A Markov Chain Study on Mortgage Loan Default Stages free essay sample

Shifting probability of credit status of past due or non-performing loans across stage has always been the center of attention not only for banking institutions but also for academicians. Mortgage loans’ changing credit status has a major influence on bank’s required reserve for capital adequacy against possible default loss. If the probability of shifting credit for default loans can be understood, calculated, controlled, or even predicted, reserve cost for the banking institutions can be alleviated to achieve higher economic efficiency. Due to the practical need to study and forecast bad credit, this research tries to explore probability distribution of past-due loans and to estimate average survival time before transferring into next non-performing loan stages. This information may be useful for bank managers to understand how to deal with the problems of classification and average delinquency related with mortgage loans for the purpose of better managing and granting loans. Bank asset may be better protected by restricting the period of years in mortgage financing especially when loans become dangerously delinquent and collaterals fail to offer adequate rotection. Banking institutions may even use life insurance to match the period of mortgage loans against potential default in the case of borrower accidents. Prediction of mortgage probability among credit stages may facilitate loan granting decision because of better quality in credit evaluation, which may, in turn, reduce a significant portion of mortgage risk. Mortgage Loan Default Stages may be commonly classified into 5 stages: normal, special mention, substandard, doubtful, and actual loss, with each stage having different probability of change either from good to bad or vice versa. This study use the Markov Chain to study the probability of shifting credit status and to estimate average survival delinquency of non-performing loans across stages, using the mortgage data collected from one of Taiwanese major banking institutions over a period of ten years (2001-2010). The study result shows that the probability distribution of mortgage loans can be classified in to the following five stages: 86. 89% belong to normal, 2. 12% need special mention, 0. 56% turn out to be doubtful, 0. 63% classify as substandard, and, finally, 9. 8% become actual loss. The probabilities for past-due loans to return back to its previous stage are 5. 64%, 3. 86%, 2. 3% and 0. 05% respectively, showing that mortgage loans once become past-due out of its regular repayment will not be easy for them to return to its previous credit status. This study also estimates average delinquent period for credit stages to be 23. 61, 7. 38, 4. 24, and 2. 40 years respectively, showing that the downward spiraling nature of non-performing loans with an ever shorter of life-cycle for worse credit. keywords:Mortgage loan, default risk, absorbing Markov chain I. Introduction Credit and loan and are the main business and a major source of earnings for banking institutions. The quality of credit and loan operations has a tremendous impact on the soundness of banking operations. One of the causes of the 2007 U. S. subprime mortgage crisis is the excessive credit expansion for financial institutions to ignore risk related to real estate loans, particularly when such loans are from high-risk populations suffering from unemployment or falling real estate prices. Bad loans did not occur instantly when credit is first given. Overdue credit happens gradually during the process when economy deteriorates causing households without the ability to repay and home prices to fall largely below the actual loan amount. A significant portion of those overdue bad loans will cause the rapid rise in the Non-Performing Loans (NPL) ratio for financial institutions, resulting in a serious erosion of profit, and causing a chain reaction of bankruptcy and escalated financial crisis. The century-old Lehman Brothers declared bankruptcy in 2008 which caused a domino effect, not only hitting the U. S. economy, but also triggering a global financial tsunami. Such disaster may be explained by the fact that banks recently owns excessive amount of poor credits which may be the result of highly competitive banking environment and reckless credit imprudence, even reaching an alarming level in banks NPL ratios. In order to correct this problem, the banking industry must make prudent and cautious decisions in the beginning of loan auditing process and also recognize the dynamic fact that credit status is not static. It shifts greatly throughout the life span of the loan credit. The change is more dramatic especially in the case of past due or non-performing loans. Only when banking institutions are fully aware of the dynamic nature of credit status can the banking institutions avoid making the same mistake again. This paper focuses on the study of the shifting probability of credit status of past due or non-performing loans. In this study, the samples are selected based on the number of different credit stages and the size of different scale from the cases of residential mortgage loans from a branch in southern Taiwan of a large scale national bank specialized real estate mortgage loans, so that the samples are representative and non-bias. During the 10-year period of study from 2001 to 2010, a total sample of 3470 cases are selected with 3455 cases of normal payments and 305 overdue repayments in order to understand the distribution of housing loans and their NPL status. According to Taiwanese banking regulations, 5 categories (or stages) of overdue loans and bad credit assets are defined as: Category I (stage 0):Normal Credit assetsnormal payment (on interests and principals); Category II (stage 1): Special Mentionoverdue 1 to 3 month stage; Category III (stage 2): Substandard overdue for 4 to 6 months; Category IV (stage 3):Doubtful/pre-write-off stage overdue for more than six months; Category V (stage 4):Losses—actual write-offs. This study uses the Markov Chain method to study the continuous process, transferal evolution, and shifting probability of loans across stages. The purpose is to investigate the distribution status and transferal probability of NPL loans in different stage to understand and forecast the probability of classification and its survival time in each of the stage for reference of the bank in auditing credit, extending credit, securing loan, and the need to attach mortgage life insurance to reduce bank’s risk. 2. 1 Definition of housing loans According to Taiwanese Bank Credit Practice, (Bank Credit of Practice Summary compiled Committee, 2008), housing loans are defined as when customers, with good credit history, may provide his or other’s real estate to banks or other financial institutions to apply for short-term or long-term loans to meet clients need of home purchase, repair or other specific purposes. According to the borrowers credit situation, solvency, and market value of collaterals, banks may provide financing to pursue maximum profit under a certain degree of risk, in order to meet customer needs and arrange loan portfolio management. . 2 Definition of bad credit assets Taiwanese NPL regulations classify credit assets (both on and off balance sheet) into normal credit assets (Category I) and other bad credit assets (Category II-V). A sound credit asset shall be evaluated based on the market status of collaterals and overdue length of time. Bad credit assets cover the stages that have overdue 1 to 6 mo nths, more than 6 months, doubtful of any payments, and real asset losses which are actually written off from banks balance sheet. Bad credit assets also have the following situations: 1. Those requiring â€Å"Special Mention† refer to the category of credit assets still having sufficient collateral but principal or interest payments in arrears for 1 to 12 months; or those unsecured credit assets having overdue for 1 to 3 months; or those credit assets that have not yet reached their maturity date, but the borrowers, nonetheless, show other instances of poor credit worthiness. 2. Those that are â€Å"Substandard refer to the category of credit assets evaluated as having sufficient collateral but the borrowers principal or interest payments have been in arrears for 12 months or more; or those credit assets evaluated as unsecured on which the borrowers principal or interest payments have been in arrears for 3 to 6 months. 3. Those that are â€Å"Doubtful† refer to the category of credit assets evaluated as unsecured and on which the borrowers principal or interest payments have been in arrears for 6 to 12 months. 4. Those that are classified as â€Å"Losses† refer to the category of credit assets evaluated as unsecured on which the borrowers principal or interest payments have been in arrears for 12 months or more; or those credit assets evaluated as impossible to obtain repayment. With regard to those credit assets to be repaid in installments by agreement, the bank may evaluate the assets in accordance with the borrowers solvency and the status of the collateral within 6 months after the establishment of a separate contract and may not be classified as bad credit asset. 1. Definitions of Non-Performing Loans Non-Performing Loans (NPLs) refer to those loans of which the principal or interest has been in arrears for 3 months or more, and those loans of which the principal or interest has not yet been in arrears for more than 3 months, but the bank has sought payment from primary/subordinate debtors or has disposed of collateral are all classified as NPLs. During the liquidation period, ei ther banks or borrower may request early repayment to amortize loans and other credit payments by notifying each other in accordance with the contract. Furthermore, Taiwanese financial authority regulates that the overdue loans more than 3 months can be handled by the following ways: (A) To dispose of collaterals, to negotiate for installment repayment of interests and principals, to restructure loan payment of interest and principals; (B) To obtain public or private credit guaranty or other government funding sources. In both cases, the credit status of loans changes dramatically from bad to ordinary performing loans. 1. 4Definitions of Non-Accrual Loans In additions, all NPLs shall be transferred to the â€Å"Non-Accrual Loans (NALs)†account within 6 months after the end of the payment period, excluding restructured loans. The NALs refer to loans and other extensions of credit transferred to the non-accrual loan accounts which are to be notified of payment by law. 1. 5Bad Loans Write-Off and Recovery Any NPLs or NALs, after subtracting the estimated recoverable portion, having any of the following characteristics, can be written off according to Taiwanese banking practices: 1. The loan cannot be recovered in full or part because the debtors have dissolved, gone into hiding, reached settlement, or declared bankruptcy. 2. The collateral and property of the primary/subordinate debtors have been appraised at a very low value or become insufficient to repay the loan after the subtraction of senior mortgages, or the execution cost approaches or possibly exceeds the amount that the bank might collect from the debtors where there is no financial benefit in execution. 3. The primary/subordinate debtors collaterals have failed to sell at successive auctions where the price of such collaterals has been successively lowered, and there is no financial benefit to be derived from the bank’s stake to continue possessing such collaterals. 4. More than 2 years have elapsed since the maturity date of the non-performing loans or non-accrual loans, and the efforts of collection have failed. II. Literature Review Previous literature tried to explore the default factors of individual mortgage loans and the reason why loans deteriorate from poor credit into overdue or even NPLs. Due to the difference in sample data and methodology, these literatures have shown very diverse conclusions. The early works of Jung (1962), Page (1964) indicates that mortgage interest rate is the main factor for causing real estate loan overdue. Von Furstenberg (1969) showed that loan-value ratio, mortgage term, borrower age and income are important default factors. Many researches have tried to applied different methodologies and variables in empirical model test to come up with distinctive but sometimes confusing results. Very little attention is paid to investigate the embedded probability iteration by stage for worse credit. In this study, we apply Markov chain to estimate shifting probability and average survival rate among different stages of home loan. Based on the probability information, the credit assessors may accurately predict default rate of home loans according to debtors’ age and loan period, and then coordinate home and life insurance to reduce credit and risk exposure to enhance the quality of home loan. Due to the fact that default rate is ignificantly affected by borrowers’ unique characteristics, i. e. age (von Furstenberg and Green 1974; Canner et al. , 1991), marital situation (Canner et al. , 1991), credit situation in the past (Grander and Mills,1989), education and so on, earlier studies of delinquency attempt to identify the relationship among these important factors. Consistent with findings of previous default studies, three loan factors have consistent and pos itive effect on delinquency: loan-to-value ratio, presence of junior financing (Herzog and Earley, 1970) and age of mortgage (von Furstenberg and Green, 1974). Claurite (1990) finds that foreclosures rise over time if interest rates rise, thus creating an incentive to skip out of high interest loans and to opt for lower ones. In addition, he finds that in markets with rising real estate values, the foreclosure rates are smaller, but the percentage of foreclosures increases with the unemployment rate. Because of its importance, mortgage credit risk evaluation has received a great deal of attention in economic and finance literature. Vandell (1978) and Ingram and Frazier (1982) mention a number of certain loan, borrower, and property characteristics which appear to correlate with loan delinquency and foreclosuresuch factors as the initial loan-to-value ratio, the contract interest rate, the housing expense-to-income ratio, term to maturity, age of loan, type of loan (conventional vs. government insured), borrowers equity, purchase price of the property, age of home (new vs. xisting), neighborhood unemployment rate, age of the borrower, borrowers income and occupational skill level and tenure on job, and the existence of refinancing or junior financing. Furthermore, Vandell and Thibodeau (1985) addressed theoretically and empirically, the structure of influences affecting the default option in mortgage contracts. A formal theoretical model recognizes that a number of loan and non-loan related effects beyond the housing unit can influence the default decision. These include 1) payment levels relative to income, which can displace other investment opportunities or cause a need for borrowing or sale to meet mortgage obligations; 2) current and expected neighborhood and housing market conditions, in particular the expected relative rate of appreciation of the unit and the relative cost of homeownership; 3) economic conditions; 4) wealth; 5) borrower characteristics such as the variability in income or the capability to survive crisis events; as well as 6) transactions costs incurred pon default. Some other macroeconomic factors and specific conditions of loan agreement which may cause later delinquency include the following: interest rate of the loan (Jung, 1962; Page, 1964), value ratio of the loan (Jung, 1962; Page, 1964; von Furstenberg, 1969; Zorn and Lea, 1989; Lawrence et al. ,1992; Kau and Keenan, 1999; Deng et al. , 1996, 2000), period of the loan (Page, 1964; von Furstenberg, 1969; Lawrence et al. , 1992), the ratio of mortgage payme nts to family income (Lawrence et al. 1992), and owner-occupation rates (Zorn and Lea, 1989). The borrower-related personal effects are often used to predict the level of borrower conscientiousness toward repayment or the likelihood of recovery from a seriously destabilizing incident, such as unemployment (Vandell, 1978; Deng et al. , 1996, 2000), death (Vandell, 1978), divorce (Vandell, 1978; Deng et al. , 1996, 2000) or housing price collapse (Kau and Keenan, 1999; Deng et al. , 1996, 2000), which will render default more likely. Their results show that unemployment and repayment have positive relation whereas economy growth rate and repayment negative relation. 2. 2Methodology Review Many literature applied the following methodologies to the study the issue of credit ratings such as multiple regression analysis (Jung, 1962; Page, 1964; von Furstenberg, 1969; von Furstenberg and Green, 1974; Vandell, 1978), discriminant analysis (Ingram and Frazier, 1982), probit model (Morton, 1975), logistic regression analysis (Vandell and Thibodeau, 1985; Grander and Mills, 1989; Canner et al. 1991; Lawrence et al. , 1992). Ingram and Frazier (1982) and Epley et al. (1996) apply the same analysis to test the significance of factors and classification and finds that classification only has small difference in validity, but significant factors varies from one research to another. On the other hand, Epley et al. (1996) show that, when same methodology are applied, there are significant difference in validity to classificatio n and positive or negative coefficients in the factors which influence on breaching the mortgage loan agreement. Since most of researchers use multi-variate methodologies, this study tries to use a different approach of markov chain methodology to analyze the situation of loan default and the nature of changing probability among different stage of loan deteriorations. This study focuses on the deterioration and change of bad loans from overdue to foreclosure with the purpose to find out shifting probability of mortgage financing and average survival rate in stages before final write-offs as bad loans. An estimate of the degree of risk associated with an home loan account is represented by the design of 5 mortgage stages: Stage 1: normal monthly payment; Stage 2: monthly overdue payment under 3 months; Stage 3 past due payments more than 3 month but under 6 months; Stage 4: delinquent period more than 6 months thus exceeding the time limit of loans; and finally Stage 5: bad loans are written off as real loss. Stages 1-5 represent the continually worsening situation of mortgage loans. This study tries to probe into the whole life range of home loan accounts in different stages, exploring their shifting probability in transit, account survival time in stages and finally predicting the chance of foreclosure for bank management concern. However, past research on mortgage households credit default model are established mainly for the purpose to achieve better prediction and warning capacity using different sample data and research methodology. Furthermore, the construction and research on credit default warning model, in most cases, seek first through calculating the probability distribution for household mortgage default to control Type I and Type II errors, and set up critical values to judge the possibility of mortgage delinquencies and, in the end, test the validity of the model using the remaining portion of sample data. Since absorption Markov chain can be used for analyzing problems related to stage change, Kijima (1998), from a technical perspective, explains how a Markov chain model can lead to the known empirical regularities such as memory in rating changes, long term reversion of ratings in bond credit assessment from class A down to E, and the probability of rating failure. Corcoran and Leininger (1973) use absorption Markov chain analysis to establish a human resources evaluation model differentiate ranks and positions into different status, use both supreme and lowest order status as the state for absorption, and calculate the time required to reach absorption. Chen, Jing-Wen (1996) uses absorption Markov chain to analyze the changing situation of account receivables (A/R) to establish the best A/R collection policy, and calculate the time and fluctuation of cash flow under conversion and balance state. Zheng, Wen-Ying (1999) use absorption Markov chain on cost benefits analysis to evaluate transfer probability on all stages of unauthorized, illegal constructions and their survival existence years within the city of Taipei. Zhou, Bai-Long (2001), through absorbing Markov chain analysis, infer the average stop over time before a bank crisis occurs for the Farmer Credit Department in Taiwan To further understand overall household mortgage overdue distribution and transfer situation under different stage, this article first arrange household mortgage loans from 2001 to 2010 according to FSB (2010) specifications, define 5 mortgage overdue lending stages for classification, then use absorption Markov chain analysis to discuss the distribution of overdue loans across stages, and finally calculate the mortgage loan transfer probability before entering final absorption state. III. Research Design This section first discusses research samples and sources, explain how NPL stage is divided, and finally introduce the research methodology. 4. 1 Research Sample Since the restoration of Taiwan in 1946, rapid economic growth and house prices rising caused a surge in mortgage business. Due to the influence of internal and external factors, real estate cycles of booming and recession affected many household incomes and thus resulted in the generation of a large amount of overdue loans since 1995. Once mortgage credit default occurred, not only were households unable to repay their debts and thus suffered from foreclosure, but also the banking experienced great damage sometimes as serious as bank-runs. This article selected mortgage household samples from a branch of a large national bank in southern Taiwans southern during the period of 2001-2010. According to the Financial Supervisory Commission (2010) specifications, as defined in the mortgage NPL stage, sample data are sorted and calculated through Markov chain analysis method to explore transfer probability of mortgage holders during stages and to estimate the average survival time of the various NPL statuses. 4. 2 Mortgage Overdue Stages As mortgage interest and principal repayment are influenced by the factors of real estate cycles and external economy, mortgage holders face a great deal of uncertainty and risk. There is a gradual process of stage occurrence from mortgage default to the end auction for doubtful accounts, rather than overnight problems occurring. Mortgage overdues are part of a continuous NPL history of credit default and should be classified by the seriousness of NPL status and divided into 5 stages, with stage 0 to stage 4 representing credit default situation getting worse. In practice, mortgage classifications make default problems easier to distinguish and to deal with. Mortgage households NPL stage definitions are summarized as following (see Table 1): Table 1 Mortgage households NPL stage definitions Mortgage households NPL stage| Definitions| 0| Category I. Normal Credit Assets| 1| Category II: Special Mention| 2| Category III: Substandard)| 3| Category IV: Doubtful| 4| Category V:Losses| Source:FSC2001 4. 3 Markov Chain Analysis Since extending loans, the NPL migration process approximates random process. In research of credit default warning model, households’ mortgage write-off stage can be regarded as the absorbing state. Based on this assumption, the study uses Markov chain’s absorbent nature to explore the distribution and migration pattern of overall mortgage NPL status. Markov chain analysis is a kind of probability process. Markov (1907) proposed the concept of Markov nature for the description and prediction of physical changes under different circumstances and the final end of a stable absorption state. Wisner (1923) develops the Markov nature into a series of useful mathematical formula. Cyert (1962) apply the concept on the research of management accounting. In addition, the Markov chain analysis is capable of dividing into stage when physical changes happen from a known state to another. Two classification criteria according to their transient† and absorbing† nature are proposed. In the former case, change always happens with distinctive characteristics and can be separated into stages; while, in the latter case, once the physical change enters the final stage, it becomes inseparable as if it was absorbed and become static during the final stage. Such a chain with stages auto-correlated to each other and with changes leading from one stage to another is called the absorbent Markov chain. † This article uses absorbent Markov chain to estimate the phase of transition probability and average survival time of the overdue loans. The Markov chain and the concept of absorbent Markov chain analytical methods, formulas are summarized below. IV. Research Results The overdue loans to total loans ratio of domestic banking sector showed a clear downward trend since the fourth quarter of 2001 until June 2011. The trend diagram in Figure 1 showed that overdue to total loans ratio gradually decreased from the ratio of 11. 27% in the fourth quarter of 2001, to 11. 74% in the first quarter of 2002, and further declining down to 0. 61% in the fourth quarter of 2010, displaying considerable credit quality improvement as well as recovery in overall economic climate and real estate business. This article use household mortgage sample from 2001 to 2010 for research object. During this period, the overdue lending rate of Taiwanese banking sector is declining every year. Thus, except individual personal factors, macroeconomic environment had little effect on the overdue lending rates during this period. Unlike other research where there is always a significant influence from the external environment. Which is always the cause of a large portion of overdue NPLs. Economic recession cause irresistible conditions and generate past-due NPLs. To avoid such influence, mortgage households sample data from 2001 to 2010 are ideally chosen for study. First, annual mortgage households growth are summarized to understand its number, size and growth ratio, then each of the data are categorized into tables according to FSC (2010) specifications of bad credit asset (mortgage overdue lending stage 0-4), and lastly calculate the relative number of distribution and arranged the statistics into the form of transfer Matrix. Through absorption Markov chain analysis method, this study estimates probability under five stages of overdue loan conditions, transfer rate at different stages, and the average survival for each of the overdue loan conditions at different stages. 5. 4 Annual Household Statistics From 2001 to the end of 2010, the mortgage sample had a total of 3819 Mortgage households to apply for loans. There were 1616 Mortgage households from 2001 and 3819 mortgage households at the end of 2010, a total growth of about 1. 36 times. During this period, the average annual growth rate increased up to 9. 80%. On the other hand, the NPL accounts grew from the number of 179 by 2001 to 305 mortgage households by the end of the 2010 (see Figure 2). 5. 5 Distribution of Household Overdue Loans Mortgage families from 2001 to 2010 are classified according to the FSC (2010) proposed NPL phases (Table 2). In Table 2, annual distribution of mortgage households of each stage is clearly shown. From year 2001 to 2010, mortgage households are normal to pay interest and principal; however, beginning from 2001, there was a downward trend that many mortgage households became overdue. In addition, Table 2 showed that, from 2005, although overdue mortgages significantly climbed, they still remain in the stage 1 condition. Since 2006, its mortgage households overdue situation is getting worse (i. e. more late payment in stage 2, 3 and 4), considerably higher than previous years. It is worthy of the attention of bankers and financial authority in charge. The NPL percentage to the total is clearly shown in Table 2. From table 2, the mortgage houses at different stages are divided against the annual total, and expressed as percentage, making clear the percentage every stage has to the total number of mortgages. As mortgages credit status may fluctuate over time, make changes in their stages of overdue loans, this article taken into account for the time (t) factors through regression analysis to forecast trend and verify whether changes are the same for each stage. If verification result is solid, the data analysis does not take into account the factor of time; If, on the contrary, the time factor will be taken into account. From Figure 3, Verification results and linear regression analysis (see table 3) show that, at different times, (t) changes for each stage and render a horizontal status, that is, the data will not change over time, mortgage loan overdue status distribution is stable.