less than or equal to 0.33, while the independent directors’ ratio was more than 0.33 in group 2. N stands for the number in each group and observed prop stands for the sample proportion. Test prop stands for lowest value and Asymp. Sig. stands for whether this lowest

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limited value can be accepted. That is to say, the original hypothesis and alternative hypothesis in the binomial test will be proposed as follows: H0：overall proportion is less than or equal to the test prop value; H1：overall proportion is more than test prop value. Because the Asymp. Sig. value is more than 0.10,

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When the Asymp. Sig. value corresponding with given Test Prop value is bigger than 0.10, the maximum value in all setting Test Prop closest to the true value, and H0 is accepted. That is to say, the smallest proportion of group1 is Test Prop value. For example, in Figure 5, the smallest proportion of listed companies, which the independent directors’ ratio is smaller than 1/3 in and which suffered from financial information distortion in 2003, is 77% in 2002. From Figure 5, we could make the conclusion: (1) compared the data between 2002 and 2004, lowest value shows an obvious declining trend either in sample and controlled group. The lowest value in the sample group decreased from 77% to 40% and the one in the controlled group decreased from 87% to 10%. This result also demonstrates the special effect of the policy. (2) to listed companies which suffered from financial information distortion in 2003，2004 and 2005，the smallest proportion of group1 has a significant reduction from T-1 to T+1. From Figure 5, the change is separately from 77% to 40%, from 21% to 11% and from 22% to 12% to listed companies which suffered from financial information distortion in 2003，2004 and 2005. But, in the controlled group, there are slight increases from T-1 to T+1 to 2004 and 2005 except 2003. For example, the change is from 25% to 28% and from 10% to 13% to the paired companies with the listed one which suffered from financial information distortion in 2004 and 2005. Thus, Hypothesis1 is confirmed.

4.2. Change Range of Independent Directors’ Ratio Analysis In this part, samples in different years were composed of the sample group and controlled group. Firstly, we computed the average value of change in the independent directors’ ratio, that is △OUTDIR, about total sample, it is defined as ΔOUTDIRall . And then, ΔOUTDIRall was adopted to be a threshold value. According to ΔOUTDIRall , the sample and controlled group were divided into two groups, such as group 1 and group 2. In group 1, change in the independent directors’ ratio (△OUTDIR) was less than or equal to ΔOUTDIRall ,

while △OUTDIR was more than ΔOUTDIRall in group 2. From Figure 5, the smallest proportion of group1 all are higher than group2 in 2003, 2004 and 2005. For example, the proportion of listed companies, in which change in independent directors’ ratio from 2002 to 2004 is higher than ΔOUTDIRall (-0.10), is equal to 57% to listed companies, which suffered from financial information distortion in 2003. But, this corresponding proportion is equal to 47% in the controlled group. And this difference is bigger than 10% in each year. So, Hypothesis2 is confirmed.

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176 Distortion year

Cheng Xin-sheng, Li Hai-ping and Luo Yan-mei

ΔOUTDIR all

2003

2004

2005

-0.10

-0.012

-0.022

Group

Category

Sample number

Observed Prop.

Sample group

Group 1

≤ -0.1

17

0.567

Group 2

＞ -0.1

13

0.433

Control group

Group 1

≤ -0.1

13

0.464

Group 2

＞ -0.1

15

0.536

Sample group

Group 1

≤ -0.012

10

0.345

Group 2

＞ -0.012

19

0.655

Control group

Group 1

≤ -0.012

6

0.207

Group 2

＞ -0.012

23

0.793

Sample group

Group 1

≤ -0.022

15

0.455

Group 2

＞ -0.022

18

0.545

Control group

Group 1

≤ -0.022

11

0.344

Group 2

＞ -0.022

21

0.656

Test Prop

Asymp. Sig.

0.570

0.555a

0.470

0.553 a,b

0.350

0.562 a

0.210

0.591 a

0.460

0.546 a

0.350

0.551 a,b

a.Alternative hypothesis states that the proportion of cases in the first group < Test Prop.；b. Sample data are missing

Figure 6. Binomial Test Result(2).

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5. Summaries and Conclusion The independence of the board has an important and direct impact on the quality of information disclosure. To a large extent, the proportion of independent directors reflects the independent characteristics of the board. A common understanding of the effect of the actual operation on the independent director has been lacking in China. In this paper, we analyzed the proportion’s change in the listed company, whose independent directors’ proportion is less than 1/3 in the distortion sample group and the control group, and the change rate of independent directors’ proportion in the sample group and the control group. The results show that a financial information distortion incident will prompt companies to increase the proportion of independent directors, and due to the mandatory effect the policy, distortion and matching the company will increase the independent directors’ proportion, but the rate in distortion companies was significantly higher than the paired companies. The study provided evidence to support the view that increasing the proportion of independent directors will help to prevent distortion of financial information. There are some limits in this paper:(1) listed companies were selected from 2003 to 2005, but the sample companies during this period may not be fully representative of the listed companies in China's overall situation; (2) we did not analyze why some companies, which suffered from financial information distortion, reduced the ratio of independent directors.

Reference [1] Beasley, M. S. (1996). An Empirical Analysis of The Relation between The Board of Director Composition and Financial Statement Fraud. The Accounting Review, 4, 443-466.

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[2] Charles, J. P. (2000). Chen, Bikki Jaggi. Association between Independent Nonexecutive Directors, Family Control and Financial Disclosures in HongKong. Journal of Accounting and Public Policy, 4-5, 285-310 [3] Chen Gongmeng, Michael Firth, Daniel, N. Gao, Oliver, M. (2006). Rui. Ownership structure, corporate governance, and fraud: Evidence from China. Journal of corporate finance, 12, 424-448 [4] Fama, E. F., Jenson. M. C. (1983). Separation of ownership and control. Journal of Law and Economics, 26, 301-325 [5] Liu Liguo, (2003). Du Ying. An empirical research on the relationship between corporate governance and the quality of accounting information. China Accounting Research, 2, 28~37 [6] Shlerfer, A., Vishny, R. W. (1997). A survey of corporate governance. The Journal of Finance, 2, 737-783 [7] Wang Yuetang, (2001). Zhang zuguo. Assesment approach of the quality of financial reporting and supervision of information disclosures. China Accounting Research, 10, 12-19. [8] Wang Bin, (2008). Liang Xinxin. Corporate governance, financial condition and quality of disclosure: evidence from Shenzhen stock exchange. China Accounting Research, 3, 31-39. [9] Wang Yuetang, Zhu Lin, Chen Shimin. (2008). Board’s independence, ownership balance and financial information quality. China Accounting Research, 1, 55-62. [10] Yu Dongzhi, (2003). Wang Huacheng. Independent directors and corporate governance theory and experience. China Accounting Research, 8, 7-14. [11] Vineeta, D. (2004). Sharma. Board of director characteristics, institutional ownership, and fraud: evidence from Australia. Auditing: A Journal of Practice & Theory, 23, 105-117.

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In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 179-184

ISBN 978-1-60876-329-0 c 2010 Nova Science Publishers, Inc.

Chapter 9

M ANAGERIAL M ETHODS TO C ONTROL D ERIVATIVES L OSSES Patrick L. Leoni∗ University of Southern Denmark, Department of Business and Economics, Campusvej 55 DK-5230 Odense M, Denmark. and EUROMED Marseille School of Management, Domaine de Luminy - BP 921, 13 288 Marseille cedex 9, France.

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Abstract The long history of financial disasters caused by derivatives has triggered a significant interest to control their downside risk, both from portfolios’ managers and regulators. In a non-technical manner, we first describe the managerial methods currently used in practice for this purpose and their relative cost. We then show that those common methods either aggravate the downside risk or are too costly. We then argue that selecting underlyings satisfying some specific statistical and easily identifiable properties is a natural way to significantly reduce the downside risk without involving costly managerial interventions.

1.

Introduction

Nowadays, derivatives are commonly used by large corporations both for hedging and speculative reasons. Non-financial institutions have found a way to hedge against previously uninsurable risk, such as weather changes or volatility of input prices, and sometimes banks may use derivatives to diversify the risk of common products as personal loans. Often, financial institutions tolerate that some traders engage in speculative trades. Over the last two decades, derivatives have consequently become one of the largest financial markets worldwide despite alarming disasters caused by those products. Financial corporations have suffered the largest losses because of derivatives. For instance, both Daiwa and Barings Bank lost $1 billion, the Japanese bank Sumitomo lost $2 billion, and the hedge funds LTCM lost $4 billion. Non-financial corporations also experienced severe losses; for instance, Shell lost $1 billion, Metallgesellschaft lost $1.8 billion ∗

E-mail address: [email protected]

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Patrick L. Leoni

and Orange County lost $2 billion (Hull [6] Ch. 21). The record to date is held by the French bank Soci´et´e G´en´erale, which realized in 2008 a staggering loss of $7.1 billion after dubious trades on standard derivatives. To fix ideas, this last loss corresponds to the overall real GDP of Nicaragua in 2008. Given the impressive magnitude of the potential losses associated with derivatives, and their always increasing volume of trades, the control of their downside risk has become the main concern of both portfolios’ managers and regulators alike. We first describe the managerial methods currently used in practice such as stop-losses and delta-hedging, and we argue that either they aggravate this downside risk or are overly costly and hardly implementable. We then describe a class of appropriate underlyings, satisfying some specific statistical properties, capable of reducing this downside risk without involving costly managerial interventions.

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2.

Current Managerial Methods

Financial regulators typically require reports of potential financial losses from financial companies, and set preemptive measures to control them (see BIS [1]). The point is that regulators are often in charge of providing federal insurance to near-bankrupt financial companies, and to avoid large-scale crackdown of the banking industry. This requirement of risk report is critical for institutions whose portfolios include large shares of derivatives because of their high downside risk, although typically difficult to establish because of the high volatility of those products. The most common report requirement is the Value at Risk (or VaR) of the business’ overall financial exposure. This VaR is broadly defined as the worst possible expected loss of a portfolio, at a given likelihood level, over a given time horizon and under normal market conditions. Once (hopefully truthfully) reported, institutional regulators typically require that businesses immobilize funds to cover for this VaR; that is, an amount of capital is set as a reserve to cover for the losses in the worst-case scenario in the same way as a margin. The direct problem to corporations is that the opportunity cost of the immobilized capital is typically high. Moreover, the length of the time of horizon where the risk is managed may vary greatly across corporations, and the opportunity cost dramatically increases for long-term hedgers (see Demirer and Lienb [2]). In the case of the derivatives’ portfolios, the VaR method for risk management is hardly implementable. The main problem is that those products are very volatile, and the VaR may significantly change over a short period of time (sometimes a few hours), even under normal market conditions. The margin requirements are often too expensive and they lack flexibility. Quick responses to a sudden change in the value of a class of underlyings are often critical to maintain the overall soundness of the portfolio, although those sudden changes are not foreseeable when setting the margins level. Financial managers dealing with derivatives use more practical methods to control the downside risk. The most common tool is the use of so-called stop-loss strategy, also called benchmarking, which come down to liquidating a whole position once a pre-determined loss level is reached (see Pedersen [14]). Jarrow and Zhao [7] give several explanations for the popularity of this method, but the most compelling reason arguably stems from psychological factors. Kahneman and Tverski [8] have shown that most individuals display

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a strong aversion to losses, which may result in panic and frenzy. The case of the French bank Soci´et´e G´en´erale is typical, since postponing the liquidation by just a few days would have saved at least $1 billion in losses. On the other hand, the potentially staggering losses of those portfolios may well trigger those drastic and costly liquidations without awaiting the prospect of even more severe losses. The method of delta-hedging is often advocated by scholars, but rarely implemented by portfolios’ managers. The point of this method is to construct a risk-free portfolio, starting with a given risky portfolio of derivatives. Long or short positions on well-chosen underlyings (often those on which the derivatives are underwritten) will typically achieve this risk-free overall portfolio, built artificially from the original portfolio and earning a risk-free interest rate. When the downside risk on the original portfolio is likely to be controlled, the underlyings used to maintain the position delta-neutral can be traded away to earn a profit on the original portfolio; on the other hand, when the risk of losses is high the return of the overall portfolio is no worse than the risk-free rate. The main problem with this method is that derivatives’ prices change very often, sometimes up to 20% within an hour for vanilla products with underlyings such as GOOGLE Inc., and thus the overall value of the original portfolio greatly varies even in a single day. To remain delta-neutral, a manager must trade away the appropriate underlyings often and at high cost (this method is called rebalancing a portfolio). Rebalancing is hardly implementable, since it requires a team of experts permanently checking the position and seeking the appropriate underlyings, whereas the gain of remaining delta-neutral is not always clear when the end of the portfolio’s horizon is far. Some scholars have argued that choosing derivatives’portfolios with strongly correlated underlyings makes the rebalancing easier, but we will see in the following section that this correlation actually aggravates the downside risk. (see Lakshman [9] for other methods and their relative costs).

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3.

Stop-Losses and Downside Risk

In this section, we argue that stop-losses aggravates this downside risk, and precipitate the first occurrence of a given loss level. Leoni [10, 11] carry out a Monte-Carlo simulation of the performance of a standard derivatives portfolio to assess the benefits of stop-losses, and to establish the importance of the underlyings’ correlation for the likelihood of activation of those strategies (see Glasserman [3] for an exhaustive coverage of Monte-Carlo methods in Finance). Leoni [10, 11] consider a portfolio of four classes of derivatives (European calls, Asian options, lookback options and feedback options), where an initial wealth is equally allocated to those classes of assets. Once the maturity of the derivatives is reached (one quarter in the experiments), the proceeds are reinvested at most 24 times in the same manner to simulate an horizon of roughly 6 years. Liquidation or equivalently activation of the stop-loss occurs when a pre-determined level of loss occur in a given quarter, which captures in a simple albeit efficient manner the notion of activation of stop-losses. The experiments rely critically on the assumption that the underlying risk-neutral price dynamics follow a Geometric Brownian Motion. This assumption is the foundation of the much-celebrated Black-Scholes framework, and it is the most used worldwide. The parameters are chosen to closely fit actual data, so as to mimic actual trades.

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Patrick L. Leoni

The numerical results show that, for every pre-determined loss level, it is always preferable not to activate the stop-loss strategy. That is, it is always preferable to accept momentary losses and to let the portfolio recover without intervention. Moreover, the higher the correlation across the underlyings the more likely and the earlier the activation of stoplosses. The intuition for those results can be derived from the well-known Gambler’s Ruin problem, as described in Grimmett and Stirzaker [4] Ch. 3. The problem is described as follows: a gambler tossing a fair coin, and winning (resp. loosing) one monetary unit if head (resp. tail) occurs at each toss. The gambler tosses the coin until either her wealth reaches a pre-determined upper-bound or ruin occurs. Standard results claim that the game will end for sure, and the average number of tosses needed to reach one of those two events decreases exponentially as the bound get closer to the initial wealth. A ruin corresponds to reaching a loss level in our setting, and thus the activation of a stop-loss strategy. It turns out that we observe similar qualitative results in the portfolio simulations. However, letting the gambler’s game continue even ruin occurs (through retaining barriers for instance) leads to a wealth distribution at a given future horizon whose mean is different from zero. In our experiment, letting the portfolio reach the end of the pre-determined horizon leads to an average return always greater than the considered loss levels.

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4.

Selecting the Appropriate Underlyings

The selection of appropriate classes of underlyings, as sometimes seen in practice, is a natural candidate for reducing the downside risk of derivatives. Leoni [13] is based on the observation that many underlyings display mean-reverting statistical properties. The insight is that the apparently random evolution of their prices actually display a recurrent attraction toward a mean value, and this property may prove valuable for controlling our downside risk. The study reproduces the same Monte-Carlo simulation of the same trading strategy as before, but the underlyings are now assumed to display this mean-reversion property. The model is taken from Heston [5], and it has actually outperformed most of the standard models to price derivatives. The model allows for the volatility of the underlying asset to be randomly determined, since it follows a Ornstein-Uhlenbeck process. This model also has the critically important empirical property that stochastic volatility and returns are correlated. The parameters are chosen to closely fit actual data of the S&P 500 in the experiment. The numerical results gives the failure rate as a function of the mean-reversion intensity, which is broadly defined as a measure of speed for the underlyings to return to its mean value. It is striking that, for every loss level, the higher the intensity the lower the failure rate. It turns out that the difference is statistically significant and large for high loss levels (15% losses and above), although it appears as minor for lower loss levels. In contrast, the failure rate is roughly halved at 30% loss level for much higher intensity levels, unambiguously showing the major reduction in downside risk reduction when doubling the intensity. It is also surprising to notice that the reduction in downside risk is sensible when switching from low to middle intensity, at least for large enough loss levels, but the improvements are largely felt at every loss level only when switching to the highest intensity level.

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The intuition is that, when exhibiting strong mean-reversion effects, the price paths of the underlyings tend to be more concentrated in a probabilistic sense to the mean of the stochastic process (see Grimmett and Stirzaker [4] Ch. 13 for more on this issue). When dealing with risk-neutral dynamics, the mean of the price dynamics for the underlyings is typically the risk-free rate. Therefore, risk-neutral price trajectories of the underlyings are increasingly unlikely to exhibit large and permanent deviations from this rate, as the intensity of mean-reversion increases. Since for most derivatives the extreme payoffs, either positive or negative, are obtained when the underlyings’ returns are far off the risk-free return, the reduction in downside risk obtains naturally. It is also tempting, albeit significantly flawed, to select underlyings displaying low fluctuations in volatility. The hope is that a low fluctuation in the underlying’s price volatility will directly translate in a low fluctuation in price volatility for the derivative, making the delta-hedging of those products significantly easier and reducing their downside risk. We next argue that those underlyings do not significantly reduce the downside risk, whereas they severely narrow down the class of underlyings to be used for trades. This point is made in Leoni [13], by using the same standard Monte-Carlo simulation as above. The experiment is thus identical, with the difference that the underlyings exhibit 0-pairwise correlation with any other underlyings. The volatility reversion captures the mean-reversion of the underlyings’ volatility to its mean value, in the sense that the higher the volatility reversion thus the lower the fluctuations of the volatility around its mean. The numerical simulation comes down to observing how an increase in this reversion effect affects the downside risk of the portfolio formation described earlier. For every loss level, the simulation shows that the difference in failure rates (or equivalently liquidation likelihood) between low and medium intensity is very small. When looking at confidence intervals that are derived from the standard errors given in Leoni [13], it turns out that the difference is not statistically significant at 95% confidence level for loss levels lower than 30%. The reduction in failure rate is statistically significant only for high loss levels greater than 30%, although most practitioners would not wait until this loss level is reached to liquidate the portfolio. The difference in failure rates become sensible when considering very high volatility reversion, for every loss level. It takes a roughly a fourfold increase in stochastic reversion to obtain a reduction that is statistically detectable, and those high effects are hardly seen in practice.

5.

Conclusion

We have surveyed the most common managerial methods to control the downside of derivatives’ portfolios. We have seen that stop-loss strategies and delta-hedging are often too expensive and hardly implementable, and we have suggested that selecting appropriate classes of underlyings is a natural way to control this downside risk. Selecting assets with high mean-reversion effects is an effective risk reduction technique that does not involve any managerial intervention once trades are started. However, it is surprising that selecting underlyings with low fluctuations in volatility is not as effective, whereas it severely reduces the class of tradable assets.

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References [1] Bank for International Settlements (2004) Financial Disclosure in the Banking, Insurance and Securities Sectors: Issues and Analysis. URL: http://www.bis.org/publ/joint08.pdf [2] Demirer, R. and D. Lienb (2003) “Downside risk for short and long hedgers.” International Review of Economics & Finance 12, 25–44. [3] Glasserman, P. (2004) Monte-Carlo Methods in Financial Engineering. New-York: Springer Science. [4] Grimmett, G. and D. Stirzaker (2006) Probability and Random Processes. Oxford: Oxford University Press. [5] Heston, S. (1993) “A Closed-Form Solution for Options with Stochastic Volatility, with Applications to Bonds and Currency Options,” Review of Financial Studies 6, 327-343. [6] Hull, J. (2006) Fundamentals of Futures and Options Markets. (6th ed.) Upper Saddle River: Prentice Hall. [7] Jarrow, R. and F. Zhao (2006) “Downside loss aversion and portfolio management,” Management Science 52, 558–566. [8] Kahneman, D. and A. Tversky (1979) “Prospect theory: An analysis of decision under risk,” Econometrica 47, pp. 263–291.

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[9] Lakshman, A. (2008) “An option pricing approach to the estimation of downside risk: A European cross-country study.,” Journal of Derivatives & Hedge Funds 14, 31–41. [10] Leoni, P. (2008) “Monte-Carlo estimations of the downside risk of derivative portfolios,” IEEE Proceedings of the 4th Conference on Wireless Communications, Networking and Mobile Computing (2008), 1-5 (DOI: 10.1109/WiCom.2008.2273). [11] —— (2008) “Stop-loss strategies and derivatives portfolios,” International Journal of Business Forecasting and Marketing Intelligence 1, 82-93. [12] —— (2009) “Stochastic volatility in underlyings and the downside risk of derivative portfolios,” forthcoming in the IEEE Proceedings on Engineering Management and Service Sciences. [13] —— (2009) “Downside risk control of derivative portfolios with mean-reverting underlyings. SDU working papers series. [14] Pedersen, C. (2001) “Derivatives and downside risk,” Derivatives Use, Trades and Regulations 7, 251–268.

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ISBN 978-1-60876-329-0 c 2010 Nova Science Publishers, Inc.

Chapter 10

A E A  F: A  C O ∗ Akihiko Takahashi and Kohta Takehara† Graduate School of Economics, University of Tokyo, Japan

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Abstract This chapter presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; we do not model a foreign exchange rate’s variance such as in Heston [27], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market.

JEL Classification: G13, C63, C65 Keywords: Asymptotic Expansion, Currency Options, Libor Market Model, Stochastic Volatility, Variance Reduction, Malliavin Calculus

1.

Introduction

In this chapter we present a brief review of an asymptotic expansion approach for the evaluation problems in finance and give approximation schemes for currency options under stochastic volatility processes of spot exchange rates in stochastic interest rates environment as important applications of this methodology. In particular, we use models of volatility processes, not variance processes such as in [27], and apply a libor market model developed by ∗ This research is partially supported by the global COE program “The research and training center for new development in mathematics.” † E-mail address: [email protected]. Research Fellow of the Japan Society for the Promotion of Science.

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Brace, Gatarek and Musiela [7] and Miltersen, Sandmann and Sondermann [53] to modeling term structures of interest rates. Moreover, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Currency options with maturities beyond one year become common in global currencies’ markets and even smiles or skews for those maturities are frequently observed. Because it is well known that the effects of interest rates become more substantial in longer maturities, we have to take term structure models into account for the currency options. Further, stochastic volatility models and/or jump components of foreign exchange rates are necessary for calibration of smiles and skews. As for term structure models, market models become popular in matured interest rates markets since calibrations of caps, floors and swaptions are required and market models are regarded as most useful. Hence, development of a model with stochastic volatilities and/or jumps of exchange rates and with a libor market model of interest rates is inevitable. Moreover, a closedform formula is desirable in practice especially for calibrations since they are very time consuming by numerical methods such as Monte Carlo simulation. Because it is too difficult to obtain an exact closed-form formula, we derive closed-form approximation formulas by an asymptotic expansion approach where a volatility of a spot exchange rate follows a general time-inhomogeneous Markovian process, and domestic and foreign interest rates are generated by a libor market model. Here is the literature on currency options: Garman and Kohlhagen [19] and Grabbe [22] started research for currency options based on a contingent claim analysis; the framework of Black and Scholes [6], Merton [51] and Black [5] was directly applied to pricing currency options. [22]’s formula also included the case of stochastic interest rates following Gaussian processes though he did not specify the processes explicitly. Rumsey [66] and Melino and Turnbull [50] developed models under the deterministic interest rates assumption. Amin and Jarrow [3] and Hilliard, Madura and Tucker [28] derived formulas of currency options with Gaussian stochastic interest rates; in particular, [3] combined term structure models under the framework of Heath, Jarrow and Morton(HJM) [23] with currency options. Amin and Bodurtha [2] and Takahashi and Tokioka [83] gave numerical solutions to price currency American options with stochastic interest rates by lattice methods; [2] used HJM [23] models and [83] applied Hull and White [29], [30] term structure models. Dempster and Hutton [13] considered terminable (Bermudan) differential swaps with Gaussian interest rates models by using the partial differential equations(PDE) approach. Schlogl ¨ [70] extended market models to a cross-currency framework. He did not take stochastic volatilities into account and focus on cross currency derivatives such as differential swaps and options on differential swaps as examples; currency options were not considered. Mikkelsen [52] considered cross-currency options with market models of interest rates and deterministic volatilities of spot exchange rates by simulation. Piterbarg [61] developed a model for cross-currency derivatives such as Power-Reverse-Dual-Currency(PRDC) swaps with calibration to currency options; neither market models nor stochastic volatility models were used. Our asymptotic expansion approach have been applied to a broad class of Itˆo processes appearing in finance. It started with pricing average options; Kunitomo and Takahashi

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[38] derived a first order approximation and Yoshida [91] applied an asymptotic expansion method developed in statistics for stochastic processes. Takahashi [74], [75] presented second or third order schemes for pricing various options in a general Markovian setting with a constant interest rate. [39] provided approximation formulas for pricing bond options and average options on interest rates in term structure models of HJM [23] which is not necessarily Markovian. Moreover, Takahashi and Yoshida [85], [86] extended the method to dynamic portfolio problems in a general Markovian setting and proposed a new variance reduction scheme of Monte Carlo simulation with an asymptotic expansion. For mathematical validity of the method based on Watanabe [89] in the Malliavin calculus, see Chapter 7 of Malliavin and Thalmaier [48], Yoshida [90], Kunitomo and Takahashi [40] and Takahashi and Yoshida [85], [86]. Other applications and extensions of asymptotic expansions to numerical problems in finance are found as follows: Kawai [34], Kobayashi,Takahashi and Tokioka [36], Takahashi and Saito [77], L¨utkebohmert [42], [43], Kunitomo and Takahashi [41], Kunitomo and Kim [37], Muroi [55], Takahashi [76], Matsuoka,Takahshi and Uchida [49], Takahashi and Uchida[84], and Takahashi and Takehara [78], [79], [80]. Moreover, the computation scheme necessary for actual evaluation of the asymptotic expansion in a general setting is given by Takahashi, Takehara and Toda [81]. The organization of this chapter is as follows: First, after some preliminaries of mathematics in Section 2., we present the framework of an asymptotic expansion in Section 3.1. in a general model. Second, Section 4. describes a basic structure of our cross-currency model as the particular setting. Then, Section 5. applies the asymptotic expansion approach to the evaluation problem in two different ways. Finally, Section 6. shows numerical examples. Some proofs, computation scheme, and concrete expressions in propositions and theorems are omitted due to limitation of space and will be found mainly in [78], [80] and [81].

2.

Preliminary Mathematics

We shall first prepare the fundamental results including Theorem 2.3 of Watanabe [89]. The theory by [89] on the Malliavin Calculus and Theorem 2.2 of Yoshida [90], [91] are the fundamental ingredients to show the validity of our asymptotic expansion method. For our purpose, we shall freely use the notations by Ikeda and Watanabe [31] as a standard textbook. The interested readers should see Watanabe [88], [89], Ikeda and Watanabe [31], Yoshida [90], [91], Shigekawa [72] or Nualart [58].

2.1.

Some Notations and Definitions

Let W be the r-dimensional Wiener space, which is a Banach space consisting of the totality of continuous functions w : [0, T ] → Rr (w(0) = 0) with the topology induced by the norm k w k= max0≤t≤T |w(t)| . Let also H be the Cameron-Martin subspace of W, where h(t) = (h j (t)) ∈ H is in W and is absolutely continuous on [0, T ] with square integrable

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˙ endowed with the inner product defined by derivative h(t) < h1 , h2 >H =

r Z X j=1

T 0

j j h˙ 1 (s)h˙ 2 (s)ds .

(1)

We shall use the notation of the H−norm as |h|2H =< h, h >H for any h ∈ H. A function f : W 7→ R is called a polynomial functional if there exist n ∈ N, h1 , h2 , · · · , hn ∈ H and a real polynomial p(x1 , x2 , · · · , xn ) of n-variables such that f (w) = j p([h1 ](w), [h2 ](w), · · · , [hn ](w)) for hi = (hi ) ∈ H, where [hi ](w) =

r Z X j=1

T 0

j h˙ i dw j

(2)

are defined in the sense of Itˆo’s stochastic integrals. R The standard L p -norm of R-valued Wiener functional F is defined by kFk p = ( W |F| p P(dw))1/p . Also a sequence of the norms of R-valued Wiener functional F for any s ∈ R, and p ∈ (1, ∞) is defined by

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kFk p,s = k(I − L) s/2 Fk p ,

(3)

where L is the Ornstein-Uhlenbeck operator and k · k p is the L p -norm. The O-U operator in P s/2 J F , where J are the projection operators in (3) means that (I − L) s/2 F = ∞ n n n=0 (1 + n) the Wiener’s homogeneous chaos decomposition in L2 . They are constructed by the totality of R-valued polynomials of degree at most n denoted by Pn . Let P(= P(R)) denote the totality of R-valued polynomials on the Wiener space (W, P). Then P is dense in L p and can be extended to the totality of smooth functionals S(= S(R)) (the R-valued C ∞ functions with derivatives of polynomial growth orders). Then we can construct the Banach space D sp as the completion of P with respect to k·k p,s . The dual space of D sp is the D−s q where s ∈ R, p > 1, and 1/p + 1/q = 1. Set D∞ = ∩ s>0,1D∞ (E) , Φ ∈ D−∞ (E), F ∈ D∞ (E)

is denoted by E[< Φ, F >E ] and it is called a generalized expectation. In particular, 1 ∈ D∞ where 1 is the functional identically equal to 1. Hence, for Φ ∈ D−∞ , D−∞ < Φ, 1 >D∞ is called the generalied expectation of Φ and is denoted by the usual notation E[Φ] because it is compatible when Φ ∈ ∪1 1, s > 0 and every k = 1, 2, · · ·, X (ε) (w) − (g1 + εg2 + · · · + εk−1 gk ) = O(εk )

(7)

in D sp (E) as ε ↓ 0, then we say that X (ε) (w) has an asymptotic expansion : X (ε) (w) ∼ g1 + εg2 + · · ·

(8)

in D∞ (E) as ε ↓ 0 with g1 , g2 , · · · ∈ D∞ (E). Also if for every k = 1, 2, · · ·, there exists s > 0 such that, for all p > 1, X (ε) (w), g1 , g2 , · · · ∈ D−s p (E) and X (ε) (w) − (g1 + εg2 + · · · + εk−1 gk ) = O(εk ) (9)

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(ε) ˜ −∞ (E) has an asymptotic expansion: in D−s p (E) as ε ↓ 0, then we say that X (w) ∈ D −∞

˜ in D

X (ε) (w) ∼ g1 + εg2 + · · · −∞

˜ (E) as ε ↓ 0 with g1 , g2 , · · · ∈ D

(10)

(E) .

Let S(Rd ) be the real Schwartz space of rapidly decreasing C∞ -functions on Rd and S (Rd ) be its dual space that is the space of the Schwartz tempered distributions. Also X (ε) ∈ D∞ (Rd ) is said to be non-degenerate (in the sense of Malliavin) if for any p > 1 the Malliavin-covariance of X (ε) satisfies  −p sup E[ det[σ MC (X (ε) )] ] < ∞. (11) ′

ε∈(0,1]

Suppose that X (ε) ∈ D∞ (Rd ) satisfies the nondegeneracy condition (11). Then, it has been known that every Schwartz tempered distribution T (x) on Rd can be lifted up or pulled˜ −∞ under the back to a generalized Wiener functional T ◦ X (ε) (denoted by T (X (ε) )) in D (ε) d (ε) −∞ ˜ , it can act on any test Wiener map: w ∈ W 7→ X (w) ∈ R . Since T ◦ X ∈ D ∞ ∞ ˜ functional in D , which is much larger than D . With these formulations and notations we are ready to state Theorem 2.3 of [89]. Theorem 1 [ Theorem 2.3 of Watanabe [89] ] : Let {X (ǫ) (w); ǫ ∈ (0, 1]} be a family of elements in D∞ (Rd ) such that it has the asymptotic expansion: X (ǫ) (w) ∼ g1 + ǫg2 + · · · in D∞ (Rd ) as ǫ ↓ 0

with gi ∈ D∞ (Rd ), i = 1, 2, · · · and satisfies

lim sup k(det σ MC (X (ǫ) ))−1 k p < ∞ for all 1 < p < ∞

(12)

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ǫ↓0

where σ MC (X (ǫ) ) = (σi j (X (ǫ) )) is the Malliavin covariance of X (ǫ) (w): ′ σi j (X (ǫ) ) =< DX (ǫ),i (w), DX (ǫ), j (w) >H . Let T ∈ S (R⌈ ). Then, Φ(ǫ, w) = T ◦ X (ǫ) (w) has ˜ −∞ (and a fortiori in D−∞ ): the asymptotic expansion in D ˜ −∞ as ǫ ↓ 0 Φ(ǫ, w) ∼ φ1 + ǫφ2 + · · · in D

˜ −∞ , i = 0, 1, · · · are determined by the formal Taylor expansion: and φi ∈ D Φ(ǫ, w) = T (g1 + [ǫg2 + ǫ 2 g3 + · · ·]) X 1 (Dα T ) ◦ g1 [ǫg2 + ǫ 2 g3 + · · ·]α = α! α = φ1 + ǫφ2 + · · · where (i) the summation is taken over all multi-indices and (ii) for every multi-index α = (α1 , α2 , · · · , αd ) and a = (a1 , a2 , · · · , ad ) ∈ Rd , we set as usual α! = α1 !α2 ! · · · αd ! and aα = aα1 1 aα2 2 · · · aαd d .

[90], [91] provided so called “the truncated version” of this theorem. His result is very important from viewpoint of applications because in his version checking the nondegeneracy of X (ǫ) (w) when ǫ = 0 is enough, which is usually much easier than in the original one. Moreover, he also derived conditional expectation formulas up to the second order that are very useful to obtain explicit approximations. See [90], [91] for the detail.

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191

An Asymptotic Expansion Approach An Asymptotic Expansion in a General Markovian Setting

Let (W, P) be the r-dimensional Wiener space. We consider a d-dimensional diffusion process X (ǫ) = {Xt(ǫ) = (Xt(ǫ),1 , · · · , Xt(ǫ),d )} which is the solution to the following stochastic differential equation: dXt(ǫ),i = V0i (Xt(ǫ) , ǫ)dt + ǫV i (Xt(ǫ) )dWt X0(ǫ)

= x0 ∈ Rd

(i = 1, · · · , d)

(13)

where W = (W 1 , · · · , W r ) is a r-dimensional standard Wiener process, and ǫ ∈ (0, 1] is a known parameter. Suppose that V0 = (V01 , · · · , V0d ) : Rd × (0, 1] 7→ Rd and V = (V 1 , · · · , V d ): Rd 7→ d R ⊗Rr satisfy some regularity conditions.(e.g. V0 and V are smooth functions with bounded derivatives at any order.) Next, suppose that a function g : Rd 7→ R to be smooth and all derivatives have polynomial growth orders. Then, g(XT(ǫ) ) has its asymptotic expansion; g(XT(ǫ) ) ∼ g0T + ǫg1T + · · · in L p for every p > 1(or in D∞ ) as ǫ ↓ 0. gnT ∈ D∞ (n = 0, 1, · · ·), the coefficients in the expansion, can be obtained by formal Taylor’s formula and represented based on multiple Wiener-Ito integrals.

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∂k X (ǫ)

Let Akt = ∂ǫ kt |ǫ=0 and Aikt , i = 1, · · · , d denote the i-th elements of Akt . In particular, A1t is represented by Z t   A1t = Yt Yu−1 ∂ǫ V0 (Xu(0) , 0)du + V(Xu(0) )dWu (14) 0

where Y denotes the solution to the differential equation; dYt = ∂V0 (Xt(0) , 0)Yt dt; Y0 = Id . j

j

∂V (x,ǫ)

j

0 Here, ∂V0 denotes the d × d matrix whose ( j, k)-element is ∂k V0 = ∂x , V0 is the j-th k element of V0 , and Id denotes the d × d identity matrix. For k ≥ 2, Aikt , i = 1, · · · , d is recursively determined by the following:

Aikt

= +

Z

t

0 k X l=1

+

∂kǫ V0i (X s(0) , 0)ds

(15)

β l X Z t d X Y k! 1 X d β (0) k−l i ∂d1 ,···,dβ ∂ǫ V0 (X s , 0) Al jj,s ds l!(k − l)! β=1 β! 0 j=1 d ,···,d =1

k X X Z β=1 ~lβ ∈Lβ,k−1

~lβ ∈Lβ,l

t 0

1

β

β r d Y 1 X X d β ∂d1 ,···,dβ Vαi (X s(0) ) Al jj,s dW sα , β! α=1 d ,···,d =1 j=1 1

β

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where ∂lǫ =

∂l , ∂ǫ l

β

∂d1 ,···,dβ = Lβ,k

∂β ∂xd1 ···∂xdβ

and

  β     X   ~  = lβ = (l1 , · · · , lβ ); l j ≥ 0( j = 1, · · · , β), l j = k .       j=1

Then, g0T and g1T can be written as g0T

= g(XT(0) ),

g1T

d X

=

∂i g(XT(0) )Ai1T .

i=1

For n ≥ 2, gnT is expressed as follows: gnT =

X

~s∈S n

  s !Y !s d  n s Y  sl  p1l sl ! 1 l X  n! pdl (0) i pi  sl  · · · ∂ A g(X ) ∂  lT T d s1 ! · · · sn ! l=1 l! p1 ! · · · pdsl ! 1 i=1 ~p sl ∈P

(16)

sl

where Sn Ps

  n   X     ~s = (s1 , · · · , sn ); sl ≥ 0(l = 1, · · · , n), :=  lsl = n ,     l=1   d   X    s  s s s s ~ :=  p = (p , · · · , p ); p ≥ 0(i = 1, · · · , d), p = s .  i i 1 d     i=1

Next, normalize g(XT(ǫ) ) to

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G for ǫ ∈ (0, 1]. Then,

(ǫ)

g(XT(ǫ) ) − g0T = ǫ

G(ǫ) ∼ g1T + ǫg2T + · · ·

in L p for every p > 1(or in D∞ ). Moreover, let

ˆ t) = (∂g(x))′ [YT Yt−1 V(x)] V(x, and make the following assumption: (Assumption 1) ΣT =

Z

T 0

ˆ t(0) , t)V(X ˆ t(0) , t)′ dt > 0. V(X

Note that g1T follows a normal distribution with variance ΣT ; the denstiy function of g1T denoted by fg1T (x) is given by ! 1 x2 fg1T (x) = √ exp − . 2ΣT 2πΣT Hence, Assumption 1 means that the distribution of g1T does not degenerate. In application, it is easy to check this condition in most cases. Hereafter, Let S be the real Schwartz space

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of rapidly decreasing C∞ -functions on R and S′ be its dual space that is the space of the Schwartz tempered distributions. Next, take Φ ∈ S′ . Then, by Watanabe theory([89], [90]) ˜ −∞ (a fortiori in D−∞ ) as ǫ ↓ 0. In other words, the Φ(G(ǫ) ) has an asymptotic expansion in D expectation of Φ(G(ǫ) ) is expanded around ǫ = 0 as follows: For M = 0, 1, 2, · · ·,    j j−m+1   M     X X X Y    1  (m)   kn (ǫ) j j,m,k M E Φ (g1T )  E[Φ(G )] = ǫ C g(n+1)T   + o(ǫ )     m! k∈K j,m  j=0 m=0 n=1   j M X X X h i 1  (m) j E Φ (g1T ) C j,m,k E X j,m,k g1T  + o(ǫ M ) = ǫ m! j=0 m=0 k∈K j,m

=

=

1 m! m=0

Z

Φ(m) (x)

j=0

j X

M X

j X

Z

Φ(x)

M X

j=0

ǫj

ǫj

1 m! m=0

R

X

k∈K j,m

R

X

i h C j,m,k E X j,m,k g1T = x fg1T (x)dx + o(ǫ M )

C j,m,k (−1)m

k∈K j,m

M

fg1T (x)}dx + o(ǫ ) ∂m Φ(x) (m) , where Φ (g1T ) = ∂xm x=g

h i ∂m j,m,k g = x {E X 1T ∂xm

(17)

1T

K j,m

  j−m+1 j−m+1   X X     = (k , · · · , k ); k ≥ 0, k = m, nk = j ,  1 j−m+1 n n n     n=1

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X j,m,k = C j,m,k =

j−m+1 Y

n=1 j−m+1 Y n=1

n=1

n gk(n+1)T ,

m! . k1 ! · · · k j−m+1 !

As shown under a simple setting in the next subsection, the conditional expectations in (17) can be expressed as linear combinations of a finite number of Hermite polynomials of g1T . Then, you can easily implement the differentiation and integration in (17) using the following property of a Gaussian distribution; 1 ∂ {Hn (x; Σ) fg1T (x)} = − Hn+1 (x; Σ) fg1T (x) ∂x Σ for n ≥ 0 where Hn (x; Σ) is the n-th order Hermite polynomial defined by

(18)

dn −x2 /2Σ e . (19) dxn These are proven in more general cases by [81] which provides us the methods for actual computation of E[X j,m,k |g1T = x] and formulas useful for high-order computation. Thus, once you compute the conditional expectations explicitly, you also have the explicit expansion of E[Φ(G(ǫ) )]. Moreover, the asymptotic expansion of the probability function of G(ǫ) can be obtained by letting Φ be δ x , the delta function with a mass at x. Hn (x; Σ) := (−Σ)n e x

2 /2Σ

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3.2.

An Asymptotic Expansion in a Black-Scholes Economy: a Simple Application

In this subsection, the asymptotic expansion approach described so far is applied to an evaluation problem in a simple Black-Scholes-type economy in order to make a whole procedure in application clearer. Let (W, P) be a one-dimensional Wiener space. Hereafter P is considered as a riskneutral equivalent martingale measure and a risk-free interest rate is set to be constantly zero for simplicity. Then, the underlying economy is specified with a (R+ -valued)single risky asset S (ǫ) = {S t(ǫ) } satisfying Z t (ǫ) σ(S (ǫ) (20) St = S0 + ǫ s , s)dW s 0

where ǫ ∈ (0, 1] is a constant parameter; σ: R2+ 7→ R satisfies some regularity conditions. We will consider the following pricing problem; V(0, T ) = E[Φ(S T(ǫ) )]

(21)

where Φ is a payoff function and E[ · ] is an expectation operator under the probability measure P. For their rigorous definitions, see Section 2. Let Akt =

∂k S t(ǫ) | . ∂ǫ k ǫ=0

Here we represent A1t , A2t and A3t explicitly by

A1t =

Z

A2t = 2

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A3t = 3

t

σ(S (0) s , s)dW s ,

(22)

0

Z

t

∂σ(S (0) s , s)A1s dW s ,

(23)

0

Z t 0

 (0) 2 ∂2 σ(S (0) s , s)(A1s ) + ∂σ(S s , s)(A2s ) dW s

(24)

recursively and then S T(ǫ) has its asymptotic expansion S T(ǫ) = S 0 + ǫA1T +

ǫ2 ǫ3 A2T + A3T + o(ǫ 3 ). 2! 3!

(25)

Note that S t(0) = limǫ↓0 S t(ǫ) = S 0 for all t. Next, normalize S T(ǫ) with respect to ǫ as G for ǫ ∈ (0, 1]. Then,

(ǫ)

S T(ǫ) − S T(0) = ǫ

ǫ ǫ2 A2T + A3T + o(ǫ 2 ) 2! 3! P in L for every p > 1. Here the following assumption is made: Z T ΣT = σ2 (S t(0) , t)dt > 0. G(ǫ) = A1T +

0

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(27)

Asymptotic Expansion Approaches in Finance

195

Note that A1T follows a normal distribution with mean 0 and variance ΣT , and hence this assumption means that the distribution of A1T does not degenerate. It is clear that this assumption is satisfied when σ(S t(0) , t) > 0 for some ht > 0. i Then setting M = 2, (17), the expansion of E Φ(G(ǫ) ) , is written as follows in the setting we are considering (hereafter in this section the asymptotic expansion of E[Φ(G(ǫ) )] up to the second order will be considered): Z Z ∂ E[Φ(G(ǫ) )] = Φ(x) fA1T (x)dx + ǫ Φ(x)(−1) {E [A2T |A1T = x ] fA1T (x)}dx ∂x R R Z ∂ + ǫ2 Φ(x)(−1) {E [A3T |A1T = x ] fA1T (x)}dx ∂x R ! Z 2 h i 1 2 2 ∂ {E (A2T ) |A1T = x fA1T (x)}dx + o(ǫ 2 ). + Φ(x)(−1) 2 R ∂x2 (28) where fA1T (x) is a probability density function of A1T following a normal distribution; ! 1 x2 fA1T (x) := √ exp − . (29) 2ΣT 2πΣT Then, all we have to do to evaluate this expansion is a computation of the conditional expectations in (28). In the following, it will be shown that A2T , A3T , (A2T )2 can be expressed as summations of a finite number of iterated Itˆo integrals. First, note that A2T is

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A2T = 2

T

Z

0

Z

t1

0

, t2 )dWt2 dWt1 , , t1 )σ(S t(0) ∂σ(S t(0) 2 1

(30)

that is a twice-iterated Itˆo’ integral. Next, by application of Itˆo’s formula to (24) we obtain A3T

= 6

Z

+ 6

Z

+ 3

Z

T 0

Z

T

Z

T

Z

0

0

t1 0

Z

t2

Z

t2

0

t1 0

0

t1 0

, t3 )dWt3 dWt2 dWt1 , t2 )σ(S t(0) , t1 )∂σ(S t(0) ∂σ(S t(0) 3 2 1 ∂2 σ(S t(0) , t1 )σ(S t(0) , t2 )σ(S t(0) , t3 )dWt3 dWt2 dWt1 1 2 3

∂2 σ(S t(0) , t1 )σ2 (S t(0) , t2 )dt2 dWt1 . 1 2

(31)

Similarly, we have (A2T )2 = 16

Z

T 0

Z

t1 0

Z

dWt2 dWt1 Z T Z t1 Z + 8 0

0

t2 0

t2 0

Z

Z

t3 0

t3 0

∂σ(S t(0) , t1 )∂σ(S t(0) , t2 )σ(S t(0) , t3 )σ(S t(0) , t4 )dWt4 dWt3 1 2 3 4

∂σ(S t(0) , t1 )σ(S t(0) , t2 )∂σ(S t(0) , t3 )σ(S t(0) , t4 )dWt4 1 2 3 4

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+ + + +

dWt3 dWt2 dWt1 Z T Z t1 Z t2 ∂σ(S t(0) , t1 )∂σ(S t(0) , t2 )σ2 (S t(0) , t3 )dt3 dWt2 dWt1 8 1 2 3 0 0 0 Z T Z t1 Z t2 ∂σ(S t(0) , t1 )∂σ(S t(0) , t2 )σ(S t(0) , t2 )σ(S t(0) , t3 )dWt3 dt2 dWt1 8 1 2 2 3 0 0 0 Z T Z t1 Z t2  2 ∂σ(S t(0) , t ) σ(S t(0) , t2 )σ(S t(0) , t3 )dWt3 dWt2 dt1 8 1 1 2 3 0 0 0 Z T Z t1  2 4 ∂σ(S t(0) , t1 ) σ2 (S t(0) , t2 )dt2 dt1 . (32) 1 2 0

0

Moreover, there is a well-known result on conditional expectations of iterated Itˆo integrals. Proposition 1 Let Jn ( fn ) denote the n-times iterated Itˆo integral of L2 (Tn )-function fn : Z

Jn ( fn ) :=

T 0

Z

t1

···

0

Z

tn−1 0

fn (t1 , · · · , tn )dWtn · · · dWt2 dWt1

for n ≥ 1 and J0 ( f0 ) := f0 (constant). Then, its expectation conditional on J1 (q) = x is given by E[Jn ( fn )|J1 (q) = x] =

T

Z

0

Z

0

t1

···

Z

tn−1 0

fn (t1 , · · · , tn )q(t1 ) · · · q(tn )dtn · · · dt2 dt1

! H (x; kqk2 ) n L2 (T) (kqk2L2 (T) )n

(33)

where T = [0, T ] and ti ∈ T(i = 1, 2, · · · , n).

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(proof) See [59] or [81]. Then, thanks to this proposition, the conditional expectations in (28) can be computed as E[A2T |A1T = x] = 2

Z Z

T 0

Z

t1

Z

t1

0

T

, t2 )dt2 dt1 , t1 )σ2 (S t(0) , t1 )σ(S t(0) ∂σ(S t(0) 2 1 1 Z

!

H2 (x; ΣT ) Σ2T

t2

(34)

, t3 )dt3 dt2 dt1 , t2 )σ2 (S t(0) , t2 )σ(S t(0) , t1 )∂σ(S t(0) , t1 )σ(S t(0) ∂σ(S t(0) 3 2 2 1 1 0 0 0 ! Z T Z t1 Z t2 H3 (x; ΣT ) (0) (0) 2 2 (0) 2 (0) + 6 ∂ σ(S t1 , t1 )σ(S t1 , t1 )σ (S t2 , t2 )σ (S t3 , t3 )dt3 dt2 dt1 Σ3T 0 0 0 ! Z T Z t1 H1 (x; ΣT ) (35) + 3 ∂2 σ(S t(0) , t1 )σ(S t(0) , t1 )σ2 (S t(0) , t2 )dt2 dt1 1 1 2 ΣT 0 0

E[A3T |A1T = x] = 6

and E[(A2T )2 |A1T = x] Z T Z t1 Z t2 Z = 16 2

σ

t3

, t1 )σ(S t(0) , t1 )∂σ(S t(0) , t2 )σ(S t(0) , t2 )σ2 (S t(0) , t3 ) ∂σ(S t(0) 1 1 2 2 3

0 0 0 0 (0) (S t4 , t4 )dt4 dt3 dt2 dt1

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+

8

Z

0

T Z

0

t1 Z

0

Asymptotic Expansion Approaches in Finance t2 Z t3 ∂σ(S t(0) , t1 )σ(S t(0) , t1 )σ2 (S t(0) , t2 )∂σ(S t(0) , t3 )σ(S t(0) , t3 ) 1 1 2 3 3 0

σ2 (S t(0) , t4 )dt4 dt3 dt2 dt1 4 Z

T

Z

t1

Z

197

 H4 (x; ΣT ) Σ4T

t2

∂σ(S t(0) , t1 )σ(S t(0) , t1 )∂σ(S t(0) , t2 )σ(S t(0) , t2 )σ2 (S t(0) , t3 )dt3 dt2 dt1 1 1 2 2 3 0 0 0 ! Z T Z t1 Z t2  2 H2 (x; ΣT ) (0) 2 (0) 2 (0) + 8 ∂σ(S t1 , t1 ) σ (S t2 , t2 )σ (S t3 , t3 )dt3 dt2 dt1 Σ2T 0 0 0 Z T Z t1  2 + 4 ∂σ(S t(0) , t ) σ2 (S t(0) , t2 )dt2 dt1 . (36) 1 1 2 +

16

0

0

h i Substituting these into (28), we have the asymptotic expansion of E Φ(G(ǫ) ) up to ǫ 2 -order.

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Here, at the end of this subsection, we state a brief summary. In the Black-Scholes-type economy, we considered the risky asset S (ǫ) and evaluate some quantities, expressed as an expectation of the function of the price in the future, such as prices or risk sensitivities of the securities on this asset. First we expanded them around the limit to ǫ = 0 so that we obtained the expansion (28) which contains some conditional expectations. Then, we gave the explicit expressions of these conditional expectation. Finally, substituting computation results into (28), the asymptotic expansion of those quantities was obtained. Even in applications under more complicated settings such as presented in Section 5. you can follow the procedure in this subsection in the same manner.

4.

European Currency Options with a Market Model of Interest Rates and Stochastic Volatility Models of Spot Exchange Rates

This section describes the framework of the cross-currency market according to [78] to which our asymptotic expansion approach will be applied in the next section. ˜ {Ft }0≤t≤T ∗ 0 are expressed as (S (T ) − K)+ and (K − S (T ))+ respectively where S (t) denotes the spot exchange rate at time t ≥ 0 and x+ denotes max(x, 0). For a while we concentrate on the valuation of a call option since the value of a put option can be obtained through the put-call parity or similar method. We also note that the spot exchange rate S (T ) can be expressed in terms of a foreign exchange forward(forex forward) rate with the same maturity T . That is, S (T ) = FT (T ) where FT (t), t ∈ [0, T ] denotes the time t value of the forex forward rate with maturity T . It is well known that the arbitrage-free relation between the forex spot rate and P (t,T ) the forex forward rate are given by FT (t) = S (t) Pdf (t,T ) where Pd (t, T ) and P f (t, T ) denote the time t values of domestic and foreign zero coupon bonds with maturity T respectively.

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Hence, our objective is to obtain the present value of the payoff (FT (T ) − K)+ . In particular, we need to evaluate:   V(0; K, T ) = Pd (0, T )EP (FT (T ) − K)+ (37)

where V(0; T, K) denotes the value of an European call option at time 0 with maturity T and strike rate K, and EP [·] denotes the expectation operator under EMM(Equivalent Martingale Measure) P ∼ P˜ whose associated numeraire is the domestic zero coupon bond maturing at T (we use a term of the domestic terminal measure in what follows). Then, the dynamics governing FT (T ) under the domestic terminal measure are necessary for pricing the option. For this objective, a market model and stochastic volatility models possibly with jumps are applied to modeling interest rates’ and the spot exchange rate’s dynamics respectively. In the rest of this section, we describe briefly the model to which an asymptotic expansion approach will be applied in the following sections, where some appropriate regularity conditions are implicitly assumed without mentioned.   P (t,T )

We first define domestic and foreign forward interest rates as fd j (t) = Pd d(t,T j+1j ) − 1 τ1j   P f (t,T j ) 1 and f f j (t) = P f (t,T − 1 τ j respectively, where j = n(t), n(t) + 1, · · · , N, τ j = T j+1 − T j j+1 ) and n(t) = min{i : t ≤ T i }. We also define spot interest rates to   the nearest fixing date

1 denoted by fd,n(t)−1 (t) and f f,n(t)−1 (t) as fd,n(t)−1 (t) = Pd (t,T − 1 (T n(t)1 −t) and f f,n(t)−1 (t) = n(t) )   1 1 P f (t,T n(t) ) − 1 (T n(t) −t) . Finally, we set T = T N+1 and will abbreviate F T N+1 (t) to F N+1 (t) in what follows. R++ -valued processes of domestic forward interest rates under the domestic terminal measure can be specified as; for j = n(t) − 1, n(t), n(t) + 1, · · · , N,

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fd j (t) =

fd j (0) +

Z

t 0

′

fd j (s)˜γd j (s)

N X

g˜ di (s)ds +

i= j+1

Z

t

′

fd j (s)˜γd j (s)dW s

0

(38)

γdi (t) i fdi (t)˜ where g˜ di (t) := −τ1+τ ; x denotes the transpose of x, and W is a D dimensional standard i fdi (t) Wiener process under the domestic terminal measure; γ˜ d j (t) is a function of time-parameter t. Similarly, R++ -valued processes of foreign ones under the foreign terminal measure are specified as ′

f f j (t) =

f f j (0) +

Z

t 0

′

f f j (s)˜γ f j (s)

N X

g˜ f i (s)ds +

i= j+1

Z

t 0

′

f

f f j (s)˜γ f j (s)dW s

(39)

−τ f (t)˜γ (t)

i fi fi ; W f is a D dimensional standard Wiener process under the where g˜ f i (t) := 1+τ i f f i (t) foreign terminal measure and γ˜ f j (t) is a function of t. Finally, it is assumed that the spot exchange rate S (t) and its volatility σ(t) ˜ follow R++ valued stochastic processes as below respectively under the domestic risk neutral measure: Z t Z t Z t ′ ˆs+ S (t) = S (0) + S (s)(rd (s) − r f (s))ds + S (s)σ(s) ˜ σ ¯ dW S (s)d A˜ s

σ(t) ˜ = σ(0) ˜ +

Z0 t 0

0

µ( ˆ σ(s), ˜ s)ds +

Z

t

0

′

ˆs ω ˜ (σ(s), ˜ s)dW 0

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Asymptotic Expansion Approaches in Finance

199

ˆ is a D dimensional standard Wiener process under the domestic risk neutral meawhere W sure and rd (t) and r f (t) denote domestic and foreign instantaneous spot interest rates respectively; σ ¯ denotes a RD -valued constant vector satisfying ||σ|| ¯ = 1, and ω(x, ˜ t) is a function of ˜ x and t. A is some martingale possibly with jumps and independent of W(then independent ˆ as well), which will be restricted to a certain class in Section 5.2. of W f and W In the model, the volatility of the forex spot rate process is allowed to be general time-inhomogeneous Markovian while the interest rates’ volatilities are specified as a lognormal structure. Note that the correlations’ structure among domestic/foreign interest rates, the spot exchange rate and its volatility can be represented through γ˜ d j (t), γ˜ f j (t), σ ¯ and ω( ˜ σ(t), ˜ t). It is also noted that our methodology can be applied not only in a Markovian setting but also in a non-Markovian framework as long as the uncertainty is generated by Wiener processes. Moreover, we have the following well known relations among Wiener processes under different probability measures; Z t ˆ Wt = Wt − σ ˜ dN+1 (s)ds 0 Z t f = Wt + {σ ˜ f N+1 (s) − σ ˜ dN+1 (s) + σ(s) ˜ σ}ds ¯ 0

where σ ˜ dN+1 (t) and σ ˜ f N+1 (t) are volatilities of the domestic and foreign zero coupon bonds with the maturity T N+1 , that is, X X σ ˜ dN+1 (t) := g˜ di (t), σ ˜ f N+1 (t) := g˜ f i (t)

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i∈JN+1 (t)

i∈JN+1 (t)

and J j+1 (t) = {n(t) − 1, n(t), n(t) + 1, · · · , j}. Because γ f j (t) = 0 and γd j (t) = 0 for all j such that T j ≤ t, the set of indices J j+1 (t) can be replaced by Jˆj+1 := {0, 1, · · · , j}, which does not depend on t. Using above equations, we can unify expressions of those processes under different measures into ones under the same measure, the domestic terminal measure P:     Z t     X X   ′   f f j (t) = f f j (0) + f f j (s)˜γ f j (s)  − g ˜ (s) + g ˜ (s) − σ(s) ˜ σ ¯ ds  f i di       0   i∈ Jˆj+1

Z

t

i∈ JˆN+1

′

f f j (u)˜γ f j (u)dWu 0 Z t Z t ′ σ(t) ˜ = σ(0) ˜ + µ(s)ds + ω ˜ (σ(s), ˜ s)dW s +

0

(41)

(42)

0

where µ(t) is defined as ′

µ(t) := µ( ˆ σ(t), ˜ t) + ω ˜ (σ(t), ˜ t)σ ˜ dN+1 (t). Since F N+1 (t) can be expressed as F N+1 (t) = S (t)

P f (t, T N+1 ) , Pd (t, T N+1 )

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200

Akihiko Takahashi and Kohta Takehara

we easily notice that it is a martingale under the domestic terminal measure. Consequently, we can obtain its process with application of Itˆo’s formula to (43): Z

t

Z

′

t

F(s)d A˜ s (44) F N+1 (0) + σ ˜ F (s)dW s + 0 0   where σ ˜ F (t) := F N+1 (t) σ ˜ f N+1 (t) − σ ˜ dN+1 (t) + σ(t) ˜ σ ¯    X ( −τ f (t)˜γ (t) −τ f (t)˜γ (t) )  j fj fj j dj dj   = F N+1 (t)  − + σ(t) ˜ σ ¯  . (45)   1 + τ f (t) 1 + τ f (t) j f j i d j ˆ F N+1 (t)

=

j∈ JN+1

It is obviously that the process of the forex forward is too complicated to derive the closedform formula of option prices. Thus, approximation schemes based on an asymptotic expansion will be applied in the following sections. Despite this difficulty, we here emphasize the generality and importance of our framework investigated in this work: For the stochastic volatility, a general time-inhomogeneous Markovian process is assumed, which is not necessarily classified in the affine model such as in [27]; Any correlation structure can be considered; In addition, we can incorporate a jump process in our model. These settings are flexible enough to capture the complexity of movements of the underlying asset and to calibrate our model to the market with ease even in the severely skewed environment as in a recent JPY-USD market, as shown in Section 6.3.

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5.

Applications of the Asymptotic Expansion Approach to Currency Options

This section applies an asymptotic expansion approach in Section 3.1. to evaluation of currency option prices in the environment described so far. Particularly, first we present a natural application of the method according to [78], which is henceforth called ‘a standard scheme,’ and then show another application in a somewhat different way, which is called ‘a hybrid scheme,’ proposed by [80]. The latter is applicable even when the dynamics of the spot forex contains a certain class of jumps.

5.1.

A Standard Scheme

This subsection presents a standard way of application of an asymptotic expansion to option pricing problem under the setting described in Section 4. Details are sometimes omitted due to limitation of space and found in [78]. (ǫ) First the processes of fd(ǫ)j (t), f f(ǫ)j (t), σ(ǫ) (t) and F N+1 (t) under the domestic terminal measure P are redefined in the framework of the asymptotic expansion method as follows; for j = n(t) − 1, n(t), n(t) + 1, · · · , N, fd(ǫ)j (t)

=

fd j (0) + ǫ

2

Z

t 0

′ fd(ǫ)j (u)γd j (s)

N X

i= j+1

g(ǫ) di (s)ds

+ǫ

Z

0

t

′

fd(ǫ)j (s)γd j (s)dW s

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Asymptotic Expansion Approaches in Finance 201     Z t     X   ′  X (ǫ)  (ǫ) (ǫ) (ǫ) (ǫ) 2 (ǫ) − f f j (t) = f f j (0) + ǫ f f j (u)γ f j (u)  g (s) + ds g (s) − σ (s) σ ¯    fi di     0  i∈ Jˆj+1  i∈ JˆN+1 Z t ′ +ǫ f f(ǫ)j (s)γ f j (s)dW s (47) 0 Z t Z t ′ (ǫ) (ǫ) σ (t) = σ(0) + µ (s)ds + ǫ ω (σ(ǫ) (s), s)dW s (48) 0 0 Z t ′ (ǫ) F N+1 (t) = F N+1 (0) + ǫ σ(ǫ) (49) F (s)dW s 0

where (ǫ) (ǫ) (ǫ) (ǫ) ¯ σ(ǫ) F (t) := F N+1 (t)[σ f N+1 (t) − σdN+1 (t) + σ (t)σ]     (ǫ) (ǫ)   X     (t)γ (t) (t)γ (t) −τ f −τ f f j d j j j   fj dj     (ǫ) (ǫ) = F N+1 (t)  − + σ (t)σ ¯      (ǫ) (ǫ)      1 + τ j f f j (t) 1 + τi fd j (t)  j∈ Jˆ N+1

and

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g(ǫ) di (t)

:=

τi fdi(ǫ) (t)γdi (t) 1 + τi fdi(ǫ) (t)

,

g(ǫ) f i (t)

τi f f(ǫ) i (t)γ f i (t)

:=

1 + τi f f(ǫ) i (t)

.

Here, γ˜ d j (t), γ˜ f j (t), σ(t) ˜ and ω(σ ˜ (ǫ) (t), t) in the previous section are replaced by ǫγd j (t), (ǫ) ǫγ f j (t), ǫσ(t), and ǫω(σ (t), t) respectively. Moreover, in this subsection it is assumed that there is no uncertainty such as jumps except for Wiener processes we have defined(i.e. A˜ ≡ 0). Under certain appropriate conditions on µ(ǫ) (t) and ω(σ(ǫ) (t), t), the system of SDEs (ǫ) (t). Note (46), (47), (48) and (49) have their unique solutions fd(ǫ)j (t), f f(ǫ)j (t), σ(ǫ) (t) and F N+1 that the limiting processes of these processes are deterministic: f f(0)j (t) := lim f f(ǫ)j (t) = f f j (0), fd(0) (t) := lim fd(ǫ)j (t) = fd j (0) j ǫ↓0 ǫ↓0 Z t and σ(0) (t) := lim σ(ǫ) (t) = σ(0) + lim µ(ǫ) (s)ds. ǫ↓0

0 ǫ↓0

In what follows, substitution ‘ǫ = 0’ into each variable will be frequently used instead of taking its limit as ǫ ↓ 0. Moreover, the maturity of the option T N+1 will be abbreviated as T. Next, substituting X (ǫ) =



X (ǫ),1 , · · · , X (ǫ),2N+4



=



 (ǫ) F N+1 , { fd(ǫ)j }Nj=0 , { f f(ǫ)j }Nj=0 , σ(ǫ) ,

(ǫ) g(XT(ǫ) ) = XT(ǫ),1 = F N+1 (T ) and M = 2 into the setting of Section 3.1., we have the following expansion.

Proposition 2 The asymptotic expansion of G(ǫ) F = as follows: h1i G(ǫ) F = AT +

(ǫ) F N+1 (T )−F N+1 (0) ǫ

up to ǫ 2 -order is given

ǫ h2i ǫ 2 h3i A + AT + o(ǫ 2 ) 2! T 3!

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(50)

202

Akihiko Takahashi and Kohta Takehara ∂k F (ǫ) (t)

(ǫ) where Athki , k = 1, 2, 3 are obtained by formal Taylor’s expansion of F N+1 |ǫ=0 , (t), ∂ǫN+1 k  (ǫ)  (ǫ) N (ǫ) N (ǫ) (ǫ) or substitution of X = F N+1 , { fd j } j=0 , { f f j } j=0 , σ into (15). For details see [78].

Note that the first order term Ah1i T = 0 and variance Σ:

RT 0

′ σ(0) F (s) dW s follows normal distribution with mean

Z

Σ :=

0

T

2 kσ(0) F (s)k ds.

(51)

With the expansion of G(ǫ) F in Proposition 2, we now focus on pricing options. Hereafter, we will consider a call option with strike rate Kǫ where Kǫ is defined for some arbitrary y ∈ R as Kǫ := F N+1 (0) − ǫy. Then, the discounted value of the option is given by V(0; Kǫ , T ) (ǫ) + = EP [(F N+1 (T ) − Kǫ )+ ] = EP [ǫ(G(ǫ) F + y) ] Pd (0, T )

(52)

Thus, letting Φ in Section 3.1. be Φ(x) = Pd (0, T )ǫ(x + y)+ , we obtain the asymptotic expansion of the option price with respect to ǫ as the following theorem through evaluation of conditional expectations. Theorem 2 We define Kǫ := F N+1 (0)−ǫy for some arbitrary y ∈ R and suppose that Σ > 0. Then an asymptotic expansion of V(0; T, Kǫ ), the value of the option with strike rate Kǫ , up to ǫ 3 -order is given as follows: " Z ∞ Z ∞ V(0; Kǫ , T ) = Pd (0, T ) ǫy φ0,Σ (x)dx + ǫ xφ0,Σ (x)dx

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+ +

ǫ2 2

∞

Z

−y Z ∞ 3 ǫ

6

−y

−y

EP [ATh2i |Ah1i T = x]φ0,Σ (x)dx E

−y

P

h1i [Ah3i T |AT

ǫ3 = x]φ0,Σ (x)dx + (EP [(Ah2i )2 |Ah1i T = x]φ0,Σ (x)) x=−y 48

+ o(ǫ 3 )

#

(53)

where φµ,Σ (x) is defined by ! (x − µ)2 φµ,Σ (x) = √ exp − . 2Σ 2πΣ 1

(54)

The conditional expectations appearing in the above equation are eventually expressed as linear combinations of Hermite polynomials; x x2 1 + C2,2 ( 2 − ) Σ Σ Σ x x2 1 x3 3x = x] = C3,1 + C3,2 ( 2 − ) + C3,3 ( 3 − 2 ) Σ Σ Σ Σ Σ x x2 1 = x] = C4,0 + C4,1 + C4,2 ( 2 − ) Σ Σ Σ x3 3x x4 6x2 3 +C4,3 ( 3 − 2 ) + C4,4 ( 4 − 3 + 2 ) Σ Σ Σ Σ Σ

h1i EP [Ah2i T |AT = x] = C 2,1

(55)

h1i EP [Ah3i T |AT

(56)

2 h1i EP [(Ah2i T ) |AT

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203

where C2,1 , C2,2 , C3,1 , C3,2 , C3,3 , C4,0 , C4,1 , C4,2 , C4,3 , and C4,4 are some constants. Calculation procedures of these quantities are found in Appendix of [78] and those under a more general framework are in [81]. Remark 1 In practice, we are often interested in the accuracy of our formulas for the prices of options whose underlying variables follow the SDEs (38), (41) and (42) with a particular set of parameters such as γ˜ d j (t), γ˜ f j (t), σ(0) ˜ , µ(t) and ω( ˜ σ(t), ˜ t). From this point (ǫ) of view, given some particular value of ǫ, γd j (t), γ f j (t), σ(0), µ (t) and ω(σ(ǫ) (t), t) in (46), (47) and (48) should be scaled so that ǫγd j (t) = γ˜ d j (t), ǫγ f j (t) = γ˜ f j (t), ǫσ(0) = σ(0), ˜ ǫµ(ǫ) (t) = µ(t) and ǫω(σ(t), t) = ω( ˜ σ(t), ˜ t) for an arbitrary t ∈ [0, T ]. For instance, γ(t) is defined as γ(t) := γ˜ ǫ(t) where ǫ is fixed at a pre-specified constant through our procedure of expansions. Moreover, it can be shown that the approximated prices are unchanged whatever ǫ ∈ (0, 1] is taken in evaluation, as long as above conditions are met.

5.2.

A Hybrid Scheme

This subsection introduces another ‘hybrid’ scheme developed by [80]. In this scheme, the option price will be derived via Fourier inversion of the characteristic function(henceforth sometimes called ch.f.) of the log-forward forex. Since the underlying framework of a standard cross-currency model with libor market models we are discussing is too complicated to obtain the closed-form solution of the ch.f., we approximate it with the asymptotic expansion. Moreover, in order to increase accuracy of our method, a certain change of the probability measure and a transformation of variable will be also applied, those are reasons why the method is called ‘hybrid’. Finally, the asymptotic expansion will be used as a control variable in Monte Carlo simulations to accelerate their convergence.

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5.2.1.

A Pricing Problem Revisited

In this subsection, we allow existence of the martingale A˜ possibly with jumps and independent of Wiener processes we have defined, which will be somewhat restricted later. Our objective is to evaluate the following quantity;   V(0; K, T ) = Pd (0, T ) × EP (FT (T ) − K)+ .

(58)

(t) ), (58) can be rewritten as: With a log-price of the forex forward fT (t) := ln( FFTT (0)

h i V(0; K, T ) = Pd (0, T ) × FT (0) EP (e fT (T ) − ek )+ where k := ln( FTK(0) ) denotes a log-strike rate. Here we note that e fT (T ) = FT (T ) is a martingale under the domestic terminal measure. Carr and Madan [10] proposed another expression of option prices as some Fourier inversion of the characteristic function of the logarithm of the underlying asset. Proposition 3 Let ΦTP (u) denote a characteristic function of fT (T ) under P. V(0; K, T ) is given by: V(0; K, T ) = Ψ(ΦTP ; FT (0), K, T )

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Then, (59)

204

Akihiko Takahashi and Kohta Takehara

where # Z ∞ 1 −iuk + e γ(u; Φ)du + (F − K) , Ψ(Φ; F, K, T ) := Pd (0, T ) × F 2π −∞ √ Φ(u − i) − 1 γ(u; Φ) := and i := −1. iu(1 + iu) "

(60) (61)

Then, we need to know the characteristic function of fT (T ) under the domestic terminal measure P for pricing the option. In particular, in our setting the log-forex forward fN+1 (t) = N+1 (t) ln( FFN+1 (0) ) follows fN+1 (t) = ln(

F N+1 (t) ) = Z(t) + A(t) F N+1 (0)

where Z(t) is an exponential-martingale continuous process given by Z Z t ′ 1 t 2 ˜ Z (s)|| ds + σ ˜ Z (s)dW s Z(t) = − ||σ 2 0 0

(62)

(63)

where σ ˜ Z (t) :=

 X  g˜ f j (t) − g˜ d j (t) +σ(t) ˜ σ ¯

j∈ JˆN+1

=

X

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j∈ JˆN+1

! −τ j f f j (t)˜γ f j (t) −τ j fd j (t)˜γd j (t) − + σ(t) ˜ σ ¯ 1 + τ j f f j (t) 1 + τi fd j (t)

and A(t) denotes a continuous or jump process that is an exponential-martingale independent from Z(t) which is directly derived by application of Ito’s ˆ fornula. Further, we assume that the characteristic function of A(t) is known in closed-form. e.g. A(t) is a compound Poisson process, a variance gamma process, an inverse Gaussian process, a CGMY model or a L´evy process appearing in the Stochastic Skew Model(Carr and Wu [11]). 5.2.2.

A Transformation of the Underlying Stochastic Differential Equations

Let ΦPN+1 (t, u) denote the characteristic function of fN+1 (t) under P. Then, ΦPN+1 (t, u) can be decomposed as; (64) ΦPN+1 (t, u) = ΦZP (t, u)ΦPA (t, u) where ΦZP (t, u) and ΦPA (t, u) denote the characteristic functions of Z(t) and A(t) under P, respectively. For evaluation of European currency options, an explicit expression of ΦPN+1 (T, u) is necessary. However, the process Z(t) is too complicated to obtain the analytical expression ¨ [9] ) of ΦZP (T, u) (see Section 6.3.2 in Brigo and Mercurio [8] or Section 25.5 in Bjork while that of ΦPA (T, u) is assumed to be known. Then, later we will suggest to utilize the asymptotic expansion for the approximation of ΦZP (T, u). In (63), Z(t), the key process for evaluation of options, has a nonzero drift. Thus, unless we provide the approximation which has not any error in the drift term, even the first moment(i.e. the expectation value) of that approximation will not match the target’s.

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Contrarily, if we can eliminate its drift term by some means, that is the objective process will be a martingale, its first moment can be much easily kept by using a martingale process as an approximation. In this light, here we consider a certain change of measures so that the main objective process of our expansion will be martingale. For a fixed u(an argument of ΦZP (T, u)) we define a new probability measure Qu on (Ω, FT ) with the Radon-Nikodym derivative of ! Z Z T ′ dQu 1 T 2 = exp − λu (s)dW s (65) ||λu (s)|| ds − dP 2 0 0 where   p ˜ σ λu (t) := (−iu) + i u2 + iu σ ˜ Z (t) = h(u) ˜ Z (t)

√ ˜ and h(u) := (−iu) + i u2 + iu. Then ΦZP (T, u), the characteristic function of Z(T ) under the measure P, is expressed as ˆ ) under Qu with a transformation of variable h(·): that of another random variable Z(T   ΦZP (T, u) = EP exp (iuZ(T )) " !# Z T ′ Qu Qu = E exp ih(u) σ ˜ Z (s)dW s 0

=: ΦQˆ u (T, h(u))

(66)

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Z

Rt ′ where EQu [·] is an expectation operator under Qu ; WtQu := Wt + 0 λu (s)ds is now a Wiener process under that measure; ΦQˆ u (t, v) denotes the characteristic function of Z√ R ′ Qu ˆ := t σ Z(t) ˜ (s)dW under Q and h(u) := u2 + iu. u s 0 Z Now, we have the martingale objective process for the approximation. Then, in the following, we will apply the asymptotic expansion method to the underlying system of stochastic differential equations under Qu . 5.2.3.

Approximating the Characteristic Function by an Asymptotic Expansion

Here, to fit the framework of the asymptotic expansion, the processes of fd(ǫ)j (t), f f(ǫ)j (t) and σ(ǫ) (t) in (38), (41) and (42) are again redefined under the measure Qu with a parameter ǫ as follows; for j = n(t) − 1, n(t), n(t) + 1, · · · , N, Z t N X ′ (ǫ) (ǫ) 2 fd j (t) = fd j (0) + ǫ fd j (s)γd j (s) g(ǫ) di (s)ds 0

2˜

−ǫ h(u) f f(ǫ)j (t)

=

f f(ǫ)j (0)

Z

t 0

+ǫ

˜ −ǫ 2 h(u)

Z

2

t 0

i= j+1

′ fd(ǫ)j (s)γd j (s)σ(ǫ) Z (s)ds

Z

t 0

+ǫ

t

Z

′

fd(ǫ)j (s)γd j (s)dW sQu

(67) 0         X   ′  X (ǫ)  (ǫ) (ǫ) (ǫ) − g (s) + g (s) − σ (s) σ ¯ ds f f j (s)γ f j (s)     f i di       i∈ Jˆj+1

′

f f(ǫ)j (s)γ f j (s)σ(ǫ) Z (s)ds + ǫ

i∈ JˆN+1

Z

0

t

′

f f(ǫ)j (s)γ f j (s)dW sQu

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Akihiko Takahashi and Kohta Takehara

and (ǫ)

σ (t) = σ(0) +

Z

0

t (ǫ)

2˜

µ (s)ds − ǫ h(u)

Z

t

′

(ǫ)

ω (σ

0

(s), s)σ(ǫ) Z (s)ds + ǫ

Z

t

′

ω (σ(ǫ) (s), s)dW sQu .

0

ˆ Then Zˆ (ǫ) (t), the analogy of Z(t), is given by Z t ′ Qu (ǫ) ˆ Z (t) = ǫ σ(ǫ) Z (s)dW s

(69)

(70)

0

where σ(ǫ) Z (t) :=

 X  (ǫ) g(ǫ) (t) − g (t) +σ(ǫ) (t)σ. ¯ fj dj

j∈ JˆN+1

In a similar manner to the standard method in the previous subsection, we can derive the following asymptotic expansion (for details and concrete expressions of expansion coefficients, see Appendix of [80]). = 1ǫ Zˆ (ǫ) (T ) up to ǫ 2 is expressed as folProposition 4 The asymptotic expansion of G(ǫ) Zˆ lows: ˆ Qu ,h1i + G(ǫ) ˆ = GT Z

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where Gˆ TQu ,hki :=

∂k Zˆ (ǫ) (T ) |ǫ=0 , ∂ǫ k

ǫ ˆ Qu ,h2i ǫ 2 ˆ Qu ,h3i + GT + o(ǫ 2 ) G 2! T 3!

(71)

k = 1, 2, 3.

Remark 2 Gˆ TQu ,hki for any k is expressed as a certain (iterated) Itˆo integral. Since (iterated) (and hence Zˆ (ǫ) (t)) is Itˆo integrals always have zero means, the martingale property of G(ǫ) Zˆ kept at any order of this expansion. Especially, the first-order term Gˆ TQu ,h1i follows a normal distribution with mean 0 and variance Σ: Z T N+1

(0)

2 (72) Σ :=

σZ (s) ds. 0

Here it is assumed that Σ > 0.

Then, letting Φ in Section 3.1. be Φ(x) = eivx for given v, the desired characteristic function can be approximated with the following theorem (for its proof and the concrete expressions of coefficients, again refer to Appendix of [80]). Theorem 3 An asymptotic expansion of ΦGQuˆ ,(ǫ) (v), the characteristic function of G(ǫ) under Zˆ Z Qu , is given by h ΦGQuˆ ,(ǫ) (v) = 1 + D2Qu ,(ǫ) (iv)2 + D3Qu ,(ǫ) (iv)3 + D4Qu ,(ǫ) (iv)4 + D5Qu ,(ǫ) (iv)5 Z i +D6Qu ,(ǫ) (iv)6 Φ0,Σ (v) + o(ǫ 2 )

(73)

Σ 2

where Φµ,Σ (v) := eiµv− 2 v . D2Qu ,(ǫ) , D3Qu ,(ǫ) , D4Qu ,(ǫ) , D5Qu ,(ǫ) and D6Qu ,(ǫ) are constants for pre-specified ǫ and u. Each subscript corresponds to the order of (iv) in the equation (73).

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Remark 3 Rigorously speaking, the specification Φ(x) = eivx does not fit in the framework in Section 3.1. Actually, h however, n oi the approximate characteristic function obtained by formal expansion of E exp ivG(ǫ) is completely the same as that given by the inversion of Zˆ approximate probability density function in our framework with letting Φ be δ x , the delta function with a mass at x. For more details about this equivalence, see Section 6 of [81]. Finally, we provide an approximation formula for valuation of European call options written (ǫ) on F N+1 (T ) by direct application of Theorem 3 to Proposition 3. ˆ K, T ) be an approximated value of V(0; K, T ) which denotes the exact Theorem 4 Let V(0; ˆ K, T ) is given by: value of the option with maturity T = T N+1 and strike rate K. Then, V(0; ˆ (ǫ) ; F N+1 (0), K, T ) ˆ K, T ) := Ψ(Φ V(0;

(74)

ˆ (ǫ) (u) := Φ ˆ Qu ,(ǫ) (ǫh(u))×ΦP (u), where the pricing functional Ψ( · ; F, K, T ) is given in (60), Φ A GZˆ Qu ,(ǫ) K ˆ ). Here, Φ (v) is defined as; and k := ln( F N+1 (0)

GZˆ

ˆ Qu ,(ǫ) (v) = 1 + DQu ,(ǫ) (iv)2 + DQu ,(ǫ) (iv)3 + DQu ,(ǫ) (iv)4 + DQu ,(ǫ) (iv)5 + DQu ,(ǫ) (iv)6 Φ Gˆ 4 3 2 6 5 Z

h

i

×Φ0,Σ (v)

where D2Qu ,(ǫ) , D3Qu ,(ǫ) , D4Qu ,(ǫ) , D5Qu ,(ǫ) and D6Qu ,(ǫ) are the coefficients in Theorem 3.

Remark 4 Note that since h(−i) = 0 and A is assumed to be an exponential martingale, (ǫ) ˆ (ǫ) (−i) = Φ ˆ Q−i ,(ǫ) (ǫh(−i)) × ΦP (−i) = 1, EP [e fN+1 (T N+1 ) ] = ΦP,(ǫ) (u) is approximated by Φ A Gˆ Z

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(ǫ) is kept. which means that in our approximation the exponential-martingale property of fN+1 Especially, when A ≡ 0 the first-order approximation of the option price coin1 cides BS (Σ 2 ; F N+1 (0), K, T ) which is the Black-Scholes price under the case where the stochastic interest rates and the stochastic volatility would be replaced by (their limiting)deterministic processes:

BS (σ; F, K, T ) := Pd (0, T ) [FN(d+ ) − KN(d− )]

(75)

where d± :=

ln(F/K) ± 21 σ2 T , N(x) := √ σ T

Z

x −∞

1 2 1 √ e− 2 z dz. 2π

Moreover, in this case(A ≡ 0), the pricing functional can be modified so that the numerical inversion is stabilized as follows; ˜ TP ; F N+1 (0), K, T N+1 ) V(0; K, T N+1 ) = Ψ(Φ

(76)

where " Z ∞   # 1 1 ˜ Ψ(Φ; F, K, T ) := Pd (0, T ) × F e−iuk γ(u; Φ) − γ(u; ΦBS ) du + BS (Σ 2 ; F, K, T ), 2π −∞ and ΦBS (u) is the first-order-approximated characteristic function, or equivalently that of the (hypothetical)Gaussian underlying log-forward forex; ΦBS (u) := Φ0,Σ (h(u)) = Φ− 1 Σ,Σ (u). 2

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Remark 5 Using these approximation formulas, we can also provide analytical approximations of Greeks of the option, sensitivities of the option price to the factors. Note that our approximation for the underlying characteristic function does not depend upon the initial value of the spot forex. Thus in particular, ∆ and Γ, the first and second derivatives of the option value with respect to S (0) respectively, can be explicitly approximated with ease. ˆ the approximations of ∆ and Γ For simplicity here we again assume A ≡ 0. Then ∆ˆ and Γ, respectively, are given by

P f (0, T ) S (0)

1 2π

Z

∞

  ˆ (ǫ) ) − γ(u; ΦBS ) du e−iuk γ(u; Φ −∞ Z ∞   ) 1 −iuk (ǫ) ˆ − (−iu)e γ(u; Φ ) − γ(u; ΦBS ) du + ∆BS , 2π −∞ ( Z ∞   1 ˆ (ǫ) ) − γ(u; ΦBS ) du × (−iu)e−iuk γ(u; Φ 2π −∞ Z ∞   ) 1 2 −iuk (ǫ) ˆ − (−iu) e γ(u; Φ ) − γ(u; ΦBS ) du + ΓBS , 2π −∞

∆ˆ := P f (0, T ) ×

Γˆ := −

(

where ∆BS and ΓBS are the risk sensitivities of the Black-Scholes price 1 BS (Σ 2 ; F N+1 (0), K, T ) given by

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∆BS = P f (0, T )N ′ (d+ ) and ΓBS =

P f (0, T ) ′ √ N (d+ ). S (0) ΣT

For other risk parameters such as Θ or Vega, sensitivities of the option price with respect to t and σ(0) respectively, their approximations are given in easy ways such as the difference quotient method, which needs few seconds for calculation with our closed-form formula and has satisfactory accuracies. 5.2.4.

A Characteristic-function-based Monte Carlo Simulation with an Asymptotic Expansion

Here we will introduce a Monte Carlo (henceforth sometimes called M.C.) simulation scheme which incorporates the analytically obtained characteristic function. Further, with the asymptotic expansion as a control variable, the variance of this characteristic-functionbased(ch.f.-based) M.C. is reduced. In a usual M.C. procedure, we discretize the stochastic differential equations (38), (41), (ǫ) (42) and (62), and generate { f j } M j=1 , M samples of fN+1 (T ) (hereafter F N+1 (0) will be abbreviated by F(0)). Then the approximation for the option value, the discounted average of terminal payoffs, is obtained by; M 1 X fj payo f f Vˆ MC (0, M; K, T ) := Pd (0, T ) (e − K)+ . M j=1

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On the other hand, via the pricing formula (59) in Proposition 3, the option price can be expressed with the pricing functional Ψ( · ; F, K, T ) substituted the characteristic function of the underlying log-process into: V(0; K, T ) = Ψ(ΦP,(ǫ) ; F(0), K, T ) # " Z ∞ 1 −iuk + e γ(u; Φ)du + (F − K) . where Ψ(Φ; F, K, T ) = Pd (0, T ) × F 2π −∞  (ǫ)  h (ǫ) i h i Since ΦP,(ǫ) (u) is defined by EP eiu fN+1 (T ) = EP eiuZ (T ) × EP eiuA(T ) , the alternative approximation with M.C. can be constructed; ch f ˆ P ( · ; M); F(0), K, T ) Vˆ MC (0, M; K, T ) := Ψ(Φ MC   M  1 X  j  ΦP (u) iuZ  ˆ P (u; M) = Φ ˆ P (u; M) × ΦP (u) :=  Φ e  A MC Z,MC A M

(78) (79)

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j=1

(ǫ) where {Z j } M j=1 are samples of Z (T ). Here it is stressed that in this approximation there does not exist any error caused by M.C. for the (jump or continuous) part A. Further, this ch.f.-based scheme can be much refined through the better estimation for P,(ǫ) ΦZ (u) by M.C., achieved with our asymptotic expansion of the first order. Since ΦZP,(ǫ) (u) is expressed as ΦGQuˆ ,(ǫ) (ǫh(u)), it is done by the approximation of ΦGQuˆ ,(ǫ) (ǫh(u)) with M.C.. Z Z In what follows in this section, we abbreviate ǫ(or set ǫ = 1) for simplicity and use the notation g1 = Gˆ TQu ,h1i , the first order coefficient of the expansion (71). Here, in order to avoid the influence appearing in this variance reduction procedure caused by the variable transformation h(·), we use the following relationship ! h i h i 1 EQu eih(u)g1 = exp − iuΣ EQu eiug1 , (80) 2

  i.e. ΦgQ1u (h(u)) = exp − 21 iuΣ × ΦgQ1u (u). ΦgQ1u (v) is the characteristic function of g1 , which is ˆ Qu ,(ǫ) (v) in Theorem 3 if the expansion were made only up to the first order. equivalent to Φ GZˆ

This equation can be easily checked with recalling ΦgQ1u (v) = Φ0,Σ (v) = exp(− Σ2 v2 ). Thus on the one hand, the closed-form characteristic function of g1 evaluated at v = h(u) is given by ! 1 Qu (81) Φg1 (h(u)) = exp − iuΣ Φ0,Σ (u). 2 But on the other hand, generating samples of g1 following N(0, Σ), {g j } M j=1 , we can further approximate the right hand side of (80) by ! X M  j 1 1 Qu ˆ Φg1 ,MC (u; M) := exp − iuΣ eiug . 2 M j=1

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(82)

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Note that because only the distribution of g1 matters here, we can simulate samples RT ′ of g˜ 1 := 0 σ(0) Z (s)dW s following N(0, Σ) under P instead of those of g1 , not under the measure Qu but under P as well as other random variables simulated for (79). Using two functions in (81) and (82), which both are the first-order approximations for ΦZQu ,(ǫ) (h(u)), define two following estimators for the option price.   AE Vˆ ana (0; K.T ) := Ψ ΦgQ1u (h(·)) × ΦPA ; F(0), K, T (83)  Q  AE ˆ u ( · ; M) × ΦP ; F(0), K, T Vˆ MC (0, M; K, T ) := Ψ Φ (84) A g1 ,MC Finally, using ΦgQ1u (h(u)) as a control variable, we can construct the more sophisticated estimator Vˆ CV (0, M; K, T ) for the option price V(0; K, T ) as   ch f AE AE Vˆ CV (0, M; K, T ) := Vˆ MC (0, M; K, T ) + Vˆ ana (0; K, T ) − Vˆ MC (0, M; K, T ) (85) n  Q o  Q P P u ˆ ˆ u = Ψ Φ Z,MC ( · ; M) + Φg1 (h(·)) − Φg1 ,MC ( · ; M) × ΦA ; F(0), K, T where T = T N+1 and M 1 X iuZ j e , M j=1 ! 1 ΦgQ1u (h(u)) = exp − iuΣ × Φ0,Σ (u), 2 ! M 1 1 X  iug j  Qu ˆ Φg1 ,MC (u; M) = exp − iuΣ × e . 2 M j=1

ˆ P (u; M) = Φ Z,MC

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Remark 6 Here we note the following fact. V(0; K, T ) − Vˆ CV (0, M; K, T )     ch f AE AE = V(0; K, T ) − Vˆ MC (0, M; K, T ) − Vˆ ana (0; K, T ) − Vˆ MC (0, M; K, T ) o    n ˆ Qu (h(·); M) × ΦP ; F(0), K, T ˆ P ( · ; M) − ΦgQu (h(·)) − Φ = Ψ ΦZP,(ǫ) − Φ A Z,MC 1 g1 ,MC where ΦZP,(ǫ) is the exact characteristic function of Z (ǫ) (T ). The former in the first parentheses is the exact characteristic function of Z (ǫ) (t) and the latter is its approximation by Monte Carlo simulations. Similarly, the former in the second parentheses is the exact one of g1 , the first-order expansion for Z (ǫ) (t), and the latter is its approximation. Thus, in the case where the first and second term in the braces cancel each other out, the error of our hybrid estimator is expected to be small. Remark 7 We here also summarize the procedures introduced in this section. 1. Discretize the processes of fd(ǫ)j (t), f f(ǫ)j (t), σ(ǫ) (t) and of Z (ǫ) (t) under P and generate (ǫ) {Z j } M j=1 , M samples of Z (T ). RT ′ 2. Also generate {˜g j } M ˜ 1 = 0 σ(0) Z (s)dW s instead of g1 , under P with the j=1 , samples of g same sequence of random numbers used in 1. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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ˆ P (u; M) with {Z j } for each u, which is the characteristic function of 3. Calculate Φ Z,MC Z (ǫ) (T ) approximated by M.C.. ˆ Qu (u; M) with {˜g j } for each u, the approximation for 4. Similarly calculate Φ g1 ,MC ΦgQ1u (h(u))by M.C..

5. Using the estimators calculated in 3. and 4., approximate ΦZP,(ǫ) (u) by   ˆ P (u; M) + ΦgQu (h(u)) − Φ ˆ Qu (u; M) Φ Z,MC 1 g1 ,MC where ΦgQ1u (u) is the exact characteristic function of g1 given in closed-form. 6. Inverting the estimated characteristic function in 5. via the pricing functional Ψ( · ; F(0), K, T ) given in (60), we finally obtain the estimator for the option price with the first-order asymptotic expansion as a control variable.

6.

Numerical Examples

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This section examines the effectiveness of our methods through some numerical examples. First, the underlying framework is specified clearly. Then, the approximate option prices by our methods are compared to their estimates by Monte Carlo simulations. Moreover, our formula is applied to calibration of volatility surfaces observed in the JPY/USD currency option market. Finally, the examples of the variance reduction by the proposed ch.f.-based Monte Carlo simulations with the asymptotic expansion as a control variable is shown.

6.1.

Model Specification

First of all, the processes of domestic and foreign forward interest rates and of the volatility of the spot exchange rate are specified. We suppose D = 4, that is the dimension of the Wiener process is set to be four; it represents the uncertainty in domestic and foreign interest rates, the spot exchange rate, and its volatility. Note that in our framework correlations among all factors are allowed. Next, we specify a volatility process, not a variance process as in affine-type models, of the spot exchange rate under the domestic risk-neutral measure as follows; σ(ǫ) (t) = σ(0) + κ

Z

t 0

(θ − σ(ǫ) (s))ds + ǫω

′

Z

t 0

p ˆs σ(ǫ) (s)dW

(86)

where θ and κ represent the level and speed of its mean-reversion respectively, and ω denotes a volatility vector on the volatility. In this section the parameters are set as follows; ǫ = 1, σ(0) = θ = 0.1, and κ = 0.1; ω = ω∗ v¯ where ω∗ = 0.1 and v¯ denotes a four dimensional constant vector given below.

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We further suppose that initial term structures of domestic and foreign forward interest rates are flat, and their volatilities also have flat structures and are constant over time: that is, for all j, fd j (0) = fd , f f j (0) = f f , γd j (t) = γd∗ γ¯ d 1{t 242) Crisis −0.18 4.04 0.86∗∗∗ 8.56 −0.49 8.71 1.15∗∗ 1.62 −0.49 −0.64 0.52 658

Diff. −0.27 1.84 0.58∗∗∗ 14.38 0.47 3.68 0.00 −1.08 −0.84 −1.87

The values in the table are obtained by running a pooled OLS regression for all observations in the selected period and quartile of the firms’ average leverage, with standard errors that allow for time correlation at firm level. Monthly data from January 2002 to March 2009; the pre-crisis period goes from January 2002 to June 2007; the post-crisis period from July 2007 to March 2009. The explanatory variables are changes of monthly averages of: the estimated theoretical spread for firm i at time t; the implied volatility of options written on the stocks of firm i at time t; the leverage ratio of firm i at time t; the 5-year zero-coupon interest rate on US government bond rate at time t; the log of the stock value of firm i at time t; the slope of the zero-coupon curve on US government bonds (10-1 yrs) at time t; the Merrill Lynch industrial bond average spread (BBB-AA) at time t; the log of the S&P Composite stock index at time t; the VIX volatility index at time t; a constant term. Observed and theoretical spreads and the corporate spread are in basis points, all other variables are in percentages. Significance levels: *** = 1%; ** = 5%; * = 10%.

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Table 7. The Determinants of CDS Spread Changes by Sector

Industrial

Theoretical spread Volatility Leverage Interest rate Stock return Slope of yield curve Corporate spreads S&P Composite VIX Intercept Adjusted R2 No. obs.

Pre Crisis Crisis Diff. ∗∗ 0.27 0.04 −0.22∗ ∗∗ −0.71 1.33 2.04∗ 0.14 0.51 0.37∗ 0.12 −21.34∗∗∗ −21.46∗∗∗ ∗ −0.49 −0.11 0.37 1.08 −0.14 −1.22 0.41∗∗∗ 0.36∗ −0.05 0.40 −0.35 −0.75 ∗∗ 0.41 −1.81 −2.21∗∗ 0.11 −2.87 −2.98 0.33 0.40 1,416 568

Communications & Technology Pre Crisis Crisis Diff. ∗∗∗ 0.16 0.05 −0.11 0.01 0.20 0.18 0.89∗∗∗ 0.81∗∗∗ −0.08 −9.95∗∗ −44.12∗ −34.17 −0.55∗ 0.40 0.96 10.39∗∗ −8.36 −18.75 0.71∗∗∗ 1.13∗∗∗ 0.42 ∗∗∗ 2.02 0.66 −1.36 2.02∗∗ −0.87 −2.89 −0.16 −5.28 −5.12 0.46 0.18 1,328 410

Basic materials & Energy Pre Crisis Crisis Diff. 0.04 0.05 0.02 0.12 0.34 0.22 0.41∗ 0.36∗∗∗ −0.05 −1.53 −30.19∗∗∗ −28.66∗∗∗ 0.07 −0.46∗ −0.53∗ 2.03 2.21 0.18 ∗∗∗ ∗∗∗ 0.51 0.29 −0.23 0.45∗ 0.06 −0.39 ∗ ∗ 0.56 −1.08 −1.64∗∗ 0.29 −1.48 −1.77 0.25 0.50 1,432 541

The values in the table are obtained by running a pooled OLS regression for all observations in the selected sector and period, with standard errors that allow for time correlation at firm level. Monthly data from January 2002 to March 2009; the pre-crisis period goes from January 2002 to June 2007; the post-crisis period from July 2007 to March 2009. The explanatory variables are changes of monthly averages of: the estimated theoretical spread for firm i at time t; the implied volatility of options written on the stocks of firm i at time t; the leverage ratio of firm i at time t; the 5-year zero-coupon interest rate on US government bond rate at time t; the log of the stock value of firm i at time t; the slope of the zero-coupon curve on US government bonds (10-1 yrs) at time t; the Merrill Lynch industrial bond average spread (BBB-AA) at time t; the log of the S&P Composite stock index at time t; the VIX volatility index at time t; a constant term. Observed and theoretical spreads and the corporate spread are in basis points, all other variables are in percentages. Significance levels: *** = 1%; ** = 5%; * = 10%.

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Table 7. Continued

Consumer Cyclical

Theoretical spread Volatility Leverage Interest rate Stock return Slope of yield curve Corporate spreads S&P Composite VIX Intercept Adjusted R2 No. obs.

Pre Crisis 0.06 2.11∗ 0.30∗∗∗ 0.00 −0.75∗∗∗ −2.27 0.90∗∗∗ 1.67∗∗ 0.05 0.70 0.64 2,026

Crisis −0.14 2.57 0.94∗∗∗ 19.49 −1.86 16.89 1.45∗∗∗ 2.11 −0.25 −4.04 0.62 726

Consumer Non cyclical Diff. −0.19 0.46 0.63∗∗∗ 19.48 −1.11 19.16 0.55 0.44 −0.30 −4.74

Utilities

Pre Pre Crisis Crisis Diff. Crisis Crisis Diff. 0.11 0.07∗∗ −0.04 0.40∗∗∗ 0.08∗∗∗ −0.33∗∗∗ 1.01∗∗∗ 0.03 −0.97∗∗ −0.50 −0.54 −0.03 ∗∗∗ ∗∗∗ −0.16 0.23 0.39∗∗∗ 0.74∗∗ −0.21 −0.95∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ −2.42 −25.43 −23.01 −14.18 −31.25 −17.06∗ ∗ ∗∗∗ ∗∗∗ −0.60 −0.64 −0.04 0.79 −1.26 −2.04∗∗ ∗∗∗ ∗∗ ∗∗∗ 3.98 19.41 15.44 23.40 −2.32 −25.72∗∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ 0.16 0.19 0.03 0.75 0.41 −0.34 −0.10 0.89∗∗∗ 0.99∗∗ 1.51 1.83∗∗∗ 0.32 −0.66 0.42 1.08 1.75 1.90∗∗∗ 0.15 0.57 −4.19∗∗∗ −4.75∗∗∗ 0.79 −0.82 −1.61 0.20 0.57 0.74 0.40 1,285 467 653 232

The values in the table are obtained by running a pooled OLS regression for all observations in the selected sector and period, with standard errors that allow for time correlation at firm level. Monthly data from January 2002 to March 2009; the pre-crisis period goes from January 2002 to June 2007; the post-crisis period from July 2007 to March 2009. The explanatory variables are changes of monthly averages of: the estimated theoretical spread for firm i at time t; the implied volatility of options written on the stocks of firm i at time t; the leverage ratio of firm i at time t; the 5-year zero-coupon interest rate on US government bond rate at time t; the log of the stock value of firm i at time t; the slope of the zero-coupon curve on US government bonds (10-1 yrs) at time t; the Merrill Lynch industrial bond average spread (BBB-AA) at time t; the log of the S&P Composite stock index at time t; the VIX volatility index at time t; a constant term. Observed and theoretical spreads and the corporate spread are in basis points, all other variables are in percentages. Significance levels: *** = 1%; ** = 5%; * = 10%.

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Table 8. The Determinants of CDS Spread Changes by Liquidity Change

1st quartile (< −0.9)

Theoretical spread Volatility Leverage Interest rate Stock return Slope of yield curve Corporate spreads S&P Composite VIX Intercept Adjusted R2 No. obs.

2nd quartile (−0.9 − 1.1)

3rd quartile (1.1 − 5.5)

4th quartile (> 5.5)

Pre Pre Pre Pre Crisis Crisis Diff. Crisis Crisis Diff. Crisis Crisis Diff. Crisis Crisis 0.25∗∗∗ 0.02 −0.23∗∗ 0.20∗∗∗ 0.04∗ −0.16∗∗ 0.21∗∗∗ 0.01 −0.20∗∗∗ 0.20∗∗∗ −0.22 0.07 0.36 0.29 0.44∗∗ 0.07 −0.37 −0.06 0.72∗ 0.77 −0.04 3.76 ∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗ 0.26 1.46 1.21 0.11 0.65 0.55 0.09 0.32∗∗∗ 0.23∗ 0.43∗∗∗ 0.86∗∗∗ −6.65∗∗ −18.20∗∗∗ −11.55∗∗∗ −0.87 −17.03∗∗∗ −16.16∗∗∗ −2.01∗∗ −24.84∗∗∗ −22.83∗∗∗ −1.08 9.14 ∗ ∗∗ ∗∗ −0.66 0.86 1.52 −0.13 0.16 0.28 −0.03 −0.33 −0.30 −0.71∗∗∗ −0.63 10.84∗∗∗ 7.93∗∗ −2.91 −0.52 6.73∗∗∗ 7.25∗∗∗ 2.01 4.92 2.92 −1.13 3.76 ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ 0.65 0.2 −0.45 0.15 0.24 0.09∗ 0.38∗∗∗ 0.74∗∗∗ 0.36∗∗∗ 0.84∗∗∗ 1.58∗∗∗ 0.91∗∗ 0.57∗ −0.33 0.11 0.03 −0.08 0.41∗∗∗ 0.41 0.00 2.18∗∗∗ 0.31 ∗∗ ∗ ∗∗∗ 0.50 0.46 −0.04 0.09 −0.07 −0.16 0.92 −0.81 −1.73 1.42∗ 0.07 0.28 −3.37∗∗∗ −3.65∗∗∗ −0.26 −3.17∗∗∗ −2.91∗∗∗ −0.03 −4.01∗∗∗ −3.98∗∗∗ 0.13 −3.11 0.51 0.48 0.21 0.43 0.33 0.41 0.47 0.52 2,155 709 1,953 750 1,757 733 1,811 752

Diff. −0.42 3.81 0.43∗∗ 10.21 0.08 4.90 0.75 −1.87 −1.36 −3.24

The values in the table are obtained by running a pooled OLS regression for all observations in the selected period and quartile of the firms’ liquidity change, with standard errors that allow for time correlation at firm level. The liquidity change is defined as the change in the average bid-ask spread of the CDSs, at the firm level, from before to after the onset of the crisis. Monthly data from January 2002 to March 2009; the pre-crisis period goes from January 2002 to June 2007; the post-crisis period from July 2007 to March 2009. The explanatory variables are changes of monthly averages of: the estimated theoretical spread for firm i at time t; the implied volatility of options written on the stocks of firm i at time t; the leverage ratio of firm i at time t; the 5-year zero-coupon interest rate on US government bond rate at time t; the log of the stock value of firm i at time t; the slope of the zero-coupon curve on US government bonds (10-1 yrs) at time t; the Merrill Lynch industrial bond average spread (BBB-AA) at time t; the log of the S&P Composite stock index at time t; the VIX volatility index at time t; a constant term. Observed and theoretical spreads and the corporate spread are in basis points, all other variables are in percentages. Significance levels: *** = 1%; ** = 5%; * = 10%.

262

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6.

Antonio Di Cesare and Giovanni Guazzarotti

Conclusion

In this paper we analyze the determinants of CDS spread changes (for a sample of 167 US non-financial firms over the period between January 2002 and March 2009) using the variables that the literature has found to have a theoretical and empirical impact on CDS spreads. We also include in our regressions the theoretical spread implied by the Merton model in order to deal with the non-linear relationships between the individual characteristics of the firms and CDS spreads. We find that the inclusion of this additional term improves the capacity of changes in the fundamental variables to explain changes in CDS spreads. When the theoretical spread calculated using Merton model is introduced in the regressions, the coefficient of the equity volatility decreases significantly, because of the high sensitivity of Merton model to this parameter. On the contrary, leverage, which has only second-order effects on the theoretical spreads, maintains its usefulness in explaining CDS spreads changes. The extended model is able to explain 54% of the variations in CDS spreads in the pre-crisis period and 51% in the crisis period, which is higher than previous findings of studies on corporate bond and CDS spread changes. We also analyze how the financial crisis has changed the way in which credit risk is priced in the CDS market. We find that the contribution of the leverage of the firms to the explanation of CDS spread changes is much higher during the crisis than before, as investors appear to have become more aware of individual risk factors. At the same time, the impact of equity volatility substantially decreases, possibly because the large swings in implied volatility during the crisis period have made this indicator a poor proxy for long-term asset volatility. We also find that the overall capacity of the model to explain CDS changes is almost the same before and during the turmoil, thus highlighting that the underlying risk factors identified by the literature as relevant for the pricing of the credit risk have maintained their explanatory power also in a period of remarkable stress for the CDS market. Finally, we also show that during the crisis CDS spreads appear to have been moving increasingly together, driven by a common factor that our model was able to explain only in part. Given that the model includes general indicators of economic activity, uncertainty, and risk aversion, our results seem to point to the presence of a market-specific factor that hit the CDS market during the crisis in forms not fully reflected in other markets. The exact identification of this factor is an interesting topic for further research.

References [1] Abid, F., & Naifar, N. (2006). The determinants of credit default swap rates: An explanatory study. International Journal of Theoretical and Applied Finance, 9 (1), 23-42. [2] Alexander, C., & Kaeck, A. (2008). Regime dependent determinants of credit default swap spreads. Journal of Banking & Finance, 32 (6), 1008-1021. [3] Amato, J., & Remolona, E. M. (2005). The Pricing of Unexpected Credit Losses. BIS Working Papers, No. 190.

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263

[4] Anderson, R., & Sundaresan, S. (2000). A Comparative Study of Structural Models of Corporate Bond Yields: An Explanatory Investigation. Journal of Banking & Finance, 24 (1-2), 255-269. [5] Annaert, J., De Ceuster, M., Van Roy, P., & Vespro, C. (2009). What determines euro area bank CDS spreads? In National Bank of Belgium, Financial Stability Review. [6] Aunon-Nerin, D., Cossin, D., Hricko, T., & Huang, Z. (2002). Exploring for the determinants of credit risk in credit default swap transaction data: Is fixed-income markets’ information sufficient to evaluate credit risk? FAME Research Paper Series, No. 65. [7] Avramov, D., Jostova, G., & Philipov, A. (2007). Understanding changes in corporate credit spreads. Financial Analysts Journal, 63 (2), 90-105. [8] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81 (3), 637-654. [9] Blanco, R., Brennan, S., & Marsh, I. W. (2005). An empirical analysis of the dynamic relationship between investment-grade bonds and credit default swap. Journal of Finance, 60 (5), 2255-2281. [10] Bystr¨om, H. (2006). CreditGrades and the iTraxx CDS index market. Financial Analysts Journal, 62 (6), 65-76. [11] Campbell, J. Y., & Taksler, G. B. (2003). Equity volatility and corporate bond yields Journal of Finance, 58 (6), 2321-2349.

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[12] Collin-Dufresne, P., Goldstein, R. S., & Martin, J. S. (2001). The determinants of credit spread changes. The Journal of Finance, 56 (6), 2177-2207. [13] Committee on the Global Financial System (2003). Credit risk transfer, Bank for International Settlements. [14] Cossin, D., & Pirotte, H. (2001). Advanced credit risk analysis. Chichester, UK: John Wiley & Sons, Ltd. [15] Cremers, M., Driessen, J., Maenhout, P., & Weinbaum, D. (2008). Individual stockoption prices and credit spreads. Journal of Banking & Finance, 32 (12), 2706-2715. [16] Di Cesare, A. (2005). Do market-based indicators anticipate rating agencies? Evidence for international banks. Economic Notes, 35 (1), 121-150. [17] Driessen, J. (2005). Is default event risk priced in corporate bonds? Review of Financial Studies, 18 (1), 165-195. [18] Elton, E. J., Gruber, M. J., Agrawal, D., & Mann, C. (2001). Explaining the rate spread on corporate bonds. The Journal of Finance, 56 (1), 247-277. [19] Eom, Y. H., Helwege, J., & Huang, J. Z. (2004). Structural Models of Corporate Bond Pricing: An Empirical Analysis. The Review of Financial Studies, 17 (2), 499-544. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

264

Antonio Di Cesare and Giovanni Guazzarotti

[20] Ericsson, J., Reneby, J., & Wang, H. (2007). Can structural models price default risk? Evidence from bond and credit derivative markets. Mimeo, electronic copy available at: http://ssrn.com/abstract=637042. [21] Ericsson, J., Jacobs, K., & Oviedo, R. (2009). The Determinants of credit default swap premia. Journal of Financial and Quantitative Analysis, 44 (1), 109-132. [22] European Central Bank (2009a). Financial Stability Review, June. [23] European Central Bank (2009b). Credit default swaps and counterparty risk. Frankfurt am Main, Germany. [24] Fitch Ratings (2006). Global Credit Derivatives Survey. [25] Giesecke, K. (2004). Credit risk modeling and valuation: An introduction. In D. Shimko (Ed.), Credit Risk: Models and Management. London: Riskbooks. [26] Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2 (2), 111-120. [27] Greatrex, C. A. (2008). The credit default swap market’s determinants. Discussion Paper Series, No. 2008-05, Department of Economics, Fordham University. [28] Guazzarotti, G. (2004). The determinants of changes in credit spreads of European corporate bonds. Mimeo, Bank of Italy, Economic Research Department.

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[29] Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46 (6), 1251-1371. [30] Hull, J., Predescu, M., & White, A. (2004). The relationship between credit default swap spreads, bond yields, and credit rating announcements. Journal of Banking and Finance, 28 (11), 2789-2811. [31] International Monetary Fund (2008). Global financial stability report. October. [32] Leland, H. E., & Toft, K. B. (1996). Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. The Journal of Finance, 51 (3), 987-1019. [33] Meng, L., & ap Gwilym, O. (2008).The determinants of CDS bid-ask spreads. The Journal of Derivatives, 16 (1), 70-80. [34] Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29 (2), 449-470. [35] Norden, L., & Weber, M. (2004). Informational efficiency of credit default swap and stock markets: The impact of credit rating announcements. Journal of Banking and Finance, 28 (11), 2813-2843. [36] Pires, P., Pereira, J. P., & Martins, L. (2009). The complete picture of credit default swap spreads – A quantile regression approach. Mimeo, electronic copy available at: http://ssrn.com/abstract=1125265.

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[37] Raunig, B., & Scheicher, M. (2009). Are banks different? Evidence from the CDS market. Oesterreichische Nationalbank, Working Paper No. 152. [38] Tarashev, N. A. (2005). An empirical evaluation of structural credit risk models. BIS Working Papers, No. 179. [39] Zhang, B. Y., Zhou, H., & Zhu, H. (2005). Explaining credit default swap spreads with equity volatility and jump risks of individual firms. BIS Working Papers, No. 181.

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[40] Zhu, H. (2004). An empirical comparison of credit spreads between the bond market and the credit default swap market. BIS Working Papers, No. 160.

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In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 267-288

ISBN 978-1-60876-329-0 c 2010 Nova Science Publishers, Inc.

Chapter 12

T HE E XPENSES P ROBLEM OF P ERSONAL F INANCIAL P LANNING Oliver Braun and Marco Spohn∗ Birkenfeld Environmental Campus University of Applied Sciences Trier, Germany

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Abstract We regard financial goals with different height, time, and type preferences which allow to reduce or to postpone the goals to a certain degree. Additionally, we show how these preferences can be determined in interaction with the decision maker and how to use the Analytic Hierarchy Process (AHP) for this purpose. Furthermore, we include the possibilty of taking out loans and to add some financial ratios which can serve as a means to indicate or to prevent from bankruptcy. Finally, we provide a Mixed Integer Program (MIP) to derive a financial plan that maximizes a person’s value of financial goals with respect to her preferences.

Keywords: Analytic Hierarchy Process (AHP), Mixed Integer Program (MIP), Multiple Criteria Decision Making (MCDM), Personal Financial Planning (PFP)

1.

Introduction

States in Europe are withdrawing more and more from a comprehensive social responsibility for their citizens (transformation of the welfare states). These social and economic changes and the complex financial marketplace make it difficult for people to both keep up with all the changes and understand how these changes may affect them. As a result, the complexity of but also the need for a comprehensive Personal Financial Planning (PFP) has increased. PFP is not only for wealthy people, everyone needs PFP, and a careful and target-oriented planning of financial decisions is one of the most urgent economic questions at the beginning of the 21st century. Among the rewards of PFP are improved standards of living, wiser spending patterns and increased wealth. Often PFP is reduced to the single aspect of answering the question of how to get rich. PFP should instead investigate the ∗

E-mail addresses: [email protected] [email protected]

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Oliver Braun and Marco Spohn

questions of how expenses should be used (view on the expenses), how incomes should be achieved (view on the incomes), and how assets should be invested (view on the assets). In each of the three cases, the preferences of a person play a crucial role, and we define PFP as the preparation of target-oriented decisions concerning personal financial affairs. In this paper, we adopt the view on the expenses. In this sense, we understand the Expenses Problem of Personal Financial Planning as a complex and dynamic process of meeting life goals through the management of finances [Braun, O.(2009), Certified Financial Planner’s Board of Standards(2009)]. Life goals can include buying a home, saving for children’s education or planning for retirement. PFP with this view on the expenses is often done by trial calculations under different scenarios. The basic objective is to reach as many financial goals as possible by obeying liquidity restrictions. Hereby, the decision maker might have various preferences for his different financial goals and these goals might be contrary in the sense that more realization of one goal means less realization of another goal. As a result, the Expenses Problem of Personal Financial Planning can be considered as a Multiple Criteria Decision Making (MCDM) problem, and Mathematical Programming appears as an appropriate method for formulating and solving this problem. The paper is organized as follows. Section 2 gives a review of related work to the field of PFP. Section 3 describes an MCDM model for the Expenses Problem for Personal Financial Planning and shows how height, type and time preferences of the decision maker (respectively the person for whom the decision maker constructs a personal Finance Plan) can be derived. In Section 4, an illustrative example of how to apply the developed model is given. Concluding remarks are given in Section 5.

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2.

Related Work

The PFP related literature is vast and originates a number of disciplines that investigate specific topics of importance for PFP (e.g. (socio-) economics [Eisenhauer(2008)], psychology [Kamleitner & Kirchler(2007)], medicine [Tobler et al.(2007)]. In addition, the field is well supplied with a lot of Textbooks (e.g. [Madura(2006), Garman & Forgue(2006)]). Most books can be used as guides to handle personal financial problems, e.g. maximizing wealth, achieving various financial goals, determining emergency savings, maximizing retirement plan contributions, etc. In this paper, we concentrate on the application of Operational Research (OR) techniques for solving the problem of determining an (concerning the preferences of the decision maker) optimal structure of future expenses. A review of the use of OR in financial management is given in [Ashford et al.(1988)]. The authors state that recent years have seen the development of numerous applications for OR models and algorithms in the financial world, as computer capacity and power were growing exponentially. In addition, financial institutions, large corporations and research centers are increasingly devoting important re-sources to research and development in financial modeling and optimization. Within the field of OR, Multiple Criteria Decision Making (MCDM) has evolved as one important discipline. The development of MCDM is based on the finding that a single objective, goal, criterion or point of view is rarely used to make real-world decisions. A state-of-the art review of the research made on the application of the techniques of MCDM to problems and issues in finance is given in [Zopounidis & Doumpos(2002)],

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[Steuer & Na(2003)], and [Spronk et al.(2005)]. The reviews show that the multidimensional nature of financial decisions has already motivated researchers to explore the potential of MCDM in addressing financial decision-making problems. They note the necessity to address financial problems in a broader and more realistic context. Especially the assets view on PFP is well supplied with a lot of research contributions. As an example, [Ehrgott et al.(2004)] describe an MCDM approach to portfolio optimization. For further references on the use of optimization models for portfolio selection, the reader is referred to [Pardalos et al.(1994)]. All those optimization models are only for the view on the assets. To the best of our knowledge, there is no optimization model for the views on the incomes and (as we are doing in this contribution) on the expenses. To deal with the complexities of the financial decision-making process, often an integration of Saaty’s Analytic Hierarchy Process (AHP) [Saaty(1980), Saaty(1990)] is proposed. An overview of the current state-of-the-art in the AHP is given in [Ho(2008)]. The AHP is a multi-attribute decision-making approach based on the reasoning, knowledge, experience, and perceptions of the decision maker. A combination of linear programming techniques and GP with AHP as we are doing in our contribution is described in numerous papers, among them [ChiangLin & Lin(2008)], [Oboulhas et al.(2004)], and [Puelz & Puelz(1992)].

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3.

Expenses Problem of Personal Financial Planning

The main planning and control instrument of Personal Financial Planning is the Finance Plan, a listing of all expected future incomes and expenses. We consider n + 1 time points t = 0, . . . , n. The difference between two time points t and t + 1 corresponds to one time period (e.g. one year). Without loss of generality there are n + 1 sums of incomes and n + 1 sums of expenses with quantities It > 0 (incomes) and Et > 0 (expenses) for t = 0, . . . , n. Let I0 > 0 be the current liquidated wealth and E0 = 0. In more detail, we define it X It = Itj (1) j=1

the sum of incomes in period t and it declares the maximum number of incomes in period t. Furthermore ix ar eF eV t t X X F ix V ar Et = Etj + Etj (2) j=1

j=1

represents the sum of fixed and variable expenses where eft ix defines the maximum number of fixed expenses and eVt ar the maximum number of variable expenses. We consider fixed expenses as exogenous variables which are determined by the decision maker. In the Expenses Problem of Personal Financial Planning, the decision maker has to decide about the quantities and realization timepoints of specific variable expenses reflecting his personal goals or wishes (e.g. buying a car or a house, raising children, saving for retirement). Therefore we have to consider only some classes of variable expenses and do not need to consider each expense separately. As a result, we introduce e classes of expenses

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E1 , . . . , Ee that occur repeatedly over the planning horizon. For all models presented in this paper we use the notation of Table 1. We define a Finance Plan as feasible if all planned future expenses can be financed by current liquidated wealth and future incomes. With respect to the Expenses Problem of Personal Financial Planning, we define a Finance Plan as optimal if it is feasible and if the utility of the planned variable expenses is maximized. In most cases, a "best-of-breed" approach by trial calculations under different scenarios is done to reach an acceptable Finance Plan satisfying most of the decision maker’s requirements. This "best-of-breed" approach is not necessarily optimal and does not necessarily lead to an optimal Finance Plan. Conflicting objectives with different goals of varying levels of importance for the decision maker might be involved in this decision problem. As a result, the Expenses Problem of PFP can be considered as a Multi-objective Decision Problem, and Mathematical Programming appears as an appropriate method for formulating and solving the problem. The rest of this section is organized as follows. In Section 3.1. we formulate liquidity constraints which ascertain the feasibility of Finance Plans. If costly expenses cannot be financed by current wealth and future incomes it is often possible to take out a loan. This possibilty will also be described in Section 3.1. Financial ratios have a long history in business as instruments for assessing the financial health of firms and can also be used as a diagnostic tool for monitoring financial well-being of individuals and families, monitoring financial progess and identifying problem areas ([Greninger et al.(1996), Mason & Griffith(1988)]). The literature indicates that a comprehensive set of ratios and benchmarks could be beneficial when making financial decisions and are described in Section 3.2. Once we have determined these liquidity and financial ratios constraints we need to introduce the preferences a decision maker might have. This affects height preferences (Section 3.3.) and type preferences (Section 3.4.). Height preferences show a decision maker’s appreciation to a particular amount of a good, whereas type preferences show the decision maker’s appreciation to the type of the expenses among each other. The decision maker’s time preferences can be used to find out if a certain expense can be postponed to the future and are described in Section 3.5. Finally, in Section 3.6., a combined model which includes all these aspects is given. Therefore we assume preference independence, i.e. all preferences can be determined separately.

3.1.

Liquidity Constraints

It is easy to see that the feasibility of a Finance Plan can be checked in (in the number of periods) linear time as the condition St > 0 must hold in every single period t. Thereby the income surplus St can be iteratively computed as St := St−1 · (1 + r) + It − Et

(3)

with r the average inflation-adjusted interest rate per period. In this case, all future expenses can be financed by current wealth and future incomes. Furthermore people often feel more safe if they have a certain amount of money that is available at any time, i.e. a liquidity reserve. Let this liquidity reserve be a constant value L. Therewith we can formulate the

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The Expenses Problem of Personal Financial Planning

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Table 1. Notation Et F ix Etj V ar Etj RC Etj DP Etj GDP Etj SC Etj EtDeb + Etj − Etj F ix et eVt ar eDP t eGDP t eSC t e E1, . . . , Ee It Itj I0 it r q c St L Kt Kt+ Ins Ktf Ann Ktf Hgt Hgt wlm , wtjk T pe wtj T me wtjk pl Hgt vlHgt , vtj T me vlT me , vtj + Etji

n

sum of fixed and variable expenses in period t amount of fixed expense j in period t amount of variable expense j in period t sum of resulting costs belonging to variable expense Etj amount of a single consumer debt payment j in period t amount of a single gross annual debt payment j in period t amount of a single shelter payment j in period t amount of a single loan repayment in period t desired amount of expense j in period t minimum amount of expense j in period t maximum number of fixed expenses in period t maximum number of variable expenses in period t maximum number of consumer debt payments in period t maximum number of gross annual debt payments in period t maximum number of shelter payments in period t number of classes of variable expenses to be considered classes of variable expenses to be considered sum of incomes in period t feasible amount of income j in period t current liquidated wealth maximum number of incomes in period t average inflation adapted interest rate per period 1+r average lending rate per period income surplus in period t liquidity reserve required amount of loan in period t credit limit annual installment of an installment credit which was granted in period t and has to be repaid in period f annuity of an annuity loan that was raised in period t and has to be repaid in period f V ar height preferences: weights for E l and Etj respectively regarding the realized quantity V ar in comparison to all type preferences: weight for expense Etj other expenses time preferences: weight for Etj if it is realized in period k number of intervals in which the height preference function of expense class E l can be split up value functions that describe height preferences of class E l and a single expense Etj respectively value functions that describe time preferences of class E l and a single expense Etj respectively upper bound of interval i belonging to the height preference function of expense tj number of periods in the planning horizon

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Oliver Braun and Marco Spohn

liquidity constraints as follows where q = 1 + r.   ar eV es is t t X s X X X X F ix V ar  t−s  Esj + Esj q ≤ Isj q t−s − L s=1

j=1

(4)

s=0 j=1

j=1

If an expense, such as the purchase of a car or a house, cannot be financed by current wealth and current income, our model allows the raising of a credit. For ease of use we regard only one credit per period. Furthermore we assume a certain credit limit Kt+ for period t. The amount of the credit is defined by Kt . As a consequence we need additional constraints Kt ≤ Kt+ for each period t = 1, . . . , n in order to assure that the credit limit is not exceeded. With respect to our model we distinguish two forms of debt capital: short and long term debt capital. We want to examine three examples which show the application of these credit forms. The first one (short term credit) implies for instance an overdraft credit that can be seen as additional income which has to repaid in the following period together with the overdraft interest. We consider again a liquidity reserve L that may be hold in an investment, c defines the lending rate. Then, the liquidity constraint for a single period t can be described as:   F ix   ar es eV is t t s X X X X X F ix V ar   Isj + Ks  · q t−s − L (5) Esj + Esj + cKs−1  q t−s ≤

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s=1

j=1

s=0

j=1

j=1

The second possibility (long term credit) depicts an installment credit, for example. In this form of credit, the annual payment rate consists of a constant repayment and an interest payment which is based on the remaining debt. Hence we obtain the liquidity constraint for a certain period t as follows:   F ix ar es eV t Ins s X X X K f −t+1 sf  t−s Ins F ix V ar  · cKsf + q Esj + Esj + f −s f −s s=1 j=1 j=1   is t X X  Isj + Ks  · q t−s − L (6) ≤ s=0

j=1

In this example c determines the lending rate of the credit and the variable Ks defines the amount of credit a consumer should borrow in period s. Consequently we can establish ( Ks if 1 < s ≤ f Ins Ksf = 0 otherwise where the index f indicates the period the credit has to be repaid. The third possibility (long term credit) displays an annuity loan (redemption at the end of duration). Therefore we can express the liquidity constraints as:   is t t X X X
t−s Ann  ·q ≤ Es + Ks−1,f Isj + Ks  · q t−s − L (7) s=1

s=0

j=1

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

The Expenses Problem of Personal Financial Planning where Ann Ksf

=

 P

Ks f −s −t t=1 (1+c)

0

=

(1+c)f −s c (1+c)f −s −1

· Ks

if s ≤ f

273

(8)

otherwise.

Ann implies the annuity of a credit that was raised in period s and has to be repaid in Ksf period f .

3.2.

Financial Ratios

Financial ratios combine numbers from the financial statements to measure a specific aspect of the personal financial situation. They are used to measure changes in the quality of the financial situation over time, to measure the absolute quality of the current financial situation, and as guidelines for how to improve the financial situation or predict a househoulds insolvency [Mason & Griffith(1988)]. In order to ensure a household’s financial health we consider the following ratios according to [DeVaney(1994)]. 1. Gross Annual Debt Payments/Income < 0, 35: This ratio indicates the portion of income going towards debt payment. The Gross Annual Debt Payments consist of the household’s debt payments and its shelter costs. This leads to PeGDP GDP t j=1 Etj < 0, 35 (9) Pit j=1 Itj

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GDP determines a single debt payment and eGDP the number of Gross Anwhere Etj t nual Debt Payments in period t.

2. Annual Consumer Debt Payments/Income < 0, 15: This consumer debt ratio examines the portion of disposable income committed to the payment of debt. With regard to our model we can formulate the constraint for a certain period t: PeDP DP t j=1 Etj < 0, 15 (10) Pit j=1 Itj DP determines a single consumer debt payment and eDP the number of At this, Etj t consumer debt payments in period t. In case of an installment credit amounting to Ks which was granted in period s and has to be repaid in period f (with s ≤ t ≤ f ) DP can be assessed as the loan repayment Etj

EtDP =

Ks f −t+1 · cKs + . f −s f −s

(11)

3. Annual Shelter Costs/Income < 0, 28: This ratio indicates the portion of income going to housing. We can formulate this constraint for period t as follows: PeSC SC t j=1 Etj < 0, 28 (12) Pit j=1 Itj

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Oliver Braun and Marco Spohn SC defines a single shelter payment. Shelter costs include rent or mortgage and Etj a maintenance fee for homeowners where the maintenance fee can be calculated by multiplying the current market value of the home by 3%.

3.3.

Height Preferences

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Note that we consider in the following only e classes of variable expenses E 1 , . . . , E l , . . . , E e . As mentioned in section 3. it is not necessary to determine preferences for every single expense but only for the classes. Height preferences reflect the decision maker’s ideals concerning each of his financial goals and can be illustrated by value functions. The value function itself can be acquired through interaction with the decision maker. Therefore it is necessary to ask for a lower bound − + E l and an upper bound E l for each of the variable expenses classes E l . In general there exist different types of value functions which correspond to the microeconomical view of consumption preferences. In our case we assume a concave height preference in the interval − + from E l to E l which is or can be approximated by a piecewise linear function. Concave height preferences implie the more of a certain financial goal can be realized the better. Each of the value functions vlHgt that belong to a certain class of expenses E l can be split into pl ranges [ul,m−1 , ul,m ] with m = 1, . . . , pl and we have vlHgt (x) = Ppl Hgt Hgt i=1 vli (x) with linear functions vli . From a practical standpoint, these intervals are often determined by model types. For example, one might be able to choose between a 100 bhp or a 150 bhp engine for a new car which have different prices and also different preference values. Furthermore the value function vlHgt is usually normalized to the interval Pl Hgt E lm where 0 ≤ E lm ≤ ulm − ul,m−1 and [0, 1] and can be written as vl = pm=1 wlm Hgt wlm defines the gradient of the corresponding line segment between ul,m−1 and ulm . The gradient itself can be computed as Hgt wlm =

v(ulm ) − v(ul,m−1 ) ulm − ul,m−1

(13)

as shown in Figure 1.

Figure 1. Concave value functions. The height preferences for each of the variable expenses can then be derived from the height preferences of the corresponding classes of expenses. In terms of our model this

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The Expenses Problem of Personal Financial Planning

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aspect leads to the following objective function: V ar

M ax

n eX t X

V ar

Hgt V ar vtj (Etj )

= M ax

t=1 j=1

3.4.

ptj n eX t X X

Hgt V ar wtji Etji

(14)

t=1 j=1 i=1

Type Preferences

Type preferences represent the decision maker’s appreciation to the type of the expenses among each other. Therefore the decision maker has to determine values wlT pe (l = 1, . . . , e) reflecting his type preferences for each of the classes of variable expenses. This can be accomplished by the following two steps: 1. In a first step, the decision maker has to determine criteria with which the classes of expenses can be made comparable. 2. In a second step, the values of the classes of expenses with respect to each of the criteria have to be compared.

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This article advances the use of the Analytic Hierarchy Process (AHP) as an effective and realistic modeling approach for determining the type preferences concerning planned classes of expenses in the personal financial planning process. AHP consists of electing pairwise comparisons from the decision maker and then applying the Eigenvector theory in order to obtain the set of weights most consistent with the pairwise comparisons. The greater the AHP weight, the greater the relative importance of that criterion. In this scale, a value of "1" implies that the two criteria or expenses are of equal importance, a value of "5" implies that one criterion/expense is strongly more important than the other, and a value of "9" implies absolute importance. Assuming k criteria/expenses, we get a k × k matrix a11 =  a21 =  M = ..  . 

ak1 =

c1 c1 c2 c1

a12 = a22 = .. .

c1 c2 c2 c2

. . . a1k . . . a2k .. .

= = .. .

c1 ck c2 ck

ck c1

ak2 =

ck c2

. . . akk =

ck ck



  . 

(15)

aij represent the number of times more important of criterion/expense i than criterion/expense j. a12 = C1 /C2 = 3 means that criterion/expense 1 is three times more important than criterion/expense 2. In total we have k · (k − 1)/2 comparisons needed for a problem with k criteria/expenses. Because all possible pairs are compared, redundant information is obtained. This redundant information adds to the robustness of the priority weights and is used to assess consistency of judgments. The resulting matrix of preferences is evaluated by using Eigenvalues to check the consistency of the responses. Consistency can be measured by the Consisency Ratio CR which is the quotient of a the Consistency Index CI of M and a random Consistency Value RI, i.e. CR := CI RI . The consistency index is obtained through λmax − k CI := (16) k−1

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Oliver Braun and Marco Spohn

where λmax defines the maximum Eigenvalue of M and k is the number of the criteria/expenses. The values of the random consistency can be calculated as RI := 1.98 ·

k−2 k

([Saaty(1980)]).

(17)

For the consisteny ratio there is a value of less than 0, 05 for 3 × 3 matrices sought, a value of less than 0, 09 for 4 × 4 matrices and a value of less than 0, 10 for larger matrices. For the cases where one has to face a problem of incomplete pairwise comparisons, e.g. if the number of alternatives is large or if it is convenient to skip some directal comparisons, there exist some approaches which try to compute the missing elements ([Carmone et al.(1997), Fedrizzi & Giove(2006), Kwiesielewicz(1996)]). The weights wlT pe , l = 1, . . . , e, that reflect the type preferences concerning classes of expenses of the decision maker can then be determined with the algorithm depicted in Figure 2.

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Input: k criteria C1 , . . . , Ck , e classes of expenses begin 1. Determine the AHP-vector ~g = (g1 , . . . , gk )T of the k criteria c1 , . . . , ck P such that kj=1 gj = 1. 2. Determine the AHP-vectors h~1 = (h1,1 . . . , hn,1 )T , h~2 = (h1,2 . . . , hn,2 )T , . . . , T h~k = (h1,k P.n. . , hn,k ) of the n expenses with respect to each of the k criteria such that t=1 ht,j = 1 for each j = 1, . . . , k. 3. The type preferences wa for the classes of expenses arise then as follows: P ∀a = 1, . . . , e : wa = ki=1 gi ht,i end; Output: w1 , . . . , we Figure 2. Determining AHP-weights. The type preferences for each of the variable expenses can again be derived from the type preference of the corresponding class of expenses.

3.5.

Time Preferences

Generally spoken, time preferences describe different value estimates for act consequences that timely fall apart. For this purpose one has to consider all the value estimates both for the past and the future. We assume the existence of an additive intertemporal value function for each of the classes of variable expenses E l that can be generally written as Pn T me v T me (E + ) where E + determines the desired value for a certain class of exl l t=1 wlt lt penses E l and vltT me defines the associated single value function of a certain period t. As we imply the same value function for all periods we want to write vl instead of vlt from now on. Furthermore we assume a decreasing run of the value curve in the intervall [0, 1], i.e. the earlier an expense can be realized the better. Therefore time preferences sometimes allow a

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The Expenses Problem of Personal Financial Planning

277

time shift of particular expenses. If it is for example not possible to afford two expenses of the same amount in period one, it is maybe possible to realize one in the first and one in the second period. Which of them should be realized in the first and the second period depends on the decision maker’s time preference. Again we can derive the time preferences for a V ar from the corresponding class of expenses. With respect to our model single expense Etj T me (E + ) = 1: this leads to the following objective function where vsj sj M ax

es X n X l X

+ T me T me wsj vsj (Esj )ysjk

(18)

s=1 j=1 k=s

The liquidity constraint for a particular period t can be displayed as es X t X t X

+ Esj ysjk ≤ I0 q t +

s=1 j=1 k=s

where

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ysjk

( 1 = 0

is t X X

Isj q t−s − L

(19)

s=1 j=1

if expense Esj can be realized in period k, otherwise

(20)

Sometimes there is also a need to consider resulting costs that are connected to acquisitions. As an example, in case of purchasing a car, these costs might be insurances or RC gasoline. If we want to take this possibility into account we can add the term ytjk Etj RC defines the sum of resulting costs of expense E V ar in to the yearly expenses where Etj tj period t. V ar is only realized once we have to add the In order to ascertain that a particular expense Etj following constraint to the model: n X ysjk ≤ 1 (21) k=s

T me can be obtained through interAs mentioned above, the weights for the periods wsj action with the decision maker. If we assume a linear run where t− sj defines the earliest and + − + tsj the latest possible realization period, the points (tsj , 1) and (tsj , 0) define a straight line. T me = Therewith the weights can be derived as wsj

t− sj −t + tsj −t− sj

+ 1.

A probably more realistic way to determine the run of the value function exists in splitting the period under consideration into several parts and defining values for the corresponding interval borders. Within the intervals a linear run of the value function can be assumed. This approach is e.g. used by the Direct-Rating-Method, Difference Standard Sequence Method or the Bisection Method.

3.6.

A Preference Based Model for the Expenses Problem of PFP

Summing up the results of the preceding sections, we come to the optimization model T me , type preferences w T pe , displayed in Figure 4. We assume that all time prefences wsjk sj Hgt height preferences wsji and incomes Isj as well as the inflation rate r and q = 1 + r are

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Oliver Braun and Marco Spohn

Figure 3. Time value functions.

previously known or defined by the decision maker, i.e. exogenously determined whereas V ar are endogenous. All variables y the expenses Esji sjk and ytjk respectively are of type V ar can be realized in the desired period boolean and indicate whether an variable expense Etjk k or not.

4.

Numerical Example

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To illustrate the Expenses Problem of Personal Financial Planning problem and a possible solution, we consider the following basic and simplified scenario that shows the basic concepts of this contribution. It should be noted that our software can handle by far more complex scenarios in reasonable time. We tested up to n = 50 timepoints with up to 50 incomes and expenses and with in total up to 5.000 constraints. The maximum amount of time our software needed to construct the optimal solution was about 150 seconds on an AMD Sempron 3800+ with 2200 MHz and with 2048 MB RAM. Mr. and Mrs. Smith (both 35 years old) have a nine years old son called Tom. Their yearly net income is 60.000 EUR, their living expenses amount to 40.000 EUR per year including 12.000 EUR rent for their apartment. All incomes and expenses are expected to increase with the inflation rate which is estimed to be 3%. The couple currently has 200.000 Euros in investment with an annual inflation-adjusted rate of return of 3%. All surplus incomes will be reinvested in the same investment. Mr. and Mrs. Smith both plan to retire at the age of 60, after their retirement their income comes down to 40.000 EUR per year, the expenses to 30.000 EUR per year. Overall their Finance Plan should cover the next 35 years and their liquidity reserve should be 10.000 EUR. The Finance Plan derived from this basic scenario is feasible as all expenses can be financed by the incomes. The situation changes if we consider financial goals exceeding regular expenses as follows. Mr. and Mrs. Smith plan to buy their own house within the next five years. They prefer a price range from 300.000 to 400.000 EUR. They also want to have a new car every five years in the category of 50.000 to 60.000 EUR until their retirement - this goal should be handled flexible. If Tom attends a university

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

The Expenses Problem of Personal Financial Planning M ax

Pn

s=1

T pe j=1 wsj

Pes

P

n T me k=s wsjk ysjk

+

Ppsj

V ar i=1 msji Esji

279



s.t. (liquidity contraints) Pt Pis Pt PeVs ar Ppsj V ar t−s t−s − L ∀t = 1, . . . , n ≤ s=0 s=1 j=1 Isj q j=1 i=1 Esji q (realize goals not more than once) Pn y ≤ 1 ∀t = 1, . . . , n k=s tjk ∀j = 1, . . . , eVt ar

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(upper Pptj bounds) V ar i=1 Etji ∀j = 1, . . . , eVt ar (lower Pptj bounds) V ar i=1 Etji ∀j = 1, . . . , eVt ar (interval constraints) V ar Etji (credit restrictions) Kt (financial ratios) PeGDP GDP t j=1 Etj Pit j=1 Itj PeDP DP t j=1 Etj Pit j=1 Itj PeSC SC t j=1 Etj Pit j=1 Itj yt , ytjk ∈ {0, 1}

+ ≤ Etj

∀t = 1, . . . , n

− ≥ Etj

∀t = 1, . . . , n

+ ≤ Etji

∀t = 1, . . . , n ∀j = 1, . . . , eVt ar

≤ Kt+ yt < 0, 35

∀t = 1, . . . , n

< 0, 15

∀t = 1, . . . , n

< 0, 28

∀t = 1, . . . , n ∀t = 1, . . . , n ∀j = 1, . . . , et ∀k = t, . . . , n

Figure 4. Linear Programming model for the Expenses Problem for Personal Financial Planning. at the age of 19 their living expenses will increase by 8.000 to 10.000 EUR per year for a period of approximately five years. They are able to use an installment credit up to the amount of 120.000 EUR in order to finance their house. The credit period would be 15 years. In case we consider a house of 400.000 EUR, a new car of 60.000 EUR every five years and an additional amount of 10.000 EUR of living expenses for University attendance, the resulting Finance Plan is not feasible as the investments are steadily lower than 0. This fact is depicted in Table 2 where the amounts are given in thousand Euros, i.e. 60’ stands for 60.000 EUR.

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Oliver Braun and Marco Spohn Table 2. Scenario 1: maximum expenses Year Age Income Credit Expenses House Tom Cars Installment Investment Year Age Income Credit Expenses House Tom Cars Installment

0 35 200’ 0

1 36 60’ 120’ 40’ 400’

2 37 60’ 40’

200’ 14 49 60’

-54’ 15 50 60’

20’ -55,6’ 16 51 60’

40’

40’

40’

60’ 9,6’

8,8’

10’ 10,4’

. . . . . . . . . . . . . . . . . . .

5 40 60’

6 41 60’

40’

40’

60’ 17,6’ -115,9’ 20 55 60’

16,8’ -116,2’ 21 56 60’

40’

40’

60’

. . . . . . . . . . . . . . . . . . .

10 45 60’

11 46 60’

40’

40’

10’ 60’ 13,6’ -179,1 25 60 40’

10’

30’

12,8’ -187,3’ . . . . . . . . .

. . . . . . . . . . 35 70 40’ 30’

However, if we regard the minimum amount there is still money available which could be invested into one of these wishes to improve the Smiths’ quality of life. Now, the questions are

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• how much money should be spend for which goal, • when should which goal be realized, and • to what amount should a credit be raised. In order to answer the questions we need to determine the corresponding height preferences (Section 4.1.), type preferences (Section 4.2.), and time preferences (Section 4.3.) of the Smiths. Hard constraints are the liquidity restrictions and financial ratios. The weights derived from these preferences are then used as parameters for the Linear Program (Section 4.4.).

4.1.

Height Preferences

The Smiths’ height preferences for their financial goals House, University attendance and Cars are displayed in Figure 5 where 10’ represent 10.000 EUR. As we can see, the height preference curve for the house can be split into four intervals with piecewise linear segments. The slope of the curve decreases in every interval, the greatest untility increase shows therefore in the first segment. The height preference for University attendance is a straight line, i.e. the utility increases continously from 8.000

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Figure 5. Height preferences: House, Tom and Cars.

EUR to 10.000 EUR. The height preference curve of the cars has its greatest slope in the interval from 50.000 EUR to 56.000 EUR where it reaches a preference value of 0,75.

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4.2.

Type Preferences

In the next step the type preferences can be defined in dialogue with the Smiths. Therefore the Smiths have to determine criteria with which the expenses can be made comparable. The Smiths might come to k = 3 criteria: C1 = Our financial freedom and our work, C2 = Our consume wishes, and C3 = Our family and our friends. In our example, the couple assigns a value of a12 = 7 in comparing C1 to C2 (i.e. C1 is very strongly more important than C2 ) and assigns a value of a23 = 1/5 (i.e. C3 is strongly more important than C2 ) in comparing C2 to C3 . Assuming perfect consistency, a value of a13 = 7/5 would be assigned in comparing C1 to C3 . Although this might be calculated in such using this method, the couple also directly compares C1 to C3 , thus providing redundant information, e. g. a13 = 1/2 (i.e. C3 is slightly more important than C1 ). In this example,   1 7 1/2 M =  1/7 1 1/5  2 5 1 is not consistent, and such inconsistencies are typical. The Eigenvalue of M is ~g = (0, 379, 0, 072, 0, 549)T . The second iteration leads to an Eigenvalue of ~g = (0, 382, 0, 077, 0, 541)T and the iteration terminates as the difference between the Eigenvalues is smaller than a prescribed value (in our case e.g. 0, 01). The consistency index is CI = (λmax − k)/(k − 1) = 0, 12. As the result, the couple gives criterion C3 = Our family and our friends the highest value (g3 = 0, 541), criterion C1 = Our financial freedom and our work the second highest value (g1 = 0, 382), and criterion C2 = Our consume wishes the lowest value (g2 = 0, 077). In the second step, the value of each of the financial goals House, University attendance, and Cars is compared in respect to the three criteria C1 , C2 and C3 . Let’s assume

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a questioning of the Smiths’ preferences yields the following matrices (with respect to the three criteria):       1 1/9 1 1 1/5 1/9 1 7 6 M (C1 ) =  9 1 9  , M (C2 ) =  5 1 1/7  , M (C3 ) =  1/7 1 1/3  . 1 1/9 1 9 7 1 1/6 3 1 The Eigenvalues are h~1 = (0, 091, 0, 818, 0, 091)T , h~2 = (0, 055, 0, 173, 0, 772)T , and ~ h3 = (0, 750, 0, 078, 0, 172)T . The consistency indexes are CI(~h1 )P= 0, 00, CI(~h2 ) = 0, 11 and CI(~h3 ) = 0, 05. Therewith the type preferences wtT pe = kj=1 ht,j · gj for the Linear Program are then w1 = 0, 445, w2 = 0.368, and w3 = 0, 187.

4.3.

Time Preferences

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Finally we need to know how flexible the goals are, i.e. the time preferences have to be determined. We could imagine that the Smiths defined them as depicted in Fig. 6. Figure 6 shows that the Smiths are indifferent about the realization point of their House within the first two periods. Each of these time points leads to a maximum utility of 1. In the following periods the utility decreases slightly until it falls down to 0 in period 5. From Figure 6 we can see that utility of the realization of the Cars decreases from 1 in period 1 to 0,8 in period 2 which means should take place within the first two years since the value function reaches its minimum value of 0 in period 3.

Figure 6. Time preferences: House and Cars .

4.4.

Linear Program for the Expenses Problem of PFP

In the end, the previous assumptions lead to the following model. In order to better Hou instead of just E V ar as proposed in the distinguish each goals we want to write E111 111 Hou general model. In the same way we also want to display all other goals. Therefore let Esji T om the amount be the amount of money that could be spent for the financial goal House, Esji Caro the amount of money for the financial of money for University attendance, and Esji goal Cars. Thereby s defines the realization period relatively to the planned realization time point (1 means the expense is realized in the same period, 2 means the expense is

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283

postponed one period) and i the interval according to the height preferences. Furthermore T om for Tom ysHou indicates whether the house can be realized in period s or not - just as yts Caro K and yts for the cars. yt indicates whether the loan should be taken out in period t or not.

 M ax 0, 445 · y1Hou + y2Hou + 0, 95y3Hou + 0, 9y4Hou + 0, 8y5Hou + 0, 0002
Hou Hou Hou Hou · E111 + E112 + E113 + E114 + ...
 Hou Hou Hou Hou +0, 000005 · E511 + E512 + E513 + E514  Car1 Car1 T om 0, 000184 · E10,1,1 + 0, 187 · y1Car1 + 0, 8y2Car1 + 0, 000125 · (E521 + E522 )+ Car1 Car1 0, 0000625 · (E611 + E612 ) + . . . + y1Car4 + 0, 8y2Car4 + 0, 000125  Car4 Car4 Car4 Car4 ·(E20,1,1 + E20,1,2 ) +0, 0000625 · (E21,1,1 + E21,1,2 )

s.t.

(liquidity contraints)

(1)

Hou Hou + . . . + E114 40.000 + E111

(2)

(3)

40.000 +

Hou E111

+ ... +

Hou E114

≤ 200.000q + 60.000 + K1 − 10.000


≤ 200.000q 2 + (60.000 + K1 ) · q+

· q+

Hou Hou 40.000 + E211 + . . . + E214 + cK1 +
2 Hou Hou 40.000 + E111 + . . . + E114 ·q +

K1 15

Hou Hou (40.000 + E211 + . . . + E214 + cK1 +

+40.000 + K1 15

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.. .

Hou E311

+ cK2 +

+ ... +

Hou E314

+

.. .

≤ 200.000q 3 + (60.000 + K1 ) · q 2 + K1 15 )

· q+ (60.000 + K2 ) · q

14cK1 15 +

K2 15

60.000 + K3 − 10.000

(realize goals not more than once)

(36) y1Hou + y2Hou + y3Hou + y4Hou + y5Hou (37)

60.000 + K2 − 10.000

y1Car1

+

y2Car1

≤1 ≤1

(upper bounds)

Hou Hou Hou Hou + E114 + E113 + E112 (41) E111

≤ 400.000y1Hou

Hou Hou Hou Hou (42) E211 + E212 + E213 + E214

≤ 400.000y2Hou

.. . T (46) E10,2,1

≤ 10.000 Car1 E522

≤ 60.000y1Car1

Car1 Car1 (48) E611 + E612

≤ 60.000y2Car1

(47)

.. .

Car1 E521

+

(lower bounds)

Hou Hou Hou Hou (55) E111 + E112 + E113 + E114

≥ 300.000y1Hou

Hou Hou Hou Hou (56) E211 + E212 + E213 + E214

≥ 300.000y2Hou

.. .

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Oliver Braun and Marco Spohn

(60)

T om E10,1,1

(61)

Car1 E522

≥ 50.000y1Car1

(62)

Car1 Car1 E611 + E612

≥ 50.000y2Car1

(interval constraints) Hou Hou Hou Hou Hou E111 , E211 , E311 , E411 , E511

≤ 320.000

.. . (69) − (73) (74) − (78) (79) − (83) (84) − (88) (89) − (93) (94) − (101) .. . (102) (103) .. . (107) (108) (109)

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≥ 8.000

Car1 E521

.. . (114) (115) .. .

+

Hou Hou Hou Hou Hou E112 , E212 , E312 , E412 , E512 Hou Hou Hou Hou Hou E113 , E213 , E313 , E413 , E513 Hou Hou Hou Hou Hou E114 , E214 , E314 , E414 , E514 Car1 Car1 Car2 Car2 Car3 Car3 E521 , E611 , E10,2,1 , E11,1,1 , E15,1,1 , E16,1,1 , Car4 Car4 E20,1,1 , E21,1,1 Car1 Car1 Car2 Car2 Car3 E522 , E612 , E10,2,2 , E11,1,2 , E15,1,2 , Car3 Car4 Car4 E16,1,2 , E20,1,2 , E21,1,2

≤ 5.000

(credit restrictions) K1 K2

≤ 120.000y1Hou ≤ 120.000y2Hou

y1K + y2K + y3K + y4K + y5K (financial ratios: shelter costs / income)
Hou Hou ) + . . . + E14 12.000 · (1 − y1Hou ) + 0, 03 · (E11 1 · 60.000 120.000 · (1 − y1Hou − y2Hou ) + 0, 03 Hou Hou + . . . + E14 · E111

+ 1 Hou Hou · 60.000 E211 + . . . + E215 (financial ratios: debt payments / income)
1 1 cK1 + K · 15 60000
14cK1 K2 1 1 +K 15 15 + cK2 + 15 · 60000

≤ 20.000 ≤ 40.000 ≤ 20.000 ≤ 55.000

≤1

< 0, 28

< 0, 28 < 0, 15 < 0, 15

(133) − (150) y1Hou , y2Hou , y3Hou , y4Hou y5Hou , y1Car1 , y2Car1 , y1Car2 , y2Car2 , y1Car3 , y2Car3 , y1Car4 , y2Car4 , y1K , y1K , y2K , y3K , y4K , y5K ∈ {0, 1}

4.5.

Discussing the Results

Soving the Linear Program leads to the result presented in Table 3. Although the House is considered the most important expense, it only can be realized to the minimum desired amount and also has to be postponed to the fourth period. This is due to the fact that we consider financial ratios, especially the annual debt payments / income quota influences the model very strongly. However, University attendance can be realized as desired. The amounts that can be spend for Car 1 and Car 2 need to be reduced, additionally the purchase of Car 3 has to be postponed one period. From the Finance Plan depicted in Table 4 we can see that the couple’s investment never falls under the desired limit of 10.000 EUR - but we get down to this level in periods 5 and 16 which means we could not have spent more money to increase the Smiths’ satisfaction. Starting at period

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Table 3. Optimal quantities and time points of realization House Tom Car 1 Car 2 Car 3 Car 4

Desired Amount 400.000 EUR 10.000 EUR 60.000 EUR 60.000 EUR 60.000 EUR 60.000 EUR

Actual Amount 300.000 EUR 10.000 EUR 59.404 EUR 60.000 EUR 55.000 EUR 60.000 EUR

Desired Time Point 1 10-14 5 10 15 20

Time Point of Realization 4 10-14 5 10 16 20

20 the family’s wealth increases again up to 279.733 EUR at the end of the period under consideration.

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5.

Summary

Personal Financial Planning investigates the question of how solid planning of financial affairs can contribute to our fundamental goals. Comprehensive Personal Financial Planning consists of planning the investment of assets as well as planning incomes and expenses during a person’s lifetime. We restrict ourselves in this paper to the view on the expenses and consider the Expenses Problem of Personal Financial Planning which is to find a feasible Finance Plan with the value of planned expenses for a decision maker to be maximized. This Expenses Problem of Personal Financial Planning can be considered as a Multiple Criteria Decision Making problem as conflicting objectives with different goals of varying levels of importance for the decision maker are involved in the problem. We propose a decision model for solving the problem based on a Mixed Integer Program with the parameters for the program derived from the Analytic Hierarchy Process. We assume the fully deterministic case, i.e. all data are given and risk or uncertainty are out of the scope of this model. It might be interesting to consider these cases in further research. We show the effectiveness of our approach by providing a numerical example that helps to compromise among the objectives and produces a feasible and (concerning the preferences of the decision maker) optimal personal Finance Plan. Our approach has the advantage to change trial calculations-based Personal Financial Planning practices that are done to reach acceptable Finance Plans satisfying most of the decision maker’s preferences by a line of action where the decision maker has to clearly define criteria based on his preferences concerning spending expenses. The decision making process concerning personal financial affairs is an iterative process and is not finished until the intuitive mental image of a solution fits with the model’s solution as far as possible. Doing this, consistency will be guaranteed and the decision maker can be sure that his objectives and preferences are correctly handled by the model. In this context it should be underlined that the purpose of our model is not the determination of an objective optimum. The purpose of our model is rather the determination of an action alternative which is optimal with respect to subjective expectations and the personal objectives, criteria, and preferences of the decision maker. In this process the decision maker has to reflect about values and criteria underlying decisions about personal

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Table 4. Resulting Finance Plan Year Age Income Credit Fixed Exp. House Car Univ. Installment Investm. 0 35 200.000 0 200.000 1 36 60.000 40.000 226.000 2 37 60.000 40.000 252.780 3 38 60.000 40.000 280.363 4 39 60.000 46.756 40.000 300.000 55.530 5 40 60.000 40.000 59.404 7.793 10.000 6 41 60.000 40.000 7.481 22.819 7 42 60.000 40.000 7.169 36.334 8 43 60.000 40.000 6.857 50.567 9 44 60.000 40.000 6.546 65.538 10 45 60.000 40.000 60.000 10.000 6.234 11.270 11 46 60.000 40.000 10.000 5.922 15.686 12 47 60.000 40.000 10.000 5.611 20.546 13 48 60.000 40.000 10.000 5.299 25.863 14 49 60.000 40.000 10.000 4.987 31.652 15 50 60.000 40.000 4.676 47.926 16 51 60.000 40.000 55.000 4.364 10.000 17 52 60.000 40.000 4.052 26.248 18 53 60.000 40.000 3.740 43.295 19 54 60.000 40.000 3.429 61.165 20 55 60.000 40.000 60.000 23.000 21 56 60.000 40.000 43.690 22 57 60.000 40.000 65.001 23 58 60.000 40.000 86.951 24 59 60.000 40.000 109.559 25 60 40.000 30.000 122.846 26 61 40.000 30.000 136.531 27 62 40.000 30.000 150.627 28 63 40.000 30.000 165.146 29 64 40.000 30.000 180.100 30 65 40.000 30.000 195.503 31 66 40.000 30.000 211.369 32 67 40.000 30.000 227.710 33 68 40.000 30.000 244.541 34 69 40.000 30.000 261.877 35 70 40.000 30.000 279.733

financial affairs. The proposed model does not make the independent reasoning person redundant, it is rather an assistance for the preparation of goal- and preferences-oriented decisions concerning personal financial affairs. In order to find a solution for the presented model, an optimization algorithm for mixed-integer programs, such as a Branch-and-Bound algorithm, has to be applied. Therefore most of the spreadsheet programs are not able to solve the proposed model. Our basic model of Personal Financial Planning and can be enlarged in several ways.

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As an example, the decision maker might have time preferences or risk preferences for specific expenses, or non-linear preferences might be of interest for consideration in the model. The preferences-oriented approach for solving the Expenses Problem of Personal Financial Planning in general is transferable from the expenses view to the incomes view and to the assets view. A general preferences-oriented Personal Financial Planning in this sense can help clarify values that guide the decision-making process about proper planning of personal financial affairs, and can show the right direction for usage of the expenses, deriving the incomes, and investing the assets.

References [Ashford et al.(1988)] Ashford, R.W., Berry, R.H., Dyson, R.G., 1988. Operational research and financial management. European Journal of Operational Research 36, 143–152. [Braun, O.(2009)] Braun, O., Entscheidungsunterstützung für die Persönliche Finanzplanung (Decision Support for Personal Financial Planning), Gabler, Wiesbaden, 2009. [Carmone et al.(1997)] Carmone, F. J., Kara, A., Zanakis, S.H., 1997. A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP. European Journal of Operational Research 102, 538–553. [Certified Financial Planner’s Board of Standards(2009)] Certified Financial Planner’s Board of Standards: Financial planning basics, http://www.cfp.net/learn/.

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[ChiangLin & Lin(2008)] ChiangLin, C.-Y., Lin, C.-C., 2008. Personal financial planning based on fuzzy multiple objective programming. Expert Systems with Applications 35, 373–378. [Ehrgott et al.(2004)] Ehrgott, M., Klamroth, K., Schwehm, C., 2004. An MCDM approach to portfolio optimization. European Journal of Operational Research 155, 752–770. [Eisenhauer(2008)] Eisenhauer, J.G., 2008. Ethical preferences, risk aversion, and taxpayer behaviour. The Journal of Socio-Economics 37, 45–63. [Fedrizzi & Giove(2006)] Fedrizzi, M., Giove, S., 2006. Incomplete pairwise comparison and consistency optimization. European Journal of Operational Research 183, 303– 313. [Garman & Forgue(2006)] Garman, T., Forgue, R., Personal Finance, Houghton Mifflin Company, New York, 2006. [Greninger et al.(1996)] Greninger, S.A., Hampton, V.L., Kitt, K.A., Achacoso, J.A., 1996. Ratios and benchmarks for measuring the financial well-being of families and individuals. Financial Services Review 5, 57–70. [Ho(2008)] Ho, W., 2008. Integrated analytic hierarchy process and its applications - a literature review, European Journal of Operational Research 186, 211–228. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Oliver Braun and Marco Spohn

[Kamleitner & Kirchler(2007)] Kamleitner, B., Kirchler, E., 2007. Consumer credit use: A process model and literature review, Revue européenne de psychologie appliquée 57, 267–283. [Kwiesielewicz(1996)] Kwiesielewicz, M., 1996. The logarithmic least squares and the generalized pseudoinverse in estimating ratios. European Journal of Operational Research 93, 611–619. [Madura(2006)] Madura, J., Personal Finance with Financial Planning Software, Addison Wesley, Boston, 2006. [Mason & Griffith(1988)] Mason, R., Griffith, R., 1988. New ratios for analyzing and interpreting personal financial statements, Journal of Financial Planning 9, 71–87. [Oboulhas et al.(2004)] Oboulhas, C.T.O., Xu, X., & Zhan, D., 2004. A decision support system for supplier selection process. International Journal of Information Technology & Decision Making 3, 453–470. [Pardalos et al.(1994)] Pardalos, P., Sandström, M., Zopounidis, C., 1994. On the use of optimization models for portfolio selection: A review and some computational results, Computational Economics 7, 227–244. [Puelz & Puelz(1992)] Puelz, A., & Puelz, R., 1992. Personal financial planning and the allocation of disposable wealth. Financial Services Review 1, 87–99. [Saaty(1980)] Saaty, T.L., The analytic hierarchy process, McGraw Hill, New York, 1980.

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[Saaty(1990)] Saaty, T.L., 1990. How to make a decision: The analytic hierarchy process. European Journal of Operational Research 48, 9–26. [Spronk et al.(2005)] Spronk, J., Steuer, R.E., Zopounidis, C., Multicriteria decision aid/analysis in finance, in: J. Figuera, S. Greco, M. Ehrgott (Eds.), Multiple criteria decision analysis: State of the art surveys, Springer, Berlin, 2005. [Steuer & Na(2003)] Steuer, R.E., Na, P., 2003. Multiple criteria decision making combined with finance: A categorized bibliographic study, European Journal of Operational Research 150, 496–515. [Tobler et al.(2007)] Tobler, P.N., Fletcher, P.C., Bullmore, E.T., Schultz, W., 2007. Learning-related human brain activations reflecting individual finances, Neuron 54, 167–175. [DeVaney(1994)] DeVaney, S.A., 1004. The usefulness of financial ratios as predictors of household insolvency: Two perspectives, Financial Counseling and Planning 5, 5–24. [Zopounidis & Doumpos(2002)] Zopounidis, C., Doumpos, M., 2002. Multi-criteria decision aid in financial decision making: Methodologies and literature review. Journal of Multi-criteria Decision Aanalysis 11, 167–186.

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In: Finance and Banking Developments Editor: Charles V. Karsone, pp. 289-332

ISBN 978-1-60876-329-0 © 2010 Nova Science Publishers, Inc.

Chapter 13

T HE S UBPRIME M ORTGAGE C RISIS AND I TS C ONNECTIONS WITH BANK BAILOUTS M.A. Petersen∗, M.C. Senosi†, J. Mukuddem-Petersen‡, B. de Waal§ and S. Thomas¶ North-West University, Potchefstroom, South Africa

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Abstract The subprime mortgage crisis (SMC) and subsequent global financial crisis (GFC) have made a better understanding of bank bailouts an imperative. Since the onset of the SMC in 2007, bailout packages have been implemented on an unprecedented scale throughout the world. In the U.S. this culminated in an intervention known as the Troubled Assets Relief Program (TARP) that enabled the purchase of toxic assets such as subprime residential mortgage loans (RMLs) and residential mortgage-backed securities (RMBSs) as well as common and preferred equity from financial institutions. Even though many other countries approved more general rescue packages, the crises demonstrated that the largest banks were considered to be too-big-to-fail by their respective governments. Although there has been very little opposition to these bailout measures, it is important to assess the effects of bailouts in terms of the risktaking and -shifting. In this book chapter, some of the SMC-related issues that we probe include the reason for and efficiency of government bailouts, liquidity and its relationship with debt market efficiency as well as the comparative effectiveness of government purchases of preferred and common equity as well as toxic RMBSs. This is done separately for the special cases involving subprime RMLs that default, refinance and fully amortize. We find that the defaulting of such RMLs is less likely to lead to bailouts than the buying of toxic RMBSs.

Keywords: Bank Bailouts; Interbank Lenders (ILs); Originators (ORs); Mortgagors (MRs); Government (G); Subprime Residential Mortgage Loans (RMLs); Residential ∗

E-mail address: E-mail address: ‡ E-mail address: § E-mail address: ¶ E-mail address: †

[email protected]. [email protected]. [email protected]. [email protected]. [email protected].

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Mortgage-Backed Securities (RMBSs); Risk-Taking, Risk-Shifting; Toxic RMBSs; Efficient Lending Constraints (ELCs); Liquidity; Preferred Equity; Common Equity; Capital Injections; Deposits; Liquidation; Audits; Tax; Dividends; Subsidies; Voluntary Participation Constraints (VPCs); Deadweight Costs and Losses; Welfare; Subprime Mortgage Crisis (SMC); Troubled Assets Relief Program (TARP); Discrete-Time Modeling.

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1.

Introduction

The subprime mortgage crisis (SMC) and subsequent global financial crisis (GFC) have rendered discussions about bank bailouts even more topical. The features of the SMC can be associated with those of a banking panic with holders of short-term liabilities refusing to fund banks due to expected losses on subprime residential mortgage loans (RMLs) as well as related securities and derivatives. This caused runs on off-balance sheet vehicles and resulted in a freezing of the repo market that was followed by a pursuit of cash as counterparties called collateral and stopped extending debt. Such economic conditions necessitated bank bailouts. These bailouts involved the lending or donating of funds to failing banks in order to save it from bankruptcy or liquidation. The four main objectives of such bailouts are to increase bank capital ratios, to increase write-offs of non-performing RMLs, to improve liquidity in order to increase lending – in particular between banks – and avoid a credit crunch as well as to encourage restructuring. During the SMC, bailout packages have been implemented on an unprecedented scale with the U.S. government bailing out banks that were considered too-big-to-fail. The bailout of such banks were seen as a necessity in order to prevent widespread instability in the financial system (see, for instance, (6)). One of the first examples of this in the current crisis was the British bank, Northern Rock, that was nationalized in February 2008. In the U.S., Fannie Mae and Freddie Mac, were taken over by the Treasury Department in September 2008. In the U.S., the Emergency Economic Stabilization Act (EESA) was passed in order to strengthen and stabilize the financial sector. In this regard, for instance, the Troubled Asset Relief Program (TARP) was established to purchase assets and equity from financial institutions (including banks). Initially, the TARP allowed the U.S. government to acquire or insure up to $700 billion of toxic assets1 . This initiative was funded by borrowing from world financial markets with the hope that the aforementioned assets could be sold when the housing market stabilized. Initially, the largest commercial and former investment banks received $ 125 billion dollars from the U.S. government primarily in exchange for preferred equity, which paid dividends far less than preferred equity sales that occurred days or weeks before. These equities were bought to restore confidence in the markets and to encourage the banks to lend (see, for instance, (20)2 ). These bailout measures have largely been uncontested. Notwithstanding this, it is important to assess the effects of bailouts in terms of the future risk-taking and -shifting of protected banks. Bank bailouts involve certain ubiquitous principles. Some of these characteristics of bailouts are mentioned below. Firstly, governments provide loans to assist the financial 1

Such assets include toxic mortgages such as subprime RMLs and any securities, obligations or other instruments that are based on or related to such mortgages – the purchase of which promotes market instability. 2 The move to buy preferred equity represented a change of heart by the U.S. Treasury secretary who originally wanted funds from EESA to be used to purchase toxic RMLs and RMBSs only.

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system in combatting liquidity concerns, where banks are unable or unwilling to extend credit. Also, insolvent institutions (i.e., those with insufficient funds to pay their short-term obligations) are allowed to fail in an orderly way. Thirdly, the true financial position of key financial institutions have to be understood via audits or other means. Here, we have to ensure the extent of losses and quality of assets are known and reported by institutions. Furthermore, banks that are deemed healthy enough (or too-big-to-fail) to survive, require capital injections which involves the government providing funds to the bank in exchange for preferred or common equity as well as toxic assets, which receives a cash dividend over time. Fifthly, when taking over an institution due to insolvency, effective control is taken via the board or new management. In this case, common equity has to be canceled (i.e., existing shareholders lose their investment) but debt holders and suppliers should be protected. Sixthly, government should take an ownership (equity) interest to the extent taxpayer assistance is provided, so that taxpayers can benefit later. In other words, the government becomes the owner and can later obtain funds by issuing new common or preferred equity to the public when the nationalized institution is later privatized. Seventhly, a special government entity is created to administer the bailout program. Finally, dividend payments should be prohibited in order to ensure taxpayer money are used for loans and strengthening the bank, rather than payments to investors. In this book chapter, we discuss issues related to subprime bank bailouts and their particular connections with the SMC. A first SMC-related issue that we probe is the comparative effectiveness of government capital injections via the purchase of toxic RMBSs as opposed to preferred and common equity. Also, we are interested in the ramifications of bailouts for defaulting, refinancing and fully amortizing subprime RMLs.

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1.1.

Literature Review on Subprime Bank Bailouts

Our chapter is related to several strands of literature on subprime bank bailouts. Theoretically, the effects of bailout policies on risk-taking are similar to those discussed in the deposit insurance literature. From (22), it is clear that unfair deposit insurance entails a riskshifting problem, similar to that arising from limited liability. Therefore, protected banks may be expected to take particularly high risks due to the implicit guarantee. However, (16) shows that this result is not robust. In their model, protected banks may decrease their risk-taking in response to a bailout policy (see, also, (13)). The article (30) asserts that if a bank is facing insolvency, it will be tempted to reject good loans and accept bad loans so as to shift risk onto its creditors. They analyze the effectiveness of buying up toxic mortgages in troubled banks as well as purchasing preferred and common equity. If bailing out banks deemed too-big-to-fail involves buying assets at above fair market values, then these banks are encouraged ex ante to gamble on bad assets. Purchasing common (preferred) equity is always the most (least) ex ante- and ex post-efficient type of capital injection, independent of whether the bank volunteers for the recapitalization (compare with (28) for the debt overhang case). The paper (29) shows that even solvent banks will be reticent to sell volatile, toxic assets at market prices. Banks’ shareholders have insolvency puts that give them limited liability in the event of default. The insolvency puts are more valuable when the banks’ assets are more volatile. Shareholders in banks will require any buyer to pay for the lost volatility as well as the market price

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of the toxic assets. Thus, taxpayers must be ready to richly overpay if they want banks to voluntarily sell their toxic assets. On the other hand, (5) argues that the government should not overpay for toxic assets and should not mix the buying of toxic assets with direct bank capital injections. In this regard, (17) proposes that the TARP should not pay hold-tomaturity prices for the toxic assets but rather a lower price aiming at providing liquidity for a 3-5 year window. The paper (15) argues that it is costly for private agents to be prepared to purchase substantial amounts of assets on short notice. Despite this, the government can create liquidity and improve welfare. Therefore, they argue that forbearance and bank bailouts are sometimes optimal (see, also, (3)). The authors argue that governments bailout banks because they can efficiently provide liquidity. As a result, there is a potential role for the government to supply liquidity by issuing government mortgages, backed by tax revenue. In Section 2. of this book chapter, we present similar arguments to those in (15), (28), (29) and (30). On the other hand, Sections 3. and 4. differ in that they provide defaultfree scenarios and their connections with bank bailouts. The article (1) argues that not all solvent banks should be closed. That paper argues that it is optimal to leave the insolvent banks with sufficiently large charter (going-concern) values open. (8) also argues that regulatory forbearance may be optimal if the lost banks charter values are large. They argue that the optimal bailout policy should be announcing and committing ex-ante to bail out insolvent institutions only in times of adverse macroeconomic condition but not otherwise. (26) analyzes how interbank lending provides the link for one bank’s problem to transmit to the other and lead to systemic banking system failure. They argue that banks become too-big-to-fail when the failure of a single bank can propagate crisis in the entire banking system. Several empirical studies document that regulators are reluctant to close down banks and will often provide some sort of government assistance during banking crises. (18) discuss resolutions adopted in 33 banking crises over the world over the period of 1977 through 2002. They find that during systemic crises, liquidity support from central banks and blanket government guarantees are granted. Despite not discussing any other types of government capital injections, (7) argues that loan guarantee bailouts will induce banks to make speculative investments ex-ante. Also, (4) and (31) assert that common equity is the most efficient way to inject capital into banks. The former punts compulsory right offerings to incentivize banks to increase common equity in their capital structure. (31) advocates a mandatory debt-for-equity swap in the financial sector to achieve a higher equity-to-assets ratio for banks. This paper has the government buying toxic assets in the troubled OR only. They find that common equity capital injections weakly dominate purchases of toxic RMBSs. (17) suggests that direct capital injection through equity investment is more effective than purchasing toxic assets and supports the intuition that forced common equity capital injections are first-best efficient. Also, this paper considers the case where the government lacks the credibility or the political will to force capital injections. In that case, (17) finds common equity capital injections are weakly the most efficient. Furthermore, (27) found that if banks are tempted to engage in risk-shifting, the mere fact that banks are voluntarily participating in a preferred equity capital injection is not sufficient to guarantee that this injection and the accompanying taxpayer subsidy will induce ORs to extend riskless RMLs. This is true because the voluntary participation subsidy for preferred equity capital injections is strictly less than the efficient lending subsidy for preferred equity.

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The paper (27) estimates that the $ 125 billion in TARP monies given to the first nine institutions included a subsidy worth between $ 13 and $ 36 billion dollars. This subsidy may not have been enough to guarantee that the voluntary participation constraint (VPC) was satisfied as well as encourage efficient lending. Nevertheless, (27) indicates that the subsidy sizes required to induce efficient lending with preferred equity capital may be very large. (27) cannot verify that the value of banks’ equity rose with the introduction of the TARP. Several contributions express dismay that so many banks have received TARP funds3 , including those that are not too-big-to-fail (see, for instance, (2)). The Capital Purchase Program (CPP) specifies that government can veto common dividend increases and share repurchases for the first three years after the institution receives funds. Both those actions would increase the bank’s leverage and counteract the beneficial effects of the capital injection. Many of the banks due to receive TARP funds probably would not pose systematic risk if they were closed down due to insolvency. It is not clear that the closure of all but the handful of giant commercial and formerly investment banks pose any short or long-term damage to the financial system as a whole. For this reason, the banking sector as a whole may be made healthier if the weaker regional banks were closed down and their assets were sold to stronger institutions. It may be more efficient to close down rather than recapitalize insolvent banks. Nevertheless, (2), for example, have more to say about how many, and which banks should be bailed out. By contrast, the present book chapter primarily answers which RMLs should be used to bail out banks that are deemed too-big-to-fail.

1.2.

Preliminaries about Subprime Bank Bailouts

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In this subsection, we discuss bank bailouts and their dynamics, provide diagrammatic overviews of U.S. bank bailouts as well as comment on the economic equilibrium appearing in this book chapter. In the sequel, the superscripts ”v” and ”nv” denote present value (PV) and nett present value (NPV), respectively. 1.2.1.

Subprime Bank Bailout Agents

Throughout our study we consider an economy with periods, t − 1, t and t + 1, and four main agents, viz., the originator (OR), interbank lender (IL), government (G) – which is the bailout agency – as well as a (subprime) mortgagor (MR). In the sequel, all economic agents are considered to be risk-neutral. In order to study subprime risks – important for loan agreements such as those for subprime residential mortgage loans (RMLs) and the risky marketable securities associated with them such as residential mortgage-backed securities (RMBSs) – we will stylize the interactions between OR, IL (potentially the ”counterparty” to OR), G and MR. In the sequel, we consider OR’s investment in period t − 1 to be exclusively in toxic RMBSs rather than RMLs. The arguments, however, are equally applicable to both. The following assumption can be made about the OR and G as well as their relationship.

3

By Monday, 8 December 2008, there were 156 financial institutions that had received at least preliminary approval for TARP.

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Assumption 1.1 (OR’s RMBS Investment Decision, Insolvency, Liquidity, Equity and Lending Policy): Suppose that the subprime RMBSs on OR’s balance sheet are at PV4 and denoted by Btv . In period t − 1, we assume that OR will undertake RMBS investment only if its expected returns strictly exceed the returns in the Treasuries, so that E[rtBv Btv ] > rtT Tt . We suppose that ORs have not failed in their present states but may become insolvent in future and that they do not have liquidity problems. Furthermore, we assume that in period t, OR’s equity capital at PV is less than the total deposits at PV, so that Etv < Dtv . Lastly, we suppose that G cannot override OR’s lending policy. In part, the above assumptions suggest that ORs could sell RMBSs to G, while they have sufficient funds to invest in new RMBSs.

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Assumption 1.2 (G’s Ex-Post Social Returns and Dividends Regulation): We assume that G acts in the public interest and maximizes ex-post social returns in period t. Furthermore, we suppose that G will provide capital to OR in period t if this strictly increases ex-post social surplus5 . Furthermore, we assume that G has the power to regulate the payment of dividends, share buybacks, or cash acquisitions for OR accepting funds from G. Thus, we will assume that any leverage decreasing capital injection cannot be undone by capital structure adjustments by OR. OR will be bailed out by G if its subprime RMBS portfolio investment fails. In period t − 1, OR and IL make their investments. The risk-free discount rate, δ, between periods is normalized to δ = 0. A diagrammatic overview of subprime bank bailout agent interactions may be represented as follows. In Figure 1, we have that depositors may choose to either invest their funds in a riskfree asset offering a gross rate of return µs ≥ 1 (refer to 1a and 1b) or deposit in IL (see 1c and 1d). IL’s deposits, DL , are fully protected by comprehensive deposit insurance, so that depositors have an incentive to invest in IL at a deposit rate rDnv ≥ µs . In period t − 1, OR and IL decide to make their investments. As in (30), in period t − 1, OR has access to subprime RML investments that may be financed by borrowing from IL. OR also collects deposits, Dv , and may invest them in subprime RML projects. IL, acting in the interest of risk-neutral shareholders, either invests DL in Treasuries, T, (refer to 1e and 1f) or in OR’s subprime RML projects with stochastic returns (compare 1g and 1h). 4 In our case, the present value of a subprime RMBSs is the value on a given date of a future RMBS payment or series of future RMBS payments, discounted to reflect the time value of money and other factors such as investment risk. 5 Social surplus is made up of surpluses from OR, IL and G. It is the primary measure used in welfare to evaluate the efficiency of a policy

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Safe Assets

1a

295

Mortgagors (MR)

1l

1b

1i 1j

1g

1c

(D)

1h

1d

1e

Mortgage-Backed Securities Portfolio (MBSs)

Interbank Borrower (IB)

Interbank Lender (IL)

Depositors

1k

1f

Treasuries (T)

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Figure 1. Diagrammatic Overview of Bailout Agent Interactions. OR is a risky bank because it is tempted to make high risk RML6 investments in period t−1. OR will only invest in such RMLs if its expected returns are more than the returns from other investments. Both OR and IL maximize expected returns to shareholders, therefore, if they fail to pay their depositors back, then their shareholders will not be left with anything. If OR’s project fails then it will be bailed out by a G via 1i. G partially finances bailouts by raising lump sum taxes after bank failures have occurred. In addition, 1j is the mechanism by which OR securitizes its subprime RMLs and 1k is the return on the securitization. MR is not aware of the agreement between IL and OR and will continue to make RML payments at the rate, r, which is represented by 1l. If MR fails to make such payments, OR and IL will face default losses. 1.2.2.

Subprime Bank Bailout Events

In the following table, we sequence the subprime bailout events. For sake of completeness, below we provide a diagrammatic overview of the U.S. bailout plan. 1.2.3.

OR’s Investment in RMBSs

During period t − 1, OR can decide to invest its deposits worth Dv in Treasuries and T T T earn a return, rt+1 t+1 = 0 in period t + 1, where rt is the rate of return on Treasuries, or invest in RMBSs with a PV denoted by Btv . The price of this RMBS investment is v v Bv v Btv + cBv t Bt > Bt , where ct Bt is the transaction costs of this purchase. The expected v nett present value (NPV) of this RMBS investment is given by E[Btnv ] = −cBv t Bt , where v v cBv t Bt > 0 can be considered to be a deadweight loss to society. In this regard, Bt is a 6

High risk RMLs are defined as RMLs that have a high credit risk associated with it. High risk RMLs cannot easily be sold or exchanged for cash without a significant loss in value.

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M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al. Table 1. Sequence of Bailout Events

Subperiod

Period t − 1

·, 1

OR decides whether or not to buy toxic RMBSs and IL decides whether to extend credit to OR to buy RMBSs

·, 2

Period t

Period t + 1

G decides whether or not to bail out OR

RML returns as well as returns from high risk RMLs are realized as high or low

OR make a choice between high and low risk RMLs

OR pays IL back

function of a Bernoulli random variable that has a probability of high returns of q and a probability of low returns of 1 − q in period t + 1, 1. The superscripts h(l) denotes a high (low) RMBS return in period t + 1, 1. The expected value of these RMBSs is v hv lv hv v lv E[Bt−1 ] = qBt+1,1 + (1 − q)Bt+1,1 , where Bt+1,1 > Bt−1 > Bt+1,1 .

(1.1)

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The evolution of the RMBS portfolio is illustrated by Figure 3 below. To incorporate the impact of counterparty risk which is important to RMBSs as well as RMLs, we will present a stylized story of lending between banks. IL is potentially the counterparty to OR. If OR decides against investing in RMBSs, then IL can invest only in T nv Treasuries, Tnv t , that generate a nett return, rt Tt = 0. However, we assume that IL has two choices in period t − 1 if OR does invest in RMBSs. IL has deposits of magnitude T nv Dtv = Bvt , that it can invest in Treasuries, Tnv t , that earn a return, rt Tt = 0, or it can lend them to OR in return for repayment of B Bvt+1 + rt+1 Bvt+1 > Bvt+1

for these borrowings in period t + 1. If IL lends to OR, IL is a junior creditor to OR’s depositors but a senior creditor to OR’s shareholders. If OR invests only in Treasuries, T, that have expected nett present value7 (NPV) given by E[Tnv t+1 ] = 0, when they mature in period t + 1. OR has equity capital in the form of cash of v B v Etv = Etr + cBv t Bt + rt Bt , 7

In our case, nett present value is the nominal amount outstanding minus the sum of all future debt-service obligations (interest and principal) on existing debt discounted at an interest rate different from the contracted rate.

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International Money Markets

$ 700 Bn Borrowed (TARP)

Liquidity

BANK

Interbank Lending Increases

U.S. Government

Stake

BANK

BANK

in Banks

Troubled Assets Bought From Banks

Repayments Credit

Individuals and Small Businesses

Figure 2. Diagrammatic Overview of the U.S. Bailout Plan.

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v B v where Etr is OR’s cash reserve and cBv t Bt , rt Bt > 0. The assumption that OR has a reserve of Etr is not necessary to obtain the risk shifting result. Instead, all that is necessary is that OR has available liquid assets to make its investment in risky RMBSs because it will be unable to profitably convince new investors to fund it. From (24), we have that

pv cv v B v v Etv = nt Et−1 + nt Et−1 = Etr + cBv t Bt + rt Bt < Dt ,

where nt , Etcv and Etpv denote the number of shares, common equity and preferred equity, respectively. In period t, OR’s balance sheet with RMBSs, B v , considered at PV is given by Mtv + Btv + Tvt = Dtv + Bvt + Etv . On the other hand, IL has equity normalized to be worth 0 at the beginning of period t − 1 in the base case where it does not grant credit to OR, i.e., IL’s balance sheet can be written as Lv Lv Lv Lv Mt−1 + Bt−1 + TLv t−1 = Dt−1 + Bt−1 , Lv Lv where MtLv , BtLv , TLv t , Dt , and Bt denote the PVs of IL’s subprime RMLs, RMBSs, Treasuries, deposits and borrowings, respectively.

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hv Bt+1,1

q v Bt−1

1−q

Period t − 1

lv Bt+1,1

Period t + 1

Figure 3. Evolution of the Value of the RMBS Portfolio. 1.2.4.

Riskless and Risky Subprime RMLs

In period t, OR has access to a riskless, positive NPV RML denoted by Mt+nv , which we will call the riskless RML with PV denoted by Mt+v . This RML is extended by OR in period t, 2 and will receive the proceeds in period t + 1, 1. The NPV of the social benefits e + > 0. The expected from extending this riskless RML, which do not accrue to IL, are B t value of the riskless RML, Mt+v , is the size of the cash reserve, Etr , so that

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E[Mt+v ] = Etr . In period t, it is not only possible for OR to extend riskless RMLs but, instead, can extend risky RMLs with the same timing as the former lending opportunity. This second type of RML, the risky RML, has a negative NPV of magnitude −Mt−nv < 0, where Mt−nv represents the expected loss from investing in the risky RML, E[(1 − rt−Rnv )rt−Snv Mt−nv ], where rt−Rnv and rt−Snv denote the recovery rate and the default rate of the nett present value of the risky RML, respectively. Thus, total investor wealth, which includes shareholder plus creditor wealth, is destroyed by investing in the risky RML. For the marginal −v cost of the risky RML, Mt−v , being denoted by c−v coincides t , we suppose the cost of Mt with the cash reserve, Etr , and E[Mt−v ] is such that −v E[Mt−v ] = Etr − Mt−nv , Etr = c−v t Mt .

The NPV of the risky RML is −E[(1 − rt−Rnv )rt−Snv Mt−nv ]t < 0, and the NPV of social e −nv = 0. benefits from the risky RML that do not accrue to IL are normalized to zero, i.e, B t Therefore, the difference in aggregate social benefits from the risky and riskless RML et = (M +nv + B e +nv ) − (−M −nv + B e −nv ) = M +nv + B e +nv + M −nv > 0. B t t t t t t

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This means that if the riskless rather than the risky RML is extended, society gains the NPV of the riskless RML to investors, Mt+nv , and the additional social benefits of the riskless e + . Further, when OR does not extend the risky RML, it does not obliterate wealth RML, B t of magnitude Mt−nv . The following assumptions about risky RMLs are also important. Assumption 1.3 (OR’s Repayment of IL’s Loan): If OR fails to pay back IL, we assume that there is an exogenous social cost of et > 0. C Also, we assume that the following holds. Assumption 1.4 (OR Insolvency in the Low Demand State): We assume that lv Bt+1,1 + Etr − Dtv − Bvt + Mt+nv < 0,

so that OR is insolvent with a low demand realization even with the increase in the NPV, Mt+nv , which comes from extending a riskless RML. Next, we decompose the NPV of subprime RMLs denoted by M into three components, viz., a fully amortizing, refinancing and defaulting components. In period t, we consider the decomposition

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Mtnv = (1 − rf nv − rSnv )Mtnv + rf nv Mtnv + rSnv Mtnv .

(1.2)

where rSnv and rf nv are the rates of defaulting and refinancing , respectively, of OR’s RMLs at NPV, M nv . An analogue of (1.2) can be written for the PV of subprime RMLs, M v . We assume that refinancing excludes default so that rSnv = 0. Fully amortizing subprime RMLs are considered to be full-term loans so that rf nv = rSnv = 0. Suppose that the above preliminaries and assumptions hold. In this case, because Btv = 2Dtv = Dtv + Bvt , and

Etr

> E[(1 −

rt−Rnv )rt−Snv Mt−nv ]

+



 q µ−Hv M −Hv , 1−q t

where µ−Hv = rt−Hv − c−Hωv − p−iHv + c−pHv rt−Hf v − (1 − rt−HRv )rt−HSv , it follows t t t t that

Btv

+

Etr

−

Dtv

−

Bvt

− E[(1 −

rt−Rnv )rt−Snv Mt−nv ]

−



 q µ−Hv M −Hv > 0. 1−q t

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300 1.2.5.

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al. G’s Subsidy and Its Losses

Both OR and IL aim to maximize expected returns to shareholders who enjoy limited liability. If either bank defaults on a RML commitment or fails to pay back depositors, their shareholders will be ruined. Any expected losses, for G from the capital injection, which may take the form of a direct or indirect subsidy, leads to deadweight losses from taxation (see, for instance, (14)). These losses are proportional to the size of any subsidy, St , so that τ |St |, St , where St ∈ (−∞, ∞) and 1 > τ > 0, where τ is a proportionality constant and |St | is the size of the subsidy. Therefore, all else being equal, G strictly prefers to offer a subsidy of zero. It seems reasonable that the deadweight losses of any subsidy are substantial, but far less than unity. 1.2.6.

Subgame Perfect Nash Equilibrium

A subgame Nash perfect equilibrium (SPE8 ) is an equilibrium that can be found by using backward induction, an iterative process for solving finite extensive form or sequential games. In other words, the last player is the first one to find the optimal strategy. Then the rest, next-to-last optimal actions will be determined based on the last player’s action. The procedure continues in this manner backwards until all the solutions for each player have been determined. In this book chapter, we consider a SPE which is formulated in a manner that depends on whether OR does or does not voluntarily participate in a bailout.

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1.3.

Main Problems of the Chapter

The main problems to emerge from the previous subsections can be formulated as follows.

Problem 1.5 (Defaulting RMLs): In the defaulting RML case, can we characterize OR’s choices of RML extension, compare preferred equity, common equity and toxic RMBS minimum subsidies and their recapitalizations as well as describe OR’s voluntary participation in bailouts ? (see Propositions 2.6, 2.7, 2.8 and 2.9 in Section 2.).

Problem 1.6 (Refinancing RMLs): In the refinancing RML case, can we characterize OR’s choices of RML extension, compare preferred equity, common equity and toxic RMBS minimum subsidies and their recapitalizations as well as describe OR’s voluntary participation in bailouts ? (see Propositions 3.5, 3.6, 3.7 and 3.8 in Section 3.). 8 A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy.

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Problem 1.7 (Fully Amortizing RMLs): In the fully amortizing RML case, can we characterize OR’s choices of RML extension, compare preferred equity, common equity and toxic RMBS minimum subsidies and their recapitalizations as well as describe OR’s voluntary participation in bailouts ? (see Propositions 4.5, 4.6, 4.7 and 4.8 in Section 4.).

Problem 1.8 (Defaulting vs Refinancing vs Fully Amortizing RMLs): How do the defaulting, refinancing and fully amortizing RML cases compare with each other in terms of bailouts ? (see Sections 2., 3. and 4.).

Problem 1.9 (Connections with the SMC): How do the subprime RMLs/RMBSs and bank bailout models developed in this book chapter relate to the SMC ? (see Section 5.).

2.

Defaulting RMLs and Subprime Bank Bailouts

In this section, we study the case involving defaulting subprime RMLs and their relation with bank bailouts.

2.1.

Background to Bank Bailouts in the Defaulting RML Case

In this section, we assume that Assumptions 1.1 to 1.4 from Subsection 1.2. hold. In addition, the following assumptions are important.

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Assumption 2.1 (Defaulting RMLs: Return in Excess): We assume that

µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > 0, t is the return in excess (return rate - risk free rate) of the amount invested in the risky RML in the high state, where + c−Hpnv − pHinv rt−Hf nv − (1 − rt−HRnv )r−HSnv . µ−Hnv = rt−Hnv − c−Hωnv t t t t Here r−Hnv , c−Hωnv , pHinv , c−Hpnv , r−Hf nv , r−HRnv and r−HSnv , are the marginal rate of return, cost of funds, default premium, cost of prepayment accruing to OR, rate of refinancing, rate of recovery, and default rate, respectively, for OR’s risky RMLs in the high state. Assumption 2.2 (Defaulting RMLs: Nett Loss From Low Demand State for Risky RMLs): We assume that   1 − q −Lnv −Lnv St−Lnv = − µt Mt q

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is the nett loss from the risky RML in the low demand state, where − pLinv + c−Lpnv rt−Lf nv − (1 − rt−LRnv )rt−LSnv . µ−Lnv = rt−Lnv − c−Lωnv t t t t Here r−Lnv , c−Lωnv , pLinv , c−Lpnv , r−Lf nv , r−LRnv and r−LSnv , are the marginal rate of return, cost of funds, default premium, cost of prepayment accruing to OR, rate of refinancing, rate of recovery, and default rate, respectively, for OR’s risky RMLs in the low state. In the high demand state, the risky RML investment returns µ−Hv Mt−Hv = Etr + µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > Etr . t t In the low demand state, the risky RML return is a positive amount, which is less than the principal

µ−Lv Mt−Lv t

=

Etr

−



 q µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] 1−q t

− pLiv + c−Lpv rt−Lf v − (1 − rt−LRv )rt−LSv . The PV of these where µ−Lv = rt−Lv − c−Lωv t t t t returns is

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−v µ−v t Mt

  −Hnv −Rnv −Snv −nv = q Etr + µ−Hnv M − E[(1 − r )r M ] t t t t t     q −Hnv −Rnv −Snv −nv +(1 − q) Etr − µ−Hnv M − E[(1 − r )r M ] t t t t 1−q t = Etr − E[(1 − rt−Rnv )rt−Snv Mt−nv ] < Etr .

−pv −f v −v −ωv where µ−v − piv rt − (1 − rt−Rv )rt−Sv . t + ct t = r t − ct The following assumptions about risky RMLs are crucial to our subsequent analysis.

Assumption 2.3 (Defaulting RMLs: Nett Returns from Risky RMLs at NPV): We assume that high nett returns for RMLs with negative NPV exceed such returns for positive NPV RMLs. Symbolically, we have that µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > µ+nv Mt+nv , t t where µ+nv = rt+nv − c+ωnv − p+inv + c+pnv rt+f nv − (1 − rt+Rnv )rt+Snv . t t t t Assumption 2.4 (Defaulting RMLs: Costs and Expected Value of Risky RMLs): Suppose the risky RML at PV, Mt−v , costs, Etr , with expected value of E[Mt−v ] = Etr − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > 0, where E[(1 − rt−Rnv )rt−Snv Mt−nv ] > 0.

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Assumption 2.5 (Defaulting RMLs: Risky RML Returns in the Low State): We assume that

Etr

2.2.

>

Etr

−



 q µ−Lv Mt−Lv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > 0. 1−q t

Defaulting RMLs: OR’s RML Extensions in Period t When It Purchases Toxic RMBSs in Period t + 1

In the next proposition, we look at OR’s defaulting RML extension behavior in period t when it purchased toxic RMBSs in period t − 1. Proposition 2.6 (Defaulting RMLs: RML Extension Choices): Suppose that Assumptions 2.1, 2.3, 2.4 and 2.5 hold. OR will choose the risky instead of the riskless RML if it buys toxic RMBSs in period t − 1. Proof. A full proof of this result can be found in Appendix 8.1..

2.3.

Defaulting RMLs: Comparing Subsidy and Recapitalization Strategies

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Next, we consider G’s recapitalization problem in period t, 1. Firstly, we compare the costs incurred during the purchase of Btv and Etpv as well as Etcv , in the recapitalization of a troubled OR. The following proposition considers VPCs for ORs for all RMLs. Proposition 2.7 (Defaulting RMLs: Comparing Minimum Subsidies): Suppose that Assumptions 2.1, 2.2, 2.3, 2.4 and 2.5 hold. The minimum subsidies for which a troubled OR’s participation constraints are satisfied are identical regardless of whether G buys toxic RMBSs, Btv , preferred equity, Etvp , or common equity, Etcv , in that OR, so that v cv b bE pv = b SB SE t = St t .

(2.1)

Proof. A full proof of this result can be found in Appendix 8.2.. The next proposition compares the ELCs for Btv , Etpv and Etcv used to recapitalize a troubled OR. Proposition 2.8 (Defaulting RMLs: Preferred Equity vs Common Equity vs Toxic RMBSs): Suppose that Assumptions 2.1, 2.2, 2.3, 2.4 and 2.5 hold. Regardless of whether voluntary participation is necessary or not (see Proposition 2.7), Etpv capital injections are strictly dominated by both Etcv capital injections and G’s purchase of Btv . Proof. A full proof of this result can be found in Appendix 8.3..

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Defaulting RMLs: Voluntary Participation in Bank Bailouts

Next, we look at the nature of the SPE that results from OR deciding to voluntarily participate in the bailout. Proposition 2.9 (Defaulting RMLs: OR’s Voluntary Participation in Bailout): Suppose that Assumptions 2.1, 2.2, 2.3, 2.4 and 2.5 hold. (a) If ORs must voluntarily participate in a bailout, then G will be indifferent between a strategy of buying a common equity, Etcv , or buying toxic RMBSs, Btv . If G buys btcv , +∞), and G will common equity, Etcv , the common equity stake will be Etcv ∈ [E cv v E B pay as subsidy b St = b St (b) If OR decides to voluntarily participate in a bailout, then the SPE may be described as follows. 1. If both

b SE t

cv

cv +nv v Bv v et+ + E[rt−Sv (1 − rt−Rv )Mt−v ] + (1 − q)C et > τ b , > cBv +B SE t t Bt + rt Bt and Mt

then OR will lend from IL to buy Btv . OR will be bailed out with Etcv if RML returns cv cv b cv are low and receive a subsidy b SE t , where Et ∈ [Et , +∞). Notwithstanding the RML returns in period t, OR will extend the low risk RML in period t − 1 and IL’s repayment by OR, in period t + 1, will be ensured.

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2. If either

b SE t

cv

cv +nv v Bv v et+ + E[rt−Sv (1 − rt−Rv )Mt−v ] + (1 − q)C et ≤ τ b , ≤ cBv +B SE t t Bt + rt Bt or Mt

then OR will invest in Treasuries and there will be no bailout. (c) If voluntary participation in the bailout is not needed, then this means that

b SE t

cv

cv +nv Bv v v et+ + E[rt−Sv (1 − rt−Rv )Mt−v ] + (1 − q)C et ≤ τ b +B SE , ≤ cBv t t Bt + rt Bt or Mt

so that OR will purchase Treasuries and no bailout will take place. Proof. A full proof of this result can be found in Appendix 8.4..

3.

Refinancing RMLs and Subprime Bank Bailouts

In this section, we study the case involving defaulting subprime RMLs and their relation with bank bailouts. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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305

Background to Bank Bailouts in the Refinancing RML Case

In this section, we assume that Assumptions 1.1 to 1.4 from Subsection 1.2. hold. In addition, the following assumptions are important. Assumption 3.1 (Refinancing RMLs: Return in Excess): We assume that µ−Hrnv Mt−Hrnv > 0, t where µ−Hrnv = rt−Hrnv −c−Hωrnv −pHirnv +c−Hprnv rt−Hf rnv . Here r−Hrnv , c−Hωrnv , t t t t pHirnv , c−Hprnv and r−Hf rnv are the marginal rate of return, cost of funds, default premium, cost of prepayment accruing to OR and rate of refinancing for OR’s risky RMLs in the high state in the refinancing case. In the high demand state, the risky RML investment returns µ−Hrv Mt−Hrv = Etrr + µ−Hrnv Mt−Hrnv > Etrr . t t where µ−Hrv = rt−Hrv − c−Hωrv − pHirv + c−Hprv rt−Hf rv . In the low demand state, the t t t t risky RML returns a positive amount, which is less than the principal

µ−Lrv Mt−Lrv t

=

Etrr

−



 q µ−Hrnv Mt−Hrnv , 1−q t

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− pLirv + c−Lprv rt−Lf rv . The PV of these returns is where µ−Lrv = rt−Lrv − c−Lωrv t t t t µ−rv Mt−rv t

= q



Etrr

+

µ−Hrnv Mt−Hrnv t



    q −Hrnv −Hrnv rr + (1 − q) Et − µ Mt . 1−q t

The following assumptions about risky RMLs in the refinancing case are crucial to our subsequent analysis. Assumption 3.2 (Refinancing RMLs: Nett Returns from Risky RMLs at NPV): We assume that high nett returns for RMLs with negative NPV exceed such returns for positive NPV RMLs. Symbolically, we have that µ−Hrnv Mt−Hrnv > µ+rnv Mt+rnv , t t where µ+rnv = rt+rnv − c+ωrnv − p+irnv + c+prnv rt+f rnv . t t t t Assumption 3.3 (Refinancing RMLs: Costs and Expected Value of Risky RMLs): Suppose the risky RML at PV, Mt−rv , costs, Etrr , with expected value of E[Mt−rv ] = Etrr > 0.

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Assumption 3.4 (Refinancing RMLs: Risky RML Returns in the Low State): We assume that

Etrr > Etrr −

3.2.



 q µ−Lrv Mt−Lrv > 0. 1−q t

Refinancing RMLs: OR’s RML Extensions in Period t When It Purchases Toxic RMBSs in Period t + 1

In the next proposition, we look at a refinancing OR’s RML extension behavior in period t when it purchased toxic RMBSs in period t − 1. Proposition 3.5 (Refinancing RMLs: RML Extension Choices): Suppose that Assumptions 3.1, 3.2, 3.3 and 3.4 are satisfied and that the subprime RMLs are refinancing and non-defaulting. In this case, OR will choose the risky RML above the riskless RML if it buys toxic RMBSs in period t − 1. Proof. A full proof of this result can be found in Appendix 8.5..

3.3.

Refinancing RMLs: Comparing Subsidy and Recapitalization Strategies

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Next, we consider G’s recapitalization problem in period t, 1. Firstly, we compare the costs incurred during the purchase of Btrv and Etprv as well as Etcrv , in a recapitalization of a troubled OR. The following proposition considers VPCs for ORs for all RMLs. Proposition 3.6 (Refinancing RMLs: Comparing Minimum Subsidies): Suppose that Assumptions 3.1, 3.2, 3.3 and 3.4 hold and that the subprime RMLs are refinancing and nondefaulting. The minimum subsidies for which the troubled OR’s participation constraints are satisfied are the same without regard for whether G buys toxic RMBSs, Btrv , preferred equity, Etprv , or common equity, Etcrv , in that OR. Thus rv prv crv b SB =b SE =b SE . t t t

(3.1)

Proof. A full proof of this result can be found in Appendix 8.6.. The next proposition compares the ELCs for Btrv , Etprv and Etcrv used to recapitalize a troubled OR. Proposition 3.7 (Refinancing RMLs: Preferred Equity vs Common Equity vs Toxic RMBSs): Suppose that Assumptions 3.1, 3.2, 3.3 and 3.4 hold and that the subprime RMLs are refinancing and non-defaulting. Regardless of whether voluntary participation is necessary or not (see Proposition 3.6), Etprv capital injections are strictly dominated by both Etcrv capital injections and G’s purchase of Btrv . Proof. A full proof of this result can be found in Appendix 8.7..

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307

Refinancing RMLs: Voluntary Participation in Bank Bailouts

Next, we look at the nature of the SPE that results from OR deciding to voluntarily participate in the bailout in the refinancing case. Proposition 3.8 (Refinancing RMLs: OR’s Voluntary Participation in Bailout): Suppose that Assumptions 3.1, 3.2, 3.3 and 3.4 hold and that the subprime RMLs are refinancing and non-defaulting. Then the following statements are true. (a) If ORs must voluntarily participate in the program, then G, acting in the public interest, will be indifferent between a strategy of purchasing common equity, Etcrv , or buying toxic RMBSs, Btrv . If G buys common equity, Etcrv , the common equity stake will be crv rv btcrv , +∞), and G will pay as subsidy b Etcrv ∈ [E SE =b SB t t

(b) If OR decides to voluntarily participate in a bailout, then the SPE is given as follows. 1. If both

crv crv +rnv e +r + (1 − q)C etr > τ b b , > cBrv Btrv + rtBrv Brv +B SE SE t t and Mt t t t

then OR will lend from IL to buy Btrv . OR will be bailed out with Etcrv if RML returns crv btcrv , +∞). Notwithstanding the , where Etcrv ∈ [E are low and receive a subsidy b SE t RML returns in period t, OR will extend the low risk RML in period t − 1 and IL’s repayment by OR, in period t + 1, will be ensured.

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2. If either

crv crv +rnv e +r + (1 − q)C etr ≤ τ b b , ≤ cBrv Btrv + rtBrv Brv +B SE SE t t t or Mt t t

then OR will invest in Treasuries and there will be no bailout. (c) If voluntary participation in the bailout is not needed, then this means that

crv crv +rnv e +r + (1 − q)C etr < τ b b SE ≤ cBrv Btrv + rtBrv Brv +B SE , t t t or Mt t t

so that OR will purchase Treasuries and no bailout will take place. Proof. A full proof of this result can be found in Appendix 8.8..

4.

Fully Amortizing RMLs and Subprime Bank Bailouts

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4.1.

Background to Bank Bailouts in the Fully Amortizing RML Case

In this section, we assume that Assumptions 1.1 to 1.4 from Subsection 1.2. hold. In addition, the following assumptions are important. Assumption 4.1 (Fully Amortizing RMLs: Return in Excess): We assume that µ−Hanv Mt−Hanv > 0, t − pHianv . Here r−Hanv , c−Hωanv and pHianv are where µ−Hanv = rt−Hanv − c−Hωanv t t t the marginal rate of return, cost of funds and default premium for OR’s risky RMLs in the high state in the fully amortizing case. In this case, in the high demand state, risky fully amortizing RML investment returns µ−Hav Mt−Hav = Etra + µ−Hanv Mt−Hanv > Etra . t t where µ−Hav = rt−Hav − c−Hωav − pHiav . In the low demand state, the risky RML returns t t t a positive amount, which is less than the principal

µ−Lav Mt−Lav t

=

Etar

−



 q µ−Hanv Mt−Hanv , 1−q t

− pLiav . The PV of these returns is where µ−Lav = rt−Lav − c−Lωav t t t

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µ−av Mt−av t

      q −Hanv −Hanv −Hanv ar = q Etar + µ−Hanv M + (1 − q) E − µ M , t t t t 1−q t

where µ−av = rt−av − c−ωav − p−iav . t t t The following assumptions about risky RMLs in the fully amortizing case are crucial to our subsequent analysis. Assumption 4.2 (Fully Amortizing RMLs: Nett Returns from Risky RMLs at NPV): We assume that high nett returns for RMLs with negative NPV exceed such returns for positive NPV RMLs. Symbolically, we have that µ−Hanv Mt−Hanv > µ+anv Mt+anv , t t where µ+anv = rt+anv − c+ωanv − p+ianv . t t t Assumption 4.3 (Fully Amortizing RMLs: Costs and Expected Value of Risky RMLs): Suppose the risky RML at PV, Mt−av , costs, Etar , with expected value of E[Mt−av ] = Etar > 0.

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Assumption 4.4 (Fully Amortizing RMLs: Risky RML Returns in the Low State): We assume that Etar

4.2.

>

Etar

−



 q µ−Lav Mt−Lav > 0. 1−q t

Fully Amortizing RMLs: OR’s RML Extensions in Period t When It Purchases Toxic RMBSs in Period t + 1

In this subsection, for fully amortizing RMLs, we discuss OR’s RML extensions in period t when it purchases toxic RMBs in period t. Proposition 4.5 (Fully Amortizing RMLs: RML Extension Choices): Suppose that Assumptions 4.1, 4.2, 4.3 and 4.4 hold and that the subprime RMLs are fully amortizing. In this case, OR will choose the risky instead of the riskless RML if it buys toxic RMBSs in period t − 1. Proof. A proof of this result is similar to that of Proposition 3.5 in Section 3. (see Appendix 8.5.) except that the cost of prepayment term is zero.

4.3.

Fully Amortizing RMLs: Comparing Subsidy and Recapitalization Strategies

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Next, we compare the costs incurred during the purchase of all Btav and Etpav as well as Etcav , in a recapitalization of a troubled OR. The following proposition considers OR’s VPCs for all RMBSs. Proposition 4.6 (Fully Amortizing RMLs: Comparing Minimum Subsidies): Suppose that Assumptions 4.1, 4.2, 4.3 and 4.4 hold and that the subprime RMLs are fully amortizing. The minimum subsidies for which troubled ORs VPCs are satisfied are identical regardless of whether G buys toxic RMBSs, Btav , preferred equity, Etpav , or common equity, Etcav , in that OR. Thus av pav cav b SB =b SE =b SE . t t t

(4.1)

Proof. A proof of this result is similar to that of Proposition 3.6 in Section 3. (see Appendix 8.6.) except that the cost of prepayment term is zero. The next proposition compares the ELCs for Btav , Etpav and Etcav used to recapitalize a troubled OR. Proposition 4.7 (Fully Amortizing RMLs: Preferred Equity vs Common Equity vs Toxic RMBSs): Suppose that Assumptions 4.1, 4.2, 4.3 and 4.4 hold and that the subprime RMLs are fully amortizing. Regardless of whether voluntary participation is necessary or not (see Proposition 4.6), Etpav capital injections are strictly dominated by both Etcav capital injections and G’s purchase of Btav . Proof. A proof of this result is similar to that of Proposition 3.7 in Section 3. (see Appendix 8.7.) except that the cost of prepayment term is zero.

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4.4.

Fully Amortizing RMLs: Voluntary Participation in Bank Bailouts

Next, we look at the nature of the SPE that results from OR deciding to voluntarily participate in the bailout. Proposition 4.8 (Fully Amortizing RMLs: OR’s Voluntary Participation in Bailout): Suppose that Assumptions 4.1, 4.2, 4.3 and 4.4 hold and that the subprime RMLs are fully amortizing. (a) If ORs must voluntarily participate in the program, then G will be indifferent between a strategy of buying common equity, Etcav , or buying toxic RMBSs, Btav . If G buys btcav , +∞), and G common equity, Etcav , the common equity stake will be Etcav ∈ [E cav av E B will pay as subsidy b St =b St

(b) If OR decides to voluntarily participate in a bailout, then the SPE may be described as follows. 1. If both

cav cav +anv e +a + (1 − q)C eta > τ b b SE > cBav Btav + rtBav Bav +B SE , t t t and Mt t t

then OR will lend from IL to buy Btav . OR will be bailed out with Etcav if RML returns cav btcav , +∞). Notwithstanding the are low and receive a subsidy b SE , where Etcav ∈ [E t RML returns in period t, OR will extend the low risk RML in period t − 1 and IL’s repayment by OR, in period t + 1, will be ensured.

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2. If either

cav cav +anv e +a + (1 − q)C eta ≤ τ b b SE ≤ cBav Btav + rtBav Bav +B SE , t t or Mt t t t

then OR will invest in Treasuries and there will be no bailout.

(c) If voluntary participation in the bailout is not needed, then this means that

cav cav +anv e +a + (1 − q)C eta < τ b b SE ≤ cBav Btav + rtBav Bav +B SE , t t t or Mt t t

so that OR will purchase Treasuries and no bailout will take place.

Proof. A proof of this result is similar to that of Proposition 3.8 in Section 3. (see Appendix 8.8.) except that the cost of prepayment term is zero.

5.

Discussion of Subprime Bank Bailouts

In this section, we discuss subprime bank bailouts in the cases where OR’s RMLs default, refinance and fully amortize. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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311

Defaulting RMLs and Subprime Bank Bailouts

In the defaulting RML case in Section 2., we characterize OR’s choices of RML extension (see Proposition 2.6), compare preferred equity, common equity and toxic RMBS minimum subsidies (see Proposition 2.7) and their recapitalizations (see Proposition 2.8) as well as describe OR’s voluntary participation in bailouts (see Proposition 2.9).

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In the case where OR’s subprime RMLs default, we investigate how various types of capital injections (purchasing of RMBSs, preferred equity and common equity) affect OR’s incentives to lend efficiently. We address the question of which RMBSs should be used to recapitalize troubled ORs. In particular, this study provides a theoretical model that analyzes recapitalizations when banks have enough liquid assets to participate in risk-shifting. We assume that G cannot contract over OR’s lending policy. Instead, G’s primary mechanism for improving the troubled OR’s lending decisions is to recapitalize it. In our paper, we assume that troubled ORs has a sufficient amount of liquid assets to extend new RMLs. Nevertheless, since OR is not solvent in all states of the world, it is tempted to shift risk onto its creditors. For defaulting RMLs, in terms of inducing efficient lending, G’s purchases of new common equity is always at least or more effective than buying toxic RMBSs or purchasing preferred equity. We find that the subsidies (overpayment for assets) are always necessary to induce OR to agree to the recapitalization voluntarily. Further, we determine that the purchasing of preferred equity is the least effective form of recapitalization. All the gains from such a recapitalization come from G’s implicit subsidy from purchasing that equity. In this case, it is only the G’s overpayment for preferred equity that improves lending incentives. Moreover, we prove that just because OR agrees to a preferred equity recapitalization does not imply that OR’s lending behavior will improve. Indeed, as long as G buys enough common equity or toxic RMBSs, lending incentives improve without a subsidy for potentially, but not yet insolvent, ORs. The previous paragraph brings into question the effectiveness of the TARP. More specifically, G has mostly used preferred equity to inject capital into ORs. There are concerns about the TARP bailout, which have not been explicitly addressed by this paper, but probably should be addressed by lawmakers or the incoming administration going forward. It could pose some problems that the recipients of the TARP monies are not prohibited from cash acquisitions. Cash acquisitions increase OR’s leverage or reduce the acquirer’s cash cushion and thus increase the risk of its equity, all other things being equal. OR will often be tempted to undo any leverage decreasing transaction, which includes a taxpayer subsidy, with a leverage increasing transaction. It is somewhat surprising that so many ORs have received TARP funds. Certainly, many of those banks are not too-big-to-fail. As of Monday 8 December 2008, there were 156 financial institutions that had received at least preliminary approval for TARP. Many of the banks due to receive TARP funds probably would not pose systematic risk if they were closed down due to insolvency. It is not clear that the closure of all but the handful of giant commercial and formerly investment banks pose any short or long-term damage to the financial system as a whole. For this reason, the banking sector as a whole may be made healthier if the weaker regional banks were closed down and their assets were sold to stronger institutions. It may be more efficient to close down rather than recapitalize insolvent banks. Nevertheless, (2), for example, have more to say about how many, and which banks should be bailed out. In contrast, the present paper primarily

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answers which RMLs should be used to bail out banks that are deemed too-big-to-fail. The analysis in Section 2. enables us to derive an originate-to-hold (OTH) model for OR’s profit with defaulting RMLs at NPV. In period t, in order to derive this model, we nv M nv , take cash inflow to be constituted by returns on risky RMBSs, rtBnv Btnv , RMLs, µM t t nv nv Treasuries, rtT Tnv t , recovery amount, Rt , CDS protection leg payments, C (S(Ct )) and Πpnv is the NPV of future profits from additional RMLs based on current RMLs. Furt thermore, we consider the average weighted cost of funds for Mtnv , ccωnv Mtnv , NPV of t RMLs in default, µSt Mtnv , CDS premium, pit (Ct )Mtnv , the all-in cost of holding securities, cBnv Btnv , interest paid to depositors, rtDnv Dtnv , cost of taking deposits, cDnv Dtnv , interest t t B nv paid to borrowers, rtB Bnv t , the cost of borrowing, ct Bt , provisions against deposit withT nv nv drawals, Pt (Tt ), and the value of RML losses S (Ct ), as cash outflow. Here rtDnv and are the deposit rate and marginal cost of deposits, respectively, rtB and cBt are the borcDnv t rower rate and marginal cost of borrowing, respectively. In this case, we have that an OTH model for OR’s profit with subprime RMLs at NPV may be expressed as Πnv t

nv nv Bnv nv = µnv Bt t Mt + C (E[S(Ct )]) + rt     pnv T nv T nv Dnv Dnv nv B B +rt Tt − P (Tt ) − rt + ct Dt − rt + ct Bnv ≥ 0, (5.1) t + Πt

nv cωnv − pinv + cpnv r f nv − (1 − r Rnv )r Snv . From equation (5.1), we where µnv t = rt − ct t t t t t may have

rtBnv Btnv

=

Πnv t

+P

T

(Tnv t )

    Dnv Dnv nv Bnv Bnv + rt + ct D t + r t + ct Bnv t

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pnv nv nv Tnv nv −µnv t Mt − C (E[S(Ct )]) − rt Tt − Πt .

(5.2)

In this case, rtBnv Btnv ≥ 0 and rtBnv Btnv < 0, if     nv ≤ Πnv + P T (Tnv ) + r Dnv + cDnv D nv + r Bnv + cBnv Bnv µnv M t t t t t t t t t t pnv −C nv (E[S(Ct )]) − rtTnv Tnv t − Πt

(5.3)

and     nv > Πnv + P T (Tnv ) + r Dnv + cDnv D nv + r Bnv + cBnv Bnv µnv M t t t t t t t t t t pnv −C nv (E[S(Ct )]) − rtTnv Tnv t − Πt ,

(5.4)

respectively.

5.2.

Refinancing RMLs and Subprime Bank Bailouts

In the refinancing RML case in Section 3., we characterize OR’s choices of RML extension, compare preferred equity, common equity and toxic RMBS minimum subsidies Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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313

and their recapitalizations as well as describe OR’s voluntary participation in bailouts (see Propositions 3.5, 3.6, 3.7 and 3.8, respectively). For the refinancing case, the paper (10) provides a relationship between OR’s subprime RML rate, rM , the LTVR, L, and a prepayment cost, cp , by means of the simultaneous equations model rtM

= α0 Lt + α1 cpt + α2 Xt + α3 Ztr

M

+ ut

Lt = β 1 rtM + β 2 Xt + β 3 ZtL + vt

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cpt

(5.5)

cp

= γ 1 rtM + γ 2 Xt + γ 3 Zt + wt .

MRs typically choose from a menu of RML rate and LTVR options, and choice of a prepayment penalty triggers an adjustment to the interest rate. Thus, L and cp are endogenous variables in the interest rate equation. We have no reason to believe that LTVR and prepayment cost are simultaneously determined. Therefore, cp does not appear in the LTVR equation, and L does not appear in the prepayment penalty equation. Matrix X comprises exogenous explanatory variables: loan characteristics (owner occupied, loan purpose, documentation requirements); MR characteristics (income and FICO score); and distribution M p channel (broker origination). The last term in each equation Z r , Z L or Z c comprises the instruments excluded from either of equations to identify our system of equations. This model is, of course, a simplification. Other terms such as type of interest rate, the term to maturity, and distribution channel may be endogenous as well. Nevertheless, by consideration of simultaneity in the choice of interest rate and prepayment penalty, we are able to address the issue of possible bias in estimates of the effect of prepayment penalties on loan prices. Section 3. shows that even if there is not a possibility of RMLs defaulting after their extension in period t, the purchase of toxic RMBSs in period t − 1 may lead to OR having to be bailed out.

5.3.

Fully Amortizing RMLs and Subprime Bank Bailouts

In the fully amortizing RML case in Section 4., we characterize OR’s choices of RML extension (see Proposition 4.5), compare preferred equity, common equity and toxic RMBS minimum subsidies (see Proposition 4.6) and their recapitalizations (see Proposition 4.7) as well as describe OR’s voluntary participation in bailouts (see Proposition 4.8). The conclusions drawn from Section 4. are similar to those of Subsection 5.2. for refinancing RMLs. For instance, it demonstrates that despite RMLs not defaulting after their extension in period t, the purchase of toxic RMBSs in period t − 1 may lead to an OR bailout.

6.

2007-2009 Timeline of SMC-related Events Pertaining to Subprime Bank Bailouts

In this section, we provide examples of notable events related to subprime bank bailouts in the period 2007 to 2009. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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6.1.

2007-2009 Timeline of Events Related to Subprime Bank Bailouts

In this subsection, we give a timeline of SMC-related events involving subprime bank bailouts. Monday, 24 December 2007: A consortium of banks officially abandons the U.S. government-supported ”super-SIV” mortgage crisis bailout plan announced in midOctober, citing a lack of demand for the risky mortgage products on which the plan was based, and widespread criticism that the fund was a flawed idea that would have been difficult to execute. Wednesday, 18 June 2008: As the chairman of the Senate Banking Committee Connecticut’s, Christopher Dodd, proposed a housing bailout to the Senate floor that would assist troubled subprime mortgage lenders such as Countrywide Bank. Wednesday, 1 October 2008: The U.S. Senate passes HR1424, their version of the $ 700 billion bailout bill. A report says that French Finance Minister, Christine Lagarde, calls for an emergency EU bailout fund for banks threatened with failure. Monday, 6 October 2008: Proposed Hypo Real Estate bailout collapses. German Chancellor, Angela Merkel, announces new plan for Hypo bailout worth $ 69 billion. Major markets in Europe, Asia and Latin America sank as traders looked past America’s bank bailout bill and focused on Europe’s growing financial crisis.

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Wednesday, 8 October 2008: The U.K. government announces details of a rescue package for the banking system worth at least GBP 50 billion ($ 88 billion). BBC Business Editor, Robert Peston, says the deal amounts to a semi-nationalization. White House considers taking ownership stakes in private banks as a part of the bailout bill. Warren Buffett and George Soros criticized the original approach of the bailout bill. Monday, 13 October 2008: EU stock markets bounce back in response to EU leaders’ bailout announcements. French president, Nicolas Sarkozy, pledges 360 billion Euros in liquidity to French banks. The plan will include 320 billion Euros in guarantees for new bank debt and a 40 billion Euros fund for recapitalizing lenders. In return for the bailout, the French government will demand conditions on the banks such as changes to pay and bonus structures. The U.K. government starts the nationalization process by injecting GBP 37 billion of taxpayers’ money into the nations three largest banks. The U.K. government will end up owning a majority share in the Royal Bank of Scotland (RBS) and over a 40 % share in Lloyds and HBOS. In return for the bailout, the banks have agreed to cancel dividend payments until the loans are repaid, have board members appointed by the Treasury and limit executive pay. Monday, 10 November 2008: The U.S. Treasury announced investment of $ 40 billion in preferred equity of AIG, adjusting the terms of the existing credit line and its amount. Total exposure, including equity and debt, is now $ 150 billion. Funds were drawn from the Troubled Asset Relief Program (TARP) which was not available at the time of the original bailout of AIG.

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Friday, 9 January 2009: The Congressional Oversight Panel issues its second monthly report on the expenditure of the Troubled Asset Relief Program (TARP). Official figures show the US jobless rate rose to 7.2 % in December 2008, the highest in 16 years. The figures also indicate that more US workers lost jobs in 2008 than in any year since World War II. Monday, 12 January 2009: The FDIC issues a letter to FDIC-supervised institutions calling on them to implement a process to monitor their use of 1) capital injections, 2) liquidity support and/or 3) financing guarantees obtained through Treasury, FDIC, and Federal Reserve financial stability programs. At the request of President–Elect Obama, President Bush submits a request to Congress for the remaining $ 350 billion in TARP funding for use by the incoming administration.

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Friday, 16 January 2009: The Treasury Department announces that it will lend $ 1.5 billion from the TARP to a special purpose entity created by Chrysler Financial to finance the extension of new consumer auto loans. Sony posted $ 1.1 billion operating loss. The US government reaches an agreement to provide Bank of America with another $ 20 billion in fresh aid from its $ 700 billion financial rescue fund. The emergency funding will help the troubled bank absorb the losses it incurred when it bought Merrill Lynch. Struggling US banking giant Citigroup announces plans to split the firm in two, as it reports a quarterly loss of $ 8.29 billion (GBP 5.6 billion). Wednesday, 21 January 2009: Britain says its bank bailouts have dealt a major blow to Britain’s public finances as the recapitalization of ailing Royal Bank of Scotland (RBS) blows out the deficit to GBP 44.2 billion ($ 62 billion) last month, its highest on record. Friday, 23 January 2009: The U.S. Treasury Department purchases a total of $ 326 million in preferred equity from 23 U.S. banks under the Capital Purchase Program. Wednesday, 28 January 2009: The U.S. House of Representatives passed President Barack Obama’s $ 819 billion (GBP 572 billion) economic stimulus package. Passed by 244 votes to 188, no Republicans backed the plan, saying it was too expensive and would not work. Friday, 30 January 2009: The U.S. Treasury Department purchases a total of $ 1.15 billion in preferred equity from 42 U.S. banks under the Capital Purchase Program. Tuesday, 3 February 2009: The Federal Reserve announces the extension through Friday, 30 October 2009, of the existing liquidity programs scheduled to expire on Thursday, 30 April 2009. The Board of Governors and the FOMC note ”continuing substantial strains in many financial markets.” Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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In addition, the swap lines between the Federal Reserve and other central banks are also extended to Friday, 30 October 2009. The expiration date for the TALF remains Thursday, 31 December 2009, and the TAF does not have an expiration date. Wednesday, 4 February 2009: The Treasury Department issues restrictions on executive pay for financial institutions that receive government assistance during the financial crisis. Any bank receiving exceptional assistance from the US government will be required to limit the pay of senior executives to $500 000 a year. The companies will be able to give executives restricted equity above the $ 500 000 limit but the equity cannot vest until the government has been completely paid back for the assistance given, with interest. Thursday, 5 February 2009: Russia announces that it will change its approach to combating the global financial crisis. Instead of bailing out individual companies, Russia will attempt to support the economy through the banking sector and limit its deficit through large budget cuts. This news followed a credit downgrade of Russia’s debt by the Fitch rating agency. Friday, 6 February 2009: The U.S. Treasury Department purchases a total of $238.5 million in preferred equity from 28 U.S. banks under the Capital Purchase Program.

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Tuesday, 10 February 2009: U.S. Treasury Secretary Timothy Geithner announces a Financial Stability Plan involving Treasury purchases of convertible preferred equity in eligible banks, the creation of a Public-Private Investment Fund to acquire troubled loans and other assets from financial institutions, expansion of the Federal Reserves Term AssetBacked Securities Loan Facility (TALF), and new initiatives to stem residential mortgage foreclosures and to support small business lending. Timothy Geithner, the US Treasury Secretary, introduces the Financial Stability Plan in an attempt to clean up the US financial system. The $2 trillion plan includes a financial stability trust to manage the US governmentfs investments, a public-private investment fund to clean up the banksf balance sheets, a consumer and business lending initiative, a small business and community lending initiative, and housing support and foreclosure prevention plan. Commentators have suggested that the Financial Stability Plan is not detailed enough to restore confidence in the financial system. UBS announces that it lost $17 billion in 2008, the largest corporate loss in Swiss history. UBS intends to keep its investment banking division despite cutting 1500-2000 more investment banking jobs. Friday, 13 February 2009: The U.S. Treasury Department purchases a total of $429 million in preferred equity from 29 U.S. banks under the Capital Purchase Program. Tuesday, 17 February 2009: The Treasury Department releases its first monthly survey of bank lending by the top 20 recipients of government investment through the Capital Purchase Program. The survey found that banks continued to originate, refinance and renew loans from the beginning of the program in October through December 2008. Monday, 23 February 2009: The Treasury Department, Federal Deposit Insurance Corporation, Office of the Comptroller of the Currency, Office of Thrift Supervision, and Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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the Federal Reserve Board issue a joint statement that the U.S. government stands firmly behind the banking system, and that the government will ensure that banks have the capital and liquidity they need to provide the credit necessary to restore economic growth. Further, the agencies reiterate their determination to preserve the stability of systemically important financial institutions. Tuesday, 24 February 2009: The U.S. Treasury Department purchases a total of $365.4 million in preferred equity from 23 U.S. banks under the Capital Purchase Program. Thursday, 26 February 2009: The FDIC announces that the number of ”problem banks” increased from 171 institutions with $116 billion of assets at the end of the third quarter of 2008, to 252 insured institutions with $159 billion in assets at the end of fourth quarter of 2008. The FDIC also announces that there were 25 bank failures and five assistance transactions in 2008, which was the largest annual number since 1993. Friday, 27 February 2009: The Treasury Department announces its willingness to convert up to $25 billion of Citigroup preferred equity issued under the Capital Purchase Program into common equity. The conversion is contingent on the willingness of private investors to convert a similar amount of preferred shares into common equity. Remaining Treasury and FDIC preferred shares issued under the Targeted Investment Program and Asset Guarantee Program would be converted into a trust preferred security of greater structural seniority that would carry the same 8% cash dividend rate as the existing issue. The U.S. Treasury Department purchases a total of $394.9 million in preferred equity from 28 U.S. banks under the Capital Purchase Program.

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Friday, 20 March 2009: The U.S. Treasury Department purchases a total of $80.8 million in preferred equity from 10 U.S. banks under the Capital Purchase Program. Monday, 23 March 2009: The Federal Reserve and the U.S. Treasury issue a joint statement on the appropriate roles of each during the current financial crisis and into the future, and on the steps necessary to ensure financial and monetary stability. The four points of agreement are 1) The Treasury and the Federal Reserve will continue to cooperate in improving the functioning of credit markets and fostering financial stability; 2) The Federal Reserve should avoid credit risk and credit allocation, which are the province of fiscal authorities; 3) The need to preserve monetary stability, and that actions by the Federal Reserve in the pursuit of financial stability must not constrain the exercise of monetary policy as needed to foster maximum sustainable employment and price stability; and 4) The need for a comprehensive resolution regime for systemically critical financial institutions. In addition, the Treasury will seek to remove the Maiden Lane facilities from the Federal Reserve’s balance sheet. Thursday, 26 March 2009: The Treasury Department outlines a framework for comprehensive regulatory reform that focuses on containing systemic risks in the financial system. The framework calls for assigning responsibility over all systemically-important firms and critical payment and settlement systems to a single independent regulator. Further, it calls for higher standards on capital and risk management for systemically-important firms;

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for requiring all hedge funds above a certain size to register with a financial regulator; for a comprehensive framework of oversight, protection and disclosure for the over-the-counter derivatives market; for new requirements for money market funds; and for stronger resolution authority covering all financial institutions that pose systemic risks to the economy. Friday, 27 March 2009: The U.S. Treasury Department purchases a total of $193 million in preferred equity from 14 U.S. banks under the Capital Purchase Program. Tuesday, 31 March 2009: The General Accounting Office (GAO) releases a report on the status of efforts to address transparency and accountability issues for the Troubled Asset Relief Program (TARP). The report provides information about the nature and purpose of TARP funding through Friday, 27 March 2009, the performance of the Treasury Department’s Office of Financial Stability, and TARP performance indicators. Four bank holding companies announced that they had redeemed all of the preferred shares that they had issued to the U.S. Treasury under the Capital Purchase Program of the Troubled Asset Relief Program (TARP). The four banks are Bank of Marin Bancorp (Novato, CA), Iberiabank Corporation (Lafayette, LA), Old National Bancorp (Evansville, IN), and Signature Bank (New York, NY).

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Friday, 3 April 2009: The U.S. Treasury purchases a total of $54.8 million in preferred equity from 10 U.S. banks under the Capital Purchase Program. Tuesday, 7 April 2009: The Congressional Oversight Panel releases its monthly report on the Troubled Asset Relief Program (TARP). This report, entitled ”Assessing Treasury’s Strategy: Six Months of TARP,” provides information about expenditures and commitments to date of TARP funds, evaluates the Treasury Department’s strategy for improving the condition and functioning of financial institutions and markets, and discusses potential policy alternatives. Friday, 10 April 2009: The U.S. Treasury purchases a total of $22.8 million in preferred equity from 5 U.S. banks under the Capital Purchase Program. Friday, 17 April 2009: The U.S. Treasury purchases a total of $40.9 million in preferred equity from 6 U.S. banks under the Capital Purchase Program. Friday, 24 April 2009: The U.S. Treasury purchases a total of $121.8 million in preferred equity from 12 U.S. banks under the Capital Purchase Program. Friday, 1 May 2009: The U.S. Treasury purchases a total of $45.5 million in preferred equity from 7 U.S. banks under the Capital Purchase Program. Friday, 8 May 2009: The U.S. Treasury purchases a total of $42 million in preferred equity from 7 U.S. banks under the Capital Purchase Program. Friday, 15 May 2009: The U.S. Treasury purchases a total of $107.6 million in preferred equity from 14 U.S. banks under the Capital Purchase Program. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Friday, 22 May 2009: The Federal Reserve Board announces the adoption of a final rule that will allow bank holding companies to include in their Tier 1 capital without restriction senior perpetual preferred equity issued to the U.S. Treasury Department under the Troubled Asset Relief Program (TARP). The U.S. Treasury purchases a total of $108 million in preferred equity from 12 U.S. banks under the Capital Purchase Program. Friday, 29 May 2009: The U.S. Treasury purchases a total of $89 million in preferred equity from 8 U.S. banks under the Capital Purchase Program. Friday, 5 June 2009: The U.S. Treasury purchases a total of $40 million in preferred equity from 3 U.S. bank under the Capital Purchase Program. Tuesday, 9 June 2009: The Treasury Department announces that 10 of the largest U.S. financial institutions participating in the Capital Purchase Program have met the requirements for repayment established by the primary federal banking supervisors. If these firms choose to repay the capital acquired through the program, the Treasury will receive up to $68 billion in repayment proceeds. Friday, 12 June 2009: The U.S. Treasury purchases a total of $39 million in preferred equity from 7 U.S. Banks under the Capital Purchase Program.

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Wednesday, 17 June 2009: The Treasury Department releases a proposal for reforming the financial regulatory system. The proposal calls for the creation of a Financial Services Oversight Council and for new authority for the Federal Reserve to supervise all firms that pose a threat to financial stability, including firms that do not own a bank. Friday, 19 June 2009: The U.S. Treasury purchases a total of $84.7 million in preferred equity from 10 U.S. banks under the Capital Purchase Program. Friday, 26 June 2009: The United States Treasury announces its policy regarding the disposition of warrants acquired under the Capital Purchase Program. For publicly traded companies, the Treasury received warrants to purchase common shares of equity; these warrants have not been exercised. The Treasury’s policy allows banks to repurchase warrants following a multi-step process to determine fair market value. Sunday, 26 July 2009: Citigroup announces the preliminary results of its offers to exchange its publicly held convertible and non-convertible preferred and trust preferred securities for newly issued shares of its common equity. Citigroup also announces that it expects to complete a further exchange with the U.S. Government of $12.5 billion in aggregate liquidation preference of Citigroup preferred equity, and that in aggregate, approximately $58 billion in aggregate liquidation value of preferred and trust preferred securities will have been exchanged to common equity as a result of the completion of all the exchange offers. Monday, 14 September 2009: The U.S. Treasury releases the report ”The Next Phase of Government Financial Stabilization and Rehabilitation Policies.” This report focuses on Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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winding down those programs that were once deemed necessary to prevent systemic failure in the financial markets and the broader economy. Thursday, 22 October 2009: The Special Master for TARP Executive Compensation releases determinations on the compensation packages for the top 25 most highly paid executives at the seven firms that received exceptional TARP assistance (AIG, Citigroup, Bank of America, Chrysler, Chrysler Financial, GM, and GMAC). Sunday, 1 November 2009: CIT Group, Inc., files for bankruptcy protection under Chapter 11 of the bankruptcy code. The U.S. Government purchased $2.3 billion of CIT preferred equity in December 2008 under the Troubled Asset Relief Program (TARP). The firm’s prepackaged bankruptcy is expected to wipe out the equity stakes of CIT’s current shareholders, including the U.S. Government. Monday, 9 November 2009: The Federal Reserve Board announces that 9 of the 10 bank holding companies that were determined in the Supervisory Capital Assessment Program earlier this year to need to raise capital or improve the quality of their capital now have increased their capital sufficiently to meet or exceed their required capital buffers. GMAC was the one firm that to date has not raised enough capital to meet its required capital buffer.

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Wednesday, 2 December 2009: Bank of America announces that it will repurchase the entire $45 billion of cumulative preferred equity issued to the U.S. Treasury under the Troubled Asset Relief Program (TARP) after the completion of a securities offering. Wednesday, 9 December 2009: U.S. Treasury Secretary Timothy Geithner sends a letter to Congressional leaders outlining the Administration’s exit strategy for the Troubled Asset Relief Program (TARP). Secretary Geithner announces that the program will be extended to Sunday, 3 October 2010, and focus on three areas: 1) foreclosure mitigation; 2) providing capital to small and community banks; and 3) possible increases in the Treasury Department’s commitment to the Term Asset-Backed Securities Loan Facility (TALF). Monday, 14 December 2009: Citigroup announces that it has reached an agreement with the U.S. Government to repay the remaining $20 billion in TARP trust preferred securities issued to the U.S. Treasury. Citi will issue $20.5 billion of capital and debt, and the U.S. Treasury will sell up to $5 billion of the common equity it holds in a concurrent secondary offering.

6.2.

Specific Subprime Bank Bailout Events

In this subsection, we highlight specific subprime bank bailout events. 6.2.1.

Bear Sterns Bailout

On Friday, 14 March 2008, the Federal Reserve Bank of New York and JP Morgan Chase jointly extended a 28-day emergency loan to Bear Stearns in order to prevent the potential market crash that would result from Bear Stearns failing. In reality, counterparty and trader belief in Bear’s ability to repay its obligations quickly receded. Since the emergency

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loan was not perceived to be enough to keep Bear Stearns solvent and because of the fear of systemic losses if Bear was permitted to open in the markets on Monday, 17 March 2008, Bernanke and Paulson Jr. persuaded Bear’s CEO Alan Schwartz to sell the bank before the opening of the Asian market. In this regard, on Sunday 16 March 2008, Bear merged with JP Morgan Chase in an equity swap worth $ 2 a share – less than 10 % of Bear’s market value. This sale price represented a significant loss as its equity had traded at $ 172 and $ 93 a share as late as January 2007 and February 2008, respectively. Furthermore, the U.S. Federal Reserve issued a non-recourse loan of $ 29 billion to JP Morgan Chase, thereby taking on the risk of Bear Stearns’s less liquid assets. This entails the collateralization of the U.S. Federal Reserve loan by RML debt and ensures that the U.S. government cannot seize J.P. Morgan Chase’s assets if the RML debt collateral becomes insufficient to repay the loan. Expert opinions attribute the collapse of Bear Stearns to a lack of confidence rather than a lack of capital. On Monday, 24 March 2008, a class action lawsuit was filed on behalf of Bear’s shareholders, challenging the terms of JP Morgan’s acquisition of the bank. As a result, new terms were agreed that raised JP Morgan Chase’s offer from $ 2 to $ 10 a share – the equivalent of a $ 1.2 billion agreement. The reconfigured deal was aimed to appease investors and prevent legal action against JP Morgan Chase. Also, it was aimed at preventing employees – whose past compensation consisted of Bear Stearns equity capital – from resigning. The Bear bailout is considered to be an extreme example, and as a consequence continues to raise important questions about U.S. Federal Reserve intervention. On Friday, 29 May 2008, Bear Stearns shareholders approved the sale to JP Morgan Chase at the $ 10-per-share price.

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6.2.2.

Goldman Sachs Group Inc. Bailout

Berkshire Hathaway purchased $ 5 billion in Goldman’s preferred equity capital and acquired warrants to buy another $ 5 billion in Goldman’s E cv . Under the TARP, in October 2008, Goldman received a $ 10 billion capital injection from the U.S. government. 6.2.3.

Morgan Stanley Bailout

On Sunday, 21 September 2008, the U.S. Federal Reserve oversaw the change in status of Morgan Stanley from an investment bank to a bank holding company. On Tuesday, 14 October 2008, Mitsubishi UFJ Financial Group – Japan’s largest bank – bought a stake of $ 9 billion (21 %) in Morgan Stanley equity. Equity growth subsequent to the purchase, was preceded by the October 2008 stock market crash during which concerns over the completion of the Mitsubishi deal caused a dramatic decrease in Morgan Stanley’s equity price to 14 year lows. 6.2.4.

2008 United Kingdom Bank Rescue Package

Due to the ongoing global financial crisis, a bank bailout totalling $ 850 billion was announced by the U.K. government on Wednesday, 8 October 2008. This was in response to major decreases in the stock market in preceding weeks and subsequent concerns about

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the financial stability of U.K. banks. The main objective of the bailout was to restore confidence in financial markets and help stabilize the U.K. banking sector. The programme also provided for a range of short-term loans and guarantees of interbank lending as well as up to £50 billion of government investment in the banks themselves. 6.2.5.

2008 Canadian Bank Bailout

By the end of the 2008 fiscal year, the Canadian government purchased an additional $ 50 billion of insured mortgage pools as part of its ongoing efforts to maintain the availability of longer-term credit in Canada. This purchase brought to $ 75 billion the maximum value of mortgages purchased through Canada Mortgage and Housing Corporation (CMHC) under this program. 6.2.6.

Some European Bank Bailouts

Fortis Bank was jointly bailed out by the Dutch, Belgium and Luxemburg governments for Euro 4.7 billion. Eventually Fortis was sold to BNP Paribas. Further European bailouts included the three largest Icelandic banks (Glitnir, Landsbanki, and Kaupthing) and UBS in Switzerland.

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6.2.7.

Bank of America Bailout

Bank of America (BoA) received $ 25 billion and $ 20 billion in bailout funds from the U.S. government through the TARP program in September 2008 and on Friday, 16 January 2009, respectively. An additional $ 118 billion in potential losses were guaranteed by the government. This extra payment formed part of a deal with the U.S. government to preserve BoA’s merger with the troubled Merrill Lynch. According to a Sunday, 15 March 2009 article in The New York Times, BoA received an additional $ 5.2 billion in government bailout money via the American International Group (AIG).

7.

Conclusions and Future Directions In this section, we provide conclusions and suggest topics for further study.

7.1.

Conclusions

This book chapter has demonstrated that the RMLs used to bail out ORs, which are perceived as too-big-to-fail, affects welfare. This paper analyzed capital injections involving buying toxic RMBSs, purchasing preferred equity and buying common equity. In particular, from both an ex post and ex ante perspective the least expensive bailout involves G’s buying common equity. Preferred equity is the most expensive in terms of its affects on ex ante and ex post welfare. The present paper considers the optimal RMLs used in OR bailouts from both an ex ante and ex post perspective. In this paper, the big bank is tempted to shift risk onto creditors when the quality of its RML portfolio deteriorates. G, attempting to maximize ex post

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welfare, chooses among buying OR’s toxic RMBSs, purchasing preferred equity or buying common equity. It is found that common equity capital injections always produce the lowest subsidy to the troubled OR. Indeed, no subsidy is needed to induce efficient lending if the troubled OR can be forced to sell common equity at its fair value. Lower subsidies in capital injections are more likely to encourage OR to buy toxic RMBSs in the first place. Therefore, common equity capital injections always lead to the lowest ex ante distortions. Preferred equity capital injections are the least efficient and lead to the largest subsidy. Indeed, the implicit subsidy in preferred equity capital injections is the only thing that induces efficient lending ex post. This paper casts doubt on the effectiveness and the efficiency of G’s attempts to recapitalize ORs through the TARP. In short, because it primarily uses preferred equity to inject capital into highly leveraged ORs, it is unlikely to curb incentives to extend speculative RMLs.

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7.2.

Future Directions

The main thrust of future research will involve models of bank items driven by L´evy processes (see, for instance, Protter in (25, Chapter I, Section 4)). Such processes have an advantage over the more traditional modeling tools such as Brownian motion in that they describe the non-continuous evolution of the value of economic and financial items more accurately. For instance, because the behavior of bank loans, profit, capital and CARs are characterized by jumps, the representation of the dynamics of these items by means of L´evy processes is more realistic. As a result of this, recent research has strived to replace the existing Brownian motion-based bank models (see, for instance, (9), (11) and (21)) by systems driven by more general processes. Also, a study of the optimal capital structure should ideally involve the consideration of taxes and costs of financial distress, transformation costs, asymmetric bank information and the regulatory safety net. Another research area that is of ongoing interest is the (credit, market, operational, liquidity) risk minimization of bank operations within a regulatory framework (see, for instance, (19) and (23)). A further possible field of study arises from the bank capital literature that motivates capital and internal financing as important in bank decisions by invoking specific market imperfections or mispricings such as costly equity-financing frictions, dead-weight costs from insolvency and risk-insensitive deposit provisions for loan losses premiums. Furthermore, the assumed asset, equity and liability processes and the bank’s objectives and control variates will be dependent on the specific market or pricing conditions being assumed. These effects are not fully recognized in our contribution and requires further attention. Also, more connections between Basel capital regulation and the SMC has to be established (see, for instance, (12)).

8.

Appendices

In this section, we provide some proofs of important results for bank bailouts with defaulting RMLs. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

324

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al.

8.1.

Proof of Proposition 2.6

We note that OR’s equity with positive NPV is

Et+

=q



hv Bt+1,1

+

Etr

−

Bvt

−

Dtv

+

Mt+nv

 ,

where hv Bt+1,1 + Etr − Bvt − Dtv + Mt+nv   q hv µ−Hnv Mt−Hnv > 0 > Bt+1,1 + Etr − Bvt − Dtv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] − 1−q t lv but Bt+1,1 + Etr − Bvt − Dtv + Mt+nv < 0.

This means that OR’s value is raised by the riskless RML but is obligations remain risky. Also, the equity with negative NPV is Et−

=q



hv Bt+1,1

+

Etr

+

µ−Hnv Mt−Hnv t

−

Bvt

−

Dtv

− E[(1 −



rt−Rnv )rt−Snv Mt−nv ]

(8.1)

in period t + 1, where µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] > Mt+nv t

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hv lv and Bt+1,1 + Etr − Bvt − Dtv + Mt+nv > 0, but Bt+1,1 + Etr − Bvt − Dtv + Mt+nv < 0.

Thus Et− > Et+ . Subtracting Et+ from Et− , we have Et− − Et+ = q(µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] − Mt+nv ) > 0. t

8.2.

Proof of Proposition 2.7

In order to deduce (2.1) we note that all VPCs emanate from +nv r v v hv Et∗∗+ − Et− = (Btv + S∗∗ ) − q(Bt+1,1 + Etr + µ−Hnv Mt−Hnv t t + Et − Dt − Bt + Mt

−Bvt − Dtv − E[(1 − rt−Rnv )rt−Snv Mt−nv ]) ≥ 0,

(8.2)

where ∗∗ is used to denote toxic RMBSs, Btv , preferred equity, Etpv , or common equity, Etcv . Solving for S∗∗ t from equation (8.2), we get

S∗∗ t

  +nv lv r v v ≥ −(1 − q) Bt+1,1 + Et − Dt − Bt + Mt +q(µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] − Mt+nv ) ≡ b S∗∗ t > 0. t

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8.3.

325

Proof of Proposition 2.8

v pv pv v The result follows from subtracting e SM from e SE , where e SE >e SM t t t t . In addition to pv that, we have that e SE > 0, therefore t pv v cv∗ e eE pv > e SE >e SM SE = 0. t t ; St t

(8.3)

An important distinguishing feature of these capital injection types is that the minimum efficient lending subsidies used to recapitalize OR are distinct. These constraints may be calculated from Et∗∗+ − Et∗∗− ≥ 0, where ∗∗ represent toxic RMBSs, Btv , preferred equity, Etpv , or common equity, Etcv . By solving S∗∗ t , all ELCs may be represented by v SB t

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SE t

pv

cv SE t

8.4.



  q −Hnv −Hnv −Rnv −Snv −nv +nv ≥ µt Mt − E[(1 − rt )rt Mt ] − Mt , 1−q   v − Btv + Etr − Dtv − Bvt + Mt+nv ≡ e SM t ≥

  q −Hnv −Rnv −Snv −nv +nv µ−Hnv M − E[(1 − r )r M ] − M t t t t t t 1−q   pv lv − Bt+1,1 + Etr − Dtv − Bvt + Mt+nv ≡ e SE > 0 and t



 q (µ−Hnv Mt−Hnv − E[(1 − rt−Rnv )rt−Snv Mt−nv ] − Mt+nv ) ≥ t 1−q   cv lv − Bt+1,1 + Etr − Dtv − Bvt + Mt+nv − Etcv ≡ e SE t . 

Proof of Proposition 2.9

(a) Proposition 2.9(a) follows from equation (2.1) given by

and

v cv b bE pv = b SB SE t = St t

pv v cv∗ e eE pv > e SE >e SM SE = 0. t t ; St t

(see Proposition 2.8, equation (8.3). The minimum equilibrium stakes of common equity are found by Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

326

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al.

Etcv

   q −Hnv −Hnv −Rnv −Snv −nv +nv b cv ≡ q ≥ E µ M − E[(1 − r )r M ] − M t t t t t t t 1−q   lv − Bt+1,1 − Dtv − Bvt + Mt+nv > 0,

if ORs must volunteer for the subprime bailout program. First, there is no difference between the three types of subprime bailouts (buying RMBSs, buying preferred equity or buying common equity) in terms of the VPC, according to equation (2.1). Yet, there is a big difference between the three alternatives in terms of the ELC, according to equation (8.3). The ELC is always slack for BtSv purchases and common equity subprime bailouts. Yet, it is always the binding constraint for preferred equity subprime bailouts. Thus, the subsidy is minimized given that voluntary participation is required for common equity or toxic RMBS purchases. (b) Social welfare is very different under each of the scenarios in Proposition 2.9(b). Ex ante, period t − 1 social welfare in scenario 1 is v etsnv − cBv bE cv Mt+nv + B t Bt − τ St .

This is clearly less than social welfare under scenario 2,

etsnv . Mt+nv + B

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Clearly, social welfare would be benefit if G could commit to not bailout OR when it must voluntarily participate. If G can force OR to participate in the common equity bailout, there is no conflict between ex post and ex ante welfare maximization for G. According to Proposition 2.9(c), G can buy an equity stake at fair market value in the troubled OR large enough cv so that no subsidy, b SE t , is necessary to induce efficient lending in the defaulting RML case. cv (c) We know from equation (8.3) that the subsidy, b SE t , required to bail out the troubled OR is weakly the smallest when Etcv is used and the troubled OR’s VPC can be ignored.

Suppose that OR did buy Btv in period t − 1. G could push the subsidy to zero in etcv , +∞). Thus, period t. In this scenario, G will weakly prefer to buy Etcv ∈ [E cv E b St will be zero in all possible states of the world if OR buys toxic RMBSs. OR’s shareholders must sacrifice

Blv lv v cBv t Bt + rt Bt > 0

to underwrite Btv . The cost Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

The Subprime Mortgage Crisis and Its Connections with Bank Bailouts

327

v Blv lv cBv t Bt + rt Bt

exceeds the benefit, which is the expected subsidy of zero. Therefore, OR will purchase Treasuries and no bailout will take place.

8.5.

Proof of Proposition 3.5

We note that OR’s equity with positive NPV is Et+r

=q



rhv Bt+1,1

+

Etrr

−

Brv t

−

Dtrv

+

Mt+rnv

 ,

where rhv + E rr − Brv − D rv + M +rnv Bt+1,1 t t t t   q rhv + E rr − Brv − D rv − µ−rHv Mt−rHv > 0 > Bt+1,1 t t t 1−q t +rnv rlv rv but Bt+1,1 + Etrr − Brv < 0. t − D t + Mt

This means that OR’s value is raised by the riskless RML but is obligations remain risky. Also, the equity with negative NPV is

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Et−r

=q



rhv Bt+1,1

+

Etrr

+

µ−rHnv Mt−rHnv t

−

Brv t

−

Dtrv



(8.4)

in period t + 1, where µ−rHnv Mt−rHnv > Mt+rnv t +rnv +rnv rv rv rlv rhv + Etrr − Brv < 0. + Etrr − Brv > 0, but Bt+1,1 and Bt+1,1 t − Dt + Mt t − Dt + Mt

Thus Et−r > Et+r . Subtracting Et+r from Et−r , we have Et−r − Et+r = q(µ−rHnv Mt−rHnv − Mt+rnv ) > 0. t

8.6.

Proof of Proposition 3.6

In order to deduce (3.1) we note that all VPCs emanate from Et∗∗+r − Et−r

=

+rnv ) (Btrv + S∗∗r + Etrr − Dtrv − Brv t t + Mt −rHnv −rHnv rhv rr Mt −q(Bt+1,1 + Et + µt rv −Brv t − Dt ) ≥ 0,

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

(8.5)

328

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al.

where ∗∗ is used to denote toxic RMBSs, Btrv , preferred equity, Etprv , or common equity, Etcrv . Solving for S∗∗r from equation (8.5), we get t

S∗∗r t

  +rnv rlv rr rv rv ≥ −(1 − q) Bt+1,1 + Et − Dt − Bt + Mt +q(µ−rHnv Mt−rHnv − Mt+rnv ) ≡ b S∗∗r > 0. t t

8.7.

Proof of Proposition 3.7

rv prv prv rv The result follows from subtracting e SM from e SE , where e SE >e SM . In addition t t t t prv to that, we have that e SE > 0, therefore t prv rv prv crv∗ e SE >e SM ; e SE >e SE = 0, t t t t

(8.6)

An important distinguishing feature of these capital injection types is that the minimum efficient lending subsidies used to recapitalize OR are distinct. These constraints may be calculated from Et∗∗+r − Et∗∗−r ≥ 0, where ∗∗ represent toxic RMBSs, Btrv , preferred equity, Etprv , or common equity, Etcrv . By solving S∗∗r t , all ELCs may be represented by

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rv SB t

SE t

prv

crv SE t

8.8.



  q −rHnv −rHnv +rnv ≥ µt Mt − Mt , 1−q   rv +rnv − Btrv + Etrr − Dtrv − Brv + M ≡e SM t t t ≥

  q −rHnv +rnv µ−rHnv M − M t t t 1−q   prv +rnv rlv rr rv rv − Bt+1,1 + Et − Dt − Bt + Mt > 0 and ≡e SE t 

 q (µ−rHnv Mt−rHnv − Mt+rnv ) ≥ t 1−q   crv +rnv rlv − Bt+1,1 + Etrr − Dtrv − Brv + M − Etcrv ≡ e SE . t t t 

Proof of Proposition 3.8

(a) Proposition 3.8(a) follows from equation (3.1),

rv prv crv b SB =b SE =b SE t t t

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329

and

prv rv prv crv∗ e SE >e SM ; e SE >e SE = 0. t t t t

(see Proposition 3.7, equation (8.6)). The minimum equilibrium stakes of common equity are found by

Etcrv

  −rHnv −rHnv +rnv µt Mt − Mt ≥   +rnv rlv rv rv > 0, − Bt+1,1 − Dt − Bt + Mt btcrv E



q ≡q 1−q

if ORs must volunteer for the subprime bailout program. First, there is no difference between the three types of subprime bailouts (buying RMBSs, buying preferred equity or common equity) in terms of the VPC, according to equation (3.1). Yet, there is a big difference between the three alternatives in terms of the ELC, according to equation (8.6). The ELC is always slack for Btrv purchases and common equity subprime bailouts. Yet, it is always the binding constraint for preferred equity subprime bailouts. Thus, the subsidy is minimized given that voluntary participation is required for common equity or toxic RMBS purchases.

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(b) Social welfare is very different under each of the scenarios in Proposition 3.8(b). Ex ante, period t − 1 social welfare in scenario 1 is

crv etrsnv − cBrv Mt+rnv + B Btrv − τ b SE . t t

This is clearly less than social welfare under scenario 2,

etrsnv . Mt+rnv + B

Clearly, social welfare would be benefit if G could commit to not bailout OR when it must voluntarily participate. If G can force OR to participate in the common equity bailout, there is no conflict between ex post and ex ante welfare maximization for G. According to Proposition 3.8(c), G can buy an equity stake at fair market value in the troubled OR large enough crv so that no subsidy, b SE ,, is necessary to induce efficient lending. t crv

(c) We know from equation (8.6) that the subsidy, b SE , required to bail out the troubled t crv OR is weakly the smallest when Et is used and the troubled OR’s VPC can be ignored.

Suppose that OR did buy Btrv in period t − 1. G could push the subsidy to zero in etcrv , +∞). Thus, period t. In this scenario, G will weakly prefer to buy Etcrv ∈ [E Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

330

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al. crv b SE will be zero in all possible states of the world if OR buys toxic RMBSs. OR’s t shareholders must sacrifice

cBrv Btrv + rtrBlv Brlv t >0 t to underwrite Btrv . The cost cBrv Btrv + rtrBlv Brlv t t exceeds the benefit, which is the expected subsidy of zero. Therefore, OR will purchase Treasuries and no bailout will take place.

References [1] Acharya S. Charter value, minimum bank capital requirement and deposit insurance pricing in equilibrium. Journal of Banking and Finance 1996; 20:351–375. [2] Acharya VV, Yorulmazer T. Cash-in-the-market pricing and optimal resolution of bank failures. Review of Financial Studies 2008; 21:2705–2742. [3] Aghion P, Bolton P, Fries S. Optimal design of bank bailouts: The case of transition economies. Journal of Institutional and Theoretical Economics 1999; 155(1999); Mohr Siebeck-ISSN 0932–4569.

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[4] Bebchuck LA. A better plan for addressing the financial crisis. Economists’ Voice 2008; 5(5):Article 7. [5] Bebchuck LA. A plan for addressing the financial crisis. Working Paper 2008; Harvard University. [6] Borio C. The financial turmoil of 2007-?: a preliminary assessment and some policy considerations. Bank for International Settlements March 2008; Working Paper 251. [7] Chaney PK, Thakor AV. Incentive effects of benevolent intervention, the case of government loan guarantees. Journal of Public Economics 1985; 26:169–189. [8] Cordella T, Yeyati EL. Bank bailouts: Moral hazard vs. value effect. Journal of Financial Intermediation 2003; 12:300–330. [9] Decamps JP, Rochet JC, Roger B. The three pillars of Basel II: Optimizing the mix. Journal of Financial Intermediation 2004; 13:132–155. [10] Elliehausen G, Staten ME, Steinbuks J. The effect of prepayment penalties on the pricing of subprime mortgages. Journal of Economics and Business 2008; 60:33–46. [11] Fouche CH, Mukuddem-Petersen J, Petersen MA. Continuous-time stochastic modeling of capital adequacy ratios for banks. Applied Stochastic Models in Business and Industry 2000; 22:41–71.

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

The Subprime Mortgage Crisis and Its Connections with Bank Bailouts

331

[12] Fouche CH, Mukuddem-Petersen J, Petersen MA, Senosi MC. Bank valuation and its connections with the subprime mortgage crisis and Basel II Capital Accord, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 740845, 44 pages, 2008. [13] Frexias X. Optimal Bail Out Policy, Conditionality and Constructive Ambiguity. Working Paper, University Poppeu Fabra 1999. [14] Goolsbee A. Taxes, organizational form and the deadweight loss of corporate income tax. Journal of Public Economics 1998; 69:143–152. [15] Gorton G, Huang L. Liquidity, efficiency and bank bailouts. NBER Working Paper Series 2002; Working Paper 9158. Available: http://www.nber.org/papers/w9158 [September 2002]. [16] Hakenes H, Schnabel I. Banks without parachutes: Competitive effects of government bail-out policies. Journal of Financial Stability 2009; 1:3–11. [17] Harvey CR. The financial crisis of 2008: What needs to happen after TARP. Working Paper 2008; Duke University. [18] Hoggarth G, Reidhill J, Sinclair P. On the resolution of banking crises: Theory and evidence. Bank of England Working Paper 2004; No. 229. [19] Jackson P, Perraudin W. Regulatory implications of credit risk modelling. Journal of Banking and Finance 2000; 24:1–14.

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[20] Landler M, Dash E. Drama behind a $ 250 billion banking deal. New York Times. Available: http://www.nytimes.com/2008/10/15/business/economy/15bailout.html? [Wednesday, 15 October 2008]. [21] Leland H. Risky debt, bond covenants and optimal capital structure. Journal of Finance 1994; 49:1213–1252. [22] Merton RC. An analyticcal derivation of the cost of deposit insurance and loan guarantees. Journal of Banking and Finance 2009; 1:3–11. [23] Mukuddem-Petersen J, Petersen MA. Bank management via stochastic optimal control. Automatica 2006; 42:1395–1406. [24] Petersen MA, Senosi MC, Mukuddem-Petersen J, Mulaudzi MP, Schoeman IM. Did bank capital regulation exacerbate the subprime mortgage crisis ? Discrete Dynamics in Nature and Society, vol. 2009, Article ID 742968, 34 pages, 2009. [25] Protter P. Stochastic Integration and Differential Equations Second Edition. Springer, Berlin, 2004. [26] Rochet J-C, Tirole J. Interbank lending and systemic risk. Journal of Money, Credit and Banking 1996; 28:733–762. [27] Veronesi P, Zingales L. Paulson’s gift. Working Paper 2008; University of Chicago. Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

332

M.A. Petersen, M.C. Senosi, J. Mukuddem-Petersen et al.

[28] Wilson L. Debt overhang and bank bailouts. Social Sciences Research Network 2009; Available: http://ssrn.com/abstract=1336288 [December 2009]. [29] Wilson L. The put problem with buying toxic assets. Applied Financial Economics 2010; 20(1-2):31–35. [30] Wilson L, Yan Wu W. Common (stock) sense about risk-shifting and bank bailouts. Financial Markets nad Portfolio Management 2010; in press.

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[31] Zingales L. Why Paulson is wrong. Economists Voice 2008; 5(5):Article 3.

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INDEX

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A accountability, 318 accounting, 10, 14, 17, 18, 38, 40, 104, 112, 114, 170, 177 accounting standards, 104, 170 acquisitions, 277, 294, 311 adaptation, 21, 109, 123, 126, 134, 135, 136 adjustment, 50, 313 Africa, 119, 134, 135, 136 agricultural sector, 120 agriculture, 126, 134 algorithm, 14, 15, 21, 22, 23, 52, 276, 286 alternative hypothesis, 83 alternatives, 54, 56, 276, 318, 326, 329 amortization, 26 annual review, 4 anthropologists, ix, 100, 102, 107 anthropology, ix, 100, 114 Asia, 314 Asian crisis, 151 assessment, 2, 3, 120, 123, 135, 136, 330 assets, viii, xii, 24, 25, 26, 27, 31, 76, 78, 79, 80, 85, 86, 88, 90, 92, 93, 94, 101, 104, 112, 127, 128, 150, 160, 162, 163, 164, 165, 166, 181, 183, 236, 237, 240, 241, 242, 243, 245, 246, 247, 248, 249, 268, 269, 285, 287, 289, 290, 291, 292, 293, 311, 316, 317, 321, 332 assignment, 4 assumptions, 10, 111, 129, 248, 282, 294, 299, 301, 302, 305, 308 asymmetry, 161 Australia, 164, 177 Austria, 164, 165, 166 authority, 111, 143, 160, 318, 319 autonomy, 28, 29, 32, 37 availability, 12, 122, 322 aversion, 181, 184, 255

B bail, 292, 293, 296, 312, 322, 326, 329

balance sheet, 43, 80, 160, 166, 239, 243, 248, 257, 294, 297, 316, 317 Bangladesh, 136 bank debt, 314 bank failure, 295, 317, 330 Bank of Canada, 167 Bank of England, 331 bankers, x, 100, 106, 112, 115 banking, vii, ix, x, 100, 107, 112, 113, 159, 160, 161, 162, 163, 164, 166, 180, 235, 290, 292, 293, 311, 314, 315, 316, 317, 319, 322, 331 banking industry, 180 bankruptcy, xii, 5, 6, 14, 19, 38, 40, 41, 44, 73, 76, 82, 159, 234, 243, 264, 267, 290, 320 banks, x, xii, 4, 5, 37, 43, 100, 107, 109, 111, 112, 159, 160, 161, 162, 163, 164, 166, 168, 179, 239, 263, 265, 289, 290, 291, 292, 293, 296, 311, 312, 314, 315, 316, 317, 318, 319, 320, 322, 330 barriers, 76, 78, 91, 182, 243 basic needs, 120 basis points, 241, 242, 244, 245, 246, 247, 248, 251, 252, 254, 258, 259, 260, 261 BBB, 5, 7, 9, 12, 28, 31, 32, 34, 243, 249 behavior, viii, ix, 40, 49, 50, 99, 100, 101, 102, 106, 107, 108, 109, 115, 140, 142, 153, 156, 170, 215, 236, 248, 303, 306, 311, 323 Belgium, 91, 93, 165, 263, 322 beliefs, ix, 100 benchmarking, 39, 180 benchmarks, 5, 270, 287 beneficial effect, 293 bias, viii, 9, 22, 41, 69, 75, 77, 81, 82, 83, 89, 313 binding, 326, 329 Binomial Test, 174, 176 bioinformatics, 42 BIS, x, 72, 159, 160, 161, 162, 166, 167, 180, 262, 265 board members, 314 bond market, 234, 235, 237, 238, 250, 252, 265 bondholders, 237, 250 bonds, 2, 4, 5, 8, 9, 11, 15, 16, 38, 39, 40, 42, 44, 47, 72, 104, 105, 117, 197, 199, 234, 237, 238, 239, 242, 243, 244, 248, 249, 251, 254, 258, 259, 260, 261, 263, 264

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334

Index

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borrowers, 109, 234, 312 borrowing, 5, 127, 128, 290, 294, 312 bounds, 279, 283 breakdown, 46, 246 Britain, 315 Brownian motion, 240, 241, 323 budget cuts, 316 buffer, 160, 161, 162, 163, 164, 166, 167, 168, 320 Bulgaria, 122 business cycle, x, 45, 61, 72, 73, 159, 162, 163, 164, 166, 168 buyer, 234, 291

compensation package, 320 competence, 6 competition, 76, 90, 91, 112, 161 competitors, 78, 91, 92, 161 complement, 20 complexity, 101, 109, 200, 267 components, ix, 3, 21, 39, 44, 45, 49, 63, 100, 113, 156, 186, 215, 222, 238, 250, 256, 299 composition, 78 computation, 187, 193, 195, 197 conditional mean, 138, 139 conditioning, 104 confidence, 44, 53, 106, 112, 155, 161, 183, 290, 316, 322 C confidence interval, 183 conflict, 326, 329 calculus, 187 confusion, 33, 34 calibration, xi, 185, 186, 211, 213, 214, 220, 221, 222, Congress, 109, 112, 315 223, 224, 225 conjecture, 45, 58, 70 Canada, 97, 322 consensus, 9, 111 candidates, 23 conservation, 111, 128, 133 capital flows, 150, 151 construction, 23, 189, 236 capital inflow, 138, 151 consumers, 109, 112 capital intensive, 9 consumption, x, 119, 122, 123, 124, 127, 133, 274 capital markets, vii, 1 contamination, 113 capital outflow, 151 control, viii, xi, 75, 77, 82, 105, 109, 112, 169, 170, capitalism, viii, 99, 106 172, 176, 177, 179, 180, 183, 184, 203, 208, 210, cash flow, 24, 26, 29 211, 214, 222, 223, 243, 250, 253, 269, 291, 323, Catholic Church, viii, 99 331 causal relationship, 138 control group, xi, 169, 170, 172, 176 causality, 138, 157 convergence, 46, 76, 83, 203, 214, 215, 220 central bank, 105, 106, 111, 162, 292, 316 conversion, 111, 317 China, xi, 169, 171, 176, 177 coping strategies, 127, 128, 133 Christianity, 106 coping strategy, 128 classes, vii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, corporate governance, 170, 177 15, 16, 17, 18, 19, 20, 21, 23, 24, 27, 28, 30, 31, 33, corporations, 11, 107, 112, 169, 179, 180, 268 34, 37, 104, 181, 182, 183, 248, 253, 269, 271, 274, correlation, 3, 22, 26, 45, 46, 47, 48, 49, 62, 63, 64, 66, 275, 276 67, 69, 70, 71, 72, 74, 82, 83, 88, 121, 138, 153, classification, vii, 1, 2, 3, 6, 8, 9, 10, 11, 12, 13, 14, 15, 157, 163, 164, 165, 166, 181, 182, 183, 200, 212, 16, 17, 18, 19, 20, 21, 22, 23, 30, 32, 33, 34, 35, 37, 215, 250, 251, 252, 254, 258, 259, 260, 261 38, 39, 40, 171 correlation analysis, 48, 157 clients, ix, 100, 101 correlation coefficient, 48, 49, 64, 66, 67, 70, 88, 163, climate change, 120, 121, 133, 134, 135, 136 165 climate extremes, x, 119, 133 correlations, vii, xi, 43, 46, 47, 48, 70, 185, 186, 199, climatic factors, 120 211, 212, 213, 215 closure, 293, 311 corruption, 169 clustering, 38, 40, 45 costs, 5, 6, 26, 78, 79, 112, 138, 161, 181, 240, 243, codes, 143, 159 271, 273, 274, 277, 284, 302, 303, 305, 306, 308, collaboration, 126 309, 323 collateral, 104, 111, 290, 321 coupling, 189 collateralization, 321 covering, 11, 45, 46, 163, 235, 318 combined effect, 163 creativity, ix, 100, 102, 107 commercial bank, 12 credibility, 292 commercials, 109 credit market, 253, 317 commodity markets, 115 credit rating, vii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, communication, 136 15, 16, 17, 18, 19, 24, 25, 27, 28, 29, 30, 31, 32, 33, community, 102, 107, 111, 121, 135, 155, 316, 320 34, 35, 36, 37, 38, 39, 41, 42, 43, 45, 235, 238, 239, compatibility, 106 264 compensation, 234, 237, 240, 249, 320, 321 creditors, 28, 79, 80, 93, 240, 243, 291, 311, 322

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Index

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creditworthiness, 2, 4, 25, 39, 40, 41, 234 criticism, ix, 100, 171, 314 crops, 110, 127 cross-validation, 11, 15 culture, 95, 102, 104, 109 cumulative distribution function, 240 currency, xi, 138, 143, 150, 156, 157, 185, 186, 197, 200, 204, 211, 213, 214, 215, 221, 223, 228 current ratio, 26 cyberspace, 107 cycles, 45, 46, 47, 63, 64, 66, 69, 73, 112 cyclical component, 64 Cyprus, 162 Czech Republic, 1

335

differential equations, 205, 208 differentiation, 193 diffusion, 191, 241 directors, xi, 169, 170, 171, 172, 173, 174, 175, 176, 177 disaster, 121 discipline, 268 disclosure, x, 169, 176, 177, 318 discounting, 101 discriminant analysis, 6, 8, 9, 11, 17, 38 dispersion, 107 disposable income, 273 disposition, 319 distortions, 323 distress, 14, 42 distribution, 22, 34, 63, 67, 73, 106, 107, 112, 140, D 143, 147, 171, 172, 190, 192, 193, 195, 206, 210, 313 data availability, 37 divergence, 106 data collection, 134 diversification, 24, 73, 76, 79, 91, 92, 93, 133, 138, data mining, 40 161, 238 data set, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 22, 27, 28, diversity, 120 29, 30, 31, 32, 34, 35, 37 division, ix, 100, 316 database, 12, 16, 28, 77, 80, 165, 171 domestic markets, 137, 138 death, 117 dominance, ix, 100 debt, vii, viii, xii, 2, 3, 5, 6, 9, 17, 25, 26, 28, 29, 31, drought, 120, 124, 133 32, 36, 41, 44, 73, 74, 75, 76, 77, 79, 80, 81, 82, 85, duplication, 141 86, 88, 89, 92, 93, 94, 95, 104, 107, 109, 111, 160, duration, 46, 55, 56, 70, 272 161, 237, 240, 241, 242, 243, 248, 264, 271, 272, dynamism, 95 273, 284, 289, 290, 291, 296, 314, 316, 320, 321, 331 E debt service, 28, 29 debtors, 162 early warning, 133 debts, 26 earnings, 9, 14, 26, 120 decay, 112 East Asia, x, 137, 138, 143, 157 decision making, 285, 288 ecology, 130 decision-making process, 19, 269, 287 economic activity, xi, 43, 233, 253, 255, 262 decisions, 2, 14, 267, 268, 269, 270, 285, 286, 311, economic boom, 43 323 economic cycle, 49, 66, 164, 167 decomposition, 188, 299 economic growth, 76, 95, 161, 317 deficit, 110, 315, 316 economic policy, 95 definition, 110, 121, 160, 162, 241 economic systems, 106 deforestation, 120 economic theory, 102, 113 degenerate, 192, 195 economics, ix, 2, 40, 47, 76, 77, 100, 101, 102, 104, degradation, 120, 136 107, 111, 112, 171, 268 Denmark, 163, 179 economies of scale, 78, 79, 90, 91, 161 density, 124 ectoplasm, 109 dependent variable, 8, 81, 82, 83, 250 educational attainment, 123 deposits, 294, 295, 296, 297, 312 Egypt, viii, 99 depreciation, 26 emerging markets, 138, 143 depression, 112, 113 employees, 29, 31, 80, 85, 101, 321 deregulation, 76, 109 derivatives, xi, 101, 104, 105, 106, 107, 109, 111, 116, employment, vii, 75, 77, 95, 127, 128, 317 EMU, 159, 161, 162, 163, 164, 165, 166, 167 179, 180, 181, 182, 183, 184, 186, 188, 191, 208, energy, 29, 111 214, 234, 235, 238, 239, 290, 318 England, 111 destruction, 112 environment, 94, 95, 110, 112, 134, 185, 200 Deutsche Bundesbank, 166, 168 environmental change, 121, 135 developed countries, 120 environmental conditions, 101 deviation, 21, 47, 173, 245

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environmental factors, 121, 129 epidemiology, 121 equality, 45, 87, 89 equilibrium, 73, 293, 300, 325, 329, 330 equities, 156, 290 equity market, vii, 43, 46, 62, 70, 138, 139, 143, 146, 150, 152, 154, 156, 239, 243, 249 erosion, 112 estimating, x, 8, 10, 77, 119, 122, 288 Estonia, 162 Euro, 322 Europe, 105, 111, 235, 267, 314 European Central Bank, 234, 264 European Union, 80, 111, 162, 163, 314 evaporation, 112 evolution, viii, x, 6, 10, 13, 38, 99, 101, 159, 160, 163, 165, 182, 296, 323 exchange rate, 72, 137, 138, 139, 140, 143, 150, 154, 156, 157 exercise, 317 expenditures, 126, 318 exploitation, 161 exposure, 121, 122, 156, 161, 169, 180, 234, 314 external shocks, 163 external validation, 5 extraction, 35

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F failure, 14, 16, 38, 39, 79, 111, 182, 183, 234, 292, 314, 320 fairness, 112 faith, viii, 99, 107, 112 family, 29, 127, 190, 281, 285 family income, 29 farmers, x, 119, 120, 123, 126, 127, 128, 130, 132, 133 farming techniques, 120 Federal Reserve Board, 317, 319, 320 feedback, 138, 181 Fiji, 135 filters, 64 filtration, 197 finance, vii, ix, 2, 28, 76, 79, 80, 95, 100, 106, 111, 112, 113, 139, 171, 177, 185, 186, 187, 268, 279, 288, 315 financial crisis, xii, 45, 239, 248, 253, 262, 289, 290, 314, 316, 317, 321, 330, 331 financial distress, 6, 323 financial institutions, xii, 111, 179, 268, 289, 290, 291, 293, 311, 316, 317, 318, 319 financial markets, x, 3, 101, 137, 150, 156, 179, 242, 290, 315, 320, 322 financial performance, 3, 24, 38 financial planning, 275, 287, 288 financial resources, 16, 76 financial sector, 290, 292 financial stability, 167, 264, 315, 317, 319, 322

financial support, 75 financial system, 101, 109, 138, 156, 164, 167, 290, 293, 311, 316, 317 financing, 5, 25, 29, 95, 315 Finland, 164, 165, 166, 167 firm size, 78 firms, 2, 6, 10, 11, 14, 16, 34, 39, 43, 44, 45, 49, 56, 76, 77, 78, 79, 80, 81, 82, 90, 91, 92, 93, 94, 95, 101, 112, 239, 241, 242, 243, 246, 248, 249, 250, 253, 255, 256, 257, 258, 261, 262, 265, 270, 317, 319, 320 fitness, viii, 99 fixed costs, 26 flexibility, xi, 78, 80, 91, 180, 185 floating, 73, 143 floating exchange rates, 143 flood, 120, 124 fluctuations, 26, 156, 183 focusing, 133 food, viii, 80, 99, 101, 103, 126, 127, 128, 134 food products, 80 forecasting, 40, 52, 59 foreclosure, 316, 320 foreign exchange, x, xi, 120, 137, 138, 139, 143, 185, 186, 197 foreign exchange market, 139 France, 19, 91, 93, 99, 165, 179 fraud, 115, 177 free association, 107 free trade, ix, 100 freedom, 54, 115, 140, 281 freezing, 290 fulfillment, 160 funding, 5, 112, 315, 318 funds, 26, 27, 28, 31, 39, 47, 104, 107, 112, 117, 157, 179, 180, 290, 291, 293, 294, 301, 302, 305, 308, 311, 312, 318, 322

G gambling, 101, 109, 110 gasoline, 277 General Accounting Office, 318 generalization, 2, 13, 18, 23 generation, 133 geography, 134 Germany, 39, 134, 163, 164, 165, 264, 267 global economy, 113 globalization, 136, 160 GNP, 120 goals, xi, xii, 104, 267, 268, 270, 274, 278, 279, 280, 281, 282, 283, 285 God, 101, 103, 105, 107, 109, 111, 113, 115, 117 gold, ix, 99 goods and services, viii, 99 governance, 170, 177 government, xii, 16, 26, 29, 38, 110, 112, 161, 234, 237, 240, 243, 248, 249, 251, 254, 258, 259, 260,

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Index 261, 289, 290, 291, 292, 293, 314, 315, 316, 317, 321, 322, 330, 331 grades, vii, 1 grants, 16 graph, 55, 56, 66, 130 Great Britain, 163 Greece, 40, 137, 164, 165, 166 Greeks, 208, 230, 231 gross domestic product (GDP), 19, 29, 41, 120, 163, 164, 180, 273, 279 group membership, 107 groups, 16, 17, 121, 133, 163, 174, 175, 250, 255 growth, 26, 27, 28, 46, 47, 49, 59, 62, 64, 66, 70, 77, 78, 96, 107, 112, 138, 161, 162, 163, 188, 191, 321 growth rate, 46, 49, 59, 62, 64, 66, 70 Guatemala, 122, 136 Guinea, 107, 115, 116

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H harvesting, 133 hazards, 121, 134 health, viii, 5, 6, 99, 113, 122, 270, 273 hedging, 101, 107, 179, 234 hegemony, ix, 100 height, xi, 267, 268, 270, 271, 274, 277, 280, 281, 283 heterogeneity, 76 heteroskedasticity, 52, 73, 74 highlands, 125 Hilbert space, 188 holding company, 321 homeowners, 274 Hong Kong, 43 hopes, 110 House, 115, 117, 280, 281, 282, 284, 285, 286, 315 household income, 123 households, 43, 122, 123, 126, 127, 129, 132, 133 housing, 103, 273, 290, 314, 316 human behavior, ix, 100 human brain, 288 human resources, 2 human welfare, 121 Hungary, 159, 162 hybrid, 2, 6, 14, 38, 40, 200, 203, 210, 212, 213, 222 hypothesis, 11, 47, 54, 59, 62, 66, 90, 91, 92, 93, 163, 174, 175, 176, 252

I ideal, 134, 162 ideals, 274 identification, 49, 54, 109, 262 identity, 191 idiosyncratic, 44, 46, 156, 238, 253 image, viii, 99, 110, 112, 114 immune system, 2, 10, 39 impact assessment, 136

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implementation, 23, 28 incentives, 95, 136, 311, 323 income, x, 26, 27, 28, 119, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 270, 271, 272, 273, 278, 284, 313, 331 independence, x, 62, 66, 70, 169, 176, 177, 270 independent variable, 8, 81, 82, 124, 128, 129 indexing, 14, 42 India, 136 indicators, xi, 3, 6, 16, 25, 26, 27, 32, 44, 74, 121, 233, 243, 255, 262, 263 indices, 21, 44, 135, 143, 199, 235, 243, 249 indigenous, 101 Indonesia, 134, 143, 144, 145, 146, 147, 150, 151, 153 induction, 14, 300 industrial sectors, 9 industry, 3, 4, 8, 10, 12, 13, 24, 25, 27, 31, 36, 76, 81, 93, 95, 107 inequality, 135 infancy, 239 infection, 111 inferences, 17, 45 inflation, 107, 227, 271, 277, 278 infrastructure, 28, 120 injections, 291, 292, 303, 306, 309, 311, 315, 322, 323 innovation, 92, 95, 117, 142 insecurity, 127, 134 insight, 182 instability, 90, 106, 109, 234, 290 institutions, 109, 111, 112, 162, 163, 167, 179, 180, 291, 292, 293, 311, 315, 317 instruments, 83, 88, 101, 109, 234, 237, 270, 290, 313 insurance, 104, 114, 123, 128, 133, 136, 161, 180, 234, 291, 294, 330, 331 integration, 138, 193, 269 intelligence, 14 interaction, xi, 8, 267, 274, 277 interaction effects, 8 interactions, x, 137, 138, 139, 156, 293, 294 interdependence, 138 interest cover, 26 interest rates, xi, 5, 44, 50, 72, 73, 74, 185, 186, 187, 198, 199, 207, 211, 212, 215, 221, 223, 227, 237, 249, 253 interference, 106, 170 internal financing, 323 international financial institutions, 160 International Monetary Fund, 161, 165, 167, 253, 264 interval, 271, 274, 277, 279, 280, 281, 283, 284 intervention, xii, 111, 143, 161, 182, 183, 289, 321, 330 interview, 104, 111 intuition, 182, 183, 237, 292 inversion, 203, 207, 214 investment, vii, ix, 1, 2, 4, 5, 8, 9, 12, 14, 17, 26, 28, 30, 31, 33, 55, 72, 76, 78, 79, 95, 100, 102, 107, 109, 110, 112, 113, 155, 272, 278, 284, 285, 290,

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Index

291, 292, 293, 294, 295, 297, 302, 305, 308, 311, 314, 316, 321, 322 investment bank, 290, 293, 311, 316, 321 investors, 2, 5, 37, 101, 107, 110, 112, 114, 138, 150, 156, 170, 171, 234, 235, 238, 249, 253, 257, 262, 291, 297, 299, 317, 321 Ireland, 137, 165 Islam, ix, 100 Italy, 19, 91, 93, 136, 164, 165, 233, 264 iteration, 281

J Japan, 96, 117, 164, 185, 229, 231, 232, 321 job creation, 76 jobless, 315 jobs, 315, 316

K Kenya, 116, 134 Keynes, 107, 115 Korea, 143, 144, 145, 148, 149, 150, 151

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L labor, 73, 107 lack of confidence, 321 Lagrange multipliers, 24 land, 124, 126 land tenure, 126 language, 109 Latin America, 314 Latvia, 162 lawyers, 104 learning, 3, 10, 12, 13, 14, 18, 19, 21, 22, 23, 24, 32, 33, 34, 38, 39, 40, 41, 42, 78, 91, 109 learning process, 18, 19, 21, 22, 23, 41 lending, 5, 113, 166, 271, 272, 290, 292, 293, 294, 296, 298, 311, 316, 322, 323, 325, 326, 328, 329, 331 letters of credit, 103 liberalization, 76, 138, 160 life expectancy, 120 lifetime, 285 likelihood, 16, 52, 54, 63, 64, 67, 73, 76, 82, 93, 134, 140, 144, 180, 181, 183 limitation, 22, 120, 187, 200 limited liability, 291 line, vii, 1, 14, 32, 45, 50, 51, 102, 132, 133, 238, 274, 277, 280, 285, 314 linear function, 274 linear model, 41, 53, 54, 56, 57, 58, 59, 248, 249, 252 linear programming, 269 linearity, 10 liquid assets, 297, 311, 321

liquidate, 183 liquidity, vii, viii, xii, 13, 25, 27, 31, 44, 45, 49, 75, 76, 77, 79, 80, 81, 82, 85, 86, 88, 89, 92, 93, 94, 104, 107, 109, 159, 234, 237, 238, 250, 253, 257, 261, 268, 270, 271, 272, 277, 278, 279, 280, 283, 289, 290, 291, 292, 294, 314, 315, 317, 323 liquidity ratio, 31 livestock, 126, 127, 128, 129, 133 loans, x, xii, 16, 24, 100, 101, 113, 179, 267, 289, 290, 291, 293, 299, 314, 315, 316, 322, 323 local authorities, 42 low risk, 296, 304, 307, 310 LTD, 25 Luxemburg, 322

M machine learning, 12 machinery, 80, 126 maintenance, 159, 274 Malaysia, 151 management, 4, 5, 6, 13, 16, 24, 25, 27, 28, 29, 36, 39, 41, 76, 77, 78, 91, 112, 123, 133, 134, 136, 167, 268, 287, 291, 331 mania, 113 manufacturing, vii, viii, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95 manure, 128 mapping, 4, 14, 135 market capitalization, 24, 26, 242, 243, 245, 246, 247, 248 market discipline, 161 market structure, 162 marketability, 2 marketing, 170 marketplace, 102, 267 markets, x, 12, 25, 26, 31, 42, 76, 78, 79, 92, 94, 101, 104, 105, 109, 120, 126, 137, 138, 139, 143, 146, 151, 153, 154, 156, 157, 160, 186, 213, 215, 235, 237, 255, 262, 263, 264, 290, 314, 318, 321 mass media, 104 mathematics, 106, 111, 185, 187 matrix, 7, 19, 33, 34, 35, 48, 62, 69, 74, 139, 140, 141, 144, 145, 147, 191, 212, 275 measurement, 39, 72 measures, x, xii, 9, 27, 36, 47, 48, 64, 81, 119, 122, 180, 199, 205, 239, 249, 289, 290 median, 143 membership, 18, 38, 106, 133 men, ix, 100 mental image, 285 metals, 80 Mexico, 135, 136 MIP, xii, 267 mixing, 133 model specification, 46, 58 modeling, 17, 21, 61, 147, 186, 198, 264, 268, 275, 323

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Index modern society, viii, 99, 113 modernity, ix, 100, 104, 111, 112 momentum, 21, 107 monetary policy, 106, 159 money, viii, ix, 26, 99, 102, 103, 104, 105, 106, 164, 165, 166, 270, 280, 282, 284, 291, 294, 314, 318, 322 money supply, 106 monopoly, 107 mood, viii, 99 Moon, 41 moral hazard, 109, 112 mortgage-backed securities, xii, 293 motivation, 91 movement, 45, 46, 49, 55, 56, 69, 70, 106, 110, 163 multidimensional, 23, 269 multiple regression, 8, 10 multiple regression analysis, 10

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N Nash equilibrium, 300 negative consequences, 76 negative relation, 45, 91, 163, 248, 253 negotiating, 5 negotiation, 162 Netherlands, 73, 164, 166 network, 10, 11, 13, 22, 23, 41, 101, 116, 171 neural network, vii, 1, 2, 3, 10, 11, 12, 13, 21, 22, 37, 38, 39, 40, 41, 42 neural networks, vii, 1, 2, 3, 10, 11, 12, 21, 22, 37, 38, 39, 40, 41, 42 neurons, 10, 11, 20, 21, 22, 23, 32, 33, 34 New England, 17 Nicaragua, 180 Nile, x, 119, 120, 124, 125, 126, 133 Nixon, Richard, 106 noise, 21, 55 non-linear equations, 241 normal distribution, 82, 140, 192, 195, 202 Norway, 164 null hypothesis, 54, 64, 66, 83, 87, 88, 89, 144, 250

O OAS, 249 objectives, 16, 77, 270, 285, 290, 323 objectivity, 4 obligation, 2, 42, 243 observations, 9, 11, 17, 47, 67, 82, 83, 140, 143, 243, 246, 247, 251, 252, 258, 259, 260, 261 Oklahoma, 17, 18 omission, 81 operator, 141, 188, 194, 198, 205 opportunism, 170 optimization, 24, 30, 39, 268, 269, 277, 286, 287, 288

Organization for Economic Cooperation and Development, 165, 168 output gap, x, 159, 163, 164, 165, 166 outsourcing, 5 overgrazing, 120 oversight, 318 ownership, 126, 129, 177, 240, 291, 314

P parameter, 15, 20, 22, 28, 53, 61, 64, 67, 124, 147, 172, 191, 194, 205, 262 parameter estimates, 64, 124 parameters, 10, 12, 20, 22, 28, 32, 33, 34, 54, 63, 67, 82, 83, 87, 88, 89, 123, 140, 144, 145, 181, 182, 203, 208, 211, 212, 213, 214, 215, 237, 280, 285 paranoia, 113 Pareto, 116 partial differential equations, 186 partition, 15 penalties, 313, 330 pensions, 101 perceptions, 126, 150, 269 performance indicator, 318 personal goals, 269 Philippines, 143, 144, 145, 146, 151, 152, 153, 154, 156 physics, 111 planning, 112, 267, 268, 269, 270, 271, 285, 287 Poland, 162 policy initiative, 138 policy makers, 138 politics, 106 polynomial functions, 188 population, viii, 6, 8, 17, 28, 29, 36, 99, 120, 122, 124, 126 population growth, 6, 29 portfolio, 138, 156, 160, 161, 162, 163, 180, 181, 182, 183, 184, 187, 238, 269, 287, 288, 294, 296, 322 portfolio investment, 294 portfolio management, 184 portfolios, xi, 179, 180, 181, 183, 184 Portugal, 75, 76, 95, 96, 165 positive correlation, 164, 166 positive relation, 50, 55, 56, 92, 161, 248 positive relationship, 56, 92, 161, 248 posture, 24 Potchefstroom, 289 poverty, x, 119, 120, 121, 122, 123, 127, 129, 130, 132, 133, 134, 136 poverty line, x, 119, 122, 129, 130, 132, 133 power, 12, 14, 15, 24, 44, 45, 78, 91, 110, 128, 235, 236, 239, 249, 252, 253, 255, 257, 262, 268, 294 precipitation, 120 predictability, 57 prediction, 6, 10, 14, 19, 34, 38, 39, 40, 41, 42, 141, 237 prediction models, 42

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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340

Index

predictors, 10, 38, 288 preference, 122, 139, 270, 271, 274, 276, 277, 280, 281, 319 premiums, 2, 39, 45, 323 present value, 198, 293, 294, 295, 296 price stability, 317 prices, viii, xi, 43, 56, 99, 102, 107, 112, 139, 157, 166, 179, 181, 182, 185, 197, 200, 203, 211, 213, 216, 218, 223, 235, 241, 249, 250, 263, 274, 291, 292, 313 principal component analysis, xi, 30, 121, 233, 239, 250, 255, 256 private banks, 314 probability, x, 2, 4, 7, 22, 26, 44, 49, 50, 62, 63, 69, 70, 74, 86, 87, 90, 94, 110, 119, 122, 123, 124, 129, 130, 133, 161, 163, 193, 194, 195, 197, 199, 203, 205, 207, 236, 238, 249, 296 probability density function, 22, 195, 207 probe, xii, 289, 291 production, ix, x, 48, 100, 101, 119, 120, 126, 133 productivity, 120 profit, 25, 110, 161, 181, 312, 323 profitability, vii, viii, 13, 24, 27, 31, 36, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 101, 163, 249 profits, 27, 91, 101, 107, 109, 112, 312 program, 75, 185, 285, 291, 307, 310, 316, 319, 320, 322, 326, 329 programming, 287 proliferation, 107 propagation, 147, 154 proportionality, 300 proposition, 107, 196, 303, 306, 309 psychology, 106, 268 public administration, 37 public finance, 315 public financing, 95 public goods, 28, 29 public interest, 294, 307 public service, 16, 28

Q quality of life, 280 quantization, 12, 13, 40 quartile, 255, 257, 258, 261 questioning, 102, 282 quick ratio, 26

R rainfall, 126, 129, 136 random numbers, 210 range, 21, 44, 121, 172, 173, 278, 322 rate of return, 48, 278, 294, 295, 301, 305, 308 rating agencies, vii, 1, 2, 3, 4, 5, 6, 14, 19, 24, 37, 40, 263

rating scale, 2, 4, 5, 16, 33 ratings, 2, 4, 5, 8, 11, 12, 14, 15, 16, 17, 24, 25, 39, 40, 41, 42, 44, 162 rationality, 110 real assets, 101 reality, 106, 112, 117, 320 reason, xii, 10, 19, 22, 162, 170, 180, 289, 293, 311, 313 reasoning, 10, 14, 15, 40, 45, 269, 286 recall, 106 recalling, 209 recession, 28, 45, 52, 57, 59, 62, 66, 112, 162, 163 reciprocity, 102, 106, 107 recognition, 102, 111 reconcile, 238 recovery, 238, 298, 301, 302, 312 redundancy, 31 refining, 159 reflection, viii, 99 region, 17, 129, 132, 157 regression, 6, 8, 9, 10, 11, 12, 17, 18, 41, 44, 47, 57, 77, 82, 83, 166, 248, 250, 251, 252, 253, 255, 256, 257, 258, 259, 260, 261, 264 regression analysis, 6, 8, 17, 166 regulation, x, 110, 112, 159, 160, 167, 323, 331 regulations, 161, 162 regulators, xi, 160, 179, 180, 292 regulatory framework, 323 regulatory requirements, 2 rejection, 87, 88, 89 relationship, vii, x, xii, 43, 46, 54, 56, 57, 64, 70, 72, 74, 89, 91, 93, 138, 156, 159, 161, 163, 164, 165, 170, 177, 209, 234, 235, 241, 248, 253, 263, 264, 289, 293, 313 relevance, 78, 80, 92, 95, 106, 236, 238, 239, 241, 253 reliability, 5, 17, 170 religion, 106, 110 rent, 274, 278 repo, 234, 290 reputation, 24, 25, 27, 31, 161 resettlement, 133 residual error, 22 residuals, 44, 140, 239, 250, 255, 256 resilience, 121 resolution, 104, 317, 318, 330, 331 resource allocation, 161 resources, 16, 76, 78, 91, 101, 110 restructuring, 234, 290 retained earnings, 26 retirement, 101, 268, 269, 278 returns, x, 26, 48, 61, 62, 66, 67, 71, 72, 101, 137, 138, 139, 140, 143, 152, 156, 182, 183, 238, 243, 248, 249, 252, 294, 295, 296, 300, 302, 304, 305, 307, 308, 310, 312 revenue, 26, 28, 29, 292 rewards, 101, 110, 267 risk assessment, 39, 109 risk aversion, 252, 262, 287 risk factors, 2, 234, 235, 236, 237, 238, 253, 255, 262

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

Index risk management, 133, 180, 317 risk-taking, 290, 291 river basins, 125 robustness, 9, 46, 47, 83, 250, 275 runoff, 125 Russia, 123, 136, 316

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S safety, 123, 133, 323 sales, 19, 26, 40, 290 Samoa, 135 sample mean, 47 Sarkozy, Nicolas, 314 satisfaction, 284 savings, 101, 163, 166, 168, 268 savings banks, 163, 166 scaling, 48 scarcity, 77 school, 104 scores, 54 search, 39 seasonality, 134 securities, 42, 113, 197, 242, 249, 289, 290, 293, 312, 319, 320 security, 317 selecting, xi, 8, 24, 30, 121, 179, 183, 243 seller, 234 Senate, 314 sensitivity, 2, 3, 32, 35, 121, 129, 133, 262 sex, 106 shareholders, 31, 161, 237, 240, 243, 250, 291, 294, 295, 296, 300, 320, 321, 326, 330 shares, 26, 27, 31, 180, 241, 297, 317, 318, 319 sharing, 138 shelter, 271, 273, 274, 284 shock, x, 119, 122, 123, 137, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 161 short run, 48, 235 shortage, 127 short-term interest rate, 249, 253 short-term liabilities, 290 SIC, 26, 27, 31, 32, 36 signals, 249 significance level, 165 signs, viii, 14, 99, 111, 249, 252, 253 simulation, 11, 181, 182, 183, 186, 187, 208, 222 Singapore, 143, 144, 145, 146, 153, 154, 155, 156 skewness, 143, 238 skills, 5, 6, 24 smiles, 186, 215 smoothing, 136 social behavior, 112 social benefits, 298, 299 social capital, 126 social group, 122 social institutions, 112

341

social relations, 108 social responsibility, 267 social structure, 113, 115 social welfare, 326, 329 socialism, ix, 100 software, 129, 278 soil, 120, 128, 136 solvency, 161 South Africa, 119, 136, 289 space, ix, 23, 24, 61, 100, 116, 187, 188, 190, 191, 192, 193, 194, 197, 200, 230 Spain, 91, 93, 164, 165, 166 species, 101, 133 speculation, 106, 112 speed, 50, 182, 211 spillovers, x, 137, 138, 139, 142, 143, 146, 150, 154, 156, 157 spot exchange rate, xi, 185, 186, 197, 198, 199, 211, 212, 222 stability, vii, 9, 15, 17, 43, 44, 106, 109, 112, 157, 162, 213, 316, 317 standard deviation, 47, 63, 86, 88, 129 standard error, 52, 53, 58, 60, 63, 64, 66, 67, 71, 72, 183, 250, 251, 258, 259, 260, 261 standard of living, 135 standardization, 30 standards, 113, 267, 317 statistics, 47, 59, 63, 66, 67, 85, 90, 93, 143, 172, 187, 239, 246, 247, 248, 252 stigma, 111 stimulus, 315 stochastic model, 330 stochastic processes, 187, 198 stock, viii, x, 26, 41, 61, 99, 100, 103, 106, 107, 137, 138, 139, 143, 146, 148, 150, 151, 156, 157, 163, 164, 177, 239, 241, 243, 245, 246, 247, 248, 249, 251, 252, 254, 258, 259, 260, 261, 263, 264, 314, 321, 332 stock exchange, 177 stock markets, 138, 151, 264, 314 stock price, 26, 41, 138, 157, 163 stock value, 249, 251, 254, 258, 259, 260, 261 strategic management, 76, 77 strategies, 41, 101, 110, 123, 127, 128, 133, 135, 138, 181, 183, 184, 300 strength, 35, 115 stress, 14, 37, 79, 93, 95, 111, 121, 162, 163, 236, 255, 262 stressors, 136 subgame, 300 subgroups, 250 subjectivity, 2, 37, 122 subsidy, 292, 293, 300, 304, 307, 310, 311, 323, 326, 327, 329, 330 substitution, 201, 202 superiority, 249 supernatural, 110, 111 supervision, 159, 160, 161, 167, 170, 171, 172, 177 supervisors, 319

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,

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Index

suppliers, 291 supply, 45, 138, 163, 237, 238, 250, 292 suppression, 112 surplus, 28, 270, 271, 278, 294 survival, 77, 78, 81, 82, 83, 86, 87, 89, 90, 91, 92, 93, 94, 95, 101, 109 susceptibility, 121 sustainability, 95 Sweden, 19, 163, 164 switching, 43, 45, 46, 49, 50, 52, 53, 54, 56, 57, 58, 59, 62, 69, 70, 73, 182 Switzerland, 322 symbols, 111 symptoms, viii, 99 synapse, 2, 21, 22, 35 syndrome, 116 synthesis, 136 systemic risk, 253, 317, 318, 331

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T Taiwan, 12 Tanzania, 122, 136 tax collection, 29 tax rates, 237 taxation, 28, 300 temperature, 120, 125, 126, 129, 136 textiles, 80 Thailand, 143, 144, 145, 150, 151 threshold, 130, 174, 175, 237 time periods, 44 time preferences, 268, 270, 271, 276, 277, 280, 282, 287 time series, 19, 47, 73, 143, 157, 250 timing, 298 topology, 187 total revenue, 26, 28, 29 trade, 181 trade-off, 10 trading, 61, 116, 182 traditions, 113 training, 2, 6, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22, 23, 37, 40, 185 transaction costs, 237, 295 transactions, 107, 109, 166, 317 transformation, 113, 203, 205, 209, 267, 323 transition, 7, 49, 50, 55, 62, 63, 64, 67, 72, 330 transitions, 74 translation, 103 transmission, x, 137, 138, 146, 154, 156 transparency, 112, 318 transportation, 9, 12, 32 trial, 268, 270, 285 triggers, 313 trust, 112, 316, 317, 319, 320 turbulence, x, 137, 138, 156 turnover, 80, 85 Tuvalu, 135

U U.S. Treasury, 290, 314, 315, 316, 317, 318, 319, 320 uncertainty, xi, 5, 112, 161, 199, 201, 211, 233, 249, 250, 252, 255, 262, 285 unemployment, 28, 29 uniform, 104, 107 uninsured, 122 unions, ix, 100 United Kingdom, 16, 41, 43, 73, 91, 93, 96, 97, 135, 136, 164, 263, 321 United Nations, 135, 136 United States, x, 97, 119, 120, 234, 319 universe, 111

V validation, 14 Vanuatu, 135 variability, 121, 122, 126 variance, xi, 48, 52, 53, 55, 56, 61, 63, 124, 139, 140, 144, 145, 185, 187, 192, 195, 202, 204, 206, 208, 209, 211, 214, 215, 222 variance-covariance matrix, 63 vector, ix, 1, 2, 10, 12, 13, 15, 20, 21, 22, 23, 38, 40, 41, 73, 82, 100, 123, 139, 140, 141, 199, 211 venture capital, 164 vertebrates, 101 Vietnam, 134 visual impression, 56 visualization, 39 vulnerability, x, 119, 120, 121, 122, 123, 124, 126, 130, 132, 133, 134, 135, 136

W war years, 112 warrants, 319, 321 wealth, vii, viii, ix, 32, 36, 75, 99, 100, 101, 102, 105, 111, 181, 182, 267, 268, 269, 270, 271, 272, 285, 288, 298, 299 wealth distribution, 182 weapons, ix, 100 welfare, 122, 123, 267, 292, 294, 322, 323, 326, 329 welfare loss, 122, 123 welfare state, 267 White House, 314 World Bank, 120, 129, 134, 135, 136 worldview, ix, 100

Z Zone 1, 126

Finance and Banking Developments, edited by Charles V. Karsone, Nova Science Publishers, Incorporated, 2010. ProQuest Ebook Central,