# A model for predicting the performance of a bank's mortgage loan portfolio.

 Author: Hassan, Morsheda

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INTRODUCTION

It is essential for sound operations of banks and lending institutions to have models and analytic tools available by which they can measure the performance (or health status) associated with a certain loan portfolio as well as predict this status over time from prevailing macroeconomic factors. A Markov chain defined on different payment states of a mortgage loan allows one to define and calculate a health index on the loan portfolio which can be used as a performance measure of that portfolio.

A performance measure, such as a health index measure, for a mortgage portfolio will be useful for a bank or lending institution in its loan or credit policy. It will help the management to monitor the performance of its portfolio over time. Furthermore, an empirical model that can relate a health index to macroeconomic factors will be useful in forecasting performance level. In a previous study (Liu et al, 2010) a Markov chain approach was developed to determine the transitions among payment states of a mortgage loan. Based on the probabilities of transitions among states, a loan health index was defined as a measure of its performance. In this paper, we will build on the previous study and develop an empirical model relating certain macroeconomic factors to the health index of the loan for forecasting purposes.

LITERATURE REVIEW

Soyer and Feng (2010) considered reliability models for assessing mortgage default risk. White (1993) presented several models employed in the banking industry. These included discriminant analysis, decision tree, expert system for static decision, dynamic programming, linear programming, and Markov chains for dynamic decision making. Markov chain modeling is a common approach used in the analysis of credit risk. As discussed by White (1993), Markov decision models have been used extensively to analyze real world data in (1) Finance and Investment, (2) Insurance, and (3) Credit area.

Cyert, Davidson and Thompson (1962) developed a finite stationary Markov chain model to predict uncollectible amounts (receivables) in each of the past due category. The states of the chain were defined as normal payment, past due, and bad-debt states.

Grinold (1983) used a finite Markov chain model to analyze a firm's market value. Lee (1997) used an ARMA model to analyze the linkage between time-varying risk premia in the term structure and macroeconomic state variables.

Esbitt, (1986) provided empirical evidence that a bank's portfolio quality has close relationship with the macroeconomic situation. Examples include the state-chartered banks' failure and the Great Depression in Chicago between 1930 and 1932.

McNulty, Aigbe, and Verbrugge (2001) proposed an empirical regression modeling approach to study the hypothesis that small community banks have an information advantage in evaluating and monitoring loan quality.

Hauswald & Marquez (2004) studied the relationship between the current regulative policy and the loan quality, or risks encountered by a financial institute.

Gambera (2000) used a vector-autoregressive (VaR) model to predict the loan quality in business cycles. D'Amico et al. (2005) applied Semi-Markov reliability models to the study of credit risk management. Douglas et al. (1996) proposed the use of non-stationary Markov and logistic modeling approaches to predict the performance of credit home mortgage portfolios. Pennington-Cross (2008) used a multinomial logit model to study the duration of foreclosure in the subprime mortgage market. Burkhard and De Giorgi (2006)used a non-parametric approach to model the probability distribution of defaults in residential mortgage portfolios. Hayre et al. (2008) presented a model that forecasts default rates as a function of economic variables and mortgage and borrower characteristics. Green and Shoven (1986) used a proportional hazard model to study the effects of interest rates on mortgage prepayment.

Deng et al (2000) used the option theory approach to predict mortgage termination by prepayment or default. They showed that the model performed well, but was not sufficient by itself. Heterogeneity among homeowners must be taken into account in estimating or predicting the prepayment behavior. Schwartz and Tourous (1993) applied a poisson regression to estimate the proportional hazard model for prepayment and default decisions in a sample of single-family fixed rate mortgages.

THE MODEL

In this model, we consider the pool of mortgage loans in the portfolio of a commercial bank in china. Based on the bank data and loan policy, each loan is classified into three states according to the mode of payment. State [S.sub.1] is the normal...