COMPARATIVE ANALYSIS OF STATISTICAL MODELS IN CREDIT ASSESSMENT BY AMOS YAW ANSAH (10357586) A THESIS SUBMITTED TO THE SCHOOL OF RESEARCH AND GRADUATE STUDIES OF THE UNIVERSITY OF GHANA, LEGON, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF A MASTER OF PHILOSOPHY (MPhil) IN STATISTICS JUNE, 2013 University of Ghana http://ugspace.ug.edu.gh i DECLARATION I hereby declare that this thesis is the result of my own research work and that no part of it has been presented for another degree in this university or elsewhere. ……………………………. DATE …………………………. Amos Yaw Ansah (Candidate) I hereby declare that the preparation and presentation of this thesis was supervised in accordance with the guidelines on the supervision of thesis laid down by the University of Ghana ……………………………………. ……………………………………. Dr. E. N. N. Nortey Dr. Isaac Baidoo (PRINCIPAL SUPERVISOR) (CO- SUPERVISOR) Date …………………………………. Date ……………………………… University of Ghana http://ugspace.ug.edu.gh ii ABSTRACT With the emergence of the current financial crisis, important advances have been made in credit risk management. Inherent in this management process is the assessment of creditworthiness routine which subsequently leads to a credit granting decision. This study is aimed at developing a statistical model that can be used to ascertain credit assessment and to predict the probability of default of firms seeking credit from a Ghanaian commercial bank. Subsequently, an attempt was made to find financial ratios that can best be made used to successfully construct the model. To achieve these purposes, the study employed the Probit and logit models for comparative reasons in terms of their predictive abilities. Performance of the models was assessed using the percentage correctly classified (PCC) and the area under the receiver operating characteristics curved (AUC) where significant differences between the two models were observed. It was found that both the Probit and the logit classifiers yield very good performance rates but the logit model performed better for credit scoring. It was also found that ratios bordering on assets to liability ratios, account receivable to liability, Cash to Assets, current liability to total liabilities , Net current asset ,and total asset firm size are those that were significantly helpful in scoring credit applicant. Practically the model assist in reducing the time spent on evaluating credit applicant of each firm subject to the model and also serve as a difference between application serving and portfolio management . Indeed the multiplier effect will be a significant improvement in loan portfolio quality of the model user. University of Ghana http://ugspace.ug.edu.gh iii DEDICATION To God Almighty ,in whom lies all the treasures of wisdom and knowledge . University of Ghana http://ugspace.ug.edu.gh iv ACKNOWLEDGEMENT To God be the Glory. Indeed I am highly indebted to my project supervisors Dr. E.N .N Nortey, and Dr. Isaac Baidoo whose suggestions, encouragements and unflinching support brought this work this far. My sincere thanks also go to all other lecturers in the Statistics Department, for their patience, tolerance and assistance they offered me during my stay with them as a student. I am also grateful to all the Non-teaching staff of the department especially Abass who typed most portions of my work several times, without whose contribution this work could not have been completed. I am also indebted to Mr. Samuel Owusu, head of Mathematics Department, in Akosombo International School and Rev. Simon Tinglafo , lecturer at Central University College, for their immense and continuous encouragement and support Not forgetting my friends Michael Larwer Tetteh and Felix A. Tetteh of Ghana Commercial Bank and my siblings Ebenezer Rockson, Timothy, Enoch ,and Dinnah Enyaah for their support and encouragement throughout the period of my study May the Almighty God Bless Us All. University of Ghana http://ugspace.ug.edu.gh v TABLE OF CONTENTS DECLARATION i ABSTRACT ii DEDICATION iii ACKNOWLEDGEMENT iv TABLE OF CONTENTS v LIST OF TABLES xi LIST OF FIGURES xii LIST OF ABBREVIATIONS xiii CHAPTER ONE: INTRODUCTION 1.0 Introduction 1 1.1 Background to the Study 1 1.2 Statement of the Problem 8 1.3 Objective of the study 10 1.4 Rationale of the Study 11 1.5 Scope and Limitation of the Study 11 University of Ghana http://ugspace.ug.edu.gh vi 1.6 Organisation of the Study 12 CHAPTER TWO: LITTERATURE REVIEW 2.0 Introduction 13 2.1 Theoretical Literature 13 2.1.1 Concept of Credit Assessment 13 2.1.2 Concept of Credit Risk Management 16 2.1.3 Sources of Credit Risk 19 2.1.4 Internal Risk Factor of Credit Risk 20 2.1.5 Definition of Credit 21 2.1.6 The Credit Process 22 2.1.7 The Traditional Credit Process 24 2.1.8 The Modern Credit Process 25 2.1.9 Loan 27 2.1.10 Definition of Default 28 2.1.11 Theoretical Perspectives on the Performance of Probit and Logit Models 31 2.1.12 Performance Criteria of Prediction Model 32 University of Ghana http://ugspace.ug.edu.gh vii 2.1.13 Similarities and Differences between Probit and Logit Models 36 2.2 Empirical Review 39 2.2.1 Financial Ratios as Predictors of Financial Default 39 2.2.2 Exploration of more Essential Ratios to Predict Default 41 2.2.3 Performance of financial distress/ Default Prediction Models 46 2.2.4 Comparing the Predictive Ability of Different Default Prediction Models 49 2.2.5 Further Review of Related Works 54 CHAPTER THREE: METHODOLOGY 3.0 Introduction 69 3.1 The Binary Dependent Variable 69 3.2 The Logit Model 70 3.2.1 Theoretical Logit Model 72 3.2.2 Assumptions of the Logit Regression 73 3.3 The Probit Model 74 3.3.1 Theoretical Probit Model 76 3.3.2 Assumption of the Probit Regression 77 University of Ghana http://ugspace.ug.edu.gh viii 3.4 The Explanatory Variables 77 3.4.1 Financial Leverage Ratios 78 3.4.2 Liquidity Ratios 79 3.4.3 Profitability Ratios 80 3.4.4 Activity Ratio 81 3.4.5 Asset Turnover Ratio 82 3.4.6 Current Liabilities to Total Liabilities 82 3.4.7 Earning to interest expense 82 3.4.8 Net current asset 83 3.4.9 Total Liability to total Current ratio 83 3.4.10 Cash to Current Liabilities 83 3.4.11 Total asset 84 3.5 Data Source 84 3.6 Population of the Study 84 3.7 Sample Size 85 3.8 Assessing the Overall Model Fit 86 3.9 Model Prediction Performance Assessment 86 University of Ghana http://ugspace.ug.edu.gh ix 3.10 Specification Error Test 88 3.11 Data Analysis 88 CHAPTER FOUR: DATA ANALYSIS 4.0 Introduction 90 4.1 Description Statistics 90 4.2 Correlation Analysis and Variance Inflation Tests 95 4.3 Analysis of Logit Results 99 4.3.1 Interpretation of Estimated Parameters 99 4.3.2 Interpretation of the Logit Model Statistics 101 4.3.3 Classification Accuracy of the Logit Model 102 4.4 Analysis of the Probit Results 105 4.4.1 Interpretation of Estimated Parameter 105 4.4.2 Interpretation of Probit Model Statistics 106 4.4.3 Classification Accuracy of the Probit Model 107 4.5 Validation Results 109 University of Ghana http://ugspace.ug.edu.gh x CHAPTER FIVE 5.0 Introduction 110 5.1 Summary 110 5.2 Conclusion 111 5.3 Recommendation and Proposition for Further Research 112 REFERENCES 113 APPENDIX 133 APPENDIX A 133 University of Ghana http://ugspace.ug.edu.gh xi LIST OF TABLES Table 2.1 list of independent variables used in the Regression Models Table 4.1 Descriptive statistics of independent variables 93 Table 4.2 Correlation Analysis 96 Table 4.3 Variance inflation Test 98 Table 4.4 Estimated logit Result 101 Table 4.5 Logit Model statistics 102 Table 4.6 Predicted Accuracy of the logit Model 104 Table 4.7 Estimated Probit result 106 Table 4.8 Probit Model statistics 107 Table 4.9 Predicted Accuracy of the Probit model 108 Table 4.10 Validation result for logit and Probit models 109 University of Ghana http://ugspace.ug.edu.gh xii LIST OF FIGURES Fig 2.1 Logit and Probit cumulative distribution 38 Fig 4.1 ROC curve for logit model 104 Fig 4.2 ROC curve for Probit model 108 University of Ghana http://ugspace.ug.edu.gh xiii LIST OF ABBREVIATIONS ANN – Artificial Neural Network AUC – Area Under receiver operating Curve BCB – Basel Committee on Banking and Supervision BPN – Back-propagation Neural Network CBR – Case Based Reasoning CRM – Credit Risk Management DEA – Data Envelopment Analysis DR – Delay Rejection EAD – Exposure At Default EL – Expected Loss EWE – Early Warning Systems University of Ghana http://ugspace.ug.edu.gh xiv FICO – Fair Isaac Company GLM – Generalised Linear Model INLA – Integrated Nested Laplace Approximation IRB – Internal Rating Base LDA – Linear Discriminant Analysis LGD – Loss Given Default LPM – Linear Probability Model LR – Likelihood Ratio MCMC – Marker Chain Monte Carlo MCR – Minimum Capital Requirement MDA – Multiple Discriminant Analysis PCC – Percentage Correctly Classified PCP – Percentage Correctly Predicted PD – Probability of Default ROA – Return on Assets ROC – Receiver Operating Curve RSBL – Random Space Binary Logit University of Ghana http://ugspace.ug.edu.gh xv SME – Small and Medium Scale Std. Dev – Standard Deviation Std. Err – Standard Error SVM – Sub-vector Machines SWOT - Strength Weaknesses Opportunity and Threats VIF – Variance Inflation Factor test University of Ghana http://ugspace.ug.edu.gh 1 CHAPTER ONE 1.0 INTRODUCTION This chapter of the study brings to light the general overview of the research. Also embedded in this chapter are: the statement of the research problem, objectives of the research, rationale, scope and limitation and organisation of the research 1.1 Background to the study Credit risk assessment is a significant area of financial management which is of major interest to practitioners and researchers. On a daily basis credit analysts have to investigate an enormous volume of financial and non-financial data of consumer credit, estimate the corresponding credit risk, and finally make crucial decisions regarding the issuance of credit ( Ruparel,1990). Embedded in this assessment process is the risk identification ,measurement and assessment process of borrowers (Santomero,1997).These aspects of credit risk assessment systems are deemed crucial in the view of the fact that credit risk emanates from the probability of default of borrowers(Doumpos et al.,2002). This is the risk of loss due to a debtor's non-payment of a loan or other line of credit. Notwithstanding, actual default occurs when a debtor fails to fulfil his or her contractual obligation according to a debt contract or has violated a loan convenant of debt agreement(Chen et al.,2010). This therefore places a major task on credit granting decision process(credit worthy assessment) which requires a distinct attention in order to properly segregate credit worthy borrowers from unworthy ones(Abdou and Pointon,2009) more so when poor loan quality is believed to have its roots in the loan information process mechanism(Richard et al., 2008) University of Ghana http://ugspace.ug.edu.gh 2 Considerable attention has been devoted in the field of credit assessment from the theoretical points of view during the last three decades. Financial and operational researchers have tried to relate the characteristics of a firm, that is financial ratios and strategic variables to its credit risk assessment. According to this relationship the components of credit risk are identified and decision models are developed to assess credit risk and the corresponding creditworthiness of firms or individuals as accurately as possible. Decisions regarding credit risk assessment concern the evaluation of the firms‟ financial and non-financial characteristics in order to make optimal decisions which incorporate a tradeoff between the potential risk of loss and the probability of profits from granting credit (Srinivasan and Kim,1987) According to Anderson (1984) , Credit-granting decisions are usually realized by credit analysts as sorting or classifying the firms seeking financing from banks or credit institutions into categories according to their creditworthiness and insolvency . Also during credit assessment evaluation process there are two major challenges which are usually encountered; the first one concerns a plethora of factors which should be examined. Factors which affect the assessment of credit include the financial characteristics of firms, strategic variables of qualitative nature which affect the general operation of the firm and its relation with the market, and even macroeconomic factors which are inflation, interest rates, and others. The credit analysts have to identify the most relevant factors for credit risk evaluation, and focus their further analysis on the examination of these factors and the second concerns, the aggregation of the factors which have been selected in the previous phase, in order to make a final decision modelling. Dillon and Goldstein (1984) asserted in their studies on credit assessment that, factors affecting credit risk assessment lead to conflicting results and decisions. The credit analysts, when University of Ghana http://ugspace.ug.edu.gh 3 performing credit risk analysis, implicitly consider the tradeoffs between the conflicting criteria, according to their global preference system. In this way, they conclude on an appropriate aggregation of the partial evaluations of firms on each one of the evaluation criteria, and derive the optimal decision. This complexity of the credit assessment process has necessitated the construction of credit risk assessment models. Lane (1972) alluded to the fact that the sorting approach to credit assessibility can be used by financial and credit analysts both as evaluation systems of new individual and firms seeking financing as well as screening tools of the firms application and portfolio models which are included in the loan portfolio of a bank or a credit institution. Credit risk evaluation ( Altman and Saunders 1998) is a very important subject as it is a difficult task to predict default probabilities and deduce risk classification. It becomes more and more important for firms to operate successfully and for banks to decide if the loan can be given to the customer or if the credit request has to be rejected. Basel II standard defines strict restrictions and auditing rules for credit risk evaluation process, thus banking activities are deeply impacted by proper risk system implementation. It is crucial to identify over some successive time periods and select the correct principle or model for credit assessibility and bankruptcy prediction as well as to decide which data and which factors are important .Credit assessment and credit scoring models have been described in diverse ways . Chijoriga (2011) describes a scoring model as, any empirically derived and statistically sound valuation device for estimating the likelihood that a customer will not pay his obligations when due. Lee and Zhang (2003) also define a credit scoring model as a statistical model that uses University of Ghana http://ugspace.ug.edu.gh 4 empirical data to predict the creditworthiness of credit applicants. In detail, it means calculating the likelihood that a borrower will repay a loan as promised on the basis of a number of quantifiable borrower characteristics through the application of statistical or operational research methods (Dinh and Kleimeier 2007,; Yap et al., 2011), From these expressions, it is evident that the objective of credit assessment models is to assign credit applicants to either a „good credit risk‟ group or a „bad credit risk‟ group (West, 2000; Lee et al., 2002; Yap et al., 2001) and also to clearly provide timely warning to banks on the vulnerability of a borrower (Hua et al., 2007; Li et al., 2011; Rafiei et al., 2011). In arriving at these scoring models thereof, scholars have relied on a number of statistical methods. Some of these techniques include; multiple discriminant analysis (MDA) (Altman, 1968), probit (Zmijewski, 1984) logit (Ohison, 1980), and artificial neural networks (Wu and Wang, 2000). In the mix of these predictive model developments, the Altman 1968 Z-score model has been popularised and commercialised as a credit assessment model being used mostly in advanced countries. However, commercially available models generally use data from listed firms, which imposes serious constraints on the generalizability of the results to the specific context of privately held firms (Huyen et al., 2007). As a remedy, researchers are now making use of bank specific data and a combination of other techniques to build scoring models (see e.g. Lin, 2009; Chijoriga, 2011) and banking institution in themselves are investing in such internal models as they deliver a well-defined information set at less expense to the bank, and permit them to make faster decisions on loan applications (De-Young et al., 2008). University of Ghana http://ugspace.ug.edu.gh 5 Deeper into internal bank credit risk management, the Bank for International Settlements (Basel II accord) has encouraged the use of internal rating based tools for curtailing internal risk. In some cases also, it is a regulatory requirement for banks to apply internal risk modeling procedures, which have placed enough responsibility on banks to lookout for new and subjective means of assessing, measuring, and managing their credit risk other than the use of the traditional 5C‟s which are character, capital, collateral, capacity and condition (Yap et al., 2011). As it stands, traditional financial ratio analysis does not allow for an objective gathering of independent variable evaluations into a single performance score for credit evaluation by credit officers (Emer et al., 2003). Following the Basel II admonition, considerable investments have been made into the development of internal risk models for credit risk assessment by some banks (Fatemi and Fooladi, 2006; Odeh et al., 2010). Further, considering the economic and financial implications of the 2007-2009 credit crunch, the importance of credit risk management in the banking industry as well as the application of internal and contemporary credit risk assessment tools to aid in the credit granting decision, it has become eminent in the face of the number of risk exposures. Some of these risks include: credit risk, liquidity risk, foreign exchange risk market risk, and interest rate risk among others which may threaten a bank‟s survival and success (Al-Tamimi and Al-Mazrooei, 2007). Among these risks, credit and liquidity risk exposures are the main causes of bank distress (Greuning and Bratanovic, 2003; Bluhm et al., 2003). However, according to Chijoriga (2011), the severity of credit risk appears to surpass the other risks as far as bank failure is concerned. In this present age, and the seemingly difficulty in predicting the financial environment, it is not sufficient to understand just the primary risks associated with a product or service but also, a subject or University of Ghana http://ugspace.ug.edu.gh 6 operational requirement for banks to constantly monitor and review their approach to credit and advances which is most often than not, the main earning instrument in their balance sheet ( BoG Financial Stability Report, 2011, pp.5). Bank loans are seen to be an alternative source of business finance, especially for small and medium size enterprises (SMEs) (Jacobson et al., 2006) in the form of start-up capital, working capital or both. These loans in return, constitute a large proportion of risk to banks as it forms part of the core business (Koch and MacDonald, 2000). In Ghana, firms, notably SMEs generally raise concerns about the difficulty in accessing credit from the banks. The banks on the other hand, paint a different picture as they link the situation to the behaviour of borrowers (moral hazards) and their associated high credit risks.With the enactment of the Ghana Credit reporting Act. 2007 (Act 726), it is anticipated that these concerns between borrows and lenders will be reduced if not resolved. The Act (Act 726) allows for the establishment of both public and private companies (called credit bureaus/external credit rating agencies) that would keep information on borrowers for the purpose of assessing their creditworthiness. Nonetheless, given the asymmetric information that exists between lenders and borrowers, it is imperative for lenders who bear the ultimate risk to have a “personal” mechanism to ensure that they do not only evaluate default risk that is unknown to the ex-ante in order to avoid adverse selection, but also the one that can evolve ex-post in order to avoid moral hazards (Richard et al., 2008). One of the key mechanisms as already noted, is the submission by the Basel II Framework for banks to have Internal Rating Based (IRB) models as one of the ways of managing the credit risk that they are exposed to and means of minimum regulatory capital calculation (BCBS, 2006). University of Ghana http://ugspace.ug.edu.gh 7 This is one important nature of model analysis as a means of managing credit risk through proper risk modelling and also as a more systematic way for banks to measure changes in the riskiness of their portfolio (Freguson, 2001) Usually, credit scoring is applied to rank credit information and to target collection activities including the applicant‟s application form details and the information held by a credit reference agency on the applicant. Besides, the evaluation performance can be improved by using credit scoring which streamlines the process and allows the credit professional to focus only on unusual accounts. Credit assessment can give the credit professional an exposure perspective, mitigate the risk flexibility, and reduce the cost of credit analysis. As a result, accounts with high probability of default can be monitored and necessary actions can be taken in order to prevent the account from being default.Statistically-based credit scoring models, such as linear probability model, discriminant analysis models can be applied to determine the factors that contribute to credit risk (Gordy, 1998) Over the past decade Bethesda (2004) found out that, the servicing of monetized assets has been reconfigured to create a more efficient credit process and loan market through the application of new technologies, new financial products, and new market participants. Unlike traditional commercial lending, which at one time was predicated on long-term relationships, today‟s emphasis is on short-term value-added customer relationships. This concept of “value-added” has also brought new meaning to commercial lending as customer relationships are defined as either profitable or not profitable. If they are profitable, this must be evidenced by returns that are University of Ghana http://ugspace.ug.edu.gh 8 commensurate with the overall portfolio objectives and for the financial institution‟s return on capital. 1.2 STATEMENT OF THE PROBLEM With the recent dramatic growth in consumer credit. Accessibility of credit has become one of the main challenges to lending institutions. Credit risk is the risk of financial loss due to the applicants‟ failure to pay the credit back. Financial institutions and banks are trying to deal with the risk associated with the accessibility of credit, by determining capital requirements according to the risk of applicants and by minimizing the default risk with the use of statistical techniques to classify the applicants into ”good” and ”bad” risk classes. By taking into account these facts Basel Committee on Banking Supervision put forward to use risk based approaches to allocate and charge capital. According to the Committee credit institutions the banks have the opportunity to use standard or Internal Rating Based (IRB) approach when calculating the minimum capital requirements The standard approach is based on the ratings of external rating agencies such as Standard and Poors and Moody‟s whereas Internal Rating Base is based on institutions‟ own estimates. Internal Rating Based system can be defined as a process of assessing creditworthiness of applicants. This requires first the determination of the probability of default of the applicant by means of statistical and machine learning credit scoring methods such as Discriminant analysis, logistic regression, probit regression, non-parametric and semi-parametric regression, decision University of Ghana http://ugspace.ug.edu.gh 9 trees, linear programming, neural networks and genetic programming. The results of credit scoring techniques can be used to decide whether an applicant qualifies. (Altman, 1968) Furthermore in Ghana, loan applicants often wait for days, or even months for loan approvals. This is because credit assessment decision and the default probability estimation have been the most challenging issues in credit risk assessment. Before the development of mathematical and statistical models Credit analysts use their own judgments in evaluating applicants. These judgments are often poorly made due to lack of symmetric information gap between lenders and borrowers. The decisions may change from one person to another, so they are not replicable and difficult to teach. They are unable to handle large number of applications.But the use of statistical models took the place of judgmental methods (Beaver, 2001). Credit Risk Assessment assists organizations, such as commercial banks and credit card companies to determine whether or not to grant credit to consumers, on the basis of a set of predefined criteria (Tawakoni, 2003) .Credit scoring tasks can be divided into two distinct types: the first type is application scoring, where the task is to classify credit applicants into „„good‟‟ and „„bad‟‟ risk groups. The data used for modeling generally consists of financial information and demographic information about the loan applicant. In contrast, the second type of task deals with existing customers and along with other information. Payment history information is also used here. This is distinguished from the first type because this takes into account the customer‟s payment pattern on the loan and the task is called behavioral scoring ( Atiya, (2005) . University of Ghana http://ugspace.ug.edu.gh 10 Recently, under Basel II committee‟s recommendations, it is increasingly becoming almost a regulatory requirement for the banks to use sophisticated credit scoring models for enhancing the efficiency of capital allocation. Usually, a credit score is a number that quantifies the creditworthiness of a person, based on a quantitative analysis of credit history and other criteria; it describes the extent to which the borrower is likely to pay his or her bills/debt. A credit score is primarily based on credit reports and information received from some major credit reporting agencies. Using credit scores, banks and credit card companies evaluate the potential risk involved in lending money, in order to minimize bad debts. Lenders can also use credit scores to determine who qualifies for what amount of loan and at what interest rate. The generic approach of credit scoring is to apply a quantitative method on some data of previous customers, both faithful and delinquent customers, in order to find a relationship between the credit scores and a set of evaluation criteria. One important ingredient to accomplish this goal is to seek a good model so as to evaluate new applicants or existing customers as good or bad. In this regard the study seeks to build a statistical model to assess the creditworthiness of new credit seeking firms or clients by using historical financial statements of some private enterprises that have already sourced credit from a commercial bank in Ghana. 1.3 Objective of the study The main objective of this study was to fit a model that can be used to decide whether or not to grant credit to client by assessing their default risk, help reduce credit granting processing time and simultaneously bringing greater accuracy and fairness to each applicant. This mainly involves: University of Ghana http://ugspace.ug.edu.gh 11  Finding out the financial ratios that offer the most predictive significant in determining credit worthiness of firms,  Building a logistic and Probit regression models and;  Comparing and evaluating the predictive powers of both logistic and probit regression model in terms of how they work  Give recommendation to researchers and lending institutions 1.4 Rationale for the study Logistic and Probit regression models are important tools in statistics and finance or lending institutions. Indeed the absence of a trusted model to help evaluate credit worthiness of clients in an economy such as Ghana‟s has led to frustrations of the parties involved in credit assessment. The study which involves building logistic and probit regression models and evaluating their predictive powers in terms of how they work will help to determine the probability of default which is a core ingredient of the client‟s repayment evaluation and will lead to an accurate and a faster evaluation of the client‟s ability to pay back credit. Applications of these models are expected to enhance decisions on clients applying for credit, the cost of processing of credit and reduction in the amount of risks of default. 1.5 Scope and Limitations of the Study This research was conducted in the Ghanaian context using data of firms who had sourced credit from one specific bank. This therefore imposes constraints on the generalizability of the models to a different bank since banks have unique internal characteristics and different borrowing University of Ghana http://ugspace.ug.edu.gh 12 mechanisms. Secondly, the sample includes firms from different sectors of the economy. This will therefore not give the model user the opportunity to associate the model to one particular sector. In effect, it limits the reflection of the exact distinct differences in these firms. 1.6 Organisation of the study The study is organised as follows: Chapter one covers a general introduction to the study including aspects such as the background to the study, statement of the problem ,objective of the study rationale for the study, scope and limitation of the study and organisation of the study. Chapter Two is devoted to consider the relevant advances made on the credit assessment, and review of related works that have been carried out by other researchers on the topic area (both theoretical and empirical) to the study while Chapter Three explores the methodological framework in dichotomous dependent regression analysis used in building the model. Chapter four focuses and discusses the application of the methodology discussed in chapter three to build the models and how they can be used to help predict the probability of default. Chapter five deals with the summary, conclusions and recommendations and suggestions for future research in the subject area. University of Ghana http://ugspace.ug.edu.gh 13 CHAPTER TWO LITERATURE REVIEW 2.0 Introduction This chapter considers the relevant advances made on the credit assessment, and review of related works that have been carried out by other researchers on the topic area (both theoretical and empirical) on credit scoring with regards to the techniques used as well as the predictors. The chapter begins with concepts of credit assessment, the definition of default followed by some theoretical issues on the performance of probit and logit models. Here, classification measures are thoroughly discussed as well as the major distinctions between the two models (probit and logit). On the empirical front, several papers on the credit scoring issues are reviewed in relation to the financial ratios that significantly predict default of firms as well as the techniques that best classifiers‟ credit applicants. 2.1 THEORETICAL LITERETURE This section of the literature review focuses on the concept of credit assessment and credit risk management, sources of credit risk, definition of default ,the modern and traditional credit processes, perspectives on the performance of probit and logit Models as well as some relationships and variances and the assessibility of their performances. 2.1.1 CONCEPT OF CREDIT ASSESSMENT Credit assessment has been a great concern to lending institutions worldwide. Regulators, banks and bondholders, pension, fund trustees and other fiduciary agents have increasingly used ratings-based criteria to constrain behaviour. The importance of ratings-based regulations have University of Ghana http://ugspace.ug.edu.gh 14 traditionally been particularly visible in some few countries where it can be traced back to the 1930s. Fernando Gonzalez et al.(2004) attested to the fact that, with the fast growth of the credit industry all over the world and portfolio management of huge loans, credit scoring is regarded as a one the most important techniques in banks, and has become a very critical tool during recent decades. Credit scoring models are widely used by financial institutions, especially banks, to assign credit to good applicants and to differentiate between good and bad credit. Using credit scoring can reduce the cost of the credit process and the expected risk associated with a bad loan, enhancing the credit decision, and saving time and effort (Lee et al, 2002). Decision-making involving accepting or rejecting a client‟s credit can be supported by judgmental techniques and or credit scoring models. The judgmental techniques rely on the knowledge and both the past and present experiences of credit analysts whose evaluation of clients includes their ability to repay credit, guarantees and client‟s character (Sarlija, et al., 2004). Due to the rapid increase in fund-size invested through credit granted, and the need for quantifying credit risk, financial institutions including banks have started to apply credit assessment models. A credit scoring system should be able to classify customers as good credit those who are expected to repay on time and as bad credit those who are expected to fail. Credit scoring, which helps to classify groups of customers correctly, can also assist banks in increasing sales of additional products. One of the main goals of credit scoring in financial credit institutions and banks is to help the development of the credit management process and to provide credit analysts and decision-makers with an efficient and effective credit tool to help to determine University of Ghana http://ugspace.ug.edu.gh 15 strengths, weaknesses, opportunities and threats (SWOT); and to help to evaluate credit more precisely. A major problem for banks is how to determine the bad credit, because bad credit may cause serious problems in the future. This leads to loss in bank capital, lower bank revenues and subsequently increases bank losses, which can lead to insolvency or bankruptcy. In developed countries, credit scoring is well established and the number of applications is increasing, because of excellent facilities and vast information being widely available, whilst in less developed or developing countries, less information and facilities are available. Advanced technologies, such as those used with credit scoring have helped credit analysts in different financial institutions to evaluate and subsequently assess the vast number of credit applications. In the findings of West (2000) on the importance of credit, has stated that credit scoring is widely used by the “financial industry”, mainly to improve the credit collection process and analysis, including a reduction in credit analysts‟ cost; faster credit decision-making; and monitoring of existing customers. Also, around 97% of banks are using credit scoring for credit card applications, and around 82% of banks (and it was not clear from the original source whether the author was referring to US banks only) are using credit scoring to decide correctly who should be approved for credit card applications. Furthermore, credit institutions and especially mortgage organizations are developing new credit scoring models to support credit decisions to avoid large losses. These losses were considerable. For example, West (2000) reported that 'in 1991 $1 billion of Chemical Bank's $6.7 billion in real estate loans were delinquent. Gathering information is a critical issue in building a credit scoring model. In general, through loan application forms, customer bank accounts, related sectors, customer credit history, other financial institutions and banks, market sector analysis and through government institutions, banks may gain competitive advantages by building a robust credit scoring models. By collecting and isolating all relevant information, University of Ghana http://ugspace.ug.edu.gh 16 credit analysts or “banks” should be able to decide whether a particular variable should be included in the final model or not, and additionally whether a variable fits the real field requirements. 2.1.2. CONCEPTS OF CREDIT RISK MANAGEMENT Risk is the probability of an event inimical to an entity. It can be positive or negative depending on the event or the circumstance under which risk was taken. In this study, focus was given to risk associated with credit scoring. There are probable risks faced by lending and financial institutions. Some of which are interest rate risk (the possibility of a reduction in the value of a security resulting in a rise in interest rate), mortgage risk (the possibility that a borrower in a mortgage agreement will fail to make timely principal and interest payments in accordance with the terms of the mortgage), currency risk (a risk that arises from a change in price of one currency against another), liquidity risk (a risk that arises from the difficulty of selling an asset), credit risk, etc. Amongst the various forms of risk, exposure to credit risk continue to be the leading source of major problems faced by financial and other lending institutions. It is the risk most likely to accelerate an institution‟s failure. Hence, it is the risk most supervisors of lending and financial institutions would not fail to pay the closest attention. Whereas credit is the benefit enjoyed by a borrower intended to be repaid at a later date, credit risk is the likelihood that a borrower will fail to pay back credit in a speculated period of time. University of Ghana http://ugspace.ug.edu.gh 17 Increasingly, lending and other financial institutions are faced with other forms of credit risk apart from the usual loans. These include interbank transactions, foreign exchange transactions, trade financing, bonds, extension of commitments and guarantees etc. Considering the little confidence lately in credit market, it makes a lot of meaning to employ a better credit risk management practices to minimize exposure to credit risk. Credit risk management identifies, measures, monitors and reports potential credit risk exposures in an institution. It also ensures that there are adequate funds against unexpected losses as proposed by the Basel Committee, an institution created by the central bank Governors of a group of ten nations. The Basel Committee has issued a document on this proposal to encourage banking supervisors globally to promote sound practices with regards to managing risk. The recommendation on banking laws and regulations issued by the Basel Committee on banking supervision is what we call Basel II. In practice, Basel II attempts to achieve this by putting in place stringent risk and capital management requirements to guarantee that banks and other lending institutions reserve capital suitable enough to protect the institution against credit risk exposure. According to Basel II, financial institutions should assess the credit exposure for each applicant applying for credit and for each credit facility using the following criteria:  Probability of Default (PD): It is the probability that an applicant will default within the next 12 months.  Loss given Default (LGD): It is the amount of capital a financial or lending institution loses when a client defaults. Calculation of the loss given default is done by comparing actual total losses to the total potential exposure at the time of default. University of Ghana http://ugspace.ug.edu.gh 18  Exposure at Default (EAD): It is a total value that a financial or lending institution is exposed to at the time of default. Each exposure is given an EAD value and is identified within the bank's internal system. Exposure at default along with loss given default (LGD) and probability of default (PD) is used to calculate the credit risk capital of financial institutions. The expected loss as a result of a client‟s default is usually measured over a year. The calculation of EAD is done by multiplying each credit obligation by an appropriate percentage. Each percentage used coincides with the specifics of each respective credit obligation. According to Mehta (1970).The minimum capital requirements (MCR) is given as , MCR EAD LGD PD b EL     (2.1) where the expected loss (EL) is EL PD EAD LGD   (2.2) and b is the proportion of the expected loss of loan covered by minimum capital requirement Once these components PD, LGD and EAD are obtained, calculation of the minimum capital requirement is simple as in equation (2.1). The main issues faced by financial and lending institutions are: the necessary information needed to evaluate the components PD, LGD and EAD for each applicant, and the execution of a risk rating system to correctly build a statistically valid and viable model. University of Ghana http://ugspace.ug.edu.gh 19 2.1.3 Sources of Credit Risk According to (Bierman and Hausman 1970) there are two main sources of credit risk factors. These are external and internal risk factors. The external risk factors are discussed below as follows:  Economic Conditions Change in national income and unemployment will have impact on credit risk through change in business cycle, exchange rate, interest rate, credit availability and credit quality. Liquidity crunch or financial problems has the ability to impact borrowers‟ ability to fulfill their obligation. In addition legal and regulatory change could cause financial institutions to change how they oversee a transaction, as well as the quality and ability of debt collection.  Competition Competition among financial institutions in terms of growth, profitability and the desire to be a market leader have the ability to cause financial institutions to lower their standards or improperly price their loan products. This could result in higher cost of increasing non- performing loans. University of Ghana http://ugspace.ug.edu.gh 20 2.1.4 The internal risk factors of credit risk include;  Underwriting standards This is a process to determine what type of, to whom, for what purpose and when credit should be granted. Proper credit approval process should comprise proper guidelines on both form and methodology in evaluating borrowers‟ credit worthiness, setting up of credit line and interest rate appropriate to borrowers‟ risk and credits. Lenient credit underwriting can incur losses to financial institutions especially when debt repayment cannot be demanded or collateral cannot be seized in time. Many credit risks arise from deficiency in underwriting standards and credit monitoring.  Inappropriate assessment of credit quality This problem may result from competitive pressure and credit growth as they tend to put a time constraint on getting accurate data. Moreover, rapid growth and/or entry into new markets can tempt the management to lend without sufficient financial and economic analysis. To facilitate quicker decision making, management may support credit decisions by using simple indicators of credit quality, such as borrowers‟ characteristics, current and expected value of collateral or support of a parent company or affiliated companies. With rapid credit growth and heightened competition, financial institutions are pressured to introduce new products and services to the market without proper testing. Not in line with the principle of proper credit underwriting, such practice can lead to several financial institutions to serious problems. Financial institutions that University of Ghana http://ugspace.ug.edu.gh 21 practice proper credit underwriting usually test new products and services before introducing to the general customers. 2.1.5 Definition of Credit Credit is the trust which allows one party to provide resources to another party where that second party does not reimburse the first party immediately thereby generating a debt, but instead arranges either to repay or return those resources (or other material of equal value) at a later date (Sullivan et al., 2003). The resources provided may either be financial (e.g. granting of loans), or they may consist of goods or services (e.g. consumer credit). Therefore credit encompasses any form of deferred payment which is extended by a creditor, also known as the lender, to a debtor also known as a borrower. Credit is advanced to beneficiaries who promise to pay in a future date. Individuals, enterprises and other corporate entities have different reasons for accessing credit. Therefore the purpose and the nature of credit have been categorized into short term, medium term and long term loans. Briefly, short term loans are advances (e.g. personal loans) extended with a repayment period of not more than five (5) years. Medium term loans (designed for Small and Medium Enterprises) have a repayment period that falls between five (5) and ten (10) years. Long term loans (for giant corporate entities) as the name implies have a repayment period of more than ten (10) years. In Ghana most of the credit accessed fall within the short and the medium term. University of Ghana http://ugspace.ug.edu.gh 22 Advancing credit is key to banks operations, weighing significantly within the asset balance file. It has the potential of generating huge profit, but equally high risk. Practice show that credit risks are the highest registered in time by banks, in connection with losses. Credit risk is an investor‟s risk of loss arising from a borrower who does not make payment as promised (Bluhn, et.al. 2002). 2.1.6 The Credit Process Oldfield and Santomero (1997) investigated risk management in financial institutions. In this study, they suggested four steps for active risk management techniques:  The establishment of standards and reports;  The imposition of position limits and rules (i.e. contemporary exposures, credit limits and position concentration);  The creation of self-investment guidelines and strategies; and  The alignment of incentive contracts and compensation (performance-based compensation contracts). Loans that constitute a large proportion of the assets in most banks‟ portfolios are relatively illiquid and exhibit the highest credit risk (Koch and MacDonald, 2000). The theory of asymmetric information argues that it may be impossible to distinguish good borrowers from bad University of Ghana http://ugspace.ug.edu.gh 23 borrowers (Auronen, 2003), which may result in adverse selection and moral hazards problems. Adverse selection and moral hazards have led to substantial accumulation of non-performing accounts in banks (Bester, 1994; Bofondi and Gobbi, 2003). The very existence of banks is often interpreted in terms of its superior ability to overcome three basic problems of information asymmetry, namely ex ante, interim and ex post (Uyemura and Deventer, 1993). The management of credit risk in banking industry follows the process of risk identification, measurement, assessment, monitoring and control. It involves identification of potential risk factors, estimate their consequences, monitor activities exposed to the identified risk factors and put in place control measures to prevent or reduce the undesirable effects. This process is applied within the strategic and operational framework of the bank. Banks must have a process to analyze beneficiaries‟ ability to service a facility advanced to them. In some instances, stringent policies must be put in place to prevent individuals that involve in fraudulent activities or crimes from accessing a facility. This can be achieved through a number of ways for example using reliable source of references, accessing credit bureaus, or becoming familiar with individuals responsible for managing a company and checking their references and financial conditions. Banks should desist from advancing credit to reputable borrowers simply because they are known to the institution. Each loan application document should carefully be analyzed by a competent credit officer with the appropriate expertise commensurate with the size and complexity of the transaction. Therefore there should be a policy to specify the type of information and documentation necessary for a new credit approval, credit renewals, and/ or change in terms and conditions of previously approved credits. The process of advancing credit is associated with many risks that financial institutions have to deal with. University of Ghana http://ugspace.ug.edu.gh 24 2.1.7 THE TRADITIONAL CREDIT PROCESS Joetta (2007) asserted that, under the classical or traditional credit process, the concept of credit risk management had always been to ensure that adequate capital was available for loan funding and that reserves were provisioned according to the borrower‟s credit assessment. Credit extensions had always used a static approach whereby subsequent to the loan origination, the credit risk of the borrower would remain on the issuing creditor‟s balance sheet until maturity. The key elements of this approach usually began with the transaction‟s origination between the account officer and the borrower. Credit requests were prepared and presented for approval to enter into a transaction that more often than not would be underpriced for the risks relative to the proposed facility terms and structure. Bethesda (2004) also examined the credit process and pointed out that, the credit granting and subsequent monitoring process was oftentimes accompanied by unpredictable financial indicators that had been derived from limited financial analysis and due diligence. Loan syndications played an active role in the credit markets at the time however, the emphasis by most lenders was foremost on mitigating credit risks through risk disaggregation rather than managing loan funding for liquidity purposes. In other words pricing was not analyzed to separately identify all of the cost components that lenders incurred for the risks of extending credit, so credit specialists were not able to precisely examine the individual variables that influenced price performance. A common problem under this approach was that the lack of risk- sensitive pricing strategies did not always result in sufficient capital being allocated against rising unexpected losses. This became quite evident as the extension of loans declined from being a leading product for lenders to one of a “loss leader,” in anticipation that future ancillary business University of Ghana http://ugspace.ug.edu.gh 25 from borrowers would compensate for the losses on loans. As a result, when defaults did occur, costs were not recovered, which served to further depress credit earnings. As the credit markets started to change over the years, the rising defaults led to diverging loan costs and firm revenues that spiraled out of control for most banks. An agency conflict started to develop between bank profitability and account officers‟ performance compensation while funding and administrative costs on defaulted loans were not being recovered. At the same time, the credit markets were also changing as innovative financial products came on stream into the markets, only to reveal the emerging credit quality disparities among borrowers. It was at this point that financial institutions began to examine their traditional credit risk assumptions by challenging their old assumptions, which had been embedded in a static mind-set, and eventually started shifting to a dynamic perspective that has now become the modern credit risk management approach. 2.1.8 THE MODERN CREDIT PROCESS According to Boyles et al. (1989) financial institutions began to make comparisons between their historically passive approach to loan management and the more active style of portfolio managers that used most of the same skills and techniques for selecting credits. They found that a distinction between these alternative credit providers and traditional commercial lenders was that portfolio and fund managers did not retain nonperforming assets if those assets failed to provide expected portfolio returns. For banks, however, this required greater emphasis to be placed on portfolio management techniques so that single stand-alone credit requests would be extended to now earn a sufficient economic return so as to maximize the expected credit portfolio returns. University of Ghana http://ugspace.ug.edu.gh 26 Credit Portfolio Management techniques have become an integral part in credit functions for business units throughout banks, beginning with the evaluation of loan originations. Supporting functions, including relationship managers, the credit department, credit administration, and credit portfolio management, all have complementary roles that are driven by several common themes to reduce the banks‟ cost of capital and to increase aggregate portfolio performance. In general, transactions are originated by relationship managers in conjunction with each supporting credit function so that when new business is developed it will be based on realizing a hurdle rate of return that is also in line with the banks‟ portfolio concentration limits. When transactions do not yield the required returns or meet the hurdle rates, the facility is deemed undesirable if the aggregate borrower relationship is found to be unprofitable. Whereas the application of concentration limits under the traditional credit approach had been to reduce the amount of exposure to single borrowers, the practice is now extended to reducing concentration limits to credit events and exposure by borrowers, industries, asset classes, and geographical regions. Credit portfolio analysis is also performed on an aggregate level for borrowers, companies, markets, as well as credit products, all of which are ultimately measured against the desired portfolio‟s return. As the new vanguards of the credit process, portfolio managers have empowered banks to adopt a defensive risk posture relative to customer relationships. For credit risk exposures that are not value-added or that increasingly outweigh the rewards, lenders will seek to transfer or mitigate them through loan sales, securitizations, or credit derivatives. Transactions are terminated from the lender‟s portfolio so that they can be quantified, unbundled, and repackaged into newly manufactured credit products for resale to third-party investors. By repacking corporate credit University of Ghana http://ugspace.ug.edu.gh 27 risk into new pools and classes of debt that are sold to a broad range of investors, the credit markets have created a new product segment in the syndicated, secondary, and capital loan markets. The expansion and growth of the credit derivative markets by adopting the practices of modern credit risk management, the banking industry has also become resilient in managing the deteriorating credit quality among corporate borrowers. 2.1.9 LOAN According to Gordy et al., (2000) a loan is a resource, mostly in momentary terms given out to a qualified applicant with an agreement to pay back the money with interest at a specified date. Typically, the money is paid back in regular installments. The loan is provided at a cost, referred to as the interest on the resource received. This provides an incentive for the bank to engage in the loan. There are two major characteristics that vary amongst loans obtained from a banking industry. These are the security required to access the loan and the terms of the loan. Considering the security required to access the loan, there are two types:  Secured loans  Unsecured loans.  Secured loan A secured loan is a loan backed by a guarantee of payment for the loan. The borrower by law gives up ownership of collateral used as security to the lender. A typical example of a secured loan is a mortgage loan. This is used by clients in purchasing properties. A mortgage loan is University of Ghana http://ugspace.ug.edu.gh 28 procured by a buyer to pay off the seller of a piece of property in full. The buyer then owes the mortgage lender the total amount borrowed with interest and fees. As collateral the lender of the mortgage keeps ownership of the said property until the buyer pays the mortgage off in full. However, the buyer occupies the property as if it were already his or her own. If the borrower defaults on the mortgage loan, the bank has the legal right to sell the property to get back the money that has been lost. Another form of a secured loan is a car loan. Just as a mortgage loan is secured by housing, a car loan may be secured by the car. There are two types of auto loans. These are direct and indirect auto loans. For a direct auto loan, the bank gives the loan directly to the client. In the case of an indirect auto loan, the car dealership acts as an intermediary between the bank or financial institution and the client.  Unsecured loans These are monetary loans not backed by any guarantee. Some of these include credit cards loans, personal loans, bank overdrafts, corporate bonds etc. ( Modigliani and Miller 1998). 2.1.10 Definition of default Historically, credit risk models were developed using the default criterion bankruptcy(Mavri,et al2008).However considering the typical operations of financial institutions and the road maps to eventual bankruptcy the banks will incur losses before the firms/s they had borrowed to even go bankrupt. Thus, by necessity, they make loan-loss provisions for such debts which eventually affect and erode their profitability. By the nature of bankruptcy, it is usually triggered by the default on debt servicing (Lennox, 1999) hence the two circumstances (default and bankruptcy) must not be mixed. Additionally, there is a legal implication to bankruptcy which varies from University of Ghana http://ugspace.ug.edu.gh 29 country to country and moreover, firms, experiencing financial distress may not automatically face legal failure or go bankrupt (Bhimani et al., 2010). Bankruptcy occurs when a company is declared insolvent and the assets liquefied in order to repay its creditors (Bhimani et al., 2010). On the other hand, default is described as the failure of a company to make timely payments of interest or principal to lenders. Furthermore, default occurs prior to bankruptcy and the former may not lead to the latter (Grammenos et al., 2008). As Barnes (1990) reiterates, the relevance of making the difference between bankruptcy and default is crucial given that failure to meet financial obligations does not necessarily lead to bankruptcy. Presently, several expressions such as distress and failure are applied to mean „default‟ . Beaver (1966) defines failure as the inability of a firm to pay its financial obligations as they mature. Due to these developments as to what distress, failure and bankruptcy are, studies carefully use the terms „failure and/or distress‟ to mean default baring any legal considerations with strict stances (see Lin, 2009, Laitinen, 2010; Chijoriga, 2011). The focus of this study is predicting default risk of firms but not bankruptcy and so it is important to describe what default actually means in this research context. The importance of defining financial failure is emphasised by Altman (1984). In Altman‟s opinion, failure is independent of its outcome. This calls for the definition of our dependent variable (default) in consistence with an ex-ante approach and for a financially based definition of distress that is independent of its legal consequences (Pindado et al., 2008). In the Basel Committee on Banking Supervisions‟ (BCBS) 2004 capital adequacy framework, the committee announced an internal ratings-based approach (IRB) which could form the basis for setting capital charges for banks with respect to credit risk (BCBS, 2004). The framework in University of Ghana http://ugspace.ug.edu.gh 30 general defines default as any credit loss event associated with any obligation of the obligor, including distressed restructuring involving the forgiveness or postponement of principal, interest, or fees and delay in payment of the obligor of more than 90 days. The revised version of the accord, Basel II framework (BCBS, 2006) exclusively outlines the following reference definition of default; “a default is considered to have occurred with regard to a particular obligor when one or more of the following events have taken place”. “The bank considers that the obligor is unlikely to pay its credit obligations (principal, interest, or fees) to the bank in full without recourse by the bank to actions such as realizing security (if held)”. “The obligor is past due more than 90 days on any material credit obligation to the bank” From our discussions so far, it is apparent that researchers and practitioners interchangeably use terminologies such as distress or failure to also mean financial default by clearly defining it and stating their stance. With the ensuring definition of default, this study adopts the definition of default that is independent of any legal implications (e.g. Beaver, 1966; BCBS, 2004; BCBS, 2006). Consequently, this present study uses a financial criterion in defining default, which is the inability or failure of a firm to fulfil its agreed upon financial obligations when due. This will facilitate the prediction of the probability of default of firms seeking credit. As such, distress and failed firms are considered as those that have defaulted on their financial obligations when they were due. 2.1.11 Theoretical Perspectives on the Performance of Probit and Logit Models University of Ghana http://ugspace.ug.edu.gh 31 Logit and probit models are two regression methods categorised under Generalized Linear Models (GLM) which can be used when the dependent variable in the analysis is categorical in nature‟ (Shariff et al., 2009). In other words, they are techniques for estimating the effects of a set of independent variables on a binary (or dichotomous) dependent variable (Berry, 2005). Logit model is used to forecast probability of an event by fitting data (represented by some variables) to the logistic curve (Li et al.,. 2011). In this research, the probability of an event happening is default, denoted by 1 (one) if the event occurred (firm defaulted) and 0 (zero) if otherwise. The purpose of logistic modelling (and aloes probit ) as in other modelling techniques, is to find a model that best fits the data and is also the simplest, yet, physically practical and resolute in describing the relationship between the dependents and the explanatory variable (Hosmer and Lemeshow, 1989). Opinions regarding the selection of probit or logit as binary response mode is mix since the two approaches basically appear to yield similar results. As it stands, there is little to differentiate between the models which party fits the question posed by Gujarati (2004) that “between logit and probit, which model is preferable”? Nonetheless, according to Hahn and Soyer (2007) this affirmation only seem to be true for univariate binary response models and therefore, for multivariate binary responses models, such opinion is misleading because model fit can be improved by the selection of the appropriate link function. Hahn and Soyer (2007) further postulates that, if the researcher is interested in both in-sample and out-of-sample predicted ability, then the probit model is clearly preferable. It is however asserted in some quarters that the logit model outperforms the probit model in terms of predictive accuracy on the field (Altman and Sabato, 2007). University of Ghana http://ugspace.ug.edu.gh 32 One major statistical multivariate assumption concerning dependence techniques is normality (Hair et al., 2006). Under this assumption, Finney (1952) suggest using the logit over the probit transformation if data is not normally distributed since the logit model will proide a better prediction accuracy owing to the distributional nature of the probit model (follows a normal distribution). Similarly, Shariff et al. (2009) argues that, a regression of the logit seems to be the most robust approach as against probit if normality of data is in doubt. This therefore means that logit estimations are expected to give better prediction accuracy and results as compared to probit when the data used does not meet the multivariate normality assumptions. In addition, Hahn and Soyer (2007) put forward that in multivariate probability models, logit provides a better fit than probit in the presence of extreme independent variable levels while on the contrary, probit offer a better fit where moderate data set (size) is available. 2.1.12 Performance Criteria of Prediction Model There are many statistical measures of model performance. That is, the ability of a risk model to rank or predict risk of a binary outcome (Beling et al., 2005). Traditionally in logit and probit model, fit, the “pseudo R 2 ”coefficient has mainly been relied on and served as a goodness-of-fit and performance measure. However according to Berry (2005), reliance on such statistics have not achieve wide acceptance as a standard measure of performance as compared to percentage correctly predicted (PCP) or percentage correctly classified (PCC). University of Ghana http://ugspace.ug.edu.gh 33 Much of the theoretical literature on the performance of prediction models is based on the evaluation of the hold-out/validation/out-of-sample predictions normally shown by the PCP or PCC (Diebold and Mariano, 1995; McCracken, 2000; Thomas et al., 2005). The percentage correctly classified or predicted, measures the proportion of correctly classified cases in a sample of estimation data (Baseness et al., 2003). Nevertheless, selection of a model based on its out-of- sample prediction as a result of the in-sample performance is also optimal (Donkers and Melenberg, 2002). In principle, a good prediction model should predict (perform) well both in- sample and out-of-sample,. Therefore a test for predictive performance should result in similar conclusions for the estimation and the valuation sample (Donkers and Melenberg 2002). Since predictive accuracy is one of the most important indicators of model effectiveness, it is imperative to compare models and settle on the one that is most accurate since a unit difference can be crucial when applying the model to default risk (Li et al., 2011). Notwithstanding the importance of PCC as a performance measure, Baesens et al. (2003) asserted that in several instances, the PCC may be an inadequate performance criterion in view of the fact that it assumes equal misclassification costs for type I error and II error predictions which is problematic since for most real life problems, one type of classification error may be much more expensive than the other. By implication, better methods of comparing scoring models would be useful (Thomas et al., 2005). A superior performance measure which is noteworthy is the receiver operating characteristic (ROC) curve (Beling et al., 2005). The ROC has mostly been employed in studies to ascertain and compare the performance of scoring models by examining the area under the ROC curve (AUC) (Verstraeten and Poel, 2005). University of Ghana http://ugspace.ug.edu.gh 34 The ROC curve is a two-dimensional graphical illustration of the sensitivity on the Y-axis (highly risky applicants who can be perfectly identified and rejected) versus 1-specificity on the X-axis (good applicants rejected) for various values of the classification threshold that yields and AUC or a plot of the cumulative score distribution of the bad sub-population versus the good sub- population (Beasens et al., 2003; Beling et al., 2005). The AUC provides a smile figure of merit for the performance or efficacy of the constructed classifier and it measurement is closely related to the Gini coefficient which is between 0 percent and 100 percent (Thomas et al., 2002; Thomas et al., 2005) meaning that the higher the value, the better the discriminatory ability of the model. Simply put, AUC offers an estimate of the probability that a randomly chosen defaulter (positive predicted borrower) is correctly rated (i.e. ranked) higher risk than a randomly selected non- defaulter (negative predicted borrower) (Verstraeten, and Poel, 2005) or where all non- creditworthy firms can be perfectly identified and rejected by scores below a given cutoff value on the line of equality where there is no discrimination power and applicants are selected at random (Beling et al.,. 2005). In ROC space, the greatest increase in expected loss is loans lines parallel to the vertical exist, pointed towards the origin thus where every applicant seem to be accepted but sensitive and the greatest increase in expected profit is loan lines pointed towards the upper-life corner where there is perfect discrimination (Beling at al. 2005). Talking about threshold or cutoff score for accepting or rejecting loan applicants, if we consider an acquisition policy with a single score or cutoff (v), where only applicants with scores higher than the cutoff are accepted, then each point on the ROC curve yields the fraction of unworthy- credit clients rejected as a function of fraction of the worthy ones rejected type II error) Beling et University of Ghana http://ugspace.ug.edu.gh 35 al., 2005). The curtoff point or value according to Capon (1982) is set by the creditor on the basis of the probabilities of repayment and non-payment associated with the various point scores and the trade-offs between type I and type II errors. The errors arise as a result of misclassification of applicants given the minimum cutoff score for accepting or rejecting credit applicants. A Type I error is identifying borrower as good (because it has a value above the cutoff) but it‟s an eventual defaulter and a Type II error is identifying a company as bad (because it has a value or score below the cutoff) but in actual fact will not default (Kealhofer, 2005) According to Kealhofer (2005), three aspects of testing default risk measures deserve special attention. These are: arbitrary metric, error trade-off, and sample dependence.  Arbitrary metrics: Different default risk procedures are not based on the same metric and as such, cutoff scores (v) are unrelated from one metric to another and therefore by comparing different techniques at arbitrary cutoff value is generally meaningless. The author however suggest that the difficulty can be overcome by comparing the Type I error rates of the models for which the cutoffs have been set to produce the same levels of Type II error.  Error trade-off: The levels of Type I and Type II errors are related to each other and to the level of the cutoff (Capon, 1982), Hence, using a very high cutoff minimizes Type I error, but maximizes Type II error. Thus, the higher an acceptance cutoff is set, the lower the type I error (accepting bad applicants), while the lower a rejection cutoff values, the lower the type II error (rejecting good applicants) (Capon, 1982).  Sample dependence: Also, Kealhofer (2005) assert that, the levels of error depend on a particular sample tested and in a broad spectrum; one cannot compare errors from one sample University of Ghana http://ugspace.ug.edu.gh 36 with errors from another sample. For instance the characteristics of sample A may be distinct from that of sample B. Consequently, the differences will invariably translate into different average default rates and different levels of error. 2.1.13 Similarities and Differences Between Probit and Logit Models It is difficult to statistically distinguish between logit and probit models, as both models are very similar and rarely lead to different conclusions (Bhimani et al., 2010). In this study we have classified them on the basis of their distribution, coefficients, and nature.  Distribution: In many applications involving the probit and logit models, particularly those concerning decision making, the latent dependent variable may represent the probability that an event occurs or the preference level that a decision maker has for two alternative outcomes (Aldrich and Nelson, 1984). On the basis of probability distribution, the probit is assumed to follow the cumulative normal distribution, while in logit, it is assumed to be based on the logistic distribution (Aldrich and Nelson, 1984; Li et al., 2011). In addition, through both models have a mean value of zero (0), their variances are different (Gujarati, 2004). That is to say that logit regression does not require multivariate normal distributed variables or equal dispersion matrices (Ohlosn, 1980; Zavgren, 1983). The cumulative distributions of the two models are depicted in Figure 2.1.  Estimated coefficients: There is little to distinguish between logit and probit models for the reason that both curves are so similar as to yield essentially identical results (Shariff et al., University of Ghana http://ugspace.ug.edu.gh 37 2009). However, applying probit and logit analysis to the same set of data produces coefficient estimates which differ approximately by a factor of proportionality, and that factor should be about 1.81 (Aldrich, and d Nelson, 1984. Therefore, if the probit coefficient is multiplied by 1.81, that is ~ 3       , you will get approximately the logit coefficient (Aldrich, and Nelson, 1984). Alternatively, if you multiply a logic coefficient by 0.55 = 1 1.81 you will get the probit coefficient (Gujarati, 2004) Despite these computations, the estimated parameters of the models are not directly comparable. It is also important to note that in predicting who is likely to repay a loan and who will default, any approximations will probably lead to misclassification of an applicant and hence lead to type I or II errors which in essence will affect the credit granting decision. As such, in risk modeling, one must bear in mind the consequences of such approximations since even an improvement in accuracy of a fraction or a percent might translate into significant future savings for the model user ( Beasens et al., 2003).  Nature : Gujarati (2004) observes that in most applications, the pobit and logit models are quite similar. However, the main difference is that, the logistic distribution has slightly fatter tails, which can be seen from figure 2.1. what this means is that, the conditional probability  iP approaches zero or one at a slower rate in logit than in probit and as such, there is no compelling reasons to choose one over the other or substitute one model for the other (Gujarati, 2004). In practice nonetheless, many researchers choose the logit model over the probit because of its University of Ghana http://ugspace.ug.edu.gh 38 comparative mathematical simplicity and the flexibility as far as multivariate normality is concerned (Gujarati, 2004; Hair et al., Figure 2.1: Probit and Logit cumulative distributions p 1 Probit Logit 0 Source Gujarati (2004) 2.2 Empirical Review This aspect of the review delves into the findings of other related studies in terms of the ratios that significantly predict default or distress and also the models that best classifies the sample. University of Ghana http://ugspace.ug.edu.gh 39 2.2.1 Financial ratios as Predictors of Financial Default It is well established that the effective use of screening technology greatly reduces the informational asymmetries between borrowers and lenders, thereby enhancing the efficiency of the financial intermediation process (Psillaki et al., 2010). Over the past decades, a vast literature has emerged concerning the development of statistical models. Designed to predict if firms will ether fail or experience some form of financial distress, such as loan default and bankruptcy with the help of financial ratios (Khatwani et al., 2006). In order to build a scoring model, historical data on the performance of previously granted loans and borrower characteristics are required (Yap et al., 2011). Based on these performance indicators notably financial ratios, a good scoring model could give a higher percentage of scores to „good borrowers‟ and lower scores to those who are „bad borrowers‟ by assessing specific performance indicators (Yap et la., 2011). Despite the skeptism surrounding the use of the ratios as means of assessing creditworthiness, they have become useful and acknowledge in a variety of areas including credit lending (beaver, 1966) One of the primary issues of credit scoring research has been to determine what variables significantly influence the probability of default (Marshall, 2010) in testing the usefulness of ratios as predictors of failure, Beaver (1966) independently tested a series of ratios including: Cash Flow Ratios, Net-Income Ratios, Debt to Total Asset Ratio, Liquid Assets to Total Asset Ratio. Liquid-Asset to Current Debt Ratio, and Turnover Ratios, After conducting the univariate analysis, the author found cash-flow to total debt ratio to be the strongest in the ability to predict failure while the net-income to total assets ratio predict second bests. In Beaver‟s paper, the third best ratio to predict failure is the total debt to total assets ratio while the liquid-asset ratio University of Ghana http://ugspace.ug.edu.gh 40 performed the least. From this study, It can be observed that, financial leverage, profitability, and liquidity are key indicators of the health of a firm and for that matter, serve as good indicators of financial distress. This pioneering work paved way or the development of multivariate predictive models to businesses. In a follow up study Altman (1968) found five financial ratios as significant predictor variables for bankruptcy in his Z-score model, these consist of: Working capital/Total assets, Retained Earnings/Total assets, Earnings before interest and taxes/Total assets, Market value equity/Book value of total debt, and Sales/Total assets ratios. Amongst these ratios, the author found the profitability ratio to be the highest contributory factor to predict distress. Altman described this outcome as not supervising considering the fact that the incidence of bankruptcy in a firm that is earning profit is almost nil. On the contrary, profitability does not necessarily means cash hence firms making or reporting profit still have a certain chance of failure as in the case of Enron. It is clear from here that firms that suffer cash flow problems are more risky and susceptible to distress. Emel et al. (2003) also found that „better‟ firms are those that in general, are less risky, financially efficient, more liquid, and are adequate in terms of capital. . Based on data from the USA telecom industry, Foreman (2003) demonstrates that traditional financial ratios (profitability, capital structure, and the power to fiancé growth internally) are good enough to tell the probability of a firm‟s failure. One surprising yet not out of place finding in Foreman‟s stud is that, the author found a positive but significant relationship between the liquidity measures and probability of failure. It must be noted however that the consequential effects of extensively large holds for the purposes of remaining highly liquid has detrimental cost University of Ghana http://ugspace.ug.edu.gh 41 as assets will be tied down without being invested. The author also attributed this deviation from the theory or norm to the extraordinarily large working capital holdings and over-expansion of the firms studied. Whereas the eligibility of financial factors as inputs for internal credit scoring is widely accepted and for that matter not in doubt (Chijoriga, 2011), the role of non-financial factors remains unclear even though in certain quarters, they have proven to be good distress predictors when used together with financial ratios (Zavgren, 1985; Bhimani, et at., 2010). Analysing credit file data from four major German banks with the aid of the probit model, Grunert et al, (2005) found evidence of improved model performance in terms of predictive accuracy of default when both financial and non-financial variable/factors are simultaneously used. The study further showed that financial profitability ratios, liquidity ratios, and leverage ratios are significant indicators of default. 2.2.2 Exploration of more Essential Ratios to Predict Default Aside the inclusion of long-established financial ratios in predictive models, efforts are being made to discover and increases the amount of variables in such models. Khatwani et al (2006) in constructing a loan default model, factored thirty one (31) financial ratios into their model. However, after careful stepwise logistic regression and multiple discernment analysis, only six significant variables were retained in the model. these are: Return on Assets (ROA) ratio, Current Ratio, Interest Converge ratio, receivables Turnover ratio, Fixed Assets/Total Assets ratio and Working Capital/Net Sales ratio. This further confirms the importance of firm profitability as key ingredient for firm survival. This outcome corroborates the Atman (1968) results which found University of Ghana http://ugspace.ug.edu.gh 42 profitability to be a significant factor in predicting failure as well as leverage and liquidity of the firm. Similar to this, Chijoriga (2011) found ratios such as profitability. Liquidity and leverage to be significant and key in the lending environment to assess the credit risk of a loan applicant. Altman and Sabato (2007) applied the logistic regression analysis as a credit risk model for SMEs in the USA. The authors manually entered seventeen (17) accounting ratios into the SME risk model. The authors however found five significant ratios in predicting distress. These ranged from profitability ratios, liquidity ratios to leverage ratios. This result indicates that for firms to be able to withstand shocks and be solvent both in the short and long term, they must be profitable and be able to transform assets into cash in order to pay of debts (be liquid). More especially when debts to creditors must be paid with cash and not profit (Appiah and Abor, 2009). As it stands, the inability of a firm to generate enough cash from its operations may force the firm to borrow more money or to dispose of its capital investments to meet its obligation (Rujoub et al., 1995). Also, it is clear that firms with huge debts are likely to face distress and interest rate risk when earnings fall short of interest expense. At this stage it is important, to talk about one other firm characteristics, size. Chen et al. (2010) found that the asset size of a firm has a significant impact on its credit risk exposure indicating that, the probability of default is biggest among small sized firms and much lower in medium and large-seized ones. The pioneering findings of Ohlson (1980) like other studies identified four basic factors as being statistically significant in affecting the probability of failure with one year. These are: the size of the University of Ghana http://ugspace.ug.edu.gh 43 company; measure of the financial structure; measure of performance; and measure of current liquidity. In a Tunisian context, Matoussi and Abdelmoula (2010)found accrual; cash-flow and collateral variables as the best default indicators or predictors. The result reiterates the significance of cash- flow to a business. This can be described as the „life-blood‟ of any firm (Rujoub et al., 1995). When this „blood‟ seizes to flow, the business „dies out‟. In addition to cash flow, the scholars also found tangible collateral as another significant predictor of default. The eminence of tangible collaterals in their results is not surprising as it gives a reflection of the credit risk assessment criterions in developing countries, where collaterals are still being used as yardsticks for lending. In a similar instance. Affuso (2006) finds that lenders‟ credit quote is provided by determining the value of collateral of the borrower mainly because of information asymmetry. To buttress the importance of cash flow ratios to the health of a firm, an earlier study by Rujoub et al. (1995) is a good example. The author extensively used only a wide array of cash flow ratios to predict financial failure. The empirical evidence of the paper revealed high performance of the ratios to predict default. Exclusively, the cash flow predictor variable (data) yielded 86.36 percent and 789.79 percent classification accuracy on in sample basic for one year and two years prior to failure respectively. This finding goes further to support how crucial cash flow is to the existence of a firm. Any seizure of which will lead to the demise of such a firm. With the aim of providing a two stage early warning model for evaluating credit default risk, Pslillaki et al. (2010), found that apart from the importance of non-financial performance indicators, profitability is a significant ex-ante predictor of firm failure. Similarly, the authors University of Ghana http://ugspace.ug.edu.gh 44 found that firms with more liquid assets have less of a chance to fail while the effects of leverage and growth opportunities (intangibles), capital-turnover ratio and firm size generally had a significantly negative relation with the likelihood of business failure. Contrary to this outcome, Jacobson and Roszbach (2003) showed that firm size does not affect the default risks associated with a loan. Bhimani et al. (2010) modelled default risk with an initial 30 accounting ratios and non- accounting information. The study found interest costs to gross income, number of days in payables and receivables to have a positive and significant influence on the probability of default. Other ratios which were found significant but negatively related to default include: financial and asset coverage, the investment ratio, return on equity and investment, solidity, variation in gross incomes, and working capital to total assets ratios. In terms of the non-accounting variables, it was established that age influences default negatively. In view of these findings, the authors re- emphasised the role of non-accounting information on default prediction which together with other influential predictor variables, can serve as early warning signals in policies underlying supervision, and the default probabilities in the assessment of financial pressures in the corporate sector. Establishing a diagnostic model for business crises prediction, Lin et al. (2011) explored potentially useful but previously unaware financial features for better prediction accuracy. The study identified five useful financial ratios to help predict financial distress. Three of the ratios relate to the company‟s overall business performance and the other two include tax rate and continuous EPS as measures of firm future development. The performance indicator borders on; profitability (Net income/total assets), liquidity (current ratio), and leverage (cash flow/total University of Ghana http://ugspace.ug.edu.gh 45 debt). This means that a healthy firm must be the one that is viable in the long term, has good returns, be able to generate enough resources to meet its financial obligations when due (interest coverage). In a related study, Thomas et al. (2011), found that operating efficiency, profitability, solvency and, cash flow variables are essential to provide an early warning signal for corporate performance and creditworthiness. The importance of these ratios has been evident in the findings of earlier reviewed studies (e.g. Beaver, 1966; Altman, 1968; Rujoub et al., 1995; Bhimani, et al., 201; Matoussi and Abdelmoula, 2010) Pindado et al., (2008) conducted a cross sectional study by using G-7 country data to develop an ex-ante model for estimating financial distress likelihood. The results revealed that profitability and financial expenses are statistically significant in predicting financial distress. Specifically, return on assets ratio (ROA) and retained earnings/total assets as measures of profitability as well as financial expense/total assets as a measure of leverage were found to be the ratios that contribute to the predictive ability of the model. Marshall et al. (2010), studied credit applicants in the United Kingdom with the motivation to reduce explanatory variable dimensions for credit scoring research. Their results produced a statistically significant correlation between loan approval and applicant performance indicators. Up till now, financial ratios have been the main means of determining credit worthiness of credit applicants and for forecasting default/distress (Laitinen, 2010). From our discourse so far, it is evident that ratios covering a company‟s profitability, liquidity, leverage levels size and general cash flow activities are necessary and key to the health and worth of a firm. These have dominated the empirical literature as far as the significant predictor University of Ghana http://ugspace.ug.edu.gh 46 variables in any credit scoring model are concerned with profitability ratios significant in most studies. Appiah and Abor (2009) however have raised concerns on the „over reliance‟ on profitability as a measure of failure of firm resilience and solvency asserting further that following the events of this present era, profitability of a firm stand in a limbo given the collapse of bi profit making firms like Enron and WorldCom. 2.2.3 Performance of Financial Distress/Default Prediction Models In practice, there are numerous statistical methods for building credit scoring or distress models, for the purpose of managing credit risk, commercial banks use these various scoring methodologies to evaluate the financial performance of client firms (Emel et al., 2003). A few of these techniques include: multiple discriminant analysis (Altman, 1968; Chijoriga, 2011), logit (Ohlson, 1980; Foreman, 2003; Lee and Zhang, 2003), probit (Zmijewski, 1984), Artificial Neural Networks (ANN) Wu and Wang, 2000; Lee and Chen, 2005), and at some instances, a combination of all four techniques (Lin, 2009). In recent times, more quantitatively demanding approaches such as data envelopment analysis (DEA) Psillaki et al., 2010), and case-based reasoning (CBR) (Li and Sun, 2011) are being employed to predict distress, assess credit risk, and support the credit decisions process. These techniques are estimated to improve the in-sample and out-of-sample predictive accuracy rates. Among these techniques, discriminant analysis is the most commonly used statistical credit scoring method, but often criticized due to its strong model assumptions (Lee et al., 2002) Multiple discriminant analysis (MDA) assumes dichotomous data, a specified prior probability of two groups (Balcaen and Ooghe, 2006; Hair et al., 2006) University of Ghana http://ugspace.ug.edu.gh 47 In reality however, the assumptions may be valid or invalid (Zavgren, 1985) due to the fact that the assumption of multivariate normality is often violated for distress data without effective solutions (Li et al., 2011), Notwithstanding, the multiple discriminant analysis stands as one of the four most used predictive models aside the light, probit, and artificial neural network models (Lin, 2009) Altman (1968) for the first time applied the MDA approach to predict bankruptcy of sixty six (66), (33 failed and 33 non-failed) United State firms with considerable amount of success. From the paper, the discriminant ratio model proved to be extremely accurate in predicting bankruptcy correctly in 94 percent of the initial sample and with 95 percent of all firms in the bankrupt and non-bankrupt groups assigned to the