Abstract
The main aim of this research is to model and analyze the probability of default of corporate entities on their bonds using the Merton Model and subsequently evaluate each of the entity’s credit spread. Financial companies have a risk of becoming insolvent due to poor credit risk assessment and management. Bankruptcy is a major issue in the financial sector as it leads to a decrease in economic growth rate. The structural credit risk model used has been effective in the determination of the probability of default. The Merton Model uses a company’s capital structure and its asset volatility to analyze the default probability at a given maturity time. The data analysis shows that default probabilities are directly proportional to the company’s liabilities, whereas the credit spread is directly proportional to the risk of default but inversely proportional to the credit quality of that particular company. This research is a comprehensive guide to the assessment, analysis and management of credit risk.
Table of Contents
Declaration and approval ii
Acknowledgement iii
Dedication iv
Abstract v
Figures and Tables viii
CHAPTER ONE: INTRODUCTION
1.1 Background 1
1.1.1 Global Perspective 1
1.1.2 Kenyan Perspective 3
1.2 Statement of Problem 5
1.3 Objectives 6
1.3.1 General Objective 6
1.3.2 Specific Objectives 6
1.4 Significance of Study 6
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction 8
2.2 Theoretical Literature Review 8
2.2.1 Credit Risk Appraisal 8
2.2.2 Portfolio Theory 14
2.2.3 Finance Distress Theory 15
2.3 Empirical Literature Review 16
2.3.1 Credit Risk Default Probabilities 16
2.3.2 Default recovery rates and loss given Defaults 16
2.3.3 Credit Risk Derivatives 17
2.4 Summary of literature and Research Gap 20
2.5 Conceptual Framework 21
CHAPTER THREE: METHODOLOGY
3.1 Introduction 22
3.2 Structural Models 22
3.2.1 The Merton Model 22
3.2.2 Valuation Using The Merton Model 24
3.2.3 The Merton Model with Stochastic Interest rates 25
3.2.4 Limitations of the Merton Model 27
3.2.5 The KMV Model 28
3.2.6 Valuation using the KMV Model 29
3.2.7 Limitations of the KMV Model 31
3.3 Other Credit Risk Models 32
3.3.1 Reduced-form Models 32
3.3.2 Liquidation Process Models 35
3.3.3 Factor Models 36
3.3.4 The Credit Risk Mixture Model Approach 37
3.4 Credit Premium 39
3.4.1 Actuarial Approach to Credit risk Pricing 39
CHAPTER FOUR: DATA ANALYSIS AND RESULTS
4.1 Introduction 43
4.2 Data Description 43
4.3 Data Analysis 43
4.3.1 Data Variables 43
4.3.2 Absa Bank Kenya 45
4.3.3 Britam Holdings Ltd. 48
4.3.4 Jubilee Holdings Ltd. 50
4.4 Discussion and Interpretation 53
4.4.1 Absa Bank Kenya 53
4.4.2 Britam Holdings Ltd 54
4.4.3 Jubilee Holdings Ltd. 56
CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions 58
5.2 Recommendations 59
References 61
Appendix A: R Codes 66
Figures and Tables
Figure 2.2.1. Visualization of a Credit Decision 9
Figure 2.2.2. Credit Risk Management 12
Figure 2.5.1. Conceptual Framework 21
Figure 3.2.1. Components of KMV’s EDF 29
Figure 4.3.1. Time plots for Absa’s Assets and Liabilities 46
Figure 4.3.2. Absa’s Survival and Default Probabilities at different maturity periods 47
Figure 4.3.3. Time plots for Britam’s Assets and Liabilities 48
Figure 4.3.4. Britam’s Survival and Default Probabilities at different Maturity periods 50
Figure 4.3.5. Time plots for Jubilee’s Assets and Liabilities 51
Figure 4.3.6. Jubilee’s Survival and Default Probabilities at different maturity periods 53
Figure 4.4.1. Absa’s time plot of its Assets against its Liabilities 53
Figure 4.4.2. Britam’s time plot of its Assets against its Liabilities 55
Figure 4.4.3. Jubilee’s time plot of its Assets against its Liabilities 56
List of Tables
Table 2.2.1. Credit Quality Assessment 10
Table 2.2.2. Credit Risk Assessment Process 11
Table 4.3.1. Absa’s Total Annual Assets and Liabilities 45
Table 4.3.2. Absa’s Asset Volatility 46
Table 4.3.3. Absa Bank Kenya (Probability of Default/Credit Spread) 47
Table 4.3.4. Britam’s Total Annual Assets and Liabilities 48
Table 4.3.5. Britam’s Asset Volatility 49
Table 4.3.6. Britam Holdings (Probability of Default/Credit Spread) 49
Table 4.3.7. Jubilee’s Total Annual Assets and Liabilities 51
Table 4.3.8. Jubilee’s Asset Volatility 52
Table 4.3.9. Jubilee Holdings (Probability of Default/credit Spread) 52
CHAPTER ONE
INTRODUCTION
1.1 Background
1.1.1 Global Perspective
Over the past decades, companies, banks and Corporate entities at large have devoted vast resources for the sole purpose of the development of Credit risk models, to beNer understand the aspect of credit risk with a goal to do away with corporate debt and have an In-dept insight into the interaction between bondholders and shareholders and the nature and risk of default. Credit risk can be defined as the degree of fluctuation in debt instrument and derivatives due to changes in the underlying credit quality of borrowers and counter parties (Chen and Pan, 2012). It is the distribution of financial losses due to unexpected changes in the credit quality of a counter party in a financial agreement (Giesecke, 2004). The creditworthiness of a borrower is of great importance as it affects a company’s decision to lend, its credit spread, cost of capital and price of its derivatives.
Due to the essence of credit risk management, there has been extensive and growing lit- erature on credit risk modelling. The measurement of Credit risk has focused majorly on the company’s probability of default. There are several approaches used to measure credit risk with the three main ones being; the structural approach, the reduced-form approach and the incomplete information approach. The Structural approach uses struc- tural models for entities which issue equity and debt. These are simple models that can’t ideally be used for credit risk pricing but studying them is essential as they clearly look into the nature of default as they make explicit assumptions about a corporate entity’s capital structure, its assets and debt. Default occurs when a corporate entity’s total value of assets is less that the actual promised debt repayment. A good example of a structural model is the Merton Model (Merton, 1974).
The reduced-form approach uses reduced-form models that use market statistics instead of particular data relating to a specific issuing organization. These market statistics are majorly credit ratings from credit rating agencies such as Poor’s and Moody’s. Default in this case is analyzed using a default rate which can be used to price credit securities by calculating a risk free rate of interest which is modified by the intensity. An example of such a model is the Jarrow-Lando-Turnbull Model which uses multiple credit ratings. The Incomplete information approach is a combination of the reduced-form models and the structural models. The incomplete information models uses the intuitive nature and tractability/empirical fit respectively of the two models mentioned above.
Credit risk is measured and managed in many different ways by different companies. In the past credit risk was analyzed subjectively in the aNempt to evaluate the credit wor- thiness of borrowers. Experts used judgments that relied on reputation, volatility, capital and collateral where borrowing and lending was driven by internal rate risk (Valášková et al., 2014). The problem with this method of analysis is that there is a lack of an objective and uniform rating algorithm. In addition, companies incurred high costs maintaining experts whose opinions may lead to adverse losses because of underestimation or over- estimation of risk, therefore with time most companies opted to rely on credit rating agencies. Rating agencies were used way before the development of mathematical mod- els and are still used to date. John Moody and Company in 1900 published a book known as "Moody’s Manual of Industrial and Miscellaneous Securities" which gave insightful information and statistics about bonds, shares and stocks of various industries and con- sequently led to introduction of bond ratings in the US in 1909. John Moody and Henry Varnum Poor are among the pioneers of credit rating agencies. Among the first credit rating companies was a company called Standard and Poor’s, established in 1922 and whose main objective was rating of bonds.
The Fitch publishing company introduced the AAA through D rating systems in 1924. The industry has since then certified and used this method of analysis as a basis for ratings. Fast forward, Beaver W.H. came up with the first scoring mathematical model used to predict credit default by use of financial ratios (Beaver, 1966). In 1968, Edward Altman added to Beaver’s concept and came up with the Altman’s Z-score model which used a combination of five financial ratios that were weighted by coefficients to predict the probability of bankruptcy. The first structural form model was the Merton Model (Merton, 1974) which was based on the Black and Scholes (1973) option pricing theory. Merton’s Model assesses a firm’s debt by relating the firm’s capital structure to its credit risk (Hull et al., 2004). The Merton Model was modified by Geske (1977) who introduced discrete interest payments on risky bonds . Black and Cox (1976) later worked on the same problem and came up with a model that analyzed the instant where default happens immediately when the value of a company’s assets falls under a positive threshold.
Jarrow, Lando and Turnbull came up with the first reduced-form credit model in 1997. They added the idea of term structure of credit risk spread and incorporated credit rat- ings into the model they built which was used to estimate corporate debt (Jarrow et al., 1997). The reduced-form models use risk rates instead of the probability of default and the default time is influenced by a stochastic process that is independent of the charac- teristic of the company. Credit ratings have allowed experts to draw conclusions about the financial well-being of corporate entities without the need to know the market value of such organizations. These reduced-form models have also been useful in pricing of credit derivatives.
In the late 1990’s some financial companies and banks started using credit value-at-risk models to valuate credit risk. A Value-at-risk model assesses loss by estimating the likeli- hood of a company under-performing by measuring downside risk. Some of the essential Credit Value-at-risk models are the credit portfolio view, credit Metrics, KMV’s credit portfolio manager and the Credit Risk+. Credit Metrics uses both structural and reduced access measurement of value-at-risk to calculate the credit risk of a portfolio. The KMV credit portfolio manager Model doesn’t focus on estimation of debt of a company but rather looks at the likelihood of default of that particular company. The credit Risk+ only focuses on defaults and therefore requires default probabilities. The model gives default rates and default rate volatility to assess and estimate the level of default. The Credit Portfolio view is a rating-based portfolio model that also looks at default probabilities but incorporates economic migration likelihood (Valášková et al., 2014). Gordy (2000) has done an in-depth comparison of these models and he concludes that they all have the same mathematical structures with the differences being in their assumptions and functional forms.
1.1.2 Kenyan Perspective
The capital market in Kenya is not highly developed compared to those in developed countries and therefore credit facilitation is a major problem. Credit risk management is a crucial area of interest because of the constant inflation and deflation of prices of shares, stocks and bonds in the financial market due to the deteriorating country’s econ- omy. There is also an issue of creditworthiness of prospective borrowers. The Central Reference Bureau (CRB) is among the founding organizations instituted by the Central Bank of Kenya (CBK) whose objective is to collect and analyze credit data from different financial organizations and facilitate credit lending and sharing of information among corporate entities. In 2013, a significant number of borrowers defaulted on there loans due to the economic depression and inflation of interest rates that was linked to the Gen- eral elections held earlier that year. This led to a five-year period of bad loans in Kenya. The Central Bank of Kenya reported that there were more that 70 billion Kenyan shillings worth of non-performing loans held by commercial banks that year. This was due to de- clined spending by the private sector and the government at large because of the adverse effects of the economic instability brought about by the general elections (Wanjagi, 2018). A report by the central bank of Kenya indicates that there was an increase from 4.7% to 5.2% of the ratio of non-performing loans to gross loans which later increased to 5.6% in the subsequent year 2014. The Capital adequacy, measured by ratio of total capital to total risky assets was also reported to have decreased in that particular year (Muriithi et al., 2016).
The Increasing level of insufficient loan collateral, faulty loan processing, increasing num- ber of non-performing loans among other things are linked to inadequate and poor credit risk analysis and management (Muriithi et al., 2016). Kithinji (2010) carries out an anal- ysis of how credit risk affects the returns on total assets in commercial banks in Kenya, concluding that the amount of credit and non-performing loans are not the only factors affecting profits generated by commercial banks in Kenya. In 2011, there was a 45% in- crease in economic crimes due to fraud with commercial banks loosing a tune of 1.7 billion Kenyan shillings between August and October 2010 (Muriithi et al., 2016). Mbua (2017) indicates in his research that there has been an aNempt by the Central Bank of Kenya to regulate lending and deposit rates at 4% above and below the 91-day T-bill respectively, from 2001 through to 2016. The Vision 2030 plan, incorporated a medium term plan be- tween 2008 and 2012 to develop a payment system that is safe and reliable in terms of ensuring smooth seNlements and transfer of funds between borrowers and lenders (Muri- ithi et al., 2016). The aim of every corporate entity in Kenya is to make profit which will maintain financial stability and facilitate growth and expansion. However, in the past 2 decades, Kenya has faced a lot of setbacks such as unstable cost of borrowing, increase in non-performing loans, political instability among many others, which have affected the financial fluency of capital markets and which in turn have affected the aspect of lending and borrowing.
Majority of financial institutions in Kenya depend on credit facilitation as the major source of income. Borrowing and lending is a key factor contributing to Kenya’s economic framework and therefore policymakers are required to do an in-dept review of creditwor- thiness of different corporations in order to reduce shortfalls that would adversely affect the progression of the economy. Therefore managing credit risk is a strategic way of con- trolling uncertainty by developing risk assessment methods that help reduce and mitigate risk in these financial institutions (Wanjagi, 2018). A sound credit risk management in- volves the establishment and proper implementation of credit policies. Inefficient credit standards and poor credit scoring methods have been a huge challenge faced by many financial institutions in Kenya. Credit risk analysis and valuation acts as a guide for these financial entities to handle and manage its clients assets while meeting the company’s objectives.
The main aim of this project is to analyze and model credit risk among financial institu- tions in Kenya. The probability of default is measured by looking at the market value of the corporate entity’s shares on the stock exchange market. The future price and market value of a particular entity can be predicted by modelling its historical data to obtain the market value of its securities. This project will assist companies in decision making regarding the amount of risk premium they should offer to lenders. The project will ana- lyze various companies by looking at their equity and debt in order to calculate its total value of assets and liabilities that will help in predicting their future value.
1.2 Statement of Problem
Credit risk assessment and management is a serious maNer of concern in some if not all financial institutions today. With regard to this crucial fact, it is evident that there is need to develop and constantly maintain effective systems to ensure beNer future performance (Gakure et al., 2012). Selection of a good strategy will lead to good pricing of financial products which consequently leads to profitability. Poor credit risk management is an issue of concern because its a major factor affecting the rate of default. According to Mutonga (2009), loan defaults are increasing in Kenya due to increasing interest rates, high rate of inflation and economic deterioration which directly affects consumer’s bud- get. This problem has led to banks in Kenya receiving a decreasing amount of savings which in turn affects lending and investment. The financial sector is affected negatively when economic activities decrease. This has led to financial institutions, such as banks, to develop methods to cub the effects of the rising loan defaults. For Instance, Barclays Bank has come up with a system that involves working with employers to deduct agreed amounts during pay roll instead of waiting for the borrowers to remit monthly install- ments for these loan repayments (Mutonga, 2009). A decrease in savings has reduced the capacity of Kenya’s banking sector and non-banking sector at large to lend, leading to stagnant, or worse, a decreasing economic growth rate. These corporate entities grant credit facilities and are therefore inevitably exposed to credit risk (Muriithi et al., 2016).
As a result of this problem, extensive resources have been devoted to model and analyze credit risk since time immemorial because of the devastating effects it has on financial markets and as a result, measures have been put in place to minimize these effects. For instant, the Central Bank of Kenya (CBK), established by an act of parliament to pro- mote price stability by formulating and implement monitory policies, formulated and implemented credit risk management guidelines in 2013 due to the fact that banks and other financial institutions were increasingly facing credit risk, asserting that loans are the largest but not the only form of risk. The assessment of credit risk has therefore been of great importance because it helps greatly in valuation of debt. There has been a com- parative mispricing of debt because the debt market is underdeveloped compared to the equity and shares market mostly due to discrepancies in their liquidity. This has led to proliferation of bankruptcies and creation of credit arbitrage opportunities which in turn has led to extortion of borrowers and lenders at large. Furthermore, it has led to loans having increased competitive margins and there has also been a decrease in the market value of real assets. With regard to the adverse effects of this problem, researchers and academics alike have developed systems to analyze credit scores and intriguing models to price credit risk. This project will provide an incisive and in-depth overview of credit risk modelling and valuation with the main focus being on the Merton Model, with the hope that it will eliminate existing credit arbitrage opportunities and create healthy and thriving competitive financial and capital markets.
1.3 Objectives
The following are the objectives of this research:
1.3.1 General Objective
The main purpose of this research is to use the Merton Model in structural credit risk modelling and valuation.
1.3.2 Specific Objectives
i. Evaluate the credit spread for different corporate entities.
ii. Assess the different methods of credit risk analysis and management.
iii. Model and analyze the probability of default of corporate entities on their bonds using the Merton Model.
1.4 Significance of Study
Credit risk assessment, analysis and management is of great importance to all financial institutions, Investors, regulators, policy makers, the government and the financial in- dustry at large. Therefore, the research findings and the knowledge shared in this work will be essential in the following ways;
Many financial institutions are facing financial problems due to devastating losses brought about by mismanagement of credit risk, to an extent of some of them going bankrupt or insolvent. This project will help financial companies and corporate entities mitigate losses by maintaining its credit risk exposure through seNing up of credit risk models.
This project’s findings can be used by policy makers to formulate and implement a proper credit risk assessment and management system. Regulators can also use this project’s findings to set up a good regulatory framework. The set up and implementation of these systems is significant as it will reduce financial losses and lead to growth in the financial sector and the industry at large.
Companies that have already set up systems to mitigate credit risk can use this project’s derivatives to develop and improve their credit policies and debt financing structures. This will help correct faulty credit risk management systems which do not meet the ob- jectives of these financial institutions.
The process of lending and borrowing is crucial as it contributes to the growth of a coun- try’s economy through facilitation of credit which makes it possible for people to trade and investors to invest into different projects and businesses. Knowledge from this project can be used by lenders, borrowers and investors to strategically plan ahead and make in- formed investment decisions.
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