Introduction
The main objective of this paper is to apply statistical techniques learned in the course. For the purposes of the current paper Bank of America was chosen. The Bank experienced hard times during mortgage crisis of 2007-2008. The statistical techniques proposed in this paper are earmarked for reduction of mortgage risk. An implementation plan for application chosen statistical technique was developed. Statistical technique will be applied according to timetable that was enclosed in the paper. Also, there were financial, human, technical, and other resources identified for the implementation plan. The implementation plan contains the information needed for application the statistical technique in practice. The implementation plan is a source of detailed information related decomposition of each step of the experiment. Statistical technique will be applied for analysis of the actual data. The discussion of the techniques implemented was supported by appropriate conclusions related short-term and long-term implications. The implications for decision making process will be also discussed in the paper.
Background of the Problem
Bank of America is subject to different risks including corporate operational risk, global banking risk, investment management risk, consumer real estate services risk, and global markets risk. In general, banking industry belongs to business with high risk level. Currently, the Bank is a customer-driven financial institution meaning easy, quality, and effective financial services for the customers (Bankofamerica.com).
The Bank pursues operational excellence in risk management creating strong balance sheet. Risk mitigation occupies central place in risk management aiming to focus on shareholder return model. Risk management plays an important role in operational excellence because the Bank started to recover from mortgage crisis. Mortgage default caused a lot of harm to the business of the Bank of America. Acquisition of Merrill Lynch reduced competition, but increased the amount of problematic assets at the same time. Volatile credit markets represent serious threat for the business of the financial institution (Bankofamerica.com).
Recently, credit risk analysis is a subject of research drawing interest of both researchers and practitioners. This paper will deal with statistical modeling related credit risk analysis. For the purposes of the current paper dual-time analysis will be used. This statistical technique will be applied to the mortgage competing risks aiming to reduce these risks. The technique that was chosen for analysis involves lifetime and calendar timescale. Dual-time survival analysis (DTSA) is often used to reveal the risk determinants related self-maturation within a period of time and exogenous influence made by macroeconomic conditions. The intrinsic problem identification will be discussed for DTSA. DTSA is important in credit risk modeling when default can be caused by exogenous and endogenous hazards. There will be nonparametric estimators, Cox regression, and first-passage-time parameterization considered in this research. The model that will be developed in this paper is aimed to provide additional information regarding survival analysis and credit risk modeling. There will be the application of DTSA demonstrated for analysis of mortgage risk thus explaining phenomenon of mortgage default (Zhang 10).
Identification of Statistical Technique
The dual-time survival analysis (DTSA) will be studied in this research. To be more precise, DTSA for time-to-default data observed will be considered. Credit risk modeling depends on exogenous and endogenous factors that could trigger default events. In this research the following events will be considered: nonparametric estimators under one-, two-, and three-way hazards models; structural parameterization through a triggering system of first-passage-time with an endogenous process defining the distance to default associated with exogenous factors transforming time; Cox regression based on dual-time semiparametric model, exogenous and endogenous factors, and effects of covariance. Also, the methods of partial likelihood estimation and the random effect of vintage heterogeneity model will be discussed. The application of DTSA model will be demonstrated on the example of mortgage risk analysis in retail banking sector helping understand the roots of mortgage crisis from dual-time perspective (Zhang 88).
The events considered in this research were observed in dual-time frame, lifetime and calendar time. The origins of the time-to-default and the events that occur at the same calendar time, but are different in age are of great interest. Age in credit risk modeling is referred to duration of a credit account since the time of origination of such account. Accounts having the same age following calendar time. They share the same origin and can be considered as a group of a single vintage (Zhang 90).
Dual-time Cox regression model will be used for estimation of hazards influencing credit risks measurements. First, a likelihood function based on data of dual-time-default will be developed. Second, one-, two-, and three-way nonparametric estimators will be considered in the process of the current research. The simulation data obtained from application of Cox regression will be used for assessment of the performance of nonparametric estimators. The structural models based on triggering system of the first-passage-time will be discussed in the framework of the dual-time feasibility. Triggering system defined by endogenous process connected with the distance-to-default will be considered with respect to the time-transformation framework related exogenous factors (Zhang 92). The development of semiparametric dual-time Cox regression will be represented based on exogenous and endogenous hazards model with consideration of covariate effects. A key role if assigned to partial likelihood estimation. The frailty type of vintage heterogeneity will be also discussed with a help of a random formulation effect. The applications of dual-time semiparametric and nonparametric survival analyses in mortgage risk modeling will be shown applied for retail banking sector. DTSA is based on real analytical data derived from the annual report for the years 2001-2009 (Bankofamerica.com).
Implementation Plan
Overview
The purpose of the implementation plan is to justify the use of chosen statistical the technique for improvement of the situation related mortgage risks. Bank of America experienced hardships during mortgage crisis of 2007-2008. The main objective of statistical technique is to evaluate potential hazard and manage consequences related mortgage crisis.
Situation Description
For the purposes of the current research, dual-time survival analysis (DTSA) was chosen because this approach is an effective tool of revelation of risk determinants. This statistical model takes into account macroeconomic conditions that follow mortgage crisis.
Assumptions
The statistical model is suggested to help manage potential hazard of mortgage default risk and its consequences. DTSA will be implemented using the Bank software; no additional technological resources are required. The end-users are Accounting Department, Risk Management Department, and Banking Credit Department.
Tasks Decomposition
Constraints
The research will be based on financial, human, and technological resources available in the Bank. It is suggested that Bank of America does not need any additional resources. However, in the process of the research the Bank may need additional software of financial resources for making in-depth research that may be considered to be the constraints lagging further research.
Risks
The risk is associated with data quality, namely: the statistical technique will not be able reflect the real situation resulting in significant data corruption. Risk mitigation strategy relates careful data selection and testing the statistical technique for appropriateness. Also, there is a risk of making mistakes by the personnel chosen for the project implementation. This risk can be eliminated or mitigated by providing necessary training.
Application of Statistical Technique
Total mortgage debt was estimated on the level of $10 trillion as of 2008 where the part of subprime mortgages was $1.2 trillion. The structure of Bank of America assets is consistent with assets structure that is observed in banking industry. In 2008 Bank of America needed $20 billion bailout to survive because it got into trouble with several other American banks aiming to benefit from economic upheaval (Bankofamerica.com).
The prime mortgages targeted the customers with positive credit histories while subprime mortgages were proposed for the borrowers with poor credit histories, but offering high leverage for the banks. Collapse of mortgage market that took place in 2007-2008 was known for a number of exacerbating consequences, such as the increased leverage, the loose of underwriting standards, the fall of real estate prices, moral hazard, and increase in unemployment rates (Zhang 124).
For the risks related mortgage competing loans the events of default correspond with censoring time. Survival analysis of competing risks model is a simple approach because it treats an alternative event as censored. Also, two marginal hazard rate models can be fitted for default and prepayment. Cox regression model for competing risks can be also referred related to robust variance estimation.
The first step is to identify nonparametric exploration of exogenous and endogenous hazards simultaneously with identification of the effects of vintage heterogeneity. The monthly vintages were grouped yearly according to credit risk modeling for the years 2001-2011 to trace the effect of mortgage crisis. Appendices 1 and 2 show MEV hazard decomposition for default and prepayment. As it can be seen from the Appendix 1, the exogenous risk was low before 2006 on the condition that exogenous multiplier was less than 1. After 2006 this factor grew 50 times while the multiplier grew twofold. The exogenous cycle of the risk of prepayment showed a down-turn trend during the same period of time (Appendix1, Appendix 2).
A higher probability of default is shown by mortgage originators of 2005-2006 in comparison to other years. Thus, the vintage heterogeneity decreased during the years preceding to 2005 (Appendix1, Appendix 2). Besides, the rise of mortgage default positively correlated with fall of the prices for real estate and negatively correlated with the rate of unemployment observed during the same period. Thus, exogenous effects can be attributed to unemployment and house prices. Besides, exogenous effects can be caused by macroeconomic indicators of different origin. It is possible to decode an effect of vintage by adding loan-level covariates. The mortgage note rate, either fixed or floating, can be also included (Zhang 127).
Categorical variable was simplified in Cox regression model by the following way:
ᴧji (m,t) = ᴧf (m) ᴧg(t) ᴧh(Vj) exp {ᶿ^T zji(m)}
where ᴧf (m) - the arbitrary maturation (endogenous indicator), ᴧg (t) and ᴧh(v) - the exogenous multiplier, the vintage heterogeneity subject to Eg = Eh = 0.
Form this formula it can be seen that the default risk is driven by high level of CLTV and low level of FICO (consumer credit scores) while prepayment risk can be driven by high face and low CLTV. The covariates of the scores of CLTV and FICO revealed their competing nature meaning that a homeowner having good credit with low leverage would rather make prepayments than choose to default that is a reasonable choice.
Resources Required for DTSA Implementation
The main benefit of chosen statistical technique is that it does not require financial inflows to be implemented. DTSA can be implemented using the Bank’s software and Microsoft Office software (Excel) that is common at any working place. However, the project will require participation of significant number of employees including Chief Executive Officer (CEO), Chief Accounting Officer (CAO), and Chief Risk Officer (CRO). Additionally, participation of 2 accounting managers will be required to carry out an analysis of data obtained. They will be assigned to make an analysis of data using the Bank’s software and Microsoft Office. CAO of the Bank will have to check data for accuracy and relevance. There will be required 2 employees from Technology and Operations Department to provide technical support for accounting managers. CEO and CAO are obliged to develop a comprehensive plan for implementation statistical techniques designed to assess mortgage risks. CAO will play the most important role carrying out control and monitoring functions to provide feasible and relevant results of implementation of DTSA. The main function of CRO is to evaluate the effectiveness of the risk assessment process. CRO is also obliged to develop risk mitigation techniques to reduce negative impact of mortgage crisis.
There will be financial resources required for conducting a seminar for the employees participating in the experiment since none of them carried out similar research before. During the seminar the schedule will be introduced to the participants. Also, the participants will be assigned the tasks they should complete during the project. The cost of the training can be allocated to the training budget for the year. The training will last for 2 days aiming to make the participants familiar with statistical technique and the objective of implementation of this technique. The results obtained from implementing DTSA will be evaluated by Chief Officers mentioned in the Table 1. The timetable of the project was outlined in the Table 2.
Timetable of the Project
The current research related the actual problem of predicting mortgage crisis and mitigating the consequences of financial crisis. The main problem Bank of America faced several years ago was mortgage default and its consequences causing significant harm to the Bank assets and being a reason for multiple lawsuits the financial institution is currently facing. In general, mitigation of financial hazards is the major goal for many financial institutions. Bank of America cannot be excluded from this list. An effective risk management can provide the Bank with stable returns and protection of the stakeholders’ interests.
Dual-time survival analysis is an effective tool of improving the quality of mortgages. This is the main reason why this statistical technique was chosen. The structural approach was based on Gaussian distribution. The analysis included semiparametric Cox regression, nonparametric estimation, and evaluation of feasibility of dual-time extension. Dual-time methods were developed on the basement of computational results that included assessment of the methodology from simulation perspective. The dual-time survival model was applied to the real situation in order to understand the roots of credit crisis from dual-time perspective. Obviously, statistical techniques play a key role in the developing of models related credit risks assessment and mitigation. The current research is mainly based on an analysis of vintage data and DTSA that can be applied in retail banking sector. The methodology that was described in the paper can be also applied for the risks assessment in corporate banking sector.
The technical part of the paper was supported by timeline of statistical technique implementation, schedule that outlined responsible persons, and time allocated for completion of each task. The resources that are necessary for implementation of this statistical model were also outlined. DTSA analysis can be applied to mitigate financial risks related possible foreclosures. In a short-term perspective it can be used for analysis of the current mortgage portfolio. It can be also used in a long-term perspective for mortgage risk assessment.
Appendices
Appendix 1 Mortgage Default: Vintage Heterogeneity (Zhang 125)
Appendix 21 Mortgage Prepayment: Vintage Heterogeneity (Zhang 125)
References
Bank of America. Annual Report 2001-2011. Bank of America, 11 Oct. 2012. Web. 3 Jan. 2013.
Siegel, Andrew F. Practical Business Statistics. 6th ed. Oxford: Elsevier Inc., 2012. Print.
Zhang, Aijun. Statistical Methods in Credit Risk Modeling. Michigan: The University of Michigan, 2009. Print.
